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Improvements in Bidirectional Power Flow Balancing and Electric Power Quality of a Microgrid with Unbalanced Distributed Generators and Loads by Using Shunt Compensators .pdf



Original filename: Improvements in Bidirectional Power-Flow Balancing and Electric Power Quality of a Microgrid with Unbalanced Distributed Generators and Loads by Using Shunt Compensators.pdf
Title: Improvements in Bidirectional Power-Flow Balancing and Electric Power Quality of a Microgrid with Unbalanced Distributed Generators and Loads by Using Shunt Compensators
Author: Wei-Neng Chang, Chia-Min Chang and Shao-Kang Yen

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energies
Article

Improvements in Bidirectional Power-Flow Balancing
and Electric Power Quality of a Microgrid with
Unbalanced Distributed Generators and Loads by
Using Shunt Compensators
Wei-Neng Chang *, Chia-Min Chang

and Shao-Kang Yen

Department of Electrical Engineering, Chang Gung University, 259 Wen-Hwa 1st Road, Kwei-Shan,
Tao-Yuan 33302, Taiwan; moonlight7901@gmail.com (C.-M.C.); m0521023@stmail.cgu.edu.tw (S.-K.Y.)
* Correspondence: nchang@mail.cgu.edu.tw; Tel.: +886-3-211-8800
Received: 28 September 2018; Accepted: 20 November 2018; Published: 27 November 2018




Abstract: Improper connections of unbalanced distributed generators (DGs) and loads in a
three-phase microgrid cause unbalanced and bidirectional power flow problems. The unbalanced
DGs and loads may also aggravate the electric power quality (EPQ), such as voltage regulation,
power factor, and unbalanced current and voltage. This increases the difficulty of operation in
a microgrid. In this study, a three-phase, delta-connected, shunt-type universal compensator
was employed for achieving the bidirectional power-flow balancing and improving the EPQ
of a three-phase, distribution-level microgrid with unbalanced DGs and loads. A feedforward
compensation scheme was derived for the compensator by using the symmetrical components
method. In practical applications, the universal compensator can be implemented as static var
compensators (SVCs), static synchronous compensators (STATCOMs), or an additional function
of active filters. With the on-line compensation of the proposed compensator, the bidirectional
power-flow balancing and EPQ improvement in the microgrid were achieved. A demonstration
system was proposed to present the effectiveness of the compensator.
Keywords: bidirectional power flow; distributed generator; electric power quality; microgrid;
performance index; shunt compensator

1. Introduction
In the past few decades, due to the proliferation of renewable energy sources (RESs) and
government policies for a reduction in the use of fossil fuel resources, the microgrid has gained
attention. The concept of microgrid was introduced in 2000 to improve the reliability, sustainability,
and efficiency of modern electric power systems [1]. An increasing number of distributed generators
(DGs) have been incorporated into power distribution systems. DGs include different power generation
units such as wind power, solar power, energy storage, and biomass energy. In a small-scale three-phase
microgrid, low-capacity DGs are connected to the microgrid system in the form of single-phase devices.
Although DGs have some advantages when used in microgrids, due to the unbalance in loads and
uncertainty of power generations in DGs, some issues such as network protection, unbalanced problem,
load shedding, voltage regulation, provision of reactive power, and bidirectional power-flow balancing
should be considered [2–7]. The power generation of DGs is not very stable due to weather conditions.
For example, a wind power unit generates electricity on a windy day. A solar power unit cannot
supply a sufficient amount of electricity on a cloudy day. Therefore, the microgrid suffers the impact of
bidirectional power flow. Moreover, most of the loads mounted on distribution feeders are unbalanced.
For example, residential loads are single-phase loads with a lagging power factor. Excessive inductive
Energies 2018, 11, 3305; doi:10.3390/en11123305

www.mdpi.com/journal/energies

Energies 2018, 11, 3305

2 of 14

loads can cause a voltage drop in the power distribution system. Thus, a microgrid with many
unbalanced loads and DGs causes problems of unbalanced voltage and current, additional power
loss, voltage regulation, and bidirectional power-flow balancing. This increases the difficulty of
operating and managing a microgrid, especially for a microgrid with islanding operation ability.
Hence, it is crucial to maintain the electric power quality (EPQ) and bidirectional power-flow balancing
in a microgrid.
The effects of DGs on distribution systems have been the subject of many research investigations.
Authors in [8] mention the behavior of a microgrid while DGs are in terms of the location of the
connection point, and control strategies are considered for a better system performance. Much research
has been proposed to improve the reliability of microgrids. In [9], a two-stage energy management
strategy for the contributions of local wind power and plug-in electric vehicles in demand response
(DR) programs of commercial building microgrids is addressed, and the power balance can be
achieved between the power supply and the load. To enhance the resilience of a photovoltaic-based
microgrid equipped with battery storage for supplying a typical commercial building, an optimization
is achieved by solving a linear optimization programming problem while the conditional value at
risk (CVaR) is incorporated in the objective function [10]. Authors in [11] propose a heuristically
guided optimization algorithm for the optimum use of existing electrical/thermal resources in home
microgrids (H-MGs). In [12], a smart transactive energy (TE) framework is proposed to maximize the
profit and energy-balancing efficiency of H-MGs. In [13–15], authors explore a reverse power problem
and load-balancing technique in a microgrid. Authors in [16–20] have discussed reactive power control
and voltage regulation issues in microgrids. However, a compensation scheme integrating bidirectional
power-flow balancing and EPQ improvement in a three-phase microgrid is seldom seen.
SVCs and STATCOMs have been frequently used in power distribution systems as load
compensation and voltage regulation devices to enhance EPQ [21–24]. In this study, a shunt-type,
delta-connected universal compensator was developed for improving the operation performance
of a three-phase, distribution-level microgrid with unbalanced DGs and loads. The symmetrical
components method was employed to derive a feedforward compensation principle for the
compensator. For practical application, the universal compensator can be used as SVCs, STATCOMs,
active filters, and a combination of delta-connected reactors and capacitors without using an energy
storage element. The major contribution of this work is that the proposed compensator can easily
achieve the bidirectional power-flow balancing and EPQ improvement caused by unbalanced DGs
and loads in a three-phase, distribution-level microgrid.
Section 2 in this paper describes the structure of a microgrid with unbalanced DGs and loads that is
used as the test system. In Section 3, use of the symmetrical components method derived the feedward
compensation principle for the compensator. A bidirectional power-flow balancing was achieved.
The power quality of the microgrid was also improved using the compensator. Several definitions of
power quality performance indexes used in the study are introduced in Section 4. Section 5 uses the
MATLAB/SimuLink program (R2017a, The MathWorks, Inc., Natick, MA, USA) to implement the
microgrid as the test system. The operation performance of the microgrid with the proposed shunt
compensators was investigated. Section 6 presents the conclusion.
2. The Microgrid Circuit Model
Figure 1 presents a radial-type microgrid with unbalanced DGs and loads. The microgrid is a
three-phase, three-wire, seven buses, radial-type microgrid with unbalanced (single-phase) DGs
and loads. These single-phase DGs are connected between phase b and phase c at Bus 2, 4, 5,
and single-phase loads are connected between phase a and phase b at Bus 2, 3, 4, and 6. The proposed
shunt compensator can be installed on selected buses to improve the EPQ and achieve bidirectional
power-flow balancing.

Energies 2018, 11, x FOR PEER REVIEW

3 of 15

P DG 2  jQ DG 2
Energies 2018, 11, 3305
Energies 2018, 11, x FOR PEER REVIEW

Bus 0

Bus 1

DG

bc

Bus 2

P DG 4  jQ DG 4

Bus 3

Bus 4

DG

bc

Bus 5

P DG 5  jQ DG 5
DG

bc

3 of 14
3 of 15

Bus 6

abc
abc
abc
Three-Phase
abc
abc
abc
DG
5
 jQ DG 5
P DG 2  jQ DG 2
P DG 4  jQ DG 4 P
Power
Source
Cable
bc
ab DG
bc
ab DG
bc DG
Bus 1Line Bus 2
Bus 0
Bus 5
Bus 6ab
Bus 3ab
Bus 4
Three-Phase
Power
Source

abc

abc

abc

abc

P L 2  jQ L 2

Cable

P L 3  jQ L 3

ab

abc

abc

P L 4  jQ L 4

P L 6  jQ L6

ab

ab

ab
Figure 1. Radial-type, three-phase
microgrid with unbalanced distributed generators (DGs)
and
Line
loads.
L2
L2
L6
L6
L3
L3
L4
L4

P

 jQ

P

 jQ

P

P

 jQ

 jQ

The
symmetrical
components
method with
can unbalanced
simplify the
unbalanced
microgrid
Figure
1. Radial-type,
three-phase microgrid
distributed
generators
(DGs) andsystem
loads. for
Figure 1. Radial-type, three-phase microgrid with unbalanced distributed generators (DGs) and
conducting
a
steady-state
analysis.
The
required
compensation
principle
of
the
proposed
shunt
loads.
The
symmetrical
components
method
can
simplify
the
unbalanced
microgrid
system
for
compensator can also be derived. Figure 2 presents the equivalent circuit model between two
conducting
a
steady-state
analysis.
The
required
compensation
principle
of
the
proposed
shunt
neighboring
buses in Figure
1. Equation
(1) can
obtained the
by applying
Kirchhoff’s
Voltage
Law.
The symmetrical
components
method
canbesimplify
unbalanced
microgrid
system
for
compensator can also be derived. Figure 2 presents the equivalent circuit model between
two
l
l
Zaa , shunt
Z
Equation
(2) apresents
the impedance
matrix
of the three-phase
distribution
conducting
steady-state
analysis. The
required
compensation
principle lines,
of thewhere
proposed
bb ,
neighboring
buses in Figure 1. Equation
(1) can bel obtained by applying Kirchhoff’s Voltage Law.
l
compensator
can also be derived.
2 presents
equivalent
circuit model
between
two
Zccl are
Zbcl , and
Zca three-phase
l
l
and
and Zab Figure
, matrix
arethe
mutual
impedance.
general,
theZmutual
Equation
(2) self-impedance
presents the impedance
of the
distributionInlines,
where
aa , Zbb ,
neighboring
buses
in
Figure
1.
Equation
(1)
can
be
obtained
by
applying
Kirchhoff’s
Voltage
Law.
l arecan
l
l distribution
l
impedance
be neglected and
in a Z
power
system [25]. By combining Equations (1) and
and Zcc
self-impedance
l
ab , Zbc , and Zca are mutual impedance. In general, the lmutual
Zaaand
Equation
(2)
presents
the
impedance
matrix
of
the
three-phase
lines,
where (1)
, Z(2),
bb ,
(2),
Equationcan
(3)be
is neglected
obtained. in
Byausing
symmetrical
components
the
sequence
networks
impedance
powerthe
distribution
system
[25]. distribution
By method,
combining
Equations
l
are
by
using
Equation
(4). In
(4),ZTcomponents
is the symmetrical
components
transformation
Zccl (3)
Zabl Equation
Zbcl , and
andderived
are
and
,symmetrical
impedance.
In general,
the mutual
Equation
isself-impedance
obtained.
By using
the
method,
the sequence
networks
are
ca are mutual
−1 is the inverse symmetrical components transformation matrix, as presented in
matrix
and
T
derived
by using
Equation
(4). in
In aEquation
(4), T is the symmetrical
transformation
matrix
impedance
can be
neglected
power distribution
system [25].components
By combining
Equations (1)
and
−1 is
Equation
(5).
and
T
the
inverse
symmetrical
components
transformation
matrix,
as
presented
in
Equation
(5).
(2), Equation (3) is obtained. By using the symmetrical components method, the sequence networks
are derived by using Equation (4). In Equation (4), T is the symmetrical components transformation
2 Bus 2
l
1 Bus 1
V acomponents
matrix and T−1 is the
symmetrical
transformation matrix, as presented in
I a2
V a inverseZ aa
Equation (5).
l
2
L2
l
l
Z bb

1

Bus 1

l
2
Zl
Z ccl aa Z bc II a2
c

1

Z cal

V1
V ca
Vb
V

Z ab I 2
b

Z ca

1

Vb

1
c

Z bbl
Z

l
cc

l
Z ab
I b2

Z bcl

I

2
c

Ia

Vb

2 Bus
DG 2 2
2
VVc a I b

I aDG 2  0
I aL 2

2

Vb

I cDG22 DG 2
V I b I DG 2
DGc
bc

I cL 2  0
I aDG 2  0

I bL 2

Load

I cL 2 two
 0 buses.
Figure 2.
2. Equivalent
Equivalentcircuit
circuit model between
Figure
I cDG 2 model between two buses.
I bL 2
DG 2
I
DG
Load
bc

I abL 2

I abL 2

11
22
22
l
VVa,b,c
−ZZal ,a,b,c
I ,c
 V a,b,c
a ,b , c=
a ,b ,c 
b , c I a , ba,b,c

Figure 2. Equivalentcircuit model between
 two buses.
l
Zlaa
  Z aal
l
Za,b,cl 2=  Z1lba
ZVaa,b,b,c,c VZabal,b,c
 Zlca

ll
l l
ac

ab ZZ
ZZab
ac
l
l 
Zl bb
Z
l2bc

l Z
bbl
bc 
ZZZ
a ,b , c IZal, b, c
l cb
l cc
Z ca Z cb Z cc 
 2   1   l
 2 
l
l
Z aaZ l Z ab
lZ ac Z l
Va
Va
Ia
Zab
aa
ac


l
l
l
 2  2  Z 1l 1  
 2 
l Z bb
lZ bc
l 2
Z







=
a
,
b
,
c
ba
Z
Z
Z
 V b  V a  VVb a   l ba l bb l  bcI a  I b 
  1   Z laa l Zlab l Zlac l 
2 
2
V c V 2  VVc 1   ZZcal ZcaZZcbl ZcbZZccl ZccI 2  I c
b
b
b
ba
bb
bc 

   
  
 2 
 2 
l 
l
l
2
V c22 V1V 1c1  Z ca ZZcbl ZZccl   I Z
l
Va
Ia
c2
a 
aa
ac




ab





l
l
l  I a
−V1 
1 Va −
a
 −1  2 
2 
−1 
1aa Zlab Z ac

Z
l
l






T  Vb  = T 
V b 1 − T  Zba Zbb Z2bc  TT  I b 
2
l
2 V b   1V
1   Zl
l  IZb l  2 
2
2
Zlbbl l Z


Zbccb
l  cc I a
Vc
Ic
V a   VcV a b   balZ l Zca
  2    1   Z aa Z lZ ab Z lZ ac  2   
2 V
cc   

V1 c
 ca  cb
c 1  2 
 b  T 1  Z bal 1 Z bbl 1 Z bcl1ITT
 I b
T 11V b 1  cT11 V
 
 
 
1
l
l
l
1 −1
  2 2



 Z ca 1 Z cb a Z cca2 , a=2 e j2π/3
V, c1T

T =  1 V ca2
=
a


2


V 
V 
IIc a
l
l 2
l
3Z aa
1  aa a2  a 
1 Z ab
a Zaac 
 
2
1
2


T 1 V b   T 1 V b   T 1  Z bal Z bbl Z bcl  TT 1  I b 
 
 


 Z cal Z cbl Z ccl 
V c2 
V 1c 
 I c2 


 
 
 

(1)
(1)
(2)
(2)
(1)

(2)
(3)
(3)

(4)
(3)
(4)

(5)
(4)

Energies 2018, 11, x FOR PEER REVIEW

4 of 15

1 1 1 
1 1 1 
11 1 1 2 
1 1 2 1  

1
T 1 a
a , T =1 1 a a , a  e j 2π 3
(5)
T  1 a 2 a 2 , T 1 = 31 a 2 a 2  , a  e j 2π 3
(5)




1
a
a
1
a
a
3  2



Energies 2018, 11, 3305
4 of 14
1 a a 2 
1 a
a 
A sequence circuit equation is obtained by solving Equation (4). The sequence circuit equation
A sequence
circuit equation
is obtained
by
solving
Equation
(4).
The sequence
circuit
equation
is presented
in Equation
(6), which
can alsoby
besolving
used toEquation
represent
sequence
networks
between
two
A sequence
circuit equation
is obtained
(4).
The sequence
circuit
equation
isneighboring
presented inbuses
Equation
(6),
which
can
also
be
used
to
represent
sequence
networks
between
two
in Figure
1.
is presented in Equation
(6), which
can also be used to represent sequence networks between two
neighboring buses in Figure 1.
neighboring buses in Figure 1.
V 02  V 10 
 2
2
1
 Z 0l 0
  2I 0 
0








V
0
0
 2  V
 l 0 l 0   I 0 2 2 
 V 2 V1 V 1   Z
 
0 l
V0
(6)
2
1
0

 0Z0 Zl 0 0 0 2I   I 0






 2  V 



V

0
Z
0
1 1 

(6)
l Z l 0I  2  2 
(6)
 V2 V +
 V−


 V+  =



  00 0Z+


I

+
l  I
V 2   1V 1    0 0 0 0 Z  ZlI 2  
2
2
V−
I−
  V −
 
− 
As presented in Figure 2, the three-phase load side current comprises currents of the
presented
in
Figure
2,are
the
three-phase
load
sidebcomprises
current
comprises
theb,
As
presented
Figure
2,
the
three-phase
load
side
current
currents
of currents
the asingle-phase
single-phase
DG in
and
load
that
connected
between
phase
and phase
c, and phase
and of
phase
single-phase
DG
and
load
that
are
connected
between
phase
b
and
phase
c,
and
phase
a
and
phase
DG
and
load
that
are
connected
between
phase
b
and
phase
c,
and
phase
a
and
phase
b,
respectively.
respectively. Hence, the sequence currents are expressed as a combination of the two currents, b,
as
respectively.
Hence,
the
sequence
are
expressed
as a of
combination
of the
currents,
as
Hence,
the in
sequence
currents
are expressed
assequence
a combination
the two
currents,
as presented
in
presented
Equation
(7).
Figure
3currents
shows the
circuit
models
of Figure
2, two
which
were used
presented
in
(7). Figure
3 shows
the
sequence
models
of Figure
which
Equation
Figure
3 shows
the sequence
circuit
modelscircuit
of
2,3.which
were2,used
to were
deriveused
the
to derive(7).
theEquation
compensation
principle
of the
compensator
inFigure
Section
to derive the compensation
principle
of the compensator
compensation
principle of the
compensator
in Section 3. in Section 3.
2
I 2 
I 2 
 I aDG 2  I aL 2    I 0DG
 IL02L 2 
 2   I 20   2 I2a 

DG
2
L 2 L2
DG
2
DG2
  I L2 
 I DG 2 +
I a IL 2   I0 DG 2IIDG2
0 2
1 a 2
1 I
0 L2 +
I0
0
(7)
  I2+   TI1 a  I2b   T1  aIDG
ba 2  ILb2 a    IDG
 2 0 IL2  
 2   I+ −1 T 2 I
I  DG
2 IDG2
L2 
IbI DG2
I b ILL2
(7)
DG 2 +
2  
2+
TT−1 
b 
 L
2=
=
(7)








 I +  = IT2  I b 
I
I
I

I
I

I
b
b
+
+
I
c 2
c 
 2
L2  
  2 
 IcDG
  IDG
2
2  2c 
DG2 I L 2 L2
L2
IIDG2
c I
 + I
 I +

I
I  Ic 
I 


c

I 2
I 2
2
2 


V
V

Z
Z l

c



c

I 2
I 2

l


V2
V

I L 2

I DG 2

Z l
Z l

2


I DG 2
I DG 2

I L 2

I DG 2

(a)
(a)



I L 2
I L 2

(b)
(b)

Figure 3. Sequence circuit models of Figure 2. (a) Positive sequence; (b) negative sequence.
Figure 3.
Sequence circuit
circuit models
(a) Positive
Positive sequence;
sequence; (b)
Figure
3. Sequence
models of
of Figure
Figure 2.
2. (a)
(b) negative
negative sequence.
sequence.

CompensationPrinciple
Principle
3.3.Compensation
3. Compensation Principle
Figure44presents
presentsthe
themain
maincircuit
circuitstructure
structureand
andthe
thecorresponding
correspondingsequence
sequencecircuit
circuitmodels
modelsofof
Figure
Figure
4
presents
the
main
circuit
structure
and
the
corresponding
sequence
circuit
models
of
theproposed
proposedcompensator
compensatorininthe
thepaper.
paper.Figure
Figure4a4aisisthe
thethree-phase,
three-phase,delta-connected
delta-connectedmain
maincircuit
circuit
the
the
proposed
compensator
in
the
paper.
Figure
4a
is
the
three-phase,
delta-connected
main
circuit
modelofof
shunt
compensator,
be converted
into sequence
circuit
models, as
model
thethe
shunt
compensator,
whichwhich
can becan
converted
into sequence
circuit models,
as illustrated
model
of the
shunt 4b.
compensator,
which
can
be for
converted
into
sequencecompensation
circuit models,
as
illustrated
in
Figure
Figure
5
shows
the
system
deriving
the
real-time
in Figure 4b. Figure 5 shows the system for deriving the real-time compensation scheme scheme
of the
illustrated
in Figure 4b.
Figure 5side
shows
the system
for deriving
the of
real-time
compensation
scheme
of the compensator.
current
comprises
theofcurrents
the single-phase
DG
and
load
compensator.
The loadThe
sideload
current comprises
the currents
the single-phase
DG and load
connected
ofconnected
the compensator.
The
load
side
current
comprises
the
currents
of
the
single-phase
DG
and
load
between
different
phases.
The
shunt
compensator
is
used
to
compensate
for
the
between different phases. The shunt compensator is used to compensate for the unbalanced load
connected
between
different
phases. The shunt compensator is used to compensate for the
unbalanced
load
side
current.
side current.
unbalanced load side current.
c
c

a
I cC

b

a

I cC
jQcaC
jQcaC

I aC

I aC

C
jQab
C
jQab

b

I bC

I bC

a0C
a0C
I 0C
I 0C

aC
aC
I C
I C

aC
aC
I C
I C

jQbcC
jQbcC

(a)
(a)

(b)
(b)

Figure
Figure4.4. Main
Main circuit
circuit structure
structure and
and corresponding
corresponding sequence
sequence circuit
circuit models
models ofofthe
theproposed
proposed
Figure
4.
Main
circuit
structure
and
corresponding
sequence
circuit
models
of
the
compensator.
structure in
in the
thea,a,b,b,c cframe;
frame;(b)(b)
sequence
circuit
models
in the
compensator. (a)
(a) Main
Main circuit structure
sequence
circuit
models
inproposed
the
0, +,0,−
compensator.
+,
− frame. (a) Main circuit structure in the a, b, c frame; (b) sequence circuit models in the 0, +, −
frame.
frame.

Energies 2018, 11, 3305
Energies 2018, 11, x FOR PEER REVIEW
S

S

Za

5 of 14
5 of 15

Zb

S

S

Ib

S

Vc

Zc

Ia , Pa  jQa

Va

L

S

S
Vb

L

S

Ia

Va

S

Ic

L

Vc

Ic , Pc  jQc

L
C

C
C
ca

jQ

a

DG

Ibc

C

Ia

Ic
c

Iab

Ib , Pb  jQb

Vb

Ib
C
ab

jQ

b

Unbalnced Load
and DG
Load side

C

jQbc

Delta-Connected
Shunt Compensator

Figure
Figure5.5.System
Systemfor
forderiving
derivingthe
thecompensation
compensationscheme.
scheme.

The
The three-phase
three-phase line
line voltages
voltages of
of the
the compensator
compensator presented
presented in
in Figure
Figure 55 are
are expressed
expressed in
in
L
Equation (8). Phase a to neutral was selected as the phase angle reference.
Vn is the effective
L
Equation (8). Phase a to neutral was selected as the phase angle reference. Vn is the effective value
value of the line-to-neutral voltage. The three-phase line currents of the load side are expressed
of the line-to-neutral voltage. The three-phase∗ line currents of the load side are expressed in
in Equation (9), in which the relationship of
V · I = P − jQ is used. By using the symmetrical
*
V

I

P  jQ is used.
Equation
(9),
in
which
the
relationship
of
By using the
symmetrical
components
components method, the positive- and negative-sequence
components
of the
load side currents
are
method,
the
positiveand
negative-sequence
components
of
the
load
side
currents
are
in
obtained in Equations (10)–(12). The zero-sequence component is zero in a three-phase, obtained
three-wire
Equations
(10)–(12) The zero-sequence component is zero in a three-phase, three-wire power
power
system.
 L  


system.
V ab
1 −1 0
1
 L L 
 2  L
V
(8)
1 −01 
a
 V bc V
ab=  0 1 -1
 1  n
L 




1
0
1
a


V ca V L  0
1 -1  a 2  VnL
(8)
 bc 



  L   




DG
L
DG
L
-1
0
1
a
Ia
1Vca 0 0
( Pa + Pa ) − j( Q a + Q a )




1 
2
 I b  = V L  0 a 0  ( PbL + PbDG ) − j( QbL + QbDG ) 
L
DG
L
DG
n
L
Ia 
Pa P DG
) )j−
(Qja( 
)  DG )
(aP L+
QQ
Ic
01 0 0 a 0   ( P
c a+ Q
c
  1 
 L c DGc 

2
L
DG 


(9)
 Pb )  j (Qb  Qb ) 
 I b   V L10 0 a 0 0   ( PPba −
jQ
a
 I c  1  n 0 2 0 a ( PcL  PcDG )  j (QcL  QcDG ) 
 = V L  0 a 0  Pb − jQb 

n
(9)
01 0 0 a 0   PaPc−jQjQ

a c
1


 L 0 a 2 0   Pb  jQb  
I
I
0
a
Vn
0 I0 a = PTc −1 jQcI  
(10)
 + 
 b 
I−
Ic
 I0 
Ia 
 
1 jQ ) + ( P − jQ )]
( P −
I + = 3V1 L [( Pa − jQaI) + 
c
c
(10)
   Tb  I b b
n
(11)
 nL − j Qa + Qb + Qc )/3VnL
= ( Pa + Pb + Pc I/3V

    I c 
= Re I + + jIm I +
1
1 L [(LP[(a P
 jQ
) a( Pbb −
 jQ
−c )]
jQc )]
I − I= 3V
−a jQ
jQbb))+( Pac2 (PcjQ
a ) a+
n

3Vn


Pb
3Qb
Pc
3Qc
(11)
= [(
a − P
2b −
P
(P
 P2c )+/ 3Vn2L  −
j (Qa 2 Qb +
 Qc ) / 3VnL
(12)
√ a

3Pb I } 3Pjc Im{I } Qb
Qc
L


j  Re{
2 − 2 − Q a + 2 + 2 )] /3Vn

1
The three arm currentsI and
compensator
are expressed in
 the
[(synthesized
Pa  jQa )  aline
( Pb currents
jQb )  a 2of
( Pcthe
 jQ
c )]
L
3
V
n By using Equations (13) and (14), the sequence components of the
Equations (13) and (14), respectively.
P obtained
P
3Qusing
3Equation
Qc
synthesized compensator line currents are
(15). By substituting Equation (14)
b
(12)
 [( Pa  b  c 

)
into Equation (15), the positive- and negative-sequence
components
of the compensator line currents
2
2
2
2
j(

3Pb
3Pc
Q Q

 Qa  b  c )]/ 3VnL
2
2
2
2

The three arm currents and the synthesized line currents of the compensator are expressed in
Equations (13) and (14), respectively. By using Equations (13) and (14), the sequence components of

Energies 2018, 11, 3305

6 of 14

can be rewritten as Equations (16) and (17), respectively. In Equation (15), the zero-sequence component
of the line currents is zero in a delta-connected compensator.

C
I ab = − jQCab /(1 − a)VnL

C
2
L
I bc = − jQC
bc / ( a − a )Vn
C
2
L
I ca = − jQC
ca / ( a − 1)Vn


C

Ia

 C
 Ib
C
Ic





C

I0

 C
 I+
C
I−

C

I+

=
=

C

=

I−

=

 C 
I ab
−1
 C 
0  I bc 
C
1
I ca

 C 
Ia

−1  C 
 = T  Ib 

1
 
 =  −1
0


(13)

0
1
−1

(14)

(15)

C
Ic

1
∠ − 90◦ [ QCab + QCbc + QCca ]
3VnL
[− j( QCab + QCbc + QCca )]/3VnL

1

C
C
2 C
L ∠ − 30 [ Q ab + aQ bc + a Q ca ]
3Vn√



C
3QC
QC
ca
[( 2 ab − 3Q
− j 2ab − QCbc
2

+

(16)

QC
L
ca
2 )] /3Vn

(17)

For unbalanced-load current compensation, the compensator should eliminate the entire
negative-sequence component and the imaginary part of the positive-sequence component of the
load current, as shown in Equations (18) and (19) [26,27]. By combining Equations (18) and (19),
the compensation command of the delta-connected compensator is obtained for each arm, as presented
in Equation (20). The rating of the compensator can also be determined from Equation (20).
C

I− + I− = 0
n


C
Im I + + Im I +

(18)

o

=0

(19)



QCab = Qc − Q a − Qb

QC
bc∗ = Q a − Qb − Qc
QC
ca = Qb − Qc − Q a

(20)

Figure 6 displays the positive- and negative-sequence circuits presented in Figure 1, where the
proposed compensator is installed at Bus 1. Equation (21) presents the positive- and negative-sequence
load side currents at each bus including the DG’s contribution. The compensator connected at Bus
n can compensate for the imaginary part of the positive-sequence load side current and the entire
negative-sequence load side current. For example, if the compensator is connected at Bus 1, then the
compensator executes the compensation rule presented in Equations (18) and (19). Thus, the power
source side only supplies a balanced three-phase current with a unity power factor, and the power
quality is improved.
n

L, n

DG,n

I+ = I+ + I+
where, n = 2, 3, 4, 5, 6.

n +1

n

L, n

DG,n

+ I+ , I− = I− + I−

n +1

+ I−

(21)

Energies 2018, 11, 3305
Energies 2018, 11, x FOR PEER REVIEW

Z S

I S
S

V

1

I 2

7 of 14
7 of 15

Z l1

2

I 3

Z l 2

Z l 3

3

4

Zl 4

5

Z l 5

6

I +C
I DG 2

I L 3 I DG 4

I L 2

I L 4 I DG 5

I L 6

(a)
I S

Z S

1

I C

I 2

Z l1

I DG 2

2

I 3

Z l 2

Z l 3

3

I L 2

I L 3

I DG 4

4

Z l 4

I L 4 I DG 5

5

Z l 5

6

I L 6

(b)
Figure 6. Sequence networks of Figure 1 with the proposed compensator installed at Bus 1.
Figure 6. Sequence networks of Figure 1 with the proposed compensator installed at Bus 1. (a)
(a) Positive-sequence network; (b) negative-sequence network.
Positive-sequence network; (b) negative-sequence network.

4. Power Quality Indexes
4. Power Quality Indexes
Four power quality performance indexes—including voltage and current unbalance ratios, voltage
Four power
quality
performance
indexes—including
voltage
and current
ratios,
regulation,
and power
factor—were
employed
for evaluating the
performance
of the unbalance
microgrid [28–30].
voltage regulation, and power factor—were employed for evaluating the performance of the
4.1. Voltage[28–30].
Unbalance Ratio (VUR)
microgrid
The three-phase voltage at the point of common coupling (PCC) should be maintained at a
4.1.
Voltage
Ratio (VUR)
satisfactoryUnbalance
balance condition
to meet the power quality requirement. Equation (22) presents the
calculation
of the phase
voltageatunbalance
(PVUR).coupling (PCC) should be maintained at a
The three-phase
voltage
the point ratio
of common
satisfactory balance condition to meet
the power
quality requirement.

Equation (22) presents the
Vb − Vavg , Vc − Vavg )
Max
( Va − Vratio
avg , (PVUR).
calculation of the phase
voltage
unbalance
× 100%
(22)
PVUR =
Vavg
Max( Va  Vavg , Vb  Vavg , Vc  Vavg )

 100%
(22)
where, Vavg = (Va + Vb + VPVUR
c ) /3 .
Vavg
The symmetrical components method can also be employed for evaluating the degree of unbalance.
Vavg 
(Va IEEE
 Vb 1159
Vc )/3standard, the three-phase voltage unbalance ratio (VUR) is defined
In thewhere,
IEC 61000
and
as the
ratio
of the negative-sequence
voltage
the be
positive-sequence
voltage, asthe
presented
in
The
symmetrical
components method
cantoalso
employed for evaluating
degree of
Equation
(23)
[31,32].
The
generally
used
limitation
value
of
VUR
in
a
power
distribution
system
unbalance. In the IEC 61000 and IEEE 1159 standard, the three-phase voltage unbalance ratio (VUR)
is 2.5%.
VUR
usedratio
in this
is
defined
asisthe
of study.
the negative-sequence voltage to the positive-sequence voltage, as
used

presented in Equation (23) [31,32]. The generally
limitation value of VUR in a power
V−

× 100%
VURin=this
d2 study.
=
(23)
distribution system is 2.5%. VUR is used
V+

V
100%
(23)
V
Similarly, the CUR is presented in Equation (24) and is defined as the ratio of the negative-sequence
current to the positive-sequence current.
4.2. Current Unbalance Ratio (CUR)

I−
Similarly, the CUR is presentedCUR
in Equation
(24) and is defined as the ratio of (24)
the
= × 100%
I
+
negative-sequence current to the positive-sequence current.
4.2. Current Unbalance Ratio (CUR)

4.3. Voltage Regulation (VR)

VUR  d 2 

I
CUR    100%
(24)
I  are connected to a power system, the resulting
According to the IEEE 1547 standard, when DGs
voltage fluctuation should not exceed ±5% [33]. Equation (25) presents the calculation of voltage

4.3. Voltage Regulation (VR)
According to the IEEE 1547 standard, when DGs are connected to a power system, the
resulting voltage fluctuation should not exceed ±5% [33]. Equation (25) presents the calculation of
Energies 2018, 11, 3305
8 of 14
voltage regulation (VR), which is used to evaluate the degree of voltage fluctuation in a power system.
The VR in a power distribution system should not exceed the nominal voltage by 5% at full load.
regulation (VR), which is used to evaluate the degree
V  VFLof voltage fluctuation in a power system. The VR
VRexceed
 NL the
100% voltage by 5% at full load.
(25)
in a power distribution system should not
nominal
VFL

VR =
4.4. Power Factor

VNL − VFL
× 100%
VFL

(25)

4.4. Power
Factor factor is the ratio of the active power to the apparent power, as presented in
The power
Equation (26), and is used to evaluate the efficiency of power utilization. Adequately correcting the
The power factor is the ratio of the active power to the apparent power, as presented in
power factor of a power system can improve the system operation performance.
Equation (26), and is used to evaluate the efficiency of power utilization. Adequately correcting
the power factor of a power system can improve
operation performance.
PF the
 Psystem
/S
(26)
PF = P/S

5. Simulation Result

(26)

5. Simulation
Resultthe study system with four single-phase DGs and loads, as presented in Figure
Figure 7 shows
1. This
created
an extreme
operating
situation
in the microgrid.
Theloads,
power
quality problem
and
Figure
7 shows
the study
system with
four single-phase
DGs and
as presented
in Figure
1.
power-flow
characteristics
were
examined
at
each
bus.
The
effects
of
installing
the
compensator
This created an extreme operating situation in the microgrid. The power quality problem and
were also observed.
Table 1were
lists the
system parameters
the test
system.
The evaluation
is divided
power-flow
characteristics
examined
at each bus.ofThe
effects
of installing
the compensator
into the
four
cases:
were
alsofollowing
observed.
Table
1 lists the system parameters of the test system. The evaluation is divided
into
foursingle-phase
cases:
Casethe
1. following
System with
loads;
Case
2.
System
with
single-phase
loads and DGs;
Case 1. System with single-phase loads;
Case 3. Case 1 system with two compensators connected at Bus 1 and Bus 4;
Case 2. System with single-phase loads and DGs;
Case 4. Case 2 system with two compensators connected at Bus 1 and Bus 4.
Case 3. Case 1 system with two compensators connected at Bus 1 and Bus 4;
Case Four
4. Case
2 system indexes—VUR
with two compensators
connected
at Bus factor—were
1 and Bus 4. employed to evaluate
performance
and CUR,
VR and power
the Four
power
quality improvement
effects
microgrid
with the
compensators.
performance
indexes—VUR and
CUR,ofVRthe
and power
factor—were
employed
to evaluateThe
the
MATLAB/SimuLink
program
was
used
to
construct
the
test
system
presented
in
Figure
7 with the
power quality improvement effects of the microgrid with the compensators. The MATLAB/SimuLink
assigned shunt
compensators.
Thethe
four
cases
werepresented
simulated,in
and
the results
in the
program
was used
to construct
test
system
Figure
7 withwere
the compared
assigned shunt
following sections.
compensators.
The four cases were simulated, and the results were compared in the following sections.
Bus 0
S
a

I aS

Bus 1 Z l1 I 2 Bus 2
a
a

Z al 2

I bS

2
Z bl1 I b

I cS

2
Z cl1 I c

Bus 3

Z al 3 Bus 4

Z al 4 Bus 5

Z al 5

Z bl 2

Z bl 3

Z bl 4

Z bl 5

Z cl 2

Z cl 3

Z cl 4

Z cl 5

Bus 6

V

S
b

V

Vc

S
S

Z a ,b ,c V Bus1
a ,b ,c
SbcDG 2 S abL 2

S abL 3

SbcDG 4 S abL 4

SbcDG 5

Figure
Microgrid study
Figure 7.
7. Microgrid
study system
system with
with unbalanced
unbalanced DGs
DGs and
and loads.
loads.

SabL 6

Energies 2018, 11, x FOR PEER REVIEW

9 of 15

Table 1. Test system parameters.

Energies 2018, 11, 3305

Item

Parameter
22.8
kV; 60 Hz
Table 1. Test system parameters.

Power Source
Item

Distribution line
Power Source

DGs and loads
Distribution line
Load 2

Source impedance: 0.03249 + j 0.51984 () ; X/R: 16
Parameter
Type: 25 kV 500 MCM; Length: 3 km/Per Section
22.8 kV; 60
Hz (Ω/km)
j 0.1241
Line impedance: 0.02536
Source impedance: 0.03249+ j0.51984 (Ω); X/R: 16
Capacity
Power Factor
Type: 25 kV 500 MCM; Length:
3 km/Per Section
5 MVA
0.85+lagging
Line impedance: 0.02536
j0.1241 (Ω/km )

DGs andLoad
loads 3

phase a-b
phase a-b

phase b-c
phase b-c

9 of 14

2.5 MVACapacity

0.85 lagging
Power Factor

Load
4 2
Load

2 MVA 5 MVA

0.85 lagging
0.85 lagging

Load
Load
6 3
Load 4
DG 2

1.5 MVA2.5 MVA
4.0 MW 2 MVA

0.85 lagging
0.85 lagging

Load 6

DG 4

2.0 MW

DGDG
5 4

2.0 MW 2.0 MW

DG 5

2.0 MW

DG 2

0.85 lagging
0.85 lagging

1.5 MVA

1.0 for all DGs

4.0 MW

1.0 for all DGs

5.1. Case 1. System with Single-Phase Loads

5.1. Case
1. System
with Single-Phase
Loadsturned-off. The power source supplies unbalanced powers
In Case
1, all DGs
in Figure 7 were
to four
loads.
Figure7 8were
shows
the power
flow
in Case
1, and
Tableunbalanced
2 summarizes
the
In single-phase
Case 1, all DGs
in Figure
turned-off.
The
power
source
supplies
powers
test
results.
The power
flowFigure
to Bus8 6shows
is slightly
lower flow
than in
theCase
assigned
demand
due to the
to four
single-phase
loads.
the power
1, andload
Table
2 summarizes
the
voltage
drop
caused
by
line
impedance.
The
VR
along
the
microgrid
is
within
the
limitation
range.
test results. The power flow to Bus 6 is slightly lower than the assigned load demand due to the
Equations
(11)caused
and (12)
used to calculate
sequence
currents is
flowing
bus. Inrange.
each
voltage drop
by were
line impedance.
The VRthe
along
the microgrid
within to
theeach
limitation
bus,
the (11)
negative-sequence
current
causedtheby
these currents
single-phase
is bus.
equal
to bus,
the
Equations
and (12) were used
to calculate
sequence
flowingloads
to each
In each
positive-sequence
current,
which
obtains
a
CUR
value
of
100%
and
produces
unbalanced
voltage
the negative-sequence current caused by these single-phase loads is equal to the positive-sequence
on
a bus.which
Hence,
the VURs
ofvalue
Bus 2ofto100%
Bus and
6 areproduces
over 2.5%,
which violate
theongenerally
used
current,
obtains
a CUR
unbalanced
voltage
a bus. Hence,
industrial
the VURs limit
of Busvalue.
2 to Bus 6 are over 2.5%, which violate the generally used industrial limit value.
S a1  6.05  j 0.38 S a2  6.03  j 0.23 S a3  3.26  j 0.11 S a4  1.89  j 0.06 S a5  0.81  j 0.02 S a6  0.81  j 0.02
S b1  2.59  j 5.38 Sb2  2.58  j 5.23 Sb3  1.37  j 2.80 Sb4  0.79  j1.62 Sb5  0.33  j 0.69 S b6  0.33  j 0.69
S c1  0.00+j 0.00 S c2  0.00+j 0.00 S c3  0.00+j 0.00 S c4  0.00+j 0.00 S c5  0.00+ j 0.00 S c6  0.00  j 0.00
Bus 0 Bus 1
Three-Phase abc
Power
Source

Bus 2
abc
ab

(Units : MVA, MW , MVAr )

Bus No.

Bus 3
abc

5MVA
0.85 lagging

Bus 4
abc

ab
2.5MVA
0.85 lagging

Bus 6

Bus 5
abc

abc

ab

ab

2.0MVA
0.85 lagging

Figure 8. Power flow of Case 1.
Figure 8. Power flow of Case 1.
Table 2. Test result of Case 1.
Table 2. Test result of Case 1.
VR (%)
VUR (%)
CUR (%)

1.5MVA
0.85 lagging

Power Factor

Bus No. VR (%) VUR (%) CUR (%) Power Factor
Bus 1
0.65
1.07
100.00
0.83
0.65
1.072.54 100.00 100.00 0.83
Bus 2 Bus 1
1.59
0.84
Bus 3 Bus 2
2.10
0.85
1.59
2.543.35 100.00 100.00 0.84
Bus 4 Bus 3
2.39
0.85
2.10
3.353.83 100.00 100.00 0.85
Bus 5
2.52
4.03
100.00
0.85
Bus 4
2.39
3.83
100.00
0.85
Bus 6
2.65
4.24
100.00
0.85
Bus 5
2.52
4.03
100.00
0.85
Bus 6
2.65
4.24
100.00
0.85
5.2. Case 2. System with Single-Phase Loads and DGs

In Case 2, all DGs were turned-on. The power source and three single-phase DGs supplied powers
to four single-phase loads at the same time. Figure 9 shows the power flow in Case 2, and Table 3
summarizes the test results. The VR along the microgrid is within the limit range. In Bus 4 and 5,

5.2. Case 2. System with Single-Phase Loads and DGs
In Case 2, all DGs were turned-on. The power source and three single-phase DGs supplied
10 of 14
powers to four single-phase loads at the same time. Figure 9 shows the power flow in Case 2, and
Table 3 summarizes the test results. The VR along the microgrid is within the limit range. In Bus 4
and 5, unbalanced
activeflows
power
to the
power
source
side were Hence,
observed.
Hence, power-flow
the reverse
unbalanced
active power
to flows
the power
source
side
were observed.
the reverse
power-flow
balancingThe
is required.
The power
Busvery
1 tolow.
BusThe
6 are
veryoflow.
VURs
of
balancing
is required.
power factors
of Bus 1factors
to Bus of
6 are
VURs
Bus The
2 to Bus
6 are
Bus
2
to
Bus
6
are
higher
than
2.5%,
which
violates
the
industrial
limit
value.
When
the
active
higher than 2.5%, which violates the industrial limit value. When the active power of DG supplies the
power
of DG the
supplies
the load demand,
the is
netreduced.
positive-sequence
current
reduced. In this
load
demand,
net positive-sequence
current
In this situation,
theisnegative-sequence
situation,
the negative-sequence
current is current.
larger than
the
positive-sequence
current.
a CUR
current
is larger
than the positive-sequence
Thus,
a CUR
value higher than
100%Thus,
is observed,
value
higher in
than
100%
is observed,
as presented
in Table
This also aggravates the VUR on a bus.
as
presented
Table
3. This
also aggravates
the VUR
on a 3.
bus.

Energies 2018, 11, 3305

S a1  5.96  j 0.31 S a2  5.94  j 0.16 S a3  3.20  j 0.06
S a4  1.86  j 0.03
S a5  0.79  j 0.01 S a6  0.79  j 0.01
1
2
3
4
S b  0.61  j 7.19 S b  0.63  j 6.97 S b   0.19  j 3.56 S b   0.73  j 2.38 S b5   0.41  j1.06 S b6  0.30  j 0.67
S c1   3.33  j1.84 S c2  3.34  j1.90 S c3   1.56  j 0.95 S c4   1.56  j 0.97 S c5   0.77  j 0.48 S c6  0.00  j 0.00
Bus 0
ThreePhase
Power
Source

Bus 1

Bus 3

Bus 2
abc

abc

abc

ab

bc

Bus 4

ab

5MVA
0.85 lagging

ab

abc

bc

bc
DG

4MW 2.5MVA
1.0 0.85 lagging

Bus 6

abc

DG

(Units : MVA, MW , MVAr )

Bus 5

abc

2.0MVA
0.85 lagging

ab
DG

2MW
1.0

2MW 1.5MVA
1.0 0.85 lagging

Figure 9.
Power flow
flow of
Case 2.
Figure
9. Power
of Case
2.
Table 3. Test result of Case 2.
Table 3. Test result of Case 2.
VR (%)
VUR (%)
CUR (%)

Bus No.

Power Factor

Bus No. VR (%) VUR (%) CUR (%) Power Factor
Bus 1
0.61
1.68
262.08
0.33
Bus 1
0.61
1.683.99 262.08 262.08 0.33
Bus 2
1.44
0.35
1.44
3.995.20 262.08 242.54 0.35
Bus 3 Bus 2
1.88
0.48
Bus 4 Bus 3
2.11
0.29
1.88
5.206.08 242.54 325.83 0.48
Bus 5 Bus 4
2.21
0.55
2.11
6.086.49 325.83 322.40 0.29
Bus 6
2.33
6.69
100.00
0.85
Bus 5
2.21
6.49
322.40
0.55
Bus 6
2.33
6.69
100.00
0.85
5.3. Case 3. Case 1 System with Two Compensators Connected at Bus 1 and Bus 4

5.3. Case
3. Case
1 System
Two
Compensators
Bus 1 and Busthe
4 test results, respectively.
Figure
10 shows
thewith
power
flow
in Case 3, Connected
and Table at
4 summarizes

Compared
1, with
assistance
compensators,
the VURs
of all buses were
significantly
Figurewith
10 Case
shows
the the
power
flow ofinthe
Case
3, and Table
4 summarizes
the test
results,
improved
to
be
within
the
industrial
limit
value.
The
VRs
and
power
factors
of
all
buses
also
respectively. Compared with Case 1, with the assistance of the compensators, the VURs ofwere
all buses
improved.
It is observed
in Figure
10 thatthe
theindustrial
two compensators
at The
Bus 1VRs
andand
Buspower
4 regulated
were significantly
improved
to be within
limit value.
factorsthe
of
unbalanced
power
flows
between
the
unbalanced
load/DG
and
the
power
source
side.
As
a
result,
all buses were also improved. It is observed in Figure 10 that the two compensators at Bus 1 and
Energies
11, x FOR
PEER
REVIEW
of 15
the
source
side
offered
balanced
three-phase
powers the
withunbalanced
unity powerload/DG
factor at and
Bus 1the
and11
Bus
4.
Buspower
4 2018,
regulated
the
unbalanced
power
flows between
power
source side. As a result, the power source side offered balanced three-phase powers with unity
1
 j 0.00 S a2  5.27  j 0.19 Sa3  2.45  j 0.08
S a4  1.05  j 0.00 S a5  0.82  j 0.03 S a6  0.83  j 0.02
a  3.05at
powerSfactor
Bus 1 and Bus 4.
1
Sb  2.99  j 0.00 Sb2  2.83  j3.88 Sb3  1.54  j1.40
Sc1  2.95+j 0.00 Sc2  0.88  j 0.03 Sc3  0.88  j 0.02

Bus 0 Bus 1
Threeabc
Phase
Power
Source
abc
S aC 1  2.22  j 0.30
SbC1  0.15  j 3.89
ScC1  2.08  j 0.04

Bus 2

(Units : MVA, MW , MVAr )

Bus 3

abc

abc
ab

Compensator

Sb4  0.97  j 0.00
S c4  0.88  j 0.00

Bus 4
abc

ab

S b5  0.37  j 0.73 Sb6  0.37  j 0.72
S c5  0.00  j 0.00 S c6  0.00  j 0.00
Bus 5
abc

abc

SaC 2  0.91  j 0.03 ab
SbC 2  0.03  j1.52
S cC 2  0.88  j 0.02 2.0MVA

5MVA
2.5MVA
0.85lagging 0.85 lagging Compensator

0.85 lagging

Figure 10.
10. Power
Power flow
flow of
of Case
Case 3.
3.
Figure

Table 4. Test result of Case 3.

Bus No.
Bus 1
Bus 2
Bus 3

VR (%)
0.07
0.79
1.08

VUR (%)
0.02
1.08
1.46

CUR (%)
2.00
76.58
53.18

Power Factor
1.00
0.91
0.96

Bus 6
abc
ab
1.5MVA
0.85lagging

Source

abc

S aC 1  2.22  j 0.30
SbC1  0.15  j 3.89
ScC1  2.08  j 0.04

ab

Compensator

(Units : MVA, MW , MVAr )

ab

abc

ab

SaC 2  0.91  j 0.03 ab
SbC 2  0.03  j1.52
S cC 2  0.88  j 0.02 2.0MVA

5MVA
2.5MVA
0.85lagging 0.85 lagging Compensator

1.5MVA
0.85lagging

0.85 lagging

Energies 2018, 11, 3305

11 of 14

Figure 10. Power flow of Case 3.
Table4.
4. Test
Test result
result of Case
Table
Case 3.
3.

VR
(%)
Bus No.Bus No. VR
(%)
Bus 1
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6

Bus 1
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6

VUR
(%)(%)CUR (%)
Power
VUR
CUR
(%) Factor
Power Factor
0.02
2.00
1.00
0.02
2.00
1.00
1.081.08
76.58 76.58 0.91
0.91
1.461.46
53.18 53.18 0.96
0.96
1.00
1.501.50
10.73 10.73 1.00
1.71
100.00
0.85
1.71
100.00
0.85
1.91
100.00
0.85
1.91
100.00
0.85

0.07

0.07
0.79
0.79
1.08
1.08
1.15
1.15
1.28
1.28
1.41
1.41

5.4.5.4.
Case
4. 4.
Case
at Bus
Bus 11and
andBus
Bus44
Case
Case2 2System
Systemwith
withTwo
TwoCompensators
Compensators Connected
Connected at
Figure
11 11
shows
the power
flow flow
in Case
and 4,
Table
the test results,
respectively.
Figure
shows
the power
in 4,Case
and5 summarizes
Table 5 summarizes
the test
results,
respectively.
Case
2, buses
the VURs
all buses
improved
to be within
the
Compared
withCompared
Case 2, thewith
VURs
of all
were of
improved
to were
be within
the industrial
limit value.
industrial
limit
value.
Thealso
VRscompensated
of all buses were
also compensated
to satisfactory
ranges. These two
The
VRs of all
buses
were
to satisfactory
ranges.
These two compensators
were
compensators
were
used
in
unbalanced
operations
for
improving
the
power
quality.
The
power
used in unbalanced operations for improving the power quality. The power flow in Figure 11 also
flow inthat
Figure
11 also
indicates
thatwith
reverse
power
balancing
withachieved
a unity atpower
wasthe
indicates
reverse
power
balancing
a unity
power
factor was
Bus 4 factor
by using
achieved at installed
Bus 4 by using
compensator
at Busthe
4. compensator installed at Bus 4.
S a1  0.53  j 0.00 S a2  3.89  j 0.19
Sb1  0.50  j 0.00 Sb2  0.18  j 4.86

Sa3  1.07  j 0.11
Sb3  0.31  j1.14
Sc3  0.21  j 0.01

Sc1  0.48  j 0.00 Sc2  2.22  j 0.93
ThreePhase
Power
Source

Bus 0 Bus 1
abc

Bus 3

Bus 2
abc

abc

S aC 1  3.37  j 0.25

S a4  0.33  j 0.00 Sa5  0.84  j 0.02 S a6  0.83  j 0.02
Sb4  0.32  j 0.00 Sb5  0.48  j1.31 Sb6  0.37  j 0.72
Sc4  0.34  j 0.00 Sc5  0.97  j 0.47 Sc6  0.00  j 0.00

abc
ab

bc
DG

Bus 4
abc

Bus 6
abc

bc

abc

ab

Bus 5
abc

S aC 2  2.28  j 0.02
S bC 2  0.54  j 2.98
S cC 2  1.74  j 0.93

Compensator
S bC 1  0.67  j 4.92
5MVA 4MW 2.5MVA
S cC1  2.70  j 0.91
0.85 lagging 1.0 0.85 lagging Compensator
(Units : MVA, MW , MVAr )

bc
ab

DG

2.0MVA 2MW
0.85 lagging 1.0

ab

DG
2MW 1.5MVA
1.0 0.85 lagging

Figure
flow of
of Case
Case4.4.
Figure11.
11. Power
Power flow
Table 5. Test result of Case 4.
Table 5. Test result of Case 4.
Bus No.
Bus 1
Bus 2
Bus 3
Bus 4
Bus 5
Bus 6

VR (%)
Bus No.
VR (%)
Bus 1 0.01 0.01
Bus 2 0.62 0.62
Bus 3 0.82 0.82
Bus 4
0.80 0.80
Bus 5
0.92
0.92
Bus 6
1.05
1.05

VUR
(%)
VUR
(%)(%)
CUR (%) CUR
Power
Factor Power Factor
0.010.01
5.13
5.131.00
1.00
1.501.50 236.09
0.34
236.09
0.34
1.811.81 126.76
0.68
126.76
0.68
1.78
1.00
1.78 28.44
28.44
1.00
2.23
286.01
0.58
2.23
286.01
0.58
2.43
100.00
0.85
2.43

100.00

0.85

5.5. Comparison of All Cases
Table 6 presents the compensation commands of compensators in cases 3 and 4, which reveal that
these two compensators were in unbalanced operations.
Table 6. Compensation commands of compensators.
Item

Bus No.

QC*
ab

QC*
bc

QC*
ca

Case 3

Bus 1
Bus 4

−4.18
−1.67

−3.66
−1.56

3.58
1.56

Case 4

Bus 1
Bus 4

−6.10
−3.89

−3.76
−2.07

5.58
3.93

Note: MVAr.

Item

Bus No.

Bus 1
Bus 4
Bus 1
Case 4
Bus 4
Note: MVAr.
Case 3

Energies 2018, 11, 3305

Qab

Qbc

Qca

-4.18
−1.67
−6.10
−3.89

−3.66
−1.56
−3.76
−2.07

3.58
1.56
5.58
3.93
12 of 14

Figure
12 presents the power quality indexes of all cases. The test results revealed that the
Figure 12 presents the power quality indexes of all cases. The test results revealed that the
powerpower
quality
waswas
significantly
improved
4,and
andbidirectional
bidirectional
power-flow
balancing
quality
significantly
improvedininCases
Cases 33 and
and 4,
power-flow
balancing
was achieved
in Case
4. 4.Ideally,
can be
be installed
installedforfor
buses
to optimize
was achieved
in Case
Ideally,a acompensator
compensator can
allall
buses
to optimize
the the
microgrid
performance.
microgrid
performance.
3.0

7
6

Case 1

2.0

VUR (%)

VR (%)

2.5
Case 2
Case 3

1.5
1.0

Case 2
Case 1

5

4
3

Case 4

2
Case 4

0.5
0

1
1

4
3
Bus Number

2

Case 3

0
5

1

6

3
4
Bus Number

2

50
0

Case 4

Case 3

0.8
0.6

Case 4

Case 1

0.4
Case 2

0.2
Case 3

1

2

4
3
Bus Number

6

(b)
1.0

Power Factor

CUR (%)

(a)
350
Case 2
300
250
200
Case 1
150
100

5

5

6

0

(c)

1

2

3
4
Bus Number

5

6

(d)

(Case 1: Blue; Case 2: Brown; Case 3: Yellow; Case 4: Green)
Figure
12. Comparison
of all
cases.(a)
(a)Voltage
Voltage regulation;
regulation; (b)
ratio;
(c) current
Figure
12. Comparison
of all
cases.
(b)voltage
voltageunbalance
unbalance
ratio;
(c) current
unbalance
(d) power
factor.
unbalance
ratio;ratio;
(d) power
factor.

6. Conclusions
6. Conclusions
Improper
connections
of unbalanced
and loads
in a three-phase
microgrid
may
Improper
connections
of unbalanced
DGs DGs
and loads
in a three-phase
microgrid
may deteriorate
deteriorate
system
performance
and
increase
the
difficulty
of
operation.
In
this
study,
a
shunt
system performance and increase the difficulty of operation. In this study, a shunt compensator was
compensator was used in a three-phase, radial-type microgrid with unbalanced DGs and loads to
used in a three-phase, radial-type microgrid with unbalanced DGs and loads to achieve bidirectional
achieve bidirectional power-flow balancing and improve the electrical power quality. The test
power-flow balancing and improve the electrical power quality. The test results revealed that the
results revealed that the proposed compensator provides satisfactory effects for enhancing the
proposed
compensator
provides
satisfactory
for enhancing
the operational
operational
performance
of a microgrid
witheffects
unbalanced
DGs and loads.
For practicalperformance
applications, of a
microgrid
with
unbalanced
DGs
and
loads.
For
practical
applications,
the
universal
the universal compensator can be implemented as SVCs, STATCOMs, or as an additionalcompensator
function
can be implemented as SVCs, STATCOMs, or as an additional function of active filters. If necessary,
an optimization method can be employed to determine the installation sites of the compensator for
optimizing the operational performance of a microgrid.

Author Contributions: W.-N.C. conceived this article and designed the study system; C.-M.C. and S.-K.Y.
conducted the theoretical study and software simulation; all authors wrote the paper.
Funding: This research received no external funding.
Acknowledgments: The authors would like to thank the reviewers for valuable comments.
Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature
General
S
P
Q
V

apparent power
active power
reactive power
voltage

Energies 2018, 11, 3305

I
Z
R
X
Superscripts
S
DG
L
l
C
C*
n
*
Subscripts
0, +, −
a, b, c
ab, bc, ca
NL
FL

13 of 14

current
impedance
resistance
reactance
source
distributed generator
load
line
compensator
compensation command
bus number
complex conjugate
zero-, positive-, negative-component
phase a, b, c
line a-b, b-c, c-a
no load
full load

References
1.
2.
3.

4.

5.

6.

7.

8.
9.

10.

11.

Sahoo, S.K.; Sinha, A.K.; Kishore, N.K. Control techniques in AC, DC, and hybrid AC–DC microgrid:
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