# Genetic Algorithm approach to find excitation capacitances for 3- phase smseig operating single phase loads

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1 Genetic Algorithm approach to find excitation capacitances for 3- phase smseig operating single phase loads Authors & Affiliation: V.Ravi Kiran, V.Manoj and P.Praveen Kumar Asst. Professor, EEE Dept GMRIT, Rajam Srikakulam, India Correspondence To: ABSTRACT This paper is to investigate an excitation scheme for a three-phase SEIG supplies isolated single-phase loads. It will be shown that by arranging the stator winding of the induction generator and appropriate excitation capacitances in the form of the Smith connection, good phase balance in the generator can be achieved, resulting in a high efficiency and large power output. In addition to providing the reactive power for selfexcitation, the capacitances also act as phase balancers. Performance analysis is based on the method with the aid of a phasor diagram, the conditions for achieving perfect phase balance are deduced and a method to compute the capacitances required is developed. V.Manoj Key Words: Smith Connected Self Excited Induction Generator (SMSEIG), Genetic Algorithm (GA), Phase Balancing The Authors. Published under Caribbean Journal of Science and Technology ISSN

5 Fig3.3 Phasor diagram showing detailed angular relationships. Consider the phasor diagram in Fig. 3.2 and 3.3, drawn for the special case for perfect phase balance. The current I 1 leads V 1 (or V AB ) by π/2 rad and hence lags V B by 2π/3 rad. The voltage V 2 (which is equal to V AB -V C ), is equal to 2V A. The capacitor current I 2 leads V 2 by π/2 rad and hence it lags V B by 5π/6 rad. For generator impedance angles between 2π/3 rad and 5π/6 rad, the phase current I B can be synthesized with the required magnitude and phase angle to give phase balance, by using suitable values of C 1 and C 2. Under perfect phase balance conditions, the phase currents of the induction generator sum must equal to zero. This requires that the currents I 2 and I 3 to be equal, implying that C 3 must be equal to twice of C 2. With balanced currents flowing in the stator phases, a perfect rotating magnetic field is created. The air gap voltages per phase, and hence the phase voltages, will also be balanced. The generator operates as if it were supplying a balanced three-phase load, hence the efficiency is the same as that obtained when the generator operates on a balanced three-phase grid. IV. DETERMINATION OF SEQUENCE IMPEDANCES The positive sequence equivalent circuit of the induction machine is given in Fig. 4.1 below where reactances correspond to the base frequency (50Hz) and X m is the saturated value corresponding to the forward revolving air gap flux. The negative sequence circuits would have the term (a-b) of Fig. 4.1 replaced by (a+b). For a given machine, the positive and negative sequence admittances Yp and Yn are calculated using the corresponding equivalent circuits as shown in the Figs. 4.1 and 4.2. Fig 4.1 Equivalent circuit for positive sequence impedance. 109

6 Fig 4.2 Equivalent circuit for negative sequence impedance. Rp = real (Zp), Xp = imag (Zp), Rn = real (Zn), Xn = imag (Zn). The degree of phase imbalance is conveniently described by the voltage unbalance factor (VUF) which is the ratio of the negative- sequence voltage to the positive-sequence voltage. A. Determination of machine variables impedance. For successful self- Fig. 4.3 is a passive circuit consisting of the load impedance Z L and the equivalent Z in excitation.of the SMSEIG, the sum of these two impedances must be equal [2], [10]. Fig 4.3 Simplified circuit of SMSEIG for determination of machine variables Z L = a R L +jx L (4.1) Z L + Z in =0 (4.2) It should be noted that for a given per-unit speed and a given set of excitation capacitances, is a highly nonlinear function of and, implying that (4.2) is a complex equation in these two variables. To avoid the lengthy mathematical manipulations involved, the solution of (4.2) is formulated as the following optimization problem. Minimize(a,X m ) = R 2 2 ( L R ) in ) (X L Xin (4.3) a Subject to constrains 0< a< b 0<X m <X mu Where X mu is the saturated value of the magnetizing reactance. It is easy to show that (4.2) is satisfied when the scalar impedance function Z(a,Xm) given by (4.3) assumes a minimum value of zero. This paper presents the genetic algorithm based optimization method to solve the above minimization function.after a and X m have been determined, the positive-sequence air-gap E 1 voltage can be obtained from the magnetization curve. The positivesequence voltage V P is next computed from the equivalent circuit. 110

7 B. Minimization Problem For starting the minimization process of the objective function, an estimate for the ranges of the unknown variables is needed. In many optimization problems even to obtain such estimates suitably, certain trials may be required. However in the present problem, it is easier to give the range for the unknown variables a and X m, because in well-designed self-excited induction generators, it is known that the slip {(a-b)/a} is small and operation of the machine is only in the saturated region of the magnetization characteristics. So, the range for a can be given as 0.8 to times the value of b and for X m as 25% to 100% of critical magnetizing reactance, X mc. In the next Section on the predetermination of performance of a generator chosen as an example, the objective function being minimized with respect to the number of generations and finally reaching zero value is shown. Fig 4.4 flowchart to the algorithm followed to solve GA based minimixation function. V. CONDITIONS FOR PERFECT PHASE BALANCE It is of interest to investigate the values of susceptances that will result in balanced operation in the three-phase induction machine. The negative-sequence voltage must vanish for the three phase, SEIG to operate with perfect phase balance. (1-a 2 )Y 1 +2Y 2 -a 2 Y p =0 (5.1) Assuming that Y1 and Y2 to be pure capacitive admittances, equation may be rewritten as two simultaneous algebraic equations Y 1 + Y 2 = - Y 1 + Y 2 = - Y P cosφ p 3 Y P sinφ p 3 Where φ p is the positive sequence impedance of the induction generator. 111

9 Fig 5.1 Flow chart for the iterative process to find the Excitation Capacitances for Perfect Phase Balance. VI. Simulation Results No load and blocked rotor tests are conducted on the machine to find out the equivalent parameter of the machine. Fig.6.1 Induction machine equivalent circuit parameters For load resistance R L =55Ω and per unit speed b=0.9 We obtain per unit frequency a= Magnetizing reactance X m = Ω Excitation capacitances c1=39.08uf c2=19.54uf c3=39.09uf positive sequence admittance Y p = negative sequence admittance Y n = For load resistance R L =55Ω and per unit speed b=

10 We obtain per unit frequency a= Magnetizing reactance X m = Ω Excitation capacitances c1= uf c2= uf c3= uf positive sequence admittance Y p = negative sequence admittance Y n = Fig 6.2 variation of per unit frequency with load admittance Fig 6.3 variation of c 1 with rotor per unit speed under balanced condition Fig 6.4 variation of capacitance with load admittance 114

11 CONCLUSION This paper has presented the principle and analysis of a novel excitation scheme for a stand-alone three-phase induction generator that supplies single-phase loads, viz. the SMSEIG. Adopting the Smith connection with appropriate values of excitation capacitances, balanced operation of the three-phase machine can be achieved. The steady-state performance of the SMSEIG is analyzed using the method of symmetrical components in association with an optimization procedure. A method to determine the capacitances to give perfect phase balance is also presented. Although only results of the resistive load case have been reported, the analysis set forth can readily be applied to different load power factor conditions. The SMSEIG has the advantages of low cost, high efficiency, and large power output and, as such, is an economical choice when developing autonomous single-phase power systems in remote regions. The effect of capacitances on the generator performance has also been investigated. GA based MATLAB program had used to solve the minimization function of two variables and then some equations are solved on base of Newton Raphson algorithm finally to attain the values of excitation capacitances to achieve perfect phase balance for single phasing operation. REFERENCES 1. B. Singh and L. B. Shilpkar, Steady-state analysis of single-phase self excited induction generator, in Proc. Inst. Elect. Eng., Elect. Power Applicat., vol. 146, 1999, pp S. S. Murthy, O. P. Malik, and A. K. Tandon, Analysis of self-excited induction generators, in Proc. Inst. Elect. Eng., vol. 129, Nov. 1982, pp G. Raina and O. P. Malik, Wind energy conversion using a self-excited induction generator, IEEE Trans. Power App. Syst., vol. PAS-102, pp , Dec M. O. Durham and R. Ramakumar, Power system balancers for an induction generator, IEEE Trans. Ind. Applicat., vol. IA-23, pp , Nov./Dec T. F. Chan, Performance analysis of a three-phase induction generator connected to a single-phase power system, IEEE Trans. Energy Conv., vol. 13, pp , Sept J. B. Ekanayake, Induction generators for small hydro schemes, Power Eng. J., vol. 16, no. 2, pp , Apr Chan, T.F.; Lai, L.L."Single-phase operation of a three-phase induction motor with the Smith connection," Power Engineering Society Summer Meeting, IEEE, vol.4, no., pp vol. 4, O. J. M. Smith, Three-phase induction generator for single-phase line, IEEE Trans. Energy Conv., vol. EC-2, pp , Sept O.J.M. Smith, "Large low-cost single-phase SEMIHEX TM motors, " IEEE Transactions on Energy Conversion, Vol. 14, No. 4, pp , December Steady-state analysis and performance of a stand-alone three phase induction generator with asymmetrically connected 115

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