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Figure from:A Method for Solving the Voltage and Torque Equations of the Split-Phase Induction Machines

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ihe derivation or these equations 1s labonous and an insight to deriving them can be found in (Krause et al, 2002). It should be noted that the gq —axis stator winding is the same as the running winding while the d — axis stator winding is the same as the starting winding. The d-q axis is a fictitious axis used to simplify the derivation of the machine equations. The d-q equivalent circuit diagrams of the machine are given in figures 2 (a) and (b) and they are easily obtained from equations (2) - (9). III. EQUATIONS OF THE SPLIT PHASE INDUCTION MOTOR

Figure 1 ihe derivation or these equations 1s labonous and an insight to deriving them can be found in (Krause et al, 2002). It should be noted that the gq —axis stator winding is the same as the running winding while the d — axis stator winding is the same as the starting winding. The d-q axis is a fictitious axis used to simplify the derivation of the machine equations. The d-q equivalent circuit diagrams of the machine are given in figures 2 (a) and (b) and they are easily obtained from equations (2) - (9). III. EQUATIONS OF THE SPLIT PHASE INDUCTION MOTOR

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machine is assumed to be a squirrel cage rotor in which the rotor bars can be represented by two un-symmetrical windings whose axes are perpendicular to each other. For this type of SPIM, Vs =Vs, Vas = Vs. In addition V' =0, V's =0 since the rotor windings are short-circuited (Krause et al, 2002). Vs, Vqs, Vas, Vr and Vr are defined in section 3. The running and the starting windings are spatially displaced 90° apart and are connected across the single phase supply as seen in Figure 1. The voltage, flux and electromagnetic torque equations are hereby written in equations (2)—(11).
machine is assumed to be a squirrel cage rotor in which the rotor bars can be represented by two un-symmetrical windings whose axes are perpendicular to each other. For this type of SPIM, Vs =Vs, Vas = Vs. In addition V' =0, V's =0 since the rotor windings are short-circuited (Krause et al, 2002). Vs, Vqs, Vas, Vr and Vr are defined in section 3. The running and the starting windings are spatially displaced 90° apart and are connected across the single phase supply as seen in Figure 1. The voltage, flux and electromagnetic torque equations are hereby written in equations (2)—(11).
Figure 2(b): d-axis equivalent circuit of the machine
Figure 2(b): d-axis equivalent circuit of the machine
Figure 2(a): q-axis equivalent circuit of the machine
Figure 2(a): q-axis equivalent circuit of the machine
Figure 11: Dynamic torque-speed characteristics of the machine The free acceleration characteristics of the split phase Induction machine are given in Figures 3 — 11 and they have been obtained at no-load. The results compare favourably well with the resu. ts obtained in (Ong, 1998). The voltages V,, and Vas across the main and auxiliary windings respectively are shown in figures 3 and 4.They are sinusoidal functions of time as expected. t can be observed that the voltage waveforms are unequal in magnitude. The reason for this is the turns ratio between the two windings. In figures 5 - 8, the stator and rotor currents I,,, ds Z’gr and J’g, are seen to take the form of the supply voltage which is sinusoidal in nature. The running or main winding current is observed in Figure 5 to be higher in magnitude than that of the starting winding shown in figure 6 which is expected. The reason is because the running winding resistance is lower than that of the starting winding.
Figure 11: Dynamic torque-speed characteristics of the machine The free acceleration characteristics of the split phase Induction machine are given in Figures 3 — 11 and they have been obtained at no-load. The results compare favourably well with the resu. ts obtained in (Ong, 1998). The voltages V,, and Vas across the main and auxiliary windings respectively are shown in figures 3 and 4.They are sinusoidal functions of time as expected. t can be observed that the voltage waveforms are unequal in magnitude. The reason for this is the turns ratio between the two windings. In figures 5 - 8, the stator and rotor currents I,,, ds Z’gr and J’g, are seen to take the form of the supply voltage which is sinusoidal in nature. The running or main winding current is observed in Figure 5 to be higher in magnitude than that of the starting winding shown in figure 6 which is expected. The reason is because the running winding resistance is lower than that of the starting winding.
Figure A2: Simulink model of the split phase induction machine Figure A1: Block Diagram of the solution of model equations
Figure A2: Simulink model of the split phase induction machine Figure A1: Block Diagram of the solution of model equations