converter.
Third, the converter is required to have good dynamics. The dynamics of a converter mainly depends on bandwidth of the close loop control systems. It is mainly constrained by the switching frequency of the converter. Generally speaking, power electronic converters have high dynamics since they use power semiconductor devices as the switch. In many applications such as ultra‐high‐speed pumps and compressors in industrial applications, power generation for aeronautics, EV, etc., it is required that the converter drives the motor to reach ultra‐high speed from tens to hundreds of thousands rpm. In some applications such as moving vehicles, the size of the electric machines can be reduced by increasing their operating frequency. To increase the fundamental frequency of the converter, it is natural to increase switching frequency. What is the limit of the switching? We will discuss it in detail later.
Another demand is lower cost. The cost of a converter or a converter system should be optimized. A converter system is generally composed of power semiconductor devices and passive components. Size of the passive components depends on operating frequency. If we can increase the frequency, their size can be reduced.
Actually, switching frequency is a critical parameter for the converter. It plays an important role in efficiency, power density, dynamics, and cost reduction.
1.1.2 Switching Frequency vs. Conversion Efficiency and Power Density
In this section, we will discuss the effects of the switching frequency on the converter. First, an inverter used for UPS is taken as an example. The main circuit of UPS is back to back (BTB) converter as shown in Figure 1.2. It is composed of three‐phase grid converter as the rectifier cascaded with a three‐phase converter as the inverter to provide high‐quality power to the load. To satisfy the load requirement, output voltage of UPS needs to be an almost sinusoidal waveform. Its output voltage quality is usually described by total harmonic distortion (THD). Filters are installed in load sides. In addition, to satisfy the grid standard, filters in utility side are also installed. Filter cost ranges from 15 to 30% of total material expenditure in the UPS (excluding the battery cost). Besides, it also occupies a large footprint. Size of the passive components depends on operating switching frequency. If we can increase the switching frequency, their size will be reduced.
Figure 1.2 Circuit diagram of UPS.
It is assumed that a UPS equipment has rated power 100 kVA at load power factor PF = 0.8. Both the input grid phase voltage and output phase voltage are 220 Vrms. Internal DC bus voltage is 750 Vdc. THD of output voltages is less than 5%. Inductor‐capacitor filters are used to improve output voltage waveform. The filter inductors are designed with amorphous core, and their maximum magnetic flux density is Bmax = 1.2 T.
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
