optimal distributed energy resources allocation for enriching … · 2020-03-26 · introduced to...

ORIGINAL PAPER

Optimal Distributed Energy Resources Allocation for EnrichingReliability and Economic Benefits Using Sine-Cosine Algorithm

Abdelazeem A. Abdelsalam1,2

Received: 28 March 2018 /Accepted: 10 March 2020# Springer Nature Singapore Pte Ltd. 2020

AbstractThis paper presents an optimization algorithm called sine-cosine algorithm (SCA) for optimal distributed energyresources (DERs) allocation in various configurations of radial distribution networks. This study is demonstratedin two statuses to find the optimal locations and sizes of DERs to be installed on the distribution system. Firststatus; the most candidate locations for connecting DERs are suggested by using the loss sensitivity factor theoryand the proposed SCA is applied to select the optimal capacities of DERs. Second status; the SCA is used todetermine both the optimal locations and sizes of DERs. The positive impact of DERs on distribution systems reliability has beeninvestigated in addition to the system power losses and bus voltages. The fitness function is to maximize the savings produced bynot only power losses reduction but also reliability enhancement. The proposed algorithm is applied to IEEE 33 and 69-bus radialdistribution networks with installing different number of DERs. The simulation results using Matlab programming environmentshow that the proposed methodology is viable, supporting reliability as well as fulfilling the conventional objectives such as costminimization, voltage profile improvement, system losses reduction. A comparison between SCA and other methods is intro-duced to verify the superiority of SCAwhere SCA fulfils the maximum saving and maximum reduction of power losses equals to61.3% and 69.2% for IEEE 33-bus and 69-bus networks, respectively.

Keywords Distributed energy resources allocation . Loss sensitivity factor . Reliability . Sine cosine algorithm . Voltage profile

NomenclatureAbbreviationsABC artificial bee colonyACO ant colony optimizationALO antlion optimizationBCBV branch current-bus voltageBFS backward/Forward sweepBIBC bus current injection-branch currentBSOA backtracking searchCS cuckoo searchCSA clonal selection algorithmCSO cat swarm optimization

CSOS chaotic symbiotic organisms searchDE differential evolutionDERs distributed energy resourcesDGs distributed generationsENS energy not suppliedET evidence theoryFPA flower pollination algorithmGA genetic algorithmGWO grey wolf optimizationIBA improved bat algorithmIDSA improved differential search algorithmIWD intelligent water dropLSF loss sensitivity factorMTLBO modified teaching–learning based optimizationNLP nonlinear programmingNSPSO non-dominated sorting particle swarm

optimizationPSO particle swarm optimizationSCA sine-cosine algorithmSFLA shuffled frog leaping algorithmTHD total harmonic distortion

* Abdelazeem A. [email protected]

1 Faculty of Energy Systems and Nuclear Science, University ofOntario Institute of Technology (UOIT), 2000 Simcoe Street North,Oshawa, ON L1H7K4, Canada

2 Electrical Engineering Department, Faculty of Engineering, SuezCanal University, Ismailia 41522, Egypt

Technology and Economics of Smart Grids and Sustainable Energy (2020) 5:8 https://doi.org/10.1007/s40866-020-00082-8

http://crossmark.crossref.org/dialog/?doi=10.1007/s40866-020-00082-8&domain=pdf

https://orcid.org/0000-0003-3103-7220

mailto:[email protected]

Variablesβi compensation coefficient of the ith branchBij branch currentBijMax branch maximum currentc1 sinusoidal control parameter that balance the ex-

ploration and exploitation phases of SCAalgorithm

cDER cost of energy generated by DERsce cost of average energycENS cost of ENSF1 energy demand from the utility reduction savingF2 system energy loss reduction savingF3 system reliability improvement savingLai average load connected to load point i in kW.λi average failure rate of the ith component in

failure/yrλs average failure ratePD total real power demandPDERs power generated by DERsPs power delivered by the utility gridti average outage time of the ith component.V*i is the conjugate of ith node voltage

Vmax upper limit of bus voltageVmin lower limit of bus voltage.V!

o is the initial bus voltage vectorS*i is the conjugate of complex power of ith nodeZD is the impedance matrix

Introduction

Recently, DERs have a great interest due to their technical andeconomic benefits. These benefits include power loss reduc-tion, improving voltage profile, enhancing system reliability,minifying operating costs and maximizing net savings. DERsshould optimally be allocated in distribution networks toachieve maximum benefits. Optimal allocation of DERsmeans determining their locations and sizes in an optimalmanner. Inappropriate allocation may cause higher powerlosses and unsatisfied characteristics as well [1, 2].

DERs allocation problem is a well-researched topic and hasbeen concerned by several authors. It is a multi-objective op-timization problem. Objectives can be both economic benefitsby decreasing the power and energy losses and/or technicalbenefits by improving voltage stability and improving voltageprofile along the feeder. A survey describing the DERs allo-cation techniques can be found in [3–6]. Different analyticalapproaches to minimizing line losses have been exploited andproposed [7–9].

Many meta-heuristic optimization algorithms have beenintroduced to find the optimal site and size of DERs. Thegenetic algorithm (GA) is one of these algorithms and is for-mulated for optimal DERs siting and sizing with the best

compromise between various costs [10, 11]. GA has beenutilized in combined with evidence theory (ET) to solve thisproblem as a multi-objective function where GA has beenused to generate different solutions and ET has been employedto assess the candidate allocations [12]. In [13], non-dominated sorting particle swarm optimization (NSPSO)method is proposed to find the optimal locations and sizes ofDERs. Multi objective function including minimization ofactive power loss, wasted energy from solar and wind gener-ation systems, and voltage deviation is considered. A differ-ential evolution (DE) algorithm is proposed for placement ofDERs in distribution networks based on voltage stability in-dex. The optimal DERs locations are selected based on incre-mental bus voltage sensitivities and the optimal sizes are com-puted by differential evolution [14]. An improved differentialsearch algorithm (IDSA) by pareto optimization technique hasbeen introduced to solve the DGs allocation problem by min-imizing the losses and operation costs and maximizing thevoltage profile [15]. A chaotic symbiotic organisms search(CSOS) approach has been suggested to determine the opti-mum location and sizes of DERs in radial distribution sys-tems. Improper allocation of DERs may increase the systemlosses. The objective function is adopted for minimizing ac-tive power loss and maximizing the voltage stability index.The suggested method is applied to IEEE 33-, 69- and 118-bustest systems [16]. In [17], A strategy has been proposed forfinding the optimal places and capacities of DERs in thedistribution systems with uncertainty environment. Fuzzynumbers are used to model uncertainties in the system. Amulti-objective function is considered which the objectivesare defined as minimization of financial cost index, technicalrisks, and economic risks. The financial cost index includesinvestment, operation cost of DERs and cost of losses. While,the technical risks include risks of voltage and loading con-straints violation because of load uncertainty and economicrisk due to electricity market price uncertainty.

A modern strategy called the loss sensitivity factor (LSF)has been utilized for selecting the candidate locations forDERs installation. Minimization of real power loss is deter-mined as objective function. The proposed formulation is ex-ecuted on the 43-bus test system [18]. Optimal DERs andenergy storage are allocated jointly using grey wolf optimiza-tion (GWO) method. The objective function is formulated tominimize the costs and the proposed algorithm is tested on34-bus test system [19]. A multi-objective framework as anonlinear programming (NLP) is suggested to determine theoptimal sites and sizes of DERs. It aims at minimizing thenumber of DERs and power losses as well as maximizingvoltage stability index. In order to avoid problems of selectingappropriate weighting factors, fuzzification is applied to theobjectives to bring them into the same scale. IEEE 34-bussystem is utilized as a test system to ensure the effectivenessof the proposed approach [20]. Minimizing the total system

8 of 18 Technol Econ Smart Grids Sustain Energy (2020) 5:8

power losses by finding the optimal places and capacities ofDERs using Artificial bee colony (ABC) is investigated in[21]. ABC is also suggested to solve the optimal DERs allo-cation problem where DERs are able to generate both activeand reactive power [22]. ABC approach is applied to IEEE 69-bus and IEEE 33-bus test systems [23] and the objective func-tion is updated to minimize the real power loss, total harmonicdistortion (THD) and voltage sag index. A hybrid of ant col-ony optimization (ACO) and ABC algorithm has been pre-sented for determining the optimal site and sizing of DERs ondistribution systems [24]. A multi-objective function includ-ing minimization of power losses, total emissions produced bysubstation and resources, total electrical energy cost, and im-proving the voltage stability has been investigated. The shuf-fled frog leaping algorithm (SFLA) is a meta-heuristic searchmethod inspired from the memetic evolution of a group offrogs when seeking food. It has been utilized for optimalDERs allocation in radial distribution system [25]. In [26],LSF has been used to determine the candidate locations forDERs connection. Then intelligent water drop (IWD) algo-rithm is utilized to find the optimal size of installed DERs.The authors in [27] have presented improved bat algorithm(IBA)to provide integrated solution for the optimal allocationof distributed generations and network reconfiguration con-sidering load patterns of customers. The antlion optimizationalgorithm (ALO) has been utilized to find the optimal size andsite of DGs by minimizing the cost of purchased energy fromthe utility grid, enhancing the reliability, and reducing thepower losses [28]. ALO has been also presented to find theoptimal size of DGs while index vector method is utilized tofind the optimal locations [[29]). In [30], the sizing of DGs isdone by analytical approach based on exact loss formula forminimum loss at the allied buses. After that Fuzzy expertsystem is used for optimal placement using distribution lossreduction index and voltage deviation reduction index as itsinput parameters. The proposed methodology is tested for apractical distribution system of Tezpur University, India. In[31], HOMER software-based gird optimization study hasbeen presented to optimally retrofit a remote off-grid powersystem in Northern Canada.

Many other meta-heuristics methods have been introducedto find the optimal allocation of DGs such as the cuckoo search(CS) algorithm [32], the backtracking search (BSOA) [33],particle swarm optimization (PSO) [34], modified teaching–learning based optimization algorithm (MTLBO) [35], compre-hensive teaching learning-based optimization (CTLBO) [36],modified harmony search algorithm [37] and a hybrid algo-rithm of ABC and clonal selection algorithm (CSA) [38].

It is observed that there is a little interest in the impact ofDERs on enhancing system reliability. A cat swarm optimiza-tion (CSO) has been presented to solve the DERs placement toincrease the reliability of distribution network. The effect ofthe number of installed DERs on power loss reduction and

system reliability enhancement is studied. It is noted that thepercentage of power loss reduction is improved by increasingthe number of installed DERs from one to three [39]. In addi-tion, as in [40, 41], installed DERs are used to improve thereliability by decreasing energy not supplied (ENS) to theload. The main contributions of this paper are:

(i) Proposing a novel algorithm called sine-cosine algorithm(SCA) for solving DERs allocation problem.

(ii) Formulating the objective function to maximize the sav-ing due to energy loss reduction in addition to the savingresulted by reliability enhancement.

(iii) Implementing the objective function to be solvedthrough two scenarios; (a) using loss sensitivity factorand (b) using SCA approach.

(iv) Validating the proposed approach by applying it to IEEE33-bus and IEEE 69-bus test systems.

(v) Comparing the results with other optimization algo-rithms such as backtracking search, cuckoo search,PSO, intelligent water drop, genetic algorithm, ant colo-ny optimization, modified teaching–learning, ABC,clonal selection, flower pollination and improved differ-ential search algorithms

Problem Description

Power Flow Analysis

The application of Newton-Raphson or Gauss-Seidel methodsfor power flow solutions is not appropriate for radial distribu-tion system as a result of its higher R/X quantitative relationand unbalanced loading nature. To find the power flow solu-tions in radial distribution system, many types of distributionload flow methods are projected and most of these methodsare established on Kirchhoff’s current and voltage laws.Backward/Forward sweep (BFS) is one of efficient and sim-plest techniques. It calculates currents at all nodes from theend node towards the source node within the backward sweepmode, whereas respective bus voltages are calculated from thesource node towards the end node within the forward sweepmode [42].

A sample of six bus radial distribution system is shown inFig. 1, the branch currents and bus voltages are computed byusing BFS based iterative technique. Equivalent currentinjected at ith node is calculated as,

I i ¼ S*iV*i

ð1Þ

where, i = 2,3,….,n; S*i is the conjugate of complex power of ith

node, V*i is the conjugate of ith node voltage and “n”

Technol Econ Smart Grids Sustain Energy (2020) 5:8 of 18 8

represents the number of nodes available in the given radialnetwork.

& Formulation of Bus Current Injection-Branch Current(BIBC) matrix

After calculation of injected node currents, the correspond-ing elements of the branch current vector are calculated as,

BC5 ¼ I6;BC4 ¼ I5;BC3 ¼ I4 þ I5;BC2

¼ I6 þ I5 þ I4 þ I3;BC1 þ I6 þ I5 þ I4 þ I3 þ I2

where, I2, I3…., I6 are the equivalent current injection of re-spective nodes.

BC1

BC2

BC3

BC4

BC5

266664

377775 ¼

1 1 1 1 10 1 1 1 10 0 1 1 00 0 0 1 00 0 0 0 1

266664

377775

I2I3I4I5I6

266664

377775 ð2Þ

Relation (2) can be represented in a compact form as,

BC�! ¼ BIBC½ � I

! ð3Þ

where, [BIBC] represents the relationship between the buscurrent injection and branch current of respective nodes.

& Formulation of Branch Current-Bus Voltage (BCBV)Matrix

The bus voltages can be calculated from the substation bustowards the terminal node after calculating the current injec-tion by each load and branch currents starting from the endnode towards the source node. The incidence matrix thatshows the relationship between the branch currents and busvoltages is abbreviated as [BCBV] and can be presented as inEq. (4)

BCBV½ � ¼ BIBC½ �T ZD½ � ð4Þ

where, [ZD] is the impedance matrix with the impedance ofeach branch as the diagonal element as shown in Eq. (5).

ZD½ � ¼

Z1 0 0 0 00 Z2 0 0 00 0 Z3 0 00 0 0 Z4 00 0 0 0 Z5

266664

377775 ð5Þ

where, Z1, Z2, Z3, Z4, Z5 are the respective branch impedancesof the sample system. The final form of BCBV matrix can berepresented as follow:

BCBV½ � ¼

Z1 0 0 0 0Z1 Z2 0 0 0Z1 Z2 Z3 0 0Z1 Z2 Z3 Z4 0Z1 Z2 0 0 Z5

266664

377775 ð6Þ

Then the bus voltages can be computed by using [BCBV]as in Eq. (7)

V2

V3

V4

V5

V6

266664

377775 ¼

V1

V1

V1

V1

V1

266664

377775−

Z1 0 0 0 0Z1 Z2 0 0 0Z1 Z2 Z3 0 0Z1 Z2 Z3 Z4 0Z1 Z2 0 0 Z5

266664

377775

BC1

BC2

BC3

BC4

BC5

266664

377775

V1

V1

V1

V1

V1

266664

377775−

V2

V3

V4

V5

V6

266664

377775 ¼

Z1 0 0 0 0Z1 Z2 0 0 0Z1 Z2 Z3 0 0Z1 Z2 Z3 Z4 0Z1 Z2 0 0 Z5

266664

377775

BC1

BC2

BC3

BC4

BC5

266664

377775

ð7Þ

and can be generalized as:

ΔV�! ¼ BCBV½ �BC�! ð8Þ

ΔV�! ¼ BCBV½ � BIBC½ � I! ð9Þ

1 2 3

4 5

6

BC1 BC2

BC3 BC4

BC5Z1 Z2

Z3 Z4

Z5

I2 I3

I4 I5

I6

Fig. 1 Sample of radialdistribution network


ΔV�! ¼ DLF½ � I! ð10Þwhere, [DLF] represents the relationship between the voltagedrop and the bus current injections.

The power flow calculations are carried out by solving thefollowing equations iteratively.

IKi ¼ SiVKi

� �*

ð11Þ

ΔV�!kþ1¼ DLF½ � IK� � ð12Þ

V!kþ1

¼ V!

o−ΔV�!kþ1

ð13Þ

where, V!

o represents the initial bus voltage vector.This iterative process is repeated until the convergence is

reached.The total power loss can be calculated using:

Ploss ¼ R½ �T : BIBC½ �: I!�� 2 ð14Þ

where, [R] ≡ branch resistances matrix.

Loss Sensitivity Factors

Loss sensitivity factors (LSF) method is a one of pop-ular methods that is utilized to select the candidate bus-es of DERs installation to help reducing the searchspace for the optimization process [43]. Considering asimple distribution line connected between nodes ‘1’and ‘2’ as displayed in Fig. 2, the active power lossin the kth line is defined by [Ik

2]* RK, and is computedby:

Plossð ÞK ¼P2ð Þ2 þ Q2ð Þ2

� � RK

V22

ð15Þ

Similarly, the reactive power loss in the kth line is computedas

Qlossð ÞK ¼P2ð Þ2 þ Q2ð Þ2

� :XK

V22

ð16Þ

where, P2 and Q2 are the total active power and total reactivepower at bus ‘2’, respectively.

The loss sensitivity factor can be calculated as

LSF ¼ ∂Ploss

∂Q¼ 2*Q2 � RK

V22

ð17Þ

The procedure of selecting the candidate locations can besummarized as follows:

(i) Computing the LSF at the different nodes of distributionsystem without DERs installation using Eq. (17)

(ii) Sorting the LSF values in descending order.(iii) Computing the normalized voltage (normi) for all nodes

as:

normi ¼ Vi=0:95 ð18Þ

(iv) Selecting the candidate buses, the buses that have normi

value less than 1.01 pu are considered as candidateplaces of DERs installation with the same sequence assorted in step (ii).

The Objective Function

The objective function of the DERs allocation problem in thisstudy is to maximize annual net savings based on three termsas follows:

Net Saving=yr ¼ max F1 þ F2 þ F3ð Þ ð19Þ

where, F1, F2 and F3 are the saving due to the reduction ofenergy demand from the utility, the saving due to the energyloss reduction, and the saving due to the system reliabilityimprovement, respectively.

Saving Due to Reduction of Energy Demand from the Utility

It is assumed that DERs are owned by customers andthe utility does not pay for installation and maintenance.It only pays for the purchased energy from the cus-tomers. Connecting DERs to the distribution systems

1 2Kth - Line

R + jXP2 + jQ2

Fig. 2 Simple distribution line


helps increasing the reduction of energy demand fromutility.

F1 ¼ PD*ce � 8760ð Þwithout DERs− PD−PDERsð Þ � ce þ PDERs � cDER½ � � 8760f gwith DERs

ð20Þ

where, PD is the total real power demand, PDERs is thepower generated by DERs, ce is the average energy costand cDER is the cost of power generated by DERs.

Saving due to energy loss reduction

Cost of Ploss should be shared between utility and customerswhose owned the DERs, but it is taken as a worst value andcomputed only on the utility as follows;

F2 ¼ Ploss � ce � 8760ð Þwithout DERs− Ploss � ce � 8760ð Þwith DERs

ð21Þ

Saving due to system reliability improvement

Basically, three indices of system reliability are considered; (i)average failure rate (γs), (ii) average outage time (ts), and (iii)annual outage time (Ts) [40]. These indices can be calculatedas:

γs ¼ ∑iγi ð22Þ

Ts ¼ ∑iγi � ti ð23Þ

where, γi is the average failure rate of the ith component(failure/yr) and ti is the average outage time of the ith

component.Energy not supplied (ENS) to the system refers to the suit-

able level of reliability and can be calculated as:

ENS ¼ ∑Ni¼1Lai � γi � ti ð24Þ

where, Lai is the average load connected to point (i) in kW.Connecting DERs to the distribution networks has a posi-

tive impact on reliability where it is considered as an alterna-tive energy sources. With increasing the output capacity ofDERs, ENS can be decreased. It is preferred to increaseDERs output from the point of view of the system re-liability to feed the entire load of the network, but thismay not be the optimal solution from energy loss

reduction or net savings improvement point of view.Therefore, it is important to satisfy the objective function ofnet savings in the form

F3 ¼ ENSwithout DERs−ENSwith DERsð Þ � cENS ð25Þ

where cENS is the cost of ENS.The annual net savings has to be maximized under the

following constraints.

& Voltage profile limitThe voltagemagnitude at different buses must bemain-

tained within predetermined limits (±10%) and isexpressed as

Vminj j≤ Vj j≤ Vmaxj j ð26Þ

where, |Vmin| and |Vmax| are the lower and upper limits of busvoltage.

& Power balance constraint

Ps þ ∑NDERk¼1 PDER ¼ PD þ Ploss ð27Þ

where Ps is the power delivered by the utility grid

& Branch thermal limits

0≤Bij≤Bij Max ð28Þ

where Bij is the branch current and BijMax is the branch max-imum current.

Overview of the Proposed SCA Algorithm

Sine Cosine Algorithm

Sine cosine algorithm (SCA) is a novel stochastic optimiza-tion algorithm proposed by Mirjalili in 2016 which based itsupdate roles on the sine and cosine functions [44]. The algo-rithm starts the first population randomly with a set of


solutions/search agents in the search space of the optimizationproblem. The search agents are guided toward an optimal point/solution in the search space via the fitness/objective functionthat evaluate each search agent in each iteration of the algorithm.In addition, the algorithm keep track of the best solution’s posi-tion P achieved by all search agents in the population at eachiteration. The mathematical model used in the SCA algorithm isbased on the following update function for any search agent Xi:

X tþ1i ¼ X t

i þ c1sin c2ð Þ c3Pti−X

ti

�� ; k < 0:5

X ti þ c1cos c2ð Þ c3Pt

i−Xti

�� ; k≥0:5

�ð29Þ

c1 ¼ s−ts

tmaxð30Þ

where, t is the current number of iteration, and c1 is the sinu-soidal control parameter that balance the exploration and ex-ploitation phases of the algorithm which decreases linearlyfrom a constant value s to 0 by each iteration according toEq. (29). Each of c2, c3, and k are random numbers.

Figure 3 shows the model of SCA. This model has a circularsearch pattern where the best solution (P) is located at the centerof a circle and the feasible solutions (search agents) is positionedaround it. The circular search space is divided into sub-regionsthat represent possible exploration regions for any solution Xi.The control parameter c1 determines the movement direction ofXi; toward P if it is higher than one or outward if it is lower thanone. Random value (0:2π) of c2 determines how far Xi movetoward or outwardP according to c1. c3 gives randomweights tothe best solution P to stochastically emphasize (c3 > 1) ordeemphasize (c3 < 1) the desalination in defining the dis-tance. Parameter k (0:1) randomly switches betweenthe sine and cosine parts of Eq. (28). When the rangeof a sine–cosine function is in the interval of [−1, +1],then Xi moves toward P and algorithm exploits thesearch space. However, out of [−1, +1] interval, Xi de-viates the P and algorithm explores the search space.

Implementation of SCA

The implementation steps of applying SCA to solve the prob-lem of determining the allocation of DERs is below:

Step #1: The input data include; Line parameters (Rij &Xij) between the ith bus and the bus j connectedto it, load data (Pi & Qi at the ith load bus), thenumber of feasible solutions/search agents, themaximum number of iterations (tmax), the num-ber of locations (all buses are available exceptthe slack bus, bus #2) and the maximum allow-able size of DERs.

Step #2: Appling BFS method to obtain node voltage valuesand line power losses.

Step #3: Generate initial populations randomly as feasiblesolutions and evaluate the objective function (max-imum annual saving) for each and set iterationnumber (t = 1).

Step #4: Determination of best locations at which the objec-tive function is maximum and the correspondingsizes as well.

Step #5: Within this population new solutions are obtainedthrough updating SCA parameters c1, c2, c3 and k.

Step #6: Calculating the objective function of each updatedsolution (new solutions).

Step #7: Updating the objective function based on the up-dated solutions.

Step #8: Determining the optimal objective function.Step #9: Comparing the value obtained in step #8 with the

preceded one and considering the largest value.Step #10: Advancing iteration number (t = t + 1).Step #11: Going to step #5 and repeat the solution until

reaching the maximum number of iteration.

The flowchart of applying SCA algorithm on DERs allo-cation is depicted in Fig. 4.

Fig. 3 Population of SCA


Simulation Results and Analysis

To evaluate the effectiveness and performance of the devel-oped SCA approach in the application of DERs allocation, ithas been tested on IEEE 33-bus and IEEE 69-bus radial dis-tribution systems. The proposed algorithm has been simulatedusing Matlab. This study is demonstrated through twostatuses:

& Status #1: Determining the candidate locations based onLSF then selecting the optimal capacities of installedDERs via SCA;

& Status #2: Determining the optimal locations and capaci-ties of DERs based on SCA only.

Each Status includes two cases:

& Case #1: Installing single DER;& Case #2: installing multi-DERs.

For reliability enhancing evaluation; it is assumed that thefailure rate of a component is 0.2 f/km.yr, the length of lateralsection between two buses is 1.5 km, the length of the mainfeeder section between two buses is 2.0 km, repairing time of acomponent is 4 h for a branch in the main feeder and 2 h forlaterals and the switching time is 0.5 h [16, 17]. The averageenergy cost (ce) is 0.06 $/kWh [45], cost of power generatedby DERs (cDER) is taken as 40 $/MWh [40], and the cost ofENS (cENS) is 4.92 $/kWh.

IEEE 33-Bus Test System

IEEE 33-bus distribution network is operating at 12.66 kVandits single line diagram is displayed in Fig. 5 [46, 47]. The totalreal and reactive power demand is 3715 kW and 2300 kVAr,respectively. From the power flow study using BFS in the basecase (without DERs), it is found that the active and reactivepower loss are 210.99 kW and 143.03 kVAr, respectively.Also, the minimum bus voltage is 0.904 pu at bus #18 andthe annual cost is computed as 2,068,101.775 $/yr consideringthe active power demand, power loss, and ENS costs.

Status #1

First, LSF is applied to obtain the candidate locations forinstalling DERs. Table 1 lists the results of applying LSF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

23 24 25 26 27 28 29 30 31 32 33

19 20 21 22

Fig. 5 single line diagram ofIEEE 33-bus distribution system

Read system

input data

Run the load flow

program

Generate the initial

population randomly

Calculate the objective

function

Set P = Xi

Max. iteration

reached?

Get the optimalsolution

Yes

NO

Update C1

Is

f(Xi)<f(P)?

Generate randomly C2,C3, k

Update the position of

Xi

Pass the current best

solution to the next

generation

Yes

NO

Fig. 4 Flowchart of SCA


technique on IEEE 33-bus test system. Candidate buses aredenoted by ′∎’ and otherwise by ′⨂ ′ . It is concluded that thecandidate locations for DERs installation are in the sequenceof {6, 28, 29, 8, 30, 9, 13, 10, 27, 31, 26, 14, 12, 7, 17, 16, 15,11, 32, 18, 33}.

Second, the proposed SCA approach is applied to deter-mine the optimal rating of installed DERs. Table 2 summa-rizes the results of allocating single and multi-DERs in IEEE33-bus distribution system. The optimal solution is that ver-ifies the best fitness function of the net saving. Therefore,installing single DER at bus #6 with capacity of 1.950 MWis considered as the optimal placement of DERs. In this case,the net saving is equal to 439,690.5 $/yr, the active power loss

is reduced to 116.79 kW, the cost of energy not supplied re-duction is maximized to be 48,535.8 $/yr, and the minimumvoltage bus is improved to 0.933 pu at bus #18. On the otherhand, from the active power loss reduction point of view,installing three DERs is the optimal allocation.

Status #2

In this case, Determining the optimal locations and sizes ofDERs are based on SCA application. Table 3 tabulates theresults of connecting single and multi-DERs in IEEE 33-busdistribution. Installing three DERs at: bus #8 with size0.550 MW, bus #15 with size 0.550 MW, and bus #30 with

Table 1 Applying LSF techniqueon IEEE 33-bus test system Bus

No.LSF Normalized

VoltageCandidateBuses

BusNo.

LSF NormalizedVoltage

CandidateBuses

6 0.0168 0.9995 ∎ 23 0.0026 1.0308 ⨂28 0.0136 0.9827 ∎ 25 0.0024 1.0203 ⨂3 0.0132 1.0346 ⨂ 20 0.0023 1.0452 ⨂29 0.0103 0.974 ∎ 14 0.0014 0.9571 ∎8 0.0101 0.9814 ∎ 7 0.0013 0.9957 ∎5 0.0077 1.0189 ⨂ 12 0.0013 0.966 ∎4 0.0076 1.0267 ⨂ 17 0.0012 0.952 ∎30 0.006 0.9703 ∎ 16 0.0009 0.9541 ∎24 0.0047 1.0238 ⨂ 11 0.0008 0.9676 ∎9 0.0046 0.9747 ∎ 15 0.0008 0.9556 ∎10 0.0045 0.9685 ∎ 32 0.0006 0.9649 ∎13 0.0045 0.9595 ∎ 18 0.0004 0.9513 ∎27 0.0037 0.9947 ∎ 21 0.0004 1.0444 ⨂31 0.003 0.9659 ∎ 22 0.0004 1.0438 ⨂2 0.0027 1.0495 ⨂ 19 0.0003 1.0489 ⨂26 0.0027 0.9974 ∎ 33 0.0002 0.9646 ∎

Table 2 Results of SCA for 33-bus system based on status #1 The Base Case

Without DERsCase #1Single DER

Case #2 [Muti-DERs]

2 DERs 3 DERs

DERs (Location, Size in MW) – (#6, 1.950) (#6, 0.550)

(#28, 1.200)

(#6, 0.450)

(#28, 0.800)

(#29, 0.550)

Total DERsinstalled (MW) – 1.950 1.750 1.800

Vmax (pu), #bus 0.997, #2 0.998, #2 0.998, #2 0.998, #2

Vmin (pu), #bus 0.904, #18 0.933, #18 0.930, #18 0.931, #18

Ploss (kW) 210.99 116.79 114.01 111.16

ENS (kWh/yr) 45,970.75 36,105.75 37,317.75 36,510.75

ENS Reduction Cost ($/yr) – 48,535.8 42,572.76 46,543.2

DERs Power Cost ($/year) – 683,280 613,200 630,720

Net Saving ($/year) – 439,690.5 400,149.8 414,379


size 1.050 MW, is selected as the optimal allocation of DERs.In this case, the net saving is reached to its peak at 539020$/yr, the active power loss is minified to be 129.35 kW, thecost of energy not supplied reduction is maximized and equalsto 94,350.84 $/yr, and the minimum voltage bus is modified to0.969 pu at bus #33.

Comparison between the Two Statuses

Application of LSF in status #1 reduces the search space of theoptimization process. A comparison between the two statusesis done based on:

(i) Improving the voltage profile: As displayed in Figs. 6, 7,and 8 for installing different number of DERs (single,two, and three respectively). It is noted that installationof multiple number of DERs has a significant enhance-ment in voltage profile. In general, the performance ofstatus #2 is better than that of status one.

(ii) Active power loss reduction: Losses are slightly de-creased by increasing the number of installed DERs.More DERs installation would not a condition to get min-imum losses. The increase in the percentage of activepower loss reduction is 44.65, 45.97, and 47.32% for sin-gle, two and three DERs installation, respectively, basedon status #1. Moreover, this percentage has increased withapplying status #2 as 45.99, 58.69, and 61.3% for single,two, and three DERs connection, respectively. Figure 9shows a comparison between the results of the two status-es for active power loss reduction.

(iii) ENS reduction and reliability enhancement: As men-tioned before, DERs are considered as alternativesources in reliability study, that leads to a reduction inENS to the network as possible failures of various com-ponents of the network. In order to improve the reliabil-ity of the given network, the locations and sizes ofinstalled DERs must be more suitable to cope the power

Table 3 Results of SCA for 33-bus system based on Status #2 The Base Case

Without DERsCase #1:Single DER

Case #2: Multi-DERs

2 DERs 3 DERs

DERs (#Location, Size in MW) – (#7, 2.100) (#13, 0.850)

(#30, 1.150)

(#8, 0.550)

(#15, 0.550)

(#30, 1.050)


Vmax (pu), #bus 0.997, #2 0.998, #2 0.998, #2 0.998, #2

Vmin (pu), #bus 0.904, #18 0.938, #18 0.968, #33 0.969, #33

Ploss (kW) 210.99 113.95 87.17 81.64

ENS (kWh/yr) 45,970.75 35,265.75 30,421.75 26,793.75

ENS Reduction cost ($/yr) – 52,668.6 76,501.08 94,350.84


Net Savings ($/year) – 471,597.9 491,985.4 539,020

Fig. 6 Voltage profile of 33-busdistribution system in case ofinstalling single


demand as possible in case of disconnection from thegrid as possible failures of various components of thenetwork. In such that, the tail end nodes of the net-work are more suitable choices for DERs placement.

Maximum ENS reduction is 41.72% has obtained incase of three DERs installation according to the status#2 that achieves a cost saving of ENS reductionequals to 94,350.84 $/yr as shown in Fig. 10.

Fig. 7 Voltage profile of 33-busdistribution system in case ofinstalling two DERs

Fig. 8 Voltage profile of 33-busdistribution system in case ofinstalling three DERs

Single DER 2 DERs 3 DERs

Status #2 45.99 58.69 61.3

Status #1 44.65 45.97 47.32

0

20

40

60

80

100

120

% P

loss

Red

uct

ion (

%)

No of Installed DERs

Status #1 Status #2

Fig. 9 Impact of connecting single andmulti-DERs on the active power loss


Status #2 23.29 33.82 41.72

Status #1 21.46 18.82 20.58

0

10

20

30

40

50

60

70

% E

NS

Red

uct

ion (

%)


Status #1 Status #2

Fig. 10 Impact of connecting single and multi-DERs on ENS reduction


(iv) Maximizing net savings ratio: To get the maximum netsaving with connecting DERs to the network, it must beallocated optimally. With increasing the activepower loss reduction and ENS reduction, the netsaving increases. Maximum annual net saving is539,020 $/yr with percentage of 26.06% and thisoccurs in case of installing three DERs, status #2as displayed in Fig. 11.

Generally, this analysis ensures that status #2 is preferredthan status #1. According to the objective function, theoptimal solution is obtained when installing three DERsat buses # 6, 28, and 29 with sizes 0.450, 0.800,0.550 MW, respectively.

IEEE 69-Bus Test System

IEEE 69-bus distribution network is operating at12.66 kV. Thesingle line diagram of the system is shown in Fig. 12 [46, 47]. Itconsists of one slack bus and 68 load buses. The total real andreactive power demand is 3801.4 kWand 2693.6 kVAr, respec-tively. From the power flow analysis using BFS in the base case(without DERs), it is found that the active and reactive powerloss are 224.96 kW and 102.14 kVAr, respectively. Also, theminimum bus voltage is 0.909 pu at bus #65 and the annual costis computed as 2,124,163.59 $/yr taking into account the activepower demand, power loss, and ENS costs.

Status #1

By applying LSF on IEEE 69-bus test system, it is observed thatthe candidate locations for DERs installation are in the sequenceof {57, 58, 61, 60, 59, 15, 64, 17, 65, 16, 21, 19, 63, 20, 62, 25,24, 23, 26, 27, 18, 22}. Table 4 lists the results of connectingsingle and multi-DERs. It can be seen that installing three DERsat buses #57, #58, and #61with total capacity of 1.950MWis the

optimal allocation of DERs where the net saving is maximized at496302.8 $/yr, the active power loss is reduced by 63.5%, thecost saving of ENS reduction is peaked at 79571.21 $/yr, and theminimum voltage bus is modified to be 0.969 pu at bus #27.

Status #2

Table 5 shows the results of connecting single and multi-DERs to IEEE 69-bus distribution system according.Installing three DERs (#17, 0.550), (#39, 0.500), and (#61,1.750) is determined as the optimal location of DERs wherethe net saving is enlarged and reached to its peak at 702192.4$/yr. The active power loss is reduced to 71.82 kW, the savingcost of ENS reduction is maximized at 131146.1 $/yr, and theminimum voltage bus is modified to be 0.978 pu at bus #65.

Comparison between the Two Statuses

A comparison between the two statuses is done based on:

(i) Improving the voltage profile: Figs. 13, 14, and 15 showthe system voltage profile for the different cases ofinstalling single, two, and three DERs, respectively.There is a significant improvement in voltage pro-file with increasing the number of installed DERs.In all cases, the performance of status #2 is betterthan that of status one.

(ii) Active power loss reduction: The maximum reduction inactive power loss is 63.5% in case of installing threeDERs, status #1. While, this percentage has increasedwith applying status #2 and becomes 68.07% whenconnecting three DERs as shown in Fig. 16. Also, it isclear that the percentage of active power loss reduction isgetting higher with increasing the number of installedDERs.

Single DER 2 DERs 3 DERsStatus #2 22.8 23.79 26.06Status #1 21.26 19.35 20.04

05

101520253035404550

Net

Sav

ings

Rat

io (

%)


Status #1 Status #2Fig. 11 Impact of connectingsingle and multi-DERs on netsavings ratio


Fig. 12 Single line diagram ofIEEE 69-bus distribution system



Case #2 Multi-DERs

2 DERs 3 DERs


(#58, 1.450)

(#57, 0.250)

(#58, 0.150)

(#61, 1.550)


Vmax (P.U.), #bus 0.999, #2 0.999, #2 0.999, #2 0.999, #2

Vmin (P.U.), #bus 0.909, #65 0.958, #65 0.964, #65 0.969, #27

Ploss (kW) 224.96 118.65 103.38 82.09

ENS (kWh/yr) 79,087.73 64,041.12 64,130.37 62,914.72



Net Savings ($/year) – 489,066.5 487,891.4 496,302.8



Case #2 Multi-DERs

2 DERs 3 DERs


(#61, 1.550)

(#11, 0.470)

(#39, 0.580)

(#61, 1.750)


Vmax (pu), #bus 0.999, #2 0.999, #2 0.999, #2 1.00, #39

Vmin (pu), #bus 0.909, #65 0.968, #27 0.973, #65 0.983, #65

Ploss (kW) 224.96 83.21 73.66 69.3

ENS (kWh/yr) 79,087.73 62,763.52 53,769.33 52,432.02



Net Savings ($/year) – 478,939.2 633,330.6 702,192.4


Fig. 13 Voltage profile of 69-busdistribution system with singleDER

Fig. 14 Voltage profile of 69-busdistribution system with twoDERs

Fig. 15 Voltage profile of 69-busdistribution system with three DERs


(iii) ENS reduction and reliability enhancement: The per-centage of ENS reduction increases with increasing en-ergy availability. The percentage of ENS reduction in-creases to 19.03, 18.91, and 20.45% when installingsingle, two, and three DERs, respectively in status #1,whereas it increases to 20.64, 32.01, and 33.7% in status#2, Fig. 17.

(iv) Maximizing net saving ratio:With increasing the activepower loss reduction and ENS reduction, the net savingincreases.Maximum annual net saving is 702,192.4 $/yrwith percentage of 33.06% when installing three DERs,status #2 status as displayed in Fig. 18.

This analysis ensures that status #2 is preferred than status#1. According to the objective/fitness function, the optimalsolution is obtained by installing three DERs at buses 17,39, and 61 with capacities of 0.550, 0.500, 1.750 MW,respectively.

Comparing the Proposed SCA with OtherOptimization Techniques

To ensure the validly of the proposed SCA approach,the results of applying the proposed SCA on IEEE 33-bus system are compared with those obtained by

applying other optimization algorithms such as BSOA[33], CS [32], PSO [34], IWD [26], IDSA [15] andflower pollination algorithm (FPA) [48] as given inTable 6. By SCA, the maximum reduction in activepower loss equals 61.3% and the voltage profile is moreenhanced where the worst value of node voltage is0.969 pu at bus #33. The optimum number of connectedDERs is three in all methods except for CS is two.

Similarly, for IEEE 69-bus system the results arecompared with optimization techniques such as GA[11], hybrid of ABC and ACO [24], modifiedteaching– learning based optimizat ion algori thm(MTLBO) [35], hybrid technique of ABC and CSA[38] IDSA [15] and flower pollination algorithm (FPA)[48] as tabulated in Table 7. The proposed SCA fulfilsthe maximum reduction in active power loss that equals69.2%. The obtained results ensure the efficiency of theproposed SCA for solving optimal DERs allocationproblem.

Conclusions

A novel optimization technique based on sine cosinealgorithm (SCA) is presented in this paper to solveDERs allocation problem for radial distribution net-works. This study has been executed through two sta-tuses; First status; the most candidate locations forconnecting DERs are suggested by using the loss sensi-tivity factor theory and the proposed SCA is applied toselect the optimal capacities of DERs. Second status;the SCA is used to determine both the optimal locationsand sizes of DERs. The objective/fitness function is tomaximize the cost saving resulted from energy lossreduction and reliability enhancement. The presentedoptimization algorithm has been applied to two testsystems; IEEE 33-bus and 69-bus radial distributionsystems with different number of installed DERs. Thesimulation results using Matlab programming environ-ment show that the proposed approach is able to


Status #2 20.64 32.01 33.7

Status#1 19.03 18.91 20.45

0

10

20

30

40

50

60

% E

NS

Red

uct

ion (

%)


Status#1 Status #2

Fig. 17 Impact of connecting single and multi-DERs on ENS reduction


Status #2 63.01 67.26 68.07

Status #1 47.26 54.04 63.5

0

20

40

60

80

100

120

140%

PLo

ss R

educ

�on

(%)


Status #1 Status #2

Fig. 16 Impact of connecting single and multi-DERs on the activepower loss


Status #2 22.55 29.82 33.06

Status #1 23.02 22.97 23.36

0102030405060

Net

Sav

ings

Rat

io (

%)


Status #1 Status #2

Fig. 18 Impact of connecting single and multi-DERs on net saving ratio


maximize the annual net saving. Results show that ap-plying status #2 gives performance better than status #1.In addition, a comparison between SCA and othermethods is introduced to verify the superiority of SCAwhere SCA fulfils the maximum saving and maximumreduction of power losses equals to 61.3% and 69.2%for IEEE 33-bus and 69-bus networks, respectively.

Compliance with Ethical Standards

Conflict of Interest There is no any conflict of interest in this study.

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