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GRID-CONNECTED PHOTOVOLTAIC POWER
SYSTEMS: MODELING AND TOPOLOGY STUDIES
MIT/MIST Collaborative Research Progress Report for Period September-2011 to
February-2012
Principle Investigator at MIT: Prof. J. Kirtley and Prof. D. Perreault
Principle Investigator at Masdar Institute: Prof. V. Khadkikar and Prof. W. Xiao
Research Project Start Date: September 1, 2010
INTRODUCTION
Background
This research project focuses on the integration of PV solar power to the existing electric grid and
addresses issues and possible solutions related with such interconnection. In this research work
following aspects will primarily be considered:

To increase the performance of photovoltaic systems through the use of innovative system
structures, advanced control and optimal power converter interfaces.

To develop an accurate computer simulation model of a grid connected PV plant with necessary
controllers to perform maximum power extraction.

To study the potential issues as well as benefits if one or more renewable systems (combination of
solar and/or wind plants) are connected on the same distribution feeder and/or nearby feeders.
It is our intention that this project will help (i) to better understand the influence of solar plant local
distribution network, (ii) improve the overall performance of solar plants.
Objective and Approach
In the third quarter of this research project (September-2011 to February-2012), following research
objectives are being undertaken:

Construction of a DAB converter prototype with the modulation strategies and test the benchmark
prototype under different load case including rated load, heavy and light load cases. (PI: Dr. Xiao,
MI and Dr. Perreault, MIT)

Analysis of distributed power loss in DAB converter and elimination the reactive power. Analysis
of the dc bus surge voltage and comparative evaluation of DC-Link Capacitors in DAB converter.
(PI: Dr. Xiao, MI and Dr. Perreault, MIT)

An LCL filter design to enhance the performance of PV system with an active damping controller.
(PIs: Dr. Khadkikar, MI and Dr. Kirtley, MIT)

New control scheme to coordinate proposed interline-photovoltaic (I-PV) system. (PIs: Dr.
Khadkikar, MI and Dr. Kirtley, MIT)
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EXECUTIVE SUMMARY
This research project is based on the grid connected photovoltaic (PV) solar power plant. Two teams are
involved out of which one team (Dr. Perreault, MIT and Dr. Xiao, MI) is focusing on the device level. The
other team (Dr. Kirtley, MIT and Dr. Khadkikar, MI) is studying the integration aspects of PV solar plant
to the main grid. During the third quarter of the joint research work, the following aspects are
accomplished or under progress:

Regarding to the subproject “Design and prototyping of Dual Active Bridge Converter”, Two
prototypes of DAB converter have been constructed. One prototype is used to evaluate the
distributed power loss for the student thesis. The benchmark system has been tested under
different load case including rated load, light load cases. Another prototype is used by Dr.Wen
for loss reduction study. The modulation strategies have been implemented and the power loss
analysis has been finished both for aspects of the hardware and software. The reactive power
calculation has been analyzed and the way to eliminate reactive power in DAB converter is also
investigated. The team has been working with several subtasks, such as reducing DC surge
voltage/current, maximum power point tracking for PV systems, and high frequency AC power
supply systems. This work results in several publications shown in the Publication section.

Dr. Perreault, please add here

PV system modeling and control: An LCL filter is designed to enhance the performance of PV
system. Furthermore, in order to overcome the problem of possible resonance condition
between L-C-L a new active damping technique is proposed. (Dr. Khadkikar and Dr. Kirtley)

Multifunction PV solar power plant operation: In the previous report, we have proposed a new
system configuration for a large-scale PV solar plant, called as Interline-PV (I-PV) system. A new
droop control method, given a name P-Q-V droop controller, to regulate the grid voltage using
the I-PV system is developed. (Dr. Khadkikar and Dr. Kirtley)

A theoretical study of network reconfiguration of power distribution system is underway. The
goal of this research is to propose a reliable and efficient topology of distribution network.
Benefits, such as deferring the investment, reducing operation costs and improving energy
efficiency of distribution systems, can be attained from the work. This work is carried out by Ms.
Jiankang Wang under the supervision of Dr. Kirtley.
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RESEARCH TASKS
Task-1:
Benchmark System Test and Power Loss Distribution Analysis (PI: Dr. Xiao, MI)
An experimental prototype is implemented using DSP 2808 control board. Main parameters are shown
as following: the input voltage Vin = 32V, the input voltage range 28V – 36V, the nominal output voltage
Vo = 320V, the maximum deliver power Pmax = 250W and the switching frequency 200 kHz. This work is
delayed by approximately by 2 to 3 months due to the procurement process and budget freezing in
summer. The research and prototyping is accordingly delayed due to the order of key components such
as magnetic core and many experimental apparatus including adjustable DC power supply, adjustable
load and impedance analyzer. Different load case including rated load, heavy and light load cases will be
tested for this prototype and some experimental results will be presented to compare with the
theoretical analysis. During the waiting time, the MI team was working with other related study
including the effect of parasitic inductance, PV system modeling, Maximum power point tracking for PV
systems. DC link capacitor optimization, and high frequency AC power supply systems. The PV modeling
work was published by IEEE. Trans. On Sustainable energy. The voltage surge reduction work is accepted
for publication on the IET journal. Another two journal submissions are waiting for review results.
Task-2:
An LCL filter design to enhance the performance of PV system with an active damping
controller. (PIs: Dr. Khadkikar, MI and Dr. Kirtley, MIT)
This task is part of Objective-1 as mentioned in the original proposal. In this work we are developing an
active damping method for an LCL filter based PV system to annul the effect of resonance on the system
performance. This work has been delayed from the beginning of the project. However, the work has
been progressing since from the hiring of Post-doc (Dr. Moin Hanif) for this project.
Task-3:
Multifunction PV System: study potential benefits of one or more renewable energy
systems connected two different feeders. (PIs: Dr. Khadkikar, MI and Dr. Kirtley, MIT)
In the last two reports, we have provided initial results on a new system configuration that we have
proposed for a large-scale PV system. Here idea is to connect a large-scale PV system to two different
feeders/networks. The newly proposed system thus can enable to manage power flow on the two
different feeders through PV solar power plant inverters. The inverter modules in a PV power plant are
configured such that the system is represented as a back-to-back inverter connected multi-line system,
called as Interline-PV (I-PV) system. In this report, newly developed P-Q-V droop control method for I-PV
system is presented. This task is mentioned as “Part A: Objective-2” in the original proposal.
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CURRENT REPORTING PERIOD SUMMARY (MARCH 2011 TO AUGUST 2011)
Task 1: Weidong, please add here (Dr. Perreault and Dr. Xiao)
Research team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr.Wen, and Yosief Abraham (graduate
student)
The high circulating current in the transformer is the drawback of the DAB converter. At light load, this
circulating current increases the conduction losses and causes the converter to lose the natural zerovoltage switching feature. Thus, the test of the benchmark prototype under different load case including
rated load, heavy and light load cases is necessary to comprehensively assess the performance of the
prototype.
The simulation model based on PSIM and simulink has been created and compared with the experiment
tests. Calculation and analysis of the DAB converter overall power losses will be performed. The
mathematical model of the reactive power will be defined corresponding to different modulation
strategies. Traditional phase-shift control strategies introduce large reactive power and contribute to
large peak current and large system loss. Thus, the proposed control strategy will eliminate reactive
power in DAB converter.
For DAB converter, the DC bus can experience large surge voltages due to the presence of parasitic
inductance in addition to the hard-switching operations of voltage source inverters. The unexpected
transient overvoltage can result in switching device failures. A surge voltage model need to be
developed that takes into account the commutation loop inductances and the switching dynamics. An
optimal design approach to lower the stray inductance will be presented. In DAB converter, sizing and
selection of DC link capacitors involve tradeoffs among system performance including lifetime,
reliability, cost, and power density. A comprehensive and comparative study on the DC-link capacitor
applications and evaluations to meet the above requirements is investigated. The analysis should
consider the facts of capacitor power loss, core temperature, lifetime, and the battery ripple current
limit, which are critical for PV applications.
Please see Appendix-1 for more details.
Task 2: Development of PV Solar Plant Model (Dr. Kirtley and Dr. Khadkikar)
Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate students: Deema Al Baik
and Ammar Elnosh; Post-doc: Dr. Moin Hanif
This work is intended to develop a generic PV solar power plant simulation model. The develop model
will serve as a benchmark simulation model for future research work at MI and MIT.
Two MI graduate students, Ms. Deema Al Baik and Mr. Ammar Elnosh, are working on the PV solar plant
model development. Ammar is focusing on developing an improved maximum power point tracking
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(MPPT) algorithm including PV solar array modeling. The MPPT work is ongoing and we expect to
complete it in next 2-3 months. The details on MPPT will be provided in the next report.
Deema is also working on PV solar plant model development. However, her goal is on the AC side of the
network. Part of her work was reported in the last report. Currently she is working on LCL filter design
with an improved active damping method.
Dr. Moin Hanif has joined the MI research group in the month October-2011. He is also working on
developing an active damping controller for LCL filter. Summary of ongoing work is given in Appendix-2.
Task 3: Multifunction PV System (Dr. Kirtley and Dr. Khadkikar)
Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate student: Ahmed Moawwad
At the beginning of this project, we (Dr. Khadkikar and Dr. Kirtley) have proposed a new system
configuration for a large-scale PV plants, given a name as “Interline PV (I-PV)” system. One of the
graduate students at Masdar Institute (Ahmed Moawwad under supervision of Dr. Khadkikar) is working
on detailed study on the proposed I-PV system. We have accomplished significant advancement in this
research work and a journal paper has been submitted. A new droop controlled method, called as P-Q-V
droop method is proposed to regulate the grid voltage at point of common coupling. The research
findings are submitted for the possible publication in IEEE Transactions on Power Delivery. The
submitted paper details are given in Appendix-3.
Task 4: High Efficiency DC-DC Converters
To connect photovoltaic panels to the grid, interface circuitry is needed. In the architecture
pursued in this project, DC/DC converters are used to boost voltage of individual photovoltaic
panels to a high dc-link voltage, and one or more inverters are used to convert DC to AC. These
DC/DC converters have to be designed with very high efficiency. In Fig. 1, the block diagram of
a grid connected PV system is shown. The focus of this project is on the DC/DC power
converter. In conventional, hard switched power converters the overlap of current and voltage is
large during switching resulting in significant power loss. Soft switching is achieved by resonant
topologies which decrease switching losses by Zero Voltage Switching (ZVS) or Zero Current
Switching (ZCS). However, the magnetic loss increases with the additional magnetics needed for
soft switching and a tradeoff of these two losses is necessary to achieve minimum overall loss.
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Figure 1: Block diagram of a grid-connected PV system
Details of this work are in Appendix-4.
Unscheduled Task: Distribution System Reconfiguration
A strong motivation of the research topic is generated by the critical role of distribution network in
the whole power system and the challenges it has been facing during the recent several decades. As the
final stage of electricity delivery to end users, it is consist of over 65% of US power network [32]-[34].
Renewable energies installed in the form of Distributed Generation (DG) and demand response show
their influence on the whole power system through the distribution system. The aging infrastructure,
yearly increasing demand, and upcoming new technologies of distribution systems raise the question of
how to operate and reinforce the distribution network in a reliable and economic way to fulfill all the
requirements.
The problem is traditionally addressing by reinforcing distribution network based on the so-called “fitand-forgot” policy [35]. The “fit and forget” approach implies the design of the distribution system so as
to meet technical constraints in the most onerous conditions (e.g. full generation/minimum load or no
generation/full load) even if such situations have a small probability of occurrence. One advantage of
this approach is that control problems were solved at the planning stage. However, under rapidly
growing demand and targets of integrating DG, this practice of passive operation can be very costly or it
will limit the capacity of distributed generation that can be connected to an existing system [36].
In contrast, network reconfiguration, which alters the network topological structure by changing the
open/close status of the sectionalizer and tie switches, actively maximizes the use of existing circuits
[37].With reconfiguration, distribution systems can keep the redundancies of extra feeders for
contingent cases in long-term and operate in optimal radial structure. In addition to existing control on
generation and demand, reconfiguration adds another control dimension by making network structure a
dispatchable resource.
In spite of many studies on operation strategies of reconfiguration, there are few of them considering
reconfiguration in the planning stage [38], [39]. However, since reconfiguration can be resource of
improving operation, considering its role in planning has a great potential to save capital investment in
generators, transformers and etc. In addition, the reconfiguration flexibility of a distribution system is
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determined at its planning stage. Planning reconfiguration capability together with other power
distribution components may save cost and improve efficiency of operation.
During this reporting period, my study mainly includes using reconfiguration to (1) guarantee the
required reliability while reducing the capital investment in distribution system planning; (2) mitigating
the deterioration of voltage profile caused by DG insertion. Comprehensive literature review about
reconfiguration algorithms and distribution system automation was conducted. Methodologies and
results of the studied two problems are summarized in the following sections. Simulations have been
conducted to verify the results.
2 OBJECTIVES AND METHODOLOGIES
2.1 Objectives
The overall objectives of this research can be summarized in the following points:



Proposing and demonstrating a planning scheme that fulfills the long-term and short-term
requirements of distribution system.
Proposing a closed-loop planning scheme that consider and optimize the operation flexibility
induced by reconfigurable network structure.
Investigating into the controllability of distribution system induced by reconfiguration.
These objectives will be addressed at the close of this research. The challenges to modern distribution
networks can be interpreted as the conflicts of its short- and long-term requirements. In short-term, we
want distribution networks to operate efficiently with fewer redundancies planned as possible. In longterm, however, the redundancies are needed to ensure reliable performance of networks with
uncertainties induced from DG and time-varying loads. Deploying reconfiguration can exploit the
existing circuits and mitigate many operation problems of distribution systems; meanwhile, it retains
multiple configurations that can satisfy various system conditions. Due to these benefits, some
investment may be unnecessary given reconfigurable networks. And these benefits are expected to be
maximized in both short- and long-term if networks’ reconfiguration ability is well planned. Therefore,
exploring reconfiguration’s effects on distribution system operation and optimizing it at the planning
stage will close the loop.
2.2 Methodologies
During this reporting period, my study mainly includes using reconfiguration to (1) guarantee the
required reliability while reducing the capital investment in distribution system planning; (2) mitigating
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the deterioration of voltage profile caused by DG insertion. Their methodologies are discussed
separately in the following subsections.
2.2.1 Optimizing Reconfiguration’s Impacts on Distribution System Planning
This section briefly states the methodology of the first problem, using reconfiguration to ensure
required reliability while reducing distribution system planning cost.
In last reporting period, I have shown that reconfiguration can provide larger contingency support
neighborhood and thus save huge investment on transformers’ capacity and reduce the no-load loss of
substations. A paper was published under the topic [40].
Following the study, customer service quality indicated by reliability of distribution systems planned is
taken into account in the reporting period. Reconfiguration generates a larger contingency support
neighborhood that in turn pushes upward the utilization rates of equipments. However, the probability
that an outage will occur among the designated support units is increased at the same time [41].
Suppose that the area of the power system being considered has 88.5% loadings on all transformers,
instead of 66%. In that case, when any transformer fails, and if the utility is to keep within a 133%
overload limit, a failed unit's load has to be spread over two neighboring transformers, not just one. The
size of the "contingency support neighborhood" for each unit in the system has increased by a factor of
fifty percent. In a system loaded to 66%, there is only one major target. In a system or area of a system
loaded to 88.5%, it occurs if a unit and either one of two neighbors is out. In an area of a system loaded
to over 100% (as some aging areas are) it occurs whenever the unit and any one of three designated
neighbors is out. But there are still Single Contingency Policy (SCP) (i.e. N-1) neighborhoods: each can
tolerate only one equipment outage and still fully meet their required ability to serve demand. A second
outage will very likely lead to interruption of service to some customers. In these larger neighborhoods,
there are more targets for that second outage to hit. 'Trouble" that leads to an inability to serve
customer demand is more likely to occur.
For this reason, reliability measured by System Average Interruption Duration Index (SAIDI) is used to
constrained the distribution system plan proposed in study of last period [9]. LP models are developed
to find the optimal decisions for the above problems.
The main implications of this study are: (1) enabling reconfigurable feeders can increase reliability
with lower capital investment and operational cost when comparing to reinforcing transformer
capacity; (2) the reliability of a set of well interconnected substations depends on the max-shortage of
one of its substations, failure rates of units in the support neighborhood and size of the support
neighborhood. The two implications disprove the statements in previous works [42], [43]. The approach
used and the results obtained are currently being drafted in a paper.
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2.2.2 Optimizing Reconfiguration’s Impacts on Distribution System Integrated with Distributed
Generation
This section summarizes the methodology and results of the second problem, using reconfiguration to
improve voltage profiles of distribution systems integrated with Distributed Generation (DG).
This study was initiated in July, 2011 and falls into two sub-problems: (1) quantifying the dependency
of voltage profiles on DG’s insertion in terms of system voltage level, location, power capacity and
dispersion level, and (2) demonstrating reconfiguration’s improvement on systems’ voltage profiles in
theory and practice/ simulation.
When generators are connected to a feeder, voltage profile is likely to increase. According to ANSI,
voltage of distribution systems are limited to 6% in normal operation. Overvoltage of the standard
will decrease lifetime and even cause failure of equipments [44] The generator voltage VG can be
approximately given by V0  RP  XQ , where V0 is the substation bus voltage, P  PG  PL and
Q  QG  QL are the active and reactive power injected in the generator bus, and R and X are the
feeder resistance and reactance. To mitigate the voltage rise, traditional methods include to [14]:
 Reduce the primary substation voltage
 Allow DG to import reactive power
 Install auto transformers, or voltage regulators
 Increase the conductor size of feeders
 Constrain the generator at times of low demand
Compared the aforementioned methods, our study employs reconfiguration to changes the topology of
distribution network, and thus to change R and X to affect the voltage profile. This method is verified
with high implementation easiness, two to ten times low cost and 10-30% high effectiveness.
Until the reporting period, a DC circuit model, which may be extended to balanced 3-phase model
easily, is built to for sub-problem (1), and simulations are conducted for sub-problem (2). The main
implications of the study are:
1.
2.
Voltage profile of a feeder can be calculated with area criteria [46].
DG has greater impact on voltage profile of a feeder when inserted at farther end of the feeder.
Therefore, to mitigate overvoltage induced:
a) Curtailment of output of DG’s at farther end of a feeder should be firstly considered.
b) A demand response program should be designed to give stronger incentive on customers at
farther end of a feeder.
3. The maximum value of voltage on a feeder can be calculated with the proposed analytical
expression, and is determined at the position where current changes direction and supplement
current density is negative.
4. Dispersion level of DG can have either positive or negative impact on voltage profiles, depending
on DG’s location on a feeder.
A paper is drafted to include the results. Theoretic part of sub-problem (2) is under development.
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This study is a part of reconfiguration’s impacts on distribution system operation, which aims at
investigating the relation of system topological flexibility and reconfiguration benefits. Results of the
study are the basis of proposing a closed-loop planning scheme, which is the final purpose of my thesis.
3 CONCLUSION
Deploying reconfiguration can exploit the existing circuits and mitigate many operation problems of
distribution systems; meanwhile, it retains multiple configurations that can satisfy various system
conditions. Due to these benefits, some investment may be unnecessary given reconfigurable networks.
And these benefits are expected to be maximized in both short- and long-term if networks’
reconfiguration ability is well planned.
FUTURE WORK (MARCH 2012 TO AUGUST 2012)
Task 1: Comprehensive evaluation of the Benchmark prototype and analysis of
the power loss and reactive power
Research team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr. Wen, and Imran Syed (graduate
student)
This part of the project involves three main areas which include:



Testing
Power loss analysis
Reactive power analysis
• Testing: Dr. Huiqing Wen (MI) and Imran Syed (MI) under supervision of Dr. Xiao (MI). The study will
focus on the DC microgrid applications to adopt on-site PV generation and battery backup systems. The
pilot project will be located in the field station of Masdar Institute. Detailed work can be found in
Apendix 1-1.
• Power loss analysis: Dr. Huiqing Wen (MI) and Imran Syed (MI) under supervision of Dr. Xiao (MI).The
Masdar team will focus on the embedded software implementation
• Reactive power analysis: Dr. Huiqing Wen (MI) and Imran Syed (MI) under supervision of Dr. Xiao (MI).
Task 2: Novel modulation strategy investigation for DAB converter
Research team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr. Wen, and Imran Syed (graduate
student)
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This work focuses a simplified dual-phase-shift (SDPS) control strategy for DAB converter in whole
operation range is analysis. The work includes analysis the analytical expression of the average output
power, the reactive power, the rms and peak current based on the switching strategy. The softswitching conditions will be analyzed and compared with the traditional PS control. The DAB converter
power loss will be calculated and the algorithm to minimize the total power loss will be discussed.
Simulations and experiments are expected to be carried out to verify the analysis. Details can be found
in appendix 1-2.
Task 3: Development of PV Solar Plant Model (Dr. Kirtley and Dr. Khadkikar)
Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate students: Ammar Elnosh
and Deema Al Baik, Post-doc: Dr. Moin Hanif
This work is delayed by 4 to 6 months. However, there is a steady progress since the hiring of Dr. Moin
Hanif. The project objective-3 in the original proposal is to validate some of the research findings using a
hardware PV system. We expect the installation of a 5kW PV system at Masdar Institute (using actual PV
panels) will be done in the month of March/April – 2012.
In the next stage of the project we plan to finalize the following research aspects:

Development of improved MPPT technique (student involved: Ammar)

Active damping controller to improve the harmonics generated by the PV solar plant (student
involved: Deema and Dr. Moin)

Perform the initial experimental studies to validate some of the research objectives. (Dr. Moin
and Dr. Khadkikar)
Task 4: Multifunction PV System (Dr. Kirtley and Dr. Khadkikar)
Research team members: MIT: Dr. Kirtley; MI: Dr. Khadkikar; MI Graduate student: Ahmed Moawwad
This task is almost completed. So far, two conference papers are resulted from this research work. A
journal paper is in under review. Furthermore, we will be concluding this task by providing an additional
functionality where an unbalance in the grid voltages will be compensated using I-PV system. An
additional conference is expected from this last piece of the research work.
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PUBLICATIONS/PRESENTATIONS
1. V. Khadkikar and J. Kirtley, “Interline Photovoltaic (I-PV) Power System – A Novel Concept of
Power Flow Control and Management”. In the conference proceedings of IEEE PES General
Meeting, 24-28 July, 2011, pages 1-6. (Included in Report-I)
2. A. Moawwad, V. Khadkikar, and J. Kirtley, “Photovoltaic Power Plant as FACTS Devices in MultiFeeder Systems”. In the conference proceedings of Industrial Electronics conference (IECON2011), 7-10 Nov. 2011, pages 1-6. (Included in Report-II)
3. D. Al-Baik and V. Khadkikar, "Effect of variable PV power on the grid power factor under
different load conditions". In the conference proceedings of IEEE Electric Power and Energy
Conversion Systems (EPECS), 15-17 Nov. 2011, pages 1-5. (Included in Report-II)
PUBLICATIONS/PRESENTATIONS
[1] Y. Mahmoud, W. Xiao, and H. H. Zeineldin, "A Simple Approach to Modeling and Simulation of
Photovoltaic Modules," IEEE Trans. Sustainable Energy, vol. 3, pp. 185-186, 2012. (Published).
[2]
H.Wen, W. Xiao, H. Li, and X. Wen, "Analysis and Minimization of DC Bus Surge Voltage for
Electric Vehicle Applications," Electrical Systems in Transportation, IET, 2011. (Accepted)
[3]
H. Wen, W. Xiao, X. Wen, and P.R. Armstrong, "Analysis and Minimization of DC-Link
Capacitance for Electric Vehicle Application," IEEE TRANSACTION ON VEHICULAR TECHNOLOGY, 2011.
(The Second Review)
[4]
H.Wen, W. Xiao, and Z. LU, "Current-Fed High-Frequency AC Distributed Power System for
Medium-High Voltage Gate Driving Applications," IEEE Transactions on Industrial Electronics, 2011.
(Under Review)
[5] Y. Mahmoud, W. Xiao, and H. H. Zeineldin, “A New Parameterization Method for Single Diode
photovoltaic Models”, submitted to IEEE Trans. Sustainable Energy in Jan 2012, (Under Review).
[6]
H. Wen, W. Xiao, Xuhui Wen, “Comparative Evaluation of DC-Link Capacitors for Electric Vehicle
Application," accepted for the presentation in the 21th IEEE International Symposium on Industrial
Electronics (ISIE) which will take place in Hangzhou, Zhejiang, China on May 28-31, 2012.
[7]
Huiqing Wen, Weidong Xiao, Han Li, and Xuhui Wen, “Analysis and Minimization of DC Bus Surge
Voltage for Electric Vehicle Applications," accepted for the presentation in the 21th IEEE International
Symposium on Industrial Electronics (ISIE) which will take place in Hangzhou, Zhejiang, China on May 2831, 2012.
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[8] W. Xiao, H. Wen, and H.H. Zeineldin, “Affine Parameterization and Anti-Windup Approaches for
Controlling DC-DC Converters”, accepted for the presentation in the 21th IEEE International Symposium
on Industrial Electronics (ISIE) which will take place in Hangzhou, Zhejiang, China on May 28-31, 2012.
[9]
Y. H. Abraham, X. Weidong, W. Huiqing, and V. Khadkikar, "Estimating power losses in Dual
Active Bridge DC-DC converter," in Electric Power and Energy Conversion Systems (EPECS), 2011 2nd
International Conference on, 2011, pp. 1-5 (Published).
[10] W. Xiao, A. Elnosh, V. Khadkikar, and H. Zeineldin, "Overview of maximum power point tracking
technologies for photovoltaic power systems," in 37th Annual Conference on IEEE Industrial Electronics
Society, 2011, pp. 3900 (Published).
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APPENDICES (IF ABSOLUTELY NECESSARY)
Appendix-1: Benchmark System Test and Power Loss Distribution Analysis (PI:
Dr. W Xiao)
The first prototype of DAB converter has been constructed in the Laboratory of MIST. Tests have been
done for different phase shift angle and load. An experimental prototype was implemented using DSP
2808 control board. Main parameters are shown in table I and figure 1 shows the schematic of a single
phase DAB converter.
Table I
Circuit Parameters of the Dual Active Bridge DC-DC Converter
Rated Power
Po
300
Rated Input Voltage
Vin
32V
Rated output Voltage
Vo
320V
Input Capacitor
Cin
100uF
OutputCapacitor
Transformer turn ratio
Inductor
Frequancy
conversion ratio
Co
n
L
f
22uF
1:6
2.5uH
200KHz
1
Qi1
Qi3 I
L
Rs
VT1
C1
Vs +-
Qi2
Qi4
Ls
Tr
d
Qo1
Qo3
VT2
Qo2
C2
R
Qo4
Fig. 1 Circuit of single phase dual active bridge DC/DC converter
A simulation model for a microgrid has been created using PSIM/Simulink. Ideal voltage and current
waveforms using the Phase-Shifted modulation for the boost and buck mode of operation have been
simulated and analyzed. Different load case including rated load, heavy and light load cases are test for
this prototype and some experimental results are presented to compare with the theoretical analysis.
Figure 2 and figure 3 show the ideal voltages and current waveforms using the PS-M for the hard
switching mode and the soft switching mode of operation.
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Qi1
Qi 2
Qi 4
Qi 3
Qo 3
Qo 4
Qo 2
Qo1
VT1

VT2
iL
Intervals
Particular
angles
1
Conducting
switches
2
4
3
5
6
2

 
0
D12
D12
T12
D11
D11
T11
D13
D13
T13
D14
D14
T14
D22
T21
D21
D21
T22
D22
D23
T24
D24
D24
T23
D23
Fig.2 Ideal voltages and current waveforms using the PS-M for the hard switching mode of operation.
Qi1
Qi 2
Qi 4
Qi 3
Qo 3
Qo 4
Qo 2
Qo1
VT1

VT2
iL
Intervals
Particular
angles
1
0
Conducting
switches
2

4
3
5
6
2


D12
T12
T12
D11
T11
T11
D13
T13
T13
D14
T14
T14
D22
T22
D21
D21
T21
D22
D23
T23
D24
D24
T24
D23
Fig.3 Ideal voltages and current waveforms using the PS-M for the soft switching mode of operation.
15 | P a g e
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23
1
d1
VT1
2
d2
VT2
iL
Intervals
Particular
angles
1
2
0 
Conducting
switches
4
3
d2
5
1

6
7
8
2
D12
T12
T12
D11
T11
T11
T11
D12
D13
T13
T13
T13
T14
T14
T14
T14
D22
T22
D21
D21
D21
T21
D22
D22
D23
T23
D24
D24
D24
D23
D23
D23
Fig.4 Ideal voltages and current waveforms using the PSPM for  D1  D2  0.5 &  D1  0.5
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23

d1
VT1

d2
VT2
d 2  d1
iL
Intervals
Particular
angles
12
Conducting
switches
4
3
5
67
8
9
10
2
d2

D12
T12
T12
T12
D11
D11
T11
T11
T11
T11
D13
T13
T13
T13
T13
D14
T14
T14
T14
D13
D22
T22
D21
D21
D21
D21
T21
T21
D22
D22
D23
T23
T23
D24
D24
D24
T24
D23
D23
D23
0 t x

16 | P a g e
Fig.5 Ideal voltages and current waveforms using the PSPM for  D1  D2  1  D1  &  D1  0.5
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23

d1
VT1

d2
VT2
d1
iL
Intervals
Particular
angles
1
2
Conducting
switches
4
3

0
tx

5
7
6
8
9
10
2

d2
D12
T12
T12
D11
D11
D11
T11
T11
T11
T11
D13
T13
T13
T13
T13
D14
T14
T14
D13
D13
D22
T22
D21
D21
D21
D21
T21
T21
T21
D22
D23
T23
T23
T23
D24
D24
T24
D23
D23
D23
Fig.6 Ideal voltages and current waveforms using the PSPM for 1  D1  D2  1 &  D1  0.5 .
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23

d1
VT1
d2

d 2  d1
VT2
iL
Intervals
Particular
angles
1 2 3
4
0  d2 
Conducting
switches
5
6 7
8
9
10
2

tx
D12
T12
T12
D11
D11
D11
T11
T11
T11
D13
T13
T13
T13
T13
D14
T14
T14
D13
T11
D13
T21
D21
D21
D21
D21
D21
D21
D22
D22
T21
D23
T23
D24
D24
T23
T23
T23
D23
D23
D23
17 | P a g e
Fig.7 Ideal voltages and current waveforms using the PSPM for  0  D2  1  D1  &  D1  0.5 .
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23

d1
VT1

d2
d 2  d1
VT2
iL
Intervals
Particular
angles
1
2
Conducting
switches
4
3

0 
5
tx
d2
6
7
8
9
10
2

D12
T12
D11
D11
D11
D11
T11
T11
T11
D13
T13
T13
T13
T13
D14
T14
D13
D13
T11
D13
T21
D21
D21
D21
D21
D21
D21
D21
D22
T21
D23
T23
T23
D24
T23
T23
T23
T23
D23
D23
Fig.8 Ideal voltages and current waveforms using the PSPM for 1  D1  D2  D1  &  D1  0.5 .
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23

d1
VT1

d2
VT2
d 2  d1
iL
Intervals
Particular
angles
12 3
0  tx
Conducting
switches
4
5

d2
67 8
9
10
2

D12
T12
T12
D11
D11
D11
T11
T11
T11
T11
D13
T13
T13
T13
T13
D14
T14
T14
D13
D13
D22
T22
D21
D21
D21
D21
T21
T21
T21
D22
D23
T23
T23
T23
D24
D24
T24
D23
D23
D23
Fig.9 Ideal voltages and current waveforms using the PSPM for 1  D1  D2  D1  &  D1  0.5 .
18 | P a g e
The high circulating current in the transformer is the drawback of the DAB converter. At light load this
circulating current will increase the conduction losses and causes the converter to lose the natural zerovoltage switching feature. Thus the test of the benchmark prototype under different load case including
rated load, heavy and light load cases is necessary to comprehensively assess the performance of the
prototype. The simulated waveform is shown in the following Figures including traditional PS-M and
other modulation strategies.
40
r1
v (V)
20
0
-20
-40
0
5
10
15
10
15
10
15
Time (us)
r2
v (V)
20
0
-20
0
5
Time (us)
i
Llk
(A)
20
10
0
-10
-20
0
5
Time (us)
Fig. 10 Waveforms using the conventional control strategy for phase angle 90°
40
r1
v (V)
20
0
-20
-40
0
5
10
15
10
15
10
15
Time (us)
r2
v (V)
20
0
-20
0
5
Time (us)
0
i
Llk
(A)
10
-10
0
5
Time (us)
Fig.11 Waveforms using the conventional control strategy for phase angle 45°
19 | P a g e
40
r1
v (V)
20
0
-20
-40
0
5
10
15
10
15
10
15
Time (us)
r2
v (V)
20
0
-20
0
5
Time (us)
0
i
Llk
(A)
10
-10
0
5
Time (us)
Fig.12 Waveforms using the conventional control strategy for phase angle 30°
40
r1
v (V)
20
0
-20
-40
0
5
10
15
10
15
10
15
Time (us)
r2
v (V)
20
0
-20
0
5
Time (us)
0
i
Llk
(A)
10
-10
0
5
Time (us)
Fig.13 Waveforms using the conventional control strategy for phase angle 15°
Ir-8.0676929e+000
10
5
0
-5
-10
Vr1
Vr2/6
40
20
0
-20
-40
0.19998
0.199985
0.19999
Time (s)
0.199995
0.2
(a)
20 | P a g e
Ir-2.6541422e+000
15
10
5
0
-5
-10
-15
Vr1
Vr2/6
40
20
0
-20
-40
0.19998
0.199985
0.19999
Time (s)
0.199995
0.2
(b)
Fig.14 Waveforms using the novel modulation strategy
Test Setup is shown as following:
(a) Dab prototype
(c) Power supply
(b) DSP control board
(d) Load
Fig.15 Experiment Test Setup
21 | P a g e
The efficiency of the DAB depends on power transfer , the input and output voltages and the
difference between them for example if the voltage V2 drops along with discharge of the energy
storage device , power loss increases at a given power transfer . Experimental Waveforms are shown as
following: The power transferred at the given value L  2.5 H and phase shift angle of 45o for input
voltage V1  29.4V and output voltage V2 
146
 24.3 , is found as 135.5 W theoretically .
6
Fig.16 Experiment Result1(Vout=106.7W,d=0.8182)
22 | P a g e
Fig.17 Experiment Result2(Vout=91.8W,d=0.8734)
Appendeix 1-2: Analysis the distribution of power loss in DAB converter and
elimination the reactive power. Analysis of the dc bus surge voltage and
comparative evaluation of DC-Link Capacitors in DAB converter. (Dr. Perreault
and Dr. Xiao)
Research team members: MIT: Dr. Perreault; MI: Dr. Xiao, Dr. Wen, and Yosief Abraham (graduate
student)
The expression of leakage inductor current for each time interval has also obtained. Soft-switching
constraints for both bridges are also derived. Power losses in MOSFETs, diodes and transformer are
calculated. The power losses in DAB can be classified as the switching and conduction losses. The
switching losses in semiconductor devices are due to continuous switching (on and off) transitions
during which a device is simultaneously exposed to high voltage and current. Although the DAB naturally
operates in zero voltage switching (ZVS), it operates in ZVS only during “ON” switching transition. The
conduction losses in DAB can further be classified as the conduction losses that occur in the
semiconductor devices (MOSFETs) and the transformer and inductor losses. The switching losses in
MOSFETs can be calculated from the following formula:
1
Psw  VDS I DS ton f sw
2
(1)
Where fsw is the switching frequency, VDS and IDS are the voltage and current at the time of switching,
respectively, and ton and toff are time intervals during switching ON and OFF, respectively. Note that the
power loss Psw represents the amount of power loss for one switch per leg during the ON switching
transition. Similarly, the losses for the OFF transition can be calculated. Hence to calculate the total
switching losses for bridge 1, for example, we can multiply Psw by 4 assuming the bridge has either on
state or off state losses. The switching transition time can be calculated with the help of the device data
sheet. To calculate the conduction losses, the losses due to the R_DS(on) and the voltage drop across
the anti-parallel diode are based on the data sheet. For example, for bridge 1, on resistance of the
MOSFET, R_DS(on) =8.2mΩ and the anti-parallel diode forward voltage drop, V_f=1.2V. Hence the
conduction losses can be calculated in as:
2
PMC  I Mrms
RDS  on
(2)
PDC  I DrmsV f
(3)
The RMS current values for both the body diodes and the MOSFETs are calculated from the inductor
current waveform depicted through the respective components. Fig.4 shows the different conduction
time intervals for the switch .The dead time has a life time D1 hence the body diode conducts during
23 | P a g e
this time interval contributing to the power losses , in the remaining segments(D2, D3, D4) the MOSFET
conducts. The RMS currents for both the body- diode and MOSFET are estimated using (4) and (5).
D1 2
( I o  I o I1  I12 )
3
(4)
D2 2 D3 2 D4 2
I1 
I 
( I o  I o I  I2 )
3
3
3
(5)
I drms 
I Mrms 
𝑖𝐿
𝐷1
𝐷2 𝐷3
𝐷4
𝜔𝑡
𝐼1
Fig.18. The different conduction time intervals of the inductor current through the bridges
The reactive power is defined corresponding to different modulation strategies and the corresponding
equations are derived. Traditional phase-shift control will induce large reactive power and contribute to
large peak current and large system loss. The control strategy to eliminate reactive power in DAB
converter is investigated.
Considerably minimized converter power loss can be achieved with the use of alternative modulation
strategies, which are basically originated from the variation the duty ratio of the H-bridge output voltage
and the phase shift angle. A phase-shift plus pulse width modulation (PSPWM) control strategy is
presented in [3] and one more degree of control freedom is added to extend the ZVS range. A optimal
selection of phase shift angle and modulation duty ratio, useful to minimize overall converter loss, is
analyzed in [4]. But the duty ratio of the gate signals is variable and calculated online, besides, the
calculation of duty ratio is dependent on the plow flow direction and buck/boost operation modes. All
these factors result in the complexity of the PSPWM control. A double-phase-shift (DPS) control is
proposed to reduce the reactive converter power [5]. This control includes two phase-shift angles, which
are phase-shift between the primary and secondary side of the transformer and phase-shift between
the gate signals of the diagonal devices of the same side. But it doesn’t full consider the efficiency
improvement, besides, the analysis of reactive power is not completed due to the complexity. The
experimental comparison of PS and DPS control is presented in [6]. The efficiency improvement is not
good as expectation in [5] due to the lack of systematic analysis of power loss distribution. In [7], the
phase-shift trajectories for the minimal reactive power, the minimal rms and peak current are analyzed.
But due to more control parameters and complex operation modes, the expression of reactive power is
extreme complicated and the optimal design is not easy to implement. Thus, a simplified dual-phase24 | P a g e
shift (SDPS) control strategy for DAB converter in whole operation range is analysis. The analytical
expression of the average output power, the reactive power, the rms and peak current are derived
based on the switching strategy. The soft-switching conditions are analyzed and compared with the
traditional PS control. The DAB converter power loss is calculated and the algorithm to minimize the
total power loss is proposed. Simulations and experiments are carried out to verify the analysis.
In Fig.16 the experimental inductor current wave form, iL , output Voltage Vo and output current Io
are shown .The experimental results have shown quite a big gap from theoretical calculations mainly
due to the exclusion of the inductor and transformer losses .As it is shown in Fig. 5 the efficiency for the
experimental converter at 45o is 91% , the theoretical efficiency at this particular operating point is
calculated to be 95.19%.. The conduction losses Pcond  1.31W and the switching losses Psw  1.73W .The
power transfer at the mentioned phase shift angle is Po  135.5W . In this analysis the switching loss is
seen to be a slightly higher than the conduction losses.
Fig. 19 and Fig. 20 shows the SDPS control strategy for the case of the phaseseparately, where, β corresponding to the inductor current iL zero crossing, vT1 and vT2 represent the
primary and secondary voltage of transformer, τ is the pulse width and is expressed by (6), the phaseshift ratio D is defined as
  
D


(6)
(7)
25 | P a g e
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23


vT1


vT2
vL
t
iL
Intervals
Particular
angles 0
Conducting
switches
1
2

4
3


5
6
7
8
D12
S12
S12
D11

2
D11
S11
S11
D13
D14
S14
S14
S11
D13
S13
S13
S13
D23
S 23
D21
D21
S 23
S 21
D22
D22
S 21
D21
D24
D24
D21
D23
D23
D23
Fig. 19 Ideal voltages and current waveforms using the SDPS for D<0.5
26 | P a g e
Q11
Q12
Q14
Q13
Q21
Q22
Q24
Q23


vT1


vT2
vL
t
iL
Intervals
Particular
angles 0
Conducting
switches
1
2

4
3


5
6
7
8
D12
S12
D11
D11

2
D11
S11
S11
D13
D14
S14
D13
S11
D13
S13
S13
S13
D23
S 23
D21
D21
S 23
S 21
S 21
D22
S 21
D21
S 23
D24
D21
D23
D23
D23
Fig. 20 Ideal voltages and current waveforms using the SDPS for D0.5
The expression of the inductor current iL can be obtained based on the voltage difference between
primary and secondary side of transformer vT1 and vT2.
Ls
diL
 vT1  t   vT2  t 
dt
(8)
Solving (3) for the inductor current iL considering each interval defined in Fig. 5 and Fig. 6 yields the
current expression shown in Table I and Table II , where respectively, where θ=ωt, ω=2πfs, fs is the
switching frequency, for the case D<0.5, α1=, α2=τ, and for the case D0.5, α1= τ, α2. n is the voltage
conversion ratio defined as
27 | P a g e
n
VT2
(9)
VT1
TABLE I
EXPRESSION OF INDUCTOR CURRENT FOR EACH TIME INTERVAL
Zone
Interval 1 and 2
SDPS,
D<0.5
iL   
V1
  iL  0 
 Ls
SDPS,
D0.5
iL   
V1
  iL  0 
 Ls
PS
iL   
Interval 3
iL   
Interval 4
V1  V2
     iL  
 Ls
iL   
V2
     iL  
 Ls
iL    iL  
iL   
V2
     iL  
 Ls
V1  V2
  iL  0 
 Ls
iL   
V1  V2
     iL  
 Ls
TABLE II
CURRENT AT THE SWITCHING ANGLES
Zone
SDPS,
D<0.5
SDPS,
D0.5
PS
iL  0
iL 1 
iL  2 
iL  
V1  n  11  D 
V1  n  1  3D  nD 
V1 1  n  3nD  D 
V1 1  n 1  D 
4 f s Ls
4 f s Ls
4 f s Ls
4 f s Ls
V1  n  11  D 
V1 1  D  n  1
V1 1  D  n  1
V1  n  1 D  1
4 f s Ls
4 f s Ls
4 f s Ls
4 f s Ls
V1  n  1  2nD 
V1  n  1  2 D 
V1  2nD  n  1
4 f s Ls
4 f s Ls
4 f s Ls
TABLE III
AVERAGE OUTPUT POWER, TRANSFORMER RMS CURRENT AND PEAK CURRENT
Zone
P
Irms
Ipeak
SDPS,
D<0.5
nV12
D  2  3D 
4 f s Ls
3 2
3
3
2 2
3V1 2D n  20D n  2D  3D n
12 f s Ls 18D2n  3D2  n2  2n  1
V1
 D  n  1  1  n 1  2 D 
4 f s Ls 
SDPS,
D0.5
nV12
2
 D  1
4 f s Ls
 2D  6n  12nD  
3V1
1  D   2

2
12 f s Ls
 2n D  n  1 
V1 1  D  n  1
PS
nV12
D 1  D 
2 f s Ls
3V1
8nD3  12nD2  n2  2n  1
12 f s Ls
V1
 D  n  1  1  n 1  D 
4 f s Ls 
4 f s Ls
Based on these relationships, the average output power, the inductor current RMS and peak current
of DAB converter will be expressed in Table III for both PS and SDPS control strategies. From Table III, it
28 | P a g e
can be concluded that the average output power of DAB converter can be controlled by the duty ratio D,
which is used as the manipulated variable. Other variables such as V1, fs, and Ls determine the
magnitude. Assuming the same average output power, the relationship of duty ratio for zone1 (D<0.5)
and zone2 (D0.5) using SDPS strategy with respect to the duty ratio D using PS strategy are given by
(10) and (11), respectively.


Dz1 2  3Dz1  2D 1  D 
D
z2

(10)
 1  2 D 1  D 
2
(11)
Solving (10) and (11) yields the corresponding expressions and application ranges given in table IV.
TABLE IV
THE CORRESPONDING EXPRESSIONS AND APPLICATION RANGES FOR TWO OPERATION ZONES
Zone
Symbol
Dz1_1
Range
1  1  6 D 1  D 


3 3  3 3
 D  1
 0  D 
 or 
6   6


3
SDPS, D<0.5
1  1  6D 1  D 
Dz1_2
SDPS, D0.5
Expression
3
2 2
3 3  3 3
2 2 
D
D

 or 

6   6
4 
 4


2 2  2 2
 D  1
 0  D 
 or 
4   4


1  2 D 1  D 
Dz2
Comparison of PS and SDPS are shown as following.
1
Dz1-1
0.8
Dz1-2
Dz2
D
i
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
D
Fig. 21 Comparison of PS and SDPS for duty ratio
29 | P a g e
423
PS
SDPS
vout (V)
422.8
422.6
422.4
422.2
422
0
2
4
6
Time (s)
8
10
Fig.22 Comparison of PS and SDPS for output voltage ripple
40
PS
SDPS
iL (A)
20
0
-20
-40
0
2
4
6
Time (s)
8
10
Fig. 23 Comparison of PS and SDPS for the inductor current
For DAB converter, the DC bus can experience large surge voltages due to the presence of parasitic
inductance in addition to the hard-switching operations of voltage source inverters. The unexpected
transient overvoltage can result in switching device failures. A surge voltage model is developed that
takes into account the commutation loop inductances and the switching dynamics. An optimal design
approach to lower the stray inductance is presented. In DAB converter, sizing and selection of DC link
capacitors involve tradeoffs among system performance including lifetime, reliability, cost, and power
density. A comprehensive and comparative study on the DC-link capacitor applications and evaluations
to meet the above requirements are investigated. The analysis considers the facts of capacitor power
30 | P a g e
loss, core temperature, lifetime, and the battery ripple current limit, which are critical for PV
applications.
Two papers on the dc bus surge voltage and comparative evaluation of DC-Link Capacitors have been
accepted for the presentation in the 21th IEEE International Symposium on Industrial Electronics (ISIE)
which will take place in Hangzhou, Zhejiang, China on May 28-31, 2012. Another paper on the power
loss analysis has been accepted for 2011 2nd International Conference on the Electric Power and Energy
Conversion Systems (EPECS).
31 | P a g e
Appendix-2: An Active Damping Technique for an LCL Filter Based System (Dr.
Khadkikar, Dr. Hanif and Dr. Kirtley)
We expect to submit a journal paper based on this research work soon. The initial draft of the paper is
given below.
An Active Damping Technique for Filtering the Resonance of an LCL
Filter Based PV System
Moin Hanif, Vinod Khadkikar and James L. Kirtley
Abstract—This paper focuses on LCL-filter based three-phase voltage source inverter control for grid
connected DG systems. Voltage –oriented PI control of grid current is normally adopted in the dq
synchronous reference frame for such inverters. Even though a LCL filter is more effective at attenuating
the switching harmonics compared to simple L-filter, it causes stability problems due to the LCL
resonance. In order to stabilize the PI controller, either a damping resistor within the filter or an active
damping method within the inverter control has to be incorporated. Due to the additional losses caused
by the damping resistors, they are seldom used. Active damping techniques are preferred, but require
extra sensors to feed back measured signals. To avoid these disadvantages, a simple active damping
technique that uses the existing grid side current sensors is provided as an active damping solution
suitable for industry applications. Stability of the technique is proven using simulation results and bode
plots of the system transfer function. Impact of dc link voltage and resonance frequency on stability is
analyzed.
Index Terms—Photovoltaic power generation, interline power system, active power control, reactive
power control, voltage regulation, power management.
I. INTRODUCTION
DG systems come as pulse width modulated (PWM) voltage source inverters (VSI) that inject controlled
active and reactive power as required. Output of such an inverter needs to be filtered in order prevent
the current harmonics around the switching frequency from entering the utility grid [1]. A filter of higher
order, such as a third order LCL filter is preferred over a simple L filter. This is not only because of the 60
dB/decade attenuation of the frequencies above the resonance frequency, but also due to the reduction
of physical size of the L [2]. A small inductance in a LCL filter is effective because the capacitor
impedance is inversely proportional to the frequency of the current. The LCL filter exhibits first order
inductive behavior to allow proper current control and high frequency rejection to guarantee proper
filtering. Nevertheless, a LCL filter can cause stability problems due to the undesired resonance caused
by the zero impedance at certain frequencies. To avoid this resonance from dominating the system, the
32 | P a g e
LCL structure is modified by incorporating passive elements, usually a resistor in series with the filter
capacitor that solves the issue, but causes energy loss that brings down the efficiency of the inverter
system. This kind of damping is referred to as passive damping [3]. Active damping that replaces passive
damping is preferred as it stabilizes the system without any energy losses. This is done by modifying the
current controller loop based on a feedback parameter. The main idea of the active damping algorithm
is that, it introduces a negative peak that compensates the positive peak caused by the presence of LCL
filter.
There are many proposed techniques in literature, most of which require an additional sensor in order
to measure the feedback variable that is used for damping the undesired resonance. A method
introduced by [4] requires feedback of the filter capacitor voltage that is based on lead-lag element.
Slight modifications made to [4] that use the filter capacitor voltage as feedback parameter for active
damping purposes are presented in [5] - [12]. Filter capacitor current has been used to form a so called
‘virtual resistor’ and several similar active damping techniques based on capacitor currents are
mentioned in [13]-[18]. In [1], [19] and [20] capacitor voltage has been estimated in order to avoid the
sensors, and the estimated capacitor voltage is filtered using a high pass filter (HPF) to add the
compensating peak within the current loop. In [21] to implement a virtual resistor, the capacitor current
is estimated instead of using an extra sensor to measure it. Estimation of the filter capacitor current or
voltage depends on the accuracy of plant parameters, which may be sometimes unknown or even vary
in a wide range for a complex power system. Therefore, active damping techniques based on high order
digital filters without the use of sensors is proposed in [22], [23]. [24]-[27] have made analysis based on
such techniques that use digital filters within the forward path of the main current control loop, i.e.
either after the PI controller or just before the PWM reference generator as described in [22]. Either
genetic algorithm based tuning or different complex offline tuning methods are considered to tune such
high order digital filters. Also, in [28] a design algorithm is proposed for optimizing LCL filters based on
which the system can be made stable at certain switching frequencies without any kind of damping. In
[29], the inherent damping characteristic of the LCL filters that may help damp the resonance is given.
This is when converter side inductor current is used instead of the grid side inductor current as the main
control parameter in the current loop. Further, [3] and [31] provide a review on couple of the
techniques discussed above. Paper [30] preserves the meaning of ‘filtering the resonance’ by using the
grid side inductor current as feedback, and also has the advantage of using the existing grid side current
inductor sensors but uses an analogue filter. The analogue filter, typically a notch filter is used and then
analogue to discrete transformation is applied based on a given set of specifications called the bilinear
transformation.
All the techniques above either use additional sensors to retrieve the filter capacitor voltage/current or
adopt a sensor-less approach based on some parameter estimation. Else higher order filters are used
without sensors, whose tuning complicates the final control algorithm. Therefore a simple active
damping technique that uses the existing grid side inductor current information in order control the
injected power and also to damp the LCL resonance is introduced. The LCL based inverter system is
simulated and the simulation results with and without active damping are analyzed. The system model
and the system open loop transfer function is derived. Open loop transfer function of the system model
is modified to accommodate the new active damping feedback loop, whose stability is proven using
bode plots. Finally the stability of the proposed controller with respect to dc link voltage and resonance
frequency is analyzed.
33 | P a g e
II. SYSTEM CONTROL, MODELING AND DESIGN
Fig. 1 shows the typical circuit diagram of a three-phase VSI connected to the grid via a LCL filter and
Table 1 gives the parameters of the system under study. Voltage oriented control is adopted as it is one
of the most commonly used control method. It is based on inverter current vector orientation with
respect to the grid voltage vector. The controller typically consists of an outer dc link voltage control
loop with an inner current loop that guarantees a good dynamic and static performance. The dc link
controller keeps the dc link maintained at the desired constant voltage level (800V in this study) and the
grid side inductor current , is expected to be sinusoidal and in phase with the grid voltage to achieve
unity power factor. A phase locked loop (PLL) is used to determine the frequency and angle reference of
the grid voltage at the point of common coupling (PCC). The three grid side inductor currents are
transformed using dq synchronous reference frame to
and
.
and
are then
compared to the
which adjusts the active power and the
for zero reactive power,
respectively. The generated errors are then passed through the current controller (PI controller) to
generate the voltage references for the inverter. To get a good dynamic response and also to have a
voltage output during no load,
and
are both fed forward. The generated reference voltages
in dq axis are transformed back into a stationary frame that can be used as command voltages to
generate high frequency PWM voltages. In order to better understand and analyze the system stability,
the system has to be modeled so that the system transfer function can be derived. All the equivalent
series resistances of the passive components including the inverter side inductor
, grid side inductor
and filter capacitor C are neglected as they provide a certain degree of resonance damping and thus
would elevate the overall system stability. Therefore the system without passive resistances represents
the ‘worst case’ during design.
Linv
Lg
Iinv abc
Vg PCC
Ig abc
AC
Vdc
AC
AC
PWM
C
Iq_ref=0
Id_CC
Vd_CC
Vq_CC
abc
dq
abc
DSP
Sin_Cos
Sin_Cos
Id_CC
Ig_abc
DSP Controller
PWM
++
Current Controller
Iq_CC
LCL Filter
dq
PI
+-
3-Phase
Load
3-Phase
AC Grid
Vg_abc
Id_ref=1
Vg PCC
Ig abc
Breaker
Switch
Vg_abc
PLL
abc
Iq_CC
Sin_Cos
Vd_CC
dq
Vq_CC
Fig.1 LCL filter based grid connected VSI (hardware and control scheme)
34 | P a g e
Table 1: System parameters used for simulation and modeling
Parameter
Value
Nominal Power
10 kW
Switching frequency
10 kHz
DC link voltage
800 V
Grid voltage (L-N)
240 V
Line frequency
50 Hz
𝐿𝑖𝑛𝑣 (filter)
4 mH
𝐿𝑔 (filter)
2 mH
C (filter)
5 µF
𝜔𝑟𝑒𝑠
1949 Hz
PI current controller
𝑘𝑝 = 0.031 , 𝑘𝑖 = 9.16
Damping gain
𝑘𝑑 = 0.051
p.u attenuation factor (p.u af)
2 × 10000/(3 × 240)
PI current controller*
𝑘𝑝 ∗ = 0.6 , 𝑘𝑖 ∗ = 180
Damping gain*
𝑘𝑑 ∗ = 1
𝑡𝑑 (time constant of HPF)
1/2𝜋(1135𝐻𝑧)
𝑇𝑆 (controller time delay)
50µs
*Gains when current is considered as per unit (p.u) value
Fig.2 (a) whose open loop transfer function
, can be written as (1) in the frequency domain,
represents the block diagram of the undamped LCL filter with the inverter bridge. The average model for
the inverter bridge is represented by a gain of
that is applied to the PWM signal reference.
(1)
where
is the dc link voltage,
is the normalized modulating signal,
is the grid side indcutor
current.
Using the parameters listed in Table 1, the bode plot of the transfer function in (1) can be seen in
Fig.2(b). It shows a sharp peak at the resonance frequency that needs to be compensated in order to
have a flattened low pass response. Applying unity feed back to (1) results in a characteristic equation of
whose denominator has a polynomial without the
term. Therefore, the overall closed loop
system is unstable according to Routh’s stability criterion which is also confirmed by the bode plot
analysis and would require additional damping to stabilize the system. Passive damping is avoided due
to the additional losses and a new improved active damping method needs to be introduced.
In Fig.1 the grid side inductor current , is already being sensed and fed to the current controller for
control purposes. Therefore, to minimize the number of additional sensors, the very same controlled
current shown in Fig.1 can now be used to damp the LCL resonance actively. This is done by modifying
the block diagram in Fig.2 (a) to look like the block diagram in Fig.3(a).
As discussed, in order to stabilize the overall closed loop system, a finite term needs to be introduced
into the denominator. This can be done by calculating the second derivative of the controlled current
35 | P a g e
which passes through a damping gain , and adding it to the modulating signal
transfer function that can be written as
. This then leads to a
(2)
(3)
Due to the noise in any measured signal, especially when using digital controllers such as digital signal
processor (DSP), the calculation of derivatives does not lead to a reasonable result. Therefore the
proposed feedback loop is introduced within the current controller with no additional sensors.
The controlled current
passes through a damping gain
which is then filtered using a first order
HPF. The HPF can be realized as a subtraction of
and their low pass filtered signals using a
LPF, which guarantees delay less higher harmonics. The transfer function of the HPF is the transfer
function of 1-LPF which can be written as
, where
is the time constant.
Vm
V dc
2
Vinv
+
-
Iinv
1
L inv s
+
-
Ic
Vc
1
Cs
1
Lgs
Ig
Bode Diagram
(a) Block diagram
Magnitude (dB)
200
150
100
50
0
Phase (deg)
-270
-315
-360
-405
-450
1
10
2
10
3
Frequency (Hz)
10
4
10
(b) Bode plot
Fig. 2 Undamped LCL system
The higher harmonics signal is then added to the modulating signal
transfer function now can be written as
as shown in Fig.3 (a). The new
(4)
36 | P a g e
The new damped LCL transfer function
constitutes, a fourth order polynomial which
contains all orders of the term and can be derived as
(5)
The modified bode plot of the open loop transfer function in (5) can be seen in Fig.3(b). Parameters
listed in Table 1 are used to retrieve the bode plot. The positive peak at the resonance frequency
,
in the undamped LCL system has now been damped and the gain in the low frequency range (below
) is un-altered, while the phase in the low frequency range (below
) has been altered. This
altered phase for frequencies below
stabilizes the closed loop system controller. It can be further
noticed that there is no change in gain or phase at higher frequencies above
guaranteeing
attenuation of higher order harmonics required by the inverter.
An important phenomenon of the proposed damping technique is observed before proceeding with the
design procedure. From (5) it can be seen that the
can have an impact on the stability besides the
damping parameters and if the other design parameters are fixed. It is understood that a good
link controller can avoid any impact, but in order to analyze the effect of
on the damped LCL system,
bode plots with different
levels have been plotted in Fig.4. It is noted that a decrease in
level
stabilizes the controller while an increase in the
level will make the system unstable. A
of up to
1200V can be tolerated to damp the LCL oscillations according to Fig.4 for this specific design.
Further, it can be noted that the control bandwidth cannot exceed or even approach close to resonance
frequency
, as it will create a
phase lag, which results in and inadequate phase margin for
closed loop control. Non negligible delays caused by digital sampling and pulse width modulation would
also further constrict the system’s gain cross over frequency .
Table 2: Different
C[µF]
5
10
15
20
𝝎𝒓𝒆𝒔 [kHz]
1.949
1.378
1.125
0.974
Therefore, as suggested in Fig.4,
is chosen such that it is
. Value of
will only be required
if the proportional and integral gains are derived using mathematical calculations. Since ideally, line
frequency currents are expected to be injected into the grid. This chosen
is fairly a conservative value
to avoid interference between the ‘maximum harmonics of current that needs to be controlled’ and
‘resonance damping’. The choice of
is such that it is below half the switching frequency, i.e. to give
sufficient harmonic attenuation of the current around switching frequency and it should be high enough
to give a larger controller bandwidth. The latter can be confirmed by plotting the bode plots of (5) with
37 | P a g e
different
,by changing only the filter capacitor values according to Table 2. Fig.5 shows that the
bandwidth of the system reduces with
, while the attenuation of high order harmonics increases as
expected.
Vm
V dc
2
+
+
Vinv
HPF
1
-
+
Iinv
+
L inv s
td s
td s  1
-
Ic
1
Cs
Vc
1
Lgs
Ig
kd
Bode Diagram
(a) Block diagram
Magnitude (dB)
80
60
40
20
0
-20
-40
-90
Phase (deg)
-135
-180
-225
-270
1
2
10
3
10
4
10
10
Frequency (Hz)
(b) Block diagram
Fig. 3 Damped LCL system
Bode Diagram
800V
Magnitude (dB)
150
400V
1200V
100
1500V
50
Controller bandwidth
region for
stable operation
0
-50
Phase (deg)
-90
-135
-180
-225
-270
0
10
1
10
2
10
Frequency (Hz)
3
10
4
10
Fig.4 Bode plots of damped LCL with different Vdc link levels
38 | P a g e
Bode Diagram
Magnitude (dB)
80
60
40
20
0
-20
Phase (deg)
-40
-90
-135
C=5uF
-180
C=10uF
C=15uF
-225
C=20uF
-270
1
2
10
3
10
10
Frequency (Hz)
4
10
Fig.5 Bode plots of damped LCL with different
Finally the systems open loop transfer function
derived using the PI current controller
as
(block diagram shown in Fig.6 (a)), can be
, a 1.5 times sampling and transport delay that is modeled
in the forward path and
as
(6)
(7)
The gains
and
shown in Table 1 are for model with real current values. If per unit (p.u) values
are used within the controller with a base power of
,
and
factor (puaf). Values of the gains
,
and a base voltage of
, then the gains
are calculated using the p.u attenuation
and the puaf are all given in Table 1. The gains
and
are initially found out by manual trial and error tuning for the current controller with passive resistances
in series with the capacitor filter (passive damping). Values of the gains
and
can also be
calculated using (8) and (9) [14].
39 | P a g e
Iref
+
kp 
-
ki
s
1.5Ts
Delay
+
+
Vm
Vinv
V dc
2
+
+
+
Vg
HPF
+
L inv s
td s
td s  1
-
Ic
Vc
1
Cs
1
Lgs
Ig
kd
(a) Block diagram
(a) Block diagram
Bode Diagram
Bode Diagram
Gm = 3.38 dB (at 1.53e+003
, Pm
50.1
deg (at 573
Hz)
Gm =Hz)
3.38
dB=(at
1.53e+003
Hz)
, Pm = 50.1 deg (at 573 Hz)
100
100
50
Magnitude (dB)
Magnitude (dB)
Iinv
1
-
0
-50
50
0
-50
-180
-100
-90
-270
-180
Phase (deg)
Phase (deg)
-100
-90
-360
-450
-540
0
10
-270
-360
1
-450
10
-540
2
3
10
Frequency (Hz)
0 plot
(b) Bode
10
4
10
1
10
10
2
3
10
Frequency (Hz)
10
4
10
(b) Bode plot
Fig. 6 Actively damped LCL system with current controller loop model (PI +1.5Ts + damped LCL)
(8)
(9)
The calculated values for the gains
manually tuned values (
and
and
(
and
) are comparable with the
). The finally chosen values for the gains are the
manually tuned ones as they provide a faster current tracking response with slightly increased integral
gain. Once the gains
and
are finalized, then the passive damping is removed and the new active
damping loop is added to the current controller. Then
such that the phase margin of the transfer function
is set to 1 and of the HPF is simply tuned
is at least
. A stable bode plot of (7) can
be confirmed in Fig.6 (b).
40 | P a g e
III. SIMULATION RESULTS
Simulation was carried out in the Matlab/Simulink environment, based on the system shown in Fig.1 and
the parameters given in Table 1. The aim was to examine the performance of the proposed active
damping method with p.u current information and to validate the gains
and
in simulation
against the designed model. The damping gain
and the time constant
of the HPF were derived for
the system whose specifications are given in Table 1 and needs further validation on simulation. The
10kW inverter supplies 5kW of power required by the parallel RLC load resonating at 50Hz (
)
and the rest is injected into the grid. Therefore, 0.5 p.u current is injected into the grid. Fig.7 shows the
results of the undamped LCL system which shows oscillations in the grid side inductor current and the
injected grid current with high amplitude as expected. The oscillations can also be observed at the filter
capacitor voltage and current. For simplicity, results of only phase A in per unit (p.u) values are shown in
Fig.7 and Fig.8. Fig.8 shows the results of proposed actively damped LCL system which shows the
oscillations have been well damped by the modified current controller. The THD of the grid side inductor
current is 2.6% at 1p.u. i.e. when the system is operated at full load. The system is again operated with
50% load (0.5 p.u) and the THD is 4.5%. It can be seen that THD of the injected grid current (difference
between the grid side inductor current and the load current) is slightly higher due to the resonating
load. In order to achieve better current THD of the grid side inductor current, the switching frequency
can be increased or analogue PWM generation is suggested.
1
0
-1
(a) Grid voltage
100
0
-100
(b) Injected grid current
200
0
-200
(c) Capacitor voltage
200
0
-200
(d) Capacitor current
100
0
-100
0
0.02
0.04
0.06
(e) Grid side inductor current
Time(s)
0.08
0.1
Fig. 5 Simulation results of the undamped LCL system
41 | P a g e
1
0
-1
(a) Grid voltage
0.5
0
-0.5
(b) Injected grid current
1
0
-1
(c) Capacitor voltage
0.2
0
-0.2
(d) Capacitor current
1
0
-1
0
0.02
0.04
0.06
(e) Grid side inductor current
Time(s)
0.08
0.1
Fig.6 Simulation results of the actively damped LCL system
IV. CONCLUSION
This paper discusses the active damping techniques in the literature that either use extra sensors to feed
back certain parameters or use high order filters if no sensors are used. An active damping technique
that uses the existing grid side inductor current information along with a simple 1st order high pass filter,
which is realized using a low pass filter is introduced. This can act as a plug and play feature within the
existing voltage oriented current controllers in order to damp the LCL oscillations without any losses.
The stability of the LCL system with and without the damping technique is discussed, i.e. using the plant
and controller model transfer functions in s domain along with their respective bode plots. A simple
design procedure to tune the parameters of the controller and the damping loop that ensures proper
damping of LCL oscillations is given. Simulations carried out, validate the current controller parameters
against the designed model. Also the impact of different
link levels and
on the stability of the
damped LCL system is analyzed using bode plots and discussed.
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45 | P a g e
Appendix-3: Interline-PV System (PIs: Dr. V Khadkikar and Dr. J Kirtley; MI
Graduate Student: Ahmed Mowwad)
This research work has been submitted for the possible publication in IEEE Transactions on Power
Delivery. The submitted paper work is attached for the further reading.
A New P-Q-V Droop Control Method for Interline Photovoltaic (I-PV)
Power System
Ahmed Moawwad, Vinod Khadkikar and James L. Kirtley
Abstract—This paper proposes a new droop control method for an interline photovoltaic (I-PV) system.
In an I-PV system, the inverters in PV plant are reconfigured in such a way that two or more distribution
networks/feeders are interconnected. The I-PV system is operated as a FACTS (flexible AC transmission
system) device to regulate the point of common coupling (PCC) voltage on either feeder. One of the key
features of I-PV system is that the real power can be exchanged between two feeders via PV plant
inverters. A P-Q-V droop control method is thus proposed, especially for system with low X/R ratio, to
facilitate simultaneous active and reactive power control to regulate the PCC voltage. A lookup table
based approach is developed and implemented to determine the P and Q droop coefficients. The
MATLAB/ Simulink based simulation model is developed to evaluate performance of the system with the
proposed controller.
Index Terms—Droop control, interline power system, active and reactive power control, voltage
regulation, photovoltaic power generation and control.
INTRODUCTION
Photovoltaic (PV) and wind power plants are considered as promising solutions to produce clean electric
energy. Their penetration in the electric network is increasing because of government policies and due
to continuous improvements in the solar cells and wind turbines technologies (Yoshino, Amboh et al. 4-7
July 2010; Reed, Grainger et al. 19-22 April 2010; Sheng, Liu et al. 2010; Borgstrom, Wallentin et al.
2011). The impact of such plants should be assessed because large-scale penetration of these renewable
power plants may affect the normal operation of the power distribution systems (Enslin and Heskes
2004; Zavadil, Miller et al. 2007; Walling, Saint et al. 2008; Barbosa, Rolim et al. Sep 1998 ).
When connected to the grid, large-scale PV/ wind power plants mainly inject active power. While in
islanding mode these power plants should inject both active and reactive power to support load
requirements. Most recent research works assign different tasks for grid-connected power plants to do
more than injecting active power. These plants can generate reactive power, either capacitive or
46 | P a g e
inductive, to regulate the point of common coupling (PCC) voltage, and/or harmonic filtering (Wu, Nien
et al. 2007; Flores, Dixon et al. 2009; Varma, Khadkikar et al. 2009; Patel and Agarwal 2010). Therefore,
it is more beneficial to control active and reactive power injected from these large-scale power plants.
Several control techniques have been developed to achieve active and/or reactive powers, such as,
master-slave control method (Chandorkar, Divan et al. 1993), power deviation control method (Chen
and Chu 1995), and frequency - voltage droop methods (Yao, Chen et al. 17-21 June 2007 ; Chandrokar,
Divan et al. 20-25 Jun 1994 ; Hanaoka, Nagai et al. 23-23 Oct. 2003 ; Arias, Lamar et al. 24-28 Feb. 2008 ;
Guerrero, Matas et al. 2006).
Flexible AC Transmission Systems (FACTS) devices are widely used to enhance the quality of power
system networks. Among useful FACTS devices are the Static Synchronous Compensator (STATCOM),
Unified Power Flow Controller (UPFC), and Interline Power Flow Controller (IPFC) (Aminifar, FotuhiFiruzabad et al. 1-3 Dec. 2008; Gyugyi, Sen et al. 1999; Hingorani, Gyugyi et al. 2000). The IPFC connects
more than one electric network together using back-to-back inverters. These back-to-back connected
inverters can control the power flow (both active and reactive) through series connected transformers.
Such a system configuration gives an opportunity to improve overall system performance (Hingorani,
Gyugyi et al. 2000).
In (Khadkikar and Kirtley 24-29 July 2011 ), we have introduced a new concept and system configuration,
called ‘Interline-PV’ (I-PV) system. An I-PV system interconnects multi-line transmission or distribution
networks using PV plant inverters. Unlike IPFC, in I-PV system two or more feeders or networks are
interconnected through shunt-connected inverters. The I-PV system can have various applications, for
example, feeder voltage regulation, load reactive power support, real power management between two
feeders and overall system performance improvement against dynamic disturbances.
The droop method is a very effective technique to control inverter based PV and wind power plants. It
tends to enforce automatic load sharing between plants and extends the operating range of inverter
active and reactive power with given ratings [13]. It was first introduced and used to control voltages of
conventional generating units over the transmission system network (Bergen 1986). Transmission
networks are generally characterized by high X/R ratio. To the extent that resistance values of these
networks can be neglected compared to their inductance values, conventional droop controllers used
for these systems rely more on the inductive nature of the lines. For such systems, the Q-V droop is very
popular technique to control the PCC voltage magnitude (De Brabandere, Bolsens et al. 2007). A second
droop method is the P-ω droop that can be used to control the frequency of the system in isolated
mode.
For distribution networks equipped with underground cables, the resistance cannot be neglected with
respect to the reactance of feeder. This yields to low X/R ratio, which causes a coupling effect between
active and reactive power. Therefore, for low X/R ratio systems, the Q-V droop method cannot achieve
the required voltage regulation. In (Yao, Chen et al. 2011), the authors suggest the use of active and
reactive power to overcome the aforementioned coupling effect for low X/R ratio system. However, it
47 | P a g e
takes into consideration the same droop coefficients for active and reactive power. This approach thus
may not be sufficient for voltage regulation for I-PV systems.
This paper proposes a new droop control method called as “P-Q-V droop controller” for I-PV system
where both active and reactive powers are used to control the PCC voltage. The necessary active power
for the compensation is drawn from the interconnected feeder via the PV solar plant inverters. The
controller is designed to circulate the minimum active power between the two feeders. The active and
reactive power droop coefficients are adjusted online through a lookup table based on the PCC voltage
level.
SYSTEM CONFIGURATION
Fig.1 shows a two-feeder distribution system in which feeder-1 and feeder-2 are considered to be
located close to each other. A large-scale PV solar power plant is connected at feeder-1. The PV plant
inverters are reconfigured in such a way that the two feeders could be interconnected with each other.
This configuration is addressed as Interline-PV (I-PV) system (Khadkikar and Kirtley 24-29 July 2011 ). The
two inverters are connected back to back through switch SD3. To operate the PV plant as I-PV system,
switches SA, SB1, SA1, SD1, SA2, SB, SD2 and SD3 are closed, while switch SB2 is kept open. During night-time
when the PV solar plant does not produce real power, switches SD1 and SD2 can be opened.
SC
Z eq1
SB
VS 1
L11
S A2
T -2
SD3
S B1
T -1

Feeder-1
S A1

PCC-1
iS 2 VS 2
Inv-2
SA
V pcc1
SD 2

iS 1

SB 2
Inv-1
L21
S D1
PCC-2
V pcc 2
PV Solar Plant
Feeder-2
Fig. 1 Interline-PV (I-PV) power plant system configuration.
For distribution systems, the resistive values of the feeders are taken into account with respect to the
reactance values of the feeders, and considered as low X/R ratio feeders. Fig.2 shows Thévenin
equivalent of feeder-2 (Vth  0, Zth = Rth+ jωLth) connected to inverter-2 (Inv-2) of the I-PV power system,
48 | P a g e
represented as power source (EPV  ). The Zth represents the feeder as well as inverter coupling
impedance. In Fig. 2,
and
represents the phase angle difference between PCC and grid voltages, whereas,
represents impedance angle due to Zth. The active and reactive power flow (S = P +jQ) from
inverter-2 (the power source) to feeder-2 (the grid) are controlled through the below equations:
(1)
(2)
EPV φ
Zth ϴ
jωLth Rth
Vth 0
S = P+jQ
Fig. 2 Thévenin equivalent circuit considering feeder-2 and inverter-2.
Usually the phase difference
between the PCC and grid voltages is very small, that is, cos ≈ 1, and sin
≈ . Hence, (1) and (2) become:
(3)
(4)
Equations (3) and (4), show the dependency of delivered active and reactive power on the impedance
angle and the phase difference angle .
DIFFERENT DROOP CONTROLS
Two conventional droop methods to regulate the PCC voltage are P-V and Q-V methods.
A].
P-V droop control method
This method is convenient for the feeder with predominant resistive value where the reactance of the
line can be neglected with respect to the resistance of the line. This makes the impedance angle
equals to zero. Hence, (3) yields that the active power delivered by the inverter is proportional to the
49 | P a g e
voltage difference (EPV – Vth), i.e. proportional to the inverter EPV. The reactive power of inverter-2 is
proportional to the phase difference , i.e. proportional to the frequency ω of the system.
Fig. 3 shows the polar plot for (3) and (4) with pure resistive impedance for different values of the
voltage magnitude EPV and phase difference angle . The polar radii denote the values of active and
reactive power, whereas, the polar angles denote the values of the phase difference angle . It should
be noticed that
is varying within small range as stated before.
 Effect of changing on P and Q:
(i) P remains constant irrespective of any change in (represented by an arc which has the same
radius).
(ii) Q significantly changes with different polar angles .
 Effect of changing EPV on P and Q:
(i) P significantly increases with increase in EPV (represented by arcs with different radii for different
values of EPV).
(ii) There is hardly any change in Q due to the changes in EPV as shown in the zoomed part of Fig. 3.
Fig.3 Polar plot for the inverter P and Q injected to the system with pure resistive impedance. Real
power is red. Reactive power is blue.
Fig. 4 shows the P-V droop characteristics of an inverter with different loading. The load lines: Load 1,
Load 2, and Load 3 represent different operating points with corresponding PCC voltages V1, V2, and V3,
respectively. The droop characteristic intersects the load characteristics to get the new operating points
of PCC voltages V’2 and V’3 with corresponding active power injected or absorbed by the inverter as P’2
and P’3, respectively. It should be noticed that the active power injected or absorbed by any inverter is
circulated between the two feeders (feeder-1 and 2). In I-PV system, this active power will be taken
from or injected to the other feeder.
50 | P a g e
V
V2
Droop characteristics
V’2
V1
V3
P’3
Load 2
Load 1
Load 3
V’3
P’2
Injected
P
Absorbed
Fig.4 P-V droop characteristics for the system with pure resistive impedance.
B].
Q-V droop control method
For high X/R ratio systems, where the reactance of the line is predominant over the resistance,
impedance angle θ goes to 90o. The reactive power of the inverter is proportional to the inverter voltage
EPV and the active power is proportional to the frequency ω. The polar plot for (3) and (4) for pure
inductive impedance is shown in Fig. 5.
 Effect of changing on P and Q:
(i) P significantly changes with different polar angles .
(ii) Q remains constant regardless of any change in angle
same radius).
(represented by an arc which has the
 Effect of changing EPV on P and Q:
(i) There are hardly any changes in P due to the changes of EPV as shown in the zoomed part of Fig.
5.
(ii) Q significantly changes when EPV increases (represented by arcs with different radii for different
values of EPV).
The Q-V droop control method is one of the widely used methods for voltage regulation. Unlike the P-Q
droop method where additional provision for real power is required; Q-V droop method does not need
such a source of real power for generating the necessary Q for compensation.
51 | P a g e
Fig. 5 Polar plot for the inverter P and Q injected to the system with pure inductive impedance. Real
power is red. Reactive power is blue.
PROPOSED P-Q-V DROOP CONTROLLER FOR I-PV SYSTEM
The power distribution networks may contain feeders with complex impedances, where neither
reactance of the line nor the resistance can be neglected with respect to each other. In some cases, the
resistance of the line may equal or even more than the reactance of line, giving a low X/R ratio feeder
system. Such a kind of situation where X/R ratio is small (close to 1), neither the P-V nor the Q-V droop
method may be sufficient to regulate the PCC voltage. Fig. 6 shows the polar plots for active and
reactive power with a complex impedance system. It is shown that active and reactive power is affected
by the changes in voltage magnitude EPV and the phase difference angle simultaneously.
The I-PV system has the advantage of circulating active power between two adjacent feeders through
back-to-back connected inverters. Furthermore, these inverters, with proper control, can also inject
reactive power while circulating the active power. Thus, the I-PV system configuration may be
considered as one of the possible solutions for voltage regulation in low X/R ratio feeder systems. In
order to achieve the desired PCC voltage regulation, a new droop control method is proposed in this
paper in which both active and reactive powers are used. Since both active and reactive powers are
utilized for voltage regulation, the proposed droop method is called as “P-Q-V droop control”. Two
different droop coefficients, namely, nd for active power and md for reactive power, are thus estimated
according to PCC voltage levels to achieve the P-Q-V droop controller objectives. However, in this
approach, the desired performance should be achieved with the least possible active power circulation
to insure minimum voltage variation on the other feeder. In the proposed method, a lookup table
approach is developed to circulate the minimum active power between two feeders.
52 | P a g e
Fig. 6 Polar plot for the inverter P and Q injected to the system with complex impedance. Real power is
red. Reactive power is blue.
For electric systems with complex impedance, both active and reactive power (P, Q) affect the voltage
magnitude (V). Such systems can be represented by the following equation:
(5)
Where Vpcc is the voltage before compensation, while nL and mL are the electric load droop coefficients.
Load characteristics (i.e. Eq. 5)
V
Line1
Vpcc
Droop characteristics (i.e. Eq.6)
-Q
+P
0
+Q
-P
0
Fig. 7 P-Q-V droop characteristics for the system with complex impedance.
53 | P a g e
The droop characteristics for the proposed P-Q-V droop method are represented by:
(6)
Where, Vref is the desired reference value of the PCC voltage, in this case 1 pu. nd and md are the active
and reactive power coefficients for the proposed P-Q-V droop method. Equations 5 and 6 are plane
functions and they are plotted as shown in Fig. 7. The droop characteristic intersects the load
characteristics in Line1 as shown in Fig. 8. Line1 contains the new operating point of the PCC voltage
after regulation.
Line1 can be obtained as follows.
Step-1: The normal vectors of the two planes (i.e. Eq.5 and Eq.6) are determined as given below:
(7)
(8)
Step-2: The cross product of both N1 and N2 yields a vector, named as U and is perpendicular to both
N1 and N2. This vector represents the direction vector of Line1 as shown in Fig. 8.
(9)
54 | P a g e
Fig. 8 Graphical comparison between the three droop methods.
Step-3: The direction vector has to stem from a point called as position vector and is referred to Ao (Fig.
8). This point can be obtained by putting P = 0 in (5) and (6), then solving for V and Q:
(10)
(11)
Step-4: Knowing both position and direction vectors, Line1 can be fully determined as follows:
(12)
Where s is an arbitrary constant.
Similar steps can be applied to express Line2 shown in Fig. 8 as follows:
(13)
Where Bo is the position vector, L is the direction vector of Line2 and t is the arbitrary constant.
Step-5: The new operating point after compensation lies on a line that is perpendicular to both Line1
and Line2. Such a line represents the shortest distance. This shortest distance between Line1 and Line2
can be calculated by Eberly (Eberly 2004) as follows:
(14)
Where |d1| is the shortest distance between line1 and Line2, sS and tS are the values of the arbitrary
constants at the shortest distance.
Step-6: d1 is perpendicular to both; U and L (Fig. 8). Thus, sS and tS can be calculated using the following
relations:
(15)
Substituting (14) into the above relations:
55 | P a g e
(16)
(17)
Considering,
8)
Solving for sS and tS:
;
(19)
Step-7: The new operating points Z3 and
shown in Fig. 8, can be expressed by:
(19)
(20)
Fig. 8 also shows a 3-dimension comparison between the three different droop control methods
mentioned above. For simplified discussion, the X/R ratio of the system is considered as 1. Inverter
capacity is defined as 1 pu on 1 MVA base. The point Vpcc is the PCC voltage before compensation. Points
Z1 and Z2 are the new operating points after compensation using P-V and Q-V methods, respectively.
Since the X/R ratio of the system under discussion is 1, both PV and Q-V droop methods will inject equal
amount P and Q to compensate the PCC voltage, in this case full inverter rating of 1 pu for example. The
new operating voltage point after compensation is depicted as point
. For this same system, to
regulate the PCC voltage from Vpcc to
the proposed P-Q-V droop control will utilize 0.707 pu active
as well as 0.707 pu reactive power. The point Z3 in Fig. 8 represents the new operating point using the
proposed P-Q-V droop controller. In other words, almost 30% of inverter rating can be utilized to
regulate the PCC voltage below
operating point. Thus, the proposed P-Q-V droop control method
may give better system voltage regulation in low X/R system.
CONTROL DESIGN FOR THE P-Q-V DROOP METHOD
In this section the I-PV inverter control algorithm with the proposed P-Q-V droop method is developed
and is shown in Fig. 9. The algorithm uses a decoupled current control strategy utilizing both direct and
quadrature components. It consists mainly of outer and inner current loops. The controller is initialized
by calculating the difference between the reference voltage Vref and the measured PCC voltage. It passes
the output signals through PID controllers to generate Id,ref and Iq,ref (compensating current in d-q frame).
The inner current loop is used to regulate the direct and quadrature components of the inverter output
current, passed through PI controller to produce the corresponding reference voltages Vd,ref and Vq,ref. A
voltage loop is used to get the ABC frame of Vd,ref & Vq,ref and produce the reference signals V*abc & Ф for
PWM operation of the inverter.
56 | P a g e
V*abc
Vd,ref
Voltage
Loop
Vq,ref
PWM + PV
Inverter
Φ
Sin ωt
Cos ωt
nd
md
Lookup
table
Vref
RMS
PLL
Vabc
Vref
Id,ref
Current
Loop
Iq,ref
PID
+
PID
Iabc
nd from Lookup table
-
Vmeas – nd*P
-
Vmeas – md*Q
+
P
Q
DQ transformation
& power
calculation
Cos ωt
Inner current loop
md from Lookup table
Vref
Sin ωt
From PLL
Outer current loop
Droop controller
Fig. 9 I-PV system control schematic-using P-Q-V droop method.
The park’s d-q transformation is used to calculate the inverter active and reactive powers used in
compensation as follow:
(21)
(22)
Using
,
,
, and
, the active and reactive powers are calculated as follows:
(23)
(24)
The active and reactive powers calculated in (23) and (24) are used with the droop coefficients from
lookup table, to droop the reference voltage by certain amount as shown in the outer control loop of
Fig. 9.
57 | P a g e
The droop coefficients nd and md are determined by calculating the difference between the measured
and reference values of PCC voltage, and comparing it with a predefined limit. Based on this
comparison, the controller starts with reactive power compensation. The droop coefficient md is
obtained first from the lookup table. If the reactive compensation is found to be insufficient to regulate
the PCC voltage within acceptable limit, the controller shifts to use both active and reactive power by
obtaining the new droop coefficients nd and md from the lookup table. In each case the controller
observes the limits of the active and reactive powers (rating of the inverter) to guarantee not exceeding
this limit.
SIMULATION STUDY
A simulation study based on the I-PV configuration illustrates the effectiveness of P-Q-V method to
regulate the PCC voltage.
A].
System under consideration
A power distribution network resembling the two-feeder network configuration and a PV solar plant of
Fig. 1 is considered. The voltage levels of both the feeders are considered as 11 kV. The acceptable range
of PCC voltage variation is considered as ±5%. Inverter-1 and 2 each have a rating of 2 MVA. It is
considered that feeders-1 and 2 can circulate a maximum of 1 MW active power between them through
the PV inverters. This limit is considered to avoid considerable voltage drop on the other feeder from
which the active power is to be taken. The loads on the feeders are considered as P and Q loads, located
at the ends of each feeder and have different values. The voltages Vpcc1 and Vpcc2 represent the PCC
voltages at feeer-1 and feeder-2, respectively. Pinv1, Qinv1, Pinv2 and Qinv2 are the active and reactive
powers injected or absorbed by Inverter-1 and Inverter-2, respectively. The leading reactive powers
supported by Inverter-1 and Inverter-2 are shown as positive quantities, while the lagging reactive
powers are shown as negative quantities.
The simulation results are expressed in per unit (pu), with base voltage of 11 kV and base power of 1
MVA. Appendix-I contains the data used for the simulated system.
B].
Simulation Results
For simplicity, only one feeder voltage, in this case feeder-2, is regulated. The change in PCC voltage
beyond ±5% is achieved by simulating the following scenarios: (i) for voltage rise more than 5% limit,
active power from another renewable source is injected into the system and (ii) for voltage drop below
5%, heavy load is connected to the feeder-2 (without additional active power injection from the
renewable source in the previous condition). The important simulation timelines are listed below:
 t1: Inverter-2 starts operation to regulate the feeder-2 PCC voltage based on P-V, Q-V or P-Q-V
droop methods, with normal loads.
 t2: Feeder-2 PCC voltage is increased above 5% limit due to active power injection from another
source.
58 | P a g e
 t3: Feeder-2 PCC voltage is decreased below 5% limit due to increased load and with no active
power injection from another source.
(i) System Performance with P-V droop method
Fig. 10 shows the performance of feeder-2 for the above mentioned three different conditions. The PCC
voltage is regulated according to the P-V droop control method. Figs. 10 (a) to (d) show the PCC voltage
before and after compensation, active and reactive powers injected by inverter-2, the circulated active
power between feeder-1 and feeder-2, and the apparent power S circulated through inverter-2 with
respect to its rated capacity of 2MVA, respectively.
For the first interval (time = t1 to t2 sec), the PCC voltage is 1.035 pu, and it is reduced to 1.015 pu using
P-V droop method. This reduction is achieved by absorbing 0.6 pu active power through inverter-2 and is
drawn from the feeder-1. For the second interval (time = t2 to t3 sec), the PCC voltage is increased to
1.089 pu and it is regulated to 1.06 pu. This reduction in PCC voltage is achieved by absorbing 1 pu active
power. It should be noted that the inverter-2 could absorb up to 2 pu to regulate the PCC voltage.
However, we have considered a maximum limit of 1 pu for active power injection in order not to
overload the feeder-1 and thus to maintain its voltage within acceptable limit. During the third interval
(time = t3 to 1.4 sec), the PCC voltage falls to 0.925 pu due to heavy load on the feeder-2. In this case,
the inverter-2 injects maximum allowable 1 pu active power to improve the PCC voltage from 0.925 to
0.945 pu. The droop coefficient for this method is 0.02 pu/MW for all the operating conditions.
(a)
Feeder-2 PCC voltage before and after compensation
(b)
Active and Reactive powers of inverter-2
59 | P a g e
(c) Active power circulated between the two feeders
(d)
Apparent power S and inverter-2 limits
Fig.10 Feeder-2 performance using P-V droop control method.
(ii) System Performance with Q-V droop method
Fig. 11 shows the performance of feeder-2 with Q-V droop method. The conditions for the PCC voltage
before compensation are kept identical as that of P-V droop method. During the first interval the voltage
is reduced from 1.035 pu to 1.02 pu [Fig. 11 (a)] by injecting 1.0 pu inductive reactive power through
inverter-2 [Fig.11 (b)]. During the second interval, the PCC voltage is regulated around 1.055 pu. This is
achieved by absorbing 2 pu inductive reactive power capacity of inverter-2 as shown in Fig. 11 (b). The
PCC voltage is raised from 0.925 to 0.948 pu for the third interval by injecting capacitive reactive power
of 2 pu. The droop coefficient for this method is 0.01 pu/MVAR. As noticed from the results of Fig. 11,
the Q-V droop method utilizes the full inverter rating to compensate for voltage rise and voltage drop. A
low X/R ratio system would require higher capacity of inverter to regulate the PCC voltage below the set
margin of ±5%.
60 | P a g e
(a)
Feeder-2 PCC voltage before and after compensation
(b)
Active and Reactive powers of inverter-2
(c) Apparent power S and inverter-2 limits
Fig.11 Feeder-2 performance using Q-V droop control method.
(iii) System Performance with P-Q-V droop method
Fig. 12 gives the performance of the same system with the proposed P-Q-V droop method. During the
first interval, as illustrated in Fig. 12 (a), the PCC voltage is reduced to 1.025 pu by absorbing 0.5 pu
inductive reactive power through inverter-2. The preceding evaluation using the Q-V droop method
suggests that only reactive power compensation may not be enough to regulate the PCC voltage within
the ± 5% limit during the second and third intervals. As viewed from Fig. 12 (a), the PCC voltage is
regulated to 1.04 pu during the second interval. This is achieved by absorbing 1.4 pu inductive reactive
power and 0.8 pu active power [Fig.12 (b)].
61 | P a g e
(a)
Feeder-2 PCC voltage before and after compensation
(b)
Active and Reactive powers of inverter-2
(c) Active power circulated between the two feeders
(d)
Apparent power S and inverter-2 limits
Fig. 12 Feeder-2 performance using the proposed P-Q-V droop control method.
62 | P a g e
Furthermore, for the third interval, the PCC voltage is improved from 0.925 to 0.96 pu. This is achieved
by injecting simultaneous 1.4 pu capacitive reactive power and 0.7 pu active power, as noticed from
Fig.12 (b). The total amount of apparent power S handled by inverter-2 using the proposed P-Q-V droop
method is given in Fig.12 (d). It can be noticed that the inverter capacity is optimally utilized to achieve
better voltage regulation over P-V and Q-V droop methods.
During the first interval, the active power coefficient is 0, as the controller primarily uses the reactive
power for the compensation. In this case the reactive power coefficient is 0.04 pu/MVAR. For the
second interval the active droop coefficient is 0.08 pu/MW, while the reactive power coefficient is 0.018
pu/MVAR. Note that the reactive power coefficient is reduced to absorb as much as possible the
reactive power from the inverter. The active power and reactive power coefficients are noticed as 0.1
pu/MW and 0.024 pu/MVAR during the third interval, respectively.
CONCLUSION
In an I-PV system, the PV solar plant inverters are reconfigured and connected back-to-back to
interconnect two feeders. The I-PV system with proposed P-Q-V system is then controlled as flexible AC
transmission system device to regulate the point of common coupling voltage. It is shown in the paper
that the coupling effect between active and reactive powers due to complex network impedance need
to be considered to achieve adequate voltage regulation. A lookup table approach is used to determine
active and reactive droop coefficients. A MATLAB/Simulink based simulation study has been performed
to evaluate the effectiveness of proposed P-Q-V droop method for the PCC voltage regulation.
ACKNOWLEDGMENT
This work is supported by Masdar Institute under MIT-Masdar Institute joint research project grant.
APPENDIX-I
Feeders-1 and -2 system voltage level, Vs1 = Vs2 = 11 kV.
Line parameters: 0.08 + j0.04 ohm/km.
Line lengths: L11 = L21 = 20 km, L12 = L22 = 4 km.
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Appendix 4: High Efficiency Resonant Power Converter For Solar Power
Applications
Introduction:
The goal of this project is to build a high efficiency dc/dc resonant power converter with
simultaneous near zero current and zero voltage switching at all power levels for a varying
input voltage and fixed output voltage.
In this project we are developing, designing, building and testing a new class of high
efficiency dc/dc resonant power converter that operates with simultaneous zero voltage
switching and near zero current switching across a wide range of input voltages and output
power levels. A converter implementation providing galvanic isolation and enabling large
voltage conversion ratios greater than 1:10 is targeted. The dc/dc converter consists of an
inverter, a transformation stage and a rectifier stage. The three stages have to be designed to
minimize the total power loss (Fig.2).
Figure 2: Block diagram of a dc-dc converter
The converter is designed for connection to photovoltaic panels with varying output voltage
depending on the solar insolation. The input voltage of the converter (from a single solar panel)
will vary from 25-40V and it will have and output voltage of 350-400V. The converter is required
to operate across an output power range of 20-200W.
The topology selected for this project is shown in Fig. 3. It consists of a converter with a
resistance compression network. The converter will operate at fixed frequency with on/off
control to vary the power output. Resistance compression networks [1] consist of inductors and
capacitors which are lossless components. The network not only makes the input look resistive
but also limits the power flow to the output in a desirable manner as the voltage conversion
ratio varies.
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Figure 3: The Resistance Compression Network (RCN) dc/dc Converter
2 Resistance Compression Network Converter
The proposed RCN converter topology is shown in Fig. 3. It consists of a full-bridge inverter (S1S4) operated at fixed switching angular frequency ω. A transformer for voltage up conversion
and isolation, and a Resistance Compression Network terminating in diode rectifiers
(synchronous rectifier may be used instead if desired). Snubbing capacitances (not shown)
enable zero voltage switching, while the resistive load provided by the RCN and rectifier
networks enable near zero- current switching. At resonant frequency ω0 the resonant tank
composed of Lr and Cr acts as a short. Also, the tank is sufficiently high Q to have nearly
sinusoidal current waveforms. The inductor Ls and the capacitor Cs with conjugate reactance
comprise the RCN. They are chosen to limit the power flow as the voltage conversion ratio
varies, and to make the impedance seen by the inverter look nearly resistive. The two diode
half bridges are present for rectification; these may be realized as synchronous rectifiers in
some implementations.
The RCN converter has near zero current switching as the resistance compression network
makes the impedance seen by the inverter look substantially resistive at the fundamental of the
switching frequency. A fundamental harmonic model of the converter is shown in Fig. 4. Here V
x is the fundamental of the input voltage as seen on the secondary side of the transformer. V x is
a function of the input voltage V in and the transformer turns ratio N and is given by:
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Figure 4: Fundamental harmonic model of the Resistance Compression Network (RCN)
dc/dc converter
(1)
The rectifier half bridges can be modeled as equivalent resistors. The effective resistance of the
rectifier is proportional to the output voltage V out and inversely proportional to average power
P delivered to the rectifier [2]:
(2)
Since the output voltage is fixed the effective resistance of the rectifier decreases when the
power increases with increase in input voltage. In our case it varies from 324.2Ω to 3242.3Ω.
The use of a resistance compression network reduces this change in resistance and also limits
the output power.
The input impedance of the RCN transformation stage looks purely resistive and is given by:
(3)
where X is the reactive impedance magnitude of the RCN elements (Ls and Cs) at the switching
frequency. The value of the impedance is selected in such a way so as to limit the output power
to 200W at an input voltage of 25V. Since the power deliver capability of the converter
increases with input voltage, this ensures that the converter can deliver at least 200W across its
entire input voltage range of 25-40V.
The current in each branch is
70 | P a g e
(4)
The effective resistance of the rectifier is
(5)
where V D is the voltage at the diode which is (2/π)V out. Using equation (4)and (5) we get an
expression for RL:
(6)
The power output is thus given by
(7)
So X has been chosen to get 200W output power with 25V input.
(8)
By increasing the input voltage from 25V to 40V the output power increases from 200W to
maximum power. In Fig. 5 transformer turns ratio of 10 has been selected.
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Figure 5: Plot of Power vs. Input voltage
Power can be further modulated by on-off control of the converter at a frequency well
below the switching frequency. Figures 6 and 7 show simulated waveforms for the proposed
converter. The transistors output capacitance was not included in the simulation. In Fig. 6 the
converter has an input voltage of 25V, while in Fig. 7 the input voltage is 40V. For this analysis
the output voltage is fixed at 400V.
Figure 6: Waveforms of voltage and current at 25V input. V(vt2) and Ix: Voltage and current at
primary of transformer. V(n009) and I(D4): Voltage and current at the D4 diode.
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Figure 7: Waveforms of voltage and current at 40V input. V(vt2) and Ix: Voltage and current at
primary of transformer. V(n009) and I(D4): Voltage and current at the D4 diode.
3 First Prototype
The converter was designed with careful selection of components to minimize all the losses to
maximize efficiency. For the first converter the operating frequency was 100kHz and the
experimentally- measured efficiency was 93.5%
3.1 Detailed Design
3.1.1 Transformer Design
To select the transformer turns ratio the tradeoff between the losses in the parasitics of the
transformer and the parasitic resistance of the RCN have to be considered. By increasing the
transformer turns ratio and accordingly increasing reactance of RCN and resonant tank we can
reduce the maximum output power at 40V (8) which reduces the current through the circuit.
Also, the impedance of the resonant tank has to be greater than the RCN so that it does not
greatly affect the resonant frequency of each branch.
Transformer turns ratio of 10 was selected which seems a reasonable tradeoff between the
two losses. Considering the power requirements three core sizes were shortlisted among which
RM10 is the smallest and RM14 the largest. The loss in a transformer can be divided into mainly
core loss and copper loss. A good design usually balances the two to minimize the overall loss.
By increasing the number of turns wound across the transformer core (increasing copper loss)
the magnetic field density can be decreased (decreasing core loss). Figure 9 shows a plot of the
total power loss versus different cores. Although RM14 has the least lost but RM12 has been
selected to tradeoff size and loss.
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Figure 8: Plot of Power vs. Transformer turns ratio (N)
Figure 9: Plot of Power loss vs. the core size
In Fig. 10 the cross-section of one of the core windows is shown. The blue circles represent
the cross-section of litz wire which is used for secondary winding and the black rectangles are
the copper foils which is used for primary winding. The black circles is the cross-section of the
total number of turns of litz wire that can fit in the allocated area. By using MATLAB both
designs in Fig. 10 is optimized to minimize the loss. The number of turns of the windings (which
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corresponds to the length of the wire) and diameter of litz wire (which corresponds to number
of strands of wire) varies in both designs.
(a)
(b)
Figure 10: Cross-sectional of core windows. RM12 and RM14
Ferrite 3F3, 3C90 and 3C94 were considered as possible options. Figure 11 is the plot of
core loss versus the change in temperature. Ferrite 3F3 was selected because it has the less loss
over the entire temperature range of operation and more experimental data for parameter
extraction was available.
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Figure 11: Plot of Power loss vs. materials
The cores loss is given by
(9)
Cm,x,y,ct0,ct1 and ct2are parameters found by curve fitting of the measured power loss data.
f is frequency, Bmax is the maximum flux density and T is the temperature [3]. The design
selected has RM12 core with 8 turns of primary winding and 80 turns of secondary winding. For
the primary copper foil is used which is 0.488 m in length, 254um (10 mils) in thickness and
0.01405m in width. For secondary winding, 40 AWG litz wire is used which is 4.88 m in length
with 30 strands in parallel.
3.1.2 Inductor
For the design of the inductors RM8, RM10, RM12 and RM14 gapped Ferrite 3F3 cores were
considered. There are three inductors in the design of which two inductors of 506uH are for the
resonant tank and an inductor of 372uH is for the resistance compression network. For 506uH
inductor RM12A160 is selected as seen in fig. 7. Some cores are out-right rejected because of
reaching the Bsat limit or thermal limit. They are replaced by zero power dissipation. The total
loss for 506uH inductor is 2.175 W with a maximum current of 2.07A at a maximum input
voltage of 40V. It has 56 turns using a 40 AWG 100 strands litz wire. It is 3.146m in length.
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Although, effort is made to balance the core and copper loss but in this case the core loss is
approximately 3 times more than the copper loss. The core loss can be decreased by decreasing
the B which in turn requires more number of turns (tradeoff between copper and core loss).
However, this also implies increase of gap size to keep the inductance constant. RM12A160
which has the largest gap size (0.058 inches) is used. There is a limit to the increase in gap size
as fringing and leakage becomes dominant. The total loss for 372 uH inductor is 1.1747W with a
maximum current of 1.85 A at a maximum input voltage of 40V. The core used is RM12A160
with 48 turns of wire. The wire is 40 AWG 125 strands litz wire which is 2.928m in length.
Figure 12: Plot of total power loss of 506uH inductor vs. cores of different gaps and sizes at 40V
input
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Figure 13: Plot of total power loss of 372uH inductor vs. cores of different gaps and sizes at
40V input
3.1.3 Transistors
For the full-bridge inverter EPC’s enhancement mode GaN transistors are being used. These
devices have a much lower RQ product (On state resistance x total charge required to turn the
device on and off) compared to the state-of-the-art silicon transistors.
LM5113 has been chosen as the gate driver. It is specially designed for the EPC GaN devices.
It is a 100V bridge driver with an integrated high-side bootstrap diode. It also has under-voltage
lockout capability.
3.2 Experimental Results
The first prototype experimentally-measured efficiency was 93.5% with the transistors
switching at 25% of the peak current.
3.2.1 Components
Components Type
Transistors
GaN HEMTs (EPC 2001)
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Diodes
SiC schottky Diode (C3D02060E)
Transformer
RM12 core , Copper foil and litz wire
Capacitors
MC and MCN Multilayer RF Capacitors
Inductors
RM12A160
Drivers
LM5113
Controller
TMS320F28335
3.2.2 Measurement Setup
The input voltage was provided by HP 6012 A DC power supply with voltage regulation. For the
output load, thick film power resistors of 800Ω of TGH series by Ohmite were used. This
resulted in a power dissipation of 200W. These were mounted on a large heat sink and cooled
using a fan. A power analyzer (Yokogawa WT1800) was used to measure the efficiency. The
converter voltage and current waveforms were obtained using Tektronix mixed signal
oscilloscope (MSO 4054B).
3.2.3 Characterization of the transformer
The transformer built according to the procedure stated above was characterized using an
impedance analyzer (Agilent 4395A). It was found to have a primary side leakage inductance of
0.689uH and mutual inductance at the primary 258.218uH. It has a secondary leakage
inductance of 78.8uH. The capacitance is 3234pF at the primary and 12.8pF at the secondary.
These are shown in fig. 14
Figure 14: Transformer parameters
79 | P a g e
Ringing was observed due to Lsl, Lpl and C2 resonating. This increases the over all loss.
Figure 15: V ds,V gsand Iprimaryat 25V input is shown
3.2.4 Soft switching
In Fig.16 the schematic of an inverter leg is shown. Dds are the body diodes of the switches and
Cds is the drain to source capacitance. This could also represent additional external capacitance.
At turn off the current Ix should be small and postive to reduce the current voltage overlap
which causes power loss. The waveforms in Fig. 17 (a) show the turn off of the bottom switch.
The bottom is turned off when the current Ix is 3.75A. It takes some time for the voltage V ds to
rise to 25V. This overlap causes power loss in the device.
At turn on the capacitor discharges and the current flows through the switch and causes
power loss. In this case, the capacitor should be fully discharged and V dsshould be zero before
the switch is turned on. This can be seen in Fig. 17(b)
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Figure 16: Schematic of inverter leg
(a)
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(b)
Figure 17: Softswitching waveforms. (a) V ds,V gsand Ixfor bottom switch at turn off .(b) V ds ,V gs and Ix
for bottom switch at turn on.
4 Second Prototype
4.1 Detailed design
An important consideration for the second prototype is the operating frequency. The loss
parameters and device area were sweeped over a frequency range of 100kHz to 600kHz to find
the frequency with the minimum total loss. 500kHz was then chosen.
In fig.18 the predicted breakdown of loss is given. With increase in switching frequency the
hard switching loss of the devices increases shown . With the help of carefully designed
magnetics we can soft switch the converter and decrease the total loss. With increase in
frequency, inductor loss and transformer loss decrease as seen in fig. 19 and fig. 20,
respectively.
Figure 18: Power loss vs Frequency. Device loss (Soft switching), Magnetic loss, Total loss and Hard
switched device loss respectively
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(a)
(b)
Figure 19: Inductor loss vs frequency. In part a resonant inductor loss is broken down in to
conductor and copper loss. In part b the compression network converter loss has is given.
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Figure 20: Transformer loss vs frequency
Two EPC GAN devices are being used in parallel to form each inverter switch, which
decreases the total device loss by almost half (fig.21)
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Figure 21: Device loss for 1, 2, 3 and 4 transistors used in parallel to decrease the
conduction loss
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