Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
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A squirrel cage induction generator (SCIG) offers many advantages for wind energy conversion systems but suffers from poor voltage regulation under varying operating conditions. The value of excitation capacitance (C exct ) is very crucial for the selfexcitation and voltage build-up as well as voltage regulation in SCIG. Precise calculation of the value of C exct is, therefore, of considerable practical importance. Most of the existing calculation methods make use of the steady-state model of the SCIG in conjunction with some numerical iterative method to determine the minimum value of C exct . But this results in over estimation, leading to poor transient dynamics. This paper presents a novel method, which can precisely calculate the value of C exct by taking into account the behavior of the magnetizing inductance during saturation. Interval analysis has been used to solve the equations. In the proposed method, a range of magnetizing inductance values in the saturation region are included in the calculation of C exct , required for the self-excitation of a 3-驴 induction generator. Mathematical analysis to derive the basic equation and application of interval method is presented. The method also yields the magnetizing inductance value in the saturation region which corresponds to an optimum C exct(min) value. The proposed method is experimentally tested for a 1.1 kW induction generator and has shown improved results.