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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**

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

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Energies 2018, 11, 3305

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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

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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. Equivalentcircuit 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 VVc 1 ZZcal ZcaZZcbl ZcbZZccl ZccI 2 I c

b

b

b

ba

bb

bc

2

2

l

l

l

2

V c22 V1V 1c1 Z ca ZZcbl ZZccl I Z

l

Va

Ia

c2

a

aa

ac

ab

l

l

l I a

−V1

1 Va −

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 1V

1 Zl

l IZb l 2

2

2

Zlbbl l Z

Zbccb

l cc I a

Vc

Ic

V a VcV 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 bcl1ITT

I b

T 11V b 1 cT11 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

11 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 = 31 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 V1 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)

V2 V +

V−

V+ =

00 0Z+

I

+

l I

V 2 1V 1 0 0 0 0 Z ZlI 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 I2a

DG

2

L 2 L2

DG

2

DG2

I L2

I DG 2 +

I a IL 2 I0 DG 2IIDG2

0 2

1 a 2

1 I

0 L2 +

I0

0

(7)

I2+ TI1 a I2b T1 aIDG

ba 2 ILb2 a IDG

2 0 IL2

2 I+ −1 T 2 I

I DG

2 IDG2

L2

IbI 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

L2

2

IcDG

IDG

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

aC

aC

I C

I C

aC

aC

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

1Vca 0 0

( Pa + Pa ) − 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+

Ic

01 0 0 a 0 ( P

c a+ Q

c

1

L c DGc

2

L

DG

(9)

Pb ) j (Qb Qb )

I b V L10 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)

01 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 − jQaI) +

c

c

(10)

Tb I b b

n

(11)

nL − j Qa + 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

Zl 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

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