UNIT 5: HIGH VOLTAGE ENGINEERING - EXAM-FOCUSED NOTES

I. FUNDAMENTALS OF HIGH VOLTAGE TECHNOLOGY

Definition and Significance

• High Voltage (HV): Typically > 1 kV AC or 1.5 kV DC.

• Classification:

  • HV: 1 kV – 36 kV (AC)

  • EHV: 72.5 kV – 245 kV (AC)

  • UHV: ≥ 800 kV (AC) / ≥ 600 kV (DC)

• Significance in Power Systems:

  • Enables long-distance power transmission with reduced I²R losses (P = VI).

  • Allows higher power transfer through a given conductor cross-section.

  • Essential for substations, transformers, and switchgear insulation coordination.

Applications

Need for HV Generation in Laboratories

• Insulation Testing: Type tests, routine tests, acceptance tests on equipment (cables, transformers, insulators).

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

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

• Simulating Overvoltages: Generating power frequency, switching impulse, and lightning impulse voltages to test equipment withstand capability.

[!TIP] Exam Focus: Be ready to list both power and non-power applications. Link HV generation directly to testing standards (IEC, IS).

II. BREAKDOWN MECHANISMS IN DIELECTRICS

Gaseous Dielectrics: Townsend's Theory

• Primary Ionization: Free electron (from natural radiation) gains energy from electric field, collides with neutral molecule → ionization (new electron + positive ion). Described by Townsend's first ionization coefficient (α): number of ionizing collisions per unit length.

• Secondary Ionization: Positive ions drift to cathode, cause secondary electron emission (via ion impact, photon impact). Described by Townsend's second ionization coefficient (γ): number of secondary electrons emitted per incident positive ion.

• Breakdown Condition: Avalanche growth becomes self-sustaining.

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

For large gaps, simplified to **αd ≈ constant** (typically 15-20).

Streamer Theory (for Non-Uniform Fields)

• Improvement over Townsend: Explains fast breakdown (nanoseconds) in highly non-uniform fields (e.g., rod-plane gap).

• Mechanism:

  1. Electron avalanche develops.

  2. Space charge of ions distorts the electric field at avalanche head.

  3. Field enhancement at the tip creates a conductive ionized channel (streamer) that propagates rapidly towards the anode.

  4. Streamer bridging the gap leads to breakdown.

Paschen's Law

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

$$ \boxed{V_b = f(pd)} $$

• Derivation (Simplified): From Townsend's condition ($$\displaystyle \alpha d = \text{constant} $$) and $$\displaystyle \alpha/p = A e^{-Bp/E} $$, where $$\displaystyle E = V/d $$. Solving yields $$\displaystyle V_b $$ as a function of $pd$.

• Paschen Minimum:

  • $$\displaystyle V_b $$ vs. $pd$ curve has a minimum ($$\displaystyle V_{\text{min}} $$) at an optimal $$\displaystyle (pd)_{\text{min}} $$.

  • For air: $$\displaystyle V_{\text{min}} \approx 327 $$ V at $$\displaystyle (pd)_{\text{min}} \approx 0.567 $$ Torr·cm.

• Practical Implications:

  • Insulation Design: For a given $V$, there is a minimum safe gap at a specific pressure. Too small a gap → breakdown; too large → Paschen minimum may be exceeded.

  • SF₆ Circuit Breakers: Operate at high pressure to shift $(pd)$ to the right of Paschen minimum, achieving high dielectric strength.

Time Lags

Vacuum Breakdown

• Mechanism in Deep Vacuum (< 10⁻³ Torr):

  1. Field Emission: High electric field at microprotrusions on cathode emits electrons.

  2. Microspot Heating: Localized heating at emission sites.

  3. Cathode Spot Formation: Vaporization of electrode material → metallic plasma → arc.

• Key Point: Vacuum has excellent dielectric strength but fails via surface phenomena (microprotrusions), not bulk gas ionization.

Solid Dielectrics

• Intrinsic Strength: Maximum electric field a perfect, defect-free material can withstand (typically 10-100 MV/m).

• Breakdown Mechanisms:

  • Electronic/Avalanche: High field accelerates electrons → impact ionization → thermal runaway (similar to gas, but in lattice).

  • Thermal: Local heating from losses (dielectric, conduction) → thermal runaway.

  • Electrical Treeing: Partial discharge-induced carbonized path growth.

• Partial Discharge (PD):

  • Concept: Localized dielectric breakdown within a small cavity or defect in a solid dielectric or at an interface, not a complete bridge.

  • Significance: Indicator of insulation degradation. Causes progressive damage (erosion, treeing).

  • PD Test on Cables: Apply AC voltage above operating level. Detect PD pulses using coupling capacitors and high-frequency current transformers (HFCT).

  • Fault Location: Measure time difference between PD pulses detected at both cable ends → calculate distance to defect using wave propagation velocity.

[!TIP] Common Pitfall: Do not confuse streamer (gas, fast) with treeing (solid, slow progressive). Paschen's law applies only to gaseous uniform fields.

III. HIGH VOLTAGE GENERATION

Series Resonant Circuit (Tesla Transformer Principle)

• Circuit: HV winding (L₂, C₂) in series with low-voltage winding (L₁) and capacitor (C₁).

• Resonance Condition:

$$ \boxed{\omega L = \frac{1}{\omega C}} \quad \text{or} \quad f = \frac{1}{2\pi\sqrt{LC}} $$

At resonance, impedance is minimum, current is maximum → high voltage across L₂C₂.

• Advantage: High voltage at low current, frequency transformation (high f).

Cockcroft-Walton (CW) Voltage Multiplier

• Principle: Cascaded voltage doubler stages using diodes and capacitors.

• Operation (2-stage):

  1. Positive half-cycle: C₁ charges to Vₘ via D₁.

  2. Negative half-cycle: C₂ charges to 2Vₘ (C₁ in series with supply).

  3. Next cycle: C₃ charges to 2Vₘ (via D₂, C₂ in series), C₄ to 3Vₘ, etc.

• Output Voltage (No Load): $$\displaystyle V_{\text{out}} \approx 2nV_{\text{peak}} $$ (n = stages).

• Advantages: No HV transformer needed for DC, compact, simple.

• Limitations: High ripple, poor regulation under load, voltage drop ∝ $$\displaystyle n^2 $$ due to capacitor charging currents.

Tesla Coil

• Construction:

  • Primary: Low turns, heavy gauge, few turns, in series with capacitor (C₁) and spark gap (SG).

  • Secondary: Many turns of fine wire, forms resonant LC circuit with inter-winding capacitance (C₂).

  • Coupling: Loose (magnetically coupled).

• Working:

  1. C₁ charges from supply.

  2. SG fires → oscillatory discharge in primary LC circuit.

  3. Resonant coupling excites secondary → high-frequency, high-voltage oscillation.

  4. Why current flows in nearby objects? High frequency → capacitive coupling to objects (displacement current) and skin effect confines current to surface.

• Application: HV AC source for testing, demonstration.

Impulse Voltage Generation (Marx Circuit)

• Basic Marx Generator: n identical capacitor stages (C) charged in parallel to Vₘ through resistors (Rₚ), then discharged in series via triggered spark gaps.

• Triggering Mechanism (Three-Electrode Gap):

  • Construction: Main gap (G₁) between stages, triggering gap (Gₜ) with third electrode (trigger pin) connected to a triggering pulse source.

  • Principle: A high-voltage pulse applied to the trigger pin creates a leader spark that bridges Gₜ, initiating breakdown of the main gap G₁.

  • Why Preferred? Provides synchronized, precise, and simultaneous triggering of all stages → clean, reproducible impulse waveform.

• Control Tripping: Using triggered spark gaps (as above) or ignitrons (gas-filled tubes) to initiate the discharge sequence at a precise instant.

[!TIP] Exam Focus: Be able to sketch the CW circuit, Tesla coil, and Marx generator with triggering. Know why Tesla coil current flows in nearby objects (high f → capacitive coupling).

IV. HIGH VOLTAGE MEASUREMENT

Potential Dividers for Impulse Voltages

• Conditions:

  1. Time Constant Matching: $$\displaystyle \tau_R = RC $$ (resistance-capacitance product) of divider must match that of the cable + oscilloscope input ($$\displaystyle \tau_C $$).

  2. Low Capacitance: To avoid loading the test circuit.

  3. Low Inductance: For fast impulse fronts.

  4. Resistance Value: High enough to minimize power draw, low enough to avoid excessive noise.

Sphere Gap

• Standard Sphere Gap: Two identical metal spheres of diameter D, separated by gap g.

• Principle: Breakdown voltage ($$\displaystyle V_b $$) is a function of D and g, independent of wave shape (for sufficiently long wavefronts).

• Measurement: Adjust g until breakdown occurs at the voltage peak. Read $$\displaystyle V_b $$ from standard tables (IEC 60052) corrected for atmospheric conditions.

• Factors Influencing Measurement:

  1. Sphere Diameter (D): Determines maximum measurable voltage.

  2. Gap Spacing (g): Must be within specified limits (0.1D < g < 0.5D).

  3. Atmospheric Conditions: Pressure (p), Temperature (T), Humidity (h). Apply correction factor:

$$ K = \frac{p}{p_0} \cdot \frac{T_0}{T} \cdot \frac{1}{1 + 0.00012 \cdot (h - h_0)} $$

    where subscript 0 = standard conditions (20°C, 760 Torr, 11 g/m³).

4.  **Polarity:** Positive polarity gives lower $$\displaystyle V_b $$ than negative for same gap.

5.  **Wavefront Time:** For very fast fronts (< 1 µs), $$\displaystyle V_b $$ is higher than for 50 µs wave.

Electrostatic Voltmeter

• Principle: Force of attraction between fixed and moving plates in a high-voltage electric field.

$$ F \propto V^2 \quad \Rightarrow \quad \text{Deflection} \propto V^2 $$

• Construction: Fixed electrode (connected to HV), movable vane/plate (spring-loaded), pointer, scale.

• Operation: For DC, direct reading. For AC, requires a rectifier (e.g., half-wave) to produce unidirectional force; scale calibrated for RMS.

• Advantages: No loading (high impedance), good accuracy, independent of frequency.

• Disadvantages: Bulky, limited range, sensitive to vibrations.

Generating Voltmeter

• Principle: Rotating vane or disk in the electric field between HV electrode and grounded case. The electric field induces charges on the rotating parts → AC current generated, proportional to V.

• Construction: Motor-driven rotor (vanes or segmented disk) inside an insulated, grounded housing connected to HV.

• Working: Rotor speed constant → generated current $$\displaystyle I_g \propto V $$. Measure $$\displaystyle I_g $$ with a sensitive microammeter.

• Application: High DC voltage measurement (kV to MV), where resistive dividers would have excessive power loss.

[!TIP] Common Pitfall: Sphere gap measures peak value of AC/impulse. For AC, if RMS is needed, divide peak by √2. Always correct for atmospheric conditions.

V. HIGH VOLTAGE TESTING OF EQUIPMENT

Circuit Breakers

• Short-Circuit Test (Making & Breaking):

  • Objective: Verify ability to interrupt (break) and make (close against) fault currents.

  • Method: Connect breaker in a test circuit with a synchronous generator or capacitor bank to simulate fault current. Measure current interruption, re-ignition, recovery voltage.

• Dielectric (Insulation) Test:

  • Objective: Verify insulation strength of main and auxiliary circuits.

  • Method: Apply power frequency (50/60 Hz) or impulse voltage between:

    • Live parts and ground.

    • Between poles (for multi-pole breakers).

    • Between auxiliary circuits and main circuits.

Insulators (Power Systems)

• Flash-Over Voltage Test:

  • Method: Apply increasing voltage (AC/impulse) across insulator string until surface flashover occurs.

  • Objective: Determine withstand voltage and critical flashover voltage.

• Mechanical Strength Test:

  • Objective: Verify ability to withstand tensile, compressive, bending, torsional loads (from conductor weight, wind, ice).

  • Method: Apply specified mechanical load in a testing machine.

• Puncture Voltage Test:

  • Objective: Verify internal dielectric strength of insulator material (porcelain, polymer).

  • Method: Apply voltage between metal fittings (pin & cap) with surface clean and dry to prevent flashover → forces breakdown through the body.

• Necessity: Ensures insulators can withstand electrical (flashover, puncture) and mechanical stresses in service, preventing line outages.

Power Transformers

• High Voltage (HV) Test (Withstand Test):

  • Purpose: Test main insulation (windings to ground, inter-winding).

  • Method: Apply AC voltage (typically 1.5-2x rated voltage) or impulse voltage (simulating lightning) for specified duration (e.g., 60s AC, 1.2/50 µs impulse).

  • Acceptance: No breakdown, discharge, or excessive leakage current.

• Difference from Insulation Resistance (IR) Test:

  | HV Test | IR Test | | :--- | :--- | | High Voltage (kV range), short duration. | Low Voltage (DC, 2.5-5 kV), long duration (10 min). | | Tests dielectric strength under stress. | Measures bulk insulation resistance (quality, moisture, contamination). | | Destructive if failure occurs. | Non-destructive, diagnostic. | | Pass/Fail based on withstand. | Quantitative (MΩ/GΩ), trend analysis. |

High-Voltage Cables

• Partial Discharge (PD) Test:

  • Procedure:

    1. Apply AC voltage (typically 1.5-2x rated) to cable sample (length ~100m).

    2. Use coupling capacitor and high-frequency current transformer (HFCT) to detect PD pulses in the ground wire.

    3. Measure PD magnitude (pC) and PD inception/extinction voltages.

  • Objective: Detect manufacturing defects (voids, impurities, poor splicing) in insulation.

• Fault Location with PD:

  • Principle: PD pulses travel along cable at propagation velocity ($v$).

  • Method: Install sensors at both ends. Measure time difference ($\Delta t$) between pulse arrivals at ends.

  • Distance to Fault: $$\displaystyle \boxed{L_1 = \frac{v \cdot \Delta t}{2}} $$ (for fault in middle). Requires known $v$ and synchronized measurement.

[!TIP] Key Distinction: HV Test on transformer is a high-stress withstand test. IR Test is a low-stress diagnostic. For cables, PD test is a sensitive diagnostic for internal defects.

VI. SPECIALIZED TOPICS & COMPARISONS

Surge Current Measurement

• Methods/Instruments:

  • Rogowski Coil: Air-cored toroidal coil around conductor. Output voltage $$\displaystyle V_o \propto di/dt $$. Requires integration to get current $i(t)$. Advantage: No magnetic saturation, wide bandwidth.

  • Shunt Resistor: Low-value, non-inductive resistor (e.g., manganin). $$\displaystyle V = iR $$. Challenge: Must handle high $di/dt$, isolation, bandwidth.

  • Magnetic Field Probes (B-dot probes): Measure $dB/dt$ near conductor → derive $di/dt$.

• Challenges:

  • Very High Magnitude: kA to MA range.

  • Extremely Fast Rise Time: ns to µs (lightning, switching).

  • Isolation: Instrument must be isolated from HV ground.

  • Bandwidth: Oscilloscope and sensor must have sufficient bandwidth ($$\displaystyle BW > 0.35 / t_r $$).

Cavity Breakdown

• Definition: Breakdown occurring within an enclosed cavity inside a solid dielectric or between metal parts (e.g., in a transformer bushing, GIS).

• Mechanism: Similar to gaseous breakdown but geometry confined. Paschen's law applies to the cavity dimensions and internal pressure (may be air, SF₆, or vacuum).

• Significance: Internal cavities are weak points. PD activity in cavities is a major degradation mechanism in composite insulation systems.

Motor Coil Insulation

• Pouring/Varnishing Methods:

  1. Dip: Coil immersed in varnish, drained.

  2. Trickle: Varnish slowly dripped onto rotating coil.

  3. Vacuum Pressure Impregnation (VPI): Coil placed in pressure vessel, vacuumed to remove air/moisture, then varnish forced in under pressure. Best method → voids eliminated, excellent adhesion, high dielectric strength.

Comparative Summaries

[!TIP] Final Exam Checklist: You must be able to:

1. Derive/Explain Townsend, Streamer, Paschen's Law.

2. Sketch & Explain CW, Tesla Coil, Marx (with 3-electrode trigger).

3. Compare all three potential divider types.

4. List factors for sphere gap measurement.

5. Differentiate HV test vs. IR test; PD test procedure for cables.

6. Explain vacuum breakdown mechanism and cavity breakdown.

7. State surge current measurement challenges.