UNIT 1: HIGH VOLTAGE ENGINEERING FUNDAMENTALS

1.0 Introduction to High Voltage Technology

1.1 Concept and Significance

• High Voltage (HV) refers to voltage levels significantly above normal operating voltages, used for specific applications where standard voltages are impractical.

• Significance in Modern Power Systems:

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

  • Increased Power Transfer Capacity: Enables transmission of large blocks of power over hundreds of kilometers.

  • System Interconnection: Facilitates linking of widely separated power grids.

  • Foundation for HVDC: HVDC converter stations inherently operate at high DC voltages.

1.2 Voltage Classification (as per IEC & national standards)

[!TIP] Exam Focus: Be prepared to quote specific voltage ranges for HV, EHV, UHV as per Indian standards (e.g., > 33 kV is HV, > 220 kV is EHV).

1.3 Applications

• Power Transmission: Overhead lines and submarine cables (HVDC).

• Non-Power Industrial Uses:

  • X-ray Generation: Accelerating electrons to high energies.

  • Particle Accelerators: For research and medical therapies.

  • Induction Heating: For metal hardening, melting.

  • Ozone Generation: For water treatment and air purification.

  • Electrostatic Precipitators: For pollution control in industries.

  • Insulation Testing: Of equipment and materials.

1.4 Need for High Voltage Generation in Laboratories

• Type Testing: To simulate overvoltages (lightning, switching) and verify insulation strength of power apparatus (transformers, cables, circuit breakers).

• Research & Development: To study breakdown mechanisms in new dielectric materials and gas mixtures.

• Calibration: To calibrate HV measuring instruments (voltmeters, dividers).

• Production Testing: Routine testing of manufactured equipment at specified test voltages.

2.0 Breakdown Mechanisms in Dielectrics

2.1 Gaseous Dielectrics

2.1.1 Primary & Secondary Ionization

• Primary Ionization: Free electrons (from natural radiation/UV) gain energy from the electric field, collide with neutral gas molecules, and ionize them, releasing more electrons and positive ions.

  • $$\displaystyle e^- + M \rightarrow 2e^- + M^+ $$

• Secondary Ionization: Positive ions drift to the cathode, strike it with high energy, causing emission of secondary electrons from the cathode surface. This is crucial for sustaining the discharge.

2.1.2 Townsend Discharge Theory

• First Townsend Ionization Coefficient ($\alpha$): Average number of ionizing collisions made by an electron per unit drift length in the direction of the field.

  • $$\displaystyle \alpha = A p e^{-B p / E} $$, where $p$ = pressure, $E$ = field, $A, B$ = gas-dependent constants.

• Second Townsend Coefficient ($\gamma$): Number of secondary electrons emitted per incident positive ion.

• Townsend Breakdown Condition: Current grows exponentially when the number of electrons multiplies sufficiently.

$$i = i_0 e^{\alpha d} \cdot \frac{1}{1 - \gamma (e^{\alpha d} - 1)}$$

**Breakdown occurs** when the denominator $$\displaystyle \rightarrow 0 $$:

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

This is the **Townsend criterion** for self-sustained discharge.

2.1.3 Streamer Mechanism (Non-uniform Fields)

• Limitation of Townsend: Cannot explain fast breakdown (microseconds) in non-uniform fields (e.g., rod-plane).

• Streamer Theory: A highly ionized, luminous channel (streamer) propagates from the anode towards the cathode.

  • Initiation: Space charge near the electrode tip distorts the field, enhancing ionization.

  • Propagation: Photons from recombination excite neutral molecules ahead, creating new electron-ion pairs. The space charge at the streamer tip has a high field gradient, driving it forward.

  • Final Breakdown: When streamer reaches the cathode, a low-resistance conductive path forms, causing spark breakdown.

2.1.4 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): From Townsend criterion, assume $$\displaystyle \alpha / p = A e^{-B p / E} $$ and $$\displaystyle E = V_b/d $$.

$$\gamma \left( e^{A d \cdot p \cdot e^{-B p d / V_b}} - 1 \right) = 1$$

For a given gas, $\gamma$ is constant. Solving for $$\displaystyle V_b $$ yields $$\displaystyle V_b = f(pd) $$.

• Paschen Minimum: The curve $$\displaystyle V_b $$ vs. $pd$ has a minimum. For air at STP, $$\displaystyle V_b^{min} \approx 327 $$ V at $pd \approx 0.567$ cm·torr.

  Practical Implication: For a given $$\displaystyle V_b $$, there is a critical $pd$. Below it, $$\displaystyle V_b $$ rises (mean free path too long for ionization). Above it, $$\displaystyle V_b $$ rises (too many collisions, electrons lose energy). HV equipment design must avoid operating near the Paschen minimum for the insulating gas used.

2.1.5 Statistical & Formative Time Lags

• Total Time Lag ($T$): Time between voltage application and breakdown.

$$T = T_s + T_f$$

• Statistical Time Lag ($$\displaystyle T_s $$): Time for a free electron to be initiated (from natural radiation/background). Random, probabilistic. Decreases with increasing overvoltage.

• Formative Time Lag ($$\displaystyle T_f $$): Time for the electron avalanche to grow to breakdown (governed by Townsend/streamer processes). Deterministic, depends on gap geometry and field.

• Importance: Crucial for impulse insulation coordination. A high $$\displaystyle T_s $$ can provide some inherent protection against very fast transients.

2.2 Vacuum Breakdown

• Mechanism in Deep Vacuum ($$\displaystyle < 10^{-4} $$ torr): No gas molecules to ionize. Breakdown occurs via field emission and microprotrusion.

  1. Field Emission: High field ($$\displaystyle > 10^7 $$ V/m) at microscopic cathode protrusions emits electrons via quantum tunneling.

  2. Micro-arc: Localized heating at the protrusion tip can vaporize metal, creating a dense vapor cloud.

  3. Self-sustained Arc: Vaporized metal ions/electrons cause ionization in the vapor, leading to a low-voltage, high-current arc.

• Causes of Arcing:

  • Cathode Spot: Localized vaporization site on the cathode.

  • Anode Spot: Formed by high-energy electron bombardment.

  • Particle Ejection: Microparticles from electrodes bridging the gap.

2.3 Solid Dielectrics

• Intrinsic Strength: The maximum electric field a perfect, defect-free dielectric material can withstand before electronic breakdown. Typically very high ($$\displaystyle \sim 10^8 $$ - $$\displaystyle 10^9 $$ V/m). Not practically achievable due to manufacturing defects.

• Electronic (Avalanche) Breakdown Mechanism:

  1. Electrons in the valence band are accelerated by the field.

  2. If field is high enough, electrons gain sufficient energy to excite other electrons across the band gap (impact ionization).

  3. This creates an electron-hole avalanche.

  4. When carrier density becomes very high, a conductive channel forms, leading to thermal runaway and material damage (tracking, carbonization).

  • Note: This is a high-field, fast process (nanoseconds). More common in crystalline, homogeneous solids like sapphire or diamond.

3.0 High Voltage Generation

3.1 AC High Voltage Generation

3.1.1 Series Resonant Circuit (Tesla Transformer Principle)

• Circuit: HV transformer (low voltage, high current) -> HV capacitor ($C$) -> HV inductor ($L$) -> Test object (capacitive load $$\displaystyle C_t $$).

• Principle: Operates at the series resonant frequency of $L$ and the combined capacitance ($C$ in series with $$\displaystyle C_t $$).

• Resonance Condition Derivation:

  Impedance $$\displaystyle Z = j\omega L + \frac{1}{j\omega C_{eq}} $$, where $$\displaystyle C_{eq} = \frac{C C_t}{C + C_t} $$.

  At resonance, $$\displaystyle Z = 0 $$ (purely resistive):

$$\omega L = \frac{1}{\omega C_{eq}} \Rightarrow \omega_0^2 = \frac{1}{L C_{eq}}$$

$$f_0 = \frac{1}{2\pi \sqrt{L C_{eq}}}$$

• Advantage: At resonance, the reactive power in $L$ and $C$ cancels. The small current drawn from the supply produces a very large voltage across $$\displaystyle C_t $$ (Q-factor magnification: $$\displaystyle V_{out} = Q \cdot V_{in} $$).

3.1.2 Tesla Coil (Air-Cored Resonant Transformer)

• Construction:

  • Primary: Few turns of heavy copper, connected to HV capacitor & spark gap.

  • Secondary: Many turns of fine wire, wound on a cylindrical form (often with a toroidal top terminal to control field gradient).

  • Coupling: Loose (magnetic) coupling between primary and secondary.

• Working:

  1. Capacitor $C$ charges from HV supply.

  2. Spark gap fires, discharging $C$ through primary, creating an oscillating current.

  3. Mutual inductance induces high voltage in secondary.

  4. System resonates at secondary's natural frequency. Energy transfers back and forth between primary inductance and secondary capacitance (including top terminal).

  5. Current Flow Near Coil: The high-frequency, high-voltage AC creates intense electrostatic and electromagnetic fields. Objects near the toroid experience corona and brush discharges as the surrounding air breaks down. Current flows through these ionized paths to ground.

3.2 DC High Voltage Generation

3.2.1 Cockcroft-Walton (CW) Multiplier

• Circuit: Cascaded stages of capacitor-diode pairs. Each stage doubles the peak AC input voltage.

• Working (for n stages):

  • Odd stages charge to peak input voltage $$\displaystyle V_m $$ during positive half-cycle.

  • Even stages charge to $$\displaystyle 2V_m $$ during negative half-cycle.

  • Output: $$\displaystyle V_{out} \approx 2n V_m $$ (neglecting ripple & load).

• Advantages:

  • Simple, no transformer needed for high output.

  • Lightweight, compact for given rating.

  • Good for portable/field testing.

• Limitations:

  • High ripple and poor voltage regulation under load.

  • Capacitor voltage stress increases with stage number.

  • Limited current output.

  • Efficiency drops with number of stages.

3.3 Impulse Voltage Generation

3.3.1 Impulse Generator Circuit (Marx Circuit)

• Basic Unit: Capacitor ($C$) charged in parallel to DC voltage $$\displaystyle V_c $$ via charging resistors ($$\displaystyle R_{ch} $$). Discharged in series via spark gaps ($G$) into the test object.

• Operation:

  1. All capacitors charge to $$\displaystyle V_c $$ (parallel).

  2. Triggering spark gap $$\displaystyle G_1 $$ fires.

  3. Voltage across $$\displaystyle G_1 $$ appears across $$\displaystyle C_1 $$ and $$\displaystyle G_2 $$, causing $$\displaystyle G_2 $$ to break down.

  4. Process continues down the line, connecting all capacitors in series.

  5. Total output voltage $$\displaystyle \approx n V_c $$ (where n = number of stages), with a fast rising front (controlled by front resistors $$\displaystyle R_f $$) and a decaying tail (controlled by tail resistors $$\displaystyle R_t $$ and load capacitance).

• Standard Waveforms: Lightning Impulse (1.2/50 μs), Switching Impulse (250/2500 μs).

3.3.2 Triggering: Three-Electrode Gap

• Arrangement: Main gap (between electrodes A & B) + a triggering electrode (C) placed near the cathode (B).

• Working:

  1. Main gap voltage is set below its self-breakdown value.

  2. A high-voltage pulse (from a separate pulser) is applied to the triggering electrode C.

  3. This creates a localized high field near C, initiating a pilot spark.

  4. The pilot spark rapidly ionizes the gap, reducing breakdown voltage, and causes the main gap to break down synchronously.

• Advantages:

  • Precise Timing: Breakdown occurs at a predetermined instant on the voltage wave.

  • Consistency: Reduces scatter in breakdown voltage measurements.

  • Synchronization: Essential for multi-stage generators to ensure simultaneous breakdown.

3.3.3 Control Tripping

• Purpose: To discharge the impulse generator safely and quickly after a shot, and to recharge it for the next operation.

• Method: A control tripping gap (or a triggered spark gap) is placed across the charging circuit.

  1. After impulse is generated and test object discharged, the control gap is triggered.

  2. This shorts the charging supply, rapidly discharging all generator capacitors through the charging resistors.

  3. Prevents prolonged high voltage on the charging circuit and allows immediate safe access.

  4. Recharging begins only after control gap de-ionizes.

4.0 High Voltage Measurement Techniques

4.1 General Requirements

• Accuracy: Known and stable division ratio.

• Wide Bandwidth: For impulse measurements (up to MHz).

• Low Loading: Minimal effect on the circuit under test.

• Safety & Insulation: Must withstand the voltage being measured.

• Screening: To avoid EMI pickup, especially for impulses.

4.2 Potential Dividers

• Principle: A known fraction of the HV is measured at the low-voltage end: $$\displaystyle V_{HV} = V_{LV} / k $$, where $k$ is the division ratio.

• Types & Comparison:

4.2.4 Conditions for Impulse Voltage Measurement

1. Step Response: The divider's response to a fast-rising step must be ** critically damped** or have minimal ringing. This is achieved by matching the time constant of the divider ($$\displaystyle R_{eff}C_{eff} $$) to the characteristic impedance of the connecting cable.

2. Screening: The entire divider and connecting cable must be in a continuous, grounded metallic shield to prevent EMI.

3. Low Inductance: All connections must be short and direct to minimize loop inductance.

4. Known Division Ratio: Must be calibrated for the specific waveform (step, impulse) under expected conditions.

4.3 Sphere Gap Method

4.3.1 Principle & Construction

• Principle: Based on the uniform field breakdown between two identical, symmetrically placed spheres. Breakdown voltage is a unique function of sphere diameter ($D$) and gap spacing ($S$), for a given $D/S$ ratio.

• Construction: Two polished, identical metal spheres mounted on insulated supports. Gap is adjustable. One sphere grounded, other connected to HV. Flashover is the breakdown event.

4.3.2 Measurement of AC, DC, Impulse

• AC/DC: Measure the 50% breakdown voltage (voltage at which 50% of applications cause breakdown). Requires multiple shots due to statistical time lag.

• Impulse: Measure the peak value of the impulse wave that causes breakdown. The breakdown is almost instantaneous (formative lag only), so the peak is read directly from the oscilloscope record of the applied voltage.

• Calibration: Standard tables/graphs exist for $$\displaystyle V_b $$ vs. $S$ for different $D$ (e.g., 25 cm, 50 cm, 100 cm, 150 cm spheres) and for different waveforms.

4.3.3 Factors Influencing Accuracy

• Sphere Surface: Must be clean, smooth, free from pits/rust.

• Gap Setting: Precise measurement of gap distance $S$.

• Ambient Conditions: Air density (pressure, temperature, humidity) affects $$\displaystyle V_b $$. Correction factors (air density factor, humidity factor) must be applied.

• Surrounding Objects: Must maintain minimum clearance from grounded objects (typically > 2D) to avoid field distortion.

• Voltage Waveform: For non-standard impulses, correction may be needed.

• Statistical Scatter: Multiple shots needed to determine 50% breakdown value.

4.4 Electrostatic Voltmeters

• Principle: Based on the force of attraction between charged plates. A moving vane (attached to a pointer) is repelled or attracted by a fixed electrode when voltage is applied. The deflection is proportional to $$\displaystyle V^2 $$.

• Construction: Fixed electrode (connected to HV) and a lightweight, pivoted moving vane (grounded or at a fixed potential). Damping is pneumatic or eddy-current.

• Use: AC and DC measurement (since force depends on $$\displaystyle V^2 $$, it reads RMS for AC sine wave). Not for impulse (too slow).

• Advantages: No loading (infinite impedance), good accuracy, direct reading.

• Disadvantages: Bulky, fragile, limited range, slow response.

4.5 Generating Voltmeters for DC HV

• Principle: A high-voltage rotating electrode (or moving vane) generates a current proportional to the applied voltage. This current is measured by a sensitive ammeter.

$$I = k V$$

where $k$ is a constant depending on geometry and rotation speed.

• Construction: A motor-driven rotor (with curved electrodes) spins inside a stationary stator. The rotor is connected to HV, stator grounded. Capacitive coupling generates an AC current in the stator circuit, which is rectified and measured.

• Advantages: True non-contact measurement, very high impedance, suitable for very high DC voltages (MV range).

• Disadvantages: Requires rotation (mechanical wear), calibration depends on speed, sensitive to vibration.

5.0 High Voltage Testing of Power System Equipment

5.1 Types of High Voltage Tests

5.1.1 Dielectric Tests

• High Voltage (Withstand) Test: Applies a specified AC, DC, or impulse voltage for a defined time (e.g., 1 min AC, 10 impulse shots). Objective: Verify that insulation can withstand the test voltage without breakdown.

• Insulation Resistance (IR) Test: Applies a low DC voltage (e.g., 2.5/5 kV Megger) and measures resistance in MΩ/GΩ. Objective: Detect gross insulation deterioration, moisture, contamination. Not a substitute for HV test (doesn't simulate high stress).

5.1.2 Partial Discharge (PD) Tests

• Principle: PD are localized electrical discharges that do not completely bridge the electrodes. They cause pulses of current lasting nanoseconds.

• On Cables: Test is performed at AC voltage (usually 1.5-2x rated voltage). PD activity is measured in pC (picocoulombs). High PD indicates voids, impurities, or defects in insulation.

• Fault Location (Time Domain Reflectometry - TDR):

  1. A fast-rising impulse is injected into the cable.

  2. PD or fault reflections are detected at the sending end.

  3. Time delay ($\Delta t$) between injected pulse and reflected pulse gives distance to fault:

$$\boxed{L = \frac{v \cdot \Delta t}{2}}$$

    where $v$ = wave propagation velocity in cable ($\approx 0.6c$ to $0.8c$), $L$ = distance to fault.

5.2 Testing of Specific Equipment

5.2.1 Power Transformers

• HV Withstand Test (Dielectric Test):

  • AC: Applied between windings and ground (or between windings) at power frequency for 1 min. Checks major insulation.

  • Impulse: Full-wave (1.2/50 μs) and chopped-wave (to simulate switching) applied to terminals. Checks longitudinal insulation (between turns) and ground insulation.

• Other Relevant Tests:

  • Ratio Test: Verify turns ratio.

  • No-Load & Short-Circuit Tests: Determine losses, impedance.

  • Temperature Rise Test.

  • Oil Tests: Dielectric strength, water content, dissolved gas analysis (DGA).

5.2.2 Circuit Breakers

• Short-Circuit (Making & Breaking) Test:

  • Objective: Verify ability to make and break fault currents.

  • Method: Tested in a synthetic test circuit or using a dedicated short-circuit generator. Parameters: rated short-circuit breaking current, recovery voltage, arcing time.

• Dielectric Test:

  • Power Frequency Withstand: Applied across open contacts (withstand voltage) and between contacts and ground.

  • Impulse Withstand: Lightning impulse applied across open contacts.

5.2.3 Insulators

• Mechanical Strength Test: Applies a specified load (tensile, bending, torsional) to verify ultimate strength (fails at > 1.2-1.5x rated load).

• Puncture Voltage Test: Voltage applied across the insulator body (between metal fittings) to determine internal dielectric strength. Should be much higher than flash-over voltage.

• Flash-Over Voltage Test: Voltage applied between top and bottom fittings (normal service condition). Measures the voltage at which surface flashover occurs along the insulator. Critical for design (creepage distance).

5.2.4 High Voltage Cables

• Partial Discharge Test: As described in 5.1.2. Primary test for cable quality assurance.

• HV Withstand Test: AC or DC voltage applied between conductor and sheath/ground for a specified time (e.g., 5 min AC).

• Insulation Resistance & Capacitance Measurement.

5.2.5 Rotating Machines (Motor Coil Insulation)

• Insulating Paint Pouring Methods (for coil impregnation):

  1. Dip-Pouring: Coil is dipped into a tank of liquid varnish/resin.

  2. Flow-Pouring: Varnish is poured over the coil while it is rotated.

  3. Vacuum-Pressure Impregnation (VPI): Coil placed in pressure vessel, vacuum drawn to remove air/moisture, then varnish introduced under pressure. Most effective for complete penetration and void removal.

  • Objective: To fill all voids in the insulation system, improve dielectric strength, mechanical strength, and thermal conductivity.

6.0 Surge Currents and Their Measurement

6.1 Nature & Sources

• Nature: Very high-magnitude, short-duration (μs to ms) currents.

• Sources:

  • Lightning Strikes: Direct strike or induced surges on lines.

  • Switching Operations: Capacitor bank switching, fault clearing, load rejection.

  • Faults: Short-circuit currents (especially near generating stations).

6.2 Measurement Methods & Instruments

• Rogowski Coil: A flexible, toroidal coil wound on a non-magnetic core. Output voltage $$\displaystyle v_o = M \cdot di/dt $$, where $M$ is mutual inductance. Integrates to get current. Advantages: No saturation, linear, isolated. Disadvantages: Needs integration, sensitive to position.

• Current Transformer (CT) with High Bandwidth: Special wide-band CTs (often air-core or with special cores) can measure fast surges up to several MHz.

• Shunt Resistor: A low-value, non-inductive resistor (e.g., metal film, special carbon). Voltage drop $$\displaystyle v = i \cdot R $$ is measured. Key: Must have very low inductance ($$\displaystyle L < 1 \mu H $$ typically). Often made of rectangular cross-section wire to minimize skin effect.

• Magnetic Field Probe (B-dot Probe): Measures rate of change of magnetic field ($dB/dt$) near a conductor. Current is derived via Ampere's law. Used for very high currents where direct contact is impossible.

6.3 Challenges

• Very High Magnitude & $di/dt$: Can saturate magnetic cores (CTs), cause large voltages on shunts.

• Bandwidth Requirement: Need instruments with bandwidth > 1 MHz to capture fast rise times.

• Electromagnetic Interference (EMI): Surge generates strong EMI, can corrupt measurement signals. Requires shielding and fiber-optic isolation.

• Safety & Insulation: Probe/measuring circuit must withstand the surge voltage environment.

• Calibration: Calibrating for fast pulses is more complex than for steady-state.

6.4 Cavity Breakdown Phenomenon

• Definition: Breakdown that occurs inside a hollow chamber or cavity within an insulating solid or at an interface (e.g., void in epoxy resin, between cable conductor and insulation).

• Mechanism:

  1. Cavity has lower dielectric strength than surrounding solid.

  2. Under AC or impulse voltage, the electric field in the cavity is higher than in the solid (due to permittivity difference: $$\displaystyle E_{cavity} = E_{solid} \cdot \epsilon_{r, solid} $$).

  3. When field in cavity exceeds its breakdown strength, internal partial discharges occur.

  4. Repeated PDs erode the cavity walls, produce gases (like $$\displaystyle O_2 $$, $$\displaystyle CO_2 $$ from decomposition), and eventually lead to tracking and complete breakdown of the main insulation.

• Significance: A major cause of long-term insulation failure in transformers, switchgear, and cable joints. PD monitoring is a key condition assessment technique.