POWER ELECTRONICS (EC-604 (C)) - Unit 4 Short Notes

UNIT 4: POWER ELECTRONICS CONVERTERS AND DEVICES

(Exam-focused short notes based on RGPV past papers)

1.0 Power Semiconductor Devices

1.1 Thyristor (SCR)

• Structure: Four-layer (p-n-p-n) device with three terminals: Anode (A), Cathode (K), Gate (G).

• Static V-I Characteristics:

  • Forward Blocking: Anode positive w.r.t. cathode, junction J2 reverse-biased. Small forward leakage current.

  • Forward Conducting: Triggered by gate signal or exceeding breakover voltage. Low forward voltage drop (~1–2 V).

  • Reverse Blocking: Reverse voltage blocked until reverse breakdown (high voltage rating).

• Dynamic Switching:

  • Turn-on Time \( t_{on} = t_d + t_r \) (delay + rise).

  • Turn-off Time \( t_{off} = t_q + t_{rr} + t_{fr} \) (recovery + fall).

• Turn-on Methods:

  • Gate Triggering: Most common (positive gate current).

  • dv/dt Triggering: False turn-on if \( dv/dt > \text{rating} \).

  • di/dt Triggering: High di/dt causes local heating.

  • Thermal Triggering: High temperature reduces breakover voltage.

• Turn-off Methods:

  • Natural Commutation: AC supply reverses polarity (line commutation).

  • Forced Commutation: External circuit forces anode current to zero (e.g., resonant, pulse commutation).

• Firing Circuits:

  • R-type: Simple, fixed firing angle.

  • RC-type: Variable firing angle with phase shift.

  • UJT-based: Pulse generation for precise triggering.

• Protection:

  • Overcurrent: Fast-acting fuses, circuit breakers.

  • Overvoltage: Snubbers (RC), surge arresters.

  • dv/dt: RC snubber across anode-cathode.

  • di/dt: Series inductor.

• Series/Parallel Operation:

  • Challenges: Static/dynamic voltage/current imbalance.

  • Equalizing Circuits:

    • Static: Shunt resistor \( R \) for steady-state voltage sharing.

    • Dynamic: RC network for transient balancing.

    • Derivation: For dynamic equalization, \( C = \frac{\Delta Q}{\Delta V} \), \( R = \sqrt{\frac{L}{C}} \) (damping).

• Applications: AC/DC converters, inverters, choppers, motor drives.

[!TIP]

Common Pitfall: Exceeding \( dv/dt \) rating causes unintended turn-on. Always use snubbers.

Exam Focus: Derive equalizing resistor \( R \) and capacitor \( C \) values.

1.2 Power MOSFET

• Structure: n-channel (most common) or p-channel. Vertical structure with source, drain, gate.

• Characteristics:

  • Transfer: \( I_D = K (V_{GS} - V_{th})^2 \) (quadratic in saturation).

  • Output: Ohmic region (linear) and saturation.

• Switching: Fast (nanoseconds), voltage-controlled, high input impedance.

• Advantages: High switching speed, low drive power, no second breakdown.

• Limitations: High on-resistance, limited voltage/current ratings.

• Applications: Switch-mode power supplies (SMPS), DC-DC converters, low-power inverters.

1.3 IGBT

• Structure: MOSFET gate + BJT output. Combines high input impedance of MOSFET with low saturation voltage of BJT.

• V-I Characteristics: Similar to BJT but voltage-controlled.

• Transfer: \( I_C = K (V_{GE} - V_{th}) \) (linear in active region).

• Switching: Turn-on/off times in microseconds. Switching losses significant at high frequency.

• Comparison:

  | Feature | MOSFET | IGBT | BJT | |---------|--------|------|-----| | Voltage Rating | Low | Medium | High | | Switching Speed | Very High | Medium | Low | | On-State Loss | High | Low | Low |

• Applications: Medium-power converters (e.g., motor drives, UPS).

1.4 GTO (Gate Turn-Off Thyristor)

• Structure: Modified SCR with gate that can turn off by applying negative current.

• Operation:

  • Turn-on: Positive gate pulse (like SCR).

  • Turn-off: High-current negative gate pulse (requires dedicated driver).

• V-I Characteristics: Similar to SCR but with gate turn-off capability.

• Applications: High-power inverters, choppers, traction drives.

1.5 Other Power Devices

• DIAC:

  • Bidirectional trigger diode. Conducts when breakover voltage exceeded in either direction.

  • Applications: TRIAC triggering in AC controllers.

• TRIAC:

  • Two SCRs back-to-back. Conducts in both half-cycles.

  • Modes: I+ (1st quadrant), I- (2nd), III+ (3rd), III- (4th).

  • Applications: Light dimmers, fan speed control.

• Power Diodes:

  • Standard: General rectification.

  • Fast Recovery: Reverse recovery time < 5 µs (used in switching supplies).

  • Schottky: Low forward drop, fast, low reverse voltage (high-frequency applications).

• LASCR (Light-Aggregated SCR):

  • Triggered by light (optically isolated).

  • Applications: High-voltage isolation, motor control.

• UJT:

  • Negative resistance device. Used in relaxation oscillators for SCR triggering.

2.0 Phase Controlled Rectifiers (AC-DC Converters)

2.1 Single-Phase Converters

• Half-Wave Controlled Rectifier:

  • R-load: \( V_{dc} = \frac{V_m}{\pi} (1 + \cos \alpha) \).

  • RL-load: Output voltage discontinuous if \( \omega L > R \).

• Full-Wave Half-Controlled Bridge: Two SCRs, two diodes.

  • RL-load: Freewheeling diode provides continuous current, improves PF.

• Full-Wave Fully Controlled Bridge:

  • R-load: \( V_{dc} = \frac{2V_m}{\pi} \cos \alpha \).

  • RL/RLE-load: Output voltage \( V_{dc} = \frac{2V_m}{\pi} \cos \alpha - \frac{2\omega L}{V_m} I_{dc} \) (with source inductance).

  • Rectification Mode: \( 0 \le \alpha \le 90^\circ \), power flows AC→DC.

  • Inversion Mode: \( 90^\circ < \alpha < 180^\circ \), power flows DC→AC (requires DC source).

• Effect of Source Impedance: Causes overlap angle \( \mu \), reduces output voltage:

  \[ V_{dc} = \frac{2V_m}{\pi} \cos(\alpha + \mu/2) \quad \text{(approx.)} \]

• Freewheeling Diode:

  • Provides path for load current during SCR off-period.

  • Improves PF by making load current unidirectional, reduces ripple.

[!TIP]

Key Formula: For single-phase full converter with RL load and no source inductance:

\[ > V_{dc} = \frac{2V_m}{\pi} \cos \alpha - \frac{2\omega L}{V_m} I_{dc} > \]

Rectification vs Inversion: Check firing angle range and power flow direction.

2.2 Three-Phase Converters

• Fully Controlled Bridge: Six SCRs.

• Continuous Constant Current:

  • Average output voltage:

    \[ V_{dc} = \frac{3\sqrt{6} V_{LL}}{\pi} \cos \alpha \]

    where \( V_{LL} \) = line voltage RMS.

  • For \( \alpha = 45^\circ \), \( V_{dc} = 1.654 V_{LL} \cos 45^\circ = 1.17 V_{LL} \).

• Effect of Source Inductance: Overlap angle \( \mu \) given by:

  \[ \cos \alpha - \cos(\alpha + \mu) = \frac{\omega L_s I_{dc}}{V_m} \]

  where \( V_m \) = peak phase voltage.

• Performance Parameters:

  • Ripple Factor: Lower than single-phase due to higher pulse number.

  • Power Factor: \( PF = \cos \phi \cdot \text{distortion factor} \).

  • Harmonics: Dominant 6th, 12th, etc.

2.3 Performance Evaluation

• Harmonic Analysis: Output voltage harmonics at \( 6k \pm 1 \) pulses for three-phase.

• Power Factor Improvement:

  • Use freewheeling diode (for RL loads).

  • Phase control technique (adjust \( \alpha \)).

• Applications: DC motor drives, battery charging, HVDC transmission.

3.0 AC Voltage Controllers

3.1 Single-Phase AC Voltage Controllers

• Phase Control:

  • SCRs triggered at delay angle \( \alpha \) each half-cycle.

  • RMS Output Voltage (full-wave bridge):

    \[ V_{rms} = V_s \sqrt{\frac{1}{2\pi} \left( \pi - \alpha + \frac{\sin 2\alpha}{2} \right)} \]

  • Input Power Factor (RL load):

    \[ PF = \frac{V_{rms} I_{rms} \cos \phi}{V_s I_s} \quad \text{(displacement + distortion)} \]

• On-Off Control (Integral Cycle):

  • Whole cycles applied/blocked. Low harmonic content, slow response.

• Firing Angle for Given Power (R-load):

  \[ P = \frac{V_s^2}{R} \cdot \frac{1}{2\pi} \left( \pi - \alpha + \frac{\sin 2\alpha}{2} \right) \]

  Solve for \( \alpha \).

[!EXAMPLE]

Given: \( R = 5\Omega \), \( V_s = 230V \), \( P = 5kW \).

\[ > \frac{P R}{V_s^2} = \frac{5000 \times 5}{230^2} = 0.472 > \]

Solve: \( \frac{1}{2\pi} \left( \pi - \alpha + \frac{\sin 2\alpha}{2} \right) = 0.472 \) → \( \alpha \approx 70^\circ \).

3.2 Advanced Control Techniques

• Two-Stage Sequence Control:

  • Two SCRs in series per half-cycle. First SCR conducts for \( \alpha_1 \), second for \( \alpha_2 \).

  • Improves PF for RL loads by reducing phase shift.

• Anti-Parallel Thyristors:

  • Two SCRs in anti-parallel.

  • Output Voltage Derivation:

    \[ V_o = \frac{1}{\pi} \left[ \int_\alpha^\pi V_m \sin \omega t \, d\omega t + \int_{\pi+\alpha}^{2\pi} (-V_m \sin \omega t) \, d\omega t \right] = \frac{2V_m}{\pi} \cos \alpha \]

  • Used for bidirectional control.

3.3 Performance and Applications

• Harmonics: Rich in odd harmonics; use filters.

• Applications: Heating (resistance welding), lighting dimmers, fan/ pump speed control.

4.0 Inverters (DC-AC Converters)

4.1 Single-Phase Inverters

• Half-Bridge: Two capacitors provide midpoint. Output voltage \( \pm V_{dc}/2 \).

• Full-Bridge: Four switches. Output voltage \( \pm V_{dc} \).

• Resistive Load: Square wave output.

• Inductive Load: Current continuous, displaced; output current lags voltage.

4.2 Three-Phase Inverters

• 120° Conduction Mode:

  • Each SCR conducts 120°.

  • Switching Sequence: T1→T2→T3→T4→T5→T6 (each 60° shift).

  • Line Voltage Waveform: Rectangular pulses of amplitude \( V_{dc} \), width 120°, with 60° gaps.

  • RMS Phase Voltage (star load):

    \[ V_{ph,rms} = \frac{V_{dc}}{\sqrt{6}} \]

  • RMS Load Current: \( I_{ph,rms} = \frac{V_{ph,rms}}{R} \).

  • Load Power: \( P = 3 I_{ph,rms}^2 R \).

• 180° Conduction Mode:

  • Each SCR conducts 180°.

  • Comparison: Higher output voltage, more switching losses, simpler commutation.

[!EXAMPLE]

Given: \( V_{dc} = 200V \), star-connected \( R = 10\Omega/\text{phase} \), 120° mode.

\[ > V_{ph,rms} = \frac{200}{\sqrt{6}} = 81.65V, \quad I_{ph,rms} = 8.165A, \quad P = 3 \times (8.165)^2 \times 10 = 2000W. > \]

4.3 Inverter Types

• Voltage Source Inverter (VSI):

  • DC voltage source with filter capacitor.

  • Output voltage fixed, current varies with load.

  • Advantages: Easy control, multiple outputs, regenerative capability.

• Current Source Inverter (CSI):

  • DC current source with large inductor.

  • Output current fixed, voltage varies.

  • Applications: High-power drives, synchronous motor control.

• Self-Commutated Inverters: Use devices with gate turn-off (GTO, IGBT, MOSFET). No separate commutation circuit needed.

4.4 Pulse Width Modulation (PWM) Inverters

• Principle: Vary pulse width to control fundamental amplitude.

• Sinusoidal PWM: Compare sinusoidal reference with triangular carrier.

• Advantages over Square-Wave:

  • Harmonic reduction (lower THD).

  • Output voltage control without changing DC link.

• Modified Sinusoidal PWM: Notching to eliminate selected harmonics.

4.5 Special Inverters

• McMurray-Bedford Inverter:

  • Uses auxiliary commutation circuit (capacitor, inductor).

  -适用于 high-power applications with forced commutation.

• Series Resonant Inverter:

  • Load in series with LC tank.

  • At resonance, output current \( I_o = \frac{V_s}{R} \) (purely resistive).

  • Example: \( f_s = 10kHz \), \( V_s = 100V \), \( R = 20\Omega \) → \( I_o = 5A \).

• Three-Phase Series Inverter:

  • Each phase has series resonant circuit.

  • Used for high-frequency applications.

4.6 Harmonic Reduction Techniques

• Multiple Pulse Modulation: Double/triple pulse per half-cycle.

• PWM Techniques: Selective Harmonic Elimination (SHE).

• Filters:

  • Passive: LC tuned filters at harmonic frequencies.

  • Active: Inject compensating currents.

• THD Reduction: Target \( \text{THD} < 5\% \) for grid-connected inverters.

5.0 Choppers (DC-DC Converters)

5.1 Basic Topologies

• Step-Down (Buck):

  • \( V_{avg} = \alpha V_s \).

  • Output voltage always less than input.

• Step-Up (Boost):

  • \( V_{avg} = \frac{V_s}{1 - \alpha} \).

  • Output voltage greater than input.

• Buck-Boost:

  • \( V_{avg} = \frac{\alpha}{1 - \alpha} V_s \), polarity reversed.

5.2 Classification of Choppers

5.3 Analysis and Calculations

• Continuity Check:

  \[ \Delta i = \frac{V_s - E}{L} T_{on} \quad \text{(if continuous, } I_{min} > 0\text{)} \]

  More accurately, solve inductor dynamics.

• Average Output Current (Type-A, continuous):

  \[ I_{avg} = \frac{\alpha V_s - E}{R} \]

• Max/Min Current:

  \[ I_{max} = I_{avg} + \frac{\Delta i}{2}, \quad I_{min} = I_{avg} - \frac{\Delta i}{2} \]

  where \( \Delta i \approx \frac{V_s - E}{L} T_{on} \) (approximation for small R).

• Chopper Efficiency:

  \[ \eta = \frac{V_{avg} I_{avg}}{V_s I_{avg} + \text{switching losses}} \approx \frac{V_{avg}}{V_s} \quad \text{(if switch drop } V_{on}\text{)}. \]

[!EXAMPLE]

Given: \( V_s = 220V \), \( T = 2000\mu s \), \( T_{on} = 600\mu s \), \( R = 1\Omega \), \( L = 5mH \), \( E = 24V \).

1. \( \alpha = 0.3 \).

2. \( I_{avg} = (0.3 \times 220 - 24)/1 = 42A \).

3. Solve exact equations (see Section 1.1 for method) → \( I_{min} \approx 32.6A > 0 \) → continuous.

4. \( I_{max} \approx 51A \).

5.4 Special Choppers

• Morgan Chopper:

  • Uses auxiliary capacitor for commutation.

  • Voltage and current waveforms show resonant turn-off.

• Jones Chopper:

  • For regenerative braking (Type-B operation).

  • Energy fed back to supply during off-period.

• Current Limit Control:

  • Maintains load current within limits by varying \( T_{on} \).

  • Advantages: Simple, protects device.

5.5 Applications

• DC motor speed control (armature/choping).

• Battery charging/discharging.

• Switched-mode power supplies (SMPS).

6.0 Cycloconverters (AC-AC Converters)

6.1 Single-Phase to Single-Phase

• Midpoint Configuration:

  • Two SCRs in each leg of transformer secondary.

  • Positive Converter: SCRs triggered in positive half-cycles.

  • Negative Converter: SCRs triggered in negative half-cycles.

  • Output Frequency: \( f_o = f_{in}/2 \) (for resistive load).

  • Waveforms: Output voltage consists of segments of input sine wave.

• Bridge Configuration:

  • Four SCRs in bridge.

  • Output frequency can be step-up or step-down.

  • Output Voltage Expression (resistive load):

    \[ v_o = \frac{V_m}{2} (\sin \omega t - \sin \omega t \text{ during blocking}) \]

    Average \( V_{dc} = \frac{V_m}{\pi} \cos \alpha \) for each converter group.

6.2 Three-Phase to Single-Phase

• Circuit: Six or more SCRs (three-phase supply).

• Operation:

  • Positive Group: SCRs triggered during positive half-cycles of respective phases.

  • Negative Group: SCRs triggered during negative half-cycles.

  • Phase control varies output voltage and frequency.

• Output Frequency: Typically \( f_o < f_{in} \) (step-down).

• Waveforms: Stepped approximation of sine wave.

6.3 Performance and Applications

• Advantages: High power, low speed synchronous motor drives.

• Limitations: Low output frequency (< 1/3 input), complex control, poor PF at low speeds.

• Applications: Rolling mills, ship propulsion, cement kilns.

7.0 Commutation and Protection Techniques

7.1 Commutation Methods

• Natural Commutation: AC supply provides reverse voltage (line commutation).

• Forced Commutation:

  • External Pulse: Auxiliary circuit injects pulse.

  • Resonant: LC circuit creates zero current/voltage.

  • Self-Commutated: Devices like GTO, IGBT turn off via gate signal.

• Self-Commutated Inverters: Use gate-turn-off devices; no separate commutation circuit.

7.2 Protection Circuits

• Overcurrent: Semiconductor fuses (fast blow), circuit breakers.

• Overvoltage: Surge arresters (metal oxide varistors), transient voltage suppressors.

• dv/dt Protection: RC snubber across device.

• di/dt Protection: Series inductor.

• Thermal Protection: Heat sinks, cooling fans, thermal sensors.

7.3 Equalizing Circuits

• Static Equalization: Shunt resistor \( R \) across each SCR in series string.

  \[ R = \frac{V_{max} - V_{min}}{I_{leakage}} \]

• Dynamic Equalization: RC network across each SCR.

  • Capacitor \( C \): Limits transient voltage difference.

    \[ C = \frac{\Delta Q}{\Delta V} \]

    where \( \Delta Q \) = charge imbalance.

  • Resistor \( R \): Damp oscillations, \( R = \sqrt{\frac{L}{C}} \).

• Derivation: From voltage balance during switching transients.

8.0 Switched-Mode Power Supplies (SMPS) and Regulators

8.1 SMPS Principles

• Comparison with Linear:

  • SMPS: High efficiency (80–90%), small size/weight (high frequency), complex control.

  • Linear: Low efficiency, large transformer, simple.

• Topologies:

  • Isolated: Flyback, forward (use transformer).

  • Non-Isolated: Buck, boost, buck-boost.

8.2 Regulator Types

• Buck Regulator:

  • \( V_{out} = \alpha V_{in} \) (continuous conduction).

• Boost Regulator:

  • \( V_{out} = \frac{V_{in}}{1 - \alpha} \).

• Buck-Boost:

  • \( V_{out} = \frac{\alpha}{1 - \alpha} V_{in} \), polarity reversed.

  • Used when \( V_{in} \) can be above or below \( V_{out} \).

8.3 Flyback SMPS

• Operation:

  • Switch ON: Energy stored in transformer primary (secondary diode reverse-biased).

  • Switch OFF: Energy transferred to secondary.

• Waveforms: Primary current ramps up; secondary current pulses.

• Design:

  • Turns ratio \( n = N_s/N_p \).

  • Duty cycle \( D \) limits.

  • Output voltage:

    \[ V_{out} = V_{in} \frac{n D}{1 - D} \]

    (continuous conduction).

9.0 Harmonics and Performance Metrics

9.1 Harmonic Analysis

• Sources: Switching action, non-linear loads.

• Effects: Heating, torque pulsations, EMI.

• THD Calculation:

  \[ \text{THD} = \frac{\sqrt{\sum_{n=2}^{\infty} I_n^2}}{I_1} \times 100\% \]

  for current; similarly for voltage.

9.2 Harmonic Reduction Methods

• Multiple Pulse Modulation: Double/triple pulse in converters.

• PWM Techniques: Sinusoidal PWM, SHE.

• Filters:

  • Passive: LC tuned at specific harmonics.

  • Active: Inject compensating currents.

• Hybrid: Combination of passive and active.

9.3 Performance Parameters

• Efficiency: \( \eta = \frac{P_{out}}{P_{in}} \times 100\% \).

• Power Factor:

  \[ PF = \cos \phi \cdot \frac{I_1}{I_{rms}} \quad \text{(displacement × distortion)} \]

• Ripple Factor (DC output):

  \[ RF = \frac{\sqrt{V_{rms}^2 - V_{dc}^2}}{V_{dc}} \]

• Form Factor: \( V_{rms}/V_{avg} \).

• Peak Factor: \( V_{peak}/V_{rms} \).

10.0 Applications and Design Considerations

10.1 Industrial Applications

• Motor Drives: DC/AC motor speed control (e.g., choppers for DC motors, inverters for AC motors).

• Power Supplies: SMPS for computers, telecom.

• UPS: Inverters for backup power.

• Renewable Energy: Solar inverters, wind turbine converters.

• HVDC Transmission: Line-commutated converters.

• Traction Drives: Electric vehicles, locomotives.

10.2 Design Aspects

• Device Selection:

  • Voltage/current ratings with derating factor (e.g., 0.1).

  • Number in series/parallel:

    \[ N_s = \frac{V_{total}}{V_{rating} \times (1 - \text{derating})}, \quad N_p = \frac{I_{total}}{I_{rating} \times (1 - \text{derating})} \]

• Heat Sinking: Air/liquid cooling, thermal resistance calculation.

• Snubber Design: RC or RCD for \( dv/dt \) and \( di/dt \) protection.

• PCB Layout: Minimize loop inductance, separate power/control grounds.

• Reliability: Protection coordination, redundancy.

• Optimization: Cost, size, weight trade-offs.

[!FINAL TIP]

Exam Strategy:

1. Derivations First: Master output voltage formulas for converters/inverters.

2. Waveforms: Sketch key waveforms (voltage/current) for each converter type.

3. Numerical Problems: Practice continuity checks, firing angle calculations, THD.

4. Device Comparison: Make a table for SCR, MOSFET, IGBT, GTO.

5. Applications Link: Relate each converter to real-world uses (e.g., chopper → DC motor drive).

All formulas boxed are high-yield for exams.