Power Electronics

Syllabus

Static V-I characteristics and gating circuits for thyristor, MOSFET and IGBT; DC-DC conversion (buck, boost, buck-boost); single and three-phase uncontrolled rectifiers; voltage and current commutated thyristor converters; bidirectional AC-DC voltage source converters; line current harmonics; power factor and distortion factor of AC-DC converters; single and three-phase voltage and current source inverters; sinusoidal PWM.

Key concepts and formulas

Devices. The SCR turns on with a gate pulse when forward biased and turns off only when its current falls below the holding current (latching current > holding current). MOSFETs are voltage-controlled and fast (low-voltage, high-frequency use); IGBTs combine MOS gate drive with bipolar conduction (medium power and frequency).

Controlled rectifiers (supply peak V_m, firing angle α, continuous conduction unless stated):

A full converter inverts (negative average voltage, power flows back to the AC side) for α > 90°.

DC-DC converters (duty ratio D, continuous conduction, ideal):

• Buck: V_o = DV_s
• Boost: V_o = V_s/(1 − D)
• Buck-boost: V_o = −DV_s/(1 − D) (polarity reversed)
• Buck inductor ripple ΔI = V_sD(1 − D)/(Lf).

Inverters. Single-phase full-bridge square wave: the fundamental RMS is 0.9V_dc (peak 4V_dc/π), and only odd harmonics appear. Sinusoidal PWM: modulation index m_a = V_control/V_carrier; for m_a ≤ 1 the fundamental amplitude is m_aV_dc (full bridge) or m_aV_dc/2 (per half bridge leg).

Harmonics and power factor. Total harmonic distortion THD = √(I_rms² − I₁²)/I₁. Power factor = distortion factor × displacement factor = (I₁/I_rms) × cos φ₁. A square-wave line current (as with a single-phase full converter on a highly inductive load) has I₁/I_rms = 2√2/π ≈ 0.9, and its displacement angle equals α.

Worked example

A single-phase full converter on a 230 V, 50 Hz supply feeds a highly inductive load at α = 30°: find V_dc and the input power factor. Find the outputs of buck, boost and buck-boost converters with V_s = 24 V and D = 0.4, and the V_dc of a three-phase full converter on 415 V at α = 45°.

import math

Vm = 230 * math.sqrt(2)
a = math.radians(30)
print(f"full converter Vdc = {2 * Vm / math.pi * math.cos(a):.2f} V")
print(f"input power factor = {2 * math.sqrt(2) / math.pi * math.cos(a):.4f}")
Vs, D = 24, 0.4
print(f"buck = {D * Vs:.2f} V, boost = {Vs / (1 - D):.2f} V, buck-boost = {-D * Vs / (1 - D):.2f} V")
VL = 415
print(f"3-phase full converter Vdc = {3 * math.sqrt(2) * VL / math.pi * math.cos(math.radians(45)):.2f} V")

full converter Vdc = 179.33 V
input power factor = 0.7797
buck = 9.60 V, boost = 40.00 V, buck-boost = -16.00 V
3-phase full converter Vdc = 396.30 V

Practice questions