Abstract: This paper concerns the optimal location of Flexible AC Transmission Systems (FACTS) in multi- machine power system using Genetic Algorithm.
H.O. Bansal et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 1556-1560
Optimal Location of FACT Devices to Control Reactive Power H O Bansal*, H P Agrawal$, S Tiwana&, A R Singal& And L Shrivastava# Abstract: This paper concerns the optimal location of Flexible AC Transmission Systems (FACTS) in multimachine power system using Genetic Algorithm. The objective is to obtain the bus voltages of the system within healthy limits. TCSC is the FACT device chosen for the proposed algorithm. The location of FACT devices and their rated values are optimized simultaneously. Simulations are done on a power system for various number of FACT devices. Results validate that the proposed algorithm is an effective and practical method for the choice and allocation of FACT devices in large and complex power systems. Key words: FACTS, Genetic Algorithm, TCSC, fitness function, Multi Machine 1.
Introduction
In recent years with the deregulation of the electricity market, the traditional concepts and practices of power systems have been changed. With the increase in demand to supply ratio, improvements in the supply chain is tremendously being done. Until a few years ago, the only means of carrying out this function were electromechanical devices such as switched inductors or capacitors banks and phase-shifting transformers. However, specific problems related to these devices make them not very efficient in some situations. They are not only relatively slow, but they also cannot be switched frequently, because they tend to wear out quickly. This led to the improvement in semiconductor technology. The concept of FACTS was first discussed by Hingorani, N.G. in 1988. FACT devices help in better utilization of the existing power system by increasing its capacity [1] – [4]. FACT device is defined by the IEEE as "a power electronic based system and other static equipment that provide control of one or more AC transmission system parameters to enhance controllability and increase power transfer capability”. FACTS technology opens up new opportunities for controlling power and enhancing the usable capacity of present, as well as new and upgraded lines. The possibility that current through a line can be controlled at a reasonable cost enables a large potential of increasing the capacity of existing lines with larger conductors, and use one of them to enable corresponding power to flow through such lines under normal and contingency conditions. The FACTS technology is not a single high-power Controller, but rather a collection of controllers, which can be applied individually or in coordination with others to control one or more of the interrupted system parameters mentioned above [2], [5]. The parameter and variables of the transmission line, i.e. line impedance, terminal voltages, and voltage angle can be controlled by FACT devices in a fast and effective way. The benefit brought about FACT includes improvement of system dynamic behavior and thus enhancement of system reliability. However, their main function is to control power flows. It can increase the system loadability and enable a line to carry power close to its thermal limits. FACT technology also lends itself to extending usable transmission limits in a step-by-step manner with incremental investment as and when required. Different types of devices have been developed and there is various ways to class them: i) the technology of the used semiconductor, ii) the possible benefits of the controllers, and iii) the type of compensation. According to the last classification, we may distinguish three categories of FACT controllers: • Series controllers • Shunt controllers • Combined series-shunt controllers Different kinds of FACT devices and their different locations have different advantages. In realizing the proposed objective, the suitable types of FACT devices, their location and their rated values must be determined simultaneously. This combinatorial analysis problem is solved using Genetic Algorithm. 2.
Material and Methods
To determine the optimum location of FACT device on a particular bus, we have taken various (variable) bus power systems. The optimum location is determined using Genetic Algorithm. The propose scheme is discussed below.
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H.O. Bansal et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 1556-1560 2.1
Choice of FACT device
There are various FACT controllers such as SVC, TCSC, STATCOM, SSSC and UPFC used to enhance power system performance [2], [5], [6]. In this paper, TCSC (Thyristor Controlled Series Capacitor) is used as a FACT device. Its block diagram is shown in figure 1.
j
i ZLine XTCSC
ZTCSC = X min X max Figure 1 Block Diagram of TCSC
TCSC can change the impedance of the transmission line. The power flow Pij through the transmission line i-j is a function of line impedance Xij, the voltage magnitude Vj , Vj and the phase angle between the sending and receiving end voltages as given below ViV j (1) Pij ( i - j ) X ij The above-mentioned TCSC is used to control the power flow by changing parameters of power systems so that the power flow can be optimized. 2.2
Mathematical Modeling:
The TCSC can serve as the capacitive or inductive compensation respectively by modifying the reactance of the transmission line. The rated value of TCSC is a function of the reactance of the transmission line where the TCSC is located. (2) Xij = XLine + XTCSC where XTCSC = a*XLine XLine is the reactance of the transmission line and “a” is the coefficient which represents the compensation degree of TCSC. To avoid overcompensation, the working range of the TCSC is between –0.7 XLine and 0.2 XLine. [6], [7]. 2.3 Genetic Algorithm (GA) To solve this optimization problem one can use any of the heuristic methods available in literature. Here we have chosen GA for the same. GA is a search technique used in computing to find exact or approximate solutions to optimization and search problems [8]. The evolution usually starts from a population of randomly generated individuals and happens in generations. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are stochastically selected from the current population (based on their fitness), and modified to form a new population. To evaluate the fitness, a fitness function is defined. As the reactive power is going to affect the voltage profile, in this paper voltage profile is selected as a fitness function. In this case it is found by the function shown in figure 2, which uses the voltage values in different branches of the power system.
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Function Vtg
H.O. Bansal et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 1556-1560
Exp [ λVtg (abs(1 - VL ) - 0.05)]
Voltage Level VL (p.u) Figure 2 The Fitness Function
We obtain the voltage values in different branches of the bus system and multiply these values by Vtg to get the fitness function of the system. The new population is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population. After initialize the population we had to implement three processes namely, reproduction, crossover and mutation. Reproduction is the process through which fit individuals are selected from the already existing individuals for creating the next set of individuals. The individual is represented by the following diagram. .3 6
.1 1
Figure 3
.3 8
.2 5
.4 10
Particular Individual
An individual is the FACT device. The “location” refers to the branch in which the FACT device (TCSC) is located and the corresponding value shows the value of reactance that the particular TCSC adds to the branch. Values can be converted to Xline added by using the following equation: (3) Xline=value*0.9 - 0.7 Crossover is the process of creating genetic diversity in the system by exchanging parts of different individuals. A two-point crossover is applied and the probability of the crossover is selected as 0.95. First, two crossing points are selected uniformly at random along the individuals. Elements outside these two points are kept to be part of the offspring. Then, from the first position of crossover to the second one, elements of the three strings of both parents are exchanged [8]. When mutation occurs on the first string, the one related to the location, a new line among the set of branches having no FACT is randomly drawn. In the case of mutation on the other string, a new value is drawn among the set of possible ones. The above-mentioned operations of selection, crossover and mutation are repeated until the best individual is found according to the flowchart shown in figure 4. 2.4
Simulation Implementation
The implementation is done in MATPOWER 3.2 [9]. We have modified and added various files in it for our requirement. A new file for creating the individual which can have the number of elements as defined by user is added. The ‘runopf’ is called and the individual created, is used to modify the value of impedances in the bus that implements a TCSC which also operates by changing the impedance values. These values are added by using the ‘value_add’ function. The main function which implements the flowchart we have shown above is ‘geneal.m’. It takes the input from the user, namely, number of individuals, tolerance1, tolerance2 and the size of each individual. Tolerance1 is concerned with reproduction. Fitness of the individual is evaluated by ‘fitness.m’. The best individual is selected if the fitness value lies within the tolerance 2. If no individual fits the desired tolerance then we go on to the process of reproduction, crossover and mutation. Only those individuals with fitness value within the limits of tolerance1 are selected for reproduction. Now, with these individuals we do the crossover
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H.O. Bansal et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 1556-1560 which is implemented through the function ‘crossover.m’. After the crossover generates new individuals we have the mutation implemented by ‘mutation.m’. For this function we pass the probability which tells us how many mutations are to be done. For example if we have number of individuals as 20 and probability as 0.05 then 0.05*20=1 individuals will be undergo mutations. Here also we have taken care of the fact that you cannot have more than one FACT device in a branch. Once an individual is selected at random then we randomly change on the branch number values and also the ‘value’ specified for a particular branch. After the mutation is over we run the ‘runopf’ again for each of the new individuals and we check their fitness values again. If the fitness value lies within the tolerance 2 specified then we are done and we have found the wanted individual. Otherwise, the whole process is repeated. One can put a limit on the number of iterations to be performed and if the number of iterations specified are over then the best individual found upto that movement is the solution.
Start Population Initialization Individual’s fitness Evaluation Reproduction, Crossover, Mutation
Achieved
No
Optimality? Yes Print Best Individual and its Fitness Figure 4
Flow Chart of GA Optimization
3. Results The 9-bus system initially had a fitness function value of 0.9816 (ideal value is 1) which is improved to the value 0.9971 after applying genetic algorithm by inserting 2 FACT in the system. This value does not improve by increasing the number of FACT devices. The 14-bus system had a fitness value of 0.9985 (close to 1) which gets improved to 0.9993 by inserting 2 FACT in the system. This value also does not improve by increasing the number of FACT. The 30-bus system has a fitness function of 0.9959 which is improved to 0.9970 by using 2 FACT controllers and this value improves to 1 by using 3 FACT controllers. This is also observed that the value of lambda () is 0.05 for optimum results. 4. Conclusion In this paper, Genetic algorithm is proposed for the allocation of FACT devices. TCSC is used for this purpose and simulations are carried out in MATPOWER 3.2. Simulation results prove the effectiveness of the genetic algorithm in keeping the bus voltages within specified limits. Furthermore, the locations of the FACT devices and their rated values are optimized simultaneously. Also, the fitness value cannot be improved beyond a point by increasing the number of FACT being inserted into the system. The proposed algorithm is an effective and practical method for the optimum allocation of FACT devices in complex power systems.
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H.O. Bansal et al. / International Journal of Engineering Science and Technology Vol. 2(6), 2010, 1556-1560 5. References 1. 2. 3. 4. 5. 6. 7. 8. 9.
Hingorani, N. G. and Gyugyi, L., Understanding FACTS, Concepts and Technology of Flexible AC Transmission Systems, IEEE Press,2000, ISBN0-7803-3455-8. FACTS Application Task Force Applications, FACTS Applications, IEEE Power Engineering Society, 1996, pp. 1.1–4.9. Galiana, F. D., Almeida, K., Toussaint, M., Griffin, J., Atanackovic, D., Ooi B.T, McGillis, D.T., Assessment and control of the impact of FACT devices on power system performance, IEEE Transaction on Power Systems, Vol. 11, No. 4,1996, pp.1931-1936. Song, Y. H., and Johns, A. T. , Flexible AC Transmission Systems (FACTS), IEE Press, London, 1999, ISBN 0-85296-771-3. Canizares C. A. and Faur Z. T., Analysis of SVC and TCSC Controllers in Voltage Collapse, IEEE Transactions on Power Systems, Vol. 14, No. 1, 1999, pp. 158–165. Gerbex, S., Cherkaoui, R. and Germond, A. J., Optimal Location Of Multi-Type FACTS Devices In A Power System By Means Of Genetic Algorithms, IEEE Transactions on Power Systems, Vol. 16, No.3, 2001, pp. 537-544. Lie, T. T., and Deng, W., Optimal Flexible AC Transmission Systems (FACTS) Devices Allocation, International Journal of Electrical Power & Energy Systems, Vol. 19, No. 2, 1997, pp. 125-134. Goldberg, D. E., Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley Publishing Company, Inc, 1989. Zimmerman, R. D. , Murillo-Sánchez, C. E., and Thomas, R. J., MATTPOWER's Extensible Optimal Power Flow Architecture, IEEE Power and Energy Society General Meeting, July 26-30, 2009, pp. 1-7.
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