The influence of filter on the voltage waveform at the terminals of PWM variable frequency speed regulating motor

1 Introduction

With the application of microelectronics technology and modern control theory in AC variable frequency speed regulation systems, the performance of frequency converters (or inverters) has also been greatly improved, and has been more and more widely used in many fields of industrial production and daily work. However, the pulse voltage with a steep rising or falling edge output by the frequency converter generates overvoltage on the motor terminals and windings, causing premature damage to the insulation of the motor windings. Experimental studies have shown that a very high voltage rise rate (dv/dt) produces extremely uneven voltage distribution on the motor windings, and as the length of the cable (wire) between the frequency converter and the motor increases, a high-frequency oscillating overvoltage is generated on the motor terminals. When the cable length exceeds a certain critical value, the amplitude of the overvoltage on the motor terminals reaches twice the output voltage of the frequency converter. The effect of long-term repetitive voltage stress will lead to premature damage to the insulation between the turns of the motor windings.

In order to reduce the overvoltage of high-frequency oscillation on the motor terminals, one of the most suitable methods is to install a specially designed filter on the motor terminals. The parameters of the filter are related to the characteristics of the inverter and the cable parameters. However, the inverter, cable and motor are generally not provided by the same manufacturer or seller. The uncertainty of the switching characteristics of the inverter, cable parameters and length makes the selection of filter parameters unstable. There is no systematic research report on the relationship between the filter parameters and the voltage or current characteristics of the motor terminals. This paper mainly studies the influence of the filter parameters on the voltage characteristics of the motor terminals under different cable lengths, determines the relationship between the cable length, the resistance and capacitance of the filter and the overvoltage amplitude and pulse rise time of the motor terminals, finds out the selection range of the filter parameters, and provides experimental basis and theoretical basis for the manufacture and use of variable frequency speed regulation drive systems.

2 Experimental research and analysis

In the PWM variable frequency speed regulation drive system, the reason why the motor terminals generate high-frequency oscillation overvoltage can be well explained by the transmission line theory and further confirmed by experimental research. It is one of the reasons for the premature damage of the motor insulation. Therefore, in order to extend the life of the motor, in addition to improving the insulation level of the motor itself, it is also necessary to suppress the overvoltage surge impact as much as possible.

2.1 Equivalent circuits of filters and drive systems

Installing an impedance matcher on the motor terminal can greatly weaken the overvoltage. The simplest way is to connect a resistor in parallel that is close to the wave impedance of the cable. However, since the wave impedance of the cable (line) is very small, generally 10Ω~500Ω, the power consumption on the parallel resistor is very large, reaching hundreds to thousands of watts. Therefore, a pure resistance matcher is generally not used, and a first-order RC low-pass filter is usually used.

The passive low-pass first-order damping filter is a resistor and a capacitor connected in series and connected to the motor terminal phase-to-phase. According to the Petersen rule of the primary wave process of the transmission line, the filter, the inverter, the cable and the motor form an equivalent circuit as shown in Figure 1, where 2US is the equivalent power supply voltage, US is the inverter output voltage, Z0 is the equivalent cable wave impedance, Zm is the motor winding wave impedance, Rf is the filter resistor, and Cf is the filter capacitor.

Figure 1 Equivalent circuit of the primary wave process

Figure 2 Relationship between the voltage rising edge waveform on the motor terminal and the filter capacitor Cf and resistor Rf

(a) Cf = 0.08 μF (b) Cf = 0.02 μF

(c) Cf=0.005μF (d) Cf=0.001μF

Previous studies have confirmed that under the carrier frequency (600Hz~15kHz) of the general PWM drive inverter, the average pulse width is more than tens of microseconds, and the high-frequency oscillation process generated by the wave process generally takes about ten microseconds. Therefore, when analyzing the wave process of the continuous pulse wave output by the PWM inverter, it can be represented by a step wave process.

The wave impedance Zc of the cable can be obtained by measuring the capacitance C0 and inductance L0 per unit length. This paper uses a low-voltage three-phase PVC insulated sheathed cable and measures that the phase-to-phase C0 is about 7.6×10-11F/m and L0 is about 6.5×10-7H/m. Therefore, according to Zc=(L0/C0)1/2, Zc is about 92Ω. Considering that the power supply has a very small internal impedance, the equivalent cable wave impedance Z0 in Figure 1 can be approximately taken as 100Ω. Since the motor is an inductive load, its wave impedance Zm is much greater than the wave impedance of the cable.

2.2 Effect of filter parameters on terminal voltage waveform

For voltage waves with steep rising edges, the filter capacitor Cf can be considered as zero wave impedance, which is equivalent to a short circuit. If the resistance of the filter resistor Rf is equal to the wave impedance of the cable, and the wave impedance of the motor is much larger than Rf, the load impedance is approximately Rf. In this way, the load impedance at the end of the cable matches the wave impedance of the cable, and no total reflection of the voltage wave will occur at the motor terminals, and no overvoltage will be formed.

However, how to determine the capacitance of the filter? In principle, the larger the capacitance value, the better the impedance matching and the smaller the overvoltage. However, as the capacitance value increases, the power consumption of the resistor increases, because under continuous rectangular pulse voltage, the total power consumption P of the filter resistor can be approximately expressed as P=3CfUo2fs (1)

Where fs is the carrier frequency of the inverter, which is about 600Hz~5kHz for ordinary inverters, about 8kHz~15kHz for low-noise inverters, and up to 20kHz for special inverters. If Uo is 400V, Cf is 0.1μF, and fs is 1kHz and 10kHz respectively, then the total power consumption on the resistor is 48W and 480W respectively according to formula (1). As the power consumption of the resistor increases, the size of the filter component also increases accordingly. Therefore, in the application of small variable-frequency speed-regulating motors, the power consumption factor cannot be ignored.

In practical applications, if the filter is not specially designed, a satisfactory matching effect cannot be achieved. That is to say, the degree of filter mismatch will affect the suppression effect of overvoltage on the motor terminals. In this paper, under different cable lengths (30m, 45m and 75m), the resistance Rf is 75Ω, 100Ω, 150Ω and 350Ω respectively, and the capacitance Cf is 0.001μF~0.16μF. The waveform of the voltage on the motor terminals, the amplitude of the rising overvoltage, and the change of the rise time are measured respectively.

Figure 2 shows the relationship between the waveform of the rising edge of the phase-to-phase voltage on the motor terminals and the filter resistance, where the cable length is 45m and the filter capacitances are 0.08μF, 0.02μF, 0.005μF and 0.001μF respectively.

As can be seen from Figure 2, when the filter resistance is approximately equal to or less than 100Ω, the filter capacitance has a significant effect on the amplitude and waveform of the high-frequency oscillation. As the filter capacitance decreases, the amplitude of the high-frequency oscillation increases and the filtering effect becomes worse. When the filter resistance is much greater than 100Ω, the filter capacitance has little effect on the amplitude and waveform of the oscillation.

Figure 4 Relationship between the voltage rise time on the motor terminal and the filter resistance and capacitance

Figure 3 Relationship between the overvoltage ratio (Ump/Ums) on the motor terminals and the filter resistance Rf and capacitance Cf

In order to further study the relationship between the resistance and capacitance of the filter and the voltage characteristics at the motor terminals, the overvoltage multiple and voltage rise time of the voltage rising edge at the motor terminals will be measured under different filter resistance and capacitance.

2.3 Relationship between filter parameters and overvoltage on terminals

According to the above method, when the cable length is 30m and 75m respectively, the waveform of the rising edge of the voltage on the motor terminal is measured under different filter resistance and capacitance, so as to obtain the relationship curve between the overvoltage ratio of the rising edge of the voltage on the motor terminal and the filter resistance and capacitance, as shown in Figure 3, where the overvoltage ratio is the ratio of the voltage peak Ump on the rising edge to the steady-state value Ums (that is, approximately equal to the output voltage amplitude of the inverter).

It can be clearly seen from Figure 3 that the larger the filter capacitance Cf and the smaller the filter resistance Rf, the smaller the overvoltage ratio. In addition, the longer the cable length L, the slightly larger the overvoltage ratio. In this way, when the cable length is 75m, if Cf is greater than 0.02μF and Rf is less than 150Ω, the overvoltage ratio will not exceed 1.2. 2.4 Relationship between filter parameters and voltage rise time on the terminal

Similarly, when the cable lengths are 30m and 75m respectively, the waveform of the voltage rising edge on the motor terminal is measured under different filter resistances and capacitances, thereby obtaining the relationship curve between the voltage rising edge time on the motor terminal and the filter resistance and capacitance, as shown in Figure 4.

It can be clearly seen from Figure 4 that the smaller the resistance value Rf of the filter, the larger the rise time tr, and it increases with the increase of the capacitance value Cf of the filter, and when Cf exceeds 0.01μF, tr tends to saturation; when Rf is greater than 150Ω, the rise time has almost nothing to do with the capacitance value; in addition, the longer the cable length L, the longer the rise time. In this way, when the cable length is 75m, if Cf is greater than 0.01μF and Rf is 100Ω, the rise time exceeds 0.9μs, which is twice that before filtering (about 0.45μs).

2.5 Selection of filter Rf and Cf

From the above test results, it can be seen that the smaller the filter resistance value Rf, the larger the capacitance value Cf, and the shorter the cable length L, the smaller the overvoltage rate on the motor terminal. Moreover, the smaller Rf, the larger Cf, the larger the rise time, that is, the smaller the voltage rise rate (dv/dt). If the cable length is about 75m, the filter capacitance value Cf is 0.02μF, and Rf is approximately 100Ω, then the overvoltage rate on the motor terminal is reduced from 1.8 before filtering to 1.2, and the rise time is increased from 0.45μs before filtering to 0.9μs, then the voltage rise rate is reduced to 1/3 before filtering, which is conducive to reducing the damage of overvoltage to motor insulation.

3 Conclusion

The RC first-order damping filter can effectively suppress the high-frequency oscillation overvoltage on the terminals of the variable frequency speed regulating motor. The smaller the resistance value of the filter and the larger the capacitance value, the smaller the overvoltage amplitude. When the capacitance of the filter is greater than a certain value (such as 0.02μF), the overvoltage amplitude decreases with the decrease of the filter resistance value, and tends to the power supply voltage value when the resistance value is equal to or less than the wave impedance of the cable, and increases slightly with the increase of the cable length, while the rise time increases with the decrease of the filter resistance value and increases with the increase of the cable length. Considering the power consumption of the filter, the capacitance value should not be too large and should be less than 0.1μF.