Power Electronics Application to Power System (EX-702 (A)) - Unit 2 Short Notes

UNIT 2: High Voltage Engineering & Power Electronics Applications in Power Systems

I. High Voltage (HV) Technology in Power Systems

Concept & Significance

• Definition: Technology concerned with the generation, transmission, measurement, and application of voltages significantly higher than those used in conventional power systems (typically > 1000 V AC or 1500 V DC).

• Significance in Power Systems:

  • Efficient Long-Distance Power Transmission: Reduces current ($$\displaystyle I = P/V $$), minimizing $$\displaystyle I^2R $$ losses and allowing thinner, cheaper conductors.

  • Increased Power Transfer Capability: Higher voltage enables greater power flow over existing corridors.

  • System Interconnection: Essential for interconnecting large regional grids.

  • Improved Stability: Reduces voltage drop and improves voltage regulation.

Voltage Classification (as per IEC & Indian Standards)

Applications

• Power System: Transmission lines, substation equipment (CBs, CTs, PTs), transformers, HVDC converter stations.

• Non-Power Industrial:

  • Industrial Processes: Electrostatic precipitators, X-ray generation, ozone generation, food sterilization.

  • Research: Particle accelerators, plasma physics, fusion research.

  • Specialized: Laser pumping, insulation testing labs.

Need for HV Generation in Laboratories

• Type Testing: To simulate overvoltages (lightning, switching) on equipment insulation.

• Routine Testing: High Potential (Hi-Pot) testing of equipment post-manufacture.

• Research & Development: Studying breakdown mechanisms, developing new insulating materials.

• Calibration: Calibrating HV measuring instruments (dividers, gaps).

Advantages & Limitations of HV Transmission

[!TIP] Exam Focus: Be prepared to contrast HV, EHV, UHV levels and give specific examples. For advantages/limitations, always link cost, technical feasibility, and application suitability.

II. Breakdown Mechanisms in Dielectrics

A. Gaseous Dielectrics

Townsend Ionization Theory (First & Second Coefficients)

• Primary Ionization ($\alpha$): Number of ionizing collisions produced by one electron per unit path length in the direction of the field. Depends on $E/P$ (Electric field / Pressure).

$$ \alpha = A P e^{-BP/E} $$

where $A, B$ are gas-dependent constants.

• Secondary Ionization ($\gamma$): Coefficient representing the number of secondary electrons released from the cathode per positive ion impact or photon interaction. Crucial for sustaining discharge.

• Condition for Breakdown (Townsend Criterion):

$$ \gamma (e^{\alpha d} - 1) = 1 $$

where $d$ = gap distance. Breakdown occurs when the number of electrons reaching the anode causes sufficient secondary emission from the cathode to multiply the discharge.

Streamer Theory of Breakdown

• Improvement over Townsend: Explains breakdown in non-uniform fields and long gaps where space charge effects distort the field.

• Mechanism:

  1. An electron avalanche develops.

  2. Space charge of positive ions at the avalanche head locally enhances the electric field ahead.

  3. This enhanced field causes ionization in the neutral gas ahead of the avalanche, forming a conductive ionized channel (streamer).

  4. Streamers propagate rapidly towards electrodes, leading to complete breakdown.

• Key Concept: Ionization front propagates due to field distortion, not just electron drift.

Statistical & Formative Time Lags

• Total Breakdown Time Lag ($$\displaystyle t_b $$): $$\displaystyle t_b = t_s + t_f $$

  • Statistical Time Lag ($$\displaystyle t_s $$): Time for initial electron (from natural radiation) to appear near the cathode. Random/variable.

  • Formative Time Lag ($$\displaystyle t_f $$): Time for the discharge to develop from the first electron to complete breakdown. Deterministic, depends on $E/P$, gap geometry.

• Significance: Explains why breakdown voltage for a given gap may vary with time, especially with impulses.

Paschen's Law

• Statement: Breakdown voltage ($$\displaystyle V_b $$) in a uniform field gap is a unique function of the product of gas pressure ($p$) and gap distance ($d$).

$$ V_b = f(pd) $$

• Derivation (Simplified Townsend): Using $$\displaystyle \alpha = A p e^{-Bp/E} $$ and $$\displaystyle E = V_b/d $$, and the breakdown condition $$\displaystyle \gamma (e^{\alpha d} - 1) = 1 $$, assuming $\gamma$ constant and $$\displaystyle \alpha d >> 1 $$:

$$ V_b = \frac{B p d}{\ln(A p d / \ln(1 + 1/\gamma))} $$

• Paschen Minimum: The curve $$\displaystyle V_b $$ vs. $pd$ has a minimum. At this point, $pd$ is optimal for breakdown.

  • Implication: For a given voltage, there is a minimum $pd$ below which breakdown won't occur (e.g., vacuum switches) and above which it may not occur (high pressure SF₆).

  • Practical Use: Design of gas-insulated systems (GIS), spark gaps.

Cavity Breakdown in Gaseous Media

• Problem: Voids/ cavities in solid insulation filled with gas (lower dielectric strength) create local field enhancement.

• Mechanism: High local stress in cavity causes partial discharge (localized breakdown). Repeated PD erodes insulation, leading to eventual failure.

• Significance: Critical in composite insulation systems (e.g., cable joints, transformer windings).

B. Vacuum Breakdown

• Mechanism in Deep Vacuum ($$\displaystyle < 10^{-4} $$ torr):

  • No particles for ionization → theoretically infinite strength.

  • Practical Breakdown Causes:

    1. Field Emission: Electrons tunnel from micro-protrusions on cathode surface at high fields.

    2. Micro-Particles: Vaporized electrode material (from field emission heating) forms conductive plasma bridges.

    3. Surface Flashover: Electrons emitted from cathode travel along insulator surface, causing secondary emission and conductive path.

• Key Feature: Breakdown voltage increases with decreasing pressure after a certain point (opposite to gases).

C. Solid Dielectrics

• Intrinsic Strength: Maximum electric field a perfect, defect-free dielectric can withstand before electronic breakdown. Very high (100 kV/mm to 1 MV/mm).

• Electronic/Avalanche Breakdown: At very high fields, electrons gain enough kinetic energy to ionize atoms via collision, creating an electron avalanche leading to catastrophic failure. Rare in practice due to impurities.

• Partial Discharge (PD) Phenomenon:

  • Definition: Localized electrical discharge that only partially bridges the insulation between conductors.

  • Cause: Exists in cavities, voids, or at interfaces where local field exceeds gas (or low-strength material) breakdown strength but not the bulk solid strength.

  • Effect: Progressive erosion of insulation, leading to ultimate failure. Key diagnostic tool for insulation health (cables, transformers).

[!TIP] Common Pitfall: Do not confuse Townsend (low pressure, uniform field) with Streamer (high pressure/long gaps, non-uniform). Paschen's Law applies to uniform field gases only. Vacuum breakdown is not due to gas ionization.

III. High Voltage Generation Methods

A. AC High Voltage Generation

• Series Resonant Circuit (Tesla Transformer Principle):

  • Circuit: HV transformer (low voltage, high current) → HV capacitor ($C$) → Spark gap (switch) → Primary coil ($$\displaystyle L_1 $$) → Secondary coil ($$\displaystyle L_2 $$, many turns) → HV output.

  • Principle: Energy oscillates between $$\displaystyle L_1 $$ and $C$. When spark gap fires, circuit becomes series $$\displaystyle L_1 $$-$C$-$$\displaystyle L_2 $$ resonant circuit.

  • Resonance Condition:

$$ \omega_0 = \frac{1}{\sqrt{L_1 C}} = \frac{1}{\sqrt{L_2 C_{eq}}} \quad \text{or} \quad f_0 = \frac{1}{2\pi\sqrt{L_1 C}} $$

    where $$\displaystyle C_{eq} $$ is effective capacitance seen by $$\displaystyle L_2 $$.

*   **Result:** High voltage magnification at $$\displaystyle L_2 $$ secondary due to turns ratio and Q-factor.

B. DC High Voltage Generation

1. Cockcroft-Walton (CW) Generator (Voltage Multiplier)

• Construction: Stages of diode-capacitor ladder. $n$ stages give $$\displaystyle \approx 2n V_{peak} $$ DC output (neglecting ripple/load).

• Working: Charging in parallel during negative half-cycle, discharging in series during positive half-cycle.

• Advantages: Simple, no transformer needed for very high voltages, good for DC/impulse testing.

• Limitations: High output impedance, poor regulation under load, high ripple at high stages, limited current.

2. Tesla Coil (Air-Core Transformer)

• Construction: Primary coil (few turns, heavy wire) + large capacitor → spark gap → Secondary coil (many turns, fine wire) on same core (often toroidal). Both coils tuned to same resonant frequency.

• Working: Oscillatory discharge from primary excites secondary. Resonant coupling transfers energy, producing very high voltage, high frequency AC at secondary.

• Principle: Resonant inductive coupling. Used for HV AC generation, wireless power demo, impulse excitation.

C. Impulse Voltage Generation

• Impulse Generator (Marx Circuit): Capacitors charged in parallel to DC voltage, then discharged in series through spark gaps to generate a standard impulse ($1.2/50 \mu s$).

• Triggering Using Three-Electrode Gap:

  • Arrangement: Main gap (between generator output and ground) + two trigger gaps in series with a triggering electrode between them.

  • Triggering: A high-voltage pulse applied to the triggering electrode initiates breakdown in the first small gap, which then triggers the main gap.

  • Why Preferred: Provides precise, synchronized triggering independent of main gap voltage level. Ensures consistent wavefront time.

[!TIP] Exam Focus: Derive resonance condition for series resonant circuit. Compare CW (DC, poor regulation) vs Tesla Coil (AC, HF). For impulse, emphasize why triggering is needed (synchronization, control).

IV. High Voltage Measurement Techniques

A. Direct Measurement Devices

1. Sphere Gap

• Principle: Breakdown voltage between two spheres is a well-defined, reproducible function of sphere diameter ($D$) and gap ($g$) for AC, DC, standard impulse.

• Construction: Two identical polished spheres (diameters 6.25 cm to 100 cm). Mounted vertically or horizontally.

• Operation: Increase voltage until sparkover. Read breakdown voltage from calibrated curve for given $D$ and $g$.

• Influencing Factors:

  • Sphere diameter & gap setting (primary)

  • Humidity (significant for AC/DC, correction factors exist)

  • Waveform (must be standard impulse for impulse measurement)

  • Polarity (for DC & impulse)

  • Surrounding objects (must maintain minimum clearance)

2. Electrostatic Voltmeter

• Principle: Attraction force between fixed and moving electrodes (in a capacitor) is proportional to $$\displaystyle V^2 $$. Deflection of a pointer indicates RMS value for AC or instantaneous for DC.

• Advantage: True RMS for AC, no loading, high accuracy.

• Limitation: Bulky, limited range, sensitive to vibration.

3. Generating Voltmeter

• Principle: Rotating vane (or disc) in electrostatic field generates a current proportional to $$\displaystyle V^2 $$. This current is measured by a sensitive DC microammeter.

• Use: High DC voltages (HVDC, particle accelerators). Advantage: No direct connection to HV, high input impedance.

B. Potential Dividers

• Principle: HV $$\displaystyle V_h $$ is divided across known impedance network; low voltage $$\displaystyle V_l $$ is measured by a standard voltmeter. $$\displaystyle V_h = V_l \times (Z_h / Z_l) $$.

• Types & Conditions:

  | Type | Composition | Use Case | Key Condition for Impulse | | :--- | :--- | :--- | :--- | | Resistance Divider | High-value resistors | AC, DC, Slow impulses | Low inductance, low capacitance. Poor for fast impulses due to wave distortion. | | Capacitance Divider | Capacitors (low loss) | Fast impulses, Lightning | Low inductance. Poor for AC/DC due to leakage. | | Mixed RC (Resistive-Capacitive) Divider | Series RC (R low, C high) | General purpose, Impulse | Critical: Time constant $$\displaystyle \tau = RC $$ must be >> impulse duration (e.g., 50µs) to avoid droop. |

• Comparative Advantages/Disadvantages:

  • Resistance: Simple, good for AC/DC. Disadvantage: High power loss, poor impulse response.

  • Capacitance: Low loss, excellent impulse response. Disadvantage: Not for steady-state, sensitive to stray capacitance.

  • RC (Mixed): Compromise. Good for impulse & AC if $\tau$ large. Disadvantage: More complex, needs careful design.

C. Surge Current Measurement

• Methods:

  1. Rogowski Coil: Air-cored toroidal coil around conductor. Output voltage $$\displaystyle v_o = M (di/dt) $$. Integrate to get current. Ideal for high di/dt surges (lightning, switching).

  2. Shunt Resistor (Low-Value): Direct measurement. Must be non-inductive, low thermal mass. Limited by power dissipation.

  3. Magnetic Field Probe (Hall Effect): Measures magnetic field around conductor, proportional to current.

• Challenges:

  • Extreme di/dt: Requires very wide bandwidth instruments.

  • High Peak Currents: Risk of saturation (Rogowski), destruction (shunt).

  • Isolation: Instrument must be isolated from high-voltage ground.

  • Electromagnetic Interference (EMI): Surge generates strong EMI, affecting measurement.

[!TIP] Key Distinction: Sphere gap is a comparative (breakdown) method, not continuous. Potential dividers are continuous. For impulse measurement, RC divider with large time constant is essential. Rogowski coil is the go-to for surge current.

V. Insulation Testing of Power System Equipment

A. Test Types Overview

B. Tests on Switching Equipment

• Circuit Breaker (CB):

  • Short-Circuit Test (Making/ Breaking Capacity): Verify CB can interrupt fault currents without damage. Tests at rated voltage & current.

  • Dielectric Test: Hi-Pot test across open contacts (withstand voltage) to ensure insulation integrity.

• Isolator / Disconnecting Switch:

  • Dielectric Withstand Test: Across open gap.

  • Contact Resistance Test: Measure milliohm resistance of closed contacts.

  • Mechanical Operation Test: Number of open/close cycles.

C. Tests on Insulators

• Mechanical Strength Test: Tensile, bending, torsional strength to withstand line tensions and environmental loads.

• Puncture Voltage Test: Voltage at which insulator bulk material fails (internal flashover). Tested with electrodes on opposite faces.

• Flash-Over Voltage Test: Voltage at which surface air path flashes over. Depends on creepage distance, weather conditions (wet test).

D. Tests on Transformers and Cables

• Power Transformer:

  • High Voltage Test (Hi-Pot): Applied between windings and ground, and between windings. Checks main insulation.

  • Induced Overvoltage Test: Applies higher frequency voltage to test turn insulation.

  • Necessity: Detect manufacturing defects (loose windings, insulation damage), ensure reliability.

• High-Voltage Cables:

  • Partial Discharge (PD) Test: Detect voids/defects in insulation. Measure PD magnitude and inception/extinction voltages.

  • Fault Location Techniques:

    • Time Domain Reflectometry (TDR): Send pulse, reflect from impedance discontinuity (fault).

    • Bridge Methods (Murray Loop): For low-resistance faults.

    • High-Voltage Surge (Flashover): For high-resistance faults; detect fault point by sound/pressure wave.

E. Insulation Manufacturing Techniques for Motor Coils

• Pouring Methods for Insulating Paint (Varnish):

  1. Dip & Bake: Coil immersed in varnish, drained, then baked. Simple, good penetration.

  2. Vacuum-Pressure Impregnation (VPI): Coil placed in vacuum, varnish introduced under pressure. Best method – eliminates voids, excellent adhesion, high mechanical strength.

  3. Autoclave (VPI with Heat): Similar to VPI but with heat, further improves flow and cure.

VI. HVDC Transmission Systems

A. Overview

• Merits:

  • No skin effect, lower line losses for same power.

  • No charging current → feasible for long, submarine cables.

  • Fast, independent control of active power & polarity (power reversal).

  • Interconnect asynchronous systems.

  • Lower right-of-way width.

• Demerits:

  • Expensive converter stations (thyristor/IGBT valves).

  • Generation of harmonics (need large filters).

  • Limited overload capability.

  • Complex control and protection.

• Types of DC Links:

  • Monopolar: One conductor (+ or -), ground/sea return. Simple, used for HVDC cables or long overhead lines.

  • Bipolar: Two conductors (+ and -), ground return for imbalance/fault. Most common for overhead lines.

  • Homopolar: Two conductors of same polarity, dual ground return. Rare.

• Power Reversal: Change direction of power flow by reversing voltage polarity while keeping current direction same (or vice versa). Achieved by control system, no physical switching.

B. Converter Station Layout & Major Equipment

• Layout: AC Switchyard → AC Filter Bus → Converter Transformer → Valve Hall (Thyristor Valves) → DC Switchyard → DC Line/Electrode.

• Major Equipment:

  • Converter Transformers: Provide necessary voltage transformation and phase shift for 12-pulse operation.

  • Thyristor Valves: Core converting elements (6-pulse or 12-pulse bridge).

  • AC & DC Filters: For harmonic suppression.

  • Smoothing Reactor: Limits ripple in DC current.

  • DC Capacitors (Surge Arresters): Protect against overvoltages.

  • Control & Protection System.

C. Control and Operation

• Principle: Control extinction angle ($\gamma$) or firing angle ($\alpha$) of thyristors to regulate average DC voltage $$\displaystyle V_d $$.

$$ V_d = V_{d0} \cos \alpha - I_d R_c \quad \text{(Rectifier)} $$

$$ V_d = -V_{d0} \cos \gamma - I_d R_c \quad \text{(Inverter)} $$

where $$\displaystyle V_{d0} $$ = ideal no-load voltage, $$\displaystyle R_c $$ = circuit resistance.

• Converter Control Characteristics: Plot of $$\displaystyle V_d $$ vs. $$\displaystyle I_d $$ for constant $\alpha$ or $\gamma$.

  • Rectifier Mode: $\alpha$ controlled (typically 15°-18°).

  • Inverter Mode: $\gamma$ controlled (typically 15°-18°). Minimum $\gamma$ limit critical for stability.

  • Constant Current (CC) & Constant Extinction Angle (CEA) Control: Primary control modes to prevent commutation failure.

D. Multi-Terminal HVDC (MTDC)

• Series MTDC: Converters connected in series on DC side. Current same through all, voltages add/subtract. Complex control, used for tapping.

• Parallel MTDC: Converters connected in parallel on DC side. Voltage same, currents add. Easier control, more common.

• Applications: Power supply to offshore platforms, urban in-feed, interconnecting multiple grids/asynchronous regions.

E. Harmonics and Filtering

• Types of Harmonics:

  • AC Side: 12-pulse → 11th, 13th, 23rd, 25th... (characteristic). Also non-characteristic from imbalance.

  • DC Side: 12-pulse → 12th, 24th... (ripple).

• Filters:

  • AC Filters: Tuned LC circuits (single-tuned, double-tuned, C-type) to shunt specific harmonic currents to ground.

  • DC Filters: Series LC circuits (or shunt with capacitor) to smooth DC ripple and block AC harmonics from entering DC line.

  • Active Filters: Power electronics-based for dynamic compensation.

VII. Flexible AC Transmission Systems (FACTS)

A. Fundamentals

• FACTS Controllers: Power electronics-based systems that control AC transmission system parameters (impedance, voltage, phase angle) to enhance controllability and increase power transfer capability.

• Classification (by Connection):

  • Series Compensators: Inserted in series with line (TCSC, SSSC, UPFC-S series part).

  • Shunt Compensators: Connected in shunt (parallel) (SVC, STATCOM).

  • Combined Series-Shunt: UPFC.

  • Phase Angle Regulators: (Not always strictly power electronics, e.g., PST).

• Principle of Conventional Reactive Power Compensators (SVC): Use switched capacitors/inductors to dynamically inject/absorb reactive power ($Q$) to control voltage. Fast, but discrete steps.

B. Major FACTS Devices

1. Static Var Compensator (SVC)

• Components: Thyristor Switched Capacitor (TSC) banks + Thyristor Controlled Reactor (TCR) in parallel.

• Operation: TCR provides continuous, fast reactive power absorption. TSC banks switch in/out to provide capacitive vars. Net $Q$ is continuous.

• Advantages: Fast response (cycles), improves voltage stability, increases power transfer.

• Disadvantages: Generates harmonics (need filters), limited range of continuous control.

2. Thyristor-Controlled Series Capacitor (TCSC)

• Construction: Capacitor bank in series with line, shunted by a Thyristor-Controlled Reactor (TCR).

• Operation: By controlling TCR firing angle, effective impedance of the series capacitor bank is varied.

  • Bypass Mode: TCR fully on → capacitor shorted → zero series compensation.

  • Control Mode: TCR partially on → variable capacitive reactance.

• Advantages: Damp power oscillations, increase power transfer, improve stability, prevent subsynchronous resonance (SSR).

• Disadvantages: Complex control, harmonic generation, capacitor overvoltage risk during faults.

3. Static Compensator (STATCOM)

• Construction: Voltage Source Converter (VSC) using IGBTs/IGCTs, connected to AC bus via a coupling transformer (or directly).

• Operation in Reactive Compensation:

  • Inductive Mode: VSC output voltage $$\displaystyle V_{conv} < V_{sys} $$ → absorbs $Q$.

  • Capacitive Mode: $$\displaystyle V_{conv} > V_{sys} $$ → injects $Q$.

  • Advantage over SVC: Better performance at low voltages (can generate $Q$ even when $$\displaystyle V_{sys} $$ is low), faster response, smaller footprint, no harmonic resonance risk (if PWM used).

• Disadvantage: Higher losses, more expensive than SVC for large ratings.

4. Static Synchronous Series Compensator (SSSC)

• Construction: VSC with DC capacitor, connected in series with transmission line via a transformer.

• Use & Operation: Injects a virtually controllable AC voltage in series with the line. This voltage is orthogonal to line current.

  • Acts as a variable inductive or capacitive reactance.

  • Can reverse power flow, damp oscillations, improve stability.

• Key Feature: Can provide negative series impedance (unlike fixed capacitor).

5. Unified Power Flow Controller (UPFC)

• Schematic Concept: Combines STATCOM (shunt) and SSSC (series) via a common DC capacitor.

  • Shunt Converter: Controls DC bus voltage & can inject/absorb $Q$ at the bus.

  • Series Converter: Injects controlled voltage in series with line.

  • Power Flow Control: By controlling magnitude and phase of injected series voltage, it can simultaneously control line active power ($P$), reactive power ($Q$), and voltage at the connection point.

• Most Powerful FACTS Device: Provides full flexibility of voltage, impedance, and phase angle control.

C. Applications and Comparisons

• Primary Applications: Increase transfer capability, damp oscillations (power swings), improve voltage profile, enhance system stability (transient, dynamic), manage loop flows, mitigate SSR.

• Comparison (SVC vs STATCOM vs TCSC):

  • SVC/STATCOM (Shunt): Primarily for voltage control and dynamic $Q$ support.

  • TCSC/SSSC (Series): Primarily for power flow control and oscillation damping by modifying line impedance.

  • STATCOM vs SVC: STATCOM has superior performance at low voltages, faster, no resonance.

  • SSSC vs TCSC: SSSC (VSC-based) offers faster, continuous, bidirectional control without capacitor overvoltage concerns.

[!TIP] Critical Distinction: SVC/STATCOM = Shunt (voltage at a bus). TCSC/SSSC = Series (impedance of a line). UPFC = Both. Remember the VSC (voltage source converter) is the heart of STATCOM, SSSC, UPFC.