POWER ELECTRONICS (EC-604 (C)) - Unit 5 Short Notes

I. POWER SEMICONDUCTOR DEVICES & CHARACTERISTICS

A. Thyristor (SCR)

• Structure: Four-layer p-n-p-n device with terminals: anode (A), cathode (K), gate (G).

• Two-Transistor Analogy: Equivalent to pnp (Q₁) and npn (Q₂) transistors in positive feedback. Gate current triggers regenerative action.

• Static V-I Characteristics:

  • Forward Blocking: Region OA (leakage current until breakover voltage \(V_{BO}\)).

  • Forward Conducting: After triggering, low voltage drop (~1–2 V), high current.

  • Reverse Blocking: Blocks up to reverse breakdown voltage.

  • Latching Current (\(I_L\)): Minimum anode current to maintain conduction after gate pulse removal.

  • Holding Current (\(I_H\)): Minimum current to keep SCR ON; \(I_H < I_L\).

  • Breakover Voltage (\(V_{BO}\)): Forward voltage at which SCR turns ON without gate signal.

• Dynamic Switching Characteristics:

  • Turn-on time (\(t_{on}\)): Delay time (\(t_d\)) + rise time (\(t_r\)).

  • Turn-off time (\(t_{off}\)): Reverse recovery time (\(t_{rr}\)) + gate recovery time (\(t_{gr}\)).

• dv/dt and di/dt Ratings:

  • dv/dt rating: Max allowable rate of rise of anode-cathode voltage in forward blocking. Exceeding causes false triggering due to capacitive current.

    \boxed{\text{Protection: Snubber circuit (RC across SCR)}}

  • di/dt rating: Max allowable rate of rise of anode current during turn-on. Exceeding damages SCR due to localized heating.

    \boxed{\text{Protection: Series inductor or controlled gate drive}}

• Turning ON Methods: Gate triggering (most common), light triggering (LASCR), thermal (not used), dv/dt (undesired).

• Turning OFF Methods: Natural commutation (AC circuits), forced commutation (DC circuits: Classes A, B, C, D, E).

B. Other Thyristor Family Devices

• GTO (Gate Turn-Off Thyristor):

  • Structure: Similar to SCR but with heavily doped p⁺ layer near anode for efficient turn-off.

  • V-I Characteristics: Like SCR but can be turned OFF by negative gate pulse.

  • Applications: High-power inverters, motor drives.

• TRIAC:

  • Structure: Two SCRs in inverse parallel with common gate.

  • Operation Modes:

    • I⁺: Gate positive, MT2 positive.

    • I⁻: Gate positive, MT2 negative.

    • III⁺: Gate negative, MT2 positive.

    • III⁻: Gate negative, MT2 negative.

  • Applications: Light dimmers, fan speed control.

• DIAC:

  • Structure: Two-terminal device with symmetrical V-I characteristic.

  • Breakover voltage \(V_{BO}\) in both directions.

  • Applications: Triggering device for TRIACs in AC controllers.

C. Transistors

• Power MOSFET (n-channel):

  • Structure: Vertical channel, source, drain, gate, body.

  • Transfer Characteristics: \(I_D\) vs \(V_{GS}\); threshold voltage \(V_{th}\).

  • Switching: Voltage-controlled, fast switching, low drive power.

  • Applications: SMPS, motor drives.

• IGBT:

  • Structure: MOSFET gate controlling a bipolar transistor.

  • V-I Characteristics: Similar to BJT but with MOSFET input.

  • Advantages: Combines MOSFET input (high input impedance) with BJT output (low saturation voltage); suitable for high voltage/current.

D. Power Diodes

• Standard Recovery Diode: Slow reverse recovery; used in low-frequency rectifiers.

• Fast Recovery Diode: Short reverse recovery time (\(t_{rr}\)); used in high-frequency rectifiers.

• Schottky Diode: Low forward voltage drop (~0.3 V), fast switching, low reverse voltage rating; used in high-frequency SMPS.

II. SERIES & PARALLEL OPERATION OF THYRISTORS

• Need: To handle voltage/current exceeding single SCR rating.

• Series Operation Challenges:

  • Steady-state: Unequal voltage sharing due to leakage current differences.

  • Dynamic: Unequal voltage during switching due to junction capacitance differences.

• Equalizing Circuits:

  • Static: Shunt resistor \(R\) across each SCR.

  • Dynamic: RC network across each SCR.

    Derivation: Capacitor \(C\) equalizes dynamic voltage (voltage across capacitor same for all SCRs). Resistor \(R\) equalizes steady-state voltage (current through \(R\) compensates leakage current difference).

    \boxed{V_{C} = \text{constant during switching}}

    \boxed{I_{R} \propto \text{leakage current}}

• Parallel Operation Challenges:

  • Current sharing: Due to on-state voltage drop differences.

  • Solution: Use identical devices, add small series resistors.

• Derating Factor and String Efficiency:

  • Derating factor = \(1 - \frac{\text{Margin}}{\text{Rating}}\).

  • String efficiency = \(\frac{\text{Total string rating}}{\sum \text{Individual ratings}}\).

  • Numerical: Given total voltage \(V_T\), current \(I_T\), derating factor \(k\), number in series \(n_s = \frac{V_T}{k V_{SCR}}\), parallel \(n_p = \frac{I_T}{k I_{SCR}}\).

III. FIRING CIRCUITS & GATING

• Types of SCR Firing Circuits:

  • R-type: Simple, limited firing angle range.

  • RC-type: Wider firing angle range, improved stability.

  • UJT-based: Pulse generation for SCR.

• UJT Firing Circuit:

  • UJT characteristics: Negative resistance region between peak point (\(V_P\)) and valley point (\(V_V\)).

  • Operation: Capacitor \(C\) charges through \(R\); when voltage reaches \(V_P\), UJT conducts, discharging \(C\) through pulse transformer to trigger SCR.

  • Pulse width determined by \(R\) and \(C\).

• LASCR (Light-Activated SCR):

  • Triggered by light incident on gate region via optical fiber.

  • Applications: Opto-isolation, high-voltage switching.

IV. PHASE-CONTROLLED RECTIFIERS

A. Single-Phase Converters

• Half-wave uncontrolled (diode):

  \(V_{dc} = \frac{V_m}{\pi}\) (R load).

• Half-wave controlled (SCR):

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

• Full-wave Half-controlled (Semi-converter):

  • Circuit: Two SCRs, two diodes.

  • With RLE load:

    \boxed{V_{dc} = \frac{2V_m}{\pi} \cos \alpha}

    Continuous if \(L\) large.

  • Freewheeling diode provides path during negative half, improving PF.

• Full-wave Fully-controlled Bridge:

  • Circuit: Four SCRs.

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

  • With RL load: Same \(V_{dc}\) expression; current continuous if \(L\) large.

  • With RLE load:

    \boxed{V_{dc} = \frac{2V_m}{\pi} \cos \alpha - E}

  • Rectification mode: \(\alpha < 90^\circ\), power from AC to DC.

  • Inversion mode: \(\alpha > 90^\circ\), power from DC to AC (requires \(E > \frac{2V_m}{\pi} \cos \alpha\)).

  • Effect of source inductance (\(L_s\)):

    • Overlap angle \(\mu\): During overlap, two SCRs conduct, output voltage drops.

    • Volt-sec balance: \(V_m \sin(\alpha+\mu) - V_m \sin \alpha = \omega L_s I_{dc}\).

    • Average output voltage:

      \boxed{V_{dc} = \frac{2V_m}{\pi} \cos(\alpha+\mu) + \frac{3\omega L_s I_{dc}}{2\pi}} \quad (\text{approx.})

• Numerical:

  • For R/RL: \(V_{dc} = \frac{2V_m}{\pi} \cos \alpha\).

  • For RLE: \(V_{dc} = \frac{2V_m}{\pi} \cos \alpha - E\).

  • Input PF: \(\text{PF} = \frac{P_{in}}{V_s I_{s,rms}}\); for R load, \(\text{PF} \approx \cos \alpha\) (ignoring harmonics).

B. Three-Phase Converters

• Fully-controlled bridge converter:

  • Circuit: Six SCRs.

  • With continuous constant load current:

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

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

  • Waveforms: Each SCR conducts 120°; output voltage has six pulses per cycle.

  • Effect of source inductance (\(L_s\)):

    • Overlap angle \(\mu\):

      \(V_m \sin(\alpha+\mu) - V_m \sin \alpha = \omega L_s I_{dc}\) (per phase).

    • Output voltage:

      \boxed{V_{dc} = \frac{3\sqrt{6} V_{LL}}{\pi} \cos(\alpha+\mu) + \frac{3\omega L_s I_{dc}}{2\pi}}

  • Numerical: Given \(V_{LL}\), \(I_{dc}\), \(\alpha\), \(V_{dc}\), find \(L_s\) or \(R\).

V. AC VOLTAGE CONTROLLERS

A. Principle

• On-Off control: Entire cycles on/off; low output frequency.

• Phase control: Delay firing within each half-cycle; continuous output.

B. Single-Phase Circuits

• Half-wave controller: One SCR; output only during positive half when triggered.

• Full-wave controller:

  • Anti-parallel thyristors: Two SCRs in anti-parallel; control both half-cycles.

  • Operation with RL load:

    • Without freewheeling: Current discontinuous for \(\alpha > \phi\) (\(\phi = \tan^{-1}(\omega L/R)\)).

    • With freewheeling diode: Current continuous; diode conducts when thyristors off, improving PF.

  • Triac-based: Single Triac replaces two SCRs; same operation.

C. Analysis & Calculations

• RMS output voltage:

  • Resistive load:

    \boxed{V_{rms} = V_s \sqrt{1 - \frac{\alpha}{\pi} + \frac{\sin 2\alpha}{2\pi}}}

  • RL load with freewheeling (continuous):

    \boxed{V_{rms} = V_s \sqrt{\frac{\pi - \alpha}{2\pi} + \frac{\sin 2\alpha}{4\pi}}}

• Input power factor: \(\text{PF} = \frac{P_{out}}{V_s I_{s,rms}}\); for R load, \(\text{PF} = V_{rms}/V_s\).

• Firing angle from load power: For R load, \(P = V_{rms}^2/R\), solve for \(\alpha\).

• Numerical Example (from past papers):

  Given \(R = 5\ \Omega\), \(V_s = 230\ \text{V}\), \(P = 5\ \text{kW}\):

  \(V_{rms} = \sqrt{P R} = \sqrt{5000 \times 5} = 158.11\ \text{V}\).

  Solve \(158.11 = 230 \sqrt{1 - \alpha/\pi + \sin 2\alpha/(2\pi)}\) → \(\alpha \approx 92.5^\circ\).

  \(\text{PF} = V_{rms}/V_s = 158.11/230 = 0.688\).

D. Advanced Control

• Two-stage sequence control for RL load:

  • Two pairs of SCRs; first pair triggers at \(\alpha_1\), second at \(\alpha_2 > \alpha_1\).

  • Waveforms: Output voltage has two pulses per half-cycle.

  • Advantage: Better PF than single-stage for same \(V_{rms}\).

VI. DC CHOPPERS

A. Classification

• Step-down (Buck): \(V_o < V_s\).

• Step-up (Boost): \(V_o > V_s\).

• Buck-Boost: \(V_o\) can be > or < \(V_s\), polarity reversed.

B. Type-A Chopper (First Quadrant)

• Circuit: Switch (SCR/MOSFET) in series with load, diode across load.

• Operation:

  • ON (\(T_{on}\)): Source supplies load, inductor stores energy.

  • OFF (\(T_{off}\)): Inductor releases energy via diode.

• Waveforms: \(v_o = V_s\) when switch on, 0 when off (R load). For RLE, \(v_o\) continuous.

• Analysis:

  • Average output voltage:

    \boxed{V_o = V_s \frac{T_{on}}{T} = D V_s}

    where \(D = T_{on}/T\) (duty cycle).

  • For RLE load with continuous current:

    Volt-sec balance:

    \((V_s - E - I_{avg}R) T_{on} + (-E - I_{avg}R) T_{off} = 0\)

    \boxed{I_{avg} = \frac{V_s D - E}{R}}

  • Ripple current:

    \(\Delta I = \frac{(V_s - E - I_{avg}R) T_{on}}{L}\)

  • Continuity condition: \(I_{min} > 0\) → \(I_{avg} > \Delta I/2\).

• Numerical Example (repeated in past papers):

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

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

  \(\Delta I = \frac{(220-24-42) \times 0.6 \times 10^{-3}}{5 \times 10^{-3}} = 18.48\ \text{A}\).

  \(I_{min} = 42 - 9.24 = 32.76\ \text{A} > 0\) → continuous.

  \(I_{max} = 51.24\ \text{A}\), \(I_{min} = 32.76\ \text{A}\).

C. Type-B & Type-C Choppers

• Type-B (Second quadrant): Switch in series with load having back EMF \(E\); switch off, inductor current freewheels through diode; power from load to source. \(V_o = 0\) when switch on, \(V_s\) when off? Actually, output voltage always positive, current can be negative.

• Type-C (Two-quadrant): Combines Type-A and Type-B; operates in first and second quadrants.

D. Step-up Chopper (Boost)

• Circuit: Switch in series with source, inductor; diode from switch node to load.

• Operation:

  • ON: Source supplies inductor, load supplied by capacitor.

  • OFF: Inductor current flows through diode to load.

• Derivation: Volt-sec across \(L\):

  \(V_s T_{on} = (V_o - V_s) T_{off}\)

  \boxed{V_o = \frac{V_s}{1-D}}

E. Step-down Chopper (Buck)

• Circuit: Switch in series with source, load; diode across load for inductive loads.

• Derivation:

  \boxed{V_o = D V_s}

  With switch voltage drop \(V_{on}\): \(V_o = D (V_s - V_{on})\).

• Efficiency: \(\eta \approx D\) (ignoring losses).

F. Special Choppers

• Morgan chopper: Two switches, two diodes; for regenerative braking.

• Jones chopper: Two inductors; for high-power applications.

G. Control Techniques

• Current Limit Control (CLC): Switch on/off to keep current within limits; variable frequency.

VII. INVERTERS

A. Voltage Source Inverters (VSI)

• Single-Phase Bridge Inverter:

  • Resistive load: Four switches, 180° conduction; output voltage square wave, current in phase.

  • Inductive load: 180° conduction; output voltage square wave, current sinusoidal due to inductance.

• Three-Phase Bridge Inverter:

  • 120° Conduction Mode:

    • Each SCR conducts 120°.

    • Line-to-line voltage: six-step waveform, amplitude \(V_{dc}\).

    • Phase voltage for star load: complex; RMS requires integration.

  • 180° Conduction Mode:

    • Each SCR conducts 180°.

    • Line-to-line voltage: six-step with 120° on, 60° off, etc.

    • RMS load current and power:

      • Star-connected load:

        Phase voltage RMS: \(V_{ph,rms} = \frac{V_{dc} \sqrt{2}}{3}\)

        \boxed{I_{ph,rms} = \frac{V_{dc} \sqrt{2}}{3 R_{ph}}}

        \boxed{P = \frac{2}{3} \frac{V_{dc}^2}{R_{ph}}}

      • Delta-connected load:

        Phase voltage = line voltage RMS: \(V_{LL,rms} = V_{dc} \sqrt{2/3}\)

        \boxed{I_{ph,rms} = \frac{V_{dc} \sqrt{2/3}}{R_{ph}}}

        \boxed{P = 2 \frac{V_{dc}^2}{R_{ph}}}

  • PWM Inverters:

    • Single-phase circuit: Four switches, carrier comparison.

    • Principle: Modulate pulse width to approximate sine wave.

    • Advantages: Reduced harmonics, adjustable voltage/frequency.

  • Harmonic Reduction Techniques:

    • PWM (sinusoidal, space vector).

    • Multiple pulse modulation.

    • Stepped-wave inverters (using transformers).

B. Current Source Inverter (CSI)

• Principle: DC current source input; output current approximately square wave.

• Circuit: Inductor in series with DC source, six SCRs with commutating capacitors.

• Comparison with VSI: CSI requires commutating components, less common; VSI more popular.

C. Resonant Inverters

• Series resonant inverter: LC tank in series with load; operates at resonance for zero-voltage switching.

• Output current at resonance:

  \boxed{I_o = \frac{V_d}{R}}

  where \(V_d\) = DC source voltage.

D. Special Inverters

• McMurray-Bedford inverter: Uses auxiliary commutating circuit; for high-power applications.

VIII. CYCLOCONVERTERS

A. Basic Principle

• Step-down: Output frequency \(f_o < f_i\) (most common).

• Step-up: Output frequency \(f_o > f_i\) (requires forced commutation).

B. Single-Phase to Single-Phase Cycloconverters

• Mid-point configuration:

  • Two single-phase converters sharing common load.

  • One converter operates during positive half-cycle, other during negative.

• Bridge configuration:

  • Four-quadrant operation; two bridges in anti-parallel.

  • Waveforms for resistive load: Output frequency \(f_o = f_i/2\) for simple case.

• Waveforms: For resistive load, output is \(|\sin \omega_i t|\) with frequency \(f_i/2\).

C. Three-Phase to Single-Phase Cycloconverter

• Principle: Uses three-phase to single-phase matrix converter.

• Applications: High-power low-speed drives (e.g., rolling mills).

D. Applications

• Large AC drives, synchronous motor drives, high-power low-speed applications.

IX. SWITCHED-MODE POWER SUPPLIES (SMPS)

A. SMPS vs Linear Supply

• SMPS: Switching regulator, high efficiency (~80–90%), small size, high frequency, more noise.

• Linear: Low efficiency (~50%), large size, low noise.

B. Buck Regulator (Step-down)

• Circuit: Switch, diode, inductor, capacitor.

• Operation: Switch on: inductor charges; switch off: inductor discharges via diode.

• Derivation:

  \boxed{V_o = D V_s}

C. Boost Regulator (Step-up)

• Circuit: Switch, diode, inductor, capacitor.

• Derivation:

  \boxed{V_o = \frac{V_s}{1-D}}

D. Buck-Boost Regulator

• Circuit: Switch, diode, inductor, capacitor; output polarity reversed.

• Derivation:

  \boxed{V_o = \frac{D}{1-D} V_s}

• Advantage: Can step up or down depending on \(D\).

E. Fly-back SMPS

• Equivalent circuit: Transformer with primary and secondary; switch on primary, energy stored in core; switch off, energy transferred to secondary.

• Waveforms: Primary current ramps up when switch on; secondary current flows when switch off.

X. PROTECTION, COMMUTATION & OTHER CONCEPTS

A. Commutation Techniques

• Natural (Line) commutation: AC supply provides reverse voltage; used in phase-controlled rectifiers.

• Forced commutation: External circuit forces SCR to turn off.

  • Class A: Self-commutation using load resonance.

  • Class B: External pulse commutation.

  • Class C: Resonant pulse commutation.

  • Class D: Separate pulse commutation.

  • Class E: AC line commutation with auxiliary SCR.

B. Protection of SCRs

• Over-voltage protection:

  • Snubber circuit (RC across SCR) for dv/dt.

  • Varistors for transient suppression.

• Over-current protection:

  • Fuses (semiconductor fuses).

  • Circuit breakers.

  • Current limiting circuits.

C. Harmonics

• Sources: Non-linear loads (rectifiers, inverters).

• Importance of reduction: Improve PF, reduce heating, avoid resonance.

• Reduction techniques: PWM, multiphase converters, filters.

[!TIP] Exam Tips:

• For numerical problems, always draw waveforms and identify conduction intervals.

• Remember key formulas: \(V_{dc}\) for converters, \(V_{rms}\) for AC controllers, \(V_o\) for choppers.

• For series/parallel SCRs, derating factor = \(1 - \text{safety margin}\).

• In inverters, distinguish between 120° and 180° conduction modes.

• For AC controllers with RL load, freewheeling diode improves PF by making current continuous.

• In choppers, check continuity condition: \(I_{min} > 0\).

• For cycloconverters, output frequency is typically less than input (step-down).

[!CAUTION] Common Pitfalls:

• Confusing RMS and average values.

• Forgetting the effect of source inductance in rectifiers (overlap angle \(\mu\)).

• Mixing up 120° and 180° conduction in inverters.

• In AC controllers, using wrong RMS formula for RL load with/without freewheeling.

• In choppers, assuming continuous current without checking.

• In series SCRs, ignoring dynamic equalization.