Modulation index and overmodulation
How much of the DC bus voltage you can actually use, and what happens when you ask for more.
- Explain modulation index and overmodulation at engineering level
- Read the numbers that define the behaviour
- Apply the idea to a real drive system
Overview
Every inverter has a hard ceiling on output voltage set by the DC-link voltage. The modulation index describes how close to that ceiling the drive is working, and pushing past the linear region changes the waveform's character.
In depth
Modulation index compares the commanded phase voltage peak to half the DC-link voltage. m = 1 is the edge of the linear SVPWM region.
Three regions
Below m ≈ 0.907 the inverter operates in the pure linear SVPWM region: harmonic content is clean and torque is smooth. Between roughly 0.907 and 1.0 the drive enters overmodulation, deliberately clipping the reference waveform to extract a bit more fundamental voltage at the cost of low-order harmonics. Beyond that, the pattern degenerates into six-step, the theoretical maximum.
Three-Phase Power Calculator
Real power from line voltage, line current and power factor.
P = √3 × V_line × I_line × cos φIn a balanced three-phase system the √3 factor relates line and phase quantities. The power factor accounts for the share of current that does no useful work.
Example: √3 × 400 V × 250 A × 0.95 ≈ 164.5 kW.
- Field-oriented control keeps the effective power factor high across the map.
- Apparent power (kVA) sizes the inverter; real power (kW) moves the car.
- Reactive current still heats the windings even though it does no work.
Key takeaways
- Modulation index compares commanded voltage to available DC-link headroom.
- Overmodulation trades harmonic cleanliness for extra usable voltage near top speed.
- Six-step is the practical ceiling of voltage utilisation.
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