Power Electronics Application to Power System (EX-702 (A)) - Unit 4 Short Notes

UNIT 4: HIGH VOLTAGE ENGINEERING & POWER ELECTRONICS APPLICATIONS TO POWER SYSTEMS

I. HIGH VOLTAGE TECHNOLOGY: FUNDAMENTALS & APPLICATIONS

A. Introduction & Significance

• Definition:

  • High Voltage (HV): Typically > 33 kV (for transmission).

  • Extra High Voltage (EHV): 220 kV – 400 kV.

  • Ultra High Voltage (UHV): > 800 kV (AC) or ±600 kV (DC).

• Significance in Modern Power Systems:

  • Enables long-distance power transmission with reduced I²R losses.

  • Increases power transfer capability for a given conductor size.

  • Essential for bulk power grid interconnections.

• Major Applications:

  • Power Applications: HV/EHV/UHV transmission lines, substations, HVDC converter stations, circuit breakers, transformers.

  • Non-Power Applications: Industrial (electrostatic precipitators, X-ray generation), medical (radiotherapy, imaging), research (particle accelerators, fusion reactors).

B. Need for High Voltage Generation in Laboratories

• Primary Purposes:

  1. Insulation Testing: Routine, type, and acceptance tests on equipment (transformers, cables, insulators).

  2. Dielectric Breakdown Research: Studying breakdown mechanisms in gases, vacuum, solids, and liquids.

  3. Calibration: Standardizing high-voltage measuring instruments (meters, dividers).

  4. Overvoltage Simulation: Generating standard lightning (1.2/50 µs) and switching (250/2500 µs) impulse waves to test equipment immunity.

• Key Testing Scenarios:

  • Dielectric Withstand Test: Applied voltage > rated voltage for a specified time.

  • Impulse Test: Simulates atmospheric lightning or switching surges.

II. DIELECTRIC BREAKDOWN PHENOMENA

A. Gaseous Dielectrics

• Ionization Processes:

  • Primary Ionization: Free electron gains energy from electric field, collides with neutral molecule → ionization (positive ion + 2 electrons) if energy > ionization potential.

  • Secondary Ionization: Positive ion drifts to cathode, emits secondary electrons upon impact (γ process). Also includes photoionization and field emission.

• Townsend's Theory of Breakdown:

  • Townsend's First Coefficient (α): Number of ionizing collisions produced by one electron per unit path length (primary process).

  • Townsend's Second Coefficient (γ): Number of secondary electrons emitted per positive ion arriving at cathode.

  • Breakdown Condition (Townsend Criterion):

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

    where `d` is gap distance. Breakdown occurs when electron multiplication becomes **self-sustaining**.

• Streamer Mechanism of Breakdown:

  • Explains breakdown in non-uniform fields and long gaps where Townsend theory fails.

  • Space charge from avalanche distorts local electric field, creating a high-field tip (streamer head) that propagates forward via photoionization.

  • Improvement over Townsend: Accounts for rapid, avalanche-to-streamer transition and leader formation in long gaps.

• Statistical and Formative Time Lags:

  • Statistical Time Lag (tₛ): Time for initial free electron to appear (random process).

  • Formative Time Lag (t_f): Time for electron avalanche to develop to breakdown after the first electron appears.

  • Total Breakdown Time Lag (T) = tₛ + t_f.

B. Paschen's Law

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

$$ V_b = f(pd) $$

• Derivation (Simplified): Based on Townsend criterion, assuming α/p = A exp(-Bp/E) (where E = V/d). Leads to:

$$ V_b = \frac{Bpd}{\ln(Apd) - \ln[\ln(1 + 1/\gamma)]} $$

• Paschen Minimum: V_b has a minimum at a specific (pd)_min. For air, V_b(min) ≈ 327 V at pd ≈ 0.567 torr-cm.

• Practical Implications:

  • Sets minimum clearance requirements for HV equipment.

  • Explains why spark gaps in vacuum or high-pressure gas have different characteristics.

  • Guides insulation coordination and gas pressure selection (e.g., in GIS).

C. Breakdown in Vacuum & Solid Dielectrics

• Breakdown in Deep Vacuum:

  • Mechanism not purely electronic. Dominated by:

    1. Cavity Breakdown: Micro-protrusions on electrodes create localized high fields → field emission → vaporization → arc.

    2. Surface Flashover: Breakdown along insulator surfaces due to adsorbed gases/desorption.

• Breakdown in Solid Dielectrics:

  • Intrinsic Strength: Theoretical breakdown strength due to pure electronic processes (~10⁶ V/cm for good solids).

  • Electronic Breakdown Mechanisms:

    • Avalanche Breakdown: Similar to gas, but in conduction/valence bands.

    • Cumulative Breakdown: Thermal or defect-induced (practical breakdown always lower than intrinsic due to impurities, voids, defects).

III. HIGH VOLTAGE GENERATION & MEASUREMENT

A. High Voltage Generation

1. AC Generation:

• Testing Transformer: Step-up transformer with insulated core to avoid core saturation. Used for power frequency (50/60 Hz) testing.

• Cascaded Transformers: Multiple transformers in series to achieve very high voltages, with each stage insulated for its own voltage.

2. DC Generation - Cockcroft-Walton (Greinacher) Multiplier:

• Principle: Uses a capacitor-diode ladder to rectify and multiply AC input.

• Operation: Each stage adds peak input voltage (V_m). n stages → n * V_m (no load).

• Advantages: No moving parts, compact, high output voltage from low input.

• Limitations: High ripple, poor voltage regulation under load, voltage drop increases with stages and current.

  Output Voltage (approx.): $$\displaystyle V_{out} \approx 2nV_m - \frac{I_{load}}{fC} \left( \frac{2n^3}{3} + \frac{n^2}{2} + \frac{n}{6} \right) $$

3. Impulse Voltage Generation - Marx Circuit:

• Principle: Capacitors charged in parallel to V then discharged in series to generate nV impulse.

• Triggering (Three-Electrode Gap):

  • Why Preferred: Ensures simultaneous discharge of all stages, minimizing wavefront time jitter.

  • Arrangement: Trigger electrode between main gap and hold-off gap. High-voltage pulse on trigger electrode initiates breakdown of all main gaps nearly simultaneously.

• Control Tripping: Triggering pulse applied to trigger electrode to initiate controlled discharge.

4. Tesla Coil (Oscillatory Impulse Generator):

• Construction: HV transformer, capacitor (primary), spark gap, large secondary coil with open core.

• Working: Capacitor charges → spark gap fires → oscillatory discharge in primary induces high voltage in secondary → high-frequency, high-voltage AC output (resonant frequency ~100 kHz - 1 MHz).

5. Series Resonant Circuit for HV Testing:

• Principle: At series resonance (ωL = 1/ωC), circuit impedance is minimum (pure resistance), current is maximum. Voltage across capacitor (V_C) or inductor (V_L) is Q-times the input voltage (V_in).

$$ \text{Resonance Condition: } \omega_0 L = \frac{1}{\omega_0 C} \quad \text{or} \quad f_0 = \frac{1}{2\pi\sqrt{LC}} $$

$$ \text{Voltage Magnification: } V_C = Q \cdot V_{in}, \quad \text{where } Q = \frac{1}{R} \sqrt{\frac{L}{C}} $$

• Use: Generates high test voltage with low input power from a low-voltage source.

B. High Voltage Measurement

1. General Requirements:

• Impulse: Low inductance, wide bandwidth, capacitive compensation.

• AC/DC: Accuracy, stability, low power loss.

2. Potential Dividers:

3. Sphere Gap:

• Principle: Breakdown voltage between two spheres is a function of diameter (D) and gap (g). Well-established by standards (IEC 60052).

• Measurement: Measures peak value of AC, DC, and impulse voltages. Polarity and wavefront time affect reading.

• Influencing Factors:

  1. Sphere diameter D

  2. Gap spacing g

  3. Atmospheric conditions (pressure, temperature, humidity) → correction factor.

  4. Polarity (for DC/impulse).

  5. Wavefront time (for impulse).

4. Generating Voltmeter (for High DC):

• Principle: Rotating vane (or disc) in electric field experiences torque proportional to V². Rotation speed measured optically → calibrated to voltage.

• Construction: Motor-driven rotor inside shielded high-voltage electrode.

5. Electrostatic Voltmeter:

• Principle: Fixed electrode and movable vane/plate. Attraction force F ∝ V². Deflection measured by pointer/mirror.

• Use: Accurate for AC and DC up to several hundred kV. High input impedance.

6. Surge Current Measurement:

• Challenges: Extremely high di/dt (kA/µs), magnetic saturation, bandwidth > 10 MHz.

• Methods:

  • Rogowski Coil: Air-cored toroidal coil around conductor. Output V_out ∝ di/dt. Integrates to get i(t). No saturation, high bandwidth.

  • Low-Value Shunt Resistor: V_shunt = i * R_shunt. Must be non-inductive, low inductance (< 10 nH), high bandwidth.

IV. HIGH VOLTAGE TESTING OF EQUIPMENT & MATERIALS

V. POWER ELECTRONICS APPLICATIONS TO POWER SYSTEMS (HVDC & FACTS)

A. High Voltage DC (HVDC) Transmission

1. Fundamentals:

2. HVDC Converter Station Layout & Equipment:

• Converters: Line-Commutated Converters (LCC - thyristor valves) or Voltage-Source Converters (VSC - IGBTs).

• AC Filters: Tuned to 5th, 7th, 11th, 13th harmonics + high-pass for RF noise.

• DC Filters: For commutating harmonics on DC side.

• Smoothing Reactor: Limits ripple current in DC line.

• DC Capacitors: For VSC-HVDC, filter DC ripple.

• Surge Arresters: Protect against overvoltages.

• Control System: Firing angle/phase control, current/voltage regulation.

3. HVDC System Control:

• Principle: Master controller sets power/current order. Converters control current (to avoid commutation failure) or extinction angle (γ) (for LCC).

• Converter Control Characteristics:

  • Rectifier: Constant Current Control (CCC) or Constant Extinction Angle (CEA).

  • Inverter: Constant Current Control (CCC) or Constant Gamma Control (CGC).

  • System Characteristic: Rectifier current order vs. voltage; Inverter current order vs. extinction angle. Intersection determines operating point.

  Power Reversal: Achieved by reversing current direction (change polarity of DC voltage or current order sign). For LCC, requires firing angle > 90° on one end.

4. Harmonics in HVDC:

• Characteristic Harmonics: h = p(k) ± 1 (for 12-pulse: 11, 13, 23, 25...). Generated by converter switching.

• Non-Characteristic Harmonics: Due to unbalance, firing angle errors, transformer saturation (e.g., 3rd, 5th, 7th).

• Sources: Converter valves, transformer magnetizing current.

5. Multi-Terminal DC (MTDC) Systems:

6. Types of DC Links:

• Point-to-Point: Two converter stations.

• Back-to-Back: No DC line; converters in same station (asynchronous tie).

• Multi-Terminal: >2 converter stations (parallel or series).

B. Flexible AC Transmission Systems (FACTS)

1. Introduction: Power electronics-based controllers that enhance controllability and increase power transfer capability of AC networks by dynamically controlling voltage, impedance, phase angle.

2. Conventional Reactive Power Compensators:

• Shunt Compensation: Capacitors/inductors in parallel → control voltage/power factor.

• Series Compensation: Capacitor in series → reduce line impedance, increase power transfer.

3. Major FACTS Devices:

• Static VAR Compensator (SVC):

  • Principle: Combination of Thyristor-Controlled Reactor (TCR) and Thyristor-Switched Capacitor (TSC) or Fixed Capacitor (FC).

  • Operation: TCR provides continuous reactive absorption (by phase-angle control), TSC/FC provides stepwise capacitive injection. Net continuous VAR control.

  • Response: Fast (~few cycles).

• Static Synchronous Compensator (STATCOM):

  • Principle: Voltage-Source Converter (VSC) with DC capacitor, connected in shunt via transformer.

  • Operation: Outputs a synchronous voltage (V_s) whose magnitude and phase relative to AC system voltage (V_sys) control reactive power flow.

    • |V_s| > |V_sys| → capacitive (inject Q).

    • |V_s| < |V_sys| → inductive (absorb Q).

  • Advantages over SVC: Better voltage support at low voltages, smaller footprint, faster response, less harmonics.

• Thyristor-Controlled Series Capacitor (TCSC):

  • Construction: Series capacitor (X_C) bypassed by a Thyristor-Controlled Reactor (TCR).

  • Working/Operation:

    • Impedance Modulation: By controlling TCR firing angle (α), the net series reactance (X_net = X_C - X_L(α)) can be varied continuously between X_C (fully ON) and X_C - X_L (fully OFF).

    • Modes: Blocking (high impedance), Bypass (low impedance, for protection/SSSC operation), Control (variable impedance).

  • Advantages: Damping of power oscillations, increased transfer capability, flexible power flow control.

  • Disadvantages: Complex control, potential for subsynchronous resonance (SSR) if not properly coordinated.

• Static Synchronous Series Compensator (SSSC):

  • Principle: VSC with DC capacitor, connected in series via transformer.

  • Operation: Injects a controllable AC voltage (V_s) in quadrature with line current (I_line). Acts as a variable series impedance (V_s / I_line).

  • Use: Power flow control (increase/reverse), damping oscillations, loop flow management.

• Unified Power Flow Controller (UPFC):

  • Schematic: Combines STATCOM (shunt) and SSSC (series) via common DC link.

  • Basic Concept: Shunt converter supplies/absorbs active power to/from DC link to support series converter's voltage injection. Provides independent control of:

    1. Bus voltage (shunt).

    2. Line impedance/voltage (series).

    3. Power flow (combined effect).

  • Most versatile FACTS device.