Power Electronics study guide

What this area covers

Power Electronics covers the converters that sit between the grid and a growing share of its sources and loads: rectifiers feeding drives and DC systems, inverters connecting solar, storage and wind, and the harmonics and power-factor effects they bring. This area accounts for 5–8 questions on the exam. Deep switching theory matters less here than three practical skills: finding an average output voltage, reading a power factor correctly when the current is not sinusoidal, and judging how an inverter-based plant behaves next to a synchronous one.

The ideas everything else rests on

A rectifier's average output follows from the waveform. A three-phase full-wave bridge produces a six-pulse output whose average, for a phase-controlled bridge with firing angle α and continuous current, is

$$V_d = \frac{3\sqrt{2}}{\pi} V_{LL} \cos\alpha$$

With diodes, α is zero and the bridge gives about 1.35 times the line-to-line RMS voltage. Delaying the firing angle lowers the average, and beyond 90 degrees the bridge can invert, sending power back to the AC side.

Inverters build a sine from switched pulses. A voltage-source inverter switches a DC bus on and off quickly, and pulse-width modulation shapes the average of each pulse so the low-frequency content follows a sine wave. The modulation index sets the amplitude of the fundamental; in the linear range it scales directly with the index. Pushing past that range adds output voltage at the cost of low-order harmonics.

Power factor has two parts. When current is distorted, true power factor is the product of the displacement factor, the cosine of the angle between the fundamental voltage and current, and the distortion factor, the ratio of fundamental to total RMS current. A diode rectifier can have a displacement factor near one and still a poor true power factor. Capacitors fix displacement, not distortion, and can resonate with the system at a harmonic frequency.

Harmonics come in predictable orders. A six-pulse converter draws characteristic harmonics at orders 6k plus or minus 1, such as the 5th, 7th, 11th and 13th; a twelve-pulse arrangement cancels the 5th and 7th. Total harmonic distortion summarises them:

$$THD = \frac{\sqrt{\sum_{h \ge 2} I_h^2}}{I_1}$$

Harmonic limits are applied at the point of common coupling, the point where the utility serves more than one customer, not at each piece of equipment.

Inverter-based resources fault differently. A synchronous generator delivers several times rated current into a nearby fault, set by its reactances. An inverter-based resource delivers a controlled current, typically little above its rating, with a sequence makeup chosen by its control. Protection that relies on large fault current or on negative-sequence current from the source may see much less than it expects.

How to study it

1. Derive average output voltage for single-phase and three-phase bridges, controlled and uncontrolled, and check DC power against AC input power.
2. Sketch PWM waveforms at a few modulation indices and relate the fundamental amplitude to the DC bus voltage.
3. Compute displacement, distortion and true power factor for a rectifier load with a given harmonic spectrum. Use the Three-phase power calculator on the fundamental quantities.
4. Size a capacitor bank for displacement power factor with the Power-factor correction calculator, then check where the bank and the source inductance resonate.
5. Compute THD for current and voltage spectra, and practise deciding where a harmonic limit applies.
6. Finish by comparing fault contribution from a synchronous generator and an inverter-based plant of the same rating.

Mistakes that cost points

• Using phase voltage in the bridge equation. The three-phase bridge formula above uses line-to-line RMS voltage.
• Reporting displacement power factor as true power factor. With distorted current, the two differ, and the true value is always the lower.
• Expecting capacitors to cure harmonics. They improve displacement only, and a bank tuned by accident near a characteristic harmonic can amplify it.
• Assuming an inverter supplies fault current like a generator. Its contribution is limited and set by its controls.

References worth having

• IEEE Std 519 (harmonic control in electric power systems)
• IEEE Std 1547 and IEEE Std 2800 (interconnection of inverter-based resources)
• Mohan, Undeland and Robbins, Power Electronics: Converters, Applications, and Design