Download DC Grids for Wind Farms

DC Grids for Wind Farms
Olof Martander
Department of Electric Power Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden 2002
THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING
DC Grids for Wind Farms
Olof Martander
Department of Electric Power Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden 2002
DC Grids for Wind Farms
Olof Martander
c Olof Martander, 2002.
°
Technical Report No. 443L
Department of Electric Power Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
SE-412 96 Göteborg
Sweden
Telephone + 46 (0)31 772 1000
Chalmers Bibliotek, Reproservice
Göteborg, Sweden 2002
Abstract
Wind turbine technology, which is one of the oldest still in use, has undergone a
revolution during the last century. The most important difference between the earliest
wind mills and the new generation of wind turbines is that the latter produce electrical
energy. In order to reduce costs, the turbines are placed in wind farms and the new
trend is offshore wind farms. If the distance to the main grid is considerable, an
interesting alternative to AC transmission can be to connect the wind farms to the
mainland using high voltage direct current connections (HVDC).
This thesis focuses on DC/DC converters for high voltage and high power and investigates different DC/DC converter topologies with respect to a wind farm application
and presents different design concepts to determine the potential for using DC grids
in a wind farm. DC/DC converters have been examined by many authors before but
mostly for low power and low voltage applications. For a high voltage and high power
application, like a wind park transmission system, the focus has to be on the utilization
factor of the used components.
The chosen electrical system for a wind farm uses a boost converter as a voltage adjuster
and a full-bridge converter as a DC transformer. Simulations are made with different
fault locations for a simplified system. Depending on the type of fault, different parts of
the transmission system have to be shut down. The DC-transformer can clear all faults
by simply turning off the switches while in contrast a short circuit on the secondary
side of the boost converter cannot be cleared and leads to a permanent fault.
Finally, a complete wind farm with 25 wind turbines was simulated and the wind and,
therefore, the produced power was increased up to a rated power of 50 MW. The system
shows good system performance when the different bus voltages change with different
wind speeds and, thus, different power flows.
iii
iv
Acknowledgement
The financial support given by the Swedish National Energy Administration is gratefully acknowledged.
Joachim Lindström introduced me to the secrets of the life of a Ph.D. student which I
appreciate. Thanks also to my roommates Andreas Petersson and Marcus Helmer for
all the laughs and the sometimes not so fruitful discussions and activities. Many thanks
to all my colleagues and the staff at the Department of Electric Power Engineering and
especially the ”lunch” group consisting of Tomas Petru, Rolf Ottersten, Dr. Torbjörn
Thiringer, Mattias Jonsson and Stefan Lundberg.
Many thanks to Robert Karlsson for his assistance, answers to various questions and
good ideas.
Thanks to Dr. Jan Svensson and Dr. Ola Carlsson for their supervision, discussions
and proof-reading during the work with this thesis.
I would also like to thank my examiner Prof. Essam Hamdi.
Finally, I owe my deepest gratitude to my family and especially to Lisa for her understanding, encouragement and love throughout this project.
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Contents
Abstract
iii
Acknowledgement
v
1 Introduction
1
1.1
Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2 Wind Energy and Wind Turbines
5
2.1
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2
Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2.1
Wind Energy in Sweden . . . . . . . . . . . . . . . . . . . . . .
6
2.2.2
Wind Energy in Europe . . . . . . . . . . . . . . . . . . . . . .
6
Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.3.1
Power Control . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.3.2
Fixed-speed Turbine . . . . . . . . . . . . . . . . . . . . . . . .
11
2.3.3
Variable Speed Turbine . . . . . . . . . . . . . . . . . . . . . . .
12
Grid Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.3
2.4
3 Wind Farm Configurations
15
3.1
Wind Farms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3.2
Offshore Wind Farms . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3.3
Connecting Offshore Wind Farms . . . . . . . . . . . . . . . . . . . . .
16
3.4
System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
3.5
Wind Farm Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
3.5.1
AC Wind Farm . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.5.2
AC/DC Wind Farm . . . . . . . . . . . . . . . . . . . . . . . .
22
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3.5.3
DC1 Wind Farm . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3.5.4
DC2 Wind Farm . . . . . . . . . . . . . . . . . . . . . . . . . .
26
3.6
Cost and Loss Estimation . . . . . . . . . . . . . . . . . . . . . . . . .
28
3.7
Future Development . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
3.8
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
4 Hard Switching DC/DC Converter Topologies
33
4.1
Converter Environment . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
4.2
DC/DC Converter Topologies . . . . . . . . . . . . . . . . . . . . . . .
35
4.2.1
Boost Converter . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
4.2.2
Cúk Converter . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
4.2.3
Sepic - Single-Ended Primary Inductance Converter
. . . . . .
42
4.2.4
Zeta Converter . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.2.5
Luo Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
4.2.6
Flyback Converter . . . . . . . . . . . . . . . . . . . . . . . . .
49
4.2.7
Forward Converter . . . . . . . . . . . . . . . . . . . . . . . . .
51
4.2.8
Two Two-Transistor Forward Converter . . . . . . . . . . . . .
55
4.2.9
Push Pull Converter . . . . . . . . . . . . . . . . . . . . . . . .
58
4.2.10 Half Bridge Converter . . . . . . . . . . . . . . . . . . . . . . .
61
4.2.11 Full Bridge Converter . . . . . . . . . . . . . . . . . . . . . . . .
63
4.2.12 Half Bridge Converter With Voltage Doubler . . . . . . . . . . .
66
Comparison of Switch Utilization for Different Converters . . . . . . . .
69
4.3.1
Voltage Adjustment Converter . . . . . . . . . . . . . . . . . . .
69
4.3.2
DC/DC Transformer . . . . . . . . . . . . . . . . . . . . . . . .
71
4.4
Losses for Different Converter Layouts . . . . . . . . . . . . . . . . . .
73
4.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
4.3
5 Dynamic Analysis of Hard-switched DC/DC converters
5.1
5.2
75
Boost Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
5.1.1
Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . .
75
5.1.2
Transmitted Power . . . . . . . . . . . . . . . . . . . . . . . . .
77
5.1.3
Transient Behavior . . . . . . . . . . . . . . . . . . . . . . . . .
78
5.1.4
Varying Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
5.1.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
Half Bridge Converter . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
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5.3
5.4
5.2.1
Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . .
83
5.2.2
Transmitted Power . . . . . . . . . . . . . . . . . . . . . . . . .
85
5.2.3
Steady-state Behavior . . . . . . . . . . . . . . . . . . . . . . .
85
5.2.4
Transient Behavior . . . . . . . . . . . . . . . . . . . . . . . . .
87
5.2.5
Half Bridge Converter With Voltage Doubler . . . . . . . . . . .
87
5.2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
Full Bridge Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
5.3.1
Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . .
90
5.3.2
Transmitted Power . . . . . . . . . . . . . . . . . . . . . . . . .
92
5.3.3
Steady-state Behavior . . . . . . . . . . . . . . . . . . . . . . .
92
5.3.4
Transient Behavior . . . . . . . . . . . . . . . . . . . . . . . . .
94
5.3.5
Full Bridge Converter with Voltage Doubler . . . . . . . . . . .
94
5.3.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
Dual Active Bridge Converter (DAB) . . . . . . . . . . . . . . . . . . .
97
5.4.1
Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . .
97
5.4.2
Comparison with General AC Theory . . . . . . . . . . . . . . . 101
5.4.3
Transmitted Power . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4.4
Steady-state Behavior . . . . . . . . . . . . . . . . . . . . . . . 103
5.4.5
Transient Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.4.6
Varying Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.4.7
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6 Wind Farm Simulation
111
6.1
Transmission System Layout for Wind Farms
. . . . . . . . . . . . . . 111
6.2
Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2.1
Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2.2
Line to Ground Faults . . . . . . . . . . . . . . . . . . . . . . . 114
6.2.3
Line to Line Faults . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3
Simulation of Complete Wind Farm . . . . . . . . . . . . . . . . . . . . 120
6.4
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7 Conclusions and Future Research
123
7.1
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.2
Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
ix
References
125
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Chapter 1
Introduction
1.1
Background and Motivation
Wind turbine technology, which is one of the oldest still in use, has undergone a
revolution during the last century. A renewed interest in wind energy arose during the
oil crisis in the mid 1970s. This attention has continued to grow as the demands on
reducing polluting emissions have increased. The most important difference between
the earliest wind mills and the new generation of wind turbines is that the latter
produce electrical energy. Nowadays, it is not necessary to build the wind turbine
close to the user, on the contrary, people do not want the wind turbines within sight.
In order to reduce cost, the turbines are placed in wind farms and the new trend is
offshore wind farms. At sea, periods of complete calm are generally extremely rare,
and quite short-lived. If the distance to the main grid is considerable, an interesting
alternative to AC transmission can be to connect the park to the mainland by using
a high voltage direct current connection (HVDC) and by using a local DC-grid in the
wind farm. New semiconductor technologies make this possible but suitable converter
topologies have not been established yet.
A DC/DC converter can be described as the DC equivalent of an AC transformer. It
changes the ratio between the input and output voltages and currents by introducing power electronics that, with the help of passive components, transmit the power
through the converter. The advantages of using DC/DC converters are many: To regulate the output voltage, to build subsystems supplied by the same bus and to reduce
transmission losses. Presently, most applications are in the low power region, often
below 200 W, and the output voltage should be controlled. Microprocessors and electronics use low voltage around one to two volts and the challenge is to adjust the supply
voltage for high efficiency. Some of the techniques used are soft switching [1], resonance
converters [2] and synchronous rectifiers [3]. A lot of DC/DC converters are also used
together with diode bridges for AC/DC-conversion, for example, in a Boost Power Factor Correction (PFC) [4] circuit to reduce the influence on the grid by reducing the
harmonics and increasing the power factor. Today, low power DC/DC converters are
common and stand for a major part of the turn-over in the power electronics market
but high power and high voltage DC/DC converters in the MW range are not readily
available on the market.
1
This thesis focuses on DC/DC converters for high voltage and high power. The objective of the first part of this project was to determine the potential for using DC grids in
a wind farm. Another objective was to investigate different configurations of electrical
systems for offshore wind farms.
The objective of the second part of the project was to investigate different DC/DC
converter topologies with respect to a wind farm application and present design concepts with different high voltage and high power converter topologies.
1.2
Literature Review
DC/DC converters have been studied by many authors before but mostly in low power
and low voltage applications.
The most common converters are covered by textbooks in power electronics for example Mohan et. al. [5], Ericson and Maksimovic [6], Hart [7], Hnatek [8] and Kassakian et. al. [9]. They all give a short introduction to converters and present some of
the design issues.
A general overview of power electronic converter technology is given by Steigerwald [10]
where he performs a conceptual design study and compares different high frequency,
high power converters. The same author et. al. has also presented a comparison of highpower DC-DC soft-switched converter topologies in [11] and states that, in the high
power areas, the trend has been to mitigate away from more complicated topologies
that require snubbers or auxiliary circuits and use more rugged, higher performance
switches in a hard switched mode in order to decrease complexity and save cost.
Fuentes and Hey [12] describes a family of soft switching converters for high power
applications and verifies the feasibility of the proposed converters by analyzing a ZeroCurrent-Switching (ZCS) Boost converter.
More special converters are found in articles by the inventors, such as the Luo converter [13] and by many others. Luo converters are described as a series of new step-up
converters using voltage lift technique.
Special studies of the Boost Converter have been reported by Javanović and Jang [14]
and He and Jacobs [15]. The first paper describes a novel active snubber and the
second paper describes how to connect IGBTs in parallel for the converter.
Half and Full Bridge Converters are further investigated in a paper by Khersonsky et. al. [16] where high frequency and tail current losses are specially addressed.
Cho et. al. [17] presents a Zero-Voltage-Switching (ZVS) DC/DC converter for high
power applications where ZVS is achieved in the entire line and load range without
increasing device voltage and current stresses. A steady state analysis with complete
characterization of the converter is given by Sabaté et. al. [18].
A more recently introduced converter is the Dual Active Bridge (DAB) Converter,
which has been studied by De Doncker et. al. [19], in which a three-phase DAB converter is presented. The three-phase DAB has lower turn-off peak currents in the power
devices and lower RMS current ratings in the filter capacitors. A significant increase in
power density is also attainable by using a three-phase symmetrical transformer. The
2
performance of a single-phase DAB converter is described by Kheraluwala et. al. [20]
and various control schemes are outlined. Zhang et. al. [21] describes a novel control
scheme for the DAB converter, which eliminates some of the problems in previous converters, like the large circulating energy and large current ripple for the capacitors,
and achieves ZVS and ZCS for all switches. Another use of the DAB converter is for
DC/AC conversion and Vangen et. al. [22, 23] describes design equations and parameters that influence efficiency. A Dual Bridge Converter with soft switching features for
applying a new modulation technique while eliminating the auxiliary circuits used in
previous versions, is presented by Torrico-Bascopé and Barbi [24].
Papers about high power components have been presented by Satoh and Yamamoto [25]
and Zeller [26] both of which describe the background to the different high-power
components used, and present current alternatives and future trends. Series connection
of IGBTs is reported by Busatto et. al., in [27]. The paper demonstrates that series
connection of IGBTs can be used to extend the trade-off between conduction and
switching losses even to high voltage modules.
Different aspects of the electrical system and components in offshore wind farms are
reported by several authors and comparisons are made between AC and DC solutions.
Bauer et. al. has made an inventory of electrical systems for offshore wind farms [28]
and has also modeled some of the wind farm components [29]. Interest lies primarily
in identifying wind farm configurations with a low cost profile and high efficiency.
Jánosi et. al. [30] presents a simulation of a 12 MW traditional wind farm with AC
transmission and describes the behavior of this system from wind to electrical power to
the grid. Christensen et. al. [31] compares AC and HVDC solutions for grid integration
of offshore wind farms and states that HVDC solves most of the integration problems
and, at the same time, also provides the possibility for staged development. However,
the potential should be verified through research and real scale demonstration projects
and the development time might become a critical limiting factor. A model of a
HVDC transmission system for offshore wind farms has been made by Rasmussen
and Pedersen [32] and some of the experiences of the model are given in the article.
DC/DC conversion for offshore wind farms is reported by Macken et. al. in [33, 34] and
Morren et. al. in [35, 36]. Both authors have designed an electronic DC transformer
for high power and also describe some of the issues concerning DC bus systems.
3
1.3
Outline
The outline of the thesis is the following:
• Chapter 2 introduces the basics of wind energy and wind turbines;
• Chapter 3 presents wind farm configurations;
• Chapter 4 gives an overview of hard-switched DC/DC converters;
• Chapter 5 presents simulations of hard-switched DC/DC converters;
• Chapter 6 presents continued simulations with simulations of faults in a wind
farm and finally a complete wind farm with a dc-grid;
• Chapter 7 includes the conclusion and future research.
4
Chapter 2
Wind Energy and Wind Turbines
2.1
Introduction
In recent years, the number of wind turbines has increased greatly. In Denmark, wind
power contributes 13-15% of the total electricity production. In Germany, wind power
produces almost 3.5% of the total electricity [37]. In this chapter, the energy in the
wind and different wind turbines will be presented. Moreover, the advantages and
disadvantages of using variable-speed wind turbines will be covered.
2.2
Wind Energy
Wind energy is a renewable energy source, i.e. a clean source, which does not pollute
or increase green house gases. Moreover, wind resources are plentiful and wind will not
run out.
Wind turbines generate no CO2 , NOx or SOx during operation, and very little energy is
required for manufacturing, maintaining and finally scrapping the plant. In fact, with
moderate wind onshore sites, a wind turbine will recover all the energy spent in its
manufacture, installation and maintenance in less than three months [38]. With a 20
year lifetime this gives a thermal efficiency of 8000%, i.e. the wind turbine recovers the
energy about 80 times in its lifetime (comparable to a conventional coal power plant’s
45% [38]). For offshore turbines, the results may be better due to the longer expected
lifetime of the turbines. Less turbulence and thus lower fatigue loads will increase the
lifetime of offshore turbines to 25-30 years.
The major drawback of wind power is the variability of the wind. In large electrical
grids, however, consumers’ demand varies, and power utilities have to keep spare capacity running idle in case a major generating unit breaks down. If a power utility can
handle varying consumer demand, it can technically also handle the ”negative electricity consumption” from wind turbines. The more wind turbines on the grid, the more
short-term fluctuations from each turbine will be cancelled out and the total power
production will be smoothed out.
At most wind turbine sites around the globe, in fact, the wind varies substantially, with
5
high winds occurring rather infrequently, and low winds occurring most of the time.
In addition, in e.g. Europe and a number of other locations around the globe, wind
speeds happen to be positively correlated with peak electricity use. More wind during
the day than at night, more wind in winter than in summer, raising the value of the
wind to the grid by 40 to 60%, compared to a completely random wind pattern [39].
2.2.1
Wind Energy in Sweden
The installed wind power capacity in Sweden was 122 MW at the beginning of year
1998, coming from 334 wind turbines and has increased to 290 MW by the end of year
2001 (565 turbines) [40].
2.2.2
Wind Energy in Europe
The European Wind Energy Association (EWEA) has set a target of 60000 MW of
installed capacity for the year 2010. This goal was set in the year 2000 when the
previous goals, set in year 1991 and 1997, 25000 MW and 40000 MW respectively, was
discovered to be too pessimistic. The total installed capacity as of the end of year
2001 was 17000 MW and was excepted to produce some 40 TWh thus preventing the
emission of 24 million tons of CO2 annually. Table 2.1 shows installed capacity and
wind energy targets for different countries [37].
Table 2.1: Installed and targeted wind power capacity.
Country
Germany
Spain
Denmark
The Netherlands
Great Britain
Sweden
Ireland
France
Finland
Norway
2.3
Year 2000
6100 MW
2400 MW
2300 MW
450 MW
400 MW
250 MW
86 MW
80 MW
38 MW
13 MW
Target
22000 MW
9000 MW
50% (>6000 MW)
1500 MW
2000 MW
8-10 TWh (4-5000 MW)
500 MW
5000 MW
500 MW
3 TWh (1000 MW)
Year
2010
2010
2030
2010
2005
2010
2005
2010
2010
2010
Wind Turbines
Wind turbines are used to capture wind power. The standard wind power turbine of
today consists of a turbine, which has three blades and the wind upwards, so the tubular
steel or concrete tower is behind the turbine (also known as the Danish concept).
Figure 2.1 shows an example of the design elements of a wind turbine generator (WTG).
The rotor captures the wind energy at the low-speed shaft. Since most generators are
designed for high speed, a gear box is used and the energy is then transferred to the
6
high-speed shaft and then to the generator. The generator is connected to a transformer
to increase the voltage level to a suitable transmission level.
low speed shaft
gearbox
high speed shaft
nacelle
generator
turbine
blades
hub
tower
Figure 2.1: Design elements of a Wind Turbine Generator (WTG).
The power in the wind of the area A, perpendicular to the wind direction, is given by
the formula:
1
P = ρAV 3
2
(2.1)
where P is the power, ρ is the air density and V is the wind speed. The fraction of the
energy captured by a wind turbine is given by a factor Cp , called the power coefficient
and is defined as [41]:
Cp (λ) =
16
ηturbine (λ)
27
(2.2)
where λ is the tip speed ratio of the blade, i.e. the tip speed divided by the wind speed
and ηturbine is the efficiency of the turbine. Betz’ law [42] states that less than 16/27
(or 59%) of the kinetic energy in the wind can be converted to mechanical energy using
a wind turbine. The power coefficient indicates how efficiently a turbine converts the
energy in wind to electricity. Very simply, the electrical power output is divided by the
wind energy input to measure how technically efficient a wind turbine is. The power
curve divided by the area of the rotor gives the power output per square meter of rotor
area. Figure 2.2 shows a power coefficient curve for a typical Danish wind turbine. The
average mechanical efficiency is somewhat above 20%, but efficiency varies very much
with wind speed and is the greatest (in this case 44%) at a wind speed around 9 m/s.
This is deliberate since at low wind speeds efficiency is not very important because
there is not much energy to capture. At high wind speeds, the turbine must waste any
excess energy above the rated power of the generator and of course this determines the
7
0.5
0.4
Cp
0.3
0.2
0.1
0
5
10
15
20
Wind speed [m/s]
25
Figure 2.2: Power coefficient Cp as a function of wind speed.
mechanical loads on the structure. Therefore, efficiency matters most in the region of
wind speeds where most of the energy is to be found [41].
A wind turbine with high technical efficiency is not an aim in itself. What matters,
really, is the cost of extracting energy from the wind during the lifetime of the wind
turbine (often 20 years). Since the fuel is free, there is no need to save it. On the
one hand, the optimal turbine is not necessarily the turbine with the highest energy
output per year. On the other hand, each square meter of rotor area costs money, so it
is necessary to capture as much energy possible - as long as the costs per kilowatt-hour
are kept down.
All fixed speed wind turbines have an overshoot in the rated power of the machine
at the beginning of a gust of wind. Depending on the design of the power control,
this overshoot increases the ratings of some components by a factor up to 50%. This
overshoot, for example, causes excessive wear on the gearbox. With variable speed,
however, this overshoot can be avoided.
There are economies of scale in wind turbines, i.e. large machines are usually able to
deliver electricity at a lower cost than small machines. The reason for this is that the
costs for foundations, road building, electrical grid connection, plus a number of components in the turbine (the electronic control system etc.), are somewhat independent
of the size of the machine.
Large machines are particularly well suited for offshore locations. The cost for foundations does not rise in proportion to the size of the machine, and maintenance costs
are almost independent of the size of the machine [43].
In areas where it is difficult to find sites for more than a single turbine, a large turbine
with a tall tower use the existing wind resource more efficiently because the wind speed
increases with the height of the tower.
2.3.1
Power Control
Wind turbines are designed to produce electrical energy as inexpensively as possible.
Wind turbines are therefore generally designed so that they yield maximum output at
8
wind speeds around 12-15 meters per second. It is inefficient to design turbines that
maximize their produced output power at stronger winds, because such strong winds
are rare. In case of strong winds, consequently,it is necessary to waste part of the excess
energy of the wind in order to avoid damaging the wind turbine. All wind turbines
are therefore designed with some sort of power control. There are two common ways
of doing this safely on modern wind turbines, either by pitch or by stall control.
Pitch Controlled Wind Turbines
On pitch controlled wind turbines, the rotor blades have to be able to turn around their
longitudinal axis (to pitch) and thus, change the angle of attack as shown in Figure 2.3.
When the power output becomes too high, the blade pitch mechanism pitches (turns)
the rotor blades slightly out of the wind. Conversely, the blades are turned back into
the wind whenever the wind drops again. During normal operation the blades will
pitch a fraction of a degree at a time, thus, changing the angle of attack. The pitch
mechanism is usually operated by using hydraulics although some manufacturers use
electric motors.
wind speed
attack angle
torque
wind component
from rotation
nacelle
tower
chord
Figure 2.3: Pitch control.
Stall-Controlled Wind Turbines
(Passive) stall-controlled wind turbines have rotor blades bolted onto the hub at a fixed
angle. The geometry of the rotor blade profile, however, is aerodynamically designed
to ensure that at the moment wind speed becomes too high, turbulence will be created
on the side of the rotor blade which is not facing the wind, as shown in Figure 2.4.
This turbulence prevents the lifting force of the rotor blade from acting on the rotor
and this phenomenon is called stall, i.e. the blades are stalled.
The blade is twisted slightly along its longitudinal axis. This is done partly in order
to ensure that the rotor blade stalls gradually rather than abruptly when the wind
speed reaches its critical value. On the one hand, the basic advantage of stall-control
9
high wind speeds
attack angle
torque
wind component
from rotation
chord
Figure 2.4: Stall regulation.
is that there are no moving parts in the rotor itself. On the other hand, stall-control
represents a very complex aerodynamic design problem, and related design challenges
in the structural dynamics of the whole wind turbine, e.g. to avoid stall-induced
vibrations.
Active Stall Controlled Wind Turbines
An increasing number of large wind turbines (1 MW and up) are being developed
with an active stall power control mechanism. Technically, the active stall machines
resemble pitch controlled machines, since they have pitchable blades. In order to obtain
a reasonably large torque (turning force) at low wind speeds, the machines are usually
programmed to pitch their blades much like a pitch-controlled machine at low wind
speeds. (Often they use only a few fixed steps depending upon the wind speed). When
the machine reaches its rated power, however, there is an important difference from
the pitch-controlled machines: If the generator is about to be overloaded, the machine
will pitch its blades in the opposite direction from that of a pitch controlled machine.
In other words, it increases the angle of attack of the rotor blades in order to make the
blades go into a deeper stall, thus wasting the excess energy in the wind. One of the
advantages of active stall is that the output power can be controlled more accurately
compared to passive stall. Another advantage is that the machine can run almost
exactly at rated power at all high wind speeds. A normal passive stall-controlled wind
turbine will usually have a drop in the electrical power output for higher wind speeds,
as the rotor blades go into deeper stall. The pitch mechanism is usually operated using
hydraulics or electric motors. As with pitch-control it is largely an economic question
whether or not it is worthwhile to pay for the added complexity of the machine when
the blade pitch mechanism is added.
10
Other Power Control Methods
Some older wind turbines use ailerons (flaps) to control the power of the rotor, just
like aircraft use flaps to alter the geometry of the wings to provide extra lift at take-off.
Another possibility is to yaw the rotor partly out of the wind to decrease power. The
technique of yaw control is, in practice, used only for tiny wind turbines (1 kW or less),
there are, nontheless, examples of wind turbines of 1.5 MW using this technique.
2.3.2
Fixed-speed Turbine
The fixed-speed turbine typically uses a squirrel cage induction generator directly connected to the grid, as shown in Figure 2.5.
Point of common
coupling
Generator
G
Capacitor battery
Turbine
Figure 2.5: Electrical system of fixed-speed wind turbine using induction generator and
capacitor batteries to improve power factor system.
One reason for choosing an induction generator is that it is reliable, and tends to be
comparatively inexpensive. One drawback is that the induction generator consumes
reactive power and that the need for reactive power increases with the produced active
power. Capacitor batteries are used to compensate for the reactive power consumption
of the induction generator and thus receive a no load power factor near one at the
point of common coupling (PCC) of the grid. The generator also has some mechanical
properties that are useful for wind turbines, for example, the slip of the generator makes
the grid connection softer, i.e. the speed changes with the mechanical load torque. The
robustness also provides a certain overload capability.
Some manufacturers fit their turbines with two generators, a small one for periods of
low winds, and a large one for periods of high winds. Another design is pole changing
generators, i.e. generators which (depending on how their stator windings are connected) may run with a different number of poles, and thus at different rotational
speeds. This design is still considered as fixed-speed regarding mechanical loads and
grid interaction. Whether it is worth using double generators or a higher number of
poles for low winds depends on the local wind speed distribution, and the extra cost of
the pole changing generator seen in comparison with the revenues the turbine owner
earns on the electricity. A good reason for having a dual generator system, however,
is that the turbine can run at a lower rotational speed at low wind speeds. This is
more aerodynamically efficient, another advantage is that the noise level from the rotor
11
blades decreases with lower rotational speed (the noise is usually only a problem at
low wind speeds due to low background noise).
2.3.3
Variable Speed Turbine
A variable-speed turbine uses power electronics apparatus to vary turbine speed and
still connect the generator to the fixed frequency of the grid. The primary advantage of
this is that wind gusts can be allowed to make the rotor turn faster, thus storing part
of the excess energy as rotational energy until the gust is over. Obviously, this requires
an intelligent control strategy, since the system has to be able to separate gusts from
high wind speed in general. Thus, it is possible to reduce the peak torque (reducing
stress on the gearbox and generator), and also reduce the fatigue loads on the tower
and rotor blades. The secondary advantage is that power electronics can control the
reactive power in order to improve the power quality in the electrical grid. This may
be useful, particularly if a turbine is running on a weak electrical grid. Theoretically,
variable speed also gives a slight advantage in terms of annual production, since it is
possible to run the machine at an optimal rotational speed, depending on the wind
speed. From an economic point of view this advantage is minor, because the apparatus
needed to obtain variable speed have losses and cost more compared with a fixed-speed
system.
One good reason to run a turbine partially at variable speed is the fact that pitchcontrol is a mechanical process. This means that the reaction time for the pitch mechanism becomes a critical factor in turbine design. However, if the variable slip generator
is used, the slip is used as a control parameter. When a wind gust occurs, the control
mechanism signals to increase generator slip to allow the rotor to run a bit faster while
the pitch mechanism begins to cope with the situation by pitching the blades more out
of the wind. Once the pitch mechanism has done its work, the slip is decreased again.
In case the wind suddenly drops, the process is applied in reverse. Thus, the mechanical pitch system controls turbine speed and the electrical system controls torque, i.e.
the electrical output power.
Running a generator at high slip releases more heat from the generator, which consequently runs less efficiently. This is not a problem in itself, however, since the only
alternative is to waste the excess wind energy by pitching the rotor blades out of the
wind. One of the real benefits of using the control strategy mentioned here is better
power quality. Fluctuations in power output are decreased by varying generator slip
and storing or releasing part of the energy as rotational energy in the wind turbine
rotor. Slip in an induction machine is usually very small for reasons of efficiency, so the
rotational speed varies by 1-2% between idle and full load. Slip, however, is a function
of the (DC) resistance (measured in ohms) in the rotor windings of the generator. The
higher the resistance, the higher the slip.
One way of varying slip and, consequently, speed is to vary the resistance in the rotor,
as shown in Figure 2.6. In this way, generator slip can be increased by, e.g. 10 %,which
gives a very limited speed range. This is usually done by having a wound rotor, i.e.
a rotor with copper wire windings, which are connected in a star, and connected with
external variable resistors, plus an electronic control system to operate the resistors.
The connection is usually done with brushes and slip rings, which is a clear drawback
12
compared with the elegantly simple technical design of a cage wound rotor machine.
The connection also introduces parts that wear down in the generator, thus requring
more maintenance on the generator. One way to avoid the problem of introducing slip
rings, brushes, and maintenance altogether is by mounting the external resistors and
the electronic control system on the rotor.
Point of common
coupling
Generator
G
Rotor resistors
Turbine
Figure 2.6: Variable rotor resistance variable speed system.
Another way of creating variable speed is the rotor cascade technique, as shown in
Figure 2.7. This technique uses a wound rotor, brushes and slip rings, but the rotor
windings are connected to an ac converter with variable frequency. The rotational
speed is proportional to the frequency difference between the stator (grid) frequency
and the rotor (converter) frequency. The speed range for a rotor cascade turbine is
proportional to the converter size. If the converter size is 25% of rated power for the
wind turbine generator, then the speed range is ±25%, i.e. between 50-100% of nominal
speed.
Point of common
coupling
Generator
G
~ =
= ~
Turbine
Rotor inverter
Rotor rectifier
Figure 2.7: Rotor cascade variable speed system.
By connecting the generator to the grid via a rectifier in series with an inverter, as
shown in Figure 2.8, the rotational speed of the turbine can be controlled independent
of the grid frequency. Another advantage of a full size converter, also called a back-toback converter, is that power electronics can control the reactive power and use active
filtering techniques to improve the power quality in the electrical grid. The speed range
is 0-100% of nominal speed, since the converter can handle rated power.
13
Point of common
coupling
Generator
G
=~
~
=
Rectifier
Inverter
Turbine
Figure 2.8: Full size converter variable speed system.
2.4
Grid Interaction
Wind turbines interact with the grid. Due to the quickly increased rated power of wind
turbines, the turbines affect the grid and the consumers, who are connected to the grid
[44].
Flicker, i.e. short lived voltage variations in the electrical grid may cause light bulbs to
flicker. This phenomenon may be relevant if a wind turbine is connected to a weak grid,
since short-lived wind variations will cause variations in power output and, therefore,
voltage variations. There are various ways of dealing with this issue in the design of
the turbine, mechanically, electrically, and by using power electronics [45].
Power electronics may introduce harmonic distortion into the alternating current in
the electrical grid, thus, reducing power quality. The problem of harmonic distortion
arises because the filtering process is not perfect, and it may leave some tones, which
are multiples of the grid frequency, in the output current.
If a turbine is connected to a weak electrical grid, (i.e. if it is very far away in a remote
corner of the electrical grid with a low power-carrying ability), there may be problems
of the sort mentioned above. In such cases, it may be necessary to reinforce the grid,
in order to carry the fluctuating current from the wind turbine. The problems are,
in fact, the same when connecting a large electricity consumer, (e.g. a factory with
large electrical motors) to the grid. Some of the problems with a weak grid can be
solved with power electronics, which can control the reactive power consumption and,
consequently, the voltage in the connection point.
14
Chapter 3
Wind Farm Configurations
In this chapter, wind farms are introduced for both onshore and offshore locations. Four
examples of complete systems together with the transmission are included. Moreover,
the cost and losses of each system are estimated.
3.1
Wind Farms
To increase the electricity produced and to keep the used land area at a minimum,
wind turbines should be put together in a group, a so-called wind farm or wind park.
A wind turbine always casts a wind shade in the downwind direction. In fact, there is
a wake behind the turbine, i.e. a long trail of wind that is quite turbulent and slowed
down, in comparison with the wind arriving in front of the turbine. As a rule of thumb,
turbines in wind parks are usually spaced somewhere between 5 and 9 rotor diameters
apart in the prevailing wind direction, and between 3 and 5 diameters apart in the
direction perpendicular to the prevailing winds [46]. Typically, the energy loss due to
wind turbines shading one another is somewhere around 5% [46].
3.2
Offshore Wind Farms
At sea, periods of complete calm are generally extremely rare, and quite short-lived.
Thus, the effective use of wind turbine generating capacity is higher at sea than on
land. Wind resources above shallow waters (5 to 15 m depth) in the seas around Europe
could theoretically supply all of Europe’s electricity several times over [47].
One of the primary reasons for moving wind farm development offshore is the lack of
suitable wind turbine sites on land. Equally important, however, is the fact that wind
speeds are often significantly higher offshore than onshore. An increase of some 20%
at some distance from the shore is not uncommon. Given the fact that the energy
content of wind increases with the cube of wind speed, the energy yield may be some
73% higher than on land. Economically optimized turbines, subsequently, will probably
yield some 50% more energy at sea than at nearby land locations.
Another argument in favor of offshore wind power is the generally smooth surface of
15
water. Thus, wind speeds do not increase as much with the height above sea level as
they do on land. This implies that it may be economic to use lower (and thus cheaper)
towers for wind turbines located offshore.
The temperature difference between the sea surface and the air above is far less than
the corresponding difference on land, particularly during the daytime. Thus, the wind
is less turbulent at sea than on land. This, in turn, results in lower mechanical fatigue
loads and, thus, a longer lifetime for turbines located at sea.
Inside the large 120-150 MW offshore wind parks being planned in Denmark, as shown
in Figure 3.1, it is likely that 30-33 kV AC grid will be used. At the center of each
park there will probably be a platform with a 30 to 150 kV transformer station, and
possibly a number of service facilities. The connection to land will consist of 150 kV AC
cables [48].
Platform with
transformer and
service facilities
Wind Turbine
G
Cable transmission
to shore
150 kV AC
G
G
Local wind
farm grid
33 kV AC
Figure 3.1: Traditional AC system for offshore wind farms planned in Denmark.
Undersea cables have to be buried in order to reduce the risk of damage due to fishing
equipment, anchors, etc. If bottom conditions permit, it is most economic to wash
cables into the seabed (using high-pressure water jets) rather than digging or ploughing
cables into the bottom of the sea. Cables have a high electrical capacitance, which
may cause problems depending on the precise grid configuration and the distance to
the shore. If the distance to the transmission grid on land is substantial, i.e. greater
than aproximately 100 km [49], an interesting alternative can be to connect the farms
to the land using high voltage direct current connections (HVDC).
3.3
Connecting Offshore Wind Farms
The pilot offshore wind farms that are being built today use an AC connection to
shore and the distance to shore is quite moderate, about 5-50 km [50, 51]. This section
describes three different solutions for a DC connection to shore and compares the cost
and losses of the DC systems with a traditional AC system as a reference.
16
However, the proper types of electrical systems for offshore wind farms have not been
established yet. A DC cable is the preferred choice when connecting large offshore
wind farms to the grid for several reasons:
• The capacitive charging current for a long, high voltage AC cable is substantial
and, thus, longer distances cannot be covered by AC cables;
• Losses in a DC system are less sensitive to variations in the transmission distance and the cables can, therefore, be more effectively connected directly to the
transmission grid on land;
• Sanctions for new over-head lines are difficult to achieve when making the necessary reinforcements for connecting offshore wind farms with the transmission grid
on land. A special transmission system design is, therefore, needed to compensate
for the weak grid (off course the same for AC cables);
• The cost of a DC system is presently higher than for traditional AC systems.
However, a major part of the cost of a DC system is power converters and their
cost pertains mainly to the semiconductors which they contain;
• Due to the extensive development of semiconductors, power density is increasing
rapidly and cost is decreasing, similar to the cost/performance of microprocessors;
• Moreover, losses in the wind farm are higher due to the converter stations but
are more or less compensated by lower transmission losses.
A theoretical analysis is made of different configurations for offshore wind farms with
respect to the system cost, the total losses in the system and the impact on the grid it is
connected to. Three different DC systems, from the wind turbines to the transmission
grid, are compared with a traditional AC system, which is used as a reference system.
3.4
System Description
The system adopted consists of wind turbines, the local grid and the transmission and
connection to the transmission grid on the mainland. The proposed and investigated
wind farm consists of 100 wind turbines each with a rated output of 1.5 MW. These are
connected together electrically to a local AC or DC grid. This grid is then connected
to the transmission cables via a converter or a transformer. The AC/DC converter is a
voltage source converter and the DC/DC converter is a half bridge converter, and both
use IGBT transistors as switches. The transmission length is the total length of the
offshore and onshore distances to the transmission grid. A transformer or a converter
makes the final connection to the transmission grid onshore, as shown in Figure 3.2.
The type of turbine or the type of generator that is used is not of interest here. Variable
speed can of course be used in all layouts, but is not specifically analyzed here. However,
when using individual AC to DC conversion at each wind turbine, variable speed can be
obtained and each wind turbine can reach optimal production and reduce mechanical
stresses and, thus, maximize the lifetime of the turbine.
17
3 km
10 km
Distribution Line
Transmission cable
Sea cable
Land cable
Transmission
Line
Offshore Distance Onshore Distance
Figure 3.2: Layout of offshore wind farm and connection to transmission grid on land.
The four rows of wind turbines are separated by nine times the turbine diameter in
the prevailing wind direction. The turbines in each row are separated by five times
the turbine diameter transverse to the prevailing wind direction. The total size of the
wind farm is ten times three kilometers. The total transmission distance is set at 20
km and consists of both sea and land cables.
The communities around the proposed wind farm sites in Denmark desire longer offshore distances and after approximately 20 - 25 km the turbines become nearly invisible [48]. The wind farms, which are being planned, have in some cases longer offshore
transmission distances, as shown in Table 3.1. Moreover, the onshore transmission
distance might also be substantial, because the connection to the onshore transmission
must be at a point with high short-circuit capacity. One example is the planned wind
farm at Horns rev in Denmark where the onshore distance is 34 km [48].
18
Table 3.1: Offshore windfarm distances from shore [50, 51].
Wind Farm
Size [MW]
Offshore Distance [km]
50
100
100
150
300
60
150
5
15
8-20
20
40
45
25
Mecklenburg-Vorpommern - D
SKY 2000 - D
Egmond aan Zee - NL
Horns rev - DK
Læsø - DK
Borkum West - D
Rødsand - DK
3.5
Wind Farm Layouts
Four different layouts are assumed and compared. The first is a traditional AC system,
the second is an AC system with a DC transmission (AC/DC) and the last two have
different systems with a DC grid and a DC transmission (DC1 and DC2). The AC
system with a DC transmission can reduce the frequency of the offshore grid and,
thereby, has the capacity for variable speed and can produce more energy from the
wind. Of course, this assumption holds true if the wind speed is the same for the
whole wind farm. The mechanical stresses of the wind turbines will, however, be
the same since the turbines are connected together. The two DC examples will have
individual variable speed and, therefore, will be able to reduce the mechanical stresses
on the turbine, as well as gain more energy. These advantages can of course be achieved
in the two first examples by having a rotor cascade with a back-to-back voltage source
converter system or any other variable speed system, but this is not included in the
estimations.
19
3.5.1
AC Wind Farm
Each wind turbine in the AC wind farm has an output voltage of 33 kV AC and each
wind turbine is connected with an AC-grid to the main transformer, 33/150 kV AC,
which is located in the center of the wind farm, as shown schematically in Figure 3.3.
Figure 3.4 shows the cable layout of the wind farm. The transmission from the wind
farm to the connection point on the transmission line onshore is made by three 20 km
150 kV AC cables. The grid inside the wind farm consists of 49 km of 33 kV AC
cables. Each wind turbine has a 33 kV transformer and there is one 33/150 kV AC
transformer. There is also an inductor onshore at the connection point for reactive
power compensation, so that the power factor becomes one.
Wind Turbine
Platform with
transformer and
service facilities
Shore
Connection point
on land
G
G
Cable transmission
150 kV AC
Reactive power
compensation
G
Local wind
farm grid
33 kV AC
Figure 3.3: Layout of AC wind farm consisting of wind turbines, local wind farm AC
grid, platform with transformer, AC transmission cables and reactive power
compensation at connection point on land.
20
33/150 kV Transformer
150 kV AC Cable
33 kV AC Cable
Wind turbine
Prevailing Wind Direction
Figure 3.4: Cable layout of AC wind farm.
21
3.5.2
AC/DC Wind Farm
On the AC/DC wind farm, each wind turbine has an output voltage of 33 kV AC and
each wind turbine is connected with an AC-grid to the main converter, 33/150 kV AC/DC,
which is located in the center of the wind farm, as shown in Figure 3.5. Figure 3.6
shows the cable layout of the wind farm. The transmission from the wind farm to the
connection point on the transmission line onshore is made by two 20 km ±75 kV DC
cable. The grid inside the wind farm consists of 49 km of 33 kV AC cables. Each wind
turbine has a 33 kV transformer and there is one DC/AC converter onshore at the
connection point.
Platform with
AC/DC converter
and service facilities
G
G
G
Shore
~
~
=
Wind Turbine
Connection point
on land
~
~
=
Cable transmission
2 x 75 kV DC
DC/AC converter
on land
Local wind
farm grid
33 kV AC
Figure 3.5: Layout of AC/DC wind farm consisting of wind turbines, local wind farm
AC grid, platform with AC/DC converter, DC transmission cables and
DC/AC converter at connection point on land.
22
150 kV HVDC Converter
150 kV DC Cable
33 kV AC Cable
Wind turbine
Prevailing Wind Direction
Figure 3.6: Cable layout of AC/DC wind farm.
23
3.5.3
DC1 Wind Farm
Each wind turbine on the DC1 wind farm has an output voltage of 15 kV DC and five
turbines are connected with a 15 kV DC sub grid to a 15/150 kV DC/DC converter.
All 15/150 kV DC/DC converters are connected in a main grid, as shown in Figure 3.7.
The transmission from the wind farm to the connection point on the transmission line
onshore is done with two 20 km ±75 kV DC cables. Figure 3.8 displays the cable layout
of the wind farm. The sub grid consists of 39 km of 2x7.5 kV DC cables and the main
grid consists of 19 km of 2x75 kV DC cables. Each wind turbine has a 15 kV AC/DC
converter and there is a total of 20 15/150 kV DC/DC converters. There is also a
DC/AC converter onshore at the connection point.
15/150 kV DC/DC
converter and
service facilities
G
~
=
G
~
=
Shore
~
~
=
Wind Turbine
Connection point
on land
=
=
Cable transmission
2 x 75 kV DC
DC/AC converter
on land
Local wind
farm main grid
150 kV DC
G
~
=
Local wind
farm sub grid
15 kV DC
Figure 3.7: Layout of DC1 wind farm consisting of wind turbines, local wind farm DC
sub grid, DC/DC converter, DC transmission cables and DC/AC converter
at connection point on land.
24
15/150 kV DC/DC Converter
150 kV DC Cable
15 kV DC Cable
Wind turbine
Prevailing Wind Direction
Figure 3.8: Cable layout of DC1 wind farm.
25
3.5.4
DC2 Wind Farm
Each wind turbine on the DC2 wind farm has an output voltage of 6 kV DC and
they are connected with a 6 kV DC sub grid to a 6/30 kV DC/DC converter. All
6/30 kV DC/DC converters are connected with another sub grid to a 30/150 kV DC/DC
converter. All 30/150 kV DC/DC converters are connected in a main grid and the
transmission from the wind farm to the connection point on the transmission grid is
done with two 20 km ±75 kV DC cables. Figure 3.10 shows the cable layout of the
wind farm. The first sub grid consists of 39 km of 2x3 kV DC cables, the second sub
grid consists of 13 km of 2x15 kV DC cables and the main grid consists of 8 km of
2x75 kV DC cables. Each wind turbine has a 6 kV AC/DC converter and there are
a total of 20 6/30 kV DC/DC converters and four 30/150 kV DC/DC converters, as
shown in Figure 3.9. There is also a DC/AC converter onshore at the connection point.
G
~
=
=
=
30/150 kV DC/DC
converter
Shore
=
=
Cable transmission
2 x 75 kV DC
G
G
~
=
~
=
Local wind farm
main grid
150 kV DC
Local wind
farm sub grid
6 kV DC
Connection point
on land
~
~
=
Wind Turbine
6/30 kV DC/DC
converter
DC/AC converter
on land
Local wind
farm sub grid
30 kV DC
Figure 3.9: Layout of DC2 wind farm consisting of wind turbines, local wind farm
DC sub grids, DC/DC converters, DC transmission cables and DC/AC
converter at connection point on land.
26
6/30 kV DC/DC Converter
150 kV DC Cable
30/150 kV DC/DC Converter
6 kV DC Cable
30 kV DC Cable
Wind turbine
Prevailing Wind Direction
Figure 3.10: Cable layout of DC2 wind farm.
27
3.6
Cost and Loss Estimation
The following cost analysis only includes the cost of the main components like the
cables, converters, transformers, and reactive power compensation for the four different
cases shown in the figures in the previous section. The costs for erection, foundations,
platforms and the cost for ploughing down the cables, etc. are not included. The
DC/AC and the AC/DC converters are traditional voltage source converters with three
phase legs. The DC/DC converter has a half bridge converter topology that uses one
phase leg. The data for the estimation are shown in Table 3.2. The transistor cost
and losses given below are for two series connected switches, which become one phase
leg. A doubling of the current for the transistors is assumed to give a 20% higher cost
since the cost depends on both the silicone cost and the cost of the series connection
required to reach a suitable voltage level.
The power semiconductors are, next to the wind turbines, the main cost of the systems
using DC transmission. The connection cost of a traditional AC system is approximately five percent of the total cost, while the connection cost of the other three types
is approximately 25%, as shown in Table 3.3 (The total cost differs depending on configuration). The cost of the semiconductors is nearly 90% of the total connection cost
for the AC/DC alternative and approximately 40% of the costs for the two alternatives with a DC grid. Consequently, the total cost of the transmission system mainly
depends on the semiconductors in the converters.
The system losses are higher in the DC alternatives and, again, it is the semiconductors
that cause the main losses. The losses are approximately 60 % higher in the AC/DC
solution and more than double in the DC solutions compared with the AC wind farm.
The semiconductors represent approximately 50 % of the total losses. The difference
between the two DC solutions is that the second (DC2) has two conversion steps.
Findings are not in favor of DC solutions. However, this example uses a very moderate
transmission distance of 20 km and, compared with grid reinforcement onshore, DC
transmission might be the most cost-effective solution.
28
Table 3.2: Data for cost and loss estimation.
Part
Parameter
Value
Wind
turbine
Size
Price
Diameter
Generator voltage
1.5 MW
7.5 Mkr
D=80 m
690 V
Wind
park
Number of turbines
Total Size
Spacing
Converter
components
100
150 MW
⊥ 9xD
k 5xD
Distance - onshore
10 km
- offshore
10 km
Transmission voltage 150 kV
±75 kV
Transformer
IGBTs
Diodes
Reactive
power
compensation
Cables
Capacitors
Switching frequency
Maximum ripple
Inductor
AC-cable
DC-cable
Losses
(estimatesd
values)
Transformer
Transistors
Diodes
AC-cable
DC-cable
Cable resistance
60 kr/kVA
6 kr/kVA
260 kr/kVA
130 kr/kVA
130 kr/kVA
65 kr/kVA
1500 kr/kJ
1000 Hz
5%
220 kr/kVA
comment
to the prevailing
wind direction
(HVAC)
(HVDC)
(50 Hz for AC)
(1000 Hz for DC/DC)
High voltage
Low voltage
High voltage
Low voltage
Input or output voltage ripple
Compensating for the
reactive power in
the AC-cable at no load
Price=(A· area + B · voltage + C) kr/m
A=0.149 kr/mm2
B=1.48 kr/kV
C=-19 kr
Price=(A· area + B · voltage + C) kr/m
A=0.201kr/mm2
B=0.60kr/kV
C=20kr
1%
0.7%
0.7%
30 W/m
30 W/m
2.65·10−8 Ω ·m
29
(of Rated power)
(of Rated power)
(of Rated power)
Determines the cable area
Determines the cable area
Aluminium conductor
Today
Table 3.3: Costs and loss estimation.
AC AC/DC DC1
Connection cost [%]
Total cost
Cost of semiconductors [%]
Connection cost
Losses at Rated Power [%]
Rated Power
Semiconductor losses [%]
Total losses
3.7
DC2
5.3
26.4
24.7
27.9
0.0
87.1
42.9
48.4
5.2
8.7
11.1
14.2
0.0
45.8
53.9
46.9
Future Development
Power semiconductors have undergone rapid development in recent years and it is likely
that this development will continue in the future [52]. Table 3.4 shows the expected
costs and losses for the next ten years assuming that the price is constant and that
the performance regarding power capability is doubled and losses are halved every
three years. Under these circumstances, the connection cost of the wind farm would
be approximately the same for all alternatives and the losses would also be the same
except for the DC2 alternative with two converter steps. Table 3.5 shows when the
other alternatives are expected to perform as well as the reference AC system, i.e.
the price and the losses for the semiconductors are lowered until they match the AC
system. In 11 years, the cost for the DC1 system will be the same as for the reference
system. For the AC/DC system, the cost will be the same after 15 years. The losses,
however, will be comparable after 10 years for the AC/DC system but not until after
more than twenty years for the DC1 system. Again, this largely depends on the short
transmission distance of 20 km.
Table 3.4: Estimation of costs and losses year 2010.
Year 2010
AC
AC/DC
DC1
DC2
Connection cost [%]
Total cost
Cost of semiconductors [%]
Connection cost
Losses at Rated Power [%]
Rated Power
Semiconductor losses [%]
Total losses
5.3
7.2
5.7
7.2
0.0
40.1
23.1
23.8
5.2
5.1
5.7
7.0
0.0
7.7
10.4
9.5
Table 3.5: Estimation when in time DC solutions give the same performance as AC.
Years from now
AC
AC/DC
DC1
DC2
Total cost [Year]
Losses [Year]
0
0
15
10
11
23
14
--
30
3.8
Conclusions
The pilot offshore wind farms that are being built today use an AC connection to the
shore and the distances to the shore are also quite moderate. This is a well-known
technology and a natural step for the first offshore wind farms. However, in ten years,
when the experiences from the first offshore wind farms have been evaluated and the
next expansion starts, alternatives using a DC grid will start to become cost-effective
solutions. Future wind farms will become larger and will be situated at a farther
distance from shore. The connection to the onshore transmission grid must be at a point
with high short circuit capacity and the transmission distance is, therefore, expected
to be greater in the future than the 20 km used in the example. The controllability
offered with the three systems using power electronics is also a great advantage for
transient stability when connecting the wind farm to a weak grid.
The cost of power electronics will be significantly lower in the future and losses will
continue to decrease, so the advantages will outweigh the disadvantages.
31
32
Chapter 4
Hard Switching DC/DC Converter
Topologies
This chapter, describes the working principles for hard switching DC/DC converter
topologies, particularly as regards transformer and semiconductor utilization. The
analysis is theoretical and the overview is made partially by using material from references [7, 8, 9, 5]. The application for the DC/DC converters is in a wind farm. In order
to reduce the transmission losses from the wind farm to the shore, the transmission
voltage has to be higher than the voltage out from the generator [53].
Voltage and current stresses on the semiconductors for the different converter topologies
are described and compared in steady state and from a wind power point of view.
Series connected IGBT transistors are used as switches to achieve the necessary voltage
ratings. No resonance is used to decrease the switching losses in the valves. The
converter topologies can be divided into different classes depending on their power
handling capability, from low to high power applications or their conversion ratios,
from moderate to high. Typically, moderate voltage changes are in the range of one to
five. For high voltage changes, where the converters use a transformer in the conversion,
the ratio is ten or more. Two other aspects are the size of passive components and the
need for bi-directional power flow.
The characteristics of the wind turbine generator can be seen in Figure 4.1. The cut-in
wind speed is 3 m/s and the output power is proportional to the third power of the
wind speed up to full power at 10 m/s. Above 10 m/s excess wind is wasted, for
example, by pitching the blades. The generator has a minimum speed of 0.5 pu from
the cut-in wind speed up to 5 m/s. The generator voltage is controlled for a constant
flux in the generator from the wind speed of 5 m/s and upwards.
33
Generator speed
1
1
0.8
0.8
0.6
0.6
N [p.u.]
Power [p.u.]
Output power
0.4
0.2
0.2
0
0
5
10
15
20
25
0
10
15
Wind [m/s]
Generator voltage
Generator current
1
1
0.8
0.8
0.6
0.4
0.2
20
25
20
25
0.6
0.4
0.2
0
0
5
Wind [m/s]
Iin [p.u.]
Uin [p.u.]
0
0.4
0
5
10
15
20
25
0
Wind [m/s]
5
10
15
Wind [m/s]
Figure 4.1: Output power, generator speed, generator voltage and generator current
from wind turbine as functions of wind speed.
34
4.1
Converter Environment
DC/DC converters are placed in a generation system where the voltage out from the
generator is low. The converters between the generator and the transmission line
increase the voltage to reduce transmission losses. The output voltages of the converters
are held constant by the next step in the transmission system by regulating the current
drawn from the previous converters. A schematic layout of the wind farm is shown in
Figure 4.2.
Wind Turbine
with Generator
G
AC/DC
Converter
Low Voltage
AC from
Generator
~
=
Low Voltage
DC Bus
DC/DC
Converter
DC/DC
Converter
Cable to
shore
=
=
=Medium Voltage = High Voltage
DC Bus
DC Bus
Direction of Power Flow
Figure 4.2: Layout of transmission system where generation is included.
The first converter in the chain is exposed to the varying input voltage of the generator. A diode bridge is assumed for rectification and, therefore, a gearbox should be
connected between the turbine and the generator. Direct-drive generators normally
have a leakage inductance that is too high to be suitable for a diode rectifier [54].
The difference between the DC transmission voltage and the voltage of the wind turbine
is generally too high, maybe 100 times, to use a single DC/DC converter. Therefore, a
number of DC/DC converters are needed to convert the voltage in a number of steps.
The resulting layout is very similar to the usual radial structure of AC distribution
power systems, with the DC/DC converters replacing the transformers. Normally,
690 V is used as the generation voltage and, therefore, two or three steps are needed.
The use of high voltage generators, with a generation voltage of ten kilovolts or more,
is one possible method to reduce the number of converters. However, one problem for
some of the converters topologies is voltage reduction at low wind speeds.
4.2
DC/DC Converter Topologies
The different DC/DC converter topologies, which will be analysed, can be divided into
two different groups: non-galvanic isolated topologies and galvanic isolated topologies [5]. The difference between them is the isolating transformer that is used in the
galvanic isolated topologies. The different topologies are listed in Table 4.1. Each of
the listed DC/DC-converters will be analysed below.
35
Table 4.1: Different investigated topologies of DC/DC-converters.
Non galvanic
isolated topologies
Galvanic isolated
topologies
Boost
Cúk
Sepic
Zeta
Luo
4.2.1
Flyback
Forward
Two transistor forward
Push pull
Half bridge
Full bridge
Half bridge with voltage doubler
Boost Converter
The boost or the step-up converter is common when no galvanic insulation is needed
and for moderate input/output voltage ratios. The converter is very simple and has
few components, as shown in Figure 4.3. However, it can only be used when the output
voltage Uout is higher than the input voltage Uin [5].
Iin
L
IL
+
+ U L
+
+ UD
Uin
Sw
Usw Cout
-
D
ID
Iout
+
Uout
I
SW
-
-
Figure 4.3: Schematic layout of boost converter.
The boost converter works cyclically by storing energy in the inductor L when the
switch Sw is on and dumps the stored energy together with energy from the input into
the load when the switch Sw is off. The output voltage Uout is controlled and regulated
by varying the amount of energy stored and dumped each cycle. When the switch is
on, the supply voltage is applied across the inductor L, and the current through the
inductor increases linearly. During the on state, the capacitor C supplies the load
with energy and, thus, the voltage across the capacitor is reduced. When the switch is
turned off, the current continues through L, supplying the load via the diode D. Thus,
the current decreases linearly. If the current through the inductor reaches zero before
the next switching cycle starts, the converter works in the discontinuous conduction
mode (DCM). Moreover, if the current through the inductor does not reach zero before the next switching cycle starts, the converter works in a continuous conduction
mode (CCM as shown in Figure 4.4). The control system has to use separate control
schemes for DCM and CCM.
In CCM, the relation between the input voltage Uin and the output voltage Uout can
be expressed as
36
Switch voltage and current
Inductor voltage and current
1
Usw (solid), Isw (dotted)
Un1 (solid), In1 (dotted)
1
0.5
0
−0.5
0.5
0
−0.5
−1
−1
0
0.5
1
1.5
0
2
0.5
1
1.5
2
Time [ms]
Time [ms]
Figure 4.4: Idealised current and voltage waveforms for inductor and switch stresses in
CCM for boost converter (duty ratio D=0.8), Left: Inductor voltage U L
(line) and inductor current IL (dotted), Right: Switch voltage USW (line)
and switch current ISW (dotted).
1
Uout
=
Uin
1−D
(4.1)
where D is the duty ratio and is defined as
D=
ton
Ts
(4.2)
where ton is the conduction time for the switch during one switching cycle Ts .
In DCM, the relation between the input and output voltage depends on the current
and the duty ratio. The ratio between the output voltage and the input voltage can
be expressed with the duty ratio D and the relative time ∆1 as expressed in Eq. (4.3).
, the switch is off and the current
During the relative time ∆1 , which is defined as ∆t
Ts
in the inductor is non-zero.
Uout
∆1 + D
=
Uin
∆1
(4.3)
Semiconductor Stresses in CCM
In this section, the stresses on the semiconductors in CCM are analyzed. The maximum
voltage over the switch is written as
ûSw = Uout
and the maximum current through the switch becomes
37
(4.4)
îSw =
Iout
1
+ ∆IL
1−D 2
(4.5)
where ∆IL is the peak-to-peak ripple current in the inductor L. The RMS current
through the switch is
ISw,RM S =
r
D((
Iout 2 1 1
) + ( ∆IL )2 )
1−D
3 2
(4.6)
The maximum voltage over the diode is
ûD = Uout
(4.7)
and the maximum current through the diode can be obtained as
îSw =
1
Iout
+ ∆IL
1−D 2
(4.8)
The RMS current through the diode is
ID,RM S =
r
(1 − D)((
Iout 2 1 1
) + ( ∆IL )2 )
1−D
3 2
(4.9)
Main Advantages and Drawbacks with Boost Converter
The main advantages of the boost converter are:
+ The converter is very simple with only two active components, the switch Sw
and the diode D, and two passive components, the inductor L and the capacitor
Cout ;
+ Low input ripple in CCM i.e. Iout ≥
of the converter.
Uout D 2
2Lfsw
where fsw is the switching frequency
The main drawbacks of the boost converter are:
- Different parasitic resistances in the switches and the inductor limit the duty
cycle to approximately 0.8-0.9 and this limits the maximum boost ratio to approximately 10;
- A large switch current when the duty cycle is high;
38
- Poor transient response due to the fact that stored energy in the inductor has to
be transferred to the output even if the load is removed;
- Regulator loop hard to stabilize since the gain is load dependent;
- No current limiting of output short circuits;
- The power can only flow in one direction due to the diode D.
Prototypes have been built up to approximately 100 kW with efficiency up to approximately 95 %.
4.2.2
Cúk Converter
The cúk converter, named after its inventor, is used when a small current ripple is
needed and for moderate voltage changes. The converter is very simple and has few
components, as shown in Figure 4.5. The output is inverted and the converter can
be used when the input voltage is lower or higher than the output voltage. Galvanic
insulation can be achieved by splitting capacitor C1 into two capacitors and applying
a transformer between the two capacitors, as shown in Figure 4.6 [5].
Iin
L1
IL1
+
+ U L1
Uin
Sw
C1
IC1
+
U
+ C1
Usw D
-
- U +
L2
+
UD Cout
-
Iout
Uout
ID
ISW
-
IL2
L2
+
Figure 4.5: Schematic layout of cúk converter.
Iin
L1
+
+ U L1
Uin
Sw
C1a I
C1a
+
U
+ C1a
n1
Usw
-
C1b
IC1b
L2
-
+
UC1b
n2
D
IL2
+ U L2
+
UD Cout
-
ID
ISW
-
IL1
Iout
+
Uout
-
Figure 4.6: Schematic layout of cúk converter with galvanic insulation.
The cúk converter displayed in Figure 4.5, works cyclically by shifting energy between
the inductors L1 and L2 , the capacitor C1 and the load. Unlike the previous converter,
where the energy transfer is associated with the inductor, the energy transfer for the
Cúk converter depends on the capacitor C1 .
39
When the switch Sw is on, the inductor L1 is charged from the supply and the inductor
L2 is charged from the capacitor C1 . In the next mode, when the switch Sw is off,
the inductor L1 charges the capacitor C1 and the inductor L2 supplies the load. The
output is inverted in comparison with the input.
When the switch is on, the supply voltage is applied across the inductor L1 and the
current in L1 increases linearly. At the same time, the capacitor C1 increases the
current in L2 through the switch and supplies the load. When the switch is turned
off, the current in L1 charges C1 through the diode and, thus, decreases. The current
in L2 continues to supply the load through the diode and decreases. The converter
normally operates in CCM, as shown in Figure 4.7, to achieve low input and output
ripple currents.
Inductor voltage and current
Switch voltage and current
1
Usw (solid), Isw (dotted)
Ul1 (solid), Il1 (dotted)
1
0.5
0
−0.5
−1
0
0.5
1
1.5
0.5
0
−0.5
−1
0
2
Time [ms]
0.5
1
1.5
2
Time [ms]
Figure 4.7: Idealised voltage and current waveforms for inductor L1 and switch stresses
in CCM for cúk converter (duty ratio D=0.8), Left: Inductor voltage U L1
(line) and inductor current IL1 (dotted), Right: Switch voltage USW (line)
and switch current ISW (dotted).
In CCM, the relation between the input voltage Uin and the output voltage Uout can
be expressed as
where D is the duty ratio.
D
Uout
=−
Uin
1−D
(4.10)
Semiconductor Stresses in CCM
In this section, the stresses on the semiconductors in CCM are analyzed. The maximum
voltage over the switch is written as
ûsw =
Uout
D
and the maximum current through the switch becomes
40
(4.11)
îsw =
Iout
1
1
+ ∆IL1 + ∆IL2
1−D 2
2
(4.12)
where ∆IL1 and ∆IL2 is the peak-to-peak ripple current in the inductor L1 and L2 ,
respectively. The RMS current through the switch is
Isw,RM S =
r
D((
1
Iout 2 1 1
) + ( ∆IL1 + ∆IL2 )2 )
1−D
3 2
2
(4.13)
The maximum voltage over the diode is
ûD =
Uout
D
(4.14)
and the maximum current through the diode is obtained by
îD =
1
1
Iout
+ ∆IL1 + ∆IL2
1−D 2
2
(4.15)
The RMS current through the diode is
ID,RM S =
r
(1 − D)((
Iout 2 1 1
1
) + ( ∆IL1 + ∆IL2 )2 )
1−D
3 2
2
(4.16)
Main Advantages and Drawbacks of Cúk Converter
The main advantages of the Cúk converter are:
+ The input and output ripples are small when operating in CCM, i.e., Iout ≥
where fsw is the switching frequency of the converter;
Uout ·D2
2L·fsw
+ Galvanic isolation can be added to the basic converter by using a transformer.
The capacitor C1 is divided into two parts and the transformer is inserted in
between them. The capacitors in series with each winding remove any DC voltage
and allow full utilization of the transformer;
+ Only two active components are used in the converter, the switch Sw and the
diode D.
The main drawbacks of the Cúk converter are:
- The ripple current in the capacitor C1 is equal to the sum of the input Iin and
output Iout currents;
41
- The switch must handle the sum of the input and the output currents;
- The energy can only flow in one direction.
Efficiency is up to approximately 94% and the converter is mainly used for low power
applications.
4.2.3
Sepic - Single-Ended Primary Inductance Converter
The sepic converter works similar to the cúk converter but has positive output, as
shown in Figure 4.8. The input current ripple is small and the converter is used for
moderate voltage changes when the input voltage is lower or higher than the output
voltage [55].
Iin
L1 I
+
+ U L1
Uin
Sw
IC1
C1
D
ID
Iout
+
Uout
IL2
+
+
U
U
+
+ C1
D
Usw L2 UL2 Cout
ISW
-
L1
-
Figure 4.8: Schematic layout of sepic converter.
The sepic converter works cyclically by shifting energy between the inductors, the
capacitor and the load. When the switch Sw is on, the inductor L1 is charged from
the supply, the inductor L2 is charged from the capacitor C1 and Cout supplies the
load. When the switch Sw is turned off, the inductor L1 charges the capacitor C1 and
supplies the load and the capacitor Cout together with inductor L2 .
When the switch is on, the supply voltage is applied across the inductor L1 and the
current in L1 increases linearly. At the same time, the capacitor C1 increases the
current in L2 through the switch and the capacitor Cout supplies the load. When the
switch is turned off, the current in L1 and L2 supply the load and charge Cout . The
current in L1 also charges C1 .
In CCM, the relation between the input voltage Uin and the output voltage Uout can
be expressed as
D
Uout
=
Uin
1−D
where D is the duty ratio.
42
(4.17)
Semiconductor Stresses in CCM
In this section, the stresses on the semiconductors in CCM are analyzed. The maximum
voltage over the switch is written as
ûSw =
Uout
D
(4.18)
and the maximum current through the switch is equal to
îSw =
Iout
1
1
+ ∆IL1 + ∆IL2
1−D 2
2
(4.19)
where ∆IL1 and ∆IL2 is the peak-to-peak ripple current in the inductor L1 and L2 ,
respectively. The RMS current through the switch is
r
Isw,RM S =
D((
1
Iout 2 1 1
) + ( ∆IL1 + ∆IL2 )2 )
1−D
3 2
2
(4.20)
The maximum voltage over the diode is obtained as
ûD1 =
Uout
D
(4.21)
and the maximum current through the diode becomes
îD1 =
Iout
1
1
+ ∆IL1 + ∆IL2
1−D 2
2
(4.22)
The RMS current through the diode is equal to
ID1 ,RM S =
r
(1 − D)((
1
Iout 2 1 1
) + ( ∆IL1 + ∆IL2 )2 )
1−D
3 2
2
(4.23)
Main Advantages and Drawbacks of Sepic Converter
The main advantages of the Sepic converter are:
+ Only two active components are used in the converter, the Switch Sw and the
diode D;
+ Low input ripple when operating in CCM, i.e., Iout ≥
switching frequency of the converter.
43
Uout ·D2
2L·fsw
where fsw is the
The main drawbacks of the Sepic converter are:
- The switch and the diode maximum voltage and current is the sum of the input
and output voltage and current, respectively;
- Large output voltage ripple;
- The power can only flow in one direction.
Efficiency at different loads is up to 94% and the converter has, so far, been used for
low power applications.
4.2.4
Zeta Converter
The Zeta converter, sometimes called the inverted Sepic converter, works similar to
the cúk converter but has positive output, as shown in Figure 4.9. The output current
ripple is small and the converter is used for moderate voltage changes when the input
voltage is lower or higher than the output voltage [56].
Iin
I
U SW
+ SW -
+
Uin
Sw L
1
C1
IC1
IL2
+ U L2
+
UD Cout
ID
IL1
+
+ UC1
UL1
D
-
L2
-
Iout
+
UOut
-
Figure 4.9: Schematic layout of Zeta converter.
The Zeta converter works cyclically by shifting energy between the inductors, the
capacitor and the load. First, the inductor L1 is charged from the input voltage, the
inductor L2 is charged from the capacitors C1 and C1 together with L2 , which also
supplies the load. Second, the inductor L1 charges the capacitor C1 and the inductor
L2 supplies the load.
When the switch Sw is on, the input voltage Uin is applied across the inductor L1 and
the current in the inductor L1 increases linearly. At the same time, the input voltage
and the capacitor C1 increase the current through the inductor L2 and supply the
load. Meanwhile, the diode D blocks. When the switch is turned off, the inductor L1
charges the capacitor C1 through the diode D and the inductor L2 supplies the load,
also through the diode D.
In CCM, the relation between the input voltage Uin and the output voltage Uout can
be expressed as
44
D
Uout
=
Uin
1−D
(4.24)
where D is the duty ratio.
Semiconductor Stresses in CCM
This section presents an analysis of the stresses on the semiconductors in CCM . The
maximum voltage over the switch is written as
ûSw =
Uout
D
(4.25)
and the maximum current through the switch is equal to
îsw =
Iout
1
1
+ ∆IL1 + ∆IL2
1−D 2
2
(4.26)
where ∆IL1 and ∆IL2 is the peak-to-peak ripple current in the inductors L1 and L2 ,
respectively. The RMS current through the switch is
Isw,RM S =
r
D((
Iout 2 1 1
1
) + ( ∆IL1 + ∆IL2 )2 )
1−D
3 2
2
(4.27)
The maximum voltage over the diode is
ûD =
Uout
D
(4.28)
and the maximum current through the diode can be obtained as
îD =
1
1
Iout
+ ∆IL1 + ∆IL2
1−D 2
2
(4.29)
The RMS current through the diode is
ID,RM S =
r
(1 − D)((
Iout 2 1 1
1
) + ( ∆IL1 + ∆IL2 )2 )
1−D
3 2
2
45
(4.30)
Main Advantages and Drawbacks of Zeta Converter
The main advantages of the boost converter are:
+ The inductor L2 and the capacitor C2 form a filter, which leads to low output
ripple;
+ Only two active components are used in the converter, the switch Sw and the
diode D.
The main drawbacks of the boost converter are:
- The ripple current in the capacitor C1 is equal to the sum of the input and output
currents;
- High semiconductor stresses;
- The switch is connected directly to the input and this causes a large input ripple;
- The power can only flow in one direction.
4.2.5
Luo Converter
The Luo converter, named after its inventor [13], is derived from the Zeta converter
and has positive output, as shown in Figure 4.10. The output current ripple is small
and the converter is used for moderate voltage changes when the input voltage is lower
than the output voltage [13].
Iin
I
USW SW
+
+
UinSw
L1
C1
D2
ID2
L2
IL2
Iout
+ U L2
+
UC2 Cout
-
+
Uout
IC2
+
U
D2
+
UD1 C2
ID1
+
+ UC1
UL1 D1
IL1
-
IC1
-
Figure 4.10: Schematic layout of Luo converter.
The Luo converter works cyclically by shifting energy between the inductors, the capacitors and the load. First, the inductor L1 is charged from the supply, the inductor
L2 and the capacitor C2 are charged from the capacitor C1 . The capacitor C1 together with the inductor L2 supplies the load. Second, the inductor L1 charges the
capacitor C1 and the inductor L2 together with the capacitor C2 supply the load.
When the switch Sw is on, the input voltage is applied across the inductor L1 and the
current in the inductor increases linearly. At the same time, the capacitor C 1 increases
46
the current in the inductor L2 , charges the capacitor C2 and supplies the load via the
diode D2 . When the switch is turned off, the inductor L1 charges the capacitor C1 via
the diode D1 . The inductor L2 and the capacitor C2 supply the load.
In CCM, the relation between the input voltage Uin and the output voltage Uout can
be expressed as
Uout
1
=
Uin
1−D
(4.31)
where D is the duty ratio.
Semiconductor Stresses in CCM
This section presents an analysis of the stresses on the semiconductors in CCM . The
maximum voltage over the switch Sw is written as
ûSw = Uout
(4.32)
and the maximum current through the switch Sw is
îSw =
Iout
1
1
+ ∆IL1 + ∆IL2 + δ(t)
1−D 2
2
(4.33)
where ∆IL1 and ∆IL2 are the peak-to-peak ripple current in the inductors L1 and L2 ,
respectively, and δ(t) is the inrush current for the capacitor C1 and the capacitor C2 .
The RMS current through the switch Sw is written as
ISw,RM S =
r
D((
1
Iout 2 1 1
) + ( ∆IL1 + ∆IL2 )2 ) + ∆δ (D)
1−D
3 2
2
(4.34)
where ∆δ (D) is the contribution to the RMS current from the inrush current δ(t). The
maximum voltage over the diodes becomes
ûD1 = ûD2 = Uout
(4.35)
and the maximum current through the diodes is obtained as
îD1 ≈
r
1
C1
DUout + ∆IL1
L1
2
47
(4.36)
when assuming that
∆IL1
∆UC1
=
IL 1
U C1
(4.37)
1
îD2 ≈ Iout + ∆IL2 + δ(t)
2
(4.38)
respective
The RMS current through the diode D1 is
ID1 ,RM S =
r
(1 − D)(
C1 p
1 1
Uout D + ( ∆IL1 )2 )
L1
3 2
(4.39)
and the RMS current through the diode D2 is equal to
ID2 ,RM S =
r
1 1
2
D(Iout
+ ( ∆IL2 )2 ) + ∆δ (D)
3 2
(4.40)
Main Advantages and Drawbacks of Luo Converter
The main advantages of the Luo converter are:
+ The switch voltage is low but the switch current is high;
+ The inductor L2 and the capacitors C2 and Cout form a filter, which results in
low output ripple.
The main drawbacks of the Luo converter are:
- The ripple current in capacitor C1 is equal to the sum of the input and output
currents;
- The switch is connected directly to the input and this causes a large current
ripple on the input;
- The power can only flow in one direction.
Efficiency at different loads is up to 95 % and the converter is used for low power
applications.
48
Iin
D2
+
n1
Uin
Sw
n2
n3
ID2
+
UD2
Cout
Iout
+
Uout
-
-
ID1
ISW
+ D1 +
Usw
UD1
-
Figure 4.11: Schematic layout of Flyback converter.
4.2.6
Flyback Converter
The Flyback converter is common when galvanic insulation is needed and for low power
applications typically below 100 W. The converter is simple and has few components,
as shown in Figure 4.11. The most complicated part of the converter is the transformer,
which has a high magnetizing inductance [5].
The Flyback converter works cyclically by storing energy in the transformer and then
dumping this stored energy into the load. The output voltage is controlled and regulated by varying the amount of energy stored and dumped each cycle.
When the switch Sw is on, the input voltage Uin is applied across the winding n1 and
the current in the transformer leakage inductance increaes linearly. The diodes D 1 and
D2 block and the capacitor supplies the load. When the switch Sw is turned off, the
energy in the transformer is discharged, via the winding n3 and the diode D2 , to the
load and the output capacitor Cout . The diode D1 and the demagnetising winding n2
are only used under no-load conditions when the energy stored in the transformer is
transferred back to the supply. The converter can be operated in CCM, as shown in
Figure 4.12, or in DCM.
In CCM, the relation between the input voltage Uin and the output voltage Uout can
be expressed as
n3 D
Uout
=
Uin
n1 1 − D
(4.41)
where D is the duty ratio.
Semiconductor Stresses in CCM
This section presents an analysis of the stresses on the semiconductors in CCM . The
maximum voltage over the switch is written as
ûsw =
n1 Uout
n3 D
49
(4.42)
Switch voltage and current
2
1.5
1.5
Usw (solid), Isw (dotted)
Un1 (solid), In1 (dotted)
Transformer voltage and current
2
1
0.5
0
−0.5
−1
0
0.5
1
1.5
1
0.5
0
−0.5
−1
0
2
0.5
Time [ms]
1
1.5
2
Time [ms]
Figure 4.12: Idealised current and voltage waveforms for transformer and switch
stresses in CCM for Flyback converter (duty ratio D=0.4), Left: Transformer voltage Un1 (line) and transformer current In1 (dotted), Right:
Switch voltage USW (line) and switch current ISW (dotted).
and the maximum current through the switch is equal to
n3 Iout
1
+ ∆ILm
n1 1 − D 2
îsw =
(4.43)
where ∆ILm is the peak-to-peak ripple current in the transformer leakage inductor Lm .
The RMS current through the switch is
Isw,RM S =
r
D((
1
n3 Iout 2
) + ∆IL2 m )
n1 1 − D
12
(4.44)
The maximum voltage over the diode D1 is equal to
ûD1 =
n1 + n 2 1 − D
Uout
n3
D
(4.45)
and the maximum voltage over the diode D2 becomes
ûD2 =
Uout
D
(4.46)
The current through the diode D1 is normally zero but if the load is disconnected the
maximum current can in the worse case become
îD1 =
1 n1
n3 1
Iout +
∆ILm
n2 1 − D
2 n2
50
(4.47)
The maximum current through the diode D2 is equal to
îD2 =
1
1 n1
Iout +
∆ILm
1−D
2 n3
(4.48)
The RMS current through the diode D1 is normally zero. For the diode D2 , the RMS
current becomes
ID2 ,RM S =
r
(1 − D)((
Iout 2 1 1 n1
) + (
∆ILm )2 )
1−D
3 2 n3
(4.49)
Main Advantages and Drawbacks of Flyback Converter
The main advantages of the Flyback converter are:
+ The Flyback converter is, from a circuit perspective, the simplest of the low-power
isolated converters and uses only three components besides the transformer (if
the no-load capability is omitted;
+ The switch current can be reduced by the turn’s ratio of the transformer but has
the disadvantage of increasing the switch voltage and the diode current.
The main drawbacks of the Flyback converter are:
- The transformer design is critical and the high energy, which must be stored in the
transformer windings in the form of a DC current, requires a high inductance, a
high current primary, which in turn requires larger cores than would be necessary
with pure AC in the windings inductance;
- Poor transformer utilization since the core is only magnetised in one direction;
- The energy is transferred when the switch is turned off and the current waveform
is triangular causing a high output ripple;
- The power can only flow in one direction.
4.2.7
Forward Converter
The Forward converter is very common when galvanic insulation is needed and for
applications above the power range of the Flyback converter. The converter is simple
and has few components, as shown in Figure 4.13. The most complicated part of the
converter is the transformer with three windings [5].
The Forward converter delivers the energy to the load when the transistor is on and
uses the transformer in the active or forward mode. The additional winding n 2 and
the diode D1 are required to reduce the voltage over the switch Sw during the turn-off
time of the switch when the core of the transformer is being demagnitized.
51
Iin
D2
+
+
n1
n3
L
-
+ UL +
UD3
-
UD2
D3
ISW
-
Iout
+
Uout
-
ID1
+ D1 +
Usw
UD1
-
Sw
IL
ID3
Uin
n2
ID2
Figure 4.13: Schematic layout of Forward converter.
When the switch is on, the supply voltage is applied across the winding n1 and energy
is transferred via the transformer and the diode D2 , to the inductor L and the load.
The diodes D1 and D3 blocks. When the switch is turned off, the inductor L supplies
the load via the diode D3 and the energy in the leakage inductance of the transformer
is transferred back to the supply, via the demagnetizing winding n2 and the diode D1 .
The converter can only run in discontinuous conduction mode, as shown in Figure 4.14,
since the winding has to be demagnetized every cycle.
Switch voltage and current
2
1.5
1.5
Usw (solid), Isw (dotted)
Un1 (solid), In1 (dotted)
Transformer voltage and current
2
1
0.5
0
−0.5
−1
0
0.5
1
1.5
1
0.5
0
−0.5
−1
0
2
Time [ms]
0.5
1
1.5
2
Time [ms]
Figure 4.14: Idealized current and voltage waveforms for the transformer and switch
stresses in Forward Converter (duty ratio D=0.4), Left: Transformer voltage Un1 (line) and transformer current In1 (dotted), Right: Switch voltage
USW (line) and switch current ISW (dotted).
The relation between the input voltage Uin and the output voltage Uout can be expressed
as
n3
Uout
= D
Uin
n1
52
(4.50)
Semiconductor Stresses
This section presents an analysis of the stresses on the semiconductors. The maximum
voltage over the switch is written as
ûsw =
n1 Uout
n1
(1 + )
n3 D
n3
(4.51)
and the maximum current through the switch is equal to
îsw =
1
n3
(Iout + ∆IL ) + îM ag
n1
2
(4.52)
where ∆IL is the peak-to-peak ripple current in the inductor L and îM ag is the peak
magnetizing current in the transformer. The RMS current through the switch can be
expressed as
Isw,RM S
r
1 1 n3
n3
∆IL + îM ag )2 )
= D(( Iout )2 + (
n1
3 2 n1
(4.53)
The maximum voltage over the diode D1 is written as
ûD1 =
n1 + n2 Uout
,
n3
D
(4.54)
and the maximum voltage over the diode D2 is equal to
ûD2 =
n1 Uout
n2 D
(4.55)
and the diode D3 has the maximum voltage written as
ûD3 =
Uout
D
(4.56)
The maximum current through the diode D1 becomes
îD1 = îM ag
and the diode D2 has the maximum current as
53
(4.57)
îD2 =
Iout
1
+ ∆IL
1−D 2
(4.58)
and, finally, the diode D3 has the maximum current, written as
îD3 =
Iout 1
+ ∆IL
D
2
(4.59)
The RMS current through the diode D1 becomes
1
ID1 ,RM S = √ îM ag
3
and the diode D2 has an RMS current equal to
r
Iout 2 1 1
ID2 ,RM S = (1 − D)((
) + ( ∆IL )2 )
1−D
3 2
(4.60)
(4.61)
and the diode D3 has an RMS current equal to
ID3 ,RM S =
r
D((
Iout 2 1 1
) + ( ∆IL )2 )
D
3 2
(4.62)
Main Advantages and Drawbacks of Forward Converter
The main advantages of the forward converter are:
+ The Forward converter is simple but compared with the Flyback converter has
an extra winding on the transformer, two more diodes and an additional output
filter inductor;
+ The output ripple is low because of the inductor L;
+ The switch current is reduced by the turn ratio of the transformer but this increases the duty cycle and decreases the dynamic range, i.e. the potential to
change the duty ratio when the load increases.
The main drawbacks of the Forward converter are:
- Poor transformer utilization since the core is only magnetized in one direction;
- The transformer design is critical to minimize the magnetizing current and, thus,
the losses in the diode D1 ;
- The converter has a high input ripple due to a low duty cycle;
- The power can only flow in one direction.
Converters have been built up to 15 kW at 100 kHz and efficiency is up to 97 %.
54
4.2.8
Two Two-Transistor Forward Converter
The Two-Transistor Forward converter can replace the Forward converter when the
switch voltage or the transformer design is critical. The converter has two transistors,
as shown in Figure 4.15. The converter has more complicated drive circuits but has the
advantage that the switch voltage is clamped to the input voltage and no demagnetizing
winding is needed on the transformer [5].
Iin
ISW1
+
+
D1
UD1
ID1
-
n1
UD2
-
D4
+
Usw2
-
IL
+ U L
+
UD4
-
ID4
-
Sw2
n2
UD3
L
Iout
+
Uout
-
ISW2
D2
ID2
+
ID3
D3
+
Uin
-
+
Usw1
-
Sw1
Figure 4.15: Schematic layout of Two-Transistor Forward converter.
As with the Forward converter this converter delivers the energy to the load when the
transistor is on and uses the transformer in the active or forward mode. It uses two
switches and two diodes but this allows the use of only two windings.
When the switches are on, energy is transferred via the transformer and the diode D 2 ,
to the inductor L and the load. The diodes D1 , D2 and D4 block. When the switches
are turned off the inductor L supplies the load via the diode D4 and the energy in the
transformer leakage inductor is transferred back to the supply, via the diodes D 1 and
D2 . The converter can only run in the discontinuous conduction mode, as shown in
Figure 4.16, since the winding has to be demagnetized every cycle.
The relation between the input voltage Uin and the output voltage Uout can be expressed
as
Uout
n2
= D
Uin
n1
where D is the duty ratio.
55
(4.63)
Transformer voltage and current
Switch voltage and current
1
Usw (solid), Isw (dotted)
Un1 (solid), In1 (dotted)
1
0.5
0
−0.5
−1
0
0.5
0
−0.5
−1
0.5
1
1.5
2
0
0.5
Time [ms]
1
1.5
2
Time [ms]
Figure 4.16: Idealised current and voltage waveforms for transformer and switch
stresses in Two-Transistor Forward converter (duty ratio D=0.4), Left:
Transformer voltage Un1 (line) and transformer current In1 (dotted),
Right: Switch voltage USW1 (line) and switch current ISW1 (dotted).
Semiconductor Stresses
This section presents an analysis of the stresses on the semiconductors. The maximum
voltage over the switches Sw1 and Sw2 is written as
ûSw =
n1 Uout
= Uin
n2 D
(4.64)
and the maximum current through the switches Sw1 and Sw2 is equal to
îSw =
n2
1
(Iout + ∆IL ) + îM ag
n1
2
(4.65)
where ∆IL is the peak-to-peak ripple current in the inductor L and îM ag is the peak
magnetizing current in the transformer. The RMS current through the switches Sw 1
and Sw2 becomes
ISw,RM S
r
1 1 n2
n2
∆IL + îM ag )2 )
= D(( Iout )2 + (
n1
3 2 n1
(4.66)
The maximum voltage over the diodes D1 and D2 is written as
ûD1 = ûD2 =
n1 Uout
= Uin
n2 D
and the diodes D3 and D4 have the maximum voltage
56
(4.67)
ûD3 = ûD4 =
Uout
D
(4.68)
The maximum current through the diodes D1 and D2 becomes
îD1 = îD2 = îM ag ,
(4.69)
and the maximum current through the diode D3 is equal to
îD3 =
Iout
1
+ ∆IL
1−D 2
(4.70)
and the diode D4 has a maximum current of
îD4 =
Iout 1
+ ∆IL
D
2
(4.71)
The RMS current through the diodes D1 and D2 is equal to
1
ID1 ,RM S = ID2 ,RM S = √ îM ag ,
3
(4.72)
and the RMS current through the diodes D3 becomes
ID3 ,RM S =
r
(1 − D)((
Iout 2 1 1
) + ( ∆IL )2 )
1−D
3 2
(4.73)
and, finally, the diode D4 has the RMS current
ID4 ,RM S =
r
D((
Iout 2 1 1
) + ( ∆IL )2 )
D
3 2
(4.74)
Main Advantages and Drawbacks of Two-Transistor Forward Converter
The main advantages of the Two-Transistor Forward Converter are:
+ The switch voltage is clamped by the diodes to the input voltage;
+ Only two windings are needed in the transformer.
57
The main drawbacks of the Two-Transistor Forward Converter are:
- Requires auxiliary power supply for one switch;
- Poor transformer utilization since the core is only magnetized in one direction;
- The transformer design is critical to minimize the magnetizing current and, thus,
the losses in the diodes;
- The power can only flow in one direction.
4.2.9
Push Pull Converter
The Push Pull Converter also has two transistors, as shown in Figure 4.17, but simpler
drive circuits than the Two-Transistor Forward Converter. Consequently, the converter
needs a transformer with two primary windings and the switch voltage is twice the input
voltage [5].
D1 + U
D1
+
Uin
-
ISW1
ISW2
Usw1
n1
Sw1
D3
n2
D4
-
+
UD4
-
+
Uout
+
D6
UD6
-
ID6
+
D5
Cout
ID4
D2
+
UD5
-
n3
Sw2
+ Usw2
+
UD3
-
ID5
+
Iout
ID3
Iin
ID1
-
UD2 I
D2
Figure 4.17: Schematic layout of push-pull converter.
The switches are on alternatively, thus, creating an alternating current, and energy is
transferred via the transformer and the diode bridge to the load. The diodes D1 and
D2 blocks and are only used under transientand no-load conditions.
When the switch Sw1 is on, the supply voltage is applied across the winding n1 and
a positive flux is induced in the winding n3 . The second switch Sw1 is turned off,
the switch Sw2 is turned on and a negative flux is induced in the winding n3 . It is
important to have a voltage-second balance to prevent the transformer from becoming
saturated. Idealised waveforms are shown in Figure 4.18.
The relation between the input voltage Uin and the output voltage Uout when the
winding n1 is equal to the winding n2 can be expressed as
58
Switch voltage and current
2
1.5
1.5
Usw (solid), Isw (dotted)
Un1 (solid), In1 (dotted)
Transformer voltage and current
2
1
0.5
0
−0.5
−1
0
0.5
1
1.5
1
0.5
0
−0.5
−1
0
2
0.5
Time [ms]
1
1.5
2
Time [ms]
Figure 4.18: Idealised current and voltage waveforms for transformer and switch
stresses in DCM for Push Pull Converter (duty ratio D=0.4), Left: Transformer voltage Un1 (line) and transformer current In1 (dotted), Right:
Switch voltage USW1 (line) and switch current ISW1 (dotted).
Uout
n3
=2 D
Uin
n1
(4.75)
where the maximum value of the duty ratio D is 0.5.
Semiconductor Stresses
This section presents an analysis of the stresses on the semiconductors in the push pull
converter. The maximum voltage over the switches Sw1 and Sw2 is written as
ûsw =
n1 Uout
= 2Uin
n3 D
(4.76)
and the maximum current through the switches Sw1 and Sw2 is equal to
îsw =
n3
Iout + îM ag
n1
(4.77)
where îM ag is the peak magnetizing current in the transformer. The RMS current
through the switches Sw1 and Sw2 is
Isw,RM S
r
1
n3
= D(( Iout )2 + î2M ag )
n1
3
The maximum voltage over the diodes D1 and D2 is written as
59
(4.78)
ûD1 = ûD2 =
n1 Uout
= 2Uin
n3 D
(4.79)
For the diodes D3 to D6 , the maximum voltage is the same and becomes
ûD3 = ûD4 = ûD5 = ûD6 = Uout
(4.80)
Under stationary conditions, the current through the diodes D1 and D2 is zero. The
maximum current through the diodes D3 to D6 becomes
îD3 = îD4 = îD5 = îD6 =
Iout
2D
(4.81)
The RMS current through the diodes D3 to D6 is the same and is written as
Iout
ID3 ,RM S = ID4 ,RM S = ID5 ,RM S = ID6 ,RM S = √
2 D
(4.82)
Main Advantages and Drawbacks of Push Pull Converter
The main advantages of the Push Pull Converter are:
+ Double frequency in the output reduces the requirements for the output filter;
+ Good utilization of the transformer while working with both positive and negative
flux;
+ Both switches are driven with respect to ground.
The main drawbacks of the Push Pull Converter are:
- The transformer needs two primary windings;
- The primary of the transformer must have a voltage-second balance to prevent
the transformer core from saturation;
- A blanking time is necessary to ensure that no overlap between the switches
occurs;
- The power can only flow in one direction.
60
Iin
Sw1
IC1
+
Usw1
-
D1
n1
Uin
D3
Cout
+
Usw2
-
D2
+
UD2
-
+
Uout
+
D4
UD4
-
ISW2
ID4
Sw2
IC2
+
U
- C2
+
UD3
-
n2
ID2
C2
+
UD1
-
ID3
+
U
- C1
ID1
C1
-
Iout
ISW1
+
-
Figure 4.19: Schematic layout of Half Bridge Converter.
4.2.10
Half Bridge Converter
The Half Bridge Converter has two transistors working together with two capacitors,
as shown in Figure 4.19. Again, the transformer is simpler in comparison with the
previous converter types and the switch voltage is the same as the input voltage, but
the drive circuit is more complicated [5].
The switches Sw1 and Sw2 are on alternatively, thus, creating an alternating voltage
and the energy is transferred via the transformer and the diode bridge to the load.
When the switch Sw1 is on, half of the input voltage Uin is applied across the winding
n1 and a positive flux is induced in the winding n2 . When the switch Sw1 is turned off,
switch Sw2 is turned on and a negative flux is induced in the winding. The primary
must have a voltage-second balance to prevent the transformer core from saturation.
This can be achieved by controlling the voltage over the capacitors C1 and C2 . Idealized
waveforms are shown in Figure 4.20.
The relation between the input voltage Uin and the output voltage Uout can be expressed
as
n2
Uout
= D
Uin
n1
(4.83)
where the maximum value of the duty ratio D is 0.5.
Semiconductor Stresses
This section presents an analysis of the stresses on the semiconductors for the half
bridge converter. The maximum voltage over the switches Sw1 and Sw2 is written as
61
Transformer voltage and current
Switch voltage and current
2
Usw (solid), Isw (dotted)
Un1 (solid), In1 (dotted)
2
1.5
1
0.5
0
−0.5
0
0.5
1
1.5
1.5
1
0.5
0
−0.5
0
2
0.5
Time [ms]
1
1.5
2
Time [ms]
Figure 4.20: Idealized current and voltage waveforms for transformer and switch
stresses in Half Bridge Converter (duty ratio D=0.4), Left: Transformer
voltage Un1 (line) and transformer current In1 (dotted), Right: Switch
voltage USW1 (line) and switch current ISW1 (dotted).
ûsw1 = ûsw2 =
n1 Uout
= Uin
n2 D
(4.84)
and the maximum current through the switches Sw1 and Sw2 is equal to
îsw1 = îsw2 =
n2 Iout
+ îM ag
n1 2D
(4.85)
where îM ag is the peak magnetizing current in the transformer. The RMS current
through the switches Sw1 and Sw2 is equal and becomes
Isw1 ,RM S = Isw2 ,RM S =
r
D((
n2 Iout 2 1 2
) + îM ag )
n1 2D
3
(4.86)
The diodes D1 to D4 have the same maximum voltage which is written as
ûD1 = ûD2 = ûD3 = ûD4 = Uout
(4.87)
The maximum current through the diodes D1 to D4 is equal and becomes
îD1 = îD2 = îD3 = îD4 =
Iout
2D
(4.88)
The RMS current through the diodes D1 to D4 is also the same and is written as
Iout
ID1 ,RM S = ID2 ,RM S = ID3 ,RM S = ID4 ,RM S = √
2 D
62
(4.89)
Main Advantages and Drawbacks of Half Bridge Converter
The main advantages of the Half Bridge Converter are:
+ Good utilization of the transformer while working with both positive and negative
currents;
+ The switches can be rated to the input voltage and the anti-parallel diodes clamp
destructive switching transients;
+ Double frequency ripple in the output reduces the requirements for the output
filter.
The main drawbacks of the Half Bridge Converter are:
- Doubled switch current for the same output power in comparison with the Full
Bridge Converter;
- The control circuits must provide isolated drive signals to the switches;
- The primary must have a voltage-second balance to prevent the core from saturation;
- A blanking time is necessary to ensure that no overlap between the switches
occurs.
4.2.11
Full Bridge Converter
The Full Bridge Converter has four transistors working together, as shown in Figure 4.21.
Again the transformer is simple and the switch voltage is the same as the input voltage,
but the drive circuitry is more complicated in comparison with the previous converters,
since there are four switches and the drive circuits have to be separated from ground [5].
The switches Sw1 to Sw4 are on alternatively, thus, creating alternating voltage, and
the energy is transferred via the transformer and the diode bridge to the load.
First, the switches Sw1 and Sw4 are on, the supply voltage is applied across the winding
n1 and a positive flux is induced in the winding n2 ; Then, the switches Sw1 and Sw4 are
turned off and the switches Sw2 and Sw3 are turned on and a negative flux is induced
in the winding n2 . The primary must have a voltage-second balance to prevent the
transformer core from saturation. Idealized waveforms are shown in Figure 4.22.
The relation between the input voltage Uin and the output voltage Uout can be expressed
as
63
Iin
SW3
+
Usw3
-
Uin
D1
n1
D2
ISW4
ISW2
-
D3
Cout
+
UD2
-
Uout
+
D4
UD4
-
ID4
+
Usw4
-
+
Usw2 Sw4
-
+
+
UD3
-
n2
ID2
Sw2
+
UD1
-
ID3
+
Usw1 Sw3
-
ID1
Sw1
Iout
I
ISW1
+
-
Figure 4.21: Schematic layout of full bridge converter.
Transformer voltage and current
Switch voltage and current
1
Usw (solid), Isw (dotted)
Un1 (solid), In1 (dotted)
1
0.5
0
−0.5
−1
0
0.5
0
−0.5
−1
0.5
1
1.5
2
0
Time [ms]
0.5
1
1.5
2
Time [ms]
Figure 4.22: Idealised current and voltage waveforms for transformer and switch
stresses for Full Bridge Converter (duty ratio D=0.4), Left: Transformer
voltage Un1 (line) and transformer current In1 (dotted), Right: Switch
voltage USW1 (line) and switch current ISW1 (dotted).
64
n2
Uout
=2 D
Uin
n1
(4.90)
where the maximum value of the duty ratio D is 0.5.
Semiconductor Stresses
This section presents and analysis of the stresses on the semiconductors. The maximum
voltage over the switches Sw1 to Sw4 has the same value and becomes
ûSw1 = ûSw2 = ûSw3 = ûSw4 =
n1 Uout
= Uin
n2 2D
(4.91)
and the maximum current through the switches Sw1 to Sw4 is equal to
îSw1 = îSw2 = îSw3 = îSw4 =
n2 Iout
+ îM ag
n1 2D
(4.92)
where îM ag is the peak magnetizing current in the transformer. The RMS current
through the switches Sw1 to Sw4 has the same value and becomes
ISw1 ,RM S = ISw2 ,RM S = ISw3 ,RM S = ISw4 ,RM S =
r
D((
n2 Iout 2 1 2
) + îM ag )
n1 2D
3
(4.93)
The maximum voltage over the diodes D1 to D4 is written as
ûD1 = ûD2 = ûD3 = ûD4 = Uout
(4.94)
and the maximum current through the diodes D1 to D4 is equal to
îD1 = îD2 = îD3 = îD4 =
Iout
2D
(4.95)
The RMS current through the diodes D1 to D4 is the same and is written as
Iout
ID1 ,RM S = ID2 ,RM S = ID3 ,RM S = ID4 ,RM S = √
2 D
65
(4.96)
Main Advantages and Drawbacks of Full Bridge Converter
The main advantages of the Full Bridge Converter are:
+ Good utilization of the transformer by working with both positive and negative
fluxes;
+ The switches can be rated to the input voltage and anti-parallel diodes clamp
destructive switching transients;
+ Double frequency in the output reduces the requirements for the output filter;
+ The output power is doubled in comparison with the Half Bridge Converter, since
the input voltage, instead of half of the input voltage, is applied to the primary
winding;
+ By replacing the diodes D1 to D4 , the power can flow in both directions. This
causes extra complexity to the control circuit and drive signals have to be provided for the double amount of switches.
The main drawbacks of the Full Bridge Converter are:
- The control circuits must provide isolated drive signals to the switches;
- The primary must have a voltage-second balance to prevent the transformer core
from saturation;
- A blanking time is necessary to ensure that no overlap between the switches
occurs.
Efficiency at different loads is up to 97 %.
4.2.12
Half Bridge Converter With Voltage Doubler
The Half Bridge Converter with voltage doubler has the same primary configuration as
the Half Bridge Converter but uses a voltage doubler on the secondary side, as shown
in Figure 4.23 [5].
The switches are on alternatively, thus creating an alternating voltage, and the energy
is transferred via the transformer and the voltage doubler to the load. First, the switch
Sw1 is on, half of the input voltage Uin is applied across winding n1 and a positive flux
is induced in the winding n2 ; Then, switch Sw1 is turned off and the switch Sw2 is
turned on and a negative flux is induced in the winding. The diodes and the capacitors
at the output work as a voltage doubler, which compensates for the voltage applied to
the transformer being reduced to half of the input voltage. This, however, doubles the
current for the same output power. The primary must have a voltage-second balance
to prevent the transformer core from saturation but this can be achieved by controlling
the voltage over the capacitors C1 and C2 .
66
Iin
Sw1
IC1
+
Usw1
-
D1
n1
Uin
C3
UC3
-
D2
Uout
+
UD2
-
ISW2
IC2
+
Usw2
-
+
+
C4
UC4
-
IC4
Sw2
+
n2
ID2
C2
+
U
- C2
+
UD1
-
IC3
+
U
- C1
ID1
C1
-
Iout
ISW1
+
-
Figure 4.23: Schematic layout of Half Bridge Converter with voltage doubler.
The relation between the input voltage Uin and the output voltage Uout can be expressed
as
Uout
n2
=2 D
Uin
n1
(4.97)
where the maximum value of the duty ratio D is 0.5.
Semiconductor Stresses
In this section the stresses on the semiconductors for the Half Bridge Converter with
a voltage doubler are analyzed. The maximum voltage over the switches Sw1 and Sw2
is written as
ûSw1 = ûSw2 =
n1 Uout
= Uin
n2 2D
(4.98)
and the maximum current through the switches Sw1 and Sw2 becomes
îsw1 = îsw2 =
n2 Iout
+ îM ag
n1 D
(4.99)
where îM ag is the peak magnetizing current in the transformer. The RMS current
through the switches Sw1 and Sw2 is written as
Isw1 ,RM S = Isw2 ,RM S =
r
D((
67
n2 Iout 2 1 2
) + îM ag )
n1 D
3
(4.100)
The maximum voltage over the diodes D1 to D2 becomes
ûD1 = ûD2 = Uout
(4.101)
and the maximum current through the diodes D1 to D2 is equal to
îD1 = îD2 =
Iout
D
(4.102)
The RMS current through the diodes D1 to D2 is written as
Iout
ID1 ,RM S = ID2 ,RM S = √
D
(4.103)
Main Advantages and Drawbacks of Half Bridge Converter with Voltage
Doubler
The main advantages of the Half Bridge Converter with a voltage doubler are:
+ Good utilization of the transformer while working with both positive and negative
currents;
+ The switches can be rated to the input voltage and anti-parallel diodes clamp
destructive switching transients;
+ The double frequency ripple in the output reduces the requirements for the output
filter;
+ By replacing the diodes D1 to D2 with switches the power can flow in both
directions. This adds extra complexity to the control circuit and drive signals
have to be provided for the double amount of switches.
The main drawbacks of the Half Bridge Converter with a voltage doubler are:
- Doubled switch and diode currents for the same output power in comparison with
the Full Bridge Converter.
- The control circuit must provide isolated drive signals to the switches;
- The primary must have a voltage-second balance to prevent the core from saturation;
- A blanking time is necessary to ensure that no overlap between the switches
occurs.
68
4.3
Comparison of Switch Utilization for Different
Converters
For high voltage and high power applications, like a wind park transmission system, the
focus has to be on the utilization factor of the used components. Thus, the switches
should not be exposed to voltages higher than the input voltage or currents higher
than the rated input current. Moreover, the diodes should not be exposed to voltages
higher than the rated output voltage or currents higher than the rated output current.
A high voltage rating is more costly than a high current rating since a higher voltage
rating means that more switches have to be series connected. A transformer would
have to work with bi-directional flux and for simplicity it should have as few windings
as possible.
The converters are compared on per unit basis where the output voltage and the
output current are assumed to be the base values. The magnetizing current for the
transformers is not included in the comparison in order to simplify the analysis. Data
for such transformers is not readily available and the simplification is not believed to
affect the results. Two different applications are compared. First, the converters are
used for voltage adjustment where the ratio between the input and the output voltage
is between 2.5 and 5. Then, a DC transformer, where the ratio between the input
and the output voltage is 10 with a small tolerance, is used. The Voltage Adjustment
Converter is used at the point closest to the generator, as shown in Figure 4.2, to
adjust the varying generating voltages at different wind speeds, as shown in Figure 4.1.
The DC transformer is used after the Voltage Adjustment Converter to reach a high
transmission voltage in order to minimize transmission losses.
4.3.1
Voltage Adjustment Converter
The different theoretical ratings for the Voltage Adjustment Converter are shown in
Table 4.2 and Table 4.3 below. The output voltage and current are equal to 1 pu and
the input voltage is equal to 0.4 pu. The Boost Converter, shown in Figure 4.3, is the
preferable choice with low semiconductor stresses and a simple structure. The nongalvanic isolated converters, except for the Luo Converter, have a higher switch peak
voltage while the Luo Converter has a higher number of components. The galvanic
isolated converters, with the exception of the Flyback Converter, have a higher switch
peak current while the Flyback Converter has a complicated transformer.
The diode stresses in the converters are similar, with the exception of the Cúk, Sepic,
Zeta and both Forward Converters that have a higher diode peak voltage. Two drawbacks of the Boost Converter are that it has no galvanic isolation and no protection
against short circuits on the output. The switch stresses are presented at rated power,
according to Figure 4.1, and the converters are modelled for the specific input voltage
variations from the generator. This results in a high turns ratio and a low duty-ratio
for the bridge converters and, therefore, a high peak current in comparison with the
Boost Converter.
69
Table 4.2: Switch stresses, duty ratio and turns ratio for converters used for voltage
adjustment.
Duty Ratio Turns Ratio Switch stresses [pu]
Converter
D
N
û
IRM S
î
Boost
0.60
1.00 2.50
1.94
Cúk
0.29
3.50 1.40
0.75
Sepic
0.29
3.50 1.40
0.75
Zeta
0.29
3.50 1.40
0.75
Luo
0.29
1.00 2.50
0.75
Flyback
0.71
1
1.40 3.50
2.96
Forward
0.25
10
0.80 10.0
5.00
Two transistor forward
0.25
10
0.40 10.0
5.00
Push Pull
0.25
5
0.80 5.00
2.50
Half Bridge
0.25
10
0.40 20.0
10.0
Full Bridge
0.25
5
0.40 10.0
5.00
Half Bridge + VD
0.25
5
0.40 20.0
10.0
Table 4.3: Diode stresses in converters
Diode A
î IRM S
Converter
û
Boost
1.0 2.5 1.6
Cúk
3.5 1.4 1.2
Sepic
3.5 1.4 1.2
Zeta
3.5 1.4 1.2
Luo
1.0 *
*
Flyback
0.8 *
*
Forward
0.8 *
*
Two-Transistor Forward 0.4 *
*
Push Pull
0.8 *
*
Half Bridge
1.0 2.0 1.0
Full Bridge
1.0 2.0 1.0
Half Bridge + VD
1.0 4.0 2.0
70
used for voltage adjustment.
Diode B
Diode C
î IRM S û
î IRM S
û
1.0
1.4
4.0
0.4
1.0
1.0
3.5
1.3
1.3
2.0
0.5
1.9
1.1
1.1
1.0
4.0 4.0
4.0 4.0
* See text for each
separate converter
2.0
2.0
Figure 4.24 shows the switch stresses for the switch depending on the wind speed for
the Boost Converter when it is used as a Voltage Adjustment Converter. The voltage
is independent of the load and is the same as the output voltage. However, the current
varies with wind speed. First, between the cut-in wind speed and 5 m/s, the current
changes cubically and then, between 5 m/s and the rated wind speed, the current
changes quadratically.
Voltage [pu], Current [pu]
2.5
2
1.5
1
0.5
0
2
3
4
5
6
7
8
9
10
Wind speed [m/s]
Figure 4.24: Stresses on switch depending on wind speed for Boost Converter when
used as a Voltage Adjustment Converter. Solid: Switch peak voltage ûSw
[pu] and dashed: Switch peak current îSw [pu].
4.3.2
DC/DC Transformer
The different theoretical ratings for the DC transformer are shown in Table 4.4 and
Table 4.5 below. The output voltage and current are equal to 1 pu and the input
voltage is equal to 0.1 pu. A Full Bridge Converter is the preferable choice, with low
semiconductor stresses and galvanic isolated output. Non-galvanic isolated converters
have a very high switch peak voltage, especially the Cúk, Sepic and Zeta Converters.
The galvanic isolated converters, with the exception of the Push Pull Converter, have
a higher switch peak current while the Push Pull Converter has a higher switch peak
voltage. The Cúk, Sepic, Zeta and both forward converters have a higher diode peak
voltage and the Boost Converter has a high diode peak current. The other converters
have similar diode stresses. However, one drawback is the number of semiconductors,
but the switches are fully utilized and the cost of the drive circuitry is manageable
71
with respect to the high power and high voltage ratings. If the current is manageable,
the Half Bridge Converter is the best alternative although the rated current for the
switches are doubled compared with the Full Bridge Converter. Moreover, the Half
Bridge Converter has a somewhat poorer fault tolerance since the transformer cannot
be completely disconnected by using the switches.
Switch stresses are presented at rated power, according to Figure 4.1 and the converters
are modelled as a DC transformer. As shown, the Full Bridge Converter has similar
peak current, but only one tenth of the peak voltage for the Boost Converter.
Table 4.4: Switch stresses in converters used as DC transformers.
Duty Ratio Turns Ratio
Switch stresses
Converter
D
N
û
IRM S
î
Boost
0.90
1.00 9.80 9.29
Cúk
0.09
10.8 1.10 0.34
Sepic
0.09
10.8 1.10 0.34
Zeta
0.09
10.8 1.10 0.34
Luo
0.09
1.00 9.80 0.34
Flyback
0.49
10
0.20 19.8 13.9
Forward
0.49
20
0.20 20.0 14.0
Two-Transistor Forward
0.49
20
0.10 20.0 14.0
Push Pull
0.49
10
0.20 10.0 7.00
Half Bridge
0.49
20
0.10 20.4 14.3
Full Bridge
0.49
10
0.1 10.2 7.14
Half Bridge + VD
0.49
10
0.10 20.4 14.3
Table 4.5: Diode stresses in converters used as DC transformers.
Converter
û
Boost
1.00
Cúk
10.8
Sepic
10.8
Zeta
10.8
Luo
1.00
Flyback
0.20
Forward
0.20
Two-Transistor Forward 0.10
Push Pull
0.20
Half Bridge
1.00
Full Bridge
1.00
Half Bridge + VD
1.00
Diode A
IRM S
î
9.80 3.13
1.10 1.05
1.10 1.05
1.10 1.05
*
*
*
*
*
*
*
*
*
*
1.02 0.71
1.02 0.71
2.04 1.43
72
Diode B
û
IRM S
î
1.00
2.02
0.10
0.10
1.00
1.00
1.98
1.96
1.96
1.02
0.30
1.41
1.40
1.40
0.71
Diode C
û
IRM S
î
2.04 2.04
2.04 2.04
* See text for each
separate converter
1.43
1.43
Figure 4.25 shows the switch stresses on the switch, depending on wind speed, for the
Full Bridge Converter when it is used as a DC transformer. The voltage is clamped
to the input voltage and is independent of the load and the current varies with wind
speed. First, between the cut-in wind speed and 5 m/s, the current changes cubically
and then, between 5 m/s and the rated wind speed, the current changes quadratically.
Voltage [pu], Current [pu]
1
0.8
0.6
0.4
0.2
0
2
3
4
5
6
7
8
9
10
Wind speed [m/s]
Figure 4.25: Stresses on switch depending on wind speed for Full Bridge Converter
when used as a DC transformer. Solid: Switch peak voltage ûSw [pu] and
dashed: Switch peak current îSw [pu].
4.4
Losses for Different Converter Layouts
Assuming that the Boost Converter is used as a voltage adjuster and a Half Bridge or
a Full Bridge Converter is used as a DC transformer, the losses for two different wind
speeds will be as presented in Table 4.6. Due to wind speed distribution, the converters
are often operated at partial load. Thus, the losses are calculated for the wind speeds
5 m/s and 10 m/s, which in this example, correspond to 12.5%, respectively, 100% of
rated power. The input voltage for the voltage adjuster is 0.5 and 1.0 kV, respectively,
and the output voltage is 2.5 kV. The input voltage for the DC transformer is 1.0 kV
and the output voltage is 10.0 kV. The switching frequency is set to 1000 Hz. Only
the semiconductors are taken into account and the conducting losses are calculated as
the RMS and average values for the currents and with data for typical semiconductors [57, 58]. The valve type IGBT has been used in the Boost Converter and the
73
bridge converters, with the ratings 3300V/1200A and 1400V/600A, respectively, and
high voltage diodes with the rating 3300V/600A have been used in all converters. The
correct voltage and current are achieved by parallel and series coupling of the components presented above. The switching losses are assumed to be of the same magnitude
as the conducting losses because of the chosen switching frequency. The results should
only be used as a guideline as the model is only basic. The Boost Converter has the
lowest losses of the three converters, especially since it is used as a voltage adjuster.
The losses are lower for the Half Bridge Converter than the Full Bridge Converter.
However, the Half Bridge has a lower current handling capability.
Table 4.6: Losses for converters.
Converter
5 m/s ⇔ Pn /8 10 m/s ⇔ Pn
Boost
Half Bridge
Full Bridge
4.5
1.2 %
1.3 %
1.3 %
0.74 %
1.5 %
1.8 %
Summary
For a high voltage and high power application, like a wind park transmission system, the
focus has to be on the utilization factor of the used components. Designing a DC/DC
converter for an input voltage down to half the rated voltage or with a high input
to output voltage ratio might decrease the performance at rated power and voltage.
Therefore, two different applications have been analyzed. One simple converter can
be used for a first adjustment of the voltage and then a second converter can be used
to raise the voltage to a suitable transmission level. The semiconductor component
stresses have been determined by a theoretical comparison of the different converter
topologies. A Boost Converter is suitable as a Voltage Adjustment Converter and a
Bridge Converter can be used as the DC transformer. The Half Bridge Converter is
used when the current is low and the Full Bridge Converter is used for higher currents.
Losses in the Boost, Half Bridge and Full Bridge Converters have also been estimated
and the converters have moderate losses.
74
Chapter 5
Dynamic Analysis of Hard-switched
DC/DC converters
In this chapter, Boost, Full Bridge, Half Bridge and Dual Active Bridge Converters are analyzed and their behavior and interaction with the DC-grid and the other
DC/DC converters are investigated by using the circuit-orientated simulation package
Saber°r . The Boost and the Dual Active Bridge Converters are controlled to transmit
a certain amount of power while the Full and Half Bridge Converters are controlled
to be DC transformers. Prior to performing transient studies, for which an analytical
solution is readily available, the steady-state performance of the converter discussed in
the previous chapter was evaluated numerically. This of course serves to provide an
indication to the degree of accuracy to be expected in all results.
5.1
Boost Converter
In this section, the Boost Converter is investigated and simulation results are presented. The schematic layout of the converter with the names of the parameters and
the variables is shown in Figure 5.1. The converter input is connected to a voltage
source Udc1 in series with a source impedance of Zsource1 and the converter output is
connected to a voltage source Udc2 in series with a source impedance of Zsource2 . The
source impedances are used to imitate the connection lines to the converter.
5.1.1
Working Principle
The switch Sw is controlled to charge the inductor L during the first period of the cycle
Ts when the switch is on and to discharge the inductor energy during the second period
of the cycle when the switch is turned off. Figure 5.2 shows the semiconductor stresses
for the converter during full load operation, according to the parameters presented in
Table 5.1.
The converter runs in CCM, i.e., the inductor current iL never drops to zero. The
voltage over the switch should be constant when the switch is off and the current
through the switch should increase linearly when the switch is on, but due to the finite
75
Iin
L
+
+ U L
ZSource1
Uin
D
+
Cin Sw
ID
+
Iout
+
UD
Usw
-
ZSource2
Cout
Uout
ISW
Udc1
+
IL
-
+
-
-
Udc2
-
Figure 5.1: Schematic layout of Boost Converter.
(V) : t(s)
u_sw
(V)
2500.0
1250.0
0.0
(A) : t(s)
i_sw
(A)
2000.0
1000.0
0.0
(V) : t(s)
u_d
(V)
2500.0
1250.0
0.0
(A) : t(s)
i_d
(A)
2000.0
1000.0
0.0
0.497
0.4975
0.498
0.4985
0.499
0.4995
0.5
t(s)
Figure 5.2: Semiconductor stresses in a Boost Converter at rated power. Top: Switch
voltage uSw [V], upper middle: Switch current iSw [A], lower middle: Diode
voltage uD [V] and bottom: Diode current iD [A].
76
size of the capacitors, Cin and Cout and the source impedance, the voltage fluctuates
and the current, therefore, does not increase linearly, as shown in Figure 5.2. The
converter uses traditional pulse width modulation (PWM) to control the voltage and/or
the current, i.e., the reference value is compared with a sawtooth wave and the switch
conducts as long as the reference value is higher than the sawtooth.
Table 5.1: System parameters of Boost Converter.
Parameter
Rated power
Rated input voltage
Rated output voltage
Switching frequency
IGBT voltage drop UT 0
series resistance ron
Diode voltage drop UT 0
series resistance ron
Blanking time Tb
5.1.2
Component
Value
2 MW
0.5-1 kV
2.5 kV
1000 Hz
2.8 V
0.45 mΩ
1.4 V
0.9 mΩ
5 µs
Turn-on time Tsw,on
Turn-off time Tsw,of f
Inductor L
Inductor resistance RL
Input capacitor Cin
Output capacitor Cout
Source impedance
(Zsource1 = Zsource2 )
Value
10 µs
10 µs
5 mH
1 mΩ
1 mF
2 mF
0.5 µH + 1 mΩ
Transmitted Power
The transferred power of the Boost Converter is adjusted by changing the duty ratio,
D. The stationary value of D, however, remains the same according to:
Uout = Uin
1
1−D
(5.1)
where Uin is the average value of the voltage on the primary side and Uout is the mean
value of the voltage on the secondary side. The losses of the converter are neglected in
the equation. If the input voltage is 1000 V and the output voltage is 2500 V, then the
duty ratio, D becomes 0.6 under stationary conditions. If D >0.6, the current increases
and the converter, thus, transmits more power. Eventually, the inductor will saturate
and the current will have to be reduced. If D <0.6, the inductor current decreases
and the converter, thus, transmits less power and if the current decreases so that the
current goes down to zero the current will go into DCM.
77
5.1.3
Transient Behavior
Step changes in the power around the operating point have been made to verify the
transient behavior of the system. The power reference is changed, +10% from an
operating point of 2 MW. The results are shown in Figure 5.3. The sampling causes
a time delay of Ts ( the controller starts to react after 1 sample). The output power,
used in the controller, is calculated as the average of the output voltage Uout times the
output current Iout for each switching period and, therefore, creates another time delay
of Ts . This is, however, negligible compared with the time constant for the converter,
which is in the order of 50 ms.
(W) : t(s)
Pref
2.4meg
(W)
2.2meg
2meg
1.8meg
(W) : t(s)
Power
2.4meg
(W)
2.2meg
2meg
1.8meg
− : t(s)
0.7
D
−
0.65
0.6
0.55
0.5
0.4
0.5
0.6
0.7
0.8
t(s)
Figure 5.3: Transient behavior during step changes. From top: Power reference P ∗
[W], power P [W] and duty ratio D.
When the power reference increases, the duty ratio changes in order to increase the
current through the inductor L and, therefore, increase the transmitted power. This
causes the transmitted power to decline since a larger part of the cycle is used to increase the inductor current and less time is used to transmit power. When the desired
transmission is reached, the duty ratio is changed back to the stationary value, according to Eq. (5.1). The power controller is assumed to use a traditional PI-controller as
shown in Figure 5.4 with Kp = 50 · 10−6 , Ti =50 ms and Ts =1 ms.
78
P∗
+
Power
reference
−
P
P I-Controller
´
³
Kp 1 + TTsi 1−Z1 −1
D
Duty
ratio
P
Measured
power
Duty ratio
executor
Sw
Valve
switching
state
Figure 5.4: Power control of Boost Converter using discrete PI-controller.
5.1.4
Varying Voltage
The input voltage of the converter was changed to verify good behavior when applied
to a varying input voltage. The power reference P ∗ and the output voltage Udc2 were
kept constant while the duty ratio D was adjusted, according to Eq. (5.1). The result
is shown in Figure 5.5.
The input voltage changes slowly from 500 V to 1000 V and the resulting transmitted
power is slightly above 1 MW, since the controller lags behind the power reference
when the input voltage is increased. As the input voltage is reduced, the duty ratio
has to be increased, according to Eq. (5.1) in order to transmit the same amount of
power and, thus, the peak current for the switches is changed according to Eq. (5.2)
(ripple is not included)
P
Uin
îsw ≈
(5.2)
The ripple current in the inductor, is according to Eq. (5.3) and with the data given
in Table 5.1, the maximum ripple current becomes 120 A when the input voltage is
1 kV. During dynamic changes, however, the maximum theoretical ripple is 200 A,
i.e., the current in the inductor can be changed at a maximum of 200 A each cycle
(corresponding to D = 1). A smaller inductor gives a higher ripple but a faster
converter response since a change in the power reference, i.e., the input current, can
be achieved faster.
iripplep−p =
Uin Ts D
L
(5.3)
Figure 5.6 shows the semiconductor stresses at 750 V input voltage. The switch stresses
at different input voltage levels at the power of 1 MW and a constant output voltage
are shown in Table 5.2. The peak current is the same for 500V input voltage as for
2 MW and 1000 V input voltage, despite that the power is halved to 1 MW.
79
(W) : t(s)
Power
(W)
1.1meg
1meg
900000.0
(−) : t(s)
D
(−)
0.8
0.6
(V) : t(s)
Uin
(V)
1000.0
750.0
500.0
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
t(s)
Figure 5.5: Simulation of Boost Converter using varying input voltage together with
constant power reference. From top: Power P [W], duty ratio D and input
voltage Uin [V].
Table 5.2: Duty ratio and switch peak current for different input voltages and constant
power of 1 MW.
Udc1
500 V
750 V
1000 V
D
0.8
0.7
0.6
îsw
2040 A
1386 A
1060 A
80
iripplep−p
80 A
105 A
120 A
Iin
2000 A
1333 A
1000 A
(V) : t(s)
u_sw
(V)
2500.0
1250.0
0.0
(A) : t(s)
i_sw
(A)
1500.0
750.0
0.0
(V) : t(s)
u_d
(V)
2500.0
1250.0
0.0
(A) : t(s)
i_d
(A)
1500.0
750.0
0.0
0.497
0.4975
0.498
0.4985
0.499
0.4995
0.5
t(s)
Figure 5.6: Semiconductor stresses in a Boost Converter with 750 V input voltage and
constant power of 1 MW. Top: Switch voltage uSw [V], upper middle:
Switch current iSw [A], lower middle: Diode voltage uD [V] and bottom:
Diode current iD [A].
81
5.1.5
Summary
The boost converter can handle both varying input voltage and dynamic changes in
the transmitted power. The design of the inductor size is a compromise between the
size of the input ripple and the speed of the dynamic response of the converter. A
smaller inductor gives a higher ripple but a faster converter response since a change
in the power reference, i.e., the input current, can be achieved faster. It has also been
shown that the input ripple is influenced by the input voltage. The input voltage has
been reduced to half of the rated voltage and still the converter is able to transmit the
same power by changing the duty ratio.
82
5.2
Half Bridge Converter
In this section, the Half Bridge (HB) Converter is investigated and simulation results
are presented. The schematic layout of the converter is shown in Figure 5.7. The
converter input is connected to a voltage source Udc1 in series with a source impedance
Zsource1 and the converter output is connected to a voltage source Udc2 in series with a
source impedance Zsource2 .
Iin
Uin
-
n2
D3
+
UTfo2
-
D2
ISW2
C2
Sw2
n1
+
UD1
-
+
UD3
-
Cout
+
UD2
-
D4
+
UD4
-
+
ZSource2
Uout
+
ID4
-
L2l
D1
ID2
Udc1
+
L1l
ITfo2
ID3
Sw1
+
USW1 ITfo1
+
UTfo1
+
USW2
ID1
C1
ZSource1
Iout
ISW1
+
-
Udc2
-
Figure 5.7: Schematic layout of Half Bridge Converter.
5.2.1
Working Principle
The switches are controlled to create a square wave on the primary side of the transformer. The switch Sw1 is on during the first half period and the switch Sw2 is on
during the second half of the period, thus, creating a voltage of UT F O1 between the
midpoint of the capacitor leg and the dc-bus. The duty ratio D is, thus, a half period,
i.e., D = 0.5. The converter is often referred to as a DC transformer, when controlled
as described above, but can also be controlled with a traditional PWM control to control the duty ratio D or any other control for regulating voltage and/or current. A
blanking time Tb , i.e., a time between the two half periods when no switch is on, is used
to ensure that the switches do not short-circuit the dc-bus. When the voltage U T F O2
produced on the secondary side of the transformer is larger than the secondary bus
voltage Uout , the diodeswill conduct and, thus, create a power transfer. The transferred
power is determined by the difference between the two voltages Lλ and Uout and the
leakage inductance in the transformer Lλ . Figure 5.8 shows the semiconductor stresses
in the converter during full load operation, according to the parameters presented in
Table 5.3.
The voltages over the switches should be constant when the switches are off and the
currents through the switches should increase linearly when the switches are on, but
due to the finite size of the capacitors, C1 , C2 and Cout together with the source
impedance, the voltage fluctuates and the current in the switches, therefore, does not
increase linearly.
83
(V) : t(s)
u_sw1
(V)
1000.0
0.0
(A) : t(s)
i_sw1
(A)
4000.0
2000.0
0.0
(V) : t(s)
u_d1
(V)
10000.0
5000.0
0.0
(A) : t(s)
i_d1
(A)
200.0
100.0
0.0
0.097
0.0975
0.098
0.0985
0.099
0.0995
0.1
t(s)
Figure 5.8: Semiconductor stresses in a Half Bridge Converter according to values in
Table 5.3. Top: voltage switch one uSw1 [V], upper middle: current switch
one iSw1 [A], lower middle: voltage diode one uD1 [V] and bottom: current
diode one iD1 [A].
Table 5.3: System parameters of Half Bridge Converter.
Parameter
Rated power
Rated input voltage
Rated output voltage
Switching frequency
IGBT voltage drop UT 0
series resistance ron
Diode voltage drop UT 0
series resistance ron
Blanking time Tb
Value
Component
1 MW
1 kV
10 kV
1000 Hz
2.8 V
0.225 mΩ
5.6 V
14 mΩ
5 µs
Turn-on time Tsw,on
Turn-off time Tsw,of f
Transformer turns ratio
Leakage inductance
(Lλ = L1λ + L02λ )
Input capacitor Cin = C1 + C2
Output capacitor Cout
Source impedance
(Zsource1 = Zsource2 )
84
Value
1 µs
1 µs
N = nn12 =21
8 µH
20 mF
2 mF
0.5 µH + 1 mΩ
5.2.2
Transmitted Power
Assuming that the mean value of the primary dc bus voltage Uin and the mean value
0
of the secondary dc bus voltage equivalent Uout
on the primary side is equal, i.e.,
0
Uin = Uout , then the peak-to-peak current ∆i will be
∆i =
1
U
2 in
0
− Uout
Ts
Lλ
2
(5.4)
where Lλ is the transformer leakage impedance. Moreover, Ts is the switching time,
i.e., Ts = f1s . The average current Iin becomes
1
0
U − Uout
Ts
1
2 in
Iin = ∆i =
2
Lλ
4
(5.5)
The transferred power function for the FB converter can be approximated with (since
Uin is constant)
1
0
Uin ( 21 Uin − Uout
)Ts
1
P = Uin Iin = 2
2
4Lλ
(5.6)
The losses for the converter are neglected in the derived function of transferred power.
5.2.3
Steady-state Behavior
The output power as a function of input voltage is shown in Figure 5.9. The deviation
between the theoretical expression and the result of the simulated system is due to
shortcomings in the Eq. (5.6) and not only to losses in the system. For example, the
switches and the diodes have voltage drops, the blanking time, turn-on and turn-off
times of the switches are neglected. The negative value of the theoretical power due to
the equation does not take diode blocking into account. Thus, the power transmission
for the simulated curve starts approximately 20 V above the theoretical curve and the
power is, therefore, 100 kW lower.
85
(W) : t(s)
Power
(W) : t(s)
1meg
1meg
(W)
(W)
Power (Theoretical)
0.0
500000.0
0.0
(V) : t(s)
Uin
(V)
1100.0
1000.0
900.0
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
t(s)
Figure 5.9: Transmitted power as a function of input voltage using Half Bridge Converter. From top: Power P from simulation (line) and analytical calculated
power (dotted) [W] and input voltage Uin [V].
86
5.2.4
Transient Behavior
Step changes in the input voltage were made to verify the transient behavior of the
system. The input voltage was changed +100 V from the operating point 1000 V and
there was no control of the converter, i.e., it was used as a DC-transformer. As seen
in Figure 5.10, the converter manages the step without oscillations.
(W) : t(s)
Power
(W)
1meg
500000.0
0.0
(V) : t(s)
Uin
(V)
1100.0
1050.0
1000.0
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
t(s)
Figure 5.10: Transient behavior during step changes using Half Bridge Converter. From
top: Power P [W], input voltage Uin [V].
5.2.5
Half Bridge Converter With Voltage Doubler
A variant of the Half Bridge Converter is the Half Bridge Converter with voltage doubler, where the output rectifier bridge is changed to a voltage doubler. The schematic
layout of the converter is shown in Figure 5.11.
The transformer turns ratio is halved to 10.5 and the currents on the secondary side of
the transformer are, therefore, doubled. Figure 5.12 shows the semiconductor stresses
in the converter. The voltage doubler increases the voltage ripple on the secondary
side, due to the doubled currents on the secondary side of the transformer, but reduces
the number of active components by removing the diodes D3 and D4 (Figure 5.7) and
by replacing the output capacitor Cout with two capacitors, C1 and C2 .
87
Iin
ZSource1
Sw1
Uin
L1l
L2l
n1
n2
ITfo2
D1
-
+
USW2
-
D2
ISW2
C2
Sw2
+
C1
ZSource2
+
UTfo2
-
+
-
+
UD1
-
Uout
+
UD2
-
+
ID2
Udc1
+
USW1 I
Tfo1
+
UTfo1
-
ID1
C1
Iout
ISW1
+
-
C2
Udc2
-
Figure 5.11: Schematic layout of Half Bridge Converter with voltage doubler.
(V) : t(s)
u_sw1
(V)
1000.0
0.0
(A) : t(s)
i_sw1
(A)
4000.0
2000.0
0.0
(V) : t(s)
U_d1
(V)
10000.0
5000.0
0.0
(A) : t(s)
i_d1
750.0
(A)
500.0
250.0
0.0
0.097
0.098
0.099
0.1
t(s)
Figure 5.12: Semiconductor stresses in a Half Bridge Converter with voltage doubler
at rated power. Top: voltage switch one uSw1 [V], upper middle: current
switch one iSw1 [A], lower middle: voltage diode one uD1 [V] and bottom:
current diode one iD1 [A].
88
5.2.6
Summary
The half bridge DC transformer can handle dynamic changes in the transmitted power
but cannot control the transferred power. The leakage inductance Lλ and the turns
ratio for the transformer are the most important parameters of the converter design.
The leakage inductance influences the current ripple, the maximum transferable power
and the sensitivity to input voltage changes. The turns ratio determines the voltage
levels for the converter.
89
5.3
Full Bridge Converter
In this section, the Full Bridge (FB) Converter is investigated and simulation results
are presented. The schematic layout of the converter is shown in Figure 5.13. The
converter input was connected to a voltage source Udc1 in series with a source impedance
of Zsource1 and the converter output was connected to a voltage source Udc2 in series
with a source impedance of Zsource2 .
Iin
Iout
n2
+
USW4
-
+
UD1
-
D3
+
UTfo2
-
D2
+
UD3
-
Cout
+
UD2
-
D4
+
UD4
-
+
ZSource2
Uout
+
ID4
-
n1
ISW4
Sw4
L2l
D1
ID2
+
USW2
ISW2
Sw2
L1l
ITfo2
ID3
+
UTfo1
-
Cin
+
-
USW3
-
ITfo1
ID1
Sw3
USW1
Uin
+
ISW3
Sw1
ZSource1
Udc1
+
ISW1
+
-
Udc2
-
Figure 5.13: Schematic layout of Full Bridge Converter.
5.3.1
Working Principle
The switches are controlled in order to create a square wave on the primary side of
the transformer. Switches Sw1 and Sw4 are on simultaneously during the first half
period and switches Sw2 and Sw3 are on during the second half period. The duty
ratio D is, thus, a half period, i.e., D = 0.5. The converter is often referred to as a
DC transformer, when controlled as described above, but can also be controlled with a
traditional PWM control in order to control the duty ratio D or any other control for
regulating the voltage and/or the current. A blanking time Tb is used to ensure that the
switches do not short-circuit the dc-bus. When the voltage produced on the secondary
side of the transformer UT F O2 is larger than the secondary bus voltage Uout , the diodes
conduct and, thus, create a power transfer. The transferred power is determined by
the difference between the two voltages Uin and Uout and the leakage inductance in the
transformer Lλ . Figure 5.14 shows the semiconductor stresses in the converter during
full load operation, according to the parameters presented in Table 5.4.
The voltages over the switches should be constant when the switches are off and the
current through the switches should increase linearly when the switches are on, but
due to the finite size of the capacitors, Cin and Cout and the source impedance, the
voltage fluctuates and the currents, therefore, do not increase linearly.
90
(V) : t(s)
u_sw1
(V)
1000.0
0.0
(A) : t(s)
i_sw1
(A)
4000.0
2000.0
0.0
(V) : t(s)
u_d1
(V)
10000.0
5000.0
0.0
(A) : t(s)
i_d1
(A)
400.0
200.0
0.0
0.097
0.098
0.099
0.1
t(s)
Figure 5.14: Semiconductor stresses in Full Bridge Converter according to values in
Table 5.4. Top: voltage switch one uSw1 [V], upper middle: current switch
one iSw1 [A], lower middle: voltage diode one uD1 [V] and bottom: current
diode one iD1 [A].
Table 5.4: System parameters of Full Bridge Converter.
Parameter
Rated power
Rated input voltage
Rated output voltage
Switching frequency
IGBT voltage drop UT 0
series resistance ron
Diode voltage drop UT 0
series resistance ron
Blanking time Tb
Component
Turn-on time Tsw,on
Turn-off time Tsw,of f
Transformer turns ratio
Leakage inductance
(Lλ = L1λ + L02λ )
Input capacitor Cin
Output capacitor Cout
Source impedance
(Zsource1 = Zsource2 )
Value
2 MW
1 kV
2.5 kV
1000 Hz
2.8 V
0.45 mΩ
5.6 V
14 mΩ
5 µs
91
Value
1 µs c
1 µs
N = nn12 =11
18 µH
50 mF
2 mF
0.5 µH + 1 mΩ
5.3.2
Transmitted Power
Assuming that the mean value of the primary dc bus voltage Uin and the mean value
0
on the primary side are equal, i.e.,
of the secondary dc bus voltage equivalent Uout
0
Uin = Uout . Then the peak-to-peak current ∆i will be
∆i =
0
Uin − Uout
Ts
Lλ
2
(5.7)
where Lλ is the transformer leakage impedance. Ts is the switching time, i.e., Ts =
And the average current Iin becomes
0
Ts
1
Uin − Uout
Iin = ∆i =
2
Lλ
4
1
.
fs
(5.8)
The transferred power function for the FB converter can be approximated with (since
Uin is constant)
P = Uin Iin =
0
)Ts
Uin (Uin − Uout
4Lλ
(5.9)
The losses for the converter are omitted in the Eq. (5.9).
5.3.3
Steady-state Behavior
The output power as a function of input voltage is shown in Figure 5.15. As in the
previous case, the deviation between the theoretical expression and the result of the
simulated system is due to shortcomings in Eq. (5.9) and not only losses in the system.
For example, the switches and the diodes have voltage drops, the blanking, turn-on
and turn-off times of the switches are neglected. The negative value of the theoretical
power is due to the equation does not take diode blocking into account. Thus, the
power transmission for the simulated curve starts at approximately 20 V above the
theoretical curve and the power is, therefore, 200 kW lower.
92
(W) : t(s)
3meg
3meg
2meg
2meg
Power
(V) : t(s)
(V)
(W)
Power (Theoretical)
1meg
1meg
0.0
0.0
(V) : t(s)
Uin
(V)
1100.0
1000.0
900.0
0.0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
t(s)
Figure 5.15: Transmitted power as a function of input voltage using Full Bridge Converter. From top: Simulated power P (line) and Theoretical power (dotted)
[W] and input voltage Uin [V].
93
5.3.4
Transient Behavior
Step changes in the input voltage were made to verify the transient behavior of the
system. The input voltage was changed +100 V from the operating point 1000 V and
there was no control of the converter, i.e., it was used as a DC-transformer. As seen
in Figure 5.16, the converter manages the step without oscillations.
(W) : t(s)
Power
(W)
2meg
1.5meg
1meg
(V) : t(s)
Uin
(V)
1100.0
1050.0
1000.0
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.07
t(s)
Figure 5.16: Transient behavior during step changes using Full Bridge Converter. From
top: Power P [W], input voltage Uin [V].
5.3.5
Full Bridge Converter with Voltage Doubler
A variant of the Full Bridge Converter is the Full Bridge Converter with a voltage doubler, where the output rectifier bridge is changed to a voltage doubler. The schematic
layout of the converter is shown in Figure 5.17.
The transformer turns ratio is halved to 5.5 and the currents on the secondary side of
the transformer are, therefore, doubled. Figure 5.18 shows the semiconductor stresses
for the converter. The voltage doubler increases the voltage ripple on the secondary
side, due to doubled currents on the secondary side of the transformer, but reduces the
number of active components by removing the diodes D3 and D4 (Figure 5.13) and by
replacing the output capacitor Cout with two capacitors C1 and C2 .
94
Iin
Uin
+
USW4
Sw4
-
-
L1l
L2l
n1
ITfo2
D1
+
UD1
-
+
C1
+
UTfo2
-
n2
D2
ZSource2
Uout
+
UD2
-
+
ID2
+
USW2
ISW4
Sw2
ITfo1
+
UTfo1
-
Cin
+
-
USW3
-
ISW2
Udc1
Sw3
USW1
-
Iout
ID1
ZSource1
+
ISW3
Sw1
+
ISW1
+
C2
-
Udc2
-
Figure 5.17: Schematic layout of Full Bridge Converter with voltage doubler.
(V) : t(s)
u_sw1
(V)
1000.0
0.0
(A) : t(s)
i_sw1
(A)
4000.0
2000.0
0.0
(V) : t(s)
U_d1
(V)
10000.0
5000.0
0.0
(A) : t(s)
i_d1
750.0
(A)
500.0
250.0
0.0
0.097
0.098
0.099
0.1
t(s)
Figure 5.18: Semiconductor stresses in a Full Bridge Converter with voltage doubler
at rated power. Top: voltage switch one uSw1 [V], upper middle: current
switch one iSw1 [A], lower middle: voltage diode one uD1 [V] and bottom:
current diode one iD1 [A].
95
5.3.6
Summary
The Full Bridge DC transformer can handle dynamic changes in the transmitted power
but cannot control the transferred power. The leakage inductance Lλ and the turns
ratio for the transformer are the most important parameters of the converter. The
leakage inductance influences the current ripple, the maximum transferable power and
the sensitivity to input voltage changes. The turns ratio determines the voltage levels
for the converter.
96
5.4
Dual Active Bridge Converter (DAB)
In this section, the Dual Active Bridge Converter (DAB) is investigated and simulation
results are shown in order to give further insight to its operation and design. The
schematic layout of the converter is shown in Figure 5.19. The DAB consists of two
H-bridges and a transformer and both bridges can be controlled individually for a bidirectional power flow [19, 21]. The converter input is connected to a voltage source
Udc1 in series with a source impedance of Zsource1 and the converter output is connected
to a voltage source Udc2 in series with a source impedance of Zsource2 .
Iin
Iout
n1
n2
+
USW4
USW5
-
Cout
+
USW6
Sw8
-
ZSource2
USW7
-
+
UTfo2
-
Sw6
+
Uout
+
+
USW8
-
-
Udc2
ISW8
-
ITfo2
ISW7
-
L2l
+
Sw7
Sw5
ISW6
Sw4
L1l
ISW5
+
USW2
+
ISW4
-
ITfo1
+
UTfo1
-
ISW2
Sw2
-
USW3
-
Cin
+
ISW3
U
- SW1
Uin
+
Sw3
Sw1
ZSource1
Udc1
+
ISW1
+
-
Figure 5.19: Schematic layout of DAB converter.
5.4.1
Working Principle
Two sets of full bridges, one on each side of the transformer, were controlled to transfer
energy to or from the low-voltage side. The switches were controlled to create a square
wave or a quasi-square wave on each side of the transformer. The switch pattern is
according to Figure 5.20. The switch pattern to the left in Figure 5.20 is a pure square
wave with blanking time. Switches Sw1 and Sw4 conduct simultaneously for a half
period, i.e. ,α ≈ 180◦ and, after the blanking time, are replaced with switches Sw2 and
Sw3 during the second half period. The switch pattern to the right in Figure 5.20 is
a quasi- square wave, where the output voltage is controlled by changing the control
angle β (0 < β < 180◦ ). The switches Sw1 and Sw3 conduct and, thus, create a short
circuit in the winding. After a time delay, determined by the control angle, switch Sw 3
is turned off and switch Sw4 is turned on in order to create a positive voltage of Utf o1
over the winding. After the controlled on-time, switch Sw1 is turned off and switch
Sw4 is turned on again, thus, creating a short circuit in the winding. Thereafter, the
second half period starts and a negative voltage is applied to the winding. All switch
events are separated by a blanking time.
The amount of transferred energy is controlled by a phase shift between the two waves,
the transformer ratio and the shape and size of the wave. In the following simulations,
only square waves are used.
Figures 5.21 and 5.22 show the semiconductor and the transformer stresses in the
converter with the two square waves, UT F O1 and UT F O2 , phase shifted 45◦ (ϕ =45◦ ),
according to the parameters presented in Table 5.5. The switching period is 1 ms and
can be divided into four different intervals:
97
PSfrag replacements
50/50
u
u
Controlled
α
β
ωt
14
ωt
13 14
23
24
23 13
Switches in
turn-on position
Figure 5.20: Output voltage and switch patterns for Bridge Converter. Left: Square
wave α = 180◦ and right: Quasi square wave 0 < β < 180◦ .
1. From the time 97 ms and 45◦ i.e. 125 µs forward. Switches Sw1 and Sw4 conduct
on the primary side and switches Sw6 and Sw7 conduct on the secondary side
of the transformer, thus, creating a positive voltage on the primary side of the
transformer UT F O1 and a negative voltage on the secondary side of the transformer
UT F O2 . The applied voltage over the leakage inductance increases the current
until switches Sw6 and Sw7 are turned off.
2. From the time 97.125 ms to 97.5 ms, i.e., the rest of the first half period. Switches
Sw1 and Sw4 conduct on the primary side and switches Sw5 and Sw8 conduct
on the secondary side of the transformer, thus, creating a positive voltage on
both sides of the transformer. The current through the leakage inductance, consequently, does not change until switches Sw1 and Sw4 are turned off.
3. From the time 97.5 ms and 45◦ forward. Switches Sw2 and Sw3 conduct on
the primary side and switches Sw5 and Sw8 conduct on the secondary side of
the transformer, thus, creating a negative voltage on the primary side and a
positive voltage on the secondary side. The resulting voltage decreases the current
through the leakage inductance until switches Sw5 and Sw8 are turned off.
4. From the time 97.625 ms to 98 ms, i.e., the rest of the second half period. Switches
Sw2 and Sw3 conduct on the primary side and switches Sw6 and Sw7 conduct
on the secondary side of the transformer, thus, creating a negative voltage on
both sides of the transformer. The current through the leakage inductance, consequently, does not change until switches Sw2 and Sw3 are turned off and the
next switching period starts.
Ideally, the voltages over and the current through the transformer windings and the
switch should be constant during intervals two and four, but the amplitudes are decreased due to the finite size of the capacitors, Cin and Cout and the source impedance.
Component values are presented in Table 5.5.
98
(V) : t(s)
u_sw1
(V)
1000.0
0.0
(A) : t(s)
(A)
2500.0
i_sw1
0.0
−2500.0
(V) : t(s)
u_sw2
(V)
1000.0
0.0
(A) : t(s)
(A)
2500.0
i_sw2
0.0
−2500.0
(V) : t(s)
u_sw5
(V)
10000.0
0.0
(A) : t(s)
(A)
250.0
i_sw5
0.0
−250.0
(V) : t(s)
u_sw6
(V)
10000.0
0.0
(A) : t(s)
(A)
250.0
i_sw6
0.0
−250.0
0.097
0.0975
0.098
0.0985
0.099
0.0995
0.1
t(s)
Figure 5.21: Semiconductor stresses in DAB converter at ϕ =45◦ . From top: voltage
over uSw1 [V], current through iSw1 [A], voltage over uSw2 [V], current
through iSw2 [A], voltage over uSw5 [V], current through iSw5 [A], voltage
over uSw6 [V] and current through iSw6 [A].
99
(V) : t(s)
u_tfo1
(V)
1000.0
0.0
−1000.0
(A) : t(s)
i_tfo1
(A)
2500.0
0.0
−2500.0
(V) : t(s)
u_tfo2
(V)
10000.0
0.0
−10000.0
(A) : t(s)
i_tfo2
(A)
250.0
0.0
−250.0
0.097
0.0975
0.098
0.0985
0.099
0.0995
0.1
t(s)
Figure 5.22: Transformer stresses in a DAB converter at ϕ =45◦ . From top: voltage
over uT F O1 [V], current through 1T F O1 [A], voltage over uT F O2 [V], current
through iT F O2 [A].
Table 5.5: System parameters of Dual Active Bridge Converter.
Parameter
Rated power
Rated input voltage
Rated output voltage
Switching frequency
IGBT voltage drop UT 0
series resistance ron
Turn-on time Tsw,on
Turn-off time Tsw,of f
Value
Component
2 MW
0.5-1 kV
10 kV
1000 Hz
2.8 V
0.45 mΩ
1 µs
1 µs
Blanking time Tb
Transformer turns ratio
Leakage inductance
(Lλ = L1λ + L02λ )
Input capacitor Cin
Output capacitor Cout
Source impedance
(Zsource1 = Zsource2 )
100
Value
5 µs
N = nn21 =10
25 µH
50 mF
2 mF
0.5 µH + 1 mΩ
5.4.2
Comparison with General AC Theory
The function of the transferred power of the DAB converter is similar to two generators
connected together with an impedance as shown in Figure 5.23. The transferred power
is [59]:
P =
U1 U2
sin ϕ
Z
(5.10)
where U1 and U2 are the RMS values of the two voltages applied on the impedance. Z
is the intermediate impedance and ϕ is the phase shift between the two voltages. The
resistance of the impedance is neglected and, therefore, the input and output power is
the same, according to Eq. (5.10). The reactive power transfer is calculated as [59],
where Q1 is reactive power produced by generator 1 and Q2 is consumed reactive power
in generator 2.
Q1 =
U12 U1 U2
−
cos ϕ
Z
Z
(5.11)
U2 2 U1 U2
+
cos ϕ
Z
Z
(5.12)
Q2 = −
PSfrag replacements
→
− −
→
P , Q2
→
− −
→
P , Q1
Z
∼
u2 (t)
u1 (t)
Generator 1
√
u1 (t) = 2U1 sin(ωt)
∼
Generator 2
√
u2 (t) = 2U2 sin(ωt − ϕ)
Figure 5.23: Two generators with an intermediate impedance
(Generator 1, Impedance Z and Generator 2).
101
5.4.3
Transmitted Power
The DAB converter does not have sinusoidal voltages and currents, consequently, the
transferred power is calculated differently.
i(t)
t
∆i
PSfrag replacements
ϕ
Ts
Figure 5.24: Idealized input current Iin for DAB converter
Assuming that the mean value of the primary dc bus voltage Uin and the mean value
0
of the secondary dc bus voltage Uout
equivalent on the primary side are equal, i.e.,
0
Uin = Uout . Then the peak-to-peak current ∆i, according to Figure 5.24 will be
∆i =
0
ϕTs (Uin + Uout
)
Uin Ts
=
ϕ
2πLλ
πLλ
(5.13)
where Lλ is the transformer leakage impedance and ϕ the phase shift between the two
square waves. Ts is the switching time, i.e., Ts = f1s . The average current Iin becomes
ϕ
Ts
1 Ts − 2π
Uin Ts
ϕ
Iin = ∆i
=
(1 − )ϕ
2
Ts
2πLλ
π
(5.14)
The average power Pin is equal to (since Uin is constant)
P = Uin Iin
(5.15)
Then the transferred power is (if |ϕ| is used, Eq. (5.16) is valid for both positive and
negative values of ϕ)
102
P =
2
|ϕ|
Ts
Uin
(1 −
)ϕ
2πLλ
π
(5.16)
The semiconductor stresses are dependent on the applied voltages and currents. As0
, the peak current for the switches is
suming that Uin = Uout
îsw =
Uin Ts
ϕ
2πLλ
(5.17)
The peak current is higher for larger Lλ at constant power P . However, the derivative
of the current becomes lower. For example, if the power is 1 MW and the leakage
inductance Lλ is 50 µH, the control angle becomes approximately 20◦ and the peak
current becomes approximately 1100 A. If, however, the leakage inductance is doubled
(Lλ = 100 µH), the control angle increases to approximately 50◦ and the peak current
increases to approximately 1400 A. Subsequently, for the same power, the peak current
will be approximately 25% higher with a leakage inductance that is twice as large.
5.4.4
Steady-state Behavior
If the voltages at both ends, Uin and Uout , are kept constant and, moreover, the frequency and the impedance are constant, the transferred power will only be dependent
on the phase shift, i.e., P = f (ϕ). Simulations with two different leakage inductances
Lλ and control angles ϕ that change linearly are shown in Figure 5.25. Moreover,
the theoretical expression in Eq. (5.16) is displayed in Figure 5.25 for the two leakage
inductances. The upper curve is Lλ = 50 µH and the lower curve is Lλ = 100 µH. The
simulated and theoretical curves deviate due to the blanking time, the turn-on and
turn-off of the switches and losses in the circuit. The irregularity around zero depends
on the blanking time.
If possible, the control angle ϕ should be kept small in order to avoid high peak currents
in the switches. This can, however, be difficult since the voltages Uin and Uout are often
fixed by the surrounding system. The frequency is determined by the switches and the
transformer leakage inductance Lλ is dependent on the transformer design. The leakage
inductance Lλ also controls the current derivative for the converter and, therefore, is
a critical design parameter.
103
(Deg) : t(s)
3meg
3meg
100.0
fi
Power L=50uH (Theoretical)
80.0
2meg
Power L=100uH (Theoretical)
2meg
60.0
(W) : t(s)
Power L=50uH
40.0
1meg
1meg
(W) : t(s)
Power L=100uH
0.0
(Deg)
0.0
(W)
(W)
20.0
0.0
−20.0
−1meg
−1meg
−40.0
−60.0
−2meg
−2meg
−80.0
−3meg
−3meg
−100.0
0.2
0.4
0.6
0.8
1.0
1.2
t(s)
Figure 5.25: Transmitted power as a function of control angle P = f (ϕ). L λ = 50 µH
Theoretical (dotted) and simulated (dashed), Lλ = 100 µH Theoretical
(dotted) and simulated (solid).
104
5.4.5
Transient Behavior
Step changes from the power operating point 2 MW were made to verify the transient
behavior of the system. The reference value was changed ±10% of the operating point
for two different values (50 µH, 25 µH) of the leakage inductances (Lλ = 100µH used
in Figure 5.25 does not allow such a high power transfer). The results are shown in
Figures 5.26 to 5.28. The sampling causes a time delay of Ts . The output power
is calculated as the average power for each switching period and, therefore, creates
another time delay of Ts .
(W) : t(s)
Pref
(W)
2.2meg
2meg
1.8meg
(W) : t(s)
Power
(W)
2.2meg
2meg
1.8meg
(Deg) : t(s)
fi
(Deg)
60.0
55.0
50.0
0.095
0.1
0.105
0.11
0.115
0.12
0.125
0.13
0.135
0.14
0.145
t(s)
Figure 5.26: Transient behavior during step changes for DAB converter using PI-control
with feed-forward Lλ = 50 µH. From top: Power reference P ∗ [W], power
P [W] and phase angle ϕ [◦ ].
The controllers in the first two cases have the same parameters and use a feed-forward
loop, as shown in Figure 5.29 [60]. The feed-forward controller uses Eq. (5.18) to create
a faster system and the PI-controller is used to correct errors since the feed-forward is
not perfect.
π
ϕ = (Uin −
2
p
2
Ts2 Uin
− 8Lλ Ts P
)
Ts
(5.18)
The third case, Figure 5.28, has a PI-controller without a feed-forward term. As
shown in the figures, the feed-forward controller results in a faster response than the
traditional PI-controller. More oscillatory behavior is also observed when no feedforward is used, because the proportional constant is larger. The simulation with the
105
(W) : t(s)
Pref
(W)
2.2meg
2meg
1.8meg
(W) : t(s)
Power
(W)
2.2meg
2meg
1.8meg
(Deg) : t(s)
fi
(Deg)
25.0
20.0
15.0
0.095
0.1
0.105
0.11
0.115
0.12
0.125
0.13
0.135
0.14
0.145
t(s)
Figure 5.27: Transient behavior during step changes for DAB converter using PI-control
with feed-forward Lλ = 25 µH. From top: Power reference P ∗ [W], power
P [W] and phase angle ϕ [◦ ].
(W) : t(s)
Pref
(W)
2.2meg
2meg
1.8meg
(W) : t(s)
Power
(W)
2.2meg
2meg
1.8meg
(Deg) : t(s)
fi
(Deg)
60.0
55.0
50.0
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
t(s)
Figure 5.28: Transient behavior during step changes for DAB converter using PI-control
Lλ = 50 µH. From top: Power reference P ∗ [W], power P [W] and phase
angle ϕ [◦ ].
106
leakage inductance Lλ , equal to 25 µH, shows more oscillations than the simulation
with the leakage inductance Lλ of 50 µH due to the stronger connection between
the two sides, according to Eq. (5.16). Some of the problems, for example, that the
positive step and the negative step are not equal, as seen in the figures, are an effect
of applying a linear controller to a non-linear system. The data of the controllers are
shown in Table 5.6.
PSfrag replacements
ϕ = f (P, Uin , Uout , Lλ )
+
P
+
∗
−
PI
Controller
P
+
ϕ
P
P
Figure 5.29: PI-controller with feed-forward to control power using dual active bridge
converter.
Table 5.6: Controller parameters.
Parameter
Kp
Ti
Ts
5.4.6
PI-controller with
feed-forward
7.5·10−6
3 ms
1 ms
PI-controller
20·10−6
3 ms
1 ms
Varying Voltage
A varying input voltage Udc1 was applied to the converter and the power P and the
output voltage Udc2 were kept constant while the phase angle ϕ between the two bridges
was adjusted, according to Eq. (5.19). The simulation result is shown in Figure 5.30.
The controller changes the phase angle ϕ, and thus, maintains a constant transferred
power when the input voltage is changed.
P =
0
Uin Uout
Ts
ϕ
(1 − )ϕ
2πLλ
π
(5.19)
The power is constant at 1 MW while the input voltage changes from 500 V to 1000 V.
The reduced input voltage increases the control angle ϕ and, thus, the peak current
for the switches is changed, according to Eq. (5.20) (derived from Eq. 5.17).
107
(W) : t(s)
Power
(W)
1.1meg
1meg
900000.0
(Deg) : t(s)
80.0
fi
(Deg)
60.0
40.0
20.0
0.0
(V) : t(s)
Uin
(V)
1000.0
750.0
500.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
t(s)
Figure 5.30: Simulations with varying input voltage. From the top: Power P [W],
phase angle ϕ [◦ ] and input voltage Uin [V].
îsw =
0
(Uin (2ϕ − π) + πUout
)Ts
4πLλ
(5.20)
Figure 5.31 shows transformer stresses at 750 V input voltage. The peak current of
the transformer is the same as for 2 MW and 1000 V input voltage despite the power
being halved to 1 MW. The switch stresses at different voltages at 1 MW and constant
output voltage are shown in Table 5.7. If the input voltage is halved to 500 V, the peak
current increases by more than three times. The maximum current for the switches is
reached earlier and, therefore, the power capability of the converter is reduced when
the input voltage is reduced, according to Eq. (5.19).
108
(V) : t(s)
u_tfo1
(V)
750.0
0.0
−750.0
(A) : t(s)
i_tfo1
(A)
2000.0
0.0
−2000.0
(V) : t(s)
u_tfo2
(V)
10000.0
0.0
−10000.0
(A) : t(s)
i_tfo2
(A)
200.0
0.0
−200.0
0.197
0.198
0.199
0.2
t(s)
Figure 5.31: Transformer stresses in a DAB converter with 750 V input voltage. From
top: voltage winding one uT F O1 [V], current winding one 1T F O1 [A], voltage
winding two uT F O2 [V], current winding two iT F O2 [A].
Table 5.7: Phase angle and switch stresses at different input voltages.
Udc1
500V
750V
1000V
ϕ
49.7◦
28.5◦
20.3◦
109
îsw1 = îtf o1
3880A
2440A
1130A
5.4.7
Summary
The converter operation can be described as two generators connected together via an
impedance where the transferred power is determined by the phase angel between the
voltages, with the exception that the DAB converter does not have sinusoidal voltages.
If possible, the phase angle should be kept small to avoid high switch currents for
the switches. As with the Half and Full Bridge Converters the leakage inductance
Lλ and the turns ratio for the transformer are the most important parameters of the
converter. Leakage inductance influences current ripple and the maximum transferable
power. The turns ratio determines the voltage levels for the converter. Feed-forward
control can be used and the converter can handle dynamic changes in the transmitted
power. The controller keeps the transferred power constant even if the input voltage is
decreased to half the rated voltage. However, a reduced input voltage increases switch
currents.
110
Chapter 6
Wind Farm Simulation
In this chapter, wind farm simulations are performed. The wind turbines, cables and
DC/DC converters are put together to form the electrical system of a wind farm. In
addition, the proposed transmission system layout is presented. Different faults and
fault locations are simulated for a simplified model of the farm and finally simulations
with the complete wind farm are conducted.
6.1
Transmission System Layout for Wind Farms
An example of a transmission system layout for a wind farm is shown in Figure 6.1.
The system uses the Boost Converter as a voltage adjuster and a Full-Bridge converter
as a DC transformer. For simplification, the feeder can be modelled as a current
source, dependent on the output power to the wind turbine generator. In addition,
the connection to the transmission cable can be modelled as a constant voltage source.
With reference to Figure 6.1 the low voltage is the rectified generator output, which is
normally 0.5 to 1 kV and the medium voltage is about 2.5 kV. The high transmission
voltage depends on the output power of the wind farm and the transmission distance,
but 150 kV is realistic for 100-150 MW and, therefore, in comparison with Figure 6.1,
an extra converter stage is needed in this case.
Boost
Converter
I1
+
U1
-
Full Bridge
Converter
I2
=
+
U2
-
=
I3
=
=
=
Voltage
source
Current
source
Controller
Controller
U*
Variable low
voltage
+
U3
-
Voltage
adjustment
converter
U*
Medium
voltage
DC/DC
transformer
High
voltage
Figure 6.1: Example layout of transmission system with converters and control system.
111
6.2
Faults
In this section, different fault types and fault locations are investigated and simulation
results are shown in order to analyze the behavior of the wind farm when faults occur.
The faults are injected into the cables and two different fault types and four different
fault locations are simulated.
6.2.1
Test Setup
The schematic layout of the simplified transmission system is shown in Figure 6.3. A
Boost Converter and a Full Bridge Converter are connected together with cables and
six different faults are applied. The Boost Converter is controlled for a rated power
of 2 MW with an input voltage U1 of 1 kV and an output voltage U2 of 2.5 kV. The
Full Bridge Converter is controlled as a DC transformer with a rated power of 5 MW
and, thus, is not fully utilized, i.e., the converter is operated at part load. The input
voltage U3 for the Full Bridge Converter is 2.5 kV and the output voltage U4 is 25 kV
(compared with 150 kV for the proposed system).
The cables are represented by a π-equivalent model, according to Figure 6.2 [59]. Cable
data are presented in Table 6.1. Faults are injected between the four cables, one at a
time, at ground or between two of the cables from the same bus. The fault location
is in the middle of the cable, as indicated in the figure, and fault impedance is set to
10 mΩ [61].
L
g replacements
C
2
L
R
C
2
R
C
2
C
2
F ault
Figure 6.2: Equivalent π-scheme with fault location.
Table 6.1: π-equivalent cable data.
Cable
Length Conductor
R
L
C
2
1.25kV/800A DC
1 km
800 mm2
37.5 mΩ
0.43 mH 0.375 µF
12.5kV/400A DC
5 km
240 mm2
625 mΩ
2.4 mH
112
1.1 µF
+
Cin Sw
+
+
+
1.25 kV
UD
Usw
-
-
C1
Cout
U2
-
+
USW4
4
-
ISW4
Sw2
+
USW2Sw
L1l
L2l
n1
n2
ITfo2
D1
D3
+
UD3
-
D4
+
UD4
-
+
ZSource2
U4
+
UD2
-
12.5 kV
C3
+
UTfo2
-
D2
Iout
+
C4
ID4
-
C2
ITfo1
+
UTfo1
-
ISW2
1.25 kV
1
USW3
-
U3
2
5
-
Sw3
USW1
-
ID2
-
Sw1
+
+
UD1
-
ID3
Udc1
U1
D
-
+
ID1
ZSource1
+ U L
+
ISW3
+
I4
I2
ISW1
L
Iin
ID
ISW
113
Figure 6.3: Schematic layout of simplified transmission system with fault locations.
I3
IL
Uout
4
6
+
-
-
12.5 kV
3
-
Udc2
6.2.2
Line to Ground Faults
Fault type 1 is a line to ground fault located on the cable with negative polarity between the two converters, as indicated in Figure 6.3. The results from the simulations
are shown in Figure 6.4. The fault creates a voltage step at Boost Converter secondary voltages U2+ and U2− . Since the Boost Converter has no galvanic isolation
the voltage disturbance is transferred through the converter and affects the input of
the converter, i.e., both U1+ and U1− jump 1250 V. The converters are shut down for
over/undervoltages (rated voltage ±20%) after approximately 2 ms and the boost inductor current iL is discharged. Since the input voltage to the DC-transformer drops
to half the power, transfer will stop and the secondary side of the DC-transformer,
therefore, will not be affected by the short circuit.
M
Fault
(A) : t(s)
Boost : i_sw
(A)
2000.0
1000.0
0.0
(A) : t(s)
Boost : i_L
(A)
2000.0
1000.0
0.0
(V) : t(s)
Boost : U2+
(V)
2500.0
1250.0
0.0
(V) : t(s)
Boost : U2−
(V)
0.0
−1250.0
−2500.0
(V) : t(s)
FB : U1+
(V)
2500.0
1250.0
0.0
(V) : t(s)
(V)
1250.0
FB : U1−
0.0
−1250.0
0.49
0.4925
0.495
0.4975
0.5
0.5025
0.505
0.5075
0.51
0.5125
0.515
0.5175
0.52
0.5225
0.525
t(s)
Figure 6.4: Simulated voltages and currents during fault type 1. From top: Fault
injection, boost switch current isw [A], boost inductor current iL [A], boost
secondary side positive bus voltage U2+ [V], boost secondary side negative
bus voltage U2− [V], full bridge primary side positive bus voltage U3+ [V]
and full bridge primary side negative bus voltage U3− [V].
114
Fault type 2 is a line to ground fault located on the cable with positive polarity between the two converters, as indicated in Figure 6.3. The results from the simulations
are shown in Figure 6.5. The fault creates a voltage drop at Boost Converter secondary voltages U2+ and U2− . Again the voltage disturbance is transferred through
the converter and both U1+ and U1− will drop 1250 V. Consequently, U1− will drop
to approximately -2500 V. The converters are shut down for over/undervoltages after approximately 2 ms and the boost inductor current iL is discharged. Since the
input voltage to the DC-transformer drops to half the power, transfer will stop and
the secondary side of the DC-transformer, therefore, will not be affected by the short
circuit.
M
Fault
(A) : t(s)
Boost : i_sw
(A)
2000.0
1000.0
0.0
(A) : t(s)
Boost : i_L
(A)
2000.0
1000.0
0.0
(V) : t(s)
Boost : U2+
(V)
2500.0
1250.0
0.0
(V) : t(s)
Boost : U2−
(V)
0.0
−1250.0
−2500.0
(V) : t(s)
(V)
1250.0
FB : U1+
0.0
−1250.0
(V) : t(s)
FB : U1−
(V)
0.0
−1250.0
−2500.0
0.49
0.4925
0.495
0.4975
0.5
0.5025
0.505
0.5075
0.51
0.5125
0.515
0.5175
0.52
0.5225
0.525
t(s)
Figure 6.5: Simulated voltages and currents during fault type 2. From top: Fault
injection, boost switch current isw [A], boost inductor current iL [A], boost
secondary side positive bus voltage U2+ [V], boost secondary side negative
bus voltage U2− [V], full bridge primary side positive bus voltage U3+ [V]
and full bridge primary side negative bus voltage U3− [V].
115
Fault type 3 is a line to ground fault located on the cable with negative polarity between the DC-transformer and source two, as indicated in Figure 6.3. The results from
the simulations are shown in Figure 6.6. The fault creates a current surge in the converter and the converter is, therefore, shut down for over currents after approximately
1 ms. Since the DC-transformer has galvanic isolation, the voltage disturbance is not
transferred through the converter and the rest of the system , therefore, will not be
affected. The converters, however, are shut down for under voltage and the boost inductor current iL has to be discharged. This causes the secondary voltage U2 of the
boost converter to rise to approximately 3000 V.
M
Fault
(V) : t(s)
FB : U2+
(V)
12750.0
12500.0
12250.0
(V) : t(s)
(V)
FB : U2−
0.0
−12500.0
(A) : t(s)
FB : i_sw1
(A)
4000.0
2000.0
0.0
(A) : t(s)
FB : i_sw2
(A)
4000.0
2000.0
0.0
(V) : t(s)
Boost : U2
(V)
3500.0
3000.0
2500.0
(A) : t(s)
Boost : i_L
(A)
2000.0
1000.0
0.0
0.4975
0.5
0.5025
0.505
0.5075
0.51
0.5125
0.515
0.5175
0.52
t(s)
Figure 6.6: Simulated voltages and currents during fault type 3. From top: Fault
injection, full bridge secondary side positive bus voltage U4+ [V], full bridge
secondary side negative bus voltage U4− [V], full bridge switch one current
isw1 [A], full bridge switch two current isw2 [A], boost secondary side bus
voltage U2 [V] and boost inductor current iL [A].
Fault type 4 is a line to ground fault located on the cable with positive polarity between
the DC-transformer and source two, as indicated in Figure 6.3. The system behavior
is the same as in fault case 3 with the only difference that the secondary voltages U4+
and U4− of the DC-transformer are affected in opposite directions, i.e., U4+ become
zero, and U4− is more or less constant.
116
6.2.3
Line to Line Faults
Fault type 5 is a line to line fault located on the cables between the two converters, as
indicated in Figure 6.3. The results from the simulations are shown in Figure 6.7. The
fault causes the voltage to drop to the critical level where the output diode in the Boost
Converter will start to conduct and, thus, short circuit source one. Consequently, the
fault can only be removed by shutting down the source Udc1 . As before, the fault does
not affect the secondary side of the full bridge.
M
Fault
(A) : t(s)
Boost : i_sw
(A)
2000.0
1000.0
0.0
(A) : t(s)
6000.0
Boost : i_L
(A)
4000.0
2000.0
0.0
(V) : t(s)
Boost : U2+
(V)
1250.0
0.0
−1250.0
(V) : t(s)
Boost : U2−
(V)
1250.0
0.0
−1250.0
(V) : t(s)
(V)
12700.0
FB : U2+
12600.0
12500.0
12400.0
(V) : t(s)
(V)
−12400.0
FB : U2−
−12500.0
−12600.0
−12700.0
0.49
0.4925
0.495
0.4975
0.5
0.5025
0.505
0.5075
0.51
0.5125
0.515
0.5175
0.52
0.5225
0.525
t(s)
Figure 6.7: Simulated voltages and currents during fault type 5. From top: Fault
injection, boost switch current isw [A], boost inductor current iL [A], boost
secondary side positive bus voltage U2+ [V], boost secondary side negative
bus voltage U2− [V], full bridge secondary side positive bus voltage U4+ [V]
and full bridge secondary side negative bus voltage U4− [V].
117
Fault type 6 is a line to line fault located on the cables between the DC-transformer
and the source Udc2 , as indicated in Figure 6.3. The results from the simulations are
shown in Figure 6.8. The fault behaves like the line to ground fault even if the current
derivatives increase and both secondary voltages U4+ and U4− drop to zero. Thus, the
fault creates a current surge in the converter and the converter, therefore, is shut down
for over currents after approximately 1 ms. Since the DC-transformer has galvanic
isolation, the voltage disturbance is not transferred through the converter and the rest
of the system, therefore, is not affected. The converters, however, are shut down and
the boost inductor current iL has to be discharged. This causes the secondary voltage
U2 of the boost converter to rise to approximately 3000 V.
M
Fault
(V) : t(s)
FB : U2+
(V)
12500.0
0.0
(V) : t(s)
FB : U2−
(V)
0.0
−12500.0
(A) : t(s)
FB : i_sw1
(A)
4000.0
2000.0
0.0
(A) : t(s)
FB : i_sw2
(A)
4000.0
2000.0
0.0
(V) : t(s)
Boost : U2
(V)
3500.0
3000.0
2500.0
(A) : t(s)
Boost : i_L
(A)
2000.0
1000.0
0.0
0.49
0.4925
0.495
0.4975
0.5
0.5025
0.505
0.5075
0.51
0.5125
0.515
0.5175
0.52
0.5225
0.525
t(s)
Figure 6.8: Simulated voltages and currents during fault type 6. From top: Fault
injection, full bridge secondary side positive bus voltage U4+ [V], full bridge
secondary side negative bus voltage U4− [V], full bridge switch one current
isw1 [A], full bridge switch two current isw2 [A], boost secondary side bus
voltage U2 [V] and boost inductor current iL [A].
118
6.2.4
Summary
Depending on the type of fault and its location on the system, different parts of the
local wind farm transmission system have to be shut down. If the fault occurs between
the two converters, both converters have to be shut down in order to isolate the fault.
Faults between the DC-transformer and the source Udc2 can only be isolated by shutting
down the complete system, including the source Udc2 . Faults between the source Udc1
and the boost converter have not been simulated here, but in such a case, the fault can
be isolated by shutting down the source Udc1 and the Boost Converter.
The most severe fault that can occur in this example, consequently, is a short circuit on
the secondary side of the boost converter cannot be shut off and leads to a permanent
fault, which has to be shut off by shutting down the feeding source Udc1 . the big
difference between the two converters. The DC-transformer can isolate the system for
all faults by just turning off the switches.
119
6.3
Simulation of Complete Wind Farm
The principal layout of a 50 MW wind farm is shown in Figure 6.9. It consists of
25 wind turbines each with a rated power of 2 MW.
=
=
Wind turbine with rectifier
and boost converter
0.5-1 / 2.5 kV DC
=
=
Two half bridge converters
25 / 150 kV DC
=
=
=
=
=
=
Transmission Cable
150 kV DC
=
=
Two full bridge converters
2.5 / 25 kV DC
Figure 6.9: Example of wind farm layout.
As shown in Figure 6.10, each generator is connected to a rectifier and a Boost Converter and each group of five generators are connected to two parallel Full Bridge Converters. The Full Bridge Converters are then connected to two Half Bridge Converters.
The converters in parallel are only used if the input power is above 50 % of rated
power and, thus, the no-load losses are reduced. The configuration also gives a small
redundancy.
The wind is increased from the cut-in wind speed 3 m/s up to the rated wind speed
10 m/s and the generated power, therefore, is increased from 0 to 50 MW. Results
from the simulation are shown in Figure 6.11. Bus voltages change with different
wind speed and, thus, different power flow. At 8 m/s (i.e., after 0.55 s) the parallel
converters are started and this causes a voltage drop on the 2.5 kV bus, the 25 kV bus
and the 150 kV bus, since the two converters in parallel have a lower voltage drop. The
connection of the parallel converters also causes some oscillations between the 25 kV
and the 150 kV buses. The generator starts at 500 V and increases to 1000 V at rated
power. The 2.5 kV bus starts at 2.2 kV and increases to approximately 2.4 kV. The
25 kV bus changes between 24 and 25 kV and,finally, the 150 kV bus increases from
150 kV to 152 kV.
120
G
G
=
=
=
=
~
=
Connection point
on land
Shore
25/150 kV DC/DC
converter
~
~
=
Wind Turbine
2.5/25 kV DC/DC
converter
=
=
=
=
Cable transmission
2 x 75 kV DC
DC/AC converter
on land
~
=
Local wind
farm grid
25 kV DC
G
Local wind
farm sub grid
2.5 kV DC
~
=
Figure 6.10: Schematic layout of complete wind farm.
(m/s) : t(s)
Wind
(m/s)
9.0
6.0
3.0
(MW) : t(s)
Power
(MW)
2.0
1.0
0.0
(V) : t(s)
150 kV_Bus
(V)
152000.0
151000.0
150000.0
(V) : t(s)
25 kV_Bus
(V)
25000.0
24000.0
(V) : t(s)
2.5 kV_Bus
(V)
2400.0
2300.0
2200.0
(V) : t(s)
Ugen
(V)
1000.0
750.0
500.0
(V) : t(s)
Voltref
(V)
1000.0
750.0
500.0
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
t(s)
Figure 6.11: Steady state behavior of a 50 MW wind farm from cut-in wind speed to
rated wind speed. From top: Wind speed [m/s], turbine power [MW],
voltage at 150 kV bus [V], voltage at 25 kV bus [V], voltage at 2.5 kV bus
[V], generator voltage [V] and generator reference voltage [V].
121
6.4
Results
The system investigated here uses Boost Converters as voltage adjusters and Full Bridge
Converters as DC transformers. The bus voltages change with different wind speeds
and thus, different power flow when the input power is changed from zero to rated
power. The control system keeps the generator voltage at the reference voltage.
Depending on the type of fault, different parts of the transmission system have to be
shut down. The DC transformer can stop the system and limit all faults by just turning
off the switches, while a short circuit on the secondary side of the Boost Converter
cannot be isolated and leads to a permanent fault.
The conversion losses are reduced by parallel converters, which also provides a small
redundancy. The connection of the parallel converters causes some oscillations but the
oscillations can be reduced by changing the control system.
122
Chapter 7
Conclusions and Future Research
7.1
Conclusions
DC/DC converters have been examined by many authors before although primarily
in low power and low voltage applications. This thesis focuses on DC/DC converters
for high voltage and high power. When the first part of the project started up, the
objective was to determine the potential for using DC grids in a wind farm. Another
objective was to investigate different configurations of electrical systems for offshore
wind farms. The objective of the second part of the project was to investigate different
DC/DC converter topologies with respect to a wind farm application and present design
concepts with different high voltage and high power converter topologies.
For a high voltage and high power application, like a wind park transmission system, the
focus has to be on the utilization factor of the used components. Designing a DC/DC
converter for an input voltage down to half the rated voltage or with a high input to
output voltage ratio, decreases performance at rated power and voltage. Therefore,
converters have been analyzed for two different applications. One simple converter can
be used for a first adjustment of the voltage and then a second converter can be used
to raise the voltage to a suitable transmission level. The semiconductor component
stresses have been determined by a theoretical comparison of the different converters.
A Boost Converter is suitable as a voltage adjustment converter and a Bridge Converter
can be used as a DC transformer. Losses in the Boost and Full Bridge Converters
have also been estimated. Simple analytical expressions have been derived in order to
determine the transferred power. However, the losses and the transition times in the
converters yield significant errors in the transmitted power.
Boost and Dual Active Bridge (DAB) Converters can handle both varying input voltage
and dynamic changes in the transmitted power. For the Boost Converter, the design of
the inductor size is a compromise between the size of the input ripple and the speed of
the dynamic response for the converter. For the DAB converter, the leakage inductance
Lλ for the transformer is the most important parameter of the converter.
Half and Full Bridge DC transformers can handle dynamic changes in the transmitted
power but are not able to control the transferred power. The leakage inductance L λ
and the turns ratio for the transformer are the most important parameters for the
123
converters.
The proposed system uses a Boost Converter as a voltage adjuster and a Full Bridge
Converter as a DC transformer. System fault analysis with various faults and fault
locations have been conducted. Depending on the type of fault and its location, different parts of the local wind farm transmission system have to be shut down. If a fault
can not be isolated by the DC/DC converters, the system has to ashore that such fault
becomes isolated by other means. The DC transformer can isolate the system for all
faults simply by turning off the switches. However, a short circuit on the secondary
side of the Boost Converter cannot be shut off and leads to a permanent fault, which
has to be isolated by shutting down the feeding source.
Finally, a complete wind farm with 25 wind turbines was simulated. The wind and,
therefore, the produced power was increased up to a rated power of 50 MW. The
system shows good system performance when the different bus voltages change with
different wind speeds and, thus, different power flows. Wind farms with DC-grid is
feasible in the future according to a rough cost and loss estimation. It is also a logical
continuation when the experiences of todays wind farms with AC transmission have
been fully digested and the transmission distances are greater than today.
7.2
Future Research
To reduce the losses in high power and high voltage DC/DC converters, soft switching
and resonance converter topologies can be used. However, with variations in the inputoutput voltage ratio and with varying load, the topology design is a great challenge.
Different control strategies for operation of parallel converters, for different types of
fault protection and to optimize the energy production are essential to maintain reliable
operation and thus support the network on shore with energy. The control strategies
is also effected by the need of communication between the converters for protection
purposes.
An area of research itself, is high frequency, high power and high voltage transformers,
which are an essential component in DC/DC converters for wind farms. Mechanisms
for the losses, stray capacitances in the windings and the leakage inductance of the
transformer have to be determined. Another issue is the insulation problems with high
voltage derivatives from the switching actions in the converters.
It is important to validate the obtained simulated results by building an experimental
system in the laboratory. The system should involve the DC network of the wind farm
and promising DC/DC converter topologies.
124
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[60] J. Svensson, “Power angle control of grid-connected voltage source converter in
a wind energy application”, Technical report no. 218l, Chalmers University of
Technology, Göteborg, Sweden, 1995.
[61] W. Rieder, Plasma und Lichtbogen, Friedr. Vieweg & Sohn GMbH, Verlag, Braunschweig, 1967.
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130
Abbreviations
Abbreviation Description
CCM
DAB
DCM
HB
HBVD
FB
FBVD
FF
PCC
PFC
PI
PWM
RMS
SEPIC
WTG
ZVS
ZCS
ZVSCS
Continuous conduction mode
Dual Active Bridge
Discontinuous conduction mode
Half Bridge Converter
Half Bridge Converter with voltage doubler
Full Bridge Converter
Full Bridge Converter with voltage doubler
Feed-forward controller
Point of common coupling
Power factor correction
Proportional, Integral controller
Pulse width modulation
Route mean square value
Single Ended Primary Inductance Converter
Wind turbine generator
Zero voltage switching
Zero current switching
Zero voltage zero current switching
131
132
Symbols
Symbol
Description
Unit
α
β
∆IL
ϕ
Primary control angle
Secondary control angle
Inductor peak-to-peak ripple current
Phase shift
Cin
Cout
Cx
D
Dx
îDx
ID x
IDx ,RM S
Iin
Iout
îSwx
ISwx
ISwx ,RM S
Itf o1
Itf o2
Kp
Lλ
Lλ 1
Lλ 2
Lx
n1
n2
P
P∗
Q
Swx
Ti
Ts
Input capacitance
F
Output capacitance
F
Capacitor number x
F
Duty ratio
Diode number x
Diode x peak current
A
Diode x current
A
Diode x RMS current
A
Primary DC bus current
A
Secondary DC bus current
A
Switch x peak current
A
Switch x current
A
Switch x RMS current
A
Transformer primary side current
V
Transformer secondary side current
V
Proportional gain
Total transformer leakage inductance H
Primary side leakage inductance
H
Secondary side leakage inductance
H
Inductor number x
H
Primary winding
turns
Secondary winding
turns
Active power
W
Active power reference
W
Reactive power
W
Switch number x
Integral time constant
Switch period
s
133
◦
◦
A
◦
Symbols cont.
Symbol Description
Unit
Tsw,on
Tsw,of f
ûDx
U Dx
Udc1
Udc2
Uin
Uout
ûSwx
USwx
Utf o1
Utf o2
Zsource1
Zsource2
s
s
V
V
V
V
V
V
V
V
V
V
Ω
Ω
Switch turn on time
Switch turn off time
Diode x peak voltage
Diode x voltage
Primary source voltage
Secondary source voltage
Primary DC bus voltage
Secondary DC bus voltage
Switch x peak voltage
Switch x voltage
Transformer primary side voltage
Transformer secondary side voltage
Primary source impedance
secondary source impedance
134