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Nr 62 Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej Nr 62 Studia i Materiały Nr 28 2008 induction slip-ring motor, losses minimization, efficiency optimization, scalar control, optimal supply voltage Henryk BANACH* METHOD OF SUPPLY VOLTAGE SELECTION FOR POWER LOSSES MINIMIZATION IN AN INDUCTION SLIP-RING MOTOR The minimizing of total losses in a slip-ring induction motor can be achieved by voltage control. For every load exists an optimal value of voltage which reduces the losses. This optimal voltage can be determined by using an analytical method, which was worked out by author. The application of this method requires knowledge of core and mechanical losses, magnetization characteristic, voltage drops on brush contacts, resistances and reactances of motor windings. The investigation of proposed method was made for a small motor with rated data: PN = 0,9 kW and nN =905 rev/min. For this motor two control characteristics Uopt =f(Ts) were prepared; first one through laboratory measurements and second one using the analytical method. The both characteristics made for five selected frequencies 10, 20, 30, 40, 50 Hz are compared in Fig. 1. The comparison shows the close similarity of both characteristics. These results proved usefulness of the proposed analytical method for calculation of optimal voltage. 1. INTRODUCTION The minimization of the total losses in an induction motor at variable load can be achieved by the voltage control. The voltage control of an inverter can be realized by using adequate strategies with different criteria. The most described criteria of search strategies are: minimum of input power or minimum of stator current. These optimal energy strategy can be realized by optimizing controllers which change suitably the output voltage of the inverter, according to the load changes. The main disadvantages of these adaptive strategies are [5]: – difficulty to minimize the input power because the minimum is shallow, __________ * Katedra Maszyn Elektrycznych Wydziału Elektrotechniki i Informatyki, Politechnika Lubelska, ul. Nadbystrzycka 38 A, 20-618 Lublin. 159 – difficulty to find the minimum of the input power while the load and the supply voltage are changing. The major advantage is, that a search controller does not require knowledge of any motor parameters. In consideration of these disadvantages, will be often used a control strategy based on the losses model. This losses model permits to derive an approach for voltage determination for each load. The model uses all expressions which describe losses. Applying the calculus of optimization we can find the optimal value of voltage. Unfortunately the considerations that can be encountered in the literature are made with many simplifications such as [1–5]: – linearization of a magnetization characteristic, – using of an electric torque instead a torque on the shaft, – neglecting of stray losses. The results of calculations for these simplifications were different then in reality. In that case it was necessary to create a precise losses model of induction motor and on base of this model to derive an analytical method for determining of an optimal voltage value for given output power. The analytical method can be worked out for a squirrel-cage motor as well as a slip-ring motor. This article presents the results of prepared method for an induction slip-ring motor of small power. 2. METHOD DESCRIPTION The precise losses model construction was made under following assumptions: – an actual magnetization characteristic is used, – power on the shaft is given, – constant frequency of supply voltage, – sinusoidal supply voltage and motor currents. On base of the losses model can be derived a condition of the total losses minimum for a given output power. This condition could be described as a losses equation: 1 3 3 Rs Rr I r2 ln I r Ub I r ln I r 3Rs I m2 ln I m PFe ln PFe 2 2 where: 3(Rs +Rr)Ir2 – the losses in stator and rotor windings caused by rotor current, Ir – the rotor current referred to stator, Im – the magnetizing current, PFe – the iron losses, ΔUb – the voltage drops on the brushes referred to stator, 3ΔUbIr – the brush contact loss, 3RsIm2 – the loss in stator winding caused by the magnetizing current, (1) 160 ln Ir – the derivative of the natural logarithm of rotor current, ln I m – the derivative of the natural logarithm of magnetizing current, ln PFe – the derivative of the natural logarithm of iron loss. Based on the equation (1), an analytical method for determining of optimal voltage was developed. The derivations of this method are very complicated and need many transformations therefore they are not presented. The algorithm for determining optimal voltage has very complicated form and must be solved numerically. The application of this method requires knowledge of following parameters of an induction slip-ring motor: – iron loss, – magnetization characteristic, – stator and rotor windings resistances, – mechanical loss. It is clear that the application of method requires to make many laboratory studies to determinate those parameters. The accuracy of this method depends mainly on windings resistances determination. The method verification was done on the induction slip-ring motor with ratings: – Typ 2SUDf 100 L-6A – PN = 0,8 kW – UN = 380 V – IN = 3,0 A – cosN = 0,61 – nN = 905 obr/min – continuous running S1 For five selected frequencies fs = 10,20,30,40,50 Hz were all necessary parameters tested, which were useful to investigate the method. The calculations allowed to prepare five steering characteristics of the optimal voltage Uopt versus the torque on the shaft Ts, Uopt = f(Ts). The next five characteristics were obtained from laboratory tests on the machines set; an induction slip-ring motor and separately excited d.c. generator. These all control characteristics were put on the same diagram, Fig.1, that enables to compare the accuracy of the calculated characteristics. The diagram shows all characteristics as a function on the shaft torque. The analysis of the diagram confirms that differences between the calculated and testing characteristics are small and accuracy of optimal voltage determination is enough good. For all frequencies the testing characteristics lie above the calculated characteristics. The prepared method allows to determinate an optimal value of supply voltage even for no-load operation. 161 U opt [V] 400 350 300 250 200 Uopt.cal. fs=50Hz Uopt.test. fs=50Hz 150 Uopt.cal. fs=40Hz Uopt.test. fs=40Hz Uopt.cal. fs=30Hz 100 Uopt.test. fs=30Hz Uopt.cal. fs=20Hz 50 Uopt.test. fs=20Hz Uopt.cal. fs=10Hz Uopt.test. fs=10Hz 0 0 1 2 3 4 5 6 7 8 9 10 Ts [Nm] Fig. 1. Comparison of control characteristics obtained from measurements (solid line ) and from calculations (dash line ) Rys. 1. Porównanie charakterystyk sterowania uzyskanych na podstawie pomiarów (linia ciągła ) oraz na podstawie obliczeń (linia przerywana ). 3. CONCLUSIONS The presented considerations of optimal voltage selection to minimize the total losses in an induction slip-ring motor lead to following conclusions: – the developed method for determination of optimal voltage for given load proved its usefulness for technical applications, – the advantage of the method is its high accuracy, 162 – the method accuracy is significant depending on assumed for calculation winding resistances; the resistances should come from present motor load, – the certain disadvantage of described method is necessity of laboratory test to measure iron losses, mechanical losses, a magnetization characteristic, windings resistance, and leakage reactance of stator winding, – the described method was developed under assumption, that currents and voltages were sinusoidal, – the verification of the method was made on a small induction slip-ring motor supplied with sinusoidal voltage from 3-phase synchronous generator. REFERENCES [1] KIOSKERIDIS I., MARGARIS N.: Loss Minimization in Induction Motor Adjustable- Speed Drives, IEEE Transactions on Industrial Electronics, Vol. 43, No. 1, February 1996, p. 226–231. [2] KRYGIER J.: Zagadnienia energooszczędnej pracy trójfazowych silników asynchronicznych klatkowych (Energy efficient operation of three-phase induction squirrel-cage motors). Prace Naukowe Politechniki Szczecińskiej nr 494, Szczecin 1992. [3] GRUSZCZYŃSKI P.: Wybrane zagadnienia optymalizacji statycznej sterowania napędów przekształtnikowych (Selected problems of state optimization of power electronic drive control). Zeszyty Naukowe PG nr 499, Elektryka, Gdańsk 1993. [4] FERNANDEZ F., GARCIA A., FAURE R.: Model-Based Loss Minimization for DC and AC VectorControlled Motors Including Core Saturation. IEEE Transactions on Industry Applictions,Vol. 36, No. 3, May/June 2000, p.755–763. [5] KAŹMIERKOWSKI M., KRISHNAN R., BLLABJERG F.: Control in power electronics Selected problems. Akademic Press, 2002. METODA DOBORU NAPIĘCIA ZASILAJĄCEGO DLA MINIMALIZACJI STRAT MOCY W INDUKCYJNYM SILNIKU PIERŚCIENIOWYM Minimalizacja całkowitych strat mocy w indukcyjnym silniku pierścieniowym realizowana jest przez odpowiednie sterowanie napięcia zasilającego. Dla każdej wartości obciążenia istnieje optymalna wartość napięcia, która powoduje maksymalną redukcję strat. Tę optymalną wartość napięcia można wyznaczyć posługując się metodą analityczną opracowaną przez autora. Zastosowanie tej metody wymaga znajomości strat mechanicznych i strat w żelazie, charakterystyki magnesowania, spadku napięcia na zestyku ślizgowym, wartości rezystancji uzwojeń oraz reaktancji rozproszenia uzwojenia stojana. Weryfikacji opracowanej metody dokonano na silniku pierścieniowym małej mocy o danych: P = 0,9 kW, nN = 905 obr/min. Dla badanego silnika wyznaczono po dwie charakterystyki sterowania Uopt = f(Ts); jedną na podstawie pomiarów laboratoryjnych i drugą stosując opracowaną metodę. Charakterystyki te sporządzono dla pięciu wartości częstotliwości; 10, 20, 30, 40, 50 Hz., i przedstawiono je na rys. 1. Porównanie obu charakterystyk potwierdza ich dużą zgodność. Przedstawione wyniki badań wskazują na dużą dokładność i tym samym przydatność opracowanej metody do wyznaczania optymalnych wartości napięcia.