In our last blog post, we delved into how pulse width modulation (PWM) causes current ripple in permanent magnet (PM) motors and can lead to increased motor heating. Finishing our blog series, we offer strategies to reduce the magnitude of current ripple.

Reducing Current Ripple Magnitude

Maximum current ripple occurs when the back-EMF voltage (V_BEMF) and the voltage drop across R are minimum and the PWM duty cycle is 50%. Under these conditions, the peak-to-peak magnitude (ΔI) of the current ripple (CR) is given by:

$$\Delta I \approx \frac{V_{BUS}}{4 * L * f_{PWM}}$$

Where:

ΔI is the peak-to-peak magnitude
V_BUS is the bus voltage
L is the inductance
f_PWM is the pulse width modulation frequency

As an example, assume V_BUS = 180 V, f_PWM = 20 kHz and the current ripple approximates a triangular wave with an RMS value of 0.6 × ΔI. A moderate-to-high inductance winding of 10 mH would have a CR_RMS of 0.225 A. A low inductance winding of 0.5 mH would have a CR_RMS of 4.5 A. Because the heat produced in the motor winding is proportional to I²R, the losses generated in low-inductance motors can be significant.

There are several options to reduce current ripple without changing the motor:

Increase the PWM frequency
Lower the bus voltage
Add external inductors

Increasing PWM Frequency

Some drives use high PWM frequencies (20-100 kHz) to reduce current ripple in low-inductance motors. Figure 1 shows that for the same PWM duty cycle, doubling the frequency reduces the amount of time the current rises relative to the L/R time constant and lowers the current ripple magnitude.

Figure 1

It is important to note that the transistors in the drive's power stage are not ideal switches.

Their "on" resistance is finite and causes conduction losses.
They do not switch instantaneously. When switched, the transistor briefly conducts current and causes switching losses during the PWM edges.

The conduction losses are unaffected by the PWM frequency. However, as frequency increases, the switching losses increase as well because there are more edge transitions in a given time.

Switching losses can be significant and their magnitude depends on the transistor technology and whether the drive uses PWM edge shaping to soften the transitions and reduce radiated emissions. Drives featuring programmable PWM switching frequency will provide power loss derating curves in the datasheet which can support selection of an appropriate heatsink.

Optimizing Bus Voltage

Minimizing V_BUS is an effective solution to lowering current ripple without drawbacks, but the voltage must be high enough to achieve the desired peak torque (T_PK) while opposed by the maximum back-EMF. At steady state, V_BUS can be calculated as shown:

$$I_{MAX} = \frac{T_{PK}}{K_T}$$

$$V_{BUS} = I_{MAX} * R + K_E * \omega$$

Where:

ω is the maximum angular velocity of the application
K_T is the motor torque constant
K_E is the back-EMF motor constant

Adding External Inductors

If a drive does not support higher PWM rates, adding inductors in series with the motor winding is an option. The additional inductance can significantly reduce current ripple, but as a consequence increases resistance and lowers efficiency. Keep in mind that external inductors increase wiring complexity and are bulky in high-power applications. After installing inductors, the drive current loop must be re-tuned.

Conclusion

Current ripple can cause significant motor heating in low-inductance motors. While increasing PWM switching frequency reduces current ripple, it increases switching losses in the drive. A larger heatsink may be required to compensate for these losses. Optimizing bus voltage to the minimum required by the application is an effective strategy with no downside. As a last resort, use external inductors to reduce current ripple.

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