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Energy 151 (2018) 954e965

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Energy

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Two-level planning for coordination of energy storage systems andwind-solar-diesel units in active distribution networks

Sajad Mahdavi, Reza Hemmati*, Mehdi Ahmadi JirdehiDepartment of Electrical Engineering, Kermanshah University of Technology, Kermanshah, Iran

a r t i c l e i n f o

Article history:Available online 23 March 2018

Keywords:Active distribution networkDistributed generationDepth of dischargeEnergy storage systemStochastic planningShort term planning

* Corresponding author. Department of ElectricaUniversity of Technology, Kermanshah, P.O.Box: 6715

E-mail addresses: smahdavik@gmail.com (S. M(R. Hemmati), m.ahmadi@kut.ac.ir (M.A. Jirdehi).

https://doi.org/10.1016/j.energy.2018.03.1230360-5442/© 2018 Elsevier Ltd. All rights reserved.

a b s t r a c t

The optimal operation strategy of active distribution networks is investigated by this paper. The energystorage system (ESS) and distributed generation (DG) are utilized in the proposed planning. The paperpresents two-level planning including short term and long term planning. The long term planning in-stalls ESSs and diesel DGs on the network and the short term one determines an hourly optimal oper-ation strategy for ESSs and diesel DGs. Different types of DG including solar photovoltaic (PV), wind, anddiesel are studied at the same time. The objective function of the planning is to minimize annualoperation cost of distribution network subject to security constraints of the network. The uncertainty ofsolar-wind units is estimated by many scenarios and stochastic programming is carried out to solve theproblem. The proposed problem is expressed as a nonlinear mixed integer programming and solved bymodified PSO algorithm. In order to cope with the real conditions, reactive power of ESSs and diesel DGsare included in the problem. Depth of discharge is also considered as a design variable and optimized forESSs. The planning optimizes a large number of design variables at the same time including size andlocation of ESSs and diesel DGs, daily operation of diesel DGs, daily charging-discharging pattern of ESSs,and optimal depth of discharge for ESSs. The results demonstrate that the proposed two-level planningcan effectively reduce cost and losses as well as increase efficiency and performance of the network.

© 2018 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. General impacts of diesel DG and ESS on the network

The distributed generation basically support both active andreactive powers in distribution networks [1]. Diesel generators(DGs) have various problems such as limitations of fossil fuels,environmental pollutions, and global warming. However, most ofthe renewable energy sources (especially wind and solar) are un-certain in their nature resulting in great challenges in electricalnetworks. The energy storage systems (ESSs) are presented to dealwith this problem. The ESSs interchange both active and reactivepowers with network [2] and they are effective in reduction of windand solar uncertainties [3]. Some applications of ESSs can be statedas voltage profile improvement [4], renewable energy integration,smoothing, and time-shift [5], peak shaving [6], loss reduction [7],

l Engineering, Kermanshah685420, Iran.ahdavi), r.hemmati@kut.ac.ir

renewable energy capacity firming [8], emission reduction [9] andfrequency control [10].

1.2. Review of previous literature

1.2.1. Optimal placement of distributed generationIn Ref. [11] a strategy for optimal operation of distributed energy

storage systems is proposed to improve the load and generationhosting capability of distribution network. Where, objective func-tion is cost and the constraints are voltage limits, voltage unbalancefactor, battery power, and battery energy. It is also assumed thatESSs only can interchange active power and diesel DG is notinstalled on the network.

A long-term expansion planning in microgrid is presented byRef. [5]. The planning installs new generating units, lines, and en-ergy storage systems in the microgrid to deal with load growth. Theproblem is presented in two levels. One level installs optimaltechnologies on the network and the other level optimizes short-term operation of the installed technologies. In Ref. [5], the reac-tive power of generating units, loads, and energy storage systemsare not considered.

Nomenclature

Parameters and symbols

ANch Number of annual chargeCESS Battery capacity of ESS (KWh)CmaxESS Maximum battery capacity of ESS (KWh)

D Depth of discharge of ESS (%)e Set of all ESSsEtESS Energy stored in ESS at hour t (kWh)

E0ESS Energy stored in ESS at initial hour of planning (kWh)

ETESS Energy stored in ESS at final hour of planning (kWh)

Edisch Energy discharged of ESS (kWh)Ech charged energy(kWh)

EminESS Minimum stored energy of ESS (kWh)

i Set of all economic functionsINc Investment cost of battery ($/KWh)INDG Investment cost of diesel DG ($/KVA)INinv Investment cost of inverter ($/KVA)k Bus numberL Set of all linesLife cyclenew New life span of batteryLife_DOD Life span of battery proportionate whit DOD (%)L S DG life span of diesel DG (year)L S inv life span of inverter (year)Losst Network losses at hour t (KVAh)n Set of all buses

Nch Number of daily chargeOP DG Operation cost of active power for diesel DG ($/KWh)OQ DG Operation cost of reactive power for diesel DG

($/Kvarh)of i Economic function No.i ($/year)OF Objective function ($/year) (annual cost

mathematical expectation)PtDG Active power of diesel DG at hour t (kW)

PnDG Nominal active power of diesel DG (kW)

PESS Rated active power of ESS (KW/h)Pin Input active power to the bus (KW)Pout Output active power to the bus (KW)

PEt Price of energy at hour t ($/Kvah)PROscen Scenario probabilityPSO1 Long term planning algorithmPSO2 Short term planning algorithmpopulation1 Generated population by PSO1population2 Generated population by PSO2

QtDG Reactive power of diesel DG at hour t (kvar)

QnDG Nominal reactive power of diesel DG (kvar)

QESS Rated reactive power of ESS (Kvar/h)Qin Input reactive power to the bus (Kvar)Qout Output reactive power to the bus (Kvar)Scen SN Set all of scenarios Number of scenariosS Apparent power flowing in line(KVA)Smax Maximum apparent power flowing in line (KVA)SESS Apparent power of ESS (KVA)SnESS Nominal apparent power of ESS (KVA)SnDG Nominal apparent power of diesel DG (KVA)

StDG Apparent power of diesel DG at hour t (KVA)t Set all of hours (t¼ 1,2, …,24)TC Coefficient to convert the daily cost to the annual costTch Time charging (hour)V Bus voltageVPt Vector with dimension 6*1 that is demonstrator

coefficient of nominal active power of diesel DG athour t (members of this vector are between 0 and 1)

VQt Vector with dimension 6*1 that is demonstratorcoefficient of nominal reactive power of diesel DG athour t (members of this vector are between 0 and 1)

Vmax Maximum allowed voltage of buses

Vmin Minimum allowed voltage of buseshESS Efficiency of ESS

AbbreviationsDOD Depth of dischargeDG Distributed generationESS Energy storage systemPDF Probability distribution functionPSO Particle swarm optimizationPV Photovoltaic

S. Mahdavi et al. / Energy 151 (2018) 954e965 955

In Ref. [12], a new objective function is presented for optimaldistributed generation placement (ODGP) problem. The mentionedODGP offers energy loss minimization considering network layoutand its load composition. Ref [13] examines the impact of thesevariations in order to verify how optimal solution should adapt toany load composition.

In the long term planning such as network expansion planning,the short term operation of DG (daily or 24-h operation) has notbeen adequately molded and discussed. In Ref. [14], the daily powerof DG is modeled as uncertain parameter and the short termplanning for 24-h operation of DG has not been addressed. Thealgorithm in Ref. [15] finds optimal size and location of DG, but itdoes not optimize the daily operation of DG and only defines ca-pacity factor of DG as design variable. The method given in Ref. [16]finds the optimal capacity of DG and assumes that the generatedpower of DG in constant at all hours over the day.

1.2.2. Optimization algorithmsThe authors in Ref. [17] propose a multi-objective optimization

including islanding mode. The referred multi-objective

optimization finds optimal siting-sizing of storage units and mini-mizes losses and expected energy not supplied (EENS) at the sametime. The authors in Ref. [18] present a multi-objective algorithmfor power-flow which is able to optimize reactive power of PV,capacity of PV, and capacity of storage systems. The algorithm in-cludes an objective function that minimizes voltage variations andcapital costs of PV and storage units as well as maximizes energysaving and peak load cutting.

An optimization-based methodological approach is presentedby Ref. [19] to address the problem of optimal power systemplanning in competitive and uncertain power markets. Where, astochastic mixed integer linear programming model (MILP) hasbeen developed, combining advanced optimization techniqueswith Monte-Carlo method in order to deal with the uncertaintyissues.

An approach to solve optimal power flow combining stochasticwind-solar power with thermal power is presented by Ref. [20].Weibull and lognormal probability distribution functions are usedfor forecasting wind-solar power. The objective function considersreserve cost for overestimation and penalty cost for

Fig. 1. Direction of active and reactive powers for equipment connected to the maingrid.

S. Mahdavi et al. / Energy 151 (2018) 954e965956

underestimation of intermittent renewable sources.In Ref. [21], a new meta-heuristic technique inspired from the

bubble-net hunting technique of humpback whales, namely whaleoptimization algorithm (WOA), has been applied to solve theoptimal reactive power dispatch problem. The WOA method hasbeen examined and confirmed on the IEEE 14-bus and IEEE 30-bus.

In Ref. [22], Teaching Learning Based Optimization (TLBO) basedoptimization algorithm is used for reactive power planning andapplied in IEEE 30 and IEEE 57 bus system. In Ref. [23], a newlysurfaced nature-inspired optimization technique called moth-flame optimization (MFO) algorithm is utilized to address theoptimal reactive power dispatch (ORPD) problem.

1.2.3. Optimal planning of energy storage systemsOptimal planning of batteries in the distribution grid is pre-

sented by Ref. [2]. The optimal planning determines location, ca-pacity, and power rating of batteries while minimizing cost subjectto technical constraints. The optimal long-term planning is basedon the short-term optimal power flow considering theuncertainties.

In Ref. [24], the authors address an effective sizing strategy forbattery energy storage system (BESS) in the distribution networksunder high photovoltaic (PV) penetration level. The main objectiveof the method given in Ref. [24] is to optimize size of BESS andderive the cost-benefit analysis when the BESS is applied forvoltage regulation and peak load shaving.

A comparison based optimal planning of several battery tech-nologies is represented by Ref. [25] to find the best choice in dis-tribution grid applications. The given methodology in Ref. [25] is anovel four-layer procedure that considers the uncertainty of batterycharacteristics as well as load and wind power. The long-termplanning layer optimizes location, capacity, and power rating ofbatteries. The short-term scheduling layer includes the probabi-listic optimal power flow with respect to the technical constraints.The numerical results show that Zn-Br technology is the mostsuitable option in the deterministic studies, and the Na-S technol-ogy can be an alternative in the uncertain conditions.

In Ref. [26], DOD has not been considered and power of dieselDG is constant. Authors in Ref. [26] propose a stochastic optimi-zation approach to cope with uncertainties associated with theproblem. In Ref. [26], many scenarios are generated using Monte-Carlo simulation and problem is solved by GAMS/SCENRED. InRef. [26], it is assumed that maximum DOD¼ 1 and minimumDOD¼ 0 and reactive power has not been studied in problem.

1.3. Contributions of current work

Considering the above literature review, the coordinated dailyoperation for ESSs and diesel DGs has not been adequatelyaddressed. This paper addresses most of the shortcomings at thesame time. In this paper, DOD is defined as a design variable andoptimally determined for batteries. Both diesel DG and ESS cansupport active-reactive powers. The planning is presented in twolevels including long-term and short-term. The long-term planningfinds places, capacity, depth of discharge, and rated power for ESSsas well as location and rated power for diesel DGs. On the otherhand, the short-term planning finds optimal daily operation ofdiesel DGs and optimal charging-discharging pattern of ESSs under24-h.

This paper considers following issues at the same time in theplanning:

✓ According to the conducted literature review, in the long termplanning, the diesel DG operation during 24-h is often modeledby constant power. But, this operation strategy is not optimal. In

this paper, a short-term planning is carried out alongside withlong term planning. The long term planning optimally installsdiesel DGs (determines optimal power of diesel DGs) and theshort term planning determines an hourly optimal operationstrategy for diesel DGs during 24-h.

✓ DGs and ESSs are usually modeled as active power sources. Butthis paper presents a comprehensive and practical model forDGs and ESSs including both active and reactive powers. In thispaper, cost of reactive power is considered in three parts of themodel including investment cost of inverter, investment cost ofDiesel DG, and operational cost of Diesel DG.

✓ Depth of discharge (DOD) of BESS is often excluded from theproblems or DOD is molded as a constant variable. While thispaper considers DOD as a design variable and determinesoptimal DOD for BESS.

✓ This paper not only determines the optimal power and capacityof BESS, but also denotes the optimal charging-dischargingregime of the BESS.

✓ Both wind and solar units are modeled as uncertain resources inthe proposed planning.

2. Distributed generators and energy storage systems

Direction of active and reactive powers for DG and ESS is shownin Fig. 1. In this paper both diesel DG and ESSs can interchangeactive and reactive power with network.

Depth of discharge (DOD) is an important issue in batteries [27].DOD describes how deeply the battery is discharged. For instance, ifbattery is 100% fully charged, the DOD is 0% and if battery hasdelivered 60% of its energy, the DOD is 60%. DOD can be treated asthe energy that battery delivers. One of the most important issueson ESSs is to exponential relationship between DOD and cycle life[28].

Cycle life is the charge/discharge cycles number that the batterycan experience before its nominal capacity falls below pre-determined threshold of its rated value. Cycle life is different invarious charge/discharge conditions [29].

ESS with higher DOD can deliver more energy to the network,but it decreases battery life cycle and increase the investment cost.

3. Stochastic programming and scenario generation

Stochastic programming is a mathematical optimization inwhich some or all parameters of the optimization problem arepresented by random variables. The source of random variablesmay be different depending on the nature of the problem. The mainidea of Monte-Carlo approach is to estimate the expected value ofobjective function which is defined by scenarios. One of the

S. Mahdavi et al. / Energy 151 (2018) 954e965 957

significant advantages of Monte-Carlo approach is that the numberof samples required to achieve a specified level of accuracy is in-dependent of the system size. Therefore, Monte-Carlo is proper toanalyze large-scale systems such as power systems [26]. The un-certainties of load demand and renewable generation are oftenmodeled by Probability Distribution Functions (PDF) [30]. It shouldbe noted that scenarios and their related probabilities are obtainedby discrete approximation of continuous PDF. Because of the sto-chastic nature of wind and sunlight, the generated power by windand solar units is considered as stochastic. This paper applies thestochastic programming for scenario-generation and scenario-reduction techniques. The details of scenario-generation andscenario-reduction technique can be found in Ref. [31].

4. Problem formulation

The objective function of the proposed planning is to minimizethe annual operation cost which is expressed as expected value ofcost for all scenarios. Equations (1)e(9) are calculated for eachscenario of performance.

The annual operation cost of active and reactive power for dieselDG is given in (1) and (2). Annul investment cost of diesel DG isexpressed by (3). Energy price is defined by (4). The purchasing costof batteries is given by (5) and its details are expressed by (6) and(7). Annual purchasing cost for inverters is expressed as (8). Thefinal objective function of the problem is given by (9). This finalobjective function comprises six terms including of1 to of6. Thefinal objective function (9) calculates the expected value of cost forall scenarios.

This function is expressed as expected value and PROscen showsthe probability related to each scenario.

of1 ¼"X24

t¼1

PtDG � OPDG

#� TC (1)

of2 ¼"X24

t¼1

QtDG � OQDG

#� TC (2)

of3 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�PnDG

�2 þ �QnDG�2q

� INDG � ðL SDGÞ�1 (3)

of4 ¼"X24

t¼1

Losst � PEt

#� TC (4)

of5 ¼X3e¼1

264 Ce

ESSLife cyclenewe

ANche

375� INC (5)

ANche ¼ 365� Nch

e (6)

Life cyclenewe ¼ 10000� life DODe (7)

of6 ¼X3e¼1

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�PeESS

�2 þ �QeESS�2q �

� INinv � ðL SinvÞ�1 (8)

OF ¼XSN

scen¼1

X6i¼1

ofsceni � PROscen

!(9)

The proposed problem for cost minimization can be expressedas a standard constrained optimization problem given by (10)e(27).

Objective function of the problem is defined by (10). Battery ca-pacity and inverter apparent power are restricted by (11) and (12).The relationship between active, reactive, and apparent power ofthe inverter are given by (13). The stored energy in battery isexpressed by (14). The efficiency of the storage system is defined as(15).

Min fOFg (10)

S.T.

CESS � CmaxESS (11)

SESS � SnESS (12)

SnESS ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP2ESS þ Q2

ESS

q(13)

Ech ¼ PESS � Tch (14)

Edisch � Ech � hESS (15)

The minimum stored energy in the battery is expressed by (16).According to this equation, whatever DOD become larger, mini-mum stored energy in the battery becomes less and vice-versa. It isclear that if DOD is not considered (i.e., DOD¼ 100%), battery can bedischarged completely. The stored energy in ESS is larger thanminimum permitted energy as given by (17). The equilibrium ofenergy is defined by (18).

EminESS ¼ Cmax

ESS ��1� D

100

�(16)

EminESS � EtESS (17)

Et¼0ESS ¼ Et¼T

ESS (18)

Apparent power of the diesel DG is restricted by (19) and rela-tionship between active and reactive powers is defined by (20). Therelationship between active, reactive, and apparent power of DGare given by (21). Active and reactive power at hour t are expressedby (22) and (23).

StDG � SnDG (19)

SnDG ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�PnDG

�2 þ �QnDG�2q

(20)

StDG ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�PtDG

�2 þ �QtDG

�2r(21)

PtDG ¼ VPt � PnDG (22)

QtDG ¼ VQt � Qn

DG (23)

Conventional power flow problem is defined through con-straints (24) and (25), voltage boundaries are given by (26), and linecapacity is limited by (27).

Xnk¼1

Pkin ¼Xnk¼1

Pkout (24)

S. Mahdavi et al. / Energy 151 (2018) 954e965958

Xnk¼1

Qkin ¼

Xnk¼1

Qkout (25)

Vmink � Vk � Vmax

k (26)

SL � SmaxL (27)

In the real conditions, the BESS performance becomes weak bypassing the time, because the chemical properties of the battery aredegraded. As a result, it would be proper to consider the degrada-tion factor in the model. The degradation factor changes the ESSlife-time, DOD, and efficiency. As a result, the ESS operation isworsened and the planning cost will increase due to installingmoreor different ESSs. However, current paper does not include thedegradation factor in the model.

5. Solving the problem by Meta-heuristic optimizationtechnique

This paper uses modified PSO technique to solve the problem. Inthe modified PSO, weighing factor is linearly reduced from onetoward zero as well as the crossover and mutation are added to thealgorithm. The problem is also solved by various optimizationtechniques and eventually the modified PSO technique is chosen asthe final one. Moreover, the problem is solved several times toguarantee the optimal solution.

As it was stated, the paper presents two plannings as short-termand long-term. The long term planning installs ESSs and diesel DGson the network and the short term planning determines an hourlyoptimal operation strategy for ESSs and diesel DGs. As a result, twoPSO algorithms are simulated to solve both the planning at thesame time. Population1 is generated by PSO1 and population2 isgenerated by PSO2.

PSO1 is related to the long-term planning and determines activeand reactive power of diesel DG, active and reactive power of ESSs,

Fig. 2. Flowchart of the proposed method.

capacity of, depth of discharge for batteries, location of diesel DGand batteries in network. PSO2 is related to the short-term planningand determines charging-discharging state of the batteries andoutput power of diesel DGs at each hour over the day. Fig. 2 showsthe flowchart of the proposed method.

6. Test system specifications

Fig. 3 shows a 30-bus-10MVA-11 kV radial distribution networkwhich is considered as case study to simulate the proposedmethod. The network consists of wind and solar PV units that areinstalled on buses 8 and 23 with nominal power 100(KW) and80(KW), respectively. Daily average generation profile of wind andsolar PV units are shown in Figs. 4 and 5. Data of the networkincluding line and loading data can be found in Ref. [32]. Candidatediesel DGs and ESSs are listed in Tables 1 and 2. Energy price isaccording to Table 3. The price of energy, ESS, and diesel DG inTables 1e3 can be found in Ref. [33], respectively. Load profile in 24-h is shown in Fig. 6 [33].

There are some assumptions in this study that can be pointedout as follows: considering constant active and reactive power fordiesel DGs at each time step, modeling DOD by discrete curveincluding four levels, modeling candidate powers of DGs and bat-teries by discrete curve with four levels, disregarding reactive po-wer of wind-solar units, considering four buses as candidatelocations of DGs and ESSs, modeling 24-h load profile by six steps.

Fig. 3. Single line diagram of the distribution network.

Fig. 4. Daily generation profile of wind unit.

Fig. 5. Daily generation profile of solar PV unit.

Table 1Candidate diesel DG of the planning.

Parameter Value

Candidate buses 18-20-26-25Candidate active powers for DGs (kW) 25-50-75-100Candidate reactive powers for DGs (kVar) 25-50-75-100Investment cost ($/kVA) 853Operation cost for active power ($/kWh) 0.142Operation cost for reactive power ($/kVarh) 0.018

Table 2Candidate ESSs of the planning.

Parameter Value

Candidate buses 8-2-19-24Candidate active powers for ESSs (kW) 10-20-30-40Candidate reactive powers for ESSs (kVar) 10-20-30-40Candidate capacities for ESSs (kWh) 250-300-350-400Investment cost for capacity ($/kWh) 45Investment cost for rated power ($/kVA) 463Candidate depth of discharge for ESSs (%) 30-50-60-90Battery life cycle ðlife DODÞ according to DOD (%) 90-80-60-50Maximum life cycle (number of charge) 10000

Table 3Energy price for the period 24-h.

Hour(s) 0e6 6e10 10e14 14e18 18e20 20e24

Energy price ($/kWh) 0.083 0.162 0.254 0.291 0.3 0.284

Fig. 6. Load profile at 24-h.

Table 4List of problem assumptions.

Parameters Value

L S DG 10 yearL S inv 5 yearhESS 90%

Vmink

0.9

Vmaxk 1.1

S. Mahdavi et al. / Energy 151 (2018) 954e965 959

In addition to the mentioned items, Table 4 describes some otherassumptions of current study. It is worth mentioning that theproposed model still works under all of the assumptions, becausethe assumptions only change the optimal solution of the planning

and they do not make impact on the feasibility of the planning. Inother words, the planning excluding such assumptions providesless planning cost compared to the model including assumptions.On the other hand, solution of the planning excluding assumptionsis time-consuming. This paper makes tradeoff between solutiontime and model simplification. The mode is simplified in order toreduce the solution time.

In this paper, the wind-solar uncertainties are modeled by sce-narios [34]. Many scenarios are made and stochastic programmingis adopted to solve the problem [35,36]. Some scenarios of perfor-mance are depicted in Fig. 7.

7. Simulation results

The proposed model is implemented in MATLAB software. Themodel is solved by PC including 16 GB RAMMemory and 3.4 GHz-4Cores Processor.

7.1. Comparison of deterministic and stochastic planning

The proposed stochastic planning is evaluated against a deter-ministic one. In the deterministic planning, power of wind andsolar PV units is considered as constant and the uncertainties arenot included. Both the deterministic and stochastic planning aresimulated on the test system and results are listed in Tables 5 and 6.

In the stochastic planning, the planning must cope with wind/solar uncertainties and it should satisfy all constraints under allscenarios of performance. As a result, the stochastic planning uti-lizes more resources and storage units to deal with such conditions.This issue increases the total planning cost of stochastic planning.The results demonstrate that active power, reactive power, andDOD of ESSs in the stochastic planning are more than the deter-ministic one.

According to the voltage profile shown in Fig. 11, the voltageprofile is dropped from bus 17 to 27 and it needs improvement. As aresult, both the stochastic and deterministic planning install ESS onbuses 19 and 24. But in the stochastic planning, ESS 3 is alsoinstalled on bus 8 to mitigate wind power uncertainty at thislocation. The wind power is on maximum at hours 0e6 and it in-creases the voltage profile at bus 8 at hours 0e6. As a result, the

Fig. 7. Wind and solar power in 4 scenarios at 24-h.

Table 5ESSs installed by stochastic and deterministic planning.

ESS Bus no. Capacity (KWh) Prate(KW/h) Qrate (Kvar/h) DOD (%)

Stoch. Deter. Stoch. Deter. Stoch. Deter. Stoch. Deter. Stoch. Deter.

ESS1 24 19 300 300 30 10 40 20 60 30ESS2 19 19 250 300 20 20 30 20 90 50ESS3 8 24 300 300 30 30 30 10 60 60

Table 6Diesel DGs installed by stochastic and deterministic planning.

Bus no. Pnominal(KW) Qnominal(Kvar)

Stochastic Deterministic Stochastic Deterministic Stochastic Deterministic

26 20 75 25 75 50

Fig. 8. Energy and reactive power of ESS on bus 8 with capacity 300 kWh and DOD 60%.

S. Mahdavi et al. / Energy 151 (2018) 954e965960

planning installs one ESS on bus 8 and this ESS absorbs reactivepower at hours 0e6 to reduce the voltage profile below thepermitted level. The operation of ESS 3 under 24-h is shown inFig. 8 and it is clear that the ESS absorbs reactive power at hours0e6.

Annual cost for both planning is listed in Table 7. The resultsshow that annual cost for deterministic planning is less than sto-chastic planning by 15.17%. It does not mean that the deterministic

Table 7Annual cost of network under stochastic and deterministic planning.

Planning Annual cost ($/year)

stochastic planning 96831 (expected value)deterministic planning 82141

planning is better, because the network under deterministic plan-ning is not flexible against uncertainties of PV and wind units. Thisissue is demonstrated in Table 8. It is clear that deterministicplanning is not robust against the fluctuations. As a result, the extracost of stochastic planning can be properly justified and this cost isnecessary to tackle such uncertainties.

7.2. Analysis of the annual cost

Annual cost of the network under different conditions is listed inTable 9. In the primary network (initial network defined in the casestudy), voltage profile is out of the permitted range under somescenarios and the operation is not safe. Among the other results, itis clear that the proposed network equipped with both diesel DGsand ESSs indicates better performance than the other cases.

Table 8Sensitivity of stochastic and deterministic planning following solar and winduncertainties.

Solar PV and wind power (%) Number of violated constraints

Solar PV Wind Stochastic Deterministic

þ100% þ100% 3 14þ80% þ80% 1 11þ60% þ60% 0 6þ30% þ30% 0 30 0 0 0�30% �30% 0 2�60% �60% 0 6�80% �80% 4 8�100% �100% 5 10 Fig. 9. Diesel DG generated active and reactive power at 24 h.

Table 10Annual cost of network with and without short term planning.

Annual cost ($/year)

With short term planning 96831Without short term planning 155107

Fig. 10. Charging-discharging states and energy of ESS on bus 19 with capacity250 kWh and DOD 90%.

S. Mahdavi et al. / Energy 151 (2018) 954e965 961

7.3. Impacts of short term planning on the network

According to the short term planning, the generated power bydiesel DG is not constant and it is optimally determined propor-tional to the network requirements at each hour. Fig. 9 shows boththe daily active and reactive powers generated by diesel DG. It isclear that diesel DG power is zero at initial hours because of lowdemand. The generated power by diesel DG increases during high-peak hours. Table 10 demonstrates that the annual cost of thenetwork without short-term planning is 60% more than thenetwork with short-term planning. It is worth mentioning that inthe network without short-term planning, the generated power ofdiesel DG is constant at 24-h.

7.4. Impacts of DOD and efficiency on the ESS

ESS is mainly charged during off-peak periods and dischargedduring on-peak hours. Fig. 10 shows the charging-dischargingpattern of one of the installed ESS on the network. In this Figure,energy of battery is shown at each hour. Battery capacity and ratedactive power of this ESS are 250 KWh and 20 kW/h, respectively. Aswell, DOD of this ESS is 90%. As a result, the minimum permittedenergy of this ESS is 25 KWh. The results confirm this issue and it isclear that the stored energy is 25 KWh at hour 24. It is also assumedthat ESSs efficiency is 90% and according to Fig. 10, ESS is chargedequal to 200 KWh, but it delivers 180 KWh to the network becauseof 90% efficiency.

7.5. Investigating the coordinated ESS-Diesel DG planning

Fig. 11 shows the voltage profile on all buses of the networkduring peak load (hours 18e20). Voltage profile is improvedbecause all of the ESSs are discharging and diesel DG power is 93.5%(70.125 KVA). According to the results, voltage profile of the pro-posed network shows significant improvement. This issue is one ofthe advantages of the proposed planning.

7.6. Analysis of the network losses

Active and reactive power losses of the network during 24-h are

Table 9Annual cost of network under different planning.

Annual cost ($/year)

Primary network Operation isn’t safeProposed network with both DG and ESS 96831Network with DG and without ESSs 99412Network with ESSs and without DG 99847

shown in Figs. 12 and 13. It is clear that by moving towards thegreater load levels, the influence of the proposed planning on thelosses is more significant. This issue is due to enhancement ofvoltage profile. In other words, in the primary network, the load issupplied by receiving power from the upstream network and theflow in lines is increased resulting in more losses. According to theresults, the proposed planning reduces both active and reactivelosses by 35.86% and 34.88%, respectively.

7.7. Line flows and congestion of the network

Reducing the network losses is certainly due to lines flowreduction. Fig. 14 shows lines flow during peak load. It is clear thatin the proposed network, capacity of lines is mostly un-occupied(33.85%), while in the primary network, the capacity of lines ishighly congested. This issue limits the network flexibility and ad-equacy. In other words, the system cannot support load growth andit needs the reconfiguration or expansion.

7.8. Sensitivity analysis

A sensitivity analysis is carried out on the load of network andload is increased by 20%. Fig. 15 shows the result. It is clear that theproposed planning satisfies all constraints, while the primarynetwork cannot tackle such uncertainty and some constraints areviolated.

Fig. 11. Voltage profile on all buses of the network at hours 18-20.

Fig. 12. Active power losses of the network for the duration of 24-h.Fig. 14. Line flows of network in the during peak load.

S. Mahdavi et al. / Energy 151 (2018) 954e965962

7.9. Network simulation under various loading profiles

In the proposed model, the steps of generation and loadingprofiles are limited in order to decrease the simulation time. Itshould be noted that the proposed two-level optimization problemincudes many design variables and it takes many hours to besolved. As a result, considering short term variations in the gener-ation and loading profiles would significantly increase the simu-lation time. However, the proposedmodel is a general model whichcan successfully consider any generation and loading profiles. Inorder to demonstrate this issue, two load profiles with 22 and 12steps are considered as shown in Figs. 16 and 17 and their results

Fig. 13. Reactive power losses of the n

are listed in Tables 11e14. It is clear that the proposed planning cansuccessfully solve the problem under the profiles with short termvariations. However, solving the problem under 12-step loadingprofile increases the simulation time by about 100% and consid-ering 22-step loading profile rises the simulation time by nearly300%.

8. Conclusions

This paper presents a strategy to improve the operation of activedistribution networks by optimal coordination of energy storagesystems and renewable distributed generations. The paper includes

etwork for the duration of 24-h.

Fig. 15. Voltage profile during peak load following 20% increasing load.

Fig. 16. Load profile with 22 steps at 24-h.

Fig. 17. Load profile with 12 steps at 24-h.

S. Mahdavi et al. / Energy 151 (2018) 954e965 963

two planning as short-term and long-term planning. The long-termplanning installs ESSs and diesel DGs on the network and the short-term planning determines an hourly optimal operation strategy forESSs and diesel DGs. Results show that short-term planning isnecessary because this planning reduces the annual cost by 60%.Furthermore, short-term planning enhances voltage of buses. The

Table 11ESSs installed by stochastic and deterministic planning for load profile with 22 steps.

ESS Bus no. Capacity (KWh) Prate(K

Stoch. Deter. Stoch. Deter. Stoch.

ESS1 21 18 400 300 30ESS2 19 22 450 400 20ESS3 6 24 300 250 40

impacts of DOD and efficiency on ESS are also investigated by theproposed planning. The results confirm that DOD and efficiencymake significant impacts of the ESS operation and it is inevitable toconsider such issues in the planning. Results indicate that theproposed planning reduces active and reactive power losses of thenetwork by 35.86% and 34.88%, respectively. As well, the congestion

W/h) Qrate (Kvar/h) DOD (%)

Deter. Stoch. Deter. Stoch. Deter.

10 40 10 50 5020 30 30 90 5020 30 10 90 60

Table 12Diesel DGs installed by stochastic and deterministic planning for load profile with 22 steps.

Bus no. Pnominal(KW) Qnominal(Kvar)

Stochastic Deterministic Stochastic Deterministic Stochastic Deterministic

19 21 100 25 50 50

Table 13ESSs installed by stochastic and deterministic planning for load profile with 12 steps.

ESS Bus no. Capacity (KWh) Prate(KW/h) Qrate (Kvar/h) DOD (%)

Stoch. Deter. Stoch. Deter. Stoch. Deter. Stoch. Deter. Stoch. Deter.

ESS1 17 19 300 250 30 10 40 20 90 30ESS2 22 16 300 300 40 10 40 10 50 30ESS3 10 20 400 250 40 20 20 10 60 60

Table 14Diesel DGs installed by stochastic and deterministic planning for load profile with 12 steps.

Bus no. Pnominal(KW) Qnominal(Kvar)

Stochastic Deterministic Stochastic Deterministic Stochastic Deterministic

18 18 100 25 100 25

S. Mahdavi et al. / Energy 151 (2018) 954e965964

of the lines during on-peak hours is relieved by 33.85%. The resultalso demonstrate that following 20% increasing load, the proposedplanning satisfies all constraints, while the primary network cannottackle such uncertainty and some constraints are violated.

Further to the current work, the following are suggested asfuture works; considering three phase network instead of single-line network, taking into consideration hybrid ESS, consideringkind of BESS technology, modeling the degradation of BESS,considering short term variations and loading ramping, andinvestigating the impacts of on-load tap-changer on the network.

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