ETEP zy Ransient Behaviour of Optimum-Designed Three-Phase Squirrel-Cage Induction Motors J. Faiz, M. B. B. Sharifian Abstract zyxwvutsr This paper describes the transient behaviour of optimum-designed three-phase squirrel-cage induction motors. These motors have been designed based upon three different objective functions. They are cost, eficiency and com- bination of eficiency-costfunctions. Transientperformance zyxwv of these optimum designs and zyx an industriai motor are compared and a suitable designfor a particular fault is then introduced. zyxw A symmetrical voltage disturbance, start- up and a symmetrical three-phase short circuit are three cases considered in this investigation. 1 Introduction zyxwvuts Many papers have been published covering the overall behaviour of a manufactured induction motor when it is subjected to a sudden change of operating con- ditions. Such conditions could be voltage disturbances, starting-ups and power-system faults. Some attempts have been made to reduce the computation time of such simulations. Forthis purpose, the machinesimulation by a fifth-order model zyxwvutsr [ 1-31 is reduced to a third-order model [4-71 which is desirable in some applications. Even it has been possible to derive a simplified second- order model [8] with accuracy sufficient for many appli- cations where a third-order model has been previously required. In a few cases a first-order model with a very shorter computation time and yet a sufficient accuracy may be employed for prediction of the motor behaviour. Starting current of induction motor generates heat and mechanical stresses in the motor and voltage dips in the supply. zyxwvutsr A large moment of inertia and torque pulsa- tions of the motor may give resonance with mechanical load. Hence it is important to predict startingcurrent and torque and the duration of the starting period. As the best of our knowledge, the transient behavi- our of the optimum designed three-phase induction mo- tors has not yet been published and comparison has not been made with the available industrial motors. This paper uses a very recent simple, fast and accurate algo- rithm for simulation of an induction motor [9]. It is fol- lowed by study of the transient behaviour of the indus- trial motor as well as by the optimised design induction motors. Different designs based on efficiency, cost and efficiency-cost optimisations reported in [ 101 are used for this investigation and their transient mode of opera- tion are compared with each other and with the available industrial induction motors. The well-established optimisation technique of Hooke-Jeeves will first be introduced. The simulation method used in this investigation will then be briefly pre- sented. Initial design based on the design program (be- fore optimisation), three optimised designs and the in- dustrial inductionmotors will be compared by simulation studies under different transient operating conditions. 2 Optimisation Technique The “pattern search method of Hooke-Jeeves” [ 111 is used to optimise the motor based upon the different ob- jective functions. The Hooke-Jeeve method varies each parameter independently, thus allowing sections and subroutines of the design program to be omitted during each function evaluation. Other more sophisticated di- rect search methods such as Han-Powell [ I21 vary all pa- rameters simultaneously and thus require that the com- plete design analysis program be used for each function evaluation. The Hooke-Jeeves method can produce an optimum design which is similar to that obtained using a more sophisticated optimisation procedure. as shown by the authors in [13]. It is generally believed that direct search methods are superior to gradient search methods if the gradient must be calculated numerically [ 141. 3 Simulation Method Details of the simulation technique, used in the present work, has been described in [9]. Fifth-order model of induction motor based on d, q-axis consists of two voltage-current equations for stator, two voitage- current equations for rotor and one dynamic equation of the motor. Direct solution of this fifth-order model using numerical methods involves a long computation time and high accuracy. Generally the time consumed for compu- tation is critical in power systems and it is preferred to ob- tain solution with a reasonableaccuracy in a shorter time. Relationships between d, q-voltages of the stator and three phase terminal voltages and also relations between flux linkages and currents of the stator and rotor can be easily written. In order to reduce the number of equations of the fifth-order model, a numerical control method is used in a matrix form. 4 Comparison of Simulated Results The machine responses of current amplitude in the stationary stator winding, power factor and slip are cho- ETEP Vol. 7, No. 6, NovembedDecember 1997 415