New approach for the analysis of a three-phase induction motor of different ratings connected to a single-phase supply zyxw M.H. El-Maghraby R.H. Thejel M.M. lbrahim zyxwvutsrqp Indexing terms: Convertors, Induction motors, Pave1 electronics zyxwvutsrqp Abstract: zyxwvutsrqpon The problem of operating a three-phase induction motor connected to a single-phase supply system using two convertors is discussed. Special attention is focused on the starting torque and minimum unbalance requirements for different motor power ratings. A new approach is suggested here, concerning the calculation of the starting and running sizes of the convertors, to enable the motor to start under full load conditions with minimum unbalance factors. These sizes are also modelled as functions of the motor power, with a wide applicable range. A method of determining the switching instant of the first convertor sizes is also introduced and modelled. Numerical applica- tion of the proposal has been carried out on differ- ent induction motors to investigate its validity. The results prove a reasonable minimum unbal- ance factor of 5.8 per cent during normal running conditions. They also demonstrate that a sufficient starting torque is at least equal to the full load figure. The models proved to be accurate, so that there would be no need for further analysis for any motor power in the range studied (0.37- 15 kW). This approach has no complex or special hard- ware control system; it needs only a simple facility to implement the switching process from starting to running sizes for one of the two convertors. The other convertor will remain fixed at its optimum size, independent of the speed. List of symbols zyxwvutsrq S = slip R,, R;, x,, x i , R,, zyxwvutsrqpon X, = stator and rotor equivalent circuit parameters of the three-phase induc- tion motor per phase, R = positive and negative sequence admittances of the motor per phase, S zyxwvutsr Yl, Y2 Paper 8412B (Pl), first received 19th December 1990 and in revised form 8th August 1991 Prof. El-Maghraby was with the Electrical Engineering Department, College of Engineering, Basrah University, Basrah, Iraq. He is now with the Electrical Power and Machines Department, Faculty of Engineer- ing, El-Mansoura University, El-Mansoura, Egypt Mr. Thejel and Mr. Ibrahim are with the Electrical Engineering Depart- ment, College of Engineering, Basrah University, Iraq IEE PROCEEDINGS-B, Vol. 139, NO. 3, MAY 1992 = magnitudes of admittances Yl and Y2, = angles of admittances Y, and Y2, respec- = admittances of the two convertors, S =magnitudes of admittances Y,, and x2, = angle of admittances zyxw x, and yC2, degrees = impedance of convertor 1 at starting, R = impedance of convertor 1 at running, R = impedance of converter 2 at starting and respectively, S tively, degrees respectively, S running conditions, R V, , V,, V, = motor phase voltages, V I,, I,, I, = motor phase currents, A I,,, I,, = convertor currents, A = single-phase supply voltage, V a &'2ff/3 V = forward torque, Nm = backward torque, Nm T/ Tb P = motor power, kW NSW = switching speed, r/min Nr zyxwvut W = 27cL rad/s f ZL. 4 6 zyxwvu z, - - = full load speed, r/min = supply frequency = jwL = inductance power factor angle, 42 rad = convertor firing angle, rad = equivalent impedance of convertor calcu- lated by eqn. 16 1 Introduction The installation of three-phase supply and its distribution system faces technical and economic difficulties, particu- larly in meeting consumer demands in rural and remote sites in developing countries. The starting point is there- fore to install a single-phase supply to meet critical loads such as lighting, water pumping and medicine refriger- ators. In the next stage, it will be possible to install three- phase distribution systems to serve these regions without exceptions. The effect of the impedance of a single-phase line on motor performance depends generally on the line length, its conductor material and cross-section, the motor rating or equivalent circuit parameters, the load power factor, and the line voltage. Flicker due to motor starting can be reduced as follows [ 13 : 145