340 PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 89 NR 12/2013 Mykhaylo ZAGIRNYAK, Andrii KALINOV, Viacheslav MELNYKOV Kremenchuk Mykhailo Ostrohradskyi National University Sensorless vector-control system with the correction of stator windings asymmetry in induction motor Abstract. Estimation of induction motor stator windings asymmetry influence on power and dynamic characteristics of sensorless vector control systems is performed. A system of vector control in a three-phase coordinate system is developed. This system makes it possible to compensate for induction motor windings asymmetry by correction of flux linkage assignment. Streszczenie. Analizowano wpływ asymetrii uzwojeń twornika silnika indukcyjnego na właściwości dynamiczne przy sterowaniu bezczujnikowym. Badano układ silnika trójfazowego. Przedstawiono metody korekcji wpływu asymetrii uzwojeń. (Bezczujnikowe wektorowe sterowanie silnikiem indukcyjnym z korekcją asymetrii uzwojeń) Key words: asymmetry, stator windings, power characteristics, vector control system. Słowa kluczowe: silnik indukcyjny, sterowanie bezczujnikowe, asymetria uzwojeń Introduction Sensorless induction motor (IM) vector control systems (VCS) are widely spread in industry. Long-term performance of IM results in occurrence of various damages. As diagnostics results show [1], at present, a great number of IM with unsymmetrical stator windings are used. According to statistic data, more than half IM failures occur due to stator windings damages [2, 3]. The main reason for this consists in damages of conductor and slot insulation which can be caused by both violation of motor production or repair methods and abuse. It results in short circuits: winding short circuits, interfacial ones and ironwork faults [4, 5]. As, due to the crisis, industrial enterprises reduce the amount of repair work, when some sections of stator winding of high- and medium-power motors fail, these sections are not removed out of the slots, but are excluded from the circuit and the sections ends are connected passing over the faulty ones [3]. As a result, the stator winding becomes asymmetric and henceforth the motor operates with this winding. Consequences of operation of IM with unsymmetrical stator windings can be rather considerable for both the motor and the working mechanism. Therefore, the aim of the research is estimation of operating conditions and correction of power indices of systems of sensorless vector control of electric drive with an asymmetric induction motor. Theory Research of dynamic and power conditions of operation of sensorless VCS with unsymmetrical IM was made using mathematical models. IM was described by differential equations in a three-phase coordinate system and VCS was created in an orthogonal coordinate system with orientation to the vector of rotor flux linkage [6]. As indirect methods of determining rotor flux linkage were considered following [7,8]: – observer No.1 – on the basis of equations of stator circuit in a fixed coordinate system; – observer No. 2 – on the basis of equations of rotor circuit in a rotating coordinate system; – observer No. 3 – on the basis of equation for the case when the real axis of the rotating coordinate system is oriented to the rotor flux linkage vector. VCS research using indirect methods for determination of motor rotation speed was carried out for observers of two types [9, 10]: – observer No. 1 - is based on the calculation of supply voltage frequency in a fixed coordinate system and calculation of rotor EMF in the rotating coordinate system with orientation to stator flux linkage vector. – observer No 2 - is based on the calculation of supply voltage frequency and rotor EMF frequency according to the projections of voltage and current space vectors on the axis connected with the stator fixed coordinate system. Research of sensorless VCS power operating conditions was carried out for control system structures based on a combination of the described observers. Mathematic modeling of these systems was performed for IM 4A100L2У3: 5 . 5  n P kW; 2820  n n rev/min; 91 . 0 cos   ; 875 . 0   ; 728 . 0  s R Ohm; 437 . 0  r R Ohm; 00209 . 0  s L H; 004249 . 0  r L H; 147 . 0   L H. Analyzed sensorless VCS power parameter dependences on the IM stator windings asymmetry level are shown in Figs. 1-2. As a winding asymmetry level we imply the following ratio:   1 100% d h R R    , where R d is the percentage of active resistance in damaged phase; R h is the active resistance of a healthy phase. Estimation of power operating conditions of the considered electric drives (ED) with VCS was made on the basis of such indices (table 1): 1 2 . 1 Cu P  – motor overload; P 5 . 1 – converter overload; 1 10 .. 5 Cu P  – quickly increasing thermal overloads; % 10  M  – admissible level of electromagnetic moment variable component; % 20  M  – inadmissible level of electromagnetic moment variable component. In figures 1-2 and table 1 we imply the following explanation: 1 Cu P  – stator copper losses, r.u.;  P – total losses, r.u.; P – power consumption, r.u.;  – efficiency, %;    cos – power coefficient, %; M  – variable component of electromagnetic moment, %; P  – variable component of instantaneous power, %. Mentioned criteria are reduced to counterparts in nominal symmetrical operation mode of IM. Boundary values of IM windings asymmetry level, according to the presented indices, are shown in table 1. It also contains the asymmetry level at which sensorless VCS fails. The mathematical research demonstrated that the use of VCS with indirect methods for determination of rotor flux linkage and motor rotation speed for IM with stator windings asymmetry results in considerable deterioration of power and dynamic characteristics or even in complete failure of ED system. The research results also showed that, in spite of considerable deterioration of power characteristics of the considered systems, direct indices of the quality of transition processes concerning IM rotation speed and electromagnetic moment remain practically unchanged.