Frequency Domain Parameter Estimation of a Synchronous Generator Using Bi-objective Genetic Algorithms

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1 Proceeings of the 7th WSEAS International Conference on Simulation, Moelling an Optimization, Beijing, China, September 15-17, Frequenc Domain Parameter Estimation of a Snchronous Generator Using Bi-objective Genetic Algorithms P. PAO-A-OR *, T. KUWORAWANICHPONG, an A. OONSIVIAI Power an Energ Research Unit, School of Electrical Engineering Institute of Engineering, Suranaree Universit of Technolog 111 Universit Avenue, Muang District, Nakhon Ratchasima, THAIAND * corresponing author: paej@sut.ac.th Abstract: - This paper presents a wa to obtain parameters of a irect-axis equivalent circuit of a snchronous generator from frequenc response ata using bi-objective genetic algorithms. The genetic algorithms is capable of fining a global minimum within a given search interval. The sum square error of magnitue an phase of the -axis equivalent circuit transfer function to formulate a bi-objective optimization problem is minimize to best fit the measure ata extracte from the frequenc response test of the machine. As a result, exploitation of the bi-objective optimization base on Genetic Algorithms gives ver goo results than those of using either the magnitue or the phase as a single objective. Ke-Wors: - Parameter Estimation, Genetic Algorithms, Bi-objective Optimization, Snchronous Generator, Frequenc Response 1 Introuction To ate uner eregulate power market environment electric utilit has become increasingl much more complex that the past. Apart from economic view point, stabilit problems are equall important to operate electric power sstem in real time. To hanle an stabilit-relate problems accurate parameter estimation of a snchronous generator is concerne in both irect an quarature moels. Several kins of tests are use to etermine the irect-axis equivalent circuit parameters. These inclue on-line tests [1], stanstill frequenc response (SSFR) [2,3,4] an time omain [5] testing. From literature, the frequenc response test has become one of the most popular approaches to obtain the snchronous transfer function parameters. With this metho, the problem is reuce to fin location of suitable poles an zeros of the machine transfer function. To complete this task, an efficient intelligent search metho can be emploe. Genetic algorithm (GA) is a searching metho base on two natural processes: selections an genetics. It is consiere as an evolutionar computation which has been prove to be a ver powerful optimization metho in an artificial intelligence area of interest. There have been various researches an applications of GA covering in most fiels of stuies. Therefore, it woul be goo for solving this problem base on the Genetic Algorithms. This paper illustrates the wa to appl the Genetic Algorithms to solve a bi-objective optimization problem in orer to estimate a -axis transfer function of a snchronous generator, which is explaine in etail in section 2. Section 3 gives a brief of the step-b-step intelligent parameter estimation base on the Genetic Algorithms. Section 4 shows test results an iscussion. The last section is the conclusion. 2 Direct-Axis Moel Structure of a Snchronous Machine The irect-axis of a snchronous machine inclues two terminal ports. These correspon to the irectaxis equivalent armature wining an the fiel wining. The complete irect-axis equivalent circuit which secon orer moel referre to the stator is shown in Fig.1 [6] Fig. 1. Direct-axis equivalent = armature leakage inuctance l = stator to rotor mutual inuctance a

2 Proceeings of the 7th WSEAS International Conference on Simulation, Moelling an Optimization, Beijing, China, September 15-17, f 1 = mutual inuctance between fiel wining an amper wining 1 = amper wining leakage inuctance R 1 = amper wining resistance = fiel wining leakage inuctance f R f = fiel wining resistance The irect-axis specificall operational inuctance (OI) transfer function (s) of snchronous machine has the form given below [7,8]. It is the aplace transform of the ratio of the irect-axis armature flux linkages to the irect-axis current, with the fiel wining short-circuite. (1+ T1s)(1+ T2s) ( s) = (1) (1+ T s)(1+ T s) 3 (s) is often expresse in terms of transient an subtransient quantities use [9], 1+ τ o s 1 τ o s + ( s) = (2) 4 ( 1+ τ s)( 1+ τ s) = snchronous inuctance = transient inuctance = subtransient inuctance τ = transient open-circuit time constant (secs) o τ = subtransient open-circuit time constant (secs) o 3 Bi-objective Intelligent Parameter Estimation Base on Genetic Algorithms There exist man ifferent approaches to ientif snchronous generator s parameters. For the GA is not new anmore. There exist a hunre of works emploing GA technique. GA is a stochastic search technique that leas a population of solutions using the principles of genetic evolution an natural selection, calle genetic operators e.g. crossover, mutation, etc. With successive upating new generation, a set of upate solution grauall converges to the real solution. Because the Genetic Algorithms is ver popular an wiel use in most research areas where an intelligent search technique o o is applie, it can be summarize briefl as follows [10,11]. 1. Initialization: Ranoml initialize populations or chromosomes an set them as a search space an then evaluate their corresponing fitness value via the objective function. 2. Evolution: Appl the genetic operators to create an offspring population as the sequence below, a. Selection: Form a set of mating pool with the same number of the population size b using a ranom proceure, e.g. the roulette-wheel or tournament schemes, with the assumption that each chromosome has a ifferent chance. The higher the fitness value, the higher the chance or probabilit. b. Crossover: This operation is applie to a subset of the mating pool b taking a pair of chromosomes calle the parents. The parents will iel a pair of offspring chromosomes. This operation involves exchanging sub-string of the parent chromosomes. It is performe b choosing a ranom position in the string an then swapping either the left or right substrings of this position (one-point crossover) with its chromosome mate. c. Mutation: For the chromosome to be mutate, the values of a few positions in the string are ranoml moifie. To prevent complete loss of the genetic information carrie through the selection an crossover processes, mutation (if use at all) is limite to tpicall 2.5% of the population. 3. Fitness Test: Evaluate the fitness value for the generate offspring population. 4. Convergence Check: Check for violation of all termination criteria. If not satisfie, repeat the evolution process. In this paper, the Genetic Algorithms is selecte to buil up an algorithm to ientif such parameters. Briefl, the proceure to perform the propose ientification is escribe as follows. First, frequenc responses of magnitue an phase base on SSFR test ata of a snchronous generator are measure. Secon, the Genetic Algorithms is emploe to generate a set of initial ranom parameters. With the searching process, the parameters are ajuste to give response best fitting close to the test ata. To perform the searching properl, a bi-objective function is the ke. In this paper, the sum of square errors (SSE) [12] is use as shown in the following equation. SSE 2 N measure simulate = (3) i= 1 measure, max

3 Proceeings of the 7th WSEAS International Conference on Simulation, Moelling an Optimization, Beijing, China, September 15-17, with the bi-objective function f an bi-obj = ( W ) SSE + ( W ) SSE (4) mag ( mag phase = mag phase phase W ) + ( W ) 1.0 (5) f is the bi-objective function bi-obj W is the weighte SSE of magnitue or phase on frequenc response characteristics measure is the measure magnitue or phase on frequenc response characteristics simulate is the simulate magnitue or phase on frequenc response characteristics Table 1. Comparison among obtaine parameters Parameters Methos Experimental mag1.00-phase0.00 mag0.75-phase0.25 mag0.50-phase0.50 mag0.25-phase0.75 mag0.00-phase0.10 τ o (secs) τ o (secs) Results an Discussion The followings escribe parameter setting for the Genetic Algorithms use in this paper. GA: Number of population = 50 Crossover probabilit = 70 % Mutation probabilit = 1.4 % Variable search spaces: [0.50, 4.00] [0.05, 1.00] [0.01, 0.50] τ [1.00, 8.00] o τ [0.01, 0.10] o Fig. 2. Frequenc response characteristics of the experiment an the Genetic Algorithms with biobjective b weighte SSE (magnitue=1.00 an phase=0.00) Termination criteria: Maximum error allowance = 0.01 (SSE) Maximum number of iteration = 1500 Table 1 also shows the parameters of turbine generator, 555 MVA/24 kv/60 Hz/0.9 pf [13] obtaine b using the experimental an the Genetic Algorithms with bi-objective b various weighte SSE. The values appeare in this table is the best of 30 trials. Comparing with the experimental results an the effectiveness an the accurac of each Genetic Algorithms with bi-objective b weighte SSE are reveale as shown in Fig.2 - Fig.6. Fig. 3. Frequenc response characteristics of the experiment an the Genetic Algorithms with biobjective b weighte SSE (magnitue=0.75 an phase=0.25)

4 Proceeings of the 7th WSEAS International Conference on Simulation, Moelling an Optimization, Beijing, China, September 15-17, Fig. 4. Frequenc response characteristics of the experiment an the Genetic Algorithms with biobjective b weighte SSE (magnitue=0.50 an phase=0.50) Fig. 6. Frequenc response characteristics of the experiment an the Genetic Algorithms with biobjective b weighte SSE (magnitue=0.00 an phase=1.00) Fig. 5. Frequenc response characteristics of the experiment an the Genetic Algorithms with biobjective b weighte SSE (magnitue=0.25 an phase=0.75) As can be seen, the results simulate b using the parameters obtaine from the bi-objective Genetic Algorithms are satisfactor an ver much better than those estimate b using a single objective function because in frequenc omain magnitue an phase are equall essential characteristics that cannot be ignore. 5 Conclusion This paper illustrates the bi-objective genetic algorithms to estimate parameters of a irect-axis equivalent circuit transfer function of a snchronous generator. As a result, magnitue an phase of its frequenc response characteristics simulate from the propose metho look goo an rather fit to those obtaine from the test ata. However, to utilize the bi-objective optimization is crucial ue to the ifficult of selecting weighte factors. It is problem-epenent an sstem esigners must experience how to choose the weighte factors themselves in orer to gain most avantages from the parameter estimation propose in this paper. References: [1] H. Tsai, A. Kehani, J. Demcko, R.G. Farmer, On-line snchronous machine parameter estimation from small isturbance operating ata, IEEE Transactions on Energ Conversion, Vol.10, No.1, 1995, pp [2] IEEE Power Engineering Societ, IEEE St 115A-1987, IEEE Stanar Proceures for obtaining snchronous machine parameters b stanstill frequenc response testing, The Institute of Electrical an Electronics Engineers, Inc., [3] R. Escarela-Perez, T. Niewierowicz, E. Campero-ittlewoo, Snchronous machine parameters from frequenc-response finite-

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