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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

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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
sidebcomprises
current
comprises
theb,
As
presented
Figure
2,
the
three-phase
side
current
currents
of currents
the asingle-phase
single-phase
DG in
and
that
connected
between
phase
and phase
c, and phase
and of
phase
single-phase
DG
and
that
are
connected
between
phase
b
and
phase
c,
and
phase
a
and
phase
DG
and
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
compensator.
current comprises
the currents
the single-phase
connected
ofconnected
the compensator.
The
side
current
comprises
the
currents
of
the
single-phase
DG
and
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
side
current.
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.