Electrical Power and Energy Systems 45 (2013) 71–77

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Electrical Power and Energy Systems

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

An application of hybrid heuristic method to solve concurrent transmissionnetwork expansion and reactive power planning

Amin Mahmoudabadi ⇑, Masoud RashidinejadDepartment of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

a r t i c l e i n f o

Article history:Received 15 October 2011Received in revised form 24 July 2012Accepted 29 August 2012Available online 6 October 2012

Keywords:Transmission expansion planningReactive power planningHybrid heuristic method

0142-0615/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijepes.2012.08.074

⇑ Corresponding author. Address: 22 Bahman BlvEngineering, Shahid Bahonar University of Kerman,3413235900.

E-mail address: a.1366.m@gmail.com (Amin Mahm

a b s t r a c t

In this paper a mathematical model for solving simultaneous transmission network expansion and reac-tive power planning problem (TEPRPP) via an AC model has been presented. A Real Genetic Algorithm(RGA) combined an Interior Point Method (IPM) aimed to obtaining a significant quality solution for sucha problem has been employed. The proposed algorithm is tested on three systems; IEEE 24-bus system,46-bus south Brazilian and the Southeast Network of Iran (SNI). The obtained results show the capabilityand the viability of the proposed methodology incorporating the AC model of the TEPRPP problem even inreal world.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Nowadays, modern electric power systems consist of large-scale and extremely complex interconnected transmission net-works. As electricity consumption grows rapidly, new transmissionlines are necessary to provide alternative paths for power transferfrom power plants to load centers to enable continuous supply. Onthe other hand, reactive power sources are desired for: increasingthe capacity of transmission lines, power factor correction, lossreduction, and voltage profile improvement. Thus, TransmissionExpansion Planning (TEP) and Reactive power planning (RPP) arecrucial issues especially in modern power systems. By using theAC model for TEP, RPP can also be exercised. One may argue thatwithout supporting reactive power in some transmission net-works, load bus voltages may differ from their prescribed magni-tudes; which may not only cause unacceptable power quality butalso increase real power losses. In such cases it may require moretransmission line additions which may not be economical for thenetwork. On the other hand, TEP and RPP, as a combinatorial prob-lem, seem very complicated and require to be solved via mixedinteger nonlinear programming. The objective of the simultaneoustransmission expansion and reactive power planning problem, re-ferred to as TEPRPP, is to determine ‘where’, ‘what’ and ‘when’ newdevices such as transmission lines and reactive power sourcesmust be added to an existing network in order to make its opera-

ll rights reserved.

d., Department of ElectricalKerman, Iran. Tel./fax: +98

oudabadi).

tion viable for a pre-defined horizon of planning at minimum totalcosts. In a static TEP the time of new lines installation is not deter-mined on the planning horizon while in a dynamic TEP in additionto ‘‘what’’ and ‘‘where’’, planners answer to ‘‘when’’ the transmis-sion facilities must be installed. Since the dimension of a dynamicTEP problem is larger the solution approaches might be compli-cated and need huge computational effort [1]. The benchmark net-work of the base year, the candidate lines and candidate load busesto install reactive sources, the power generation and power de-mand in a planning horizon associated with the investment con-straints are the basic data for such a general TEP problem. In fact,such a problem has been researched for a long time and a reviewof the literature can be found in [2], while the earlier well citedwork is developed by Garver [3]. Albeit most of these studies onlyconsider simplified DC models while recently an accurate AC net-work modeling has been proposed [4]. Generally in TEP steady-state analysis is usually performed using simplified models like:transportation models, linearized power flow models or other sim-ilar techniques. Transportation models, hybrid models, the lineardisjunctive model, the DC model [5], among others, have been usedto achieve the primary topology in the first stage. Solving a TEPproblem can be handled both by classical optimization techniques[6,7] as well as meta-heuristics, such as: Simulated Annealing [8],Genetic Algorithms [9,10], Tabu Search [11] Greedy RandomizedAdaptive Search Procedure (GRASP) [12], Ant Colony [13] and Dif-ferential Evolution [14]. In all cases, usually in a subsequent stage,the obtained expansion plan is checked for other operational con-straints. In short-term planning, the steady-state studies use an ACmodel in order to assess real-power losses accurately and reactivecompensation requirements, both for the basic configuration as

72 Amin Mahmoudabadi, Masoud Rashidinejad / Electrical Power and Energy Systems 45 (2013) 71–77

well as contingencies. The use of the complete AC model in the firstphase is incipient but there are few technical literatures on thesubject [4,15].

In this paper, on the other hand, an integrated AC TEPRPP isintroduced, in which the following advantages have been realized:

� Efficiently allocating reactive power sources during the plan-ning and consequently decreasing the cost of new linesinstallation.� Using an integrated mathematical model that allows TEP and

the optimal allocation of reactive power simultaneously in aunique stage via and AC model.� Incorporating the determination of the transmission system’s

precise real power losses in a trivial approach.

As it can be seen, in [16] the authors use a constructive heuris-tics algorithm to solve AC-TEP and introduce two indexes for find-ing weak buses for the potential location of reactive power sources.In fact, after transmission lines are constructed then reactivepower sources will be allocated to weak buses. In the present work,a Real Genetic Algorithm (RGA) is used to solve TEPRPP via an ACmodel, while an Interior Point Method (IPM) is employed to solvean NLP problem that should be solved during the solution step ofRGA. In fact, IPM provides a better computational performancefor large scale problems than classical approaches, such as the Sim-plex method. It is worth noting that in the literature, IPM hasmostly been used to solve problems like optimal power flow forlarge-scale systems [17], state estimation [18] and security con-strained economic dispatch [19].

2. TEPRPP mathematical modeling

A mathematical model for the TEPRPP problem can be formu-lated via the following equations.

min v0 ¼ cT n ð1Þmin v1 ¼ f ðq;uÞ ð2Þ

s.t.

PðV ; h;nÞ � PG þ PD ¼ 0 ð3ÞQðV ; h;nÞ � Q G þ Q D � q ¼ 0 ð4ÞPG 6 PG 6 PG ð5ÞQ G 6 Q G 6 Q G ð6Þq 6 q 6 �q ð7ÞV 6 V 6 V ð8ÞðN þ N0ÞSfrom

6 ðN þ N0ÞS ð9ÞðN þ N0ÞSto

6 ðN þN0ÞS ð10Þ0 6 n 6 �n ð11Þ

where c and n represent the circuit costs’ vector and the addedlines’ vector, respectively. N and N0 are diagonal matrices contain-ing the integer-valued vector n and the existing circuits in the baseconfiguration, respectively. f(q,u) Is the cost function of reactivepower (VAr) sources, q is the MVAr size of VAr sources vector. uis the binary vector that indicates whether to install reactive powersources at load buses or not and has an integer value. v0 is theinvestment due to adding new circuits to the network and v1 isthe costs of VAr sources. �n is a vector containing the maximumnumber of circuits that can be added. h is the unbounded phase an-gle vector, while PG and QG are the existing real and reactive powergenerating vectors. Similarly, PD and QD are the real and reactivepower demand vectors; V is the voltage magnitude vector; PG;Q G

and V are the vectors of maximum real and reactive power

generating limits and voltage magnitudes, respectively; and PG, QG

and V are the vectors of minimum real and reactive power generat-ing limits and voltage magnitudes. In this paper 105% and 95% ofthe nominal value are used for the maximum and minimum voltagemagnitude limits, respectively. Sfrom,Sto and S are the apparentpower flow vectors (MVA) through the branches in both terminalsand their limits. The first objective function considers only theexpansion costs of transmission lines while the second objectivefunction considers the minimum costs of VAr sources that mightbe installed. The limits for real and reactive power in the generatorsare expressed by Eqs. (5) and (6) respectively; and for VAr sourcesby Eq. (7) while voltage magnitudes are restricted by Eq. (8).Capacity limits (MVA) of the line flows are presented by Eqs. (9)and (10), while capacity constraints of the newly added circuitsare shown by Eq. (11). The costs of VAr sources can be defined asfollows:

f ðq;uÞ ¼Xk2Xl

ðc0k þ c1kqkÞuk ð12Þ

where k 2Xl represents the load buses, Xl is the set of all loadbuses; and c0k and c1k are the installation costs and unit costs fora VAr source at busk. qk is the MVAr size of a VAr source installedat bus k and uk is a binary variable that indicates whether to installreactive power source at bus k or not. Eqs. (3) and (4) represent theconventional equations of AC power flow consideringn, the numberof circuits (lines and transformers), and q, the size of VAr sourcestreated as variables. The elements of vectors P(V,h,n) andQ(V,h,n) are calculated by Eqs. (13) and (14), respectively.

PiðV ; h;nÞ ¼ Vi

Xj2NB

Vj½GijðnÞ cos hij þ BijðnÞ sin hij� ð13Þ

QiðV ; h;nÞ ¼ Vi

Xj2NB

Vj½GijðnÞ sin hij � BijðnÞ cos hij� ð14Þ

where i, j 2 NB represent buses and NB is the set of all buses, ij rep-resents the circuit between buses i and j and hij = hi � hj is the differ-ence in phase angle between buses i and j. The elements of the busadmittance matrix (G and B) are:

G ¼GijðnÞ ¼ � nijgij þ n0

ijg0ij

� �GiiðnÞ ¼

Xj2Xl

nijgij þ n0ijg

0ij

� �8>><>>:

9>>=>>; ð15Þ

B ¼BijðnÞ ¼ � nijbij þ n0

ijb0ij

� �BiiðnÞ ¼ bsh

i þXj2Xl

nij bij þ bshij

� �þ n0

ij b0ij þ ðb

shij Þ

0� �h i

8>><>>:

9>>=>>; ð16Þ

Here, gij,bij and bshij are the conductance, susceptance and shunt

susceptance of the transmission line or transformer ij (if ij is atransformer bsh

ij ¼ 0Þ, respectively; and bshi is the shunt susceptance

at bus i, while the proposed model does not consider the phaseshifters. Elements (ij) of vectors Sfrom and Sto of (9) and (10) are gi-ven by the following relationship:

Sfromij ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPfrom

ij

� �2þ Q from

ij

� �2r

ð17Þ

Pfromij ¼ V2

i gij � ViVjðgij cos hij þ bij sin hijÞ ð18Þ

Qfromij ¼ �V2

i bshij þ bij

� �� ViVjðgij sin hij � bij cos hijÞ ð19Þ

Stoij ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPto

ij

� �2þ Q to

ij

� �2r

ð20Þ

Ptoij ¼ V2

j gij � ViVjðgij cos hij � bij sin hijÞ ð21Þ

Qtoij ¼ �V2

j bshij þ bij

� �þ ViVjðgij sin hij þ bij cos hijÞ ð22Þ

Amin Mahmoudabadi, Masoud Rashidinejad / Electrical Power and Energy Systems 45 (2013) 71–77 73

The integer vector variable n, i.e. the number of circuits addedin branch ij, and the binary variable u, that shows the connectionor disconnection of VAr sources to a load bus, are the most impor-tant decision variables such that any feasible operation solution ofpower system depends on their values.

3. Real Genetic Algorithm

As explained before, in this paper a Real Genetic Algorithm(RGA) is used for solving AC TEP as well as RPP [15]. The proposedRGA method comprises five stages: problem codification, selection,recombination, mutation, and fitness evaluation that are explainedin the following subsections.

3.1. Problem codification

One of the most important factors in representing a candidatesolution in the proposed method is codification. A proper codifica-tion may prevent complexity in the implementation of RGA. Theindividual is a solution proposal for the planning problem, or bettersaid, it is the topology made up of all transmission lines added tothe system corresponding to their investment proposal. In TEPRPP,the individuals of RGA are represented by a vector. Each vector isconsisted of the number of new lines that are proposed to be addedto respective branches. Each member (gene) of this vector can varyfrom zero to the maximum number of lines. Thus, in the codifica-tion stage shown in Fig. 1, branch 2–6 has two new lines; branch3–5 has one new line, etc.

The number of individuals in RGA population, for the transmis-sion network expansion problem, depends on the dimensions ofthe system. Similar to ordinary GA, RGA operators are: selection,recombination and mutation, which are explained in the followingsections.

3.2. Selection

Chromosome selection is a random process in which individualchromosomes are mapped to the adjacent segments of a line andthe length of each segment on the line corresponds to the levelsof fitness (i.e. fitness values) of each individual. It is assumed thatthe number of individuals in the population is N, while P is the po-sition of each individual in the population. Eq. (23) can be used tocalculate the rank of each individual [20].

RankðPÞ ¼ 1� SP þ 2ðSP � 1ÞðP � 1ÞN � 1

ð23Þ

The minimum and maximum values of P are 1 and N, while SP isa random number between 1 and 2.

3.3. Recombination

At the recombination stage, the next generation is created andin RGA this is one of the differences of this technique to that of

1-2 1-4 3-5 2-6 4-6

00 1 12

Chromosome

Line codification

Fig. 1. Simple codification.

ordinary GA. Three kinds of recombination are used in RGA [20],designated by the following equations.

O1 ¼ kP1 þ ð1� kÞP2

O2 ¼ kP2 þ ð1� kÞP1; k 2 f0;1gð24Þ

O1 ¼ k1P1 þ ð1� k1ÞP2

O2 ¼ k2P2 þ ð1� k2ÞP1; k1; k2 2 ½�0:25;1:25�ð25Þ

O1 ¼ kP1 þ ð1� kÞP2

O2 ¼ kP2 þ ð1� kÞP1; k 2 ½�0:25;1:25�ð26Þ

where P1,P2 are the two parents, O1,O2 are their two offspring andk,k1 and k2 are randomly generated numbers. A typical individualchromosome with two genes, in which two parents can mergebased on three forms, are shown in Fig. 2a–c.

RGA recombination shown in Fig. 2a generates the offspringthat is located on the corners of the hypercube defined by theparents. The line recombination shown in Fig. 2b can generateany offspring by the parents on the specified line and Fig. 2cshows the intermediate recombination capable of producing anypoint within the hypercube that is slightly larger than the one de-fined by the parents. The line recombination is similar to inter-mediate recombination, except that only one k value is used forall variables.

3.4. Mutation

In order to achieve a high degree of precision in the proposedmethod a dynamic mutation is designed for fine-tuning to providea degree of control [21]. For example, in mutation if gene Pk is se-lected from parent P, then there is an equal chance that the result-ing gene to be either of the following choices:

OK ¼ PK � rðPK � aKÞ 1� tT

� �c

OK ¼ PK þ rðbK � PKÞ 1� tT

� �c

( )ð27Þ

where aK and bK are respectively the lower and upper bound of PK, ris a uniform random number between (0,1), t is the number of cur-rent generation, T is maximum number of generation, and c is aparameter determining the degree of non-uniformity.

3.5. Fitness evaluation

The fitness function defined in this paper pursues to minimizethe following two objectives: the cost of installation new transmis-sion line and the cost of installation new reactive sources. Depend-ing on the objective function, fitness evaluation can be deployedusing the following equation.

fitness ¼ w1ðv0Þ þw2ðv1Þ ð29Þ

where v0 is the total costs of new lines, v1 is the costs of VAr sources,w1 and w2 are weights that can be selected by decision maker [22],in which Eq. (30) should be satisfied.

w1 þw2 ¼ 1 ð30Þ

4. Solution methodology

The overall procedure of using RGA in TEPRPP is as follows:

I. Initialize first generation at random: each individual is cho-sen at random.

II. Feasibility checking: Each chromosome is checked in termsof cost. Those individuals that their investments are too highwill be pruned.

Possible offspring

Parents

Area of Possible offspring

Line of Possible offspring

(a) (b) (c)Fig. 2. Different schemes of recombination.

74 Amin Mahmoudabadi, Masoud Rashidinejad / Electrical Power and Energy Systems 45 (2013) 71–77

III. The data of each individual, consisting of the number andlocation of new lines are read out and the new network isconstructed.

IV. AC Optimal Power Flow with real power and reactive powersources as an objective is solved for each individual. In thisstep the problem that is solved is as follows:

min v ¼Xn

i¼1

ðf1iðPGiÞ þ f2ðQ GiÞÞ þ f ðq;uÞ ð31Þ

s.t.

PðV ; hÞ � PG þ PD ¼ 0 ð32ÞQðV ; hÞ � QG � qþ QD ¼ 0 ð33ÞPG 6 PG 6 PG ð34ÞQG 6 Q G 6 Q G ð35Þq 6 q 6 �q ð36Þ

Sfrom6 S ð37Þ

Sto6 S ð38Þ

Here, f1i and f2i are the costs of active and reactive power gen-eration for generator i at a given dispatch point. Both f1i andf2i are assumed to be polynomial or piecewise-linear func-tions. When new lines are embedded in the initial network,there would be no need to separate existing lines and newlines in formulation; so in this formulation there is no integervariable and we just need to solve an AC OPF. Since the cost

Fig. 3. IEEE-24 bus syste

of new reactive power sources is one of the objectives of OPF,new and existing reactive power sources must be separatedin formulation. At this step an Interior Point Method (IPM)is utilized for solving the OPF [14].

V. The results of OPF are used to calculate the fitness function.VI. When OPF is solved for the entire set of individuals and the

fitness of each member is calculated, the Selection, Recombi-nation and Mutation of RGA is carried out and the new gen-eration is constructed. When all the individuals are the sameand there is no new individual, the process can be stopped.Another stop criterion is the number of generations fromthe beginning of our evolutionary process.

VII. Depending on the convergence of RGA and the stop criteria,the process will be stopped or continued into step II.

5. Illustrative tests

The proposed algorithm is implemented to some case studiesusing AMPL (A Modeling Language for Mathematical Program-ming). AMPL is a language platform for large scale mathematicalprogramming and optimization in many applications such as pro-duction, distribution, and scheduling. For the illustrative tests,three systems were simulated: IEEE 24-bus system, the 46-bussouth Brazilian system and Southern Network of Iran (SNI). Themain objectives of these tests are to show that TEP and RPP canbe handled simultaneously while the total cost might be decreased

m.

Table 1IEEE 24-bus results.

Lines added to network Reactive power planning (MVAr)

n6�10 = 1, n14�16 = 1 Q3 = 198.67, Q4 = 29.58, Q8 = 171.90,Q9 = 277.77, Q10 = 190.29,

Total linesinvestment = $70million

Q12 = 101.41, Q24 = 94.86

Total cost reactive power sources = $3.19million

Table 2IEEE 24-bus results comparison.

Lines investment(million $)

VAr cost(million)

Total cost(million)

Proposedmethod

70 3.19 73.19

CHA method 86 2.55 88.55

Amin Mahmoudabadi, Masoud Rashidinejad / Electrical Power and Energy Systems 45 (2013) 71–77 75

significantly. A fixed cost c0 = $1000 and a variable cost of $3/KVArare assumed [5].

5.1. IEEE 24-bus system

This system has 24 buses, 41 circuits and the original data is in[4]. The single line diagram of IEEE 24-bus system is shown inFig. 3.

Fig. 4. Southern Brazili

By implementing the proposed approach, results show that se-ven reactive sources should be installed at load buses and the fol-lowing lines are also added to the existing network: n6�10 = 1,n14�16 = 1. The line investment cost is $70 million and the invest-ment cost of reactive power sources is about $3.1935 million.The details are shown in Table 1.

By comparing the above results with those reported in [4], theaverage investment cost of transmission lines and total cost de-creases significantly whereas VAr sources cost $0.64 million in-creased. Table 2 shows this comparison.

5.2. 46-bus South Brazilian system

This system has 46 buses and 79 circuits. This system repre-sents a good test to the proposed methodology because it is a realsystem and also highly complex for an AC TEP problem. The basicdata of the southern Brazilian system (for the DC model) is in [5]. Infact, some modifications in the data of the system had to be intro-duced in order to use the AC model. The reactive power demand (ineach bus) is 15% of the real power, the upper limits of the transmis-sion lines are increased by 20%, and the resistance and susceptanceare 10% and 1% of the impedance of the transmission line, respec-tively [15]. This system is shown in Fig. 4.

The details of results derived through the proposed method isshown in Table 3, the line investment cost is $46.807 million andthe investment cost of reactive power sources is about $10.92 mil-lion, while active power loss is 240.19 MW.

Table 4 compares the investment cost, VAr source cost, powerloss and total cost between proposed method and method in [4].In this test not only lines investment and VAr sources cost is de-

an 46-bus system.

Table 346-Bus South Brazilian results.

Lines added to network Reactive power planning (MVAr)

n20�23 = 1, n20�21 = 1,n42�43 = 1,

Q1 = 7.01, Q4 = 142.69, Q6 = 8.17, Q7 = 22.46,Q8 = 90, Q9 = 326.64,

n46�6 = 1, n5�6 = 1 Q12 = 182.39, Q13 = 261.71, Q20 = 140.4,Q21 = 525.44, Q22 = 153.54,

Total linesinvestment = $46.807million

Q23 = 20.54, Q24 = 334.67, Q26 = 103.76,Q33 = 124.76, Q38 = 183.77,

Q42 = 432.61, Q43 = 505.84, Q44 = 46.91,Q45 = 26.01Total cost reactive power sources = $10.92million

Table 446-Bus South Brazilian results comparison.

Lines investment(million$)

VAr cost(million)

Power loss(MW)

Total cost(million)

Proposedmethod

46.807 10.92 240.19 57.727

CHAmethod

102.58 10.765 310.6 113.345

76 Amin Mahmoudabadi, Masoud Rashidinejad / Electrical Power and Energy Systems 45 (2013) 71–77

creased but also power loss is improved significantly. It is impor-tant to highlight that the main difference between the solutionpresented in [4] and the solution presented in this work is in the

19

14

2

50494746

5148

27

54

23

22

5229

39

35

4034

53

33

30

31

32

41

36

42

43

44

45

Fig. 5. Single diagram of Ir

lines added. In CHA method one line was added in paths 19–25,20–21, 24–25, 42–43, 42–44, 46–6 and two lines was added inpath 5–6, totaling an investment of $102.58 million.

In fact, with regards to Table 4 the significant differences be-tween results are because of the following crucial points:

� CHA is an iterative heuristic method which works based uponan index by solving an NLP that my get a Local Optimumthrough adding a new transmission line sequentially until nonew line is needed. While in TEP is a MINLP and if CHA in anystage reaches to a Local Optimum deferring from the globaloptimum the final solution may get to Local Minimum.� In CHA proposed in [4], lines and reactive sources are added to

the network sequentially (rather than concurrently). In thatwork, first new lines are added to the network and then reactivesource will be allocated to the weak buses while those addedlines that are not necessary any more will be dropped fromthe network. That method may use some expensive lines inorder to overcome the voltage constraint as well as reactivepower procurement in the first round. In fact, in this methodol-ogy after allocating reactive sources some added transmissionline may not be dropped anyway. While in our proposed meth-odology that is concurrent TEPRPP all are happened in one stageoptimally.� Although CHA is a very simple and efficient method for solving

TEP problems but the global optimal solution may not be guar-anteed. The present work is one of the earliest research reportsbased upon using an AC-TEP model incorporating reactivepower sources simultaneously. Since there is a few published

1

20

151013166

18

4

35

17

91211

2126

7

28

8

25

24

3738

an Southeast Network.

Table 5TEPRPP result of the Southeast Network of Iran.

Lines added to network Reactive power planning (MVAr)

n1�9 = 1, n1�19 = 1, n2�21 = 1,n14�22 = 1, n22� 27 = 1

Q3 = 106.51, Q4 = 176.33, Q6 = 122.53

n43�44 = 1, n18�61 = 1, n53�51 = 1,n52�51 = 1, n28� 31 = 1

Q8 = 114.75, Q9 = 132.84, Q16 = 74.71,Q28 = 72.07, Q29 = 188.09,

Total lines investment = $316.7million

Q30 = 306.11, Q31 = 255.96, Q37 = 22.01,Q40 = 97.05, Q41 = 35.55,Q43 = 44.72, Q45 = 95.99, Q46 = 50.57,Q48 = 222.54, Q50 = 41.07,Q54 = 80.18, Q55 = 52, Q57 = 23.93,Q56 = 18.83, Q61 = 112.19Total cost reactive powersources = $7.362 million

Amin Mahmoudabadi, Masoud Rashidinejad / Electrical Power and Energy Systems 45 (2013) 71–77 77

papers for similar study we could not compare exactly ourmethodology with the same overall conditions. In Brazillian46-bus network study using CHA, the only five reactive powersources are used, while our proposed model will suggest morereactive power sources and three less new transmission linesare added resulting less expansion costs significantly.

5.3. Southeast Network of Iran (SNI)

In this section, the proposed method is applied to the southeastnetwork of Iran as a first attempt for TEPRPP. SNI is a part of inter-connected electric power network in Iran, which is divided intofour regions (provinces): Kerman, Yazd, Hormozgan and Sistan-Baluchestan. Southeast Network of Iran procures the electricpower for an area about 381787 km2. Main tie lines betweensoutheast network and other regions are: four (2 � 400 KV and2 � 230 KV) lines connected to Esfahan, three lines (2 � 400 KVand 1 � 230 KV) connected to Fars. The total length of 230 KV linesis about 2372 km and the total length of 400 kv lines is about4635 km. This system has 63 buses and 87 right-of-ways for theaddition of new circuits and a total demand 10268 MW. The baseyear topology is 2010 and the expansion is targeted for year 2016.Single line diagram of SNI is illustrated in Fig. 5.

The detail of results solved by proposed method is shown in Ta-ble 5, the line investment cost is $316.7 million and the investmentcost of reactive power sources is about $7.362 million. Also, activepower loss is 255.02 MW.

6. Conclusions

This paper develops a Real Genetic Algorithm for solving TEP-RPP problem such a multi-objective optimization problem basedon AC model. Moreover an Interior Point Method (IPM) is appliedto solve an OPF such as a nonlinear programming (NLP) duringthe solution steps of the RGA. The main contribution of this paperis to show that TEP and RPP can be carried out simultaneously onreal world network and also it can get better solution than tradi-tional planning methods. Fitness function is derived from theinvestments of new lines associated with the costs of VAR sources.AC optimal power flow tries to minimize the costs of active andreactive power generation as well as the investments of VAR

sources. The proposed algorithm is tested the Southeast Networkof Iran (SNI) as a first attempt for TEPRPP. The obtained resultshows the performance and robustness of the proposed methodol-ogy using AC model for solving TEPRPP problem even in real worldand large scale system. It has been shown that proposed methodcan be improved by adding new indices to identify weak busesto install new reactive sources.

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