Electrical Power and Energy Systems 61 (2014) 239–247

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Electrical Power and Energy Systems

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

Optimal placement and schedule of multiple grid connected hybridenergy systems

http://dx.doi.org/10.1016/j.ijepes.2014.03.0400142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Tel.: +20 1007384174; fax: +20 35778640.E-mail address: amanyelz@yahoo.com

Amany El-Zonkoly ⇑Arab Academy for Science & Technology, Faculty of Eng. & Tech, Miami, P.O. 1029, Alexandria, Egypt

a r t i c l e i n f o

Article history:Received 2 March 2013Received in revised form 24 August 2013Accepted 21 March 2014

Keywords:Hybrid photovoltaic-diesel systems(HPVDS)Artificial bee colony (ABC)Distributed generation (DG)Load shedding

a b s t r a c t

This paper presents an artificial bee colony (ABC) based algorithm to optimally solve the problem of allo-cation and the problem of design and schedule of multiple hybrid photovoltaic (PV)-diesel distributedgeneration in distribution systems. Both problems are solved simultaneously. The objective of the pro-posed algorithm is to minimize the overall investment, replacement and operation and maintenancecosts of each located hybrid photovoltaic-diesel system (HPVDS). As the hybrid energy systems are gridconnected, the algorithm considers also the minimization of the distribution system power loss, theamount of imported power from the transmission grid and the un-served load in case of emergency.Meanwhile, the algorithm aims to maximize the excess generated power by the HPVDS that may beinjected into the distribution network. These objectives are to be achieved while satisfying the opera-tional constraints of the system. The proposed algorithm is applied to two test systems to validate itseffectiveness.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Distributed generation (DG) has been considered as an impor-tant alternative to centralized energy resources. As the penetrationof DG systems into distribution and transmission networksincrease, they are more likely to be grid connected. These DG sys-tems are located in close proximity to energy users. The DGs andtheir loads can operate as grid connected or in a stand-alone(islanded) mode [1,2]. Therefore, these systems are to be ratedand designed as if they are to operate in stand-alone mode butscheduled for being grid connected as introduced in this paper.

The interest in DGs increases because it can provide reliable,secure, efficient and sustainable electricity from renewable energyresources [3]. The deregulated energy environment has encour-aged the usage of DG sources near the energy consumers. Thesesources comprise many technologies such as diesel engines, windturbines, photovoltaic, microturbines, and hydroturbines [1].Hybrid energy systems are recognized as a viable alternative togrid supply or conventional fuel-based power supplies [4].

Optimal design of various combinations of these technologieshas been studied in stand-alone and/or grid connected modes. In[5], a probabilistic approach to design an optimal size of PV

distributed generators in a distribution system to only minimizethe active power loss was presented. Optimal design of singlestand-alone hybrid PV/wind/diesel systems was presented in[6,7] in order to minimize the total cost of the system. Likewise,the economic analysis of the stand-alone hybrid energy systemshas been proposed in [8,9] while the economic analysis of such sys-tem in grid connected mode was also presented in [10]. In [11], thefeasibility of hybridization of diesel power plant with a photovol-taic (PV) system was investigated whereby the performances ofeach part have been simulated. Investigating economic feasibilityof a PV/diesel HPS in various climatic zones within South Africawas reported in [12].

Many optimization algorithms have been reported to solve thehybrid energy systems design problem [13]. However, all of theseresearches addressed the design of hybrid energy systems which,when grid connected, were at fixed locations of the grid and didnot consider the optimal placement of such systems. Nevertheless,when the locations of these systems change, their ratings, designand schedule change too.

Other researches addressed the optimal siting and sizing of DGunits or microgrids without dealing with the detailed design ofthese systems. In order to optimally allocate DG units someresearchers used analytical methods [14] and others usedevolutionary computational methods such as genetic algorithm[15], tabu search [16] and particle swarm optimization [17,18].

Nomenclature

xi the position of the ith onlooker beet the iteration numberhi the position of the ith employed bee which is selected

by roulette wheelhk the position of a randomly selected employed beeu a random variable in the range of [�1,1] or [0,1] as used

in this paperS the number of employed beesD the number of parameters to be optimizedMCN the maximum number of iterations of the search pro-

cessr random number in the range of [0,1]hmin

ij ; hmaxij the minimum and maximum limits of the ith parameter

A, B the fuel curve coefficientsPNgen the diesel generator rated capacityPrfuel the fuel priceCO&Mgen the diesel generator’s hourly operation and mainte-

nance costCrep gen h the diesel hourly replacement costCcycling_bat

the cost of cycling energy through the batteriesCPV the PV panels costCPV-inv the investment cost of PV panelsCPV-rep the replacement cost of PV panelsCPV-O&M the operation and maintenance cost of PV panelsCds the diesel generators costCds-inv the investment cost of diesel generatorsCds-rep the replacement cost of diesel generatorsCds-O&M the operation and maintenance cost of diesel generatorsCb the batteries banks costCb-inv the investment cost of batteries banksCb-rep the replacement cost of batteries banksCb-ch the energy cost for charging the batteries banks

Cb-dis the energy cost for the discharge of the batteries banksCsh the cost of energy not servedCloss the cost of energy loss of the distribution networkCslack the cost of energy imported from the transmission gridCex the cost of excess energy of HPVDS injected to the dis-

tribution networkPPV the power generated by photovoltaic panelsPds the power generated by diesel generatorsPb-dis the batteries banks power dischargePb-ch the batteries banks power chargePsh the un-served (shed) powerPslack the imported power from the transmission gridPloss the active power loss of the distribution networkPD the load (demand) powerPmax

PV the PV maximum generation capacityPmax

ds ; Pminds the diesel maximum and minimum generation capac-

ity, respectivelyPS the batteries banks power statePmax

S ; PminS the maximum and minimum batteries banks capacity

limits, respectivelyPHDG the hybrid distributed generation capacityPmax

D the maximum load powerPmax

slack the maximum limit of the slack bus powerVi the voltage magnitude at the ith busVmax

i ;Vmini the maximum and minimum limits of bus voltage

magnitudenbus the number of system’s busesSij the power capacity in the distribution line between bus

i and bus jSmax

ij the maximum power capacity of the distribution linebetween bus i and bus j

240 A. El-Zonkoly / Electrical Power and Energy Systems 61 (2014) 239–247

However, up till now, these two problems of siting and sizingthe hybrid energy systems and designing and scheduling themhave been separately solved.

In this paper, both the siting and designing of multiple gridconnected HPVDS in distribution networks are introduced. Theproposed algorithm formulates the two problems as one optimiza-tion problem which is solved using artificial bee colony (ABC) algo-rithm. Moreover, in the proposed algorithm, neither the number ofHPVDS nor their locations are specified. Hence, different designsfor different locations are considered. The main idea of this paperis that, while sizing the hybrid DG systems, these systems aredesigned as if they will operate in stand-alone mode although theyare grid connected. The systems are designed such that they totallysupport their local loads without the need of imported power fromthe distribution network to supply these loads. That is why eachsystem located in the network is designed to include storagebatteries.

Recently, many blackout incidences in many cities around theworld such as the ones occurred in Newdelhi, India and Cairo,Egypt at the summer of 2012 were because of the overloadingand tripping of one or more of the lines connecting the distributionnetwork of the cities to the transmission grids. Therefore, thepower taken by the distribution network from the transmissiongrid must be limited. In this paper, the HPVDS are considered tobe grid connected only to support the distribution network by sup-plying it with their extra PV power. This support will reduce thepurchased power from the main transmission grid (reduce theloading of upstream feeders) and reduce the amount of un-served(shed) loads once a loss of one or more of the upstream feedersoccur. In order to achieve such purpose, an optimal scheduling of

the HPVDS and other DG units of the system is considered in thispaper. The distribution network is assumed to be connected tothe transmission network through the slack bus. Therefore, in addi-tion to including the slack bus power in the objective function to beminimized, the slack bus power is limited to certain percentage ofthe total demand of the distribution network.

The proposed algorithm is applied to two test systems to vali-date its ability to solve the problem. The two systems are the radial33-bus test system and the Egyptian meshed 45-bus system ofAlexandria.

This paper is organized as follows. Section ‘Artificial bee colonyoptimization algorithm’ describes the ABC optimization algorithm.Section ‘Problem formulation’ presents the problem formulation.Section ‘ABC application to HPVDS siting and sizing problem’ intro-duces the application of the ABC algorithm to the problem. Sec-tion ‘Test results’ presents the obtained results and the relevantdiscussion. Finally, the main conclusions are given in Section‘Conclusion’.

Artificial bee colony optimization algorithm

The ABC optimization technique belongs to the group of swarmintelligence techniques. It was introduced in 2005 by Karaboga[19]. The performance of the ABC algorithm was compared withthose of some well-known population based optimization algo-rithms such as genetic algorithm (GA) and particle swarm optimi-zation (PSO). The results and the quality of the solutions matchedor improved over those obtained by other methods [20]. The ABCalgorithm is developed by simulating the behaviors of the real bees

A. El-Zonkoly / Electrical Power and Energy Systems 61 (2014) 239–247 241

on finding food source, which is called the nectar, and sharing theinformation of food sources to the bees in the hive. The colony ofartificial bees consists of three groups of bees which are theemployed bees, the onlooker bees and the scout bees. Each of themplays different role in the process by flying around in a multi-dimensional search space representing the solution space. Theemployed bees randomly search for food source positions (solu-tions) and provide the neighborhood of the source in their memory.The onlooker bees get the information of food sources form theemployed bees in the hive. Each onlooker bee selects one of the foodsources exploited by the employed bees according to the quality ofthat food source. That means that good food source positions attractmore bees. This phase of solution mimics the behavior of PSO inwhich each particle in the swarm uses the experiences and posi-tions exploited by other particles. The last phase of ABC algorithmis the scout phase. The scouts control the exploration process wherethe scout bee is responsible for finding new food sources accordingto the foraging behavior of the honey bee. This phase of the algo-rithm mimics the mutation process of GA [20–22].

The ABC algorithm proceeds by setting one half of the colonysize to be employed bees and the other half to be onlooker bees.Each cycle of the ABC algorithm consists of three steps [21,22]:

1. Spray the employed bees into the solution space (food sources)and calculate their fitness values (nectar amounts).

2. Move the onlooker bees by selecting a food source to move tousing a selection method such as roulette wheel selection. Themove of onlooker bees follows (1) [22].

xijðt þ 1Þ ¼ hijðtÞ þ u � ðhijðtÞ � hkjðtÞÞ ð1Þ

i ¼ 1; . . . ; S; k ¼ 1; . . . ; S k – i

j ¼ 1; . . . ;D; t ¼ 1; . . . ;MCN

where j is the dimension of the solution.3. Move the scout when the fitness of the employed bee does not

improve for a number of iterations called Limit. When the foodsource position has been abandoned, the employed bee associ-ated with it becomes a scout. The scout then produces a com-pletely random new food source position according to (2) [22].

hij ¼ hminij þ r � hij

max � hminij

� �ð2Þ

The three steps are repeated for a number of cycles (iterations)equal to MCN. The best fitness value and position are memorizedeach cycle to determine the global best solution at the end ofiterations.

Problem formulation

The optimal siting and sizing of multiple HPVDS in distributionnetworks is formulated as an optimization problem. The objectiveis to find the optimal locations of HPVDS out of a certain number ofcandidate locations in the distribution network. Therefore, neitherthe number nor the locations of the HPVDS are pre-specified. Theyare left for the optimization algorithm to determine. At each loca-tion, the optimal sizing and scheduling of each component of theHPVDS are determined. The main objective is to find the minimaloverall cost function of the system. This function consists of severalterms to be minimized along with other terms to be maximized forwhich they are introduced with a negative sign. The costs to beminimized are the investment, replacement and operation andmaintenance (O&M) costs of the components of each of the HPVDS.It is also required to minimize the active power loss in the distribu-tion network, the power imported from the main transmission gridand the un-served (shed) power during emergency in the

distribution network. In addition, it is required to increase theamount of HPVDS power injected to the distribution network suchthat the imported power from the transmission grid and the shedloads are reduced. The simulation span in this paper is one year.

Operation strategy

This paper proposes an operation strategy to obtain optimalscheduling of the hybrid energy system located in the network.Each HPVDS is composed of PV energy source, diesel generatorand battery banks. As mentioned before, the HPVDS are designedas stand-alone systems which take no power from the distributionnetwork to supply their local loads. Meanwhile, these systems aregrid-connected to supply the distribution network with their extra,un-needed (surplus) PV power. The relation between the HPVDSand the distribution network will formulate the operation strategyand hence the generation schedule of the HPVDS components. Inaddition, the solar power is an uncertain data and is not alwaysavailable that is why a forecasted daily solar radiation during oneyear is used in simulation. The operation strategy will be asfollows:

(a) In the presence of PV power:

� If the PV power is greater than the local load and the bat-

teries are not fully charged, the PV power exceeding thelocal load demand will first be used to charge the batter-ies. When the batteries are fully charged and there is stillextra PV power remaining, this power is supplied to thedistribution network.

� If the PV power is lower than the local load, the load ispartially supplied by the PV panels. The remaining loadis then supplied either by the batteries or the diesel gen-erator according to ‘‘Frugal’’ option [4] if the batteries canmeet the remaining load. If the batteries cannot meet theremaining load, the load will be supplied by the dieselgenerator.

(b) In the absence of the PV power:

� If the batteries cannot meet the local load, the load will

be supplied by the diesel generator.� If the batteries can meet the local load, then the ‘‘Frugal’’

option is applied again to determine if the load will besupplied by the batteries or by the diesel generator.

According to ‘‘Frugal’’ option [4], the diesel generator meets thenet load whenever the net load is above the critical discharge load(Ld), regardless of whether or not the batteries bank is capable ofmeeting this load. The critical discharge load is the net load abovewhich the marginal cost of generating energy with the diesel gener-ator is less than the cost of drawing energy out of the batteries [4].

Ld ¼ðB � PNgen � Prfuel þ CO&Mgen þ Crep gen hÞ

Ccycling bat � A � Prfuelð3Þ

This strategy is very similar to the load following strategy [4]except for the grid connection part. According to the proposedstrategy, the batteries will only be charged whenever the PV powerexceeds the power required by the local load and never be chargedby the diesel generator. Also, the diesel generator will operate at arate that produces only enough power to meet the net load that isnot supplied by PV and it will not exchange power with the distri-bution network.

Objective function

The objective is to minimize the following function,

min f ¼ CPV þ Cds þ Cb þ Csh þ Closs þ Cslack � Cex ð4Þ

242 A. El-Zonkoly / Electrical Power and Energy Systems 61 (2014) 239–247

where

CPV ¼ CPV inv þ CPV rep þ CPV O&M ð5Þ

Cds ¼ Cds inv þ Cds rep þ Cds O&M ð6Þ

Cb ¼ Cb inv þ Cb rep þ Cb dis � Cb ch ð7Þ

Operational constraints

� Power balance constraint:At any time interval t, the total power generation should beequal to the total system power demand in addition to the dis-tribution network power losses as follows.

PPVðtÞ þ PdsðtÞ þ Pb disðtÞ þ PshðtÞ þ PslackðtÞ � Pb chðtÞ� PlossðtÞ � PDðtÞ ¼ 0 ð8Þ

� PV power generation limits:The PV is assumed to produce electricity in proportional to thecapacity limit of the installed system and the amount of thesolar irradiation.

0 6 PPVðtÞ 6 PmaxPV ð9Þ

� Diesel generator output power limits:The diesel generator may be operating at a time t or it may beshut down. When it is operating, its output power is limited bya minimum and a maximum value.

Pminds 6 PdsðtÞ 6 Pmax

ds ð10Þ

� Storage batteries constraints:The storage batteries have the same characteristics. Therefore,the batteries bank is considered as one battery having the fol-lowing technical constraints:i. Storage capacity limits:

PminS 6 PSðtÞ 6 Pmax

S ð11Þ

ii. Maximum power discharge limits:

Pb disðtÞ 6 PSðt � 1Þ � PminS ð12Þ

iii. Maximum power charge limits:

Pb chðtÞ 6 PmaxS � PSðt � 1Þ ð13Þ

iv. Power balance state:

PSðtÞ ¼ PSðt � 1Þ � Pb disðtÞ � XðtÞ þ Pb chðtÞ � YðtÞ ð14Þ

Where XðtÞ ¼1 if the batteries are discharging0 if the batteries are not discharging

�

YðtÞ ¼1 if the batteries are charging

0 if the batteries are not charging

�

v. The batteries cannot charge and discharge power at thesame time interval. That can be formulated as the followingconstraint.

XðtÞ þ YðtÞ 6 1 ð15Þ

� The penetration level of HPVDS:

PHDG 6 30% � PmaxD ð16Þ

� Slack power limits:In this paper, the maximum value of the power imported fromthe transmission grid to the distribution network through the

slack bus is limited to 30% of the total maximum demand ofthe distribution network.

PslackðtÞ 6 Pmaxslack ð17Þ

� The bus voltage limits:

Vmini 6 Vi 6 Vmax

i i ¼ 1; . . . nbus ð18Þ

� The power capacity limits of distribution lines:

SijðtÞ 6 Smaxij i ¼ 1; . . . ;nbus; j ¼ 1; . . . ;nbus; i – j ð19Þ

Load shedding

When one or more of the upstream feeders, connecting the dis-tribution system to the transmission grid, is disconnected due tooverloading or disturbance and there is not enough generatedpower in the distribution network, load shedding is considered.In other words, load shedding is performed to satisfy the con-straints given in (8) and (17).

In the load shedding procedure, the loads are shed according totheir priority and starting with lower priority loads. In this paper,the priorities of loads are determined according to the amount ofload where higher loads are assigned with higher priority.

ABC application to HPVDS siting and sizing problem

In this paper, the ABC algorithm is applied to the optimizationproblem. The parameters to be optimized are the buses at whichHPVDS are placed, the rating of the PV systems and the ratings ofthe batteries banks. As for the diesel generators, they are assumedto have ratings equal to the maximum local load at the buses theyare connected to because, as will be seen in Section ‘Test results’,the peak load hours are not the maximum solar irradiation hours.The flow chart of the proposed algorithm is shown in Fig. 1.

Test results

The proposed ABC algorithm is applied to two test system. Thefirst one is the 33-bus, radial system [23]. The second system is theEgyptian 45-bus, meshed system of Alexandria [24]. To comparethe convergence efficiency of the proposed algorithm, the problemis solved using particle swarm optimization (PSO) algorithm too. Apopulation size of 50 solutions and maximum cycle of 100 are con-sidered for both ABC and PSO. The convergence characteristics ofthe objective value for the two systems are shown in Fig. 2.

As shown in Fig. 2, the ABC resulted in better values of theobjective function in case of the 33 bus system while reachedalmost the same objective function value in case of the 45 bus sys-tem. It is also shown that the ABC algorithm converges sooner thanthe PSO algorithm. For illustration, a summer day (July 15th) isselected to observe the power flow through the HPVDS and loadshedding when a part of the transmission network power is lost.A multiple peak load profile is used. The normalized load curveand the normalized daily irradiation curve used for simulatingboth test systems are shown in Fig. 3 while the average daily irra-diation through the year is given in Table 1. The irradiation synthe-sized values were created using the Graham algorithm, whichresults in a data sequence that has realistic day-to-day and hour-to-hour variability and autocorrelation [25]. For both systems theminimum diesel generator output is assumed to be 18% of its ratedcapacity and at the beginning of the simulation the batteries areassumed to be fully charged.

Fig. 1. A flow chart of the proposed algorithm.

(a) Objective function convergence for the 33 bus system

(b) Objective function convergence for the 45 bus system

0 20 40 60 80 1008.8

9

9.2

9.4

9.6

9.8

10

10.2

10.4

10.6x 10

6

Iterations

Obj

ectiv

e Va

lue

ABCPSO

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3x 10

9

Iterations

Obj

ectiv

e Va

lue

ABCPSO

Fig. 2. Convergence characteristics of the objective function of the two testsystems.

A. El-Zonkoly / Electrical Power and Energy Systems 61 (2014) 239–247 243

Radial 33-bus system

The 33-bus system is a radial system with 32 lines and is con-nected to transmission grid through bus 1. The system generatorsare placed at buses 11, 13, 25 and 30 with maximum capacity of1 MW. The system is shown in Fig. 4 and the system data are givenin [23].

Applying the ABC algorithm to the system resulted in placingthree HPVDS at buses 2, 14 and 29. The ratings of each HPVDS com-ponents are given in Table 2. The batteries used are 6 V, 1156 A h. Itis also shown in Table 2 that the diesel generators minimum out-puts do not fall below 18% of their capacities.

The system’s generation schedule during one day is shown inFig. 5. As shown in Fig. 5(a), when the PV energy is not availableat the beginning of the day and the batteries are charged, the bat-teries start supplying energy as long as they can meet the requiredload. The batteries keep discharging and supplying the local loadfor almost 1 h then the diesel generators take over and start

supplying the local load instead. When the PV energy is availablefrom 8 h to 18 h, the local loads are then supplied by PV and notthe diesel generators. At 10 h, because the PV energy is more thanthe load energy needed, the excess energy is used to charge thebatteries. When the batteries are fully charged at 14 h and thereis still excess PV energy, the HPVDS start injecting this excessenergy to the distribution grid from 11 h to 16 h. By the time thePV energy start to decrease almost at 17 h, the batteries start sup-plying the local load again then the diesel generator take over oncemore. The results show that the proposed operation strategy isaccomplished where the diesel generator starts supplying powerwhen the PV power is not enough and the batteries charge onlywhen enough PV power is available. It is also shown that theHPVDS supply power to the distribution network only when excessPV power is available. As shown in Fig. 5(b), the power importedfrom the transmission network does not exceed 30% of the loadat normal operation. The total power loss during the 24 h is4.12 MW which is about 5.7% of the total load. In case of loss of50% the power supplied by the transmission grid due to upstreamfeeder outage during the same day, the load is partially shed forfew hours, as shown in Fig. 6, with a total load shedding of11.62 MW in the presence of the HPVDS which is about 16% of a

(a) The normalized load curve

(b) The normalized daily irradiation

0 5 10 15 20 250.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Hours

Nor

mal

ized

Loa

d

0 5 10 15 20 250

0.2

0.4

0.6

0.8

1

Hours

Nor

mal

ized

Irra

diat

ion

Fig. 3. The normalized daily loading and solar irradiation of test systems.

Fig. 4. The radial 33-bus system.

Table 2The ratings of HPVDS components for the radial 33-bus system.

Locations Ratings (MW) Number of batteries Min. diesel output (%)

PV Diesel

2 0.176 0.2 27 18.914 0.2112 0.2 23 18.9229 0.227 0.2 27 18.92

(a) Power schedule of the HPVDS

(b) The slack power as percentage of the total load power

2 4 6 8 10 12 14 16 18 20 22 240

0.2

0.4

0.6

0.8

1

Hours

Pow

er (M

W)

PpvPdieselPb-chPb-disPex

2 4 6 8 10 12 14 16 18 20 22 240

5

10

15

20

25

30

35

Hours

Perc

enta

ge p

ower

Fig. 5. The generation schedule of the radial 33-bus system.

244 A. El-Zonkoly / Electrical Power and Energy Systems 61 (2014) 239–247

total load of 72.16 MW. In case of absence of HPVDS, the load shed-ding is about 44.28% of the total load.

Meshed 45-bus system

The Egyptian 45-bus system of Alexandria is a meshed systemwith 47 lines, and connected to the transmission grid throughbuses 1, 2, 5 and 9. The system generators are placed at buses 2,5 and 9 with maximum capacity of 853 MW. The system is shownin Fig. 7 and the system data are given in [24].

Applying the ABC algorithm to the system resulted in placingthree HPVDS at buses 11, 24 and 27. The ratings of the componentsof each HPVDS are given in Table 3. The batteries used are 24 V,1156 A h. It is also shown in Table 3 that the diesel generators min-imum outputs do not fall below 18% of their capacities.

The system’s generation schedule during one day is shown inFig. 8. As shown in Fig. 8(a), when the PV energy is not available

Table 1The average daily irradiation.

Month January February March April May June July August September October November December

kW h/m2/d 5.451 5.734 5.995 6.008 5.649 5.26 4.811 4.778 5.15 5.63 5.838 5.565

5 10 15 200

2

4

6

8

10

Hours

Pow

er (M

W)

PloadPsh with HPVDSPsh without HPVDS

Fig. 6. The load served and the load shed of the radial 33-bus system.

Fig. 7. The meshed

Table 3The ratings of HPVDS components for the meshed 45-bus system.

Locations Ratings (MW) Number of batteries Min. diesel output (%)

PV Diesel

11 5.72 8 245 18.924 5.368 8 282 18.927 6.072 8 176 20.27

A. El-Zonkoly / Electrical Power and Energy Systems 61 (2014) 239–247 245

at the beginning of the day and the batteries are charged, the bat-teries start supplying energy as long as they can meet the requiredload. The batteries keep discharging and supplying the local loadfor almost 1 h then the diesel generators take over and start sup-plying the local load instead. When the PV energy is available from8 h to 18 h, the local loads are then supplied by PV and not the die-sel generators. At 10 h, because the PV energy is more than the loadenergy needed, the excess energy is used to charge the batteries.When the batteries are fully charged at 14 h and there is stillexcess PV energy, the HPVDS start injecting this excess energy tothe distribution grid from 11 h to 16 h. By the time the PV energystart to decrease almost at 17 h, the batteries start supplying the

45-bus system.

2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

200

Hours

Pow

er (M

W)

PpvPdieselPb-chPb-disPex

2 4 6 8 10 12 14 16 18 20 22 240

5

10

15

20

25

30

35

Hours

Perc

enta

ge P

ower

(a) Power schedule of the HPVDS

(b) The slack power as percentage of the total load power

Fig. 8. The generation schedule of the meshed 45-bus system.

0 5 10 15 20 250

1000

2000

3000

4000

5000

6000

Hours

Pow

er (M

W)

PloadPsh with HPVDSPsh without HPVDS

Fig. 9. The load served and the load shed of the meshed 45-bus system.

246 A. El-Zonkoly / Electrical Power and Energy Systems 61 (2014) 239–247

local load again then the diesel generator take over once more.That shows that the proposed operation strategy is accomplishedwhere the diesel generator starts supplying power when the PVpower is not enough and the batteries charge only when enoughPV power is available. It is also shown that the HPVDS supply

power to the distribution network only when excess PV power isavailable. As shown in Fig. 8(b), the power imported from thetransmission network does not exceed 30% of the load. The totalpower loss during the 24 h is 686.087 MW which is about 1.5% ofthe total load. As shown in Fig. 9, In case of loss of 40% the powersupplied by the transmission network due to upstream feeder out-age during the same day, the load is partially shed for few hourswith a total load shedding of 4640 MW in the presence of theHPVDS which is about 10.5% of a total load of 44141.9 MW. In caseof absence of HPVDS, the load shedding is about 32.84% of the totalload.

Conclusion

The objective of this paper was to solve both the problem ofoptimal allocation of multiple HPVDS and the problem of optimaldesign and schedule of these HPVDS at the same time. The twoproblems were combined as one optimization problem in whichthe overall costs of the HPVDS were minimized. An operation strat-egy was proposed to schedule the HPVDS in order to minimize thedistribution system power loss, the imported power from thetransmission grid and the un-served or shed load in case of emer-gency. Meanwhile, the algorithm tried to maximize the excess gen-erated power by the HPVDS that may be injected into thedistribution network. The proposed algorithm was able to solvethe two combined problems as required. The proposed algorithmwas applied to radial and meshed test systems. As shown by theresults, the proposed operation strategy was applied accuratelyand the objective function was minimized while satisfying the sys-tem’s operational constraints. For both test systems, at normal con-ditions, the power imported from the transmission network didnot exceed 30% of the total load and the power loss was verylow. In case of radial system, the power loss was about 1.5% ofthe total load and in case of meshed system was about 5.7% ofthe total load. In case of upstream feeder outage and loss of a partof the power imported from the transmission grid, the amount ofload shedding in case of the presence of HPVDS was less that inthe absence of HPVDS while satisfying the operational constraintsof the systems. The load shedding was decreased from 44.28% to16% of the total load at the loss of 50% of the transmission gridpower in case of radial system. In case of meshed system, the loadshedding decreased from 32.84% to 10.5% of the total load in caseof loss of 40% of the transmission grid power. Finally, the proposedalgorithm was capable of dealing successfully with both systems.

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