80 PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 88 NR 12b/2012 Mykhaylo ZAGIRNYAK 1 , Viacheslav PRUS 1 , Ihor KOLOTYLO 1 , Damijan MILJAVEC 2 Kremenchuk Mykhailo Ostrohradskyi National University (1), University of Ljubljana, Faculty of Electrical engineering (2) Determination of power indices for a three-phase induction motor with a phase-wound rotor through particular losses components Abstract. A method of determination of power indices for a three-phase induction motor with a phase-wound rotor through particular losses components in the function of their integral and instantaneous values is developed. The adequacy of the method is confirmed. The prospect of its use is grounded for the situation when the state of structural assemblies and motor elements changes in the process of long-term operation and after repair. Streszczenie. Przedstawiona została metoda określenia wskaźników trójfazowego silnika indukcyjnego z wirnikiem uzwojonym poprzez poszczególne składniki strat w funkcji ich integralnych i chwilowych wartości. Odpowiedniość metody została potwierdzona. Perspektywa stosowania tej metody oparta jest ukierunkowana na sytuacje kiedy konstrukcyjny montaż i elementy silnika zmieniły się w procesie długotrwałego działania oraz po remoncie. (Określenie wskaźników mocy dla trójfazowego silnika indukcyjnego z uzwojonym wirnikiem poprzez poszczególne składniki strat). Key words: induction motor, phase-wound rotor, losses components, power indices. Słowa kluczowe: silnik indukcyjny, wirnik uzwojony, składniki strat, wskaźniki mocy. Introduction In a competitive market, which is especially acute during crisis years, the industrial production aims at considerable decrease of various kinds of expenditure influencing the prime cost of manufactured goods. For most enterprises of metallurgic, chemical and other adjacent industries electric power costs, coming to 30-35 % in the total cost, are considerable. This poses the problem of optimization of power costs in control of various technological objects and processes at an enterprise. It is possible to optimize power consumption in an electric drive by means of control systems estimating real power conditions of electric machines operation and their efficiency. The prospect of the use of such systems is determined by availability of reliable methods of finding power and moment on the electric machine shaft, as well as particular power losses components under different operational conditions. In this case directly controlled values are to be easily determined according to the reading of as few standard sensors used in the electric drive system as possible. In a number of cases this problem is aggravated due to absence of methods taking into account both particular losses components and their total value, which can be explained by complexity of mathematical description of real power processes in different electric machines types. Besides, the existing power processes analysis methods are mostly based on simplified notions and take into consideration neither motor natural parameter variation within one series nor the fact of their change during the process of long-term operation and repair. However, there exist a number of electric machines for which this problem can be solved with admissible errors. As to AC machines, first of all they include phase-wound rotor induction motors (PRIM). Problem statement The aim of the paper is to substantiate the method of determination of PRIM power indices through power losses components according to values of integral parameters and through instantaneous variables functions. In this case losses components are to be determined taking into account the state of the main PRIM structural assemblies and elements and are to be unambiguously expressed by the parameters measured with a minimal number of typical sensors. Theory Let us assume the current values of power coefficient  cos and efficiency coefficient  to be PRIM power indices. Their determination and expression through particular losses components is the most accurate method of their finding in any operation conditions [1]. In PRIM the following losses components can be singled out: iron losses in stator P m1 and rotor P m2 , copper losses in stator P cu1 and rotor P cu2 , mechanical P mac and additional P add losses [1]. According to [2], in the process of long-term operation and repair of electric machines a considerable change of electric and magnetic properties in stator core iron takes place. It results in the increase of the degree of magnetic material saturation, growth of nonlinear distortions coefficient 1 e THD of stator EMF curve e 1 and redistribution of losses P m1 in stator iron [2]. Losses P m10 in idle running iron can be determined according to the results of no-load test for supply voltage variable frequency, separating them from losses P cu10 in idle running copper and mechanical losses P mac [1]. To divide them into hysteresis and eddy currents components it is necessary to use the expression obtained in [3]: (1)       n ,... , i i * i ec i * i h m E f c E f c P 5 1 2 10 2 2 10 10 where i * i E , f 10 – values of i -th relative frequencies and EMF harmonic components, respectively; c h, c ec – coefficients taking into account the division of iron losses into hysteresis and eddy current ones, respectively. Iron losses P m10 value obtained from no-load test can be used later to determine them under any load [3]: (2)   2 10 1 10 1 E E P P m m  where E 1 – stator winding EMF in the mode for which value P m1 is determined. Its value for PRIM can be found on the basis of directly measured rotor EMF E 2 and motor rotation angular frequency  . Rotor iron losses P m2 are usually neglected due to their small amount, as rotor current frequency f 2 in the area of operating slip is not large. In case of high degree of saturation of PRIM magnetic system losses P m2 grow because of high slips of current higher harmonics. This