Download The Impact of the Reactive Power Sharing Methods on Transmission

The Impact of the Reactive Power Sharing Methods
on Transmission Power Losses in Islanded AC
Microgrid
Adam Milczarek
Warsaw University of Technology (Poland)
[email protected]
Abstract—One of the most promising modern electricity
system is microgrid (MG). Usually it based on AC transmission
lines and integrates many renewable energy sources (RES).
RESs are connected to microgrid by power converters, which
allow to active and reactive power management. MG can work
as support for traditional grid as well as stand-alone system for
local loads. One of the topic issues in actual research is reactive
power management. There are proposed solutions in literature
like Equal Reactive Power Sharing, Proportional Reactive
Power Sharing or Optimization algorithm, which minimize the
transmission power losses. However, the reactive power causes
transmission power losses regardless of the chosen control
method. For each solution that losses can be different. It depends
on line distances and the apparent power of each converter. The
analysis of transmission power losses for different power
management methods was performed and described. The
comparison of the results and conclusions are presented in this
paper.
The most important is a primary level, where usually the
droop control method [3]–[6] or Master-Slave control [7]–[9]
are implemented. Due to the fact, that there is only one
voltage control source (VCS) in Master-Slave and others
(Slaves) are current control sources (CCS), this solution is
more popular in MG connected to the main grid. In islanded
MGs the Hierarchical Droop Control [10] is implemented,
which allows to parallel work of many VCS. It is based on
adjust voltage frequency and amplitude of the converters in
order to proper share active and reactive power (Fig. 1).
ω
∆ω1
I. INTRODUCTION
E
E*
ω*
E1
E2
∆ω2
∆ P1
Microgrids (MG) are local power energy systems, which
becoming more important due to increased energy demand
and decreasing fossil fuels. MG can manage energy
generation, storage and demand, making the user less
dependent of the main grid, but more responsible for energy
utilization and generation. This responsibility means that the
microgrid should be able to work in islanded mode of
operation and needs advanced controllers [1]. Moreover, MG
is adapted system for Renewable Energy Sources (RES),
which became the key solution in the energy sector. The
possibility of advanced control and management system
application in microgrid is provided by energy converters,
which are used in almost every RES.
The most used control solution in MG is the hierarchical
control structure. It based on the international standard ISA95 [2], which has been developed for global manufacturers to
be applied in all industries and in all sorts of processes, like
batch, continuous, and repetitive processes. For MGs, it is
divided into three levels: primary control: usually droop
control algorithm; secondary control: adjust frequency and
amplitudes as well as improve power quality in the microgrid;
tertiary control: power flow between the microgrid and the
main grid. On the one hand, the primary control is
autonomous, being able to make the distributed generation
(DG) units work independently in an autonomous way. On
the other hand, secondary and tertiary controls are placed in
the microgrid central controller (MGCC) and needs
communications infrastructure. The communication used
between control levels can enhance the operation of such
system.
∆ P2
P
Q1
Q2
Q
Fig. 1. P-ω and Q-E characteristics in Classical Droop Control.
However, depending on the RES, active power is fixed by
the maximum power point, so that active power cannot be
managed, but it should be store in energy magazines. The
important issue in islanded MG is reactive power managing,
which is investigated and described in literature.
In islanded MG with Classical Droop Control, the reactive
power for each converter depends mainly on the mismatches
between the inverter’s output filters and the control
coefficient n, which can be described as:
n=
∆ E max ,
Q max
(1)
where ∆Emax – maximum voltage amplitude droop, Qmax –
maximum reactive power of converter.
Hence, it is constant value, the reactive power sharing
cannot be controlled, but it will be changing, when the output
current is changing (related to actual active power value). In
order to allow reactive power sharing, the coefficient n can be
replaced by PI controller and the control algorithm at
secondary level calculates reference signals of reactive power
for each converter. Usually the Equal Reactive Power Sharing
method is used, where the total reactive power in MG is
equally divided between all converters [11]–[13]. This
solution allows avoiding the reactive power mismatches and
prevents the circulation of reactive power between converters.
Another solution presented in literature [14], [15] based on
Proportional Reactive Power Sharing, where the total reactive
41
power is divided proportionally to actual active power. In this
case, converters can work with maximum active power,
keeping apparent power below the nominal value. Therefore,
the algorithm prevents overload of converters and circulation
of reactive power, providing better exploitation of RESs. The
different approach to reactive power sharing is transmission
power losses minimization. Usually it is realized by advanced
optimization algorithm like Particle Swarm Optimization [16],
[17]. Hence, the optimization algorithms require high
computational power this solution is difficult to
implementation in real-time control system. However, the
transmission power losses occur for each of the reactive
power sharing strategy and they will be different for each
method.
In this paper, the transmission power losses for islanded
low-voltage AC microgrid are described and calculated for
mentioned reactive power sharing algorithms. In section II the
analysis of transmission power losses in MG is presented. In
addition, the calculations were performed in Matlab and the
results are shown in section III.
2
VSI
VLi1
VRl1
PIos1
PI1+jQI1
II. TRANSMISSION POWER LOSSES
Microgrids are energy systems that usually are built with
low voltage transmission lines, since they integrate many
small RESs, which are installed in urban areas. A general
model of transmission line (Fig.2a) can be simplified for short
distances, as it is shown in Fig. 2b.
2
PI + Q I
(2)
RL ,
2
VI
where: RL – resistance of transmission line, Plosses – power
dissipation of the resistor RL, PI – converter’s output active
power, QI – converter’s output reactive power, VI –
converter’s output voltage.
In islanded MG many converters work parallel and they
share load active and reactive power. Therefore, the
equivalent circuit of MG can be presented by Fig. 3. In that
case, sum of the active power of the first converter PI1 and the
second PI2 has to be equal to sum of load active power PO and
transmission power losses Plos1 and Plos2. Then the load
voltage RMS value Vo is kept at the same level but the
converter’s output voltages VI1 and VI2 are changing,
depending on active and reactive power sharing.
VI1
LI1 II1
RL1
VO
VS1
Plosses =
VS2
VSI
LI2 II2
VLi2
VI2
RO
LO
VRo
VLo
RL2
Po+jQo
VO
VRl2
PIos2
PI2+jQI2
Fig. 3. The equivalent circuit of a one converter with transmission line and
RL load.
In that case, in order to calculate transmission power losses
for each line the equation (2) has to be replaced by:
Fig. 2. Model of a transmission line.
The most important parameter in transmission losses is line
resistance, since the inductance is very low (Table I)
especially at short distances in MG.
Plosk =
APPROXIMATED PARAMETERS OF THE TRANSMISSION LINE [18]
Voltage
range (Vrms)
≤1k
Low-voltage line
Medium-voltage
line
High-voltage line
R (Ω/km)
XL (Ω/km)
0.642
0.083
0.161
0.19
1k – 60k
0.06
60k ≥
2
Plos k =
0.191
Because the inductance can be neglected in losses
calculations the equivalent circuit of one converter with
transmission line and load can be represented by:
VS
VI
LC
RL
VO
RO
LO
VSC
VRl
VRo
VLo
((P
Ik
)
− Plosk ) + QIk ,
2
2
(3)
4
2
2
2 PIk Rk + VO − VO + 4 PIk RkVO − 4QIk Rk
2 Rk
2
, (4)
where: Plosk – transmission power losses for k-th line, PIk –
active power of k-th converter, QIk – reactive power of k-th
converter, VO – load voltage RMS value, Rk – resistance of kth line.
III. RESULTS
Il
VL
VO
2
where the constant load voltage RMS value VO is used
instead of variable converter voltage. Then the final equation
for transmission power losses in islanded microgrid can be
described by:
TABLE I
Type of line
Rk
Based on equation (4) the transmission power losses were
calculated in Matlab. The calculations were performed for
islanded MG model presented in Fig. 3 with detailed
parameters of load shown in Table II. In MG any RES can be
away from point of common coupling (PCC) of few km.
Therefore, the different line resistances have to be considered
in transmission power losses analysis. Moreover, the active
power sharing can be changed depending on maximum power
from each RES, what also has to be considered. In performed
PI+jQI
Fig. 2. The equivalent circuit of a one converter with transmission line and
RL load.
Basing on this model the power losses Plosses for each line
can be calculated as [19]:
42
calculations, the five situations have been included and
described. The transmission power losses have been
compared for equal reactive power sharing (ERPS),
proportional reactive power sharing (PRPS), reactive power
sharing based on optimization of transmission power losses.
The optimization process was performed in Matlab
Optimization Tool, where the equation (4) was implemented
in order to minimize the transmission power losses. Moreover,
the difference between reactive power sharing methods and
optimum solution was shown in percentage absolute values
related to total active power.
TABLE II
differences between analyzed algorithms are only 0.15% what
is a negligible value.
C. Case 3 – Unequal Active Powers and Equal Resistances
The third analysis shows the unequal active powers
PI1=2PI2 with equal 2 km distances between converters and
PCC (similar to case 1). The results are shown in Table V.
The reactive powers are equal for ERPS and optimum sharing,
because line resistances are equal, but in PRPS the reactive
power is proportional to active power and the transmission
power losses are higher. However, the differences between
analyzed algorithms are only 0.07% what is lower value than
in previous case and it can also be neglected.
LOAD PARAMETERS IN CONSIDERED MICROGRID
Parameter
TABLE IV
Value
TRANSMISSION POWER LOSSES FOR PI1=PI2 AND RL1=3RL2
VO = 230 2 sin 314t V
Voltage
EEPS
Current (RMS value)
I O ( rms ) = 10 A
Resistance
RO = 20,7123 Ω
Inductance
LO = 0,0318 H
Active power
PO = 2072 W
Reactive power
QO = 999 Var
Apparent power
S O = 2300 VA
Converter
In first analysis, the equal active powers PI1=PI2 have been
considered with the same 2 km distances between converters
and PCC (RL1=RL2). The results of calculated powers and
losses are presented in Table III. Notice, that in this case, the
reactive powers are equal independently of used sharing
method. It means, that transmission power losses are the same
in each situation.
1
2
PI (W)
QI (Var)
1
499,5
1
499,5
499,5
499,5
499,5
SI (VA)
1150
1150
1150
1150
1150
1150
Plos (W)
32,52
32,52
32,52
32,52
32,52
32,52
Total Plos
(W)
Difference
%
65,04
65,04
65,04
0,00
0,00
0,00
2
499,5
258,5
1036
1036
740,5
SI (VA)
1150
1150
1150
1150
1068
1274
32,52
32,52
32,52
32,52
42,04
19,93
65,04
65,04
61,97
0,15
0,15
0,00
1
Optimization
Tool
PRPS
2
1
2
1
2
PI (W)
1381
691
1381
691
1381
691
QI (Var)
499,5
499,5
666
333
499,5
499,5
SI (VA)
1469
853
1534
767
1469
853
Plos (W)
53,04
17,86
57,81
14,45
53,04
17,86
Total Plos
(W)
Difference
%
1036
499,5
1
Plos (W)
Converter
2
1036
499,5
EEPS
Optimization
Tool
2
1036
499,5
2
TABLE V
TRANSMISSION POWER LOSSES FOR PI1=PI2 AND RL1=RL2
Converter
1
TRANSMISSION POWER LOSSES FOR PI1=2PI2 AND RL1=RL2
TABLE III
PRPS
2
1036
499,5
Total Plos
(W)
Difference
%
A. Case 1 – Equal Active Powers and Equal Resistances
EEPS
1
PI (W)
QI (Var)
Optimization
Tool
PRPS
70,9
72,26
70,9
0,00
-0,07
0,00
D. Case 4 – Unequal Active Powers and Larger First
Resistance
The analysis in fourth case was performed for PI1=3PI2 like
in previous case, but the line resistances were equal to
RL1=3RL2. It means the RES with higher power is located
farther to PCC than the second RES. The results presented in
Table VI shows that PRPS causes the highest transmission
losses, because the majority of active and reactive power is
transferred by larger resistor. However, similarly to previous
cases the differences are negligible.
B. Case 2 – Equal Active Powers and Unequal Resistances
The second analysis presents the equal active powers
PI1=PI2 with the distances 3 km and 1 km between converters
and PCC. In that case (PI1=PI2) there is no necessity to
distinguish which RES is further from PCC, thus only one
possible situation (RL1=3RL2 or 3RL1=RL2) can be analyzed.
The results are presented in Table IV. Notice, in that case the
reactive powers are equal for ERPS and PRPS, because the
active powers are equal, but in optimum solution the reactive
power is sharing proportionally to line resistances and the
transmission power losses are lower. However, the
43
ACKNOWLEDGMENT
Described problems are part of the project number
2013/09/N/ST7/02814 “Development and investigation of
reactive power and energy storage management algorithms in
smart microgrid” funded by the National Science Centre.
TABLE VI
TRANSMISSION POWER LOSSES FOR PI1=2PI2 AND RL1=3RL2
EEPS
Optimization
Tool
PRPS
Converter
1
2
1
2
1
2
PI (W)
1381
691
1381
691
1381
691
QI (Var)
499,5
499,5
666
333
264,2
734,8
SI (VA)
1469
853
1534
767
1407
1009
Plos (W)
79,56
8,93
86,72
7,23
72,92
12,5
Total Plos
(W)
Difference
%
88,49
93,94
85,42
0,15
0,41
0,00
REFERENCES
[1]
[2]
[3]
E. Case 5 – Unequal Active Powers and Larger Second
Resistance
[4]
The last case was performed for unequal active powers
PI1=2PI2 with longer distance between second RES and PCC
(3RL1=RL2). As a result, the lower power is transferred by
higher resistance. In Table VII the results of analysis are
presented. In that case, the PRPS gives similar results like
optimum solution. The differences between transmission
losses for included reactive power sharing method can be also
neglected as above.
[5]
[6]
[7]
TABLE VII
TRANSMISSION POWER LOSSES FOR PI1=2PI2 AND 3RL1=RL2
EEPS
[8]
Optimization
Tool
PRPS
Converter
1
2
1
2
1
2
PI (W)
1382
691
1382
691
1382
691
QI (Var)
499,5
499,5
666
333
747
252
SI (VA)
1469
853
1534
767
1570
736
Plos (W)
26,52
26,79
28,91
21,68
30,3
19,94
Total Plos
(W)
Difference
%
[9]
[10]
53,31
50,58
50,24
[11]
0,15
0,02
0,00
[12]
IV. CONCLUSIONS
[13]
There are different ways to manage the reactive power
sharing in islanded AC microgrid. There can be highlighted
Equal Reactive Power Sharing (ERPS), Proportional Reactive
Power Sharing (PRPS) and Optimization Algorithm. The last
one is to minimize the transmission power losses in microgrid.
However, for each sharing method the transmission power
losses issue is appearing, and the impact of different
strategies on this losses was investigated. The performed
analysis in section III shows, that transmission power losses
are not much different for any control method, hence the
control selection has not significant impact on transmission
losses. Moreover, in AC microgrid the low-voltage
transmission lines are usually used, so the transmission power
losses can be neglected in more complicated simulation
researches.
44
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