1-s2.0-S014206151400101X-main

Electrical Power and Energy Systems 60 (2014) 221–233

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Volt/var/THD control in distribution networks considering reactivepower capability of solar energy conversion

http://dx.doi.org/10.1016/j.ijepes.2014.02.0380142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel./fax: +98 341 3235900.E-mail addresses: [email protected] (S. Jashfar), [email protected]

(S. Esmaeili).

Sajad Jashfar a, Saeid Esmaeili b,⇑a Department of Electrical and Computer Engineering, Graduate University of Advanced Technology, Kerman, Iranb Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 17 February 2013Received in revised form 19 January 2014Accepted 27 February 2014Available online 29 March 2014

Keywords:Distribution networksVoltage and reactive power controlSolar energy systemHarmonic distortions

Voltage and reactive power (volt/var) control have been widely employed to reduce power losses and sat-isfy the main distribution system operational constraints. In the proposed volt/var/THD control the reac-tive power capability from PV solar is considered as additional control variable in presence of non-linearloads. So, the limitations on deliverable power for each operation point affect inverter reactive powerscheduling. Therefore, the main aim is to find proper dispatch schedules for the substation capacitors(SCs), along feeder capacitors (FCs), on-load tap changer (OLTC) tap positions, and photovoltaic systems(PVs) inverter reactive power considering power quality constraints. In order to reduce effect of uncer-tainty in the forecast plan and to reduce switching operations for OLTC, a new load and generationtime-interval division (over 24-h period) is introduced based on both load curve and solar power outputcurve. Optimization problem is formulated for minimizing fuzzy membership functions values based on amulti-objective genetic algorithm solution method. For improving the search ability by multi-objectiveapproach a method which guarantees the suppression of maximum allowable daily SCs switching andeffectively corrects the convergence process is utilized. For more practical application of the proposedmethod, simulation is carried out in the large distorted distribution system with a number of non-linearloads and solar energy generation system.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Currently, PV solar panels are used to generate electric power asclean and sustainable energy resources which can mitigate theload on the transmission lines [1]. The DC/AC inverter is able to lo-cally balance reactive power on network with faster response timethan shunt capacitors. So, modifying PV inverters as static synchro-nous compensators (STATCOMs) [2] makes it possible to operatethem in non-sunny conditions to increase distribution and trans-mission capacity as well as stability of the system. On the otherhand, considering the intermittent output power of PVs, the idlecapacity can be utilized to reactive power control of the system.

Daily volt/var control at distribution system level has beenwidely employed to reduce energy losses and maintain voltageprofiles within permissible limits. Control variables planning ofthe system depend on various factors, such as harmonics and typesof renewable energy sources (RESs). High penetration of non-linearloads and RESs in distribution networks lead to more complexity of

optimal operation scheduling of these networks. Significantimprovement in the efficiency and quality of power system opera-tion achieve by coordinated operation [3]. Daily off-line volt/varcontrol is a tool to coordinate the centralized and local controllersin distribution management networks [4]. Different volt/var con-trol methods have been proposed to improve network conditionsup to now. The daily optimal volt/var control integrating distrib-uted generators (DGs) under steady-state sinusoidal operationcondition has been investigated in previous research. Viawan andKarlsson [5] suggested a coordination strategy to voltage and reac-tive power control in presence of DG and conventional controlequipment such as OLTC and capacitors. The authors in [6], pre-sented application of automatic voltage regulators (AVRs) banksand capacitors to volt/var control. Fuzzy logic is utilized to improvethe multi-objective optimization procedure. Dynamic program-ming method under sinusoidal operating system conditions acrossthe real medium-voltage distribution system by Liang and Chengpresented in [7]. However, in large systems dynamic programmingmethod is not appropriate due to the computational burden in-volved with it. Niknam et al. [8–12] present a cost-based method-ology for daily volt/var control without harmonic consideration indistribution systems including DGs. They used evolutionary

Nomenclature

Ctn state of capacitor nth at hour t

CSC ‘on’/’off’ states of substation capacitorsD number of optimization parametersdFC ‘on’ time duration of feeder capacitorsdSC ‘on’/’off’ state time duration for substation capacitorsF i ith objective functionF i;max maximum limit of ith objective functionhmax highest harmonic order of interesth0 smallest harmonic order of interestIC converter output currentIC,max maximum value of converter output currentJ junction of ith interval’s end to start of (i + 1)th intervalk number of objective functions‘ index of a non-dominated frontLB lower boundLoss energy losses of compensated systemLoss0 energy losses of uncompensated systemm number of iterationsMKC the maximum limit of capacitor switchingMKSC the maximum limit of substation capacitor switchingMKT maximum allowable number of OLTC daily switching

operationsn number of intervals for the entire load periodNb total number of busesNC total number of capacitorsNFC total number of feeder capacitorsNL total number of linesNP population sizeNPV number of PVsNSC number of substation capacitorsoi ith offspringPt

L active load at hour tPt

LossðfhÞ a component of real power loss in frequency fh at hour tPt

Loss;LðfhÞ a component of line real power loss in frequency fh athour t

PtLoss;TðfhÞ a component of transformer real power loss in fre-

quency fh at hour tPt

PV active power output of PV solar inverter at hour tPPV,R rated active power value from PVQt

c;PV PV system reactive power constraint due to convertercurrent at hour t

QtL reactive load at hour t

QtPV hourly PV inverter reactive power

QtPV ;max maximum possible PV inverter reactive power at hour t

QtPV ;min minimum possible PV inverter reactive power at hour t

QPV,R rated reactive power value from PVQt

v;PV PV system reactive power constraint due to convertervoltage at hour t

TAPt OLTC tap position at hour tt index which represents time in a 24-h periodtFC start time of switching feeder capacitors to ‘on’ statetss start time of ‘th time-intervalTHDt

Vitotal harmonic distortion factor at bus i and hour t

THDV,max maximum value of total harmonic distortionUB upper boundVC converter output voltageVC,max maximum value of converter voltageVdc,max maximum value of converter voltageDVt

i the voltage deviation at bus i and hour tVt

i ðfhÞ a component of voltage in frequency fh for bus ith andhour t

DVmax maximum allowable voltage deviation valueVPV voltage at the PV system connection pointVPV,max maximum value of voltage at the PV system connection

pointVPV,min minimum value of voltage at the PV system connection

pointVref the reference value for voltageXC the total equivalent reactance from the PV system low-

voltage terminal to the grid connection point# start time vectorhR the rated power factor angle of the PV nodek total crowding distancekj crowding distances with respect to kth objective func-

tionlj the kth objective functionlj,max maximum value of the kth objective functionlj,min minimum value of the kth objective functionn non-dominated frontsqi ith parents index of time-intervalv parent population! offspring population,i

j ith solution in the sorted list with respect to the objec-tive function k

W‘ point of active power or reactive power at ‘th time-interval

W‘ average of active power or reactive power at ‘th time-interval

222 S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233

methods such as ant colony optimization (ACO) [8], honey-beemating optimization (HBMO) [9], particle swarm optimization(PSO) [10], gravitational search algorithm (GSA) [11], and bacterialforging algorithm (BFA) [12] to determine solution of the problem.Liang and Wang in [13] proposed a fuzzy-simulated annealingmethod for volt/var control strategy in distribution systems to findthe combinatorial operation control of devices. The authors in [13]proposed a dispatching schedule in real distribution networkregardless of harmonic. Propagation of harmonics through the sys-tem causes damage to devices and consequently more losses.Capacitors may have an important role in the propagation of har-monics in the networks. The ‘on/off’ capacitor switching does notintroduce new harmonics into the network, but may lead to ampli-fy already present currents and voltages harmonic due to possibleresonance at one or more harmonic frequencies [14–17]. Harmon-ics put power quality greatly at risk and lead to undesirable solu-tions at the operational level. Volt/var control with harmonicconsideration is discussed in a few papers [18,19]. In these papers,

OLTC tap positions planning and shunt capacitors ‘on/off’ switchingstates have been done based on optimal time-interval division forthe forecasted daily load to decrease energy losses and improvepower quality.

This paper proposes precise mutual impact of power qualityconstraints and PVs in volt/var planning which has not been con-sidered in previous research. Considering active power output ofPV as well as active and reactive power demand of load, leads toprocurement of optimal time-interval division. Based on the ob-tained time-interval division, a novel method for considering PVsfor volt/var/total harmonic distortion (THD) control in distributionnetworks is achieved. PVs inverters can provide necessary reactivepower for the grid. In the proposed method, injection of harmoniccurrents to the system caused by PVs inverters operation is alsoconsidered. The control possibility should be performed in switch-able capacitor banks, transformer load tap changers, and reactivepower outputs of specific embedded generators. The active poweroutputs often specified by characteristics of energy resource or by

S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233 223

market decisions [20]. In addition to conventional control, vari-ables such as OLTC tap positions and capacitors ‘on/off’ switchingstates, reactive power of PVs are also scheduled and consideredas additional control variables. In order to perform precise calcula-tions, a hybrid joint programming (HJP) to volt/var/THD control isdeveloped and implemented utilizing integration of MATLAB andDIgSILENT software. The paper is outlined as follows: Section 2presents problem formulation. PV solar systems consideration indistribution systems to propose a novel control scheme is intro-duced in Section 3. Implementation of a HJP method to determinethe optimal dispatch schedules for all capacitors, OLTC tap positionand PVs inverters reactive power scheduling is proposed in Sec-tion 4. Section 5 describes multi-objective optimization fundamen-tal and method to find the best decision space in the proposedcontrol scheme. Simulation results of applying the suggested con-trol scheme to 5 test cases is demonstrated in Section 6, while de-tailed discussion of these obtained results are presented inSection 7. Finally, the major contributions and conclusions aresummarized in Section 8.

2. Problem formulation

Volt/var/THD control optimization problem is a discrete prob-lem with inequality constraints. The values of objective functionsare determined through harmonic load flow calculation (HLFC)based on the provided control variables. These control variables in-clude tap positions of OLTC, SCs and FCs ‘on/off’ switching states,and PVs hourly reactive power schedule. The aim is to find theminimum value of objective functions while satisfying the con-straints. The objectives of the coordinated schedule include systemlosses reduction, distribution system and customer voltage varia-tion as well as THD restriction.

2.1. Objective functions

2.1.1. Energy losses over a 24-h periodThe active power losses at hour t can be defined as the sum of

losses in each line and transformer. The first objective function involt/var/THD control problem is total real power losses at all fre-quency components over a 24-h period which has to be minimized

PLoss;Transformer ¼ PLoss;Tðf1Þ þXhmax

h¼h0

PLoss;TðfhÞ ð1Þ

PLoss;Line ¼XNL

L¼1

PLoss;Lðf1Þ þXNL

L¼1

Xhmax

h¼h0

PLoss;LðfhÞ ð2Þ

PLoss ¼ PLoss;Transformer þ PLoss;Lines ð3Þ

Loss ¼X24

t¼1

PtLoss ð4Þ

2.1.2. Voltage deviation at each busVoltage deviation is considered as the second objective function

which may occur due to time-variant nature of loads consumptionand RESs generation. The root mean square (rms) value of voltageat bus i at hour t, is defined by

Vti;rms ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffijVt

i ðf1Þj2 þXhmax

h¼h0jVt

i ðfhÞj2r

ð5Þ

To minimize the difference between bus voltages from the ac-tual operating voltage Vt

i ¼ 1p:u:� �

and enhance voltage security,voltage deviation can be calculated as

DVti ¼ 1� Vt

i;rms

��� ��� i ¼ 1; . . . ;Nb; t ¼ 1; . . . ;24 ð6Þ

A well-designed distribution system must keep the voltages atall nodes within the allowed limits:

DVti ð%Þ � DVmax ð7Þ

2.1.3. Total harmonic distortion at each busThe third objective function is the voltage-THD at bus i at hour t,

which is expressed as

THDtVi¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðVt

i;rmsÞ2 � jVt

i ðf1Þj2q

Vrefi ¼ 1 . . . ;Nb; t ¼ 1; . . . ;24 ð8Þ

The amount of rms voltage improvement not only relies on fun-damental voltage but also harmonic components play an impor-tant role in the improvement.

Vti;rms ¼ Vt

i ðf1Þ�� ���

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ THDt

Vi

� �2r

ð9Þ

Therefore, THDtVi

is limited to a maximum value as follows

THDtVið%Þ � THDV ;max ð10Þ

THDV,max should be within acceptable operating limits throughoptimization process. The steady state voltage deviation (6) andvoltage THD (8) are restricted according to IEEE-519 standard [21].

2.2. Operational constraints

Practical constraints such as maximum allowable number ofswitching operation in a day for OLTC, SCs and FCs are defined asfollows [22]:

2.2.1. Maximum switching operations of OLTC

X24

t¼1

jTAPt � TAPt�1j �MKT ð11Þ

The maximum permissible operating times of OLTC in a day isconsidered 30 [18,23,24].

2.2.2. Maximum switching operations of capacitors

X24

t¼1

jCtn � Ct�1

n j �MKC n ¼ 1;2 � � � ;Nc; ð12Þ

The maximum permissible switching operating times for thecapacitors installed at the secondary bus in a day is considered 6and for those installed along the feeder is assumed 2 [24].

2.2.3. Reactive power limits of PVAt any time the reactive power generated from PV is bonded to

several limitations which are depended on the operating point. Thereactive power constraints of PVs are described in considerable de-tail in the next section.

QtPV ;min � Qt

PV � QtPV ;max ð13Þ

3. PV reactive power capability

In this paper, PV solar systems are considered in distributionsystems to propose a novel control scheme. The controllable do-main of photovoltaic converter reactive power capability to controlthe appropriate action is taken into account [25]. Fig. 1 shows the

VC

DC

Link

Voltage Source

Inverter

jXC

VPV

PV Solar Array

P , QPV PVDC

DC

DC

DC

DC

AC

Battery

Storage

LC

Filter

Output

Filter

1/z

Controller

++

actV

VΔ

*P*Q

GridjXG

VG

IC

Vdc

Fig. 1. The typical layout of a grid connected PV solar system which is interfaced with full-scale power electric converter.

224 S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233

typical layout of a grid connected PV solar system which is inter-faced with full-scale power electric converter. There are some lim-its to the reactive power that can be transmitted between theconverter and the electrical grid [26–28]. The acceptable reactivepower schedule depends on maximum value of voltage and currentcapacity of converter, which imposes a limit on the P and Q-capa-bility of PV system. For computing the PPV–QPV controllable domainof the PV system, it is required to consider the converter’s VC,max

and IC,max values. The active and reactive power correlation of theconverter current limit can be written as

P2PV þ Q 2

PV ¼ ðICVPV Þ2: ð14Þ

And the relation between PPV and QPV considering the convertervoltage limit is

P2PV þ QPV þ

V2PV

XC

!2

¼ VCVPV

XC

� 2

: ð15Þ

This equation can be used to calculate the design valueVC,max, which determines the maximum value of dc-link voltageVdc,max in the inverter-based DG, and IC,max. The converter volt-age VC relies on the dc-link voltage, the parameters of theamplitude modulation index and the adopted modulation tech-nique [26,28].

The maximum value of the converter current will stem from therated value of PV system active and reactive power and the mini-mum value of VPV, which is [28]

IC;max ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP2

PV ;R þ Q 2PV ;R

qVPV ;min

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP2

PV ;R þ ðPPV ;R tan hRÞ2q

VPV ;min: ð16Þ

The maximum value of the converter voltage can be derivedfrom the rated value of PV system active and reactive power andthe maximum value of VPV as follows [28]

VC;max ¼XC

VPV ;max

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP2

PV ;R þ PPV ;R tan hR þV2

PV ;max

XC

!2vuut : ð17Þ

The idle capacity to produce reactive power in the PV system isconstrained by the converter current rating and voltage rating lim-its. Thus, the hourly PV system reactive power limitations due toconverter current rating Q t

c;PV and voltage rating Q tv ;PV can be calcu-

lated as follows [28]

Q tc;PV ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVPV IC;maxð Þ2 � Pt

PV2

q;

Q tv;PV ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVC;maxVPV

XC

� 2

� PtPV

2

s� V2

PV

XC: ð18Þ

Finally, for each operating point, the maximum reactive powerinjection capability at tth hour for the control action can be deter-mined as [28]

QtPV ;max ¼ min Qt

c;PV ;Qtv;PV

n o: ð19Þ

considering PV voltage ðVPV Þ of 1.0, VPV,max = 1.05 AndVPV,min = 0.95[(all in per-unit)], XC = 0.30, and the rated power factorof cos hR = 0.9 and cos hR = 0.95, Fig. 2 shows the set of P and Q capa-bility curves of PV system which expresses the fact that both theconverter’s maximum current-carrying capacity and the maximumvalue of converter voltage will impose limits on its capability.

4. Implementation of the proposed hybrid joint programmingmethod

The proposed scheme comprises two outstanding features.Firstly, the forecasted load demand and PVs active power outputgeneration of the day-ahead is divided into several levels. Sec-ondly, the combination of optimal dispatch schedule of all controldevices such as OLTC, SCs, FCs and PV inverter reactive powersimultaneously besides considering harmonics is performed usingmulti-objective genetic algorithm. A feasible solution for volt/var/THD control includes OLTC and capacitors 24-hours’ settings andPVs inverters reactive power at each hour where the node voltagesand harmonic distortions are within the acceptable limits. The con-trol variables for each interval include 17 OLTC tap position states([�8. . . �101. . .8]) and 2 capacitors’ states (0 = ’off’; 1 = ’on’) foreach capacitor at each hour [23].

4.1. Time-interval method

The first crucial step during distribution systems operationalplanning in the presence of RESs, is forecasting load demandand RESs power output in order to adjust and optimize systemperformance. Nowadays, high precision techniques to load fore-casting [29,30] and prediction for intraday solar forecasting [31]are available. The optimal time-intervals can be determined tosatisfy the maximum switching operations of OLTC [18,23] andalso, to reduce effect of uncertainty and slight variations in theforecast plan. The OLTC tap position during all hours at eachinterval remains constant. The method presented in paper hasbeen upgraded for both load demand and alternative energy gen-eration, simultaneously.

In the proposed time-interval method, regarding to the consid-ered number of intervals, every chromosome contains start time ofeach time-interval. Solution structure of time-interval divisionproblem which represents the start time of each interval is formedas # ¼ ½ts1 ts2 � � � tsn �ð1�nÞ. The value of any gen suggests the start timeof each time-interval ðtss Þ. In this paper number of time-intervals ischosen 4. Fig. 3(a and b) shows characteristic curve of load demandand PV aggregate power output used in the network. Genetic ap-proach is employed to determine the start time of each time-inter-val for the specified numbers. Start time of each interval can beobtained with minimizing the Fitness (#).

0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

P [p.u.]

Q [

p.u.

]

cos θR = 0.95

cos θR = 0.9

0 0.5 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

P [p.u.]

Q [

p.u.

]

(a) (b)Fig. 2. PV systems capability diagram for different power factor values (a) without converter limits consideration. (b) with converter limits consideration.

5 10 15 200

10

20

30

40

50

60

70

80

90

100

Per

cent

of

peak

load

, %

Time, h

(a)

5 10 15 200

10

20

30

40

50

60

70

80

90

100

Time, h

(b)

Per

cent

of

PV

sol

ar g

ener

atio

n, %

active powerreactive power

active power

Fig. 3. (a) Typical daily load curve [18]. (b) Typical daily PV aggregate power output curve [26].

S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233 225

226 S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233

Fitnessð#Þ ¼ minXn

‘¼1

kW‘ �W‘k2 ð20Þ

This formula consists of two sub-equations as follows:

8s2f1;2; � � � ;ng)9#¼ ½ts1 ts2 � � �tsn �ð1�nÞ : 1� tss �24 & tss�1 < tss

8Ws 2 PtL;Q

tL;P

tPV

�)9W¼ ½W1W2 � � �Wn�ð1�24Þ :

W1 ¼ ½Wðts1 Þ Wðts1 þ1Þ � � � Wðts2 �1Þ�ð1�ðts2�ts1 ÞÞ

W2 ¼ ½Wðts2 Þ Wðts2 þ1Þ � � � Wðts3 �1Þ�ð1�ðts3�ts2 ÞÞ

� � �Wn ¼ ½Wðtsn Þ � � � Wð24Þ Wð1Þ � � � Wðts1 �1Þ�ð1�ðtsn�tsðn�1Þ ÞÞ

8>>>>><>>>>>:

9>>>>>=>>>>>;ð21Þ

4.2. HJP applied to volt/var/THD control

A feasible solution includes OLTC and capacitors 24-hours’ set-tings and PV inverter reactive power at each hour where the nodevoltages and harmonic distortions are within the acceptable limits.Fig. 4 represents a possible solution of the problem. The optimiza-tion problem is solved using two separate modules. The flowchartin Fig. 5 demonstrates the calculation process of the optimizationproblem. GA is implemented in MATLAB software. The algorithmused in multi-objective genetic algorithm is described in [32].DIgSILENT Programming Language (DPL) is utilized to performthe objective function’s calculations. The proposed procedure fordaily volt/var/THD control is iterated utilizing the combinatorialmethod until convergence is achieved. The modules are describedas follows:

4.2.1. MATLAB moduleThe output of this module is utilized as the initial values for the

next module. As shown in Fig. 4, solution generated by MATLAB iscomposed of three parts. The first part is related to capacitor ‘on/off’switching modes, second part is related to OLTC tap positionmodes and the final part is dedicated to hourly PV inverter reactivepower scheduling. Therefore, if the constraint of maximum OLTCswitching operations is satisfied, MATLAB writes on the chromo-some available in a text file. It is obvious that the computationalburden will be much less, especially when the number of compen-sation buses is getting large.

4.2.2. DIgSILENT moduleThe outputs of this module are used, in a cyclic procedure, as

the initial values for the previous described module. DIgSILENTreads the chromosome data as input and applies them to performhourly ‘on/off’ capacitor switching, OLTC tap position, and PVsinverters reactive power scheduling. Dispatch of shunt capacitorsto perform hourly ‘on/off’ capacitor switching is presented in nextsection. Afterwards, HLFC is run based on assigned hourly optimalscheduling and the objective function values are calculated. Again,DIgSILENT exports the objective functions values through a text fileinto MATLAB as input data. Finally, fuzzy reasoning is applied todetermine the optimal dispatch schedule in multi-objective opti-mization problem (MOP).

Fig. 4. Solution structure for

4.2.3. Dispatch of shunt capacitorsAt each hour, power quality improvement greatly depends on

the location and size of the switched capacitors. Also, frequentswitching operations may reduce switchable capacitor banks life-time. It is necessary to consider life expectancies of them. In thispaper, a method which guarantees the suppression of maximumallowable daily FCs and SCs switching and effectively corrects theconvergence process is utilized. As the FCs switching techniquepresented in [18] has a satisfactory computational efficiency, it isadopted in this paper but the method for switching capacitors in-stalled at the substation is improved. Considering the limitation ofcapacitors daily operation, these capacitors should be programmedin a way that the constraints in switching capacitors become impli-cit. Such a programming procedure would lead to appropriate con-vergence despite the complexity and computational burden. Fig. 6illustrates the programming of capacitors installed at a substation.The red line shows the change in the state of switching. The Un-changed switching blue line is followed by a reduction of theswitching states.

At each interval, the values zero or one represent ‘on/off’ state ofthe capacitor. Maximum time-interval is achieved by dividing 24-hto MKSC and minimum of it is 0. Therefore, it is obvious that if eachdi is zero or a value in two consecutive intervals, the number ofcapacitors switching will decrease. This idea would satisfy maxi-mum allowable capacitors switching as well as ‘on/off’ periods ofcapacitors (see Fig. 6(a)).

For example, Fig. 6(b) presents the sample data of a chromosomerepresenting the scheduling of a substation’s capacitor which is fedinto DIgSILENT module. Considering these data for Fig. 6(a) impliesthat the capacitor would stay ‘on’ from hour 1 for three hours. Sinced2 is assigned by 0, ‘on/off’ state is not determined in this intervaland there would only be one switching reduction. In hour 4, thecapacitor is switched ‘off’ for two hours. In hour 6, ‘on’ state isscheduled for two consecutive periods of three and four hours. Thisstate also represents a switching reduction. In the remaining hours,‘off’ state is scheduled for the capacitor (see Fig. 6(c)).

5. Multi-objective optimization fundamental and method

5.1. Construction of membership functions

Fuzzy theory is suitable to deal with unclear linguistic expres-sions. Since the objectives proposed in (3), (6), and (8) do not havesimilar units and variation ranges, a membership degree is as-signed to each parameter using fuzzy sets. Various membershipfunctions have been examined and the most suitable membershipfunctions are selected and utilized. A vector evaluated fuzzy multi-objective optimization is employed to determine the optimal dis-patch schedule that provides the best compromise among all theobjectives. The membership functions lDV, lTHD, And lLoss whichare mathematically presented in (22)–(24) are used for controllingthe buses voltage deviation, THD and system’s total energy losses,respectively.

lDV ¼maxðDVt

i ÞDVmax

max DVti

� �� DVmax

1 others

(ð22Þ

volt/var/THD problem.

Fig. 5. Flowchart of the proposed algorithm for optimal scheduling.

S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233 227

lTHD ¼maxðTHDt

viÞ

THDmaxmaxðTHDt

v iÞ � THDmax

1 others

(ð23Þ

lLoss ¼Loss

Loss0Loss � Loss0

1 others

(ð24Þ

Fig. 7 shows the ith continuous objective function described asfuzzy subset in the lðF iÞ space. The lower and upper bound of themembership functions are restricted to zero and one, respectively.According to Eqs. (22)–(24), if F i were smaller than F i;max; themembership value will monotonically decrease to zero with slopedependent on F i;max and the optimization is creditable, otherwisemembership value is equal to one.

5.2. Multi-objective genetic algorithm procedure

5.2.1. Basic concept of multi-objective problemThere are two general approaches to solve the MOPs. In MOPs,

there is a vector of objective functions and usually there is no sin-gle optimal solution that together optimizes all objective functions.In these cases the decision makers are looking for the most-pre-ferred solution [22].

Optimal v that minimizes objective functions of volt/var/THDproblem indicates the best decision space which is characterizedby lF i

:

It can be express as follow:

ObjectðvÞ ¼ min½lDV ðvÞ;lTHDðvÞ;lLossðvÞ� ð25Þ

(a) (b) (c)Fig. 6. Illustrates the programming of capacitors installed in the substation. (a) Hourly schedule of capacitors installed at the substation secondary bus. (b) Sample data of achromosome representing the scheduling of a substation’s capacitor. (c) Example of Hourly schedule of capacitors installed at the substation secondary bus.

Fig. 7. Membership function for objective functions.

228 S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233

5.2.2. Initialization populationThe initial solutions v generated in a random manner consists

of operating point of capacitor ‘on/off’ switching modes, OLTC tapposition modes and the hourly PV inverter reactive power schedul-ing as

vfNP�Dg ¼ SCfNP�ðNSC ð2�MKSC�1ÞÞg FCfNP�ð2�NFC Þg OLTCfNP�ðnÞg QPVfNP�ð24�NPV Þg

h ið26Þ

Considering the bounds on the decision variables, new ran-domly solution (power system variables) is produced. The relatedpart of capacitor ‘on/off’ switching modes and hourly PV inverterreactive power scheduling in each generated solution is spontane-ously restricted by operational constraints.

5.2.3. Evaluation of populationWith initial random values of control variables, energy losses

with each hour, voltage deviation and voltage THD at each bus iscalculated from HLFC. Total energy losses are calculated by com-bining energy losses of all 24 h, and the maximum voltage devia-tion and maximum voltage THD of all 24 h power systemoperation are calculated.

5.2.5. Non-dominated sortingThe population is sorted based on non-domination using the

following sorting algorithm. The sort algorithm is described asbelow:

Step 1: the set of solutions dominated by solution i, is obtainedin the population NP.

Step 2: The number of solutions that dominate the solution i, isobtained.Step 3: If solution i dominates solution j in NP, then j is added toset of solutions. If j dominates i, i is incremented.

Step 4: If no solutions dominate i then i belongs to the firstfront. In other words, rank of solution i is set to one. This proce-dure is repeated for rest of the solutions in NP.Step 5: Likewise, for kth front (nj), the set of solutions for sort-ing the solutions for (k + 1)th front is done.

5.2.6. Calculate crowding distanceThe crowding distance method obtains a uniform deployment

of solutions along the best-known Pareto front. For each objectivefunction k, sort the solutions in the ascending order. Boundary val-ues for each solution are allocated infinite value kjðv1

jÞ ¼ 1 andkjðv‘jÞ ¼ 1, then [33]

kj vij

� �¼ ljðviþ1

j Þ � ljðvi�1j Þ

lj;max � lj;mini ¼ 2; � � � ; ‘� 1; ð27Þ

5.2.7. Selection and recombinationBy means of tournament selection with crowed comparison

operator, the elitism solutions as all the previous and currentbest solutions are selected. Selection for solutions for nextgeneration (vm+1) is done by combining the current generationpopulation and the offspring population (vm [!m). Based onnon-domination, population is sorted and the new generationis completed by each front subsequently until current populationsize is obtained.

5.2.8. Crossover and mutationNew solutions (power system variables) !0 of size NP are

generated by crossover and mutation employed to v0.Crossover and mutation scheme is employed in this paperas below [34]:

The mathematic description of crossover is:

o1 ¼ q1 þ rand� a� ðq2 � q1Þ ð28Þ

o2 ¼ q2 þ rand� a� ðq2 � q1Þ ð29Þ

The mathematic description of mutation is:

o ¼ qþ b� rand� ðUB� LBÞ ð30Þ

where rand is a random number in the range zero to one, a and bare the scalar parameters.

5.2.9. Save best solutionThe best solution is memorized and retained which comply

with lowest total energy losses, voltage deviation and voltageTHD at each bus during a 24-h period.

Table 1Results from proposed control method in an IEEE 123 bus test system.

Item Case 1 Case 2 Case 3 Case 4 Case 5

DVmax (%) 12.5027 3.8713 4.2307 3.1482 3.5961

S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233 229

5.2.10. Stopping criteriaStopping criteria is decided based on experience and in this

volt/var/THD problem. The value of maximum cycle number ischosen 100.

THDmax (%) 6.2213 9.614 3.6773 15.6515 4.3808Loss (MW h) 4.5636 4.1131 4.1407 3.9168 3.9352lDV 1 0.77426 0.8461 0.6296 0.7192lTHD 1 1 0.7355 1 0.8762lLoss 1 0.9013 0.9073 0.8583 0.8623Computation time (s) – 437.16 4192.43 5463.34 6475.71

6. Simulation results and discussion

The proposed method for daily volt/var/THD control is appliedto a 4.16 kV, IEEE 123-bus distribution test system [35]. This sys-tem is considered as a distorted distribution system in [18,19] asa case study, where bus-150 is considered a swing bus (referencebus). However, the IEEE 123-bus test system considered in this pa-per contains non-linear loads besides PV solar arrays (see Fig. 8).The OLTC is used to keep the secondary bus voltage profile closedto the rated value under all load conditions. The tap changer is in-stalled on the high-voltage or low-current side of transformerwinding. Shunt capacitor banks connected to the substation’s sec-ondary bus are used to compensate the reactive power flowthrough the main transformer and those on feeder are used to im-prove the voltage profile along feeder. All switching capacitors in-clude one bank. The data of shunt capacitors installed in thedistribution system are given in [19]. Two 200 kW PV arrays are in-stalled at buses 95 and 108. Typical daily PV aggregate power out-put curve is shown in Fig. 3(b) [26].

The system includes five types of non-linear loads with the har-monic spectrum given in [19]. The harmonic spectrum for PVs istaken from [36]. The harmonic currents injected by non-linearloads and PV solar inverters are considered in the calculations. Inthe presence of harmonics and PVs inverters reactive power, fivedifferent cases are considered to investigate the effectiveness ofproposed method:

Fig. 8. IEEE 123-bus dis

Case 1: Represents the system initial condition with no controlscheme.Case 2: Proposes the control scheme with no PV solar inverterreactive power consideration as well as no harmonicconsideration.Case 3: Represents the control scheme considering no PV solarinverter reactive power but harmonic consideration.Case 4: Proposes the control scheme considering PV solar inver-ter reactive power regardless of harmonic.Case 5: Represents the control scheme considering both PVsolar inverter reactive power and harmonic.

The computation is carried out on an Intel core i7 2.6 GHz pro-cessor, 4 GB RAM, PC. Optimal dispatch scheduling results of theIEEE 123-bus system under non-sinusoidal operating conditionproposed control method is demonstrated in Table 1. Dissimilarschedule of shunt capacitors and OLTC tap positions generatedby proposed method are given in Tables 2 and 3 for different cases.Also, the results of time-interval approach can be seen at the OLTCtap position dispatch schedules in Tables 2 and 3. Fig. 9(a and b)

tribution network.

Table 2The non-sinusoidal IEEE 123 bus radial network operating condition without PV inverter reactive power schedule.

Optimal dispatch schedule of OLTC and shunt capacitors for case 2 Optimal dispatch schedule of OLTC and shunt capacitors for case 3

Hour OLTC C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 Hour OLTC C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

1 �3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 �2 0 1 0 0 0 0 0 0 0 0 0 0 0 02 �3 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 �2 0 1 0 0 0 0 0 0 0 0 0 0 0 03 �3 0 1 0 0 0 0 1 0 0 0 0 0 0 0 3 �2 0 0 0 0 0 1 0 0 0 0 0 0 0 14 �3 1 1 0 0 0 1 1 0 0 0 0 1 0 0 4 �2 1 0 0 0 0 1 0 0 1 0 0 0 0 15 �3 1 1 0 1 0 1 1 0 0 0 0 1 0 0 5 �2 1 0 0 0 0 1 0 0 1 0 0 0 0 16 �3 1 0 0 1 1 1 1 1 0 1 0 1 0 0 6 �2 1 1 0 0 0 1 0 0 1 0 0 0 0 17 �3 0 0 1 1 1 1 1 1 0 1 0 1 1 0 7 �2 0 0 0 0 0 1 0 1 1 0 0 0 1 18 �1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 8 �3 0 0 0 1 1 1 1 1 1 0 0 0 1 19 �1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 9 �3 0 0 0 1 1 1 1 1 1 0 0 1 1 1

10 �1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 10 �3 0 0 1 1 1 1 1 1 1 0 0 1 1 111 �1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 11 �3 0 1 1 1 1 1 1 1 1 1 0 1 1 112 �1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12 �3 0 1 1 1 1 1 1 1 1 1 1 1 1 113 �1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13 �3 1 1 1 1 1 1 1 1 1 1 1 1 0 114 �1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14 �3 1 1 1 1 1 1 1 1 1 1 1 1 0 115 �3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 �4 1 0 1 1 1 1 1 1 1 1 1 1 0 016 �3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 �4 1 0 1 1 1 1 1 1 1 1 1 1 0 017 �4 1 1 1 1 1 1 1 1 1 0 1 1 1 1 17 �3 1 0 1 0 1 1 1 1 1 1 0 1 0 018 �4 1 1 1 1 1 1 1 1 1 0 1 1 1 1 18 �3 1 0 1 0 1 1 0 1 1 1 0 1 0 019 �4 1 1 1 0 1 1 1 1 1 0 1 1 1 1 19 �3 1 0 1 0 1 1 0 1 1 0 0 1 0 020 �4 1 1 1 0 1 1 1 1 1 0 0 1 1 1 20 �3 1 0 1 0 0 1 0 1 1 0 0 1 0 021 �4 1 1 1 0 1 1 1 1 1 0 0 1 0 1 21 �3 0 0 1 0 0 1 0 0 1 0 0 1 0 022 �3 1 0 0 0 0 1 1 0 1 0 0 1 0 0 22 �2 0 0 0 0 0 1 0 0 1 0 0 1 0 023 �3 1 0 0 0 0 1 1 0 1 0 0 1 0 0 23 �2 0 0 0 0 0 1 0 0 0 0 0 0 0 024 �3 1 0 0 0 0 0 0 0 1 0 0 0 0 0 24 �2 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Table 3The non-sinusoidal IEEE 123 bus radial network operating condition with PV inverter reactive power schedule.

Optimal dispatch schedule of OLTC and shunt capacitors for case 4 Optimal dispatch schedule of OLTC and shunt capacitors for case 5

Hour OLTC C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 Hour OLTC C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

1 �4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 �4 0 0 0 0 0 0 0 0 0 0 0 0 0 02 �4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 �4 0 1 0 0 0 0 0 0 0 0 0 0 0 03 �4 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 �4 1 1 0 0 0 0 0 0 0 0 0 0 0 14 �4 1 0 0 0 0 0 0 0 0 0 0 1 1 1 4 �4 1 1 0 0 0 0 0 0 0 0 0 1 0 15 �4 1 1 0 0 0 0 0 0 0 0 1 1 1 1 5 �4 1 0 0 0 0 0 0 0 0 0 0 1 0 16 �4 1 1 0 0 0 0 0 0 0 0 1 0 1 1 6 �4 1 0 0 0 0 0 0 0 0 0 0 1 0 17 �4 1 0 0 0 0 1 0 0 0 0 1 0 1 1 7 �4 0 0 0 0 0 0 0 0 0 1 0 1 0 18 �1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 8 �2 0 0 1 0 1 0 0 1 0 1 0 1 0 19 �1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 9 �2 0 0 1 0 1 0 0 1 1 1 1 0 1 1

10 �1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 10 �2 1 0 1 0 1 1 0 1 0 1 1 0 1 011 �1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 11 �2 1 0 1 1 1 1 1 1 0 1 1 0 1 012 �1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 12 �2 0 1 1 1 1 1 1 1 0 1 1 0 1 013 �1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 13 �2 0 1 1 1 1 1 1 1 0 1 1 0 1 014 �1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 14 �2 0 1 1 1 1 1 1 0 0 1 0 0 1 015 �3 0 1 1 1 1 1 1 1 1 1 0 0 1 0 15 �3 0 1 1 1 1 1 1 0 0 1 0 0 1 016 �3 0 1 1 1 1 1 1 1 1 1 0 0 1 0 16 �3 0 1 1 1 0 1 1 0 0 1 0 0 1 017 �2 1 1 1 1 1 1 1 1 1 1 0 0 0 0 17 �4 0 0 0 1 0 1 1 0 0 1 0 0 0 018 �2 1 1 1 1 1 1 1 1 1 1 0 0 0 0 18 �4 1 0 0 1 0 1 1 0 0 1 0 0 0 019 �2 0 1 1 1 1 1 1 1 1 1 0 0 0 0 19 �4 1 0 0 1 0 1 1 0 0 1 0 0 0 020 �2 0 1 1 0 1 1 1 1 1 1 0 0 0 0 20 �4 1 1 0 0 0 1 1 0 0 1 0 0 0 021 �2 0 1 1 0 1 0 1 1 0 1 0 0 0 0 21 �4 1 1 0 0 0 1 1 0 0 0 0 0 0 022 �4 0 1 0 0 0 0 0 0 0 0 0 0 0 0 22 �4 1 0 0 0 0 0 1 0 0 0 0 0 0 023 �4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 �4 0 0 0 0 0 0 0 0 0 0 0 0 0 024 �4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24 �4 0 0 0 0 0 0 0 0 0 0 0 0 0 0

230S.Jashfar,S.Esm

aeili/ElectricalPow

erand

EnergySystem

s60

(2014)221–

233

S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233 231

shows the daily optimal dispatch of PVs inverters reactive powergeneration and absorption for the best solutions in two cases 4and 5. THD reduction and voltage improvement are plotted inFig. 10(a–c), respectively. THD reductions of the most distortedbuses, before and after optimization (through different cases sim-ulation), are plotted in Fig. 10(a and b). Exact inspection of the sys-tem conditions before compensation (OLTC tap at +8 position, allcapacitors are switched ‘off’ and reactive power of PVs are not con-sidered) reveals that the system is unfavorably distorted. Voltageimprovement of the worst bus (bus 66) after applying the controlscenarios in comparison with no control execution, are plotted inFig. 10(c). However, after compensation, the voltage deviationand harmonic distortion levels are effectively suppressed below

5 10 15 20

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

PV

inve

rter

s V

Ar

sche

dulin

g, p

.u.

Time, h

PV 1PV 2

(a)Fig. 9. PV inverters reactive power scheduling (a) PV 1 and 2 inverter operatio

5 10 15 200

1

2

3

4

5

6

Time, h

TH

D, %

5 100

1

2

3

4

5

6

7

8

Tim

TH

D, %

(a) (bFig. 10. Simulation results for the 123-bus system for non-sinusoidal operating conditimprovement of the bus 66.

the permitted level of 5%. Summary of voltage, THD, and energysaving in system with different cases are visible in Table 4. In cases4 and 5, precise inspection of the schedules confirms that applica-tion of PVs inverters reactive power leads to higher energy savingin comparison with cases 2 and 3.

7. Discussion of results

The proposed HJP is applied to the IEEE 123-bus test-systemincluding PV systems, capacitors, and OLTC to obtain acceptablevoltage deviation, harmonic distortion, and energy losses in differ-ent cases. The reactive power capability of the PV inverter is

5 10 15 20

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time, h

(b)n mode for case 4 and (b) PV 1 and 2 inverter operation mode for case 5.

15 20e, h

5 10 15 20

0.88

0.9

0.92

0.94

0.96

0.98

1

Time, h

Vol

tage

, p.u

.

Case 1Case 2Case 3Case 4Case 5

) (c)ion. (a) THD reduction of the bus 83. (b) THD reduction of the bus 86. (c) Voltage

Table 4Summary results of approaches.

Minimum voltage (pu) Maximum voltage (pu) Average system voltage (pu) Energy saving (%)

Case 1 0.87497 1.0 0.9013 –Case 2 0.96128 1.03871 0.9901 9.871593Case 3 0.95769 1.04230 0.9826 9.266807Case 4 0.96851 1.03148 0.9969 14.17302Case 5 0.96403 1.03596 0.9891 13.76983

232 S. Jashfar, S. Esmaeili / Electrical Power and Energy Systems 60 (2014) 221–233

considered to voltage and reactive power control. The applicationof PV inverter reactive power leads to higher energy saving. Theimpact of energy saving for the compensated network consideringPV inverter is summarized in column 5 of Table 4. As can be ob-served, the energy saving with PV inverter reactive power consid-eration (cases 4 and 5) is better than without considering thiscapability (cases 2 and 3). Therefore, executing appropriate controlscheme on PV inverter reactive power leads to less electrical en-ergy losses in comparison with the other cases. Also, hourly voltageimprovements indicate that average voltage deviations decreasefrom 9.44% to less than 1.06% for different cases. Considering inev-itable propagation of harmonics in distribution networks, theyshould be considered to keep the harmonic distortion levels withinthe permitted limits. Non-linear load level increase results in THDvalue increment in the network. However, after compensation, thecompensating capacitors play more important roles. Outputs ofHLFC before optimization show a maximum voltage THD of6.24% for this system as given in Table 1 for case 1. Results showmaximum voltage THD is limited to 3.68% and 4.38% for cases 3and 5, respectively. After applying the proposed control scheme,the distortion levels are effectively suppressed below the permit-ted level of 5%. The reduction in the maximum total harmonic dis-tortion level in case 3 and 5 with respect to cases 1, 2 and 4 justifiesthe inclusion of harmonics in the optimal planning. Since, schedul-ing without taking harmonics into account causes a severe har-monic distortion problem i.e., 9.61% in case 2 and 15.65% in case4 which is higher than standard limit. These facts are also demon-strated in Fig. 10(a–c) for two distorted buses 83 and 86. Voltageprofile of node 66, which is the node with lowest voltage in thenetwork, is shown through 24-h in Fig. 10(c). The proposed HJPmethod is precise in obtaining a much better optimal solution.Inclusion of PV in the proposed dispatch algorithm results in differ-ent schedules for the OLTC and switch capacitors under non-sinu-soidal conditions (see Tables 2 and 3). The OLTC taps positions andcapacitors ‘on/off’ switching status vary at substations and alongfeeders through 24-h. Total OLTC and capacitors switching opera-tions numbers per day satisfy the constraints. A more precise com-parison of results in case 3 and 5 shows that, considering PVsreactive power capability, harmonic values are decreased. This isdue to more effective utilization of PV units which may lead toavoidance of resonance condition by changing capacitors schedule(the same result can be acquired by comparison of case 2 and 4).Moreover, the loss reduction is improved about twice the case 3.In case 4 network losses are reduced in comparison with case 5.This is a sacrifice for harmonic reduction in case 5. The results alsodiscover a dependent operation between PVs and capacitors’ ‘on/off’ states (For example PV system in bus 108 and capacitor number12 and 13). It can be the subject of future research for coordinatedcontrol of PV and compensating devices to improve the overalloptimization performances.

8. Conclusion

It is necessary to decrease burden on grid capacity of the distri-bution networks. Volt/var/THD control makes it possible to im-prove the energy delivery efficiency on existing distribution

networks. This paper proposes a hybrid joint programming tovolt/var/THD control action utilizing integration of MATLAB andDIgSILENT software. The suggested methodology is applied to IEEE123-bus radial test feeders with promising results. The proposedscheme comprises two outstanding features. Firstly, the forecastedload demand and PV solar active power output generation of theday-ahead is divided into several load levels. Secondly, the combi-nation of optimal dispatch schedule of all control devices such asOLTC, SCs, FCs, and PVs inverters reactive power simultaneouslyin addition to considering harmonics is performed using multi-objective genetic algorithm. This control scheme leads to energylosses reduction and voltage profile improvement. The control sys-tem regarding regulation of its action considers constraints relatedto maximum voltage violation and THD violation. The applicationof the conventional optimal dispatch scheduling for non-sinusoidaloperating conditions is not acceptable as it leads to high THD volt-age distortions. A proper coordination between OLTC, SCs, FCs, andPVs has been treated. The simulation results indicate that in a sys-tem with PVs inverters reactive power consideration, the on dura-tion time of FCs and SCs is considerably decreased. It is concludedfrom the study results that the proposed HJP method is very effi-cient in obtaining the solution of the fuzzy-based volt/var/THDcontrol problem.

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