According to the aforementioned assumption, filter inductance of the output converter is designed with different switching frequency as shown in Figure 1.3a. It is observed that the filter inductance decreases with an increase in the switching frequency. Similarly, the size of the filter inductor is also reduced with an increase in the switching frequency as shown in Figure 1.3b. The shaded bar shows the weight of the magnetic core of the filter. The blank bar shows the weight of the copper winding of the filter. The weight of the inductor is reduced about to one of the fifth by increasing switching frequency from 10 to 100 kHz. Figure 1.3c shows total loss of three output filter inductors vs. the switching frequency. The inductor loss also decreases with an increase in the switching frequency. It is because we use a smaller inductance when the switching frequency is higher. A smaller inductance means it has short length of winding so that copper loss is reduced. A smaller inductance needs a smaller core, whose loss depends on its magnetic core volume for a given maximum magnetic flux density. The smaller the core, the smaller the core loss. Thus, a small inductance results in both smaller copper loss and core loss. As a result, with an increase in the switching frequency, both the filter inductor size and loss decrease. Cost of the filter inductor is also cut down. It seems that it is better to design the UPS at higher switching frequency. Unfortunately, there is a switching frequency limit due to the loss of the power semiconductor devices in UPS. It will be discussed later.
Now an inverter used for power trains of electric vehicles is investigated. The main circuit of power train is shown in Figure 1.4. It is composed of battery, film capacitor, three‐phase switch bridge and motor. Power density is critical for the power train. The film capacitor Cdc occupies a large footprint. To suppress voltage ripple on the battery to a certain value, following capacitance is required [3]:
(1.1)
Figure 1.3 Filter inductance, weight and loss vs. switching frequency. (a) Filter inductance vs. fs. (b) Weight of each filter inductor vs. fs. (c) Total loss of three filter inductors vs. fs.
where Io is output phase current (rms value), cos(φ) is load power factor, fs is switching frequency, and ΔVdc is maximum DC voltage ripple allowed on the battery. It is observed that the required DC bus capacitance is inversely proportional to switching frequency fs.
It is assumed that DC bus voltage Vdc is 320 V, the inverter power is 120 kW, load current is 400 A, power factor of the motor is 0.93, and maximum DC voltage ripple allowed on the battery ΔVdc = 32 V. The relationship between the DC side capacitance and the switching frequency is shown in Figure 1.5. The capacitance is reduced to one of the tenth if the switching is increased by ten times. Therefore, the DC side film can be reduced if we can increase the switching frequency. It is helpful to increase the power density of the power train of the EV. Similar to the discussion earlier, there is an upper limit to the switching frequency due to the loss of the power semiconductor devices in the power train.
Figure 1.4 Power trains of electric vehicles: (a) circuit of power trains; (b) air‐cooled 34 kW inverter for battery EV.
Figure 1.5 DC side capacitance vs. switching frequency.
1.1.3 Switching Frequency and Impact of Soft‐switching Technology
As we mentioned earlier, if the inverter operates at higher switching frequency, the inverter will have smaller filter size and smaller loss on the filter in UPS and smaller DC‐side film capacitor in EV power train. In addition, we can get better dynamics. In some applications of ultra‐high‐speed drives for the industry or aeronautics, inverters are required to operate at very high switching frequency to provide lower ripple fundamental frequency current to the motor/generators. It seems higher switching frequency operating has advantage. What is the maximum switching frequency the inverter can operate at?
Actually, the switching frequency is limited by loss of the power semiconductor devices in the inverter. Figure 1.6 shows loss of the power semiconductor switches of the inverter of 100 kVA UPS exampled in the last section. Typical Insulated Gate Bipolar Transistor (IGBT) devices (Si IGBT FF300R12KT) are used as the switches. The loss of the inverter power semiconductor devices is composed of conduction loss, turn‐on loss, turn‐off loss, and reverse recovery loss. Conduction loss is static loss, which does not change with the switching frequency shown as the black part of the bar at the bottom of the figure. The other three losses – turn‐on loss, turn‐off loss, and reverse recovery loss – are dynamic losses, which increase linearly with the switching frequency as shown in the figure. As a result the dynamic loss of the power device depends on the switching frequency. If we want to design the inverter with required efficiency, its maximum switching frequency should be restricted to constrain total power device loss to certain value. Dynamic loss has another commonly used name: switching loss. It means the loss is caused by the device switching actions, either turning on or turning off.
For the same inverter parameters, when SiC MOSFET (CAS300M12BM2) is used, total SiC MOSFET loss of the inverter vs. the switching frequency is shown in Figure 1.7. Since the recovery loss is smaller, it is ignored. The loss of the inverter power semiconductor devices is composed of conduction loss, turn‐on loss, and turn‐off loss. Similar to the IGBT inverter, the conduction loss is constant while the dynamic loss is proportional to the switching frequency. Although the power device loss of the SiC inverter loss is much smaller than that of the IGBT inverter, the dynamic loss is still the main factor to limit the upper switching frequency.
Figure 1.6 Power semiconductor loss of the inverter vs. switching frequency.
Figure 1.7 Total SiC MOSFET loss of the inverter vs. switching frequency.