Power Distribution Network Expansion Planning Considering Distribution Automation

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IEEE TRANSACTIONS ON POWER SYSTEMS 1

Power Distribution Network Expansion PlanningConsidering Distribution Automation

Saeed Heidari, Mahmud Fotuhi-Firuzabad, Fellow, IEEE, and Shahram Kazemi, Member, IEEE

Abstract—This paper presents a novel profit-based modelfor multistage distribution network expansion planning. In theproposed model, some capabilities of the distribution automationsystem are considered to achieve a plan that is more compatiblewith the strategic plan towards a smart distribution grid. More-over, a method for reliability evaluation of a distribution networkin the planning studies is proposed. The objective function ofthe planning problem is the net present value of the company’sprofit. The problem is solved by employing the genetic algorithmapproach as a promising technique in solving the mixed-integernonlinear programming problem. The proposed method is eval-uated on an illustrative test network and the obtained results arepresented and discussed.

Index Terms—Distribution automation (DA), distributionsystem planning (DSP), distribution system reliability, geneticalgorithm (GA), smart grid.

NOMENCLATURE

Sets and Indices:

Set/number of the existing and proposed lines.

Set/number of the existing lines.

Set/number of the proposed lines.

Set/number of the existing and proposedsubstations.

Set/number of the existing substations.

Set/number of the proposed substations.

Set/number of the load buses.

Number of buses.

Number of circuit types.

Number of substation types (capacity).

Total number of customers.

Number of customers fed from load point .

Manuscript received November 05, 2013; revised March 19, 2014; acceptedJuly 07, 2014. Paper no. TPWRS-01417-2013.S. Heidari and M. Fotuhi-Firuzabad are with the Center of Excellence in

Power System Management and Control, Department of Electrical Engineeringat Sharif University of Technology, Tehran 11155-8639, Iran (e-mail: [email protected]; [email protected]).S. Kazemi is with the Department of Electrical Engineering, Razi University,

Kermanshah 67149-67346, Iran (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRS.2014.2339301

Variables and Functions:

Total revenue of the distribution company ($).

Total investment cost for network expansion($).

Total salvage cost of disposed lines ($).

Total maintenance cost of the system ($).

Total operation cost of the system ($).

Total interruption cost ($).

Average outage time of load point at year(hr).

Expected energy not supplied for load pointat year (kWh).

Expected energy not supplied for network atyear (kWh).

System average interruption duration index atyear (hr/cstmr).

Average energy not supplied at year(kWh/cstmr).

Capacity of substation at year (kVA).

Capacity of line at year (kVA).

Active power supplied by substation at year(kW).

Reactive power supplied by substation atyear (kVAR).

Active power flow in line at year (kW).

Reactive power flow in line at year (kVAR).

Total average demand of network at year(kW).

Active power loss in line at year (kW).

Voltage of load point at year (kV).

Constants:

Time horizon of planning.

Annual interest rate of investment.

Forecasted peak demand of load point atyear (kW).

Price of energy ($/kWh).

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2 IEEE TRANSACTIONS ON POWER SYSTEMS

Cost per unit of energy lost ($/kWh).

Investment cost for a substation of type ($).

Investment cost for a line of type ($/km).

Investment cost for replacing line of typewith line of type ($/km).

Investment cost for element ( ) ($).

Salvage cost of a line of type ($/km).

Substation annual operation cost ($/kVA).

Substation annual maintenance cost ($/kVA).

Line annual maintenance cost ($/km).

Annual maintenance cost of element ( ) ($).

Nominal voltage of the network (kV).

Maximum allowable voltage variation (perunit).

Loss factor of lines.

Load factor of load point .

Length of line (km).

Value of lost load at load point ($/kWh).

Threshold of network AENS index(kWh/yr.cstmr).

Threshold of network SAIDI index(hr/yr.cstmr).

I. INTRODUCTION

D UE to the load growth, electric power distribution net-works should be expanded to provide a reliable and cost-

effective service to new and existing customers. System plan-ners consider the existing network, load and price forecasting,and technical and economical considerations and determines theoptimal size, location, and time in which a new resource suchas a feeder or a substation must be added, replaced, or rein-forced [1], [2]. This expansion plan should be aligned with thecompany’s strategic plan that is usually having a smart distribu-tion grid with technologies such as advanced metering, demandresponse, distribution automation (DA), distributed generation(DG), and distributed storage [3]. If technologies such as DAare considered in the expansion planning process, the developedplan would be more consistent with the strategic plan towardssmart grid.In the literature of distribution network planning, the pos-

sible impact of employing new technologies in the planningprocess of distribution networks has not been well examined.The research in this field has almost been limited to the effectof DG units, e.g., [4], [5]. In addition, the majority of worksdone in the field of distribution system planning (DSP) try topropose methods to deal with the nonlinear and discrete nature

of the DSP problem and to present new optimization techniques[6]–[13].Most of the DSP models proposed in the literature employ a

cost-based objective function to be minimized, e.g., [1], [2], and[6]. The investment cost and the operation cost are the majorterms of this objective [1], [2], [4], [14]. In [2] and [4], themaintenance cost is also taken into account. Additionally, in [2],[14], and [15], the interruption cost is considered in the objec-tive function. However, cost of the network expansion includessome other expenses such as salvage cost of disused equip-ments, that may be significant and it is usually not consideredin the DSP models. Moreover, with the electricity industry re-structuring trend and privatization process of distribution com-panies, the main goal of these companies is to maximize theirprofits of business. So the resulted expansion plan designedby the cost-based model is not necessarily the best choice fora distribution company (DISCO) in the nowadays deregulatedstructure.In this paper, a multistage profit-based model for expansion

planning of the primary distribution networks is proposed. Thismodel performs the expansion planning from a DISCO’s per-spective that must compete to survive in the deregulated struc-ture. To consider the functions of DA, the proposed model as-sumes that the network under study is an automated distributionsystem, and it has some of the DA functions including automaticvoltage and VAR control (AVVC) and automatic fault manage-ment (AFM). In general, these DA functions can improve theoperation of distribution system and enhance the service relia-bility while reducing the related costs.In this paper, the DSP problem is modeled as a mixed integer

nonlinear programming (MINLP) problem. Due to combinatorynature of the problem, genetic algorithm (GA) method is usedfor the optimization that can find good solutions for such prob-lems [7], [12], [16]. Because of structural changes of the net-work in each iteration of the optimization algorithm, reliabilityevaluation in this problem is faced with some difficulties. There-fore, amethod for reliability evaluation of a distribution networkin the planning studies is proposed as well.This paper is organized as follows. Section II deals with

modeling of the DA functions targeted in this paper. Themathematical model formulation for the DSP is presented inSection III. Section IV explains the proposed method for dis-tribution system reliability evaluation in the planning studies.Section V describes the test system, the obtained results andthe discussions. Finally, Section VI draws conclusions.

II. MODELING OF DA FUNCTIONS

As mentioned in the Introduction, it is assumed that thedistribution system under study has specific DA functions forAVVC and AFM. These automation functions can be imple-mented through installing of devices such as remote controlledswitches, remote controlled capacitors, fault passage indicators(FPIs), distance to fault estimators (DTFEs), and remote ter-minal units (RTUs) in appropriate locations based on the resultsof optimal placement study. Therefore, when directing theDSP studies for an automated distribution network, in additionto planning to supply the loads, it should also be planned toextend the DA functions by installing automation devices in


HEIDARI et al.: POWER DISTRIBUTION NETWORK EXPANSION PLANNING CONSIDERING DISTRIBUTION AUTOMATION 3

appropriate locations. Although considering DA functions inthe DSP studies increases the investment cost of the plan, itcan result in a more efficient and reliable network with reducedoperational and interruption costs [17], [18]. Therefore, con-sidering the DA functions in the DSP studies may lead to thedevelopment of more economic expansion plans.

A. AVVC

The AVVC function regulates the voltage and minimizeslosses through coordinated regulator and capacitor bank control[19]. With this function, if the voltage drop at a bus exceeds thedetermined threshold, the capacitor banks that are connectedto the buses of the related feeder are switched on. Each bankacts like an almost constant source of reactive power, so it ismodeled as a constant kVAR source in the power flow program[20].

B. AFM

The AFM function significantly reduces outage time ofcustomers and the consequence costs. This function is accom-plished by sequential process of fault detection, fault location,fault isolation, and service restoration to the unfaulted feedersegments [19]. For modeling this function, it is assumedthat DA system is fully reliable, therefore outage time of thecustomers that can be restored without repairing the fault isconsidered to be zero if the distribution system is fully auto-mated, while in an unautomated system it equals to the sumof the fault detection time ( ), fault location time ( ), andswitching time ( ) for fault isolation and service restoration.If switching is performed remotely, switching time could bemuch shorter compared to manual switching ( ).On the other hand, outage duration of customers that cannot beisolated from the faulted section is equal to fault repair time( ) either in automated or unautomated systems.

III. PROBLEM FORMULATION

In the proposed DSP model, it is assumed that the early phasestudies such as spatial load forecasting have been conducted.Consequently, the proposed locations and routes for the con-struction of the substations and feeders have been determinedbased on the environmental limitations and the results of loadforecasting. Moreover, it is assumed that the switch and capac-itor placement study has been done for the proposed network.Therefore, in the final phase of expansion planning study, a setof lines and substations must be selected so that the constraintsof the problem are satisfied and the achieved plan is the mosteconomic one.The model considers that there are several alternatives for ex-

panding each resource, depending on the size and type of theconductors or the transformer’s capacity. Additionally, somelines may be decided to be removed from the network in theplanning horizon or to be reinforced or replaced. The decisionmight be to increase the capacity of some substations providedthat they have enough space for expansion.

A. Decision Variables

According to the model descriptions, the DSP is formulatedas a MINLP problem. Decision variables of the optimization

problem can be represented by . For the lines, this variablecan take value from the set , where:• ( ) shows that a line with conductorof type has been added to (removed from) to route atyear ;

• shows that a line with conductor of type hasbeen neither added nor removed to/from route at year .

For substations, can take value from the set ,where ( ) shows that a transformer withsize has been (not) added to substation at year .To determine whether an element is present in the network

or not, another variable must be defined. This variable can becalculated from the decision variables as follows:

if

if

if

if

(1)

where if element is in the network at year . Other-wise, it equals zero.

B. Objective Function

The objective function of the DSP model is the net presentvalue of the DISCO’s profit that can be calculated as follows:

(2)

where

(3)

(4)



(5)

(6)

(7)

Equation (3) calculates the present value of the total revenuea DISCOwill gain through selling electrical energy during plan-ning time horizon. In this equation, can be calculated asfollows:

(8)

Equations (4) and (5) calculate the present value of the totalinvestment and salvage cost which must be paid for network ex-pansion. In (4), the investment needed for substations, feeders,lines’ reinforcement, and load points are calculated by the first,second, third, and fourth terms, respectively. These terms havecoefficients that may be confusing. Therefore, it is necessary toexplain that these coefficients are applied to ensure that the costassociated with each element (substation, line, load point) is ac-counted once when the respective decision variable is toggled.This explanation also helps to understand (5)–(7).The present value of the cost of the operation and mainte-

nance of the system during planning time horizon are calculatedin (6) and (7), respectively. Finally, (7) calculates the presentvalue of the interruption cost assuming that the regulations forcethe DISCO to pay off this cost to customers through discountingtheir bills. Moreover, each interruption reduces DISCO’s profitby decreasing the amount of sold energy that is taken into ac-count in calculation of the revenue in (3) by means of (8).In (4) and (6), variable indicates the presence ( ) or

absence ( ) of load point in the network at year . Variableis defined in Table I.

TABLE IDEFINITION OF VARIABLE

C. Constraints

In this model, constraints of the optimization problem aredivided into two categories, technical constraints and nontech-nical constraints.Technical constraints ensure that the final solution of the

problem is a network that distributes the required energy tocustomers while it is compliant with standards and meets thecustomers’ and regulator expectations. These constraints are asfollows:

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

Equation (9) ensures that all load points are connected to thenetwork through a feeder and there is no isolated load point.To determine the value of , the planned network graphis traversed to determine whether each feeder is a connectedgraph ( ) or not ( ). In a subconnectedgraph, (10) is a sufficient condition for radiality of the network,because a network is radial if and only if each feeder is a con-nected graph and the number of lines ( ) equals to thenumber of load buses ( ) [6]. Equation (11) checks theconvergence of the power flow calculations using one of the out-puts of power flow program that is a binary variable ( )equals to one if calculations converge and goes to zero if powerflow diverges due to mismatch of active or reactive power at anynode. Equations (12) and (13) represent the maximum capacityof the substations and lines respectively, and (14) represents theconstraints of the voltage magnitude of nodes. Equations (15)and (16) ensure that the reliability indices of the network meetthe thresholds determined by the regulator.Nontechnical constraints that act on the chromosomes and

check the feasibility of the solutions are as follows:

(17)

(18)



Fig. 1. Structure of the chromosome.

(19)

(20)

(21)

(22)

Equation (17) represents the constraints of the available areaof the substations for the expansion. Parameter indi-cates the number of transformers that can be added to substationwhich is at least equal to one for proposed substations. Equa-tions (18) and (19) assure that duplication of circuits (existingand proposed respectively) is not allowed. Equations (20)–(22)indicate that salvage is only possible for a line and for a type ofthis line that previously exists in the network. In (20) and (21),parameter indicates the type of line .

D. Optimization

In order to apply the GA to the DSP problem, the first stepis to determine structure of the chromosome. Fig. 1 shows howa chromosome is constructed from the decision variables. Thelast row of this figure represents string of the chromosome.After structuring the chromosome, how the constraints are

handled should be specified. The method that is used for dealingwith the nontechnical constraints is the rejecting technique inwhich the infeasible chromosomes are discarded all over thegenerations. For technical constraints, the penalty method isused in which a negative penalty is added to the objective func-tion of themaximization problem for violation of any constraint.The value of the penalty varies depending on the importance ofthe violated constraint.Designing the basic operators and control parameters of the

GA is the next step.Many selection schemes such as uniform se-lection, stochastic uniform selection, tournament selection, andRoulette selection can be used for solving the DSP problem. Forthe population size, crossover, andmutation rates, typical valuesare selected in the intervals (20,50), (0.5,1.0), and (0.001,0.05),respectively. For stopping the algorithm, several criteria such asthe number of generations and the tolerance of the fitness func-tion can be used. The solution procedure of the DSP problem ispresented in Fig. 2.

Fig. 2. Solution procedure of the DSP problem.

IV. RELIABILITY EVALUATION METHOD

There is a population of solutions in each iteration of the GA.Each solution (chromosome) represents a different plan for ex-pansion of the distribution network. Thus, the fitness calculatingprogram faces a different network in each run. This creates diffi-culties in reliability evaluation, because for assessing reliabilityindices, in addition to data such as failure rate ( ) and repairtime of all equipment, structure of the network (the location ofsubstations, lines, switches, and other protection devices) mustbe given. Thus, the reliability calculating subprogram shouldfirst identify the network structure using the value of the genesin the related chromosome.Network identification process is done with five matrices,

given here.• :Elements of this matrix are obtained from the linedata. If there is no lines between bus and bus ,

; otherwise if lineis located between bus and bus ,

ifif

(23)

• :To determine the elements of this matrix, first the elementscorresponding to substation buses are set to zero (zero-level buses). Then the elements related to the buses thatare connected to zero-level buses are set to one (level-onebuses) and so on. So, this matrix is constructed using ma-trix connect and a graph traversal algorithm such as BFS(breadth-first search).

•This matrix specifies the load points that are fed from acommon feeder. To construct this matrix, first the elementscorresponding to level-one buses are set to the bus number.



Then by using matrices connect and bus_level and BFSalgorithm, the load points that are connected to a commonfeeder is specified and their corresponding elements are setto the level-one bus number.

•This matrix specifies the load points that are fed from acommon substation. Therefore by using the matrices con-nect and com_feed and BFS algorithm, the elements cor-responding to the load points of feeders that are connectedto a common substation are set to the substation number.

•This matrix specifies the route of supplying a load point.If line is not on the feeding route of bus , we have

, else if line is the th line in thesupplying route of load point , then. The elements of this matrix can be obtained using arecursive algorithm from the elements of matrices connectand bus_level.

It can be easily shown that the network structure can beuniquely identified by having two matrices com_sub andfeed_rout.After identifying the network structure, reliability evaluation

process starts with the definition of matrix . Eachelement of this matrix represents the outage time of loadpoint due to the failure of element . After construction ofmatrix , reliability indices are calculated as follows [21]:

(24)

(25)

(26)

(27)

(28)

V. NUMERICAL RESULTS

The proposed DSP model is implemented in MATLAB usingMATPOWER 4.1 M-files (function runpf) for power flow cal-culations [22] and Global Optimization Toolbox (function ga)for developing the optimization algorithm.The developed model is examined to solve the multistage

expansion planning problem on a 24-node test network shownin Fig. 3. This test network is a 20-kV distribution systemthat is supplied by two 20-MVA, 63-kV/20-kV substations.The proposed feasible routes and locations for constructingfuture feeders and substations are displayed in Fig. 3. Table IIrepresents the data related to the load points, including theforecasted peak power demand over five years and the datarequired for reliability evaluation. Table III gives the locationof the switches, capacitors, and protection and automationdevices in the existing and proposed network. It is assumed thatthe location of these devices has been determined through the

Fig. 3. 24-node test network under study.

TABLE IIDATA RELATED TO THE LOAD POINTS

TABLE IIILOCATION OF THE PROTECTION AND AUTOMATION DEVICES

placement studies. In addition to the devices listed in Table III,there is a circuit breaker at the beginning of each feeder.For constructing new subtransmission substations or ex-

panding the existing ones, the 20-MVA or 30-MVA trans-formers are used, and the 600-kVAR capacitor banks areutilized for voltage and VAR control. The conductor that isused in the existing network is of overhead type, LA56. Fornetwork expansion, in addition to this conductor, other type



TABLE IVDATA OF CONDUCTORS USED IN THE EXISTING NETWORK AND FOR EXPANSION

TABLE VOTHER REQUIRED DATA

of conductors such as LA110 and XLPE cable can also beused. Table IV gives the data related to the conductors. Otherrequired data are shown in Table V.For the sake of comparison, three case studies are performed:• Case I: Planning with the common minimum-cost modelwithout considering automation.

• Case II: Planning with the proposed maximum-profitmodel without considering automation.

• Case III: Planning with the maximum-profit model consid-ering DA with AVVC and AFM functions.

A. Case I

In the minimum-cost model, the objective function is the netpresent value of the total cost that is the sum of the cost of invest-ment, salvage, operation, maintenance and interruption. Fig. 4represents the final scheme of the network according to the ex-pansion plan achieved in this case.Table VI gives details of the multistage plan, showing the ele-

ments that must be added/removed to/from the network at eachstage (year) to expand the network according to the proposedplan.According to the developed plan, one 20-MVA substation

must be constructed in the first year, line 3 should be removedat year 2, and the LA56 conductor of lines 1 and 8 should bereplaced with XLPE and LA110 at years 3 and 5, respectively.

Fig. 4. Expansion plan achieved in Case I.

TABLE VIDETAIL OF THE MULTISTAGE PLAN IN CASE I

TABLE VIICOSTS CALCULATED IN CASE I

Table VII shows the present value of the costs, revenue, andprofit associated with each expansion plan.

B. Case II

In this case, the proposed maximum-profit model is usedto develop an expansion plan for the test network. Fig. 5 andTable VIII present the expansion plan achieved in this case.According to this plan, two substations are added to the net-

work in the first and fourth year of the planning horizon, andthe layout of the feeders is different from the scheme that isproposed by the cost-based model. Moreover, the overhead con-ductor of lines 1 and 9 should be replaced with XLPE cable atthe first and fifth year respectively, and line 3 should be removedat year 2. This plan proposes XLPE cable for constructing line17 at year 5 and LA56 for other lines.From Table VII, it can be seen that the proposed model leads

to a more expensive plan than the cost-based model. This in-consistency can be explained by the fact that a profit-maxi-mizing firm should often invest more than a cost-minimizing



Fig. 5. Expansion plan achieved in Case II.

TABLE VIIIDETAIL OF THE MULTISTAGE PLAN IN CASE II

Fig. 6. Expansion plan achieved in Case III.

one. Therefore, a DISCO that develops its network according tothe plan achieved from the presented model, can expect betterperformance in the competitive environment.

C. Case III

In this case the expansion plan is developed using the profit-based model considering DA with AVVC and AFM functions.Fig. 6 and Table IX present the expansion plan that is achievedin this case.According to the proposed plan, the conductor of line 1

should be replaced with LA110 at year 3, and two substationsshould be constructed at years 1 and 4. In this plan, lines 3and 6 are not removed, but they are disconnected from thenetwork by means of normally open switches (at Buses 1 and

TABLE IXDETAIL OF THE MULTISTAGE PLAN IN CASE III

5) during system normal condition to meet the radial operationconstraint. On the other hand, when a fault occurs, these linesmay be used by AFM system through manoeuvring betweenfeeders to reduce the number of the affected load points andconsequently reduce the interruption cost.In this plan, the investment for the replacement of the over-

head lines with underground cables that have very low failurerate and guarantee high reliability indices, is prevented. Thisis because equipping the network with DA and its AFM func-tion improves the reliability of the network and there is no needfor improvement of the reliability by using underground cables.Moreover in this plan the conductor with the smallest cross sec-tion is used for construction of lines, because AVVC functionreduces voltage drop and losses. Thus, the implementation ofthis plan is more profitable than the plan proposed in Case II.

VI. CONCLUSION

A methodology for distribution network expansion planningconsidering distribution automation functions was developed.The planning was performed from the DISCO’s perspectiveusing maximum-profit model, and the MINLP optimizationproblem was solved using the genetic algorithm. Also, a relia-bility evaluation method for using in the planning studies wasproposed in order to evaluate the reliability of the network forcalculating the interruption cost and its impact on corporateearnings.The comparison of the results associated with the conven-

tional minimum-cost model and the proposed maximum-profitmodel shows that there are considerable differences betweenthe plans designed by these two models. These differences sug-gest that, if the company expands the network based on the plandeveloped by maximum-profit model, higher productivity andbetter performance can be achieved in a competitive environ-ment. The results of case studies show that the plan proposedby the maximum-profit model may be more expensive than thecost-based plan. This is not a contradiction, because achievingmaximum profit usually needs more investment than that of costminimization.Furthermore, considering automation functions such as

AVVC and AFM prevents investing for replacement of the ex-isting conductors with cables or conductors with more capacity,because considering these technologies reduces the calculatedcost of operation and interruption.It should be noted that, if the challenges facing distribution

networks, including smart grid technologies, are consideredproperly in the planning stage of distribution systems, the



achieved expansion plan can be more compatible with thecorporate strategic goals.

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Saeed Heidari received the B.Sc. and M.Sc. degreesin electrical engineering from Sharif Universityof Technology, Tehran, Iran, in 2010 and 2012,respectively, where he is currently working towardthe Ph.D. degree in the Electrical EngineeringDepartment.His research interests include distribution system

reliability, smart grid, distribution automationsystem, as well as distribution system planning andoperation.

Mahmud Fotuhi-Firuzabad (F’14) received theB.Sc. degree from Sharif University of Technology,Tehran, Iran, in 1986, the M.Sc. degree from theUniversity of Tehran, Tehran, in 1989, and theM.Sc. and Ph.D. degrees from the University ofSaskatchewan in 1993 and 1997 respectively, all inelectrical engineering.He is presently a Professor and Head of the Elec-

trical Engineering Department with Sharif Universityof Technology, Tehran, Iran.Dr. Fotuhi-Firuzabad is a member of the Center of

Excellence in Power System Control and Management. He serves as the Editorof the IEEE TRANSACTIONS ON SMART GRID and has served as a guest editor-in-chief of a Special Issue (Microgrids) of the same journal.

Shahram Kazemi (M’09) received the M.Sc. andPh.D. degrees in electrical engineering from SharifUniversity of Technology, Tehran, Iran in 2004 and2011, respectively, and the D.Sc. degree in powersystems and high-voltage engineering from AaltoUniversity, Espoo, Finland, in 2011.He has working experience with several world

leading transmission and distribution utilities,consulting companies, oil and gas companies, andresearch institutes. He is currently an AssistantProfessor with the Department of Electrical Engi-

neering, Razi University, Kermanshah, Iran. His main research interest is thereliability evaluation of smart distribution grids.

Documents

Power Distribution Network Expansion Planning Considering Distribution Automation