**5.1. Steady state analysis**

The main objective of the modifications done in terms of the addition of the auxiliary winding is to improve the poor power factor an induction motor has. It is therefore important to focus on the behaviour of the machine parameters that involves power factor when introducing reactive power injection.

Figure 6 shows that the injection of reactive power in the auxiliary winding improves the power factor of the motor. The bigger the size of the capacitor, the more reactive power is injected and hence the better the power factor. For this specific machine, capacitors of 30µF connected per phase as in Figure 4 leads to a power factor very close to unity.

**Figure 6.** Torque – Power Factor waveform

**Figure 7.** Torque – Reactive Power waveform

The derived mathematical models implemented in the Matlab/Simulink environment can be used to generate steady-state and dynamic simulation results. The machine without compensation is used as reference. Capacitance is added to the auxiliary winding and compared with the behaviour of the reference machine. This will show the effect of the capacitors connected to the auxiliary winding on the performance of the modified machine. The dynamic model can be used for steady state analysis by taking readings after the

The main objective of the modifications done in terms of the addition of the auxiliary winding is to improve the poor power factor an induction motor has. It is therefore important to focus on the behaviour of the machine parameters that involves power factor

Figure 6 shows that the injection of reactive power in the auxiliary winding improves the power factor of the motor. The bigger the size of the capacitor, the more reactive power is injected and hence the better the power factor. For this specific machine, capacitors of 30µF

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 <sup>0</sup>

Uncompensated 10 microF 20 microF 30 microF

**Load Torque (pu)**

connected per phase as in Figure 4 leads to a power factor very close to unity.

**5. Simulation results** 

**5.1. Steady state analysis** 

when introducing reactive power injection.

**Figure 6.** Torque – Power Factor waveform

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

**Power Factor**

transient.

With the increase in power factor as seen in Figure 6 it is expected that less reactive power will be drawn from the source with the addition of capacitors to the auxiliary winding. Figure 7 supports this expectation. In Figure 7 the reactive power drawn from the source reduces with increasing capacitor size.

Because the reactive component of the supply current decreases with the reactive power injection, the magnitude of the supply current therefore decreases. This is shown in Figure 8.

**Figure 8.** Torque–Current waveform

Modelling and Analysis of Squirrel Cage Induction Motor with Leading Reactive Power Injection 119

The effect that the change of capacitance has on the performance of the machine is studied in Figures 10 and 11. Figure 10 shows that as the capacitance increase the power factor also increases. It also shows that it is possible to over-compensate the machine which will lead to a decreasing power factor. With the current machine at the current load it can be seen that the optimum value for the capacitor is slightly less than 35µF and will lead to a power factor close to unity. Figure 11 shows the improvement in efficiency as capacitance increases. The efficiency of this machine at current load can be improved with about 0.07 as seen in Figure 11.

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> 0.83

**Capacitance (micro F)**

Steady-state analysis is not always sufficient in determining the behaviour of an electrical machine. Transient and dynamic periods are the most likely periods for harming an electrical machine. The dynamic model will show the exact behaviour of the machine during

0.5 1 1.5 2 2.5 3

Uncompensated Compensated

**Time (seconds)**

**Figure 11.** Capacitance-Efficiency waveform

0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91

**Efficiency**

**5.2. Dynamic analysis** 

**Figure 12.** Power Factor

transient and or dynamic periods.

0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

**Power Factor**

**Figure 9.** Torque Efficiency waveform

The active power drawn from the source consists of different components of which one is copper losses (I2R losses). With the decrease of current shown in Figure 8, it is logical that the copper losses of the main stator winding will also decrease. This will lead to a decrease in active power drawn from the source without a change in output power and hence the improvement in the efficiency of the motor as seen in Figure 9.

**Figure 10.** Capacitance-Power Factor waveform

**Figure 11.** Capacitance-Efficiency waveform

The effect that the change of capacitance has on the performance of the machine is studied in Figures 10 and 11. Figure 10 shows that as the capacitance increase the power factor also increases. It also shows that it is possible to over-compensate the machine which will lead to a decreasing power factor. With the current machine at the current load it can be seen that the optimum value for the capacitor is slightly less than 35µF and will lead to a power factor close to unity. Figure 11 shows the improvement in efficiency as capacitance increases. The efficiency of this machine at current load can be improved with about 0.07 as seen in Figure 11.

### **5.2. Dynamic analysis**

118 Induction Motors – Modelling and Control

**Figure 9.** Torque Efficiency waveform

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

**Efficiency**

**Figure 10.** Capacitance-Power Factor waveform

0.75

0.8

0.85

**Power Factor**

0.9

0.95

1

The active power drawn from the source consists of different components of which one is copper losses (I2R losses). With the decrease of current shown in Figure 8, it is logical that the copper losses of the main stator winding will also decrease. This will lead to a decrease in active power drawn from the source without a change in output power and hence the

<sup>0</sup> <sup>5</sup> <sup>10</sup> <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> 0.7

**Capacitance (micro F)**

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 <sup>0</sup>

Uncompensated 10 microF 20 microF 30 microF

**Load Torque (pu)**

improvement in the efficiency of the motor as seen in Figure 9.

Steady-state analysis is not always sufficient in determining the behaviour of an electrical machine. Transient and dynamic periods are the most likely periods for harming an electrical machine. The dynamic model will show the exact behaviour of the machine during transient and or dynamic periods.

**Figure 12.** Power Factor

Modelling and Analysis of Squirrel Cage Induction Motor with Leading Reactive Power Injection 121

In order to validate the theoretical model with the practical model, three capacitor values of

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 1.6 1.8 <sup>2</sup> -2

Iy

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 1.6 1.8 <sup>2</sup> -2

Iz

<sup>0</sup> 0.2 0.4 0.6 0.8 <sup>1</sup> 1.2 1.4 1.6 1.8 <sup>2</sup> -2

**Time (seconds)**

Ix

**Figure 15.** Phase Currents – Auxiliary Stator Winding

10, 20 and 30µF are used for the three phase auxiliary winding.

**6. Experimental validation** 

0 2

0 2 **Current (pu)**

> 0 2

**Figure 16.** The Experimental set up

**Figure 13.** Efficiency

The dynamic behaviour of a compensated and uncompensated induction machine is compared in Figure 12. The uncompensated machine (dashed waveform) has a low power factor when starting and settles at a power factor of just more than 0.7. The compensated machine (solid waveform) has a higher power factor when starting and settles at a power factor close to unity. This shows how effective this concept is in power factor correction.

The earlier statement that the improvement in power factor will improve the efficiency is supported in Figure 13.

The inrush current of the machine is shown in Figure 14. This machine has a transient state when starting where the current can reach eight times rated current.

The current of the auxiliary winding is shown in Figure 15.

**Figure 14.** Phase Currents – Main Stator Winding

**Figure 15.** Phase Currents – Auxiliary Stator Winding
