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GA Determination of Location and Capacity of Power Facilities Using UPFC

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This article was downloaded by:[National Institute of Technology Calicut] On: 31 March 2008 Access Details: [subscription number 773426689] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Electric Power Components and Systems Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713399721 Determination of Location and Capacity of Power Facilities by Genetic Algorithm Tomonobu Senjyu a ; Kai Shimabukuro a ; Hirohito Yamashiro a ; Katsumi Uezato a ; Toshihisa Funabashi b a Faculty of Engineering, University of the Ryukyus, Okinawa, Japan. b Meidensha Corporation, Tokyo, Japan. Online Publication Date: 01 April 2004 To cite this Article: Senjyu, Tomonobu, Shimabukuro, Kai, Yamashiro, Hirohito, Uezato, Katsumi and Funabashi, Toshihisa (2004) 'Determination of Location and Capacity of Power Facilities by Genetic Algorithm', Electric Power Components and Systems, 32:4, 1 To link to this article: DOI: 10.1080/759369249 URL: http://dx.doi.org/10.1080/759369249 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
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Page 1: GA Determination of Location and Capacity of Power Facilities Using UPFC

This article was downloaded by:[National Institute of Technology Calicut]On: 31 March 2008Access Details: [subscription number 773426689]Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Electric Power Components andSystemsPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713399721

Determination of Location and Capacity of PowerFacilities by Genetic AlgorithmTomonobu Senjyu a; Kai Shimabukuro a; Hirohito Yamashiro a; Katsumi Uezato a;Toshihisa Funabashi ba Faculty of Engineering, University of the Ryukyus, Okinawa, Japan.b Meidensha Corporation, Tokyo, Japan.

Online Publication Date: 01 April 2004To cite this Article: Senjyu, Tomonobu, Shimabukuro, Kai, Yamashiro, Hirohito,Uezato, Katsumi and Funabashi, Toshihisa (2004) 'Determination of Location andCapacity of Power Facilities by Genetic Algorithm', Electric Power Components and

Systems, 32:4, 1To link to this article: DOI: 10.1080/759369249URL: http://dx.doi.org/10.1080/759369249

PLEASE SCROLL DOWN FOR ARTICLE

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction,re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expresslyforbidden.

The publisher does not give any warranty express or implied or make any representation that the contents will becomplete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should beindependently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings,demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with orarising out of the use of this material.

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Electric Power Components and Systems, 32:375–390, 2004Copyright c© Taylor & Francis Inc.ISSN: 1532-5008 print/1532-5016 onlineDOI: 10.1080/15325000490217470

Determination of Location and Capacity ofPower Facilities by Genetic Algorithm

TOMONOBU SENJYUKAI SHIMABUKUROHIROHITO YAMASHIROKATSUMI UEZATOFaculty of EngineeringUniversity of the RyukyusOkinawa, Japan

TOSHIHISA FUNABASHIMeidensha CorporationTokyo, Japan

This article presents the determination of optimal location and capacity ofpower facilities by using genetic algorithm (GA) based on reliability, loss ofload and dump power. We determine optimal capacity after optimal location;however, since the optimal location and capacity are closely related, the optimallocation varies with the capacity and vice versa. Hence, we propose the methodthat determines the optimal location and capacity at the same time. Using theproposed method, expected loss of load in faults can be reduced by 32.3% incomparison with that of separate optimization techniques.

Keywords power system reliability, loss of load, dump power, geneticalgorithm

1. Introduction

In recent years, the demand of power has been increasing with rapid industrializa-tion. Since electric power systems play a major role in a modern society, professionalengineers are responsible for proper planning, design, and operation of power sys-tems. Further, the modern power systems are required to have better reliability.Under these circumstances, new generation facilities and expansion of the trans-mission lines must be planned and constructed accordingly to maintain reliabilityof power systems and reduce loss of load during faults. Large reserve can maintainreliability and decrease loss of load during faults. However, this reserve increases

Manuscript received in final form on 23 December 2002.Address correspondence to Tomonobu Senjyu, Faculty of Engineering, University

of the Ryukyus, 1 Senbaru Nishihara-cho Nakagami Okinawa 903-0213 Japan. E-mail:[email protected]

375

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cost and dump power that indicates the excess electricity. Hence, there is an im-portance of not only location but also capacity on power system planning.

To solve these optimization problems, algorithms for heuristic techniques havebeen presented. Among the various techniques are Tabu search, Lagrangian relax-ation (LR) methods, and neural network [1]. However, since these methods are localsearch techniques, it is difficult to obtain the optimal solution.

To achieve global search, we propose a genetic algorithm (GA) solution to theoptimal location and capacity problem. GA is an optimization technique basedon a model of evolutionary adaptation in nature [2, 3, 6]. The objective of theproblem mentioned above is maintenance of reliability and reducing the loss ofload and dump power. Since power system reliability and loss of load have diversedimensions, they cannot be evaluated at the same time. This is the multi-objectiveoptimization problem for that reason.

In this article, objective functions are incorporated for the evaluation of thesevariables at the same time. Using the proposed method, optimal location andcapacity can be optimized at the same time, and the expected value of loss ofload in faults can be reduced by 32.3% in comparison with the method optimizingthe location and capacity separately.

2. Power System Reliability

There are many variations on the definition and evaluation of reliability. We adoptthe following definition of reliability; reliability is the probability of a device per-forming its purpose adequately for the period of time intended under the operatingconditions encountered [4, 5]. Since the power system is playing a major role inmodern society, its reliability evaluation is essential. Figure 1 shows the operatingcondition and failure condition of power facilities. Reliability is decided with theavailability given by equation (1), which includes durability and maintainability ofpower facilities.

A =operating time

operating time + failure time(1)

Equation (1) can be further written as,

A =MTBF

MTBF +MTTR(2)

Figure 1. Power system conditions.

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Determination of Power Facilities 377

where MTBF and MTTR are the mean time between failure and mean time torepair, respectively. Here, we define the new variable,

ρ =MTTRMTBF

(3)

where ρ is the coefficient of maintainability.Using the relationship given in equation (3), we obtain the following expression

for A as,

A =1

1 + ρ. (4)

From equation (4), the availability A increases with decrease the coefficient ofmaintainability.

3. Genetic Algorithm

The model of power system used in this article is shown in Figure 2, where G, T , N ,L represent power plant, transmission line, transformer, and load point, respectively.Suppose that two generators and two transmission lines are added in Figure 2. Wewould then determine the optimum setup point and capacity using GA. Figure 3shows the flowchart of genetic algorithm and each step of the flowchart is describedas follows:

STEP 1 Generating Initial Population

Initial population is randomly generated using binary strings (0 and 1). The popu-lation strings consists of 14 bits. Figure 4 shows an initial population. Generators

Figure 2. Power system configuration.

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Figure 3. GA flowchart.

Figure 4. Initial population.

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Determination of Power Facilities 379

1 through 9 in Figure 2 are candidates for new generator setup point. New trans-mission lines are set up in the existing transmission lines. Setup point and capacityof those new facilities are expressed by bit row in Figure 4.

STEP 2 Evaluation

Populations are evaluated by the fitness function. Fitness function is the mostimportant factor in GA.

STEP 3 Selection

The selection creates a new population from the old one. We adopt the elite selectionand roulette selection.

STEP 4 Crossover

Crossover is the most important operator in GA and many new solutions aregenerated by crossover. This operator simply combines the parent symbol strings,forming a new chromosome strings that inherits solution characteristic from bothparents. The crossover scheme used in this paper is an one-point crossover. We usevariable crossover rate. The crossover rate is given by

Pcr = Pc × (Fave/Fmax ) (5)

where Pc is coefficient of crossover rate. Fave and Fmax are the average andmaximum fitnesses respectively. An example of the one-point crossover operatoris shown in Figure 5.

STEP 5 Mutation

The mutation operator is applied for the maintenance of diversity of the solutions.Generally, the mutation operator is applied with a small probability. The mutationscheme used is an one-point mutation. This operator randomly chooses bits of theoffspring genotypes, change from 0 to 1. We use a variable mutation rate given by

Pmr = Pm/(Fmax − Fave) (6)

Figure 5. One-point crossover operator.

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Figure 6. One-point mutation operator.

where Pm is coefficient of mutation rate. Fave and Fmax are the average andmaximum fitness respectively. If Fmax = Fave , then Pmr = Pm. An example ofthe one-point operator is shown in Figure 6.

STEP 6 Final Decision

The above procedures repeat itself until final generation is achieved.

4. Simulation Results

4.1. Setup of Fitness Function

The objective of this article is the maintenance of reliability, reducing loss of loadand dump power. Hence, these variables are used within the fitness function.

4.1.1. Fitness Function for Setup Point. Equation (7) is used as a fitness functionto determine optimal setup point.

Ffit =M∑

m=1

{ALmDP (m)− (1− ALm

)LOL(m)} (7)

where ALmis the reliability at load point m, DP (m) is the demand power at load

point m, LOL(m) is the total loss of load at load point m, and M is the totalnumber of load points in the system. Reliability is the probability of possible powersupply and the term ALmDP (m) is expected power supply. Subtracting reliabilityfrom equation (1), we get loss of load probability. The term, (1− ALm)LOL(m) isthe expected loss of load.

4.1.2. Fitness Function for Capacity. Equation (8) is fitness function to determinethe capacity

Ffit =M∑

m=1

{ESP (m)− αELOL(m)} − βD − γPT (8)

where ESP (m) is the expected supply power, ELOL(m) is the expected loss ofload, D is the dump power, PT is the margin of transmission capacity, and α,β, γ are weight factors. D and PT represent the upper bound constraint of thecapacity.

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Determination of Power Facilities 381

4.2. Individual Optimization

At first, we determine the optimal locations by using equation (7). The optimallocations are determined by varying both the transmission and generation capacityfrom 200 MW to 400 MW by a step of 50 MW. The total numbers of runs are 25for each of transmission capacity and generation capacity. For each run, two setuppoints, which indicate the location of generator or transmission line, are determinedas the optimal setup points. Figures 7 and 8 show the number of times the optimalsetup points for each setup point are selected. In Figure 7, the numbers on horizontalaxis corresponds to the load points in Figure 2. For example, a number 3 in Figure 7corresponds to a load point L7 in Figure 2. In Figure 8, the numbers on horizontalaxis corresponds to the transmission lines in Figure 2 as is. From Figures 7 and 2,since the load points L3 and L7 are selected as the optimal setup points among allthe setup points, the new generators are set up in the load points L3 and L7. FromFigures 8 and 2, since the transmission lines T5 and T7 are selected as the optimalsetup points among all the setup points, the new transmission lines are set up intransmission lines T5 and T7.

After performing the optimal point selection, we determine the optimal capacityof these facilities using equation (8) subject to the constraints given in Table 1. Weset α = 9, β = 0.0006, γ = 0.0001. Figure 9 shows the optimal capacity at loadfactor 1.4. In Figure 9a, G.b and T.a are aligned to the same direction, which startfrom 250 MW at 0 generation and then go down to 200 MW at 50 generationand finally converge to 200 MW at 400 generation. G.a starts from 200 MW at0 generation, and then up to 250 MW at 50 generation, finally converges to 250 MWat 400 generation. T.b always maintains 200 MW. That means the capacity ofgenerators G.a and G.b are 250 MW and 200 MW, respectively, and that of bothcapacity of transmission lines T.a and T.b are 200 MW. Figure 10 shows optimal

Figure 7. Number of times selected as optimal set up point (generator).

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Figure 8. Number of times selected as optimal set up point (transmission line).

capacity at load factor 1.6. From Figure 10a, the capacity of generators G.a andG.b are 400 MW and 250 MW, respectively, and the capacity of transmission linesT.a and T.b are 450 MW and 200 MW, respectively.

4.3. Optimization Simultaneously

In the previous section, we determined the optimal capacity after determining theoptimal locations as shown in Figure 11. However, since the optimal location andcapacity are closely related, the optimal location varies with the capacity and viceversa. But this optimization problem is more difficult than the optimal setup pointproblem or optimal capacity problem.

In this article, we propose the determination technique for the optimal locationand capacity at the same time, as shown in Figure 12. Equation (8) is used asthe fitness function to determine the optimal location and capacity. We set α = 9,β = 0.0006, γ = 0.0001 in equation (8), and compare with the dump power andexpected loss of load obtained in Section 4.2.

We determine the optimal location and capacity by equation (8). From Fig-ure 13, the generators G.a and G.b are set up in the load point L3 and L8 whenthe load factor is 1.4 and the corresponding capacities are 150 MW and 300 MW,

Table 1Parameter constraints

Constraint of set up point Constraint of capacity

1 ≤ G.a, G.b ≤ 9 100 MW ≤ G.a, G.b ≤ 550 MW1 ≤ T.a, T.b ≤ 10 100 MW ≤ T.a, T.b ≤ 550 MW

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Determination of Power Facilities 383

(a)

(b)

Figure 9. Optimal capacity at load factor 1.4. (a) Optimal capacity; (b) maximum andaverage fitness.

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(a)

(b)

Figure 10. Optimal capacity at load factor 1.6. (a) Optimal capacity; (b) maximum andaverage fitness.

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Determination of Power Facilities 385

Figure 11. Conventional method to determine the optimal capacity and optimal locationseparately.

Figure 12. Proposed method to determine the optimal capacity and optimal locationsimultaneously.

respectively. New transmission lines T.a and T.b are set up in transmission line T5and T9. The transmission capacities of these new transmission lines are 500 MWand 450 MW, respectively.

From Figure 14, the generators G.a and G.b are set up in the load point L3and power plant G2 when the load factor is 1.6, and these generation capacitiesare 400 MW and 350 MW, respectively. New transmission lines T.a and T.b areset up in the transmission line T3 and T5. Transmission capacities of these newtransmission lines are 300 MW and 500 MW, respectively.

From Figure 15, we see that expected value of loss of load are equal in bothmethods but the dump power can be reduced by 4.5% in comparison with that ofindividual optimization technique in Section 4.2. In Figure 15b, the change in theshape of stairs in case of simultaneous occurrence indicates that the search of GAproceeds successfully.

Figure 16 shows the dump power and expected loss of load when load factorequal to 1.6. There are slight differences in the dump power between these twomethods; however, the loss of load can be reduced to 32.3% by simultaneousoptimization.

5. Conclusions

This article presents a determination of optimal location and capacity of power fa-cilities by using genetic algorithm. Since power system plays a major role in modernsociety, power supply reliability and loss of load in fault are important factors inpower system planning. Large reserves can maintain reliability and decreasing lossof load during faults; however, this reserve increases cost and dump power. More-over, since reliability and loss of load have different dimension, they cannot be eval-uated at the same time. To achieve an optimal configuration of a power system, thenew evaluation method and optimization technique are introduced. Using the pro-posed method, the maintenance of power supply reliability, reducing loss of load anddump power are done favorably in comparison with the other optimization method.

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(a)

(b)

(c)

Figure 13. Load factor at 1.4. (a) Optimal set up points; (b) optimal capacity; and(c) maximum and average fitness.

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Determination of Power Facilities 387

(a)

(b)

(c)

Figure 14. Load factor at 1.6. (a) Optimal set up points; (b) optimal capacity; and(c) maximum and average fitness.

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(a)

(b)

Figure 15. Load factor at 1.4. (a) Dump power; (b) expected value of loss of load.

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Determination of Power Facilities 389

(a)

(b)

Figure 16. Load factor at 1.6. (a) Dump power; (b) expected value of loss of load.

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References

[1] T. Yalcinoz and M. J. Short, “Neural networks approach for solving economic dis-patch problem with transmission capacity constraints,” IEEE Transactions on PowerSystems, vol. 13, no. 2, pp. 307–313, 1998.

[2] D. C. Walters and G. B. Sheble, “Genetic algorithms solution of economic dispatchwith valve point boding,” IEEE Transactions on Power Systems, vol. 8, no. 3, pp. 1325–1332, 1993.

[3] I. J. Ramirez-Rosado and J. L. Bernal-Agustin, “Genetic algorithms applied to thedesign of large power distribution systems,” IEEE Transactions on Power Systems,vol. 13, no. 2, pp. 696–703, 1998.

[4] R. Billinton and R. N. Allan, Reliability Evaluation of Engineering Systems, SecondEdition, New York: Plenum Publishing Co., 1992.

[5] R. Billinton and R. N. Allan, Reliability Evaluation of Power Systems, Second Edition,New York: Plenum Publishing Co., 1996.

[6] S. A. Kazarlis, A. G. Bakirtzis, and V. Petridis, “A genetic algorithm solution tothe unit commitment problem,” IEEE Transactions on Power Systems, vol. 11, no. 1,pp. 83–92, 1996.


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