ТЕОРІЯ АВТОМАТИЗОВАНОГО ЕЛЕКТРОПРИВОДА Електромеханічні і енергозберігаючі системи. Випуск 3/2012 (19) 48 UDC 621.313.3 CRITICAL LOADS OF INDUCTION GENERATORS WITH SERIES SELF-EXCITATION O. Kiselychnyk, M. Pushkar National Technical University of Ukraine “Kiev Polytechnic Institute” рrosp. Peremohy, 37, Kiev, 03056, Ukraine. E-mail: koi.fea.kpi@gmail.com, pushkar.mykola@gmail.com M. Bodson University of Utah 50 South Central Camp. Dr. Rm. 3280, Salt Lake City, UT 84112-9206, USA. E-mail: bodson@eng.utah.edu The paper develops analytic conditions for series-connected self-excitated induction generators, based on the results obtained for shunt self-excitation. Formulas for critical loads of the generator with series self-excitation are obtained as a function of capacitance and angular frequency. Features of the series self-excitation boundaries compared to the boundaries for the shunt case are shown in plots for computed and experimental data. Computed three-dimensional plots of critical loads are also presented for both cases. It is found that the critical load as a function of the capacitance and velocity does not exhibit an extremum point under series self-excitation, as opposed to the shunt case. Кey words: induction generator, series self-excitation, critical load, self-excitation boundary. КРИТИЧНІ НАВАНТАЖЕННЯ АСИНХРОННИХ ГЕНЕРАТОРІВ З ПОСЛІДОВНИМ САМОЗБУДЖЕННЯМ О. І. Кіселичник, М. В. Пушкар Національний технічний університет України “Київський політехнічний інститут” просп. Перемоги, 37, Київ, 03056, Україна. E-mail: koi.fea.kpi@gmail.com, pushkar.mykola@gmail.com М. Бодсон Університет Юти 50 South Central Camp. Dr. Rm. 3280, Солт Лейк Сіті, UT 84112-9206, США. E-mail: bodson@eng.utah.edu Представлено аналітичні умови для послідовного самозбудження асинхронних генераторів, отримані на основі результатів для паралельного самозбудження. Виведено формули для розрахунку критичного навантаження генератора з послідовним самозбудженням у функціях ємності та кутової частоти. Показано особливості границь послідовного самозбудження в порівнянні з паралельним. Представлено розрахункові та експериментальні графіки границь самозбудження, а також розрахункові тривимірні графіки критичного навантаження для обох варіантів самозбудження. Виявлено, що при послідовному самозбудженні, на відміну від паралельного, залежність критичного навантаження від ємності та швидкості не має точки екстремуму. Ключові слова: асинхронний генератор, послідовне самозбудження, критичне навантаження, границя само- збудження. PROBLEM STATEMENT. Self-excited induction generators (SEIG) have found applications in renewable energy (wind and hydro). One of the challenges of power generating systems based on SEIG’s is their poor voltage and frequency regulation in the presence of load changes. An approach to improve voltage regulation is to provide reactive power for SEIG excitation not only from shunt (parallel) capacitors, but also from series capacitors [1], [2]. If series capacitors are connected between the load and the shunt capacitors, one talks of a short-shunt confi- guration. When series capacitors are placed between the shunt capacitors and the generator, one talks of a long- shunt configuration. The voltage of series capacitors va- ries with the load current, resulting in lower deviations of the load voltage from a rated value. The model of the SEIG with short or long shunt is nonlinear and of dimension eight. [1] and [2] present results concerning only voltage regulation, leaving open the problem of self-excitation conditions and load lim- its. These issues were addressed in [3]–[8] for the case of shunt excitation, utilizing the fact that the matrix dif- ferential equation of SEIG’s has a special symmetric structure allowing to reduce the order of the system by a factor of 2. The present paper makes a first step towards analysis of long/short shunt configurations by consider- ing the case of pure series self-excitation. Objectives of the paper are to obtain analytic conditions and critical loads for series self-excitation and to study their features compared to shunt self-excitation. EXPERIMENTAL PART AND RESULTS OBTAINED. 1. Self-excitation boundaries of induction generator. Consider a two-phase induction generator with resistive loads connected in parallel with shunt capacitors to the stator windings. The self-excitation boundary of the generator is described by the quartic equation [3], [5] 4 2 1 2 3 0 e e f f f      , (1) where 2 2 1 ( ) 0, S S R M f CL LL L    2 3 ( 1) 0, R L S f L YR    2 2 2 2 2 2 ( ) (2 ) L S S R M S R S R M f YL LL L CRL C LL L      with S S M L L L    , R R M L L L    . The following notation is used: e  is the angular electrical frequency, C is the capacitance, L Y is the admittance of the resistive load, S L  and R L  denote the stator and rotor leakage inductances, S L and R L denote the stator and rotor inductances, and S R is the stator resistance. Fig. 1 shows the general shape of the magnetization inductance M L as a function of the magnitude of the magnetizing current M i [7]. The curve includes an as- cending part rising from 0 M L to MAX L , a flat part at