## Appendix C
Static power losses of one IGBT transistor are determined as follows [44]:  
\[\mathrm{P_{VT\_stat}}=\mathrm{U_{CE(on)}}\big{(}\mathrm{I_{C}},\mathrm{T_{j}} \big{)}\cdot\mathrm{I_{C}}\cdot\mathrm{S},\] (A40)  
where \(\mathrm{U_{CE(on)}}\) is the transistor collector-emitter voltage in the open state, \(\mathrm{I_{C}}\) is the average value of the collector current over the period, \(\mathrm{S}=0.5\) is the pulse duty cycle, and \(\mathrm{T_{j}}=125\)\({}^{\circ}\mathrm{C}\) is the transistor temperature. Since the current, the collector current of the transistor has a non-sinusoidal shape, its average value over the period is determined as follows [44]:  
\[\mathrm{I_{C}}=\frac{1}{2\cdot\pi}\cdot\int_{0}^{2\cdot\pi}\sum_{i=0}^{\mathrm{N }}\mathrm{I_{s(i)}\cdot sin(i\cdot\omega\cdot t)\cdot d(\omega\cdot t)}\] (A41)  
where \(\mathrm{I_{s(i)}}\) is the higher harmonics of the stator phase current, \(\mathrm{I}\) is the harmonic sequential number, \(\mathrm{N}=40\) is the number of harmonics, \(\omega=2\cdot\pi\cdot\mathrm{f}\) is the fundamental harmonic angular frequency, and \(\mathrm{f}\) is the fundamental harmonic frequency. As can be seen from Equation (A38), the collector-emitter voltage of the transistor in the open state is a function of the collector current average value (\(\mathrm{I_{C}}\)) and transistor temperature (\(\mathrm{T_{j}}\)). The collector-emitter voltage values of a transistor in the conducting state can be determined based on the average values of the collector current over one period [12]. A static power loss of a single reverse diode is determined as follows [44]:  
\[\mathrm{P_{VD\_stat}}=\mathrm{U_{VD}}\cdot\mathrm{I_{VD}}\cdot\mathrm{D}\] (A42)  
where \(\mathrm{U_{VD}}\) is the forward diode voltage and \(\mathrm{I_{VD}}=\mathrm{I_{C}}\) is the average value of the forward diode current over the period. Power losses when the transistor is switched on [44] are as follows:  
\[\mathrm{P_{VT\_sw(on)}}=\mathrm{E_{on}}\cdot\mathrm{K}\cdot\mathrm{f_{f}}\] (A43)  
where \(\mathrm{E_{on}}\) is the energy loss for the switching transistor (Table 2), \(\mathrm{f}\) is the fundamental frequency value, and \(\mathrm{K}\) is the number of PWM pulses. The power loss for switching off the transistor [44] is as follows:  
\[\mathrm{P_{VT\_sw(off)}}=\mathrm{E_{off}}\cdot\mathrm{K}\cdot\mathrm{f_{f}}\] (A44)  
where \(E_{on}\) is the energy loss for switching off the transistor (Table 2). Total losses in one transistor are as follows:  
\[\mathrm{P_{VT}}=\mathrm{P_{VT\_stat}}+\mathrm{P_{VT\_sw(on)}}+\mathrm{P_{VT\_ sw(off)}}\] (A45)  
The diode recovery power loss is as follows:  
\[\mathrm{P_{1}^{\prime}}=\mathrm{P_{1}}=\mathrm{U_{d}}\cdot\mathrm{I_{d}}\]0 (A46)  
where \(E_{rev}\) is the diode recovery energy loss (Table 2). Total losses in one diode are as follows:  
\[\mathrm{P_{1}^{\prime}}=\mathrm{P_{1}}=\mathrm{U_{d}}\cdot\mathrm{I_{d}}\]1 (A47)  
Since the inverter circuit consists of six IGBTs and six reverse diodes, the total power loss in the inverter can be determined as follows:  
\[\mathrm{P_{1}^{\prime}}=\mathrm{P_{1}}=\mathrm{U_{d}}\cdot\mathrm{I_{d}}\]2 (A48)  
In order to prevent the DC current components from entering the compensator inverter, high frequency RC-filters are used in the output section of the drive with a reactive power compensator (Figure 2). These filters are tuned to a cut-off frequency, which is 10 times lower than the rotation frequency of the induction motor. In other words, the cut-off frequency of the filter is equal to \(\mathrm{f_{RC}}=0.1\cdot\mathrm{f_{nom}}=0.1\cdot 55.8=5.58\) Hz. The active resistance of the filter resistor R\({}_{\rm f}\) is chosen to be 56 \(\Omega\). Then, the capacitance of the filter capacitor C\({}_{\rm f}\) will be equal to C\({}_{\rm f}\) = 1/(f\({}_{\rm RC}\cdot\)R\({}_{\rm f}\)) = 3200 \(\mu\)F.  
Since the high-pass filter will suppress harmonics with frequencies lower than 5.58 Hz, only the zero harmonic of the current (its DC component) will flow through the filter resistor \(R_{f}\).