Modeling and Control of Single-Phase Rectifiers and Inverters Course

Lesson 1 • Review of Circuit Analysis Essentials

Covers Kirchhoff's laws, phasor analysis, and Thevenin/Norton equivalents applied to AC-DC circuits. Establishes the mathematical toolkit used throughout the course.

Lesson 2 • Semiconductor Switches in Power Circuits

Introduces diodes, thyristors, MOSFETs, and IGBTs as ideal and practical switches. Connects device behaviour to converter topology selection.

Lesson 3 • Power Quality Metrics and Standards

Defines THD, power factor, crest factor, and harmonic distortion indices for single-phase systems. Provides the evaluation criteria applied in later converter design chapters.

Lesson 1 • Capacitive Filter Design

Analyses the effect of a DC-side filter capacitor on output ripple and input current distortion. Quantifies the trade-off between ripple reduction and harmonic injection.

Lesson 2 • Full-Wave Bridge Rectifier Analysis

Examines the four-diode bridge topology for both resistive and inductive loads. Connects bridge operation to improved ripple and higher average output voltage.

Lesson 3 • Transformer Utilisation and Ratings

Evaluates transformer utilisation factor and secondary current waveform distortion in rectifier circuits. Links transformer sizing to converter efficiency and cost.

Lesson 1 • Fully Controlled Bridge Rectifier

Derives output voltage and current for the four-thyristor bridge across continuous and discontinuous conduction modes. Addresses inverter mode operation for energy regeneration.

Lesson 2 • Firing Circuit Design and Synchronisation

Covers zero-crossing detection, ramp-comparator firing circuits, and digital pulse generation for thyristor control. Connects synchronisation accuracy to output voltage regulation.

Lesson 3 • Thyristor Firing Angle Fundamentals

Defines firing angle alpha and derives output voltage as a function of alpha for resistive loads. Establishes the control variable used in all subsequent controlled rectifier analysis.

Lesson 4 • Performance Metrics and Load Regulation

Evaluates voltage regulation, efficiency, and form factor across the firing angle range. Provides design criteria for selecting converter topology and control strategy.

Lesson 1 • Input Impedance and Source Interaction

Models the rectifier input impedance and analyses interaction with the AC source impedance. Identifies conditions for instability caused by negative incremental input resistance.

Lesson 2 • State-Space Averaging Technique

Introduces the averaging method to eliminate switching harmonics and obtain a continuous-time model. Applies the technique to the single-phase rectifier with an LC output filter.

Lesson 3 • Transfer Function Derivation

Derives Bode plots of control-to-output and audio susceptibility transfer functions. Connects frequency-domain characteristics to stability and disturbance rejection requirements.

Lesson 1 • Lead-Lag and Type-II Compensators

Designs lead-lag networks and type-II compensators for improved phase margin and low-frequency gain. Addresses practical implementation in analogue and digital circuits.

Lesson 2 • PID Compensator Design

Applies frequency-domain loop-shaping to design PID compensators meeting bandwidth and phase margin targets. Connects Bode plot analysis to time-domain transient performance.

Lesson 3 • Digital Control Implementation

Covers sampling, quantisation, computational delay, and discrete-time compensator design for microcontroller-based rectifier control. Links digital effects to achievable bandwidth.

Lesson 4 • Closed-Loop Performance Verification

Validates controller designs through simulation and hardware-in-the-loop testing against load step and input disturbance specifications. Confirms stability margins under parameter variation.

Lesson 1 • Full-Bridge Inverter Operation

Analyses the four-switch H-bridge producing bipolar and unipolar output voltage waveforms. Compares switching losses and harmonic content between the two modulation schemes.

Lesson 2 • Output Filter Design for Inverters

Designs LC and LCL output filters to attenuate switching harmonics and produce a sinusoidal output voltage. Addresses filter resonance damping and its impact on control bandwidth.

Lesson 3 • Dead-Time Compensation Techniques

Quantifies dead-time-induced voltage error and presents feedforward and feedback compensation methods. Connects compensation accuracy to output voltage THD reduction.

Lesson 4 • Multilevel Inverter Concepts

Introduces the neutral-point-clamped and cascaded H-bridge multilevel topologies for reduced harmonic content. Provides a foundation for advanced modulation strategies in later chapters.

Lesson 1 • Random and Spread-Spectrum PWM

Introduces randomised carrier frequency and phase techniques to spread harmonic energy and reduce acoustic noise. Evaluates EMI and filter design implications.

Lesson 2 • Selective Harmonic Elimination PWM

Formulates and solves nonlinear equations to eliminate specific low-order harmonics by optimising switching angles. Demonstrates superior harmonic performance at low switching frequencies.

Lesson 3 • Space-Vector PWM for Single-Phase Systems

Adapts the space-vector concept to single-phase inverters using a fictitious two-phase representation. Compares SV-PWM harmonic performance with SPWM.

Lesson 4 • Sinusoidal PWM Fundamentals

Derives switching instants by comparing a sinusoidal reference with a triangular carrier and analyses the resulting harmonic spectrum. Establishes the baseline modulation method for the chapter.

Lesson 1 • Current Control in the Stationary Frame

Implements proportional-resonant and repetitive controllers to achieve zero steady-state error for sinusoidal current references. Connects resonant controller tuning to harmonic rejection capability.

Lesson 2 • Anti-Islanding Detection Methods

Presents passive and active anti-islanding schemes required by grid interconnection standards. Evaluates detection speed, non-detection zone, and power quality impact of each method.

Lesson 3 • Active and Reactive Power Control

Derives instantaneous power expressions and designs outer power control loops for unity and variable power factor operation. Links power references to current reference generation.

Lesson 4 • Grid Synchronisation Techniques

Covers zero-crossing detection, phase-locked loops, and second-order generalised integrators for single-phase grid synchronisation. Accurate synchronisation is prerequisite to all grid-tied control strategies.