High Voltage Engineering (EX-702 (C)) - Unit 2 Short Notes

UNIT 2: HIGH VOLTAGE ENGINEERING

I. Introduction to High Voltage Technology

High Voltage (HV) is generally defined as voltage levels significantly above low-voltage (LV) distribution levels (e.g., > 1 kV AC or 1.5 kV DC). It is the backbone of modern power systems for efficient long-distance transmission.

Voltage Classifications:

Key Applications:

1. Power Applications:

   • Transmission: Bulk power transfer over long distances with reduced losses ($$\displaystyle P_{loss} \propto I^2R $$, higher V → lower I).

   • Distribution: Feeder networks in cities/industrial areas.

   • Equipment: Power transformers, circuit breakers, instrument transformers (CTs, PTs), surge arresters.

2. Non-Power Applications:

   • Industrial: X-ray generators, electrostatic precipitators, paint spraying, food processing.

   • Scientific: Particle accelerators, plasma research, high-voltage testing laboratories.

   • Medical: Diagnostic X-ray machines, radiation therapy.

[!TIP] Exam Focus: Be ready to differentiate HV/EHV/UHV ranges and give specific examples for both power and non-power applications.

II. High Voltage Generation in Laboratories

Need: To test the dielectric strength of insulation, simulate lightning/switching surges, and research breakdown phenomena.

1. Series Resonant Circuit

• Principle: Uses the high voltage across a capacitor ($C$) in a series $LCR$ circuit at resonance. Impedance is minimum ($$\displaystyle Z = R $$), current is high, and voltage magnification occurs.

• Resonance Condition:

$$X_L = X_C \implies \omega L = \frac{1}{\omega C}$$

$$\boxed{f_r = \frac{1}{2\pi\sqrt{LC}}}$$

Voltage across capacitor: 

$$V_C = Q \cdot V_{source}$$

where $Q$ (quality factor) is high.

• Use: Primarily for generating high-frequency AC for testing cable insulation and capacitors.

2. Cockcroft-Walton (CW) Voltage Multiplier

• Construction: Cascaded stages of diodes and capacitors. A 2-stage circuit has 4 diodes ($$\displaystyle D_1 $$ to $$\displaystyle D_4 $$) and 4 capacitors ($$\displaystyle C_1 $$ to $$\displaystyle C_4 $$). Input is a high-frequency AC source (transformer secondary).

• Working Principle: During positive half-cycle, $$\displaystyle C_1 $$ charges via $$\displaystyle D_1 $$. During negative half-cycle, $$\displaystyle C_1 $$ and $$\displaystyle C_2 $$ charge in series via $$\displaystyle D_2 $$. This cascading effect multiplies voltage. Output $$\displaystyle V_{out} \approx 2n \cdot V_{peak} $$ (n = stages), reduced by ripple and loading.

• Advantages: Simple, no core saturation (HF operation), good for DC high voltage.

• Limitations: High output impedance, poor regulation under load, significant voltage drop with increasing stages.

3. Tesla Coil

• Construction: Two resonant circuits (primary & secondary) magnetically coupled. Primary: few turns, large capacitor, spark gap. Secondary: many turns, high Q, toroidal terminal.

• Working Principle: Primary circuit oscillates at its resonant frequency. Energy transfers magnetically to secondary, which oscillates at its higher resonant frequency. The high $Q$ and voltage transformation ratio produce extremely high voltages (MV) at very high frequencies (100s of kHz).

• Effect of High Frequency: Skin effect forces current to flow on the surface of nearby objects. Capacitive coupling allows current to flow through insulating materials (e.g., a person can light a bulb without direct contact).

4. Impulse Generator (Marx Circuit)

• Need: To generate standard lightning impulse (1.2/50 μs) and switching impulse (250/2500 μs) voltages for insulation coordination tests.

• Triggering Mechanism (Three-Electrode Gap):

  • Construction: Each stage has a main spark gap ($$\displaystyle G_M $$) and a triggering gap ($$\displaystyle G_T $$) in series. A separate triggering pulse is applied to the third (trigger) electrode of $$\displaystyle G_T $$.

  • Why Preferred: Provides precise, simultaneous breakdown of all stage gaps, ensuring a clean, undistorted output waveform. Mechanical/electrical triggering is unreliable.

• Control Tripping Methods:

  1. Electrical Triggering: Using a separate pulse generator (most common, precise).

  2. Optical Triggering: Using laser pulses to ionize gap (for highest precision, EMI immunity).

  3. Mechanical Triggering: Using a rotating commutator (obsolete).

• Necessity of Triggering: To synchronize the discharge of all capacitors in series, producing the desired fast-rising impulse waveform. Without synchronized triggering, the output would be distorted and non-standard.

[!TIP] Exam Focus: Distinguish CW (DC, poor regulation) from Tesla Coil (HF AC, capacitive coupling). Know the Marx circuit triggering method and the difference between lightning & switching impulse waveshapes.

III. Breakdown Mechanisms in Gaseous Dielectrics

A. Ionization Processes

1. Primary Ionization: Free electrons (from cosmic rays/background radiation) gain energy from electric field. If energy > ionization energy of gas molecule, collision creates a new electron-ion pair.

   • Townsend's First Ionization Coefficient ($\alpha$): Number of ionizing collisions per unit length traveled by an electron.

$$\alpha = A p e^{-Bp/E}$$

where $p$ = pressure, $E$ = field, $A,B$ = gas-dependent constants.

2. Secondary Ionization: Positive ions drift to cathode, cause emission of secondary electrons via:

   • Ion impact (heavy ions knock out electrons)

   • Photon emission (excited atoms emit UV photons)

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

B. Townsend Discharge Theory & Breakdown Condition

• Theory: Electron avalanche grows as:

$$n = n_0 e^{\alpha d}$$

where $$\displaystyle n_0 $$ = initial electrons, $d$ = gap distance.

• For steady breakdown, electrons from one avalanche must trigger the next. Condition:

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

$$\boxed{\text{Townsend Breakdown Criterion: } \gamma (e^{\alpha d} - 1) = 1}$$

For large $\alpha d$: 

$$e^{\alpha d} = \frac{1}{\gamma}$$

• Limitation: Fails for large gaps (> few cm) and non-uniform fields. Cannot explain rapid current rise and spark formation.

C. Streamer Mechanism (Improvement over Townsend)

• Theory for Non-Uniform Fields: In a strong field region (e.g., around a point), an electron avalanche develops a space charge of positive ions. This space charge distorts the local electric field, enhancing it at the avalanche head and weakening it behind.

• Streamer Formation: The enhanced field at the head ionizes new gas ahead, causing the avalanche to propagate forward like a finger (streamer). Once streamers bridge the gap, a conducting channel forms → spark breakdown.

• Improvement: Explains fast breakdown (microseconds) and is valid for large gaps and non-uniform fields.

D. Time Lags in Breakdown

1. Statistical Time Lag ($$\displaystyle t_s $$): Time to form initial electron(s) from natural radiation. Random, follows stochastic distribution.

2. Formative Time Lag ($$\displaystyle t_f $$): Time from first electron to complete breakdown (avalanche/streamer development). Depends on $E/p$ and gap geometry.

   • Total Breakdown Time Lag:

$$t_{total} = t_s + t_f$$

E. 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 ($d$).

• Mathematical Expression:

$$V_b = f(pd)$$

From Townsend criterion, for air: 

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

Simplified: 

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

• Paschen Minimum: The curve $$\displaystyle V_b $$ vs. $pd$ has a minimum. For air, $$\displaystyle V_{b(min)} \approx 327 V $$ at $pd \approx 0.567$ Torr·cm.

  Significance: Below the minimum, $$\displaystyle V_b $$ rises because mean free path is too large for ionization. Above minimum, $$\displaystyle V_b $$ rises because collisions are too frequent for electrons to gain sufficient energy.

• Practical Implications:

  • Clearance Design: For a given $$\displaystyle V_{max} $$, minimum safe distance $d$ is determined from Paschen curve at operating pressure.

  • Vacuum Systems: At very low $p$, $pd$ is small → $$\displaystyle V_b $$ is high. This is why vacuum is an excellent insulator.

  • Gas-Filled Equipment: SF₆ circuit breakers operate at pressures where $pd$ is on the rising part of Paschen curve for high dielectric strength.

[!TIP] Exam Focus: Derive Townsend criterion. Contrast Townsend vs. Streamer. Sketch and explain Paschen curve, marking minimum. Relate $pd$ to insulation coordination.

IV. Breakdown in Vacuum and Solid Dielectrics

A. Vacuum Breakdown

• Mechanism (Deep Vacuum, ~10⁻⁶ Torr):

  1. Field Emission: Very high electric field (>10⁷ V/m) at cathode micro-protrusions causes electron emission.

  2. Micro-discharges: If anode has insulating films (e.g., adsorbed gases), emitted electrons cause localized heating/vaporization → micro-arcs.

  3. Particle-initiated: Microparticles from electrodes are accelerated, strike electrode, cause local melting/vaporization → arc.

• Factors Causing Arcing:

  • High surface electric field (field enhancement).

  • Presence of insulating contaminants or microparticles.

  • Poor surface finish (roughness).

  • Ultimate Limitation: Not the vacuum itself, but electrode surface conditions.

B. Solid Dielectrics

1. Intrinsic Breakdown Strength: The maximum electric field a perfect, defect-free crystal can withstand before electronic breakdown. Very high (100s of MV/m), but rarely achieved in practice due to defects.

2. Electron Avalanche Breakdown (Practical Mechanism):

   • Electrons injected from cathode or generated by ionization.

   • Accelerate, collide with lattice → create electron-hole pairs (avalanche).

   • Heat generation from collisions → thermal runaway → thermal breakdown.

   • Also includes electric breakdown (direct field ionization).

3. Insulation Application (Motor Coils):

   • Pouring Methods: Varnish or resin is poured/impregnated into the wound coil under vacuum to remove air and fill all voids. Prevents partial discharges in voids.

   • Other Methods: Dip & bake, VPI (Vacuum Pressure Impregnation).

C. Partial Discharge (PD)

• Definition: Localized electrical discharge that only partially bridges the insulation between conductors. Occurs in cavities/voids within solid insulation or at gas-solid interfaces.

• PD in Cables: Tested using Oscillating Wave (OW) testing or AC PD testing.

  • Fault Location: Using Time Domain Reflectometry (TDR) or pulse-echo method. PD pulses reflect from cable ends/faults; time delay gives distance.

• Cavity Breakdown: Void filled with gas (lower dielectric strength). When local $E$ exceeds gas $$\displaystyle V_b $$, PD occurs. Erodes insulation over time → eventual failure.

[!TIP] Exam Focus: Contrast vacuum breakdown (field emission, particles) with solid breakdown (avalanche, thermal). Explain why voids cause PD and how it leads to failure. Know cable PD test principle and fault location.

V. High Voltage Measurement Techniques

A. Potential Dividers

Condition for Accurate Impulse Measurement: The divider's impedance must be much higher (for voltage dividers) or lower (for current dividers) than the system under test, and its response time must be much faster than the impulse front time.

B. Sphere Gap

• Standard Construction: Two identical, polished, spherical electrodes (diameters: 6.25 cm, 12.5 cm, 25 cm, 50 cm, 100 cm). Mounted horizontally/vertically with fixed gap.

• Operation:

  • AC/DC: Breakdown voltage is a function of gap distance ($d$) and sphere diameter ($D$). Tables/curves provided in standards (IEC 60052).

  • Impulse: Measures peak value. Breakdown voltage is slightly higher than for DC due to statistical time lag. Standard tables exist for 1.2/50 μs wave.

• Factors Influencing Accuracy:

  • Gap distance ($d$)

  • Sphere diameter ($D$) and $d/D$ ratio

  • Polarity (for DC/Impulse)

  • Atmospheric conditions (pressure, temperature, humidity) → correction factors.

  • Electrode surface condition, alignment, nearby earthed objects.

C. Generating Voltmeter

• Principle: Measures high DC voltage by generating a current proportional to voltage, which drives a standard low-voltage meter.

• Construction/Working:

  1. Motor-Driven Generator: A small DC motor (driven by separate low-voltage supply) drives a DC generator. The generator's field winding is excited by the HV to be measured.

  2. The generated voltage $$\displaystyle V_g \propto I_f \propto V_{HV} $$. $$\displaystyle V_g $$ is measured by a standard voltmeter.

  3. Key: Motor and generator are in a shielded, grounded enclosure; only field winding is at HV. Provides galvanic isolation.

D. Electrostatic Voltmeter

• Principle: Attraction force between fixed and moving vanes in a capacitor is proportional to $$\displaystyle V^2 $$. This force rotates a pointer.

• Construction: Two sets of vanes (fixed & movable) form a capacitor. One set connected to HV via a high-value protective resistor. Damping provided by air vanes or magnetic disk.

• Use: For AC & DC high voltage measurement. Very high input impedance (MΩ-GΩ), low power consumption. Accuracy depends on calibration.

E. Surge Current Measurement

• Methods & Instruments:

  1. Rogowski Coil: A toroidal, air-cored coil around the conductor. Output voltage $$\displaystyle v_o = M \cdot di/dt $$, where $M$ is mutual inductance. Integrator needed to get $i(t)$. Advantages: No saturation, linear, isolated.

  2. Shunt Resistor (Current Viewing Resistor - CVR): Low-value, non-inductive resistor. $$\displaystyle V_{shunt} = i \cdot R_{shunt} $$. Must handle high peak currents, low inductance critical.

  3. Current Transformer (CT): Not suitable for DC or very high-frequency surge components due to core saturation.

• Challenges:

  • Isolation: Sensor must provide high isolation from HV circuit.

  • Bandwidth: Must respond to fast rise-times (nanoseconds for lightning impulses).

  • Saturation: Magnetic cores (CTs) saturate; use air-core (Rogowski) or special low-saturation materials.

  • Impedance: Sensor must not disturb the circuit (low impedance for current measurement).

[!TIP] Exam Focus: Compare dividers in a table. Know sphere gap factors. Explain Rogowski coil principle (di/dt measurement, need for integration). Contrast shunt vs. Rogowski for surge current.

VI. High Voltage Testing of Electrical Equipment

A. Circuit Breakers

1. Short-Circuit Test (Making & Breaking Capacity Test):

   • Procedure: Breaker is connected to a special test circuit with a source, current-limiting reactor, and a "test" object (often a parallel breaking unit). A trigger signal initiates a short-circuit current from the source. Breaker must make (close on) and break (interrupt) this current.

   • Objectives: Verify ability to withstand and interrupt maximum fault current (rated short-circuit current) without excessive arcing, contact welding, or failure. Tests at various currents (up to 100% rated) and recovery voltages.

2. Dielectric Test (Insulation Test):

   • Procedure: Apply a specified AC (power frequency) or impulse voltage between:

     • Main circuits and ground.

     • Main circuits of different poles.

     • Main circuits and operating mechanism.

   • Objectives: Verify integrity of main insulation (support insulators, bushings, arc chutes). No flashover or breakdown should occur.

B. Insulators

1. Mechanical Strength Test:

   • Purpose: Verify ability to withstand specified mechanical loads (tension, compression, bending, torsion) without failure.

   • Method: Apply static load in a testing machine until failure or for a specified duration (proof load). Measured in kN.

2. Puncture Voltage Test:

   • Purpose: Determine voltage at which insulation material itself breaks down (through the body of the insulator, not over the surface).

   • Method: Apply voltage between the metal pin and the metal cap (through the insulator body). Usually destructive.

3. Flash-Over Voltage Test:

   • Purpose: Determine voltage at which an arc forms over the surface of the insulator (from pin to cap).

   • Method: Apply voltage between pin and cap in a clean, dry condition. Increase until flashover occurs. Non-destructive if flashover is temporary. Wet flashover test also performed.

C. Power Transformers

1. High Voltage Test (Dielectric Test):

   • Purpose: Verify insulation strength between windings, windings-to-ground, and between different voltage level windings.

   • Procedure:

     • Applied Voltage Test: AC voltage (usually 2x rated voltage + 1 kV, for 60 sec) applied to one winding with others grounded.

     • Induced Voltage Test: Lower voltage applied to LV winding to induce overvoltage in HV winding (tests inter-turn insulation). Frequency is increased (usually 100-400 Hz) to avoid core saturation.

     • Lightning Impulse Test: Standard impulse (1.2/50 μs) applied to terminals.

D. General Insulation Tests: Comparison

Necessity of Multiple Tests: No single test gives complete picture. IR test is quick & non-destructive for routine monitoring. HV test is a proof test for quality assurance after manufacture/repair. Both are complementary.

[!TIP] Exam Focus: For each equipment (CB, insulator, transformer), list the specific tests, their purpose, and procedure. Contrast HV test vs. IR test clearly. Know the difference between puncture and flashover for insulators.