High Voltage Engineering (EX-702 (C)) - Unit 4 Short Notes

UNIT 4: HIGH VOLTAGE GENERATION, MEASUREMENT & BREAKDOWN

I. INTRODUCTION TO HIGH VOLTAGE TECHNOLOGY

Definition & Significance

• High Voltage (HV): A relative term; typically voltages > 1 kV AC or 1.5 kV DC. In power systems, it refers to levels enabling efficient long-distance power transmission.

• Significance:

  • Reduces Current: For same power (P = VI), higher V means lower I.

  • Lowers I²R Losses: Power loss in conductors is proportional to I².

  • Enables Long Distance: Allows transmission over hundreds of km with economical conductor sizes.

  • Improves System Stability: Higher voltage levels enhance power transfer capability and grid stability.

Voltage Classifications (IEEE/CIGRE Standards)

Key Applications

• Power Systems: Generation (generator terminals), Transmission (lines, substations), Distribution (substations).

• Non-Power: Industrial (X-ray, electrostatic precipitators, painting), Medical (radiography, MRI), Scientific Research (particle accelerators, fusion reactors).

Laboratory HV Generation Need

• Testing & Certification: Type tests, routine tests, acceptance tests on equipment (cables, transformers, insulators, circuit breakers).

• Research & Development: Studying insulation characteristics, new materials, discharge phenomena.

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

• Insulation Coordination Studies: Simulating lightning and switching surges to determine equipment insulation levels.

II. HIGH VOLTAGE GENERATION METHODS

1. Series Resonant Circuit (Tesla Coil Driver Principle)

• Principle: Uses resonance to magnify voltage across a capacitor (C₂) in a series L-C circuit when driven at resonant frequency.

• Circuit: HV transformer (T) with low leakage inductance, connected in series with a tuning inductor (L) and a test capacitor (C₂). A small capacitor (C₁) is across the transformer secondary.

• Resonance Condition:

$$ \omega L = \frac{1}{\omega C_2} \quad \text{or} \quad f = \frac{1}{2\pi\sqrt{LC_2}} $$

At resonance, circuit impedance is minimal (purely resistive), current is maximum, and voltage across C₂ is Q times the transformer secondary voltage, where Q = quality factor.

$$ V_{C_2} = Q \cdot V_{tr} $$

• Advantages: Current magnification allows use of smaller transformer; voltage is easily controlled by varying frequency; efficient for testing large capacitive loads (cables, capacitors).

• Disadvantages: Requires variable frequency source; narrow bandwidth (only resonates at one frequency).

2. Cockcroft-Walton (CW) Voltage Multiplier

• Construction: Cascaded stages of capacitors (C) and diodes (D). Each stage doubles the peak input voltage.

• Working: During positive half-cycle, capacitors C₁, C₃... charge through diodes D₁, D₃... During negative half-cycle, charged capacitors cascade through diodes D₂, D₄..., adding voltages.

• Voltage Multiplication: For n stages, no-load output:

$$ V_{out} = 2n \cdot V_{peak} $$

• Ripple & Regulation:

  • Ripple voltage: $$\displaystyle \Delta V \approx \frac{I}{fC} \cdot \frac{2n(n+1)}{3} $$ (I = load current, f = frequency)

  • Poor regulation under load; voltage drops significantly with increasing current.

• Advantages: No HV transformer needed (uses low-voltage source); compact, portable; produces pure DC.

• Limitations: High ripple; poor voltage regulation; current capacity limited; unsuitable for heavy loads.

3. Tesla Coil (Resonant Transformer)

• Construction:

  • Primary Circuit: Low-turn copper coil (L₁) in series with a spark gap (SG) and a capacitor (C₁).

  • Secondary Circuit: High-turn coil (L₂) wound on a hollow, insulated former (often with a toroidal top load "toroid" or "extra coil").

  • Both L₁ and L₂ are tuned to same resonant frequency (L₁C₁ ≈ L₂C₂, where C₂ is self-capacitance of secondary + toroid).

• Working:

  1. C₁ charges from a HV DC source.

  2. When voltage across C₁ exceeds spark gap breakdown, it discharges rapidly through L₁.

  3. This creates an oscillating LC circuit (L₁C₁) at its resonant frequency.

  4. The oscillating magnetic flux couples energy to the secondary L₂, which is also resonant.

  5. Due to high turns ratio and resonance, extremely high voltage (MV range) appears across the toroid.

• Current Flow in Nearby Objects: The Tesla coil produces high-frequency, high-voltage AC. Nearby objects act as capacitors (capacitive coupling) to the oscillating electric field. At high frequencies, capacitive reactance $$\displaystyle X_C = 1/(2\pi f C) $$ becomes very small, allowing significant displacement current to flow through the "capacitor" formed by the coil and the object, even without direct contact. Skin effect also plays a role.

4. Impulse Generator (Marx Circuit)

• Purpose: Generate standard lightning (1.2/50 μs) and switching (250/2500 μs) impulse waveforms for insulation testing.

• Principle: Charging capacitors in parallel, discharging them in series.

• Construction: n stages, each with a capacitor (C) charged through charging resistors (R_ch) to voltage V via a DC HV source. Each stage has a triggered spark gap (G) and a discharge resistor (R_d).

• Operation:

  1. Charging: All capacitors charge to voltage V in parallel (through high R_ch, slow).

  2. Triggering: The first spark gap (G₁) is triggered (by impulse, UV, or third electrode). It fires, applying ~2V to the next gap (G₂).

  3. Cascade: G₂ fires, applying ~3V to G₃, and so on. All gaps fire in a rapid cascade.

  4. Discharge: All capacitors connect in series across the output, delivering a voltage ~ nV to the test object, with a fast rise time determined by the front resistor (R_f) and load capacitance.

• Triggering Mechanisms:

  • Three-Electrode Gap (Preferred): Main gap (G) between electrodes 1 & 2. A third electrode (trigger electrode) is placed near the cathode (1). A trigger pulse (HV) applied to this electrode creates a localized high field, initiating an electron avalanche that bridges the main gap. Why Preferred? Provides precise, synchronous, and reliable triggering of all stages, essential for reproducible waveforms.

  • Control Tripping: Using a separate trigger generator to apply a pulse to the first stage's trigger electrode. Ensures all gaps fire simultaneously.

III. HIGH VOLTAGE MEASUREMENT TECHNIQUES

1. Sphere Gap

• Principle: Breakdown voltage between two identical spheres is a well-established, reproducible function of sphere diameter (D) and gap distance (d), for a given voltage waveform (AC, DC, impulse). It is a peak voltmeter.

• Measurement: Adjust gap until breakdown occurs (audible snap, visible spark). Read breakdown voltage from standard tables/curves for given D and d.

• Influencing Factors:

  • Humidity: Increases breakdown voltage (for AC/DC); correction factors exist.

  • Sphere Surface Condition: Must be clean, smooth, unpainted.

  • Surrounding Objects: Must be far away (distance > 2.5D) to avoid field distortion.

  • Waveform: Different tables for AC, DC, impulse (1.2/50 μs).

  • Polarity: For DC and impulse, polarity matters (positive breakdown voltage lower than negative for small gaps).

• Advantages: Simple, robust, no calibration needed, accurate for peak values.

• Disadvantages: Destructive (breaks down); slow; limited to peak measurement; affected by environment; requires careful setup.

2. Potential Dividers

• Purpose: Scale down high voltage to a measurable low voltage (mV-V) for oscilloscopes or digital meters.

• Key Requirement for Impulse: The divider must have a flat frequency response up to frequencies corresponding to the impulse rise time (e.g., for 1.2/50 μs, up to ~100 kHz to 1 MHz). This requires proper damping and matched propagation times.

[!TIP] Exam Focus: Always compare the three types. For impulse measurement, damped RC or capacitance dividers are used. Resistance dividers alone are unsuitable.

3. Electrostatic Voltmeter

• Principle: Based on electrostatic attraction force between fixed and moving vanes/plates. Voltage applied creates an electric field, causing a torque that moves a pointer against a spring.

$$ \text{Deflection} \propto V^2 $$

• Construction: Fixed stator plates, movable rotor vanes, spring suspension, damping vane, pointer.

• Operation: HV applied to stator. Rotor moves to a position where spring torque balances electrostatic torque. Scale is non-linear (calibrated for V, not V²).

• Advantages: No current draw (infinite input impedance); works for AC and DC (rectifier not needed); accurate for RMS AC.

• Limitations: Low sensitivity; limited range (usually up to 100-200 kV); fragile; slow response (not for transients).

4. Generating Voltmeter

• Principle: For high DC voltage measurement. A rotating, segmented electrode (or vane) alternately couples to and decouples from the HV field, generating an AC current proportional to V. This current is integrated (by a moving coil meter) to give a reading proportional to V.

• Construction: Motor-driven rotor with conductive segments inside a stationary housing. The rotor is capacitively coupled to the HV line. A mechanical or electrical integrator (low-pass filter) converts the AC signal to a DC reading.

• Working: As a segment enters the field, it charges to HV potential; as it leaves, it discharges. This creates a current pulse per segment. Pulse frequency * amplitude ∝ V. Integration gives average value ∝ V.

• Advantages: True RMS for DC; high range (MV); no direct connection to HV.

• Disadvantages: Mechanical (wear, speed stability); requires calibration; not for AC or impulses.

5. Surge Current Measurement

• Purpose: Measure high-amplitude, short-duration currents (kA to MA, μs to ms) during faults, lightning strikes, or switching operations.

• Methods:

  • Rogowski Coil: A toroidal, air-core coil placed around the conductor. The surge current creates a changing magnetic field, inducing a voltage proportional to di/dt. Integrating this voltage gives i(t).

    • Advantages: No magnetic core (no saturation); wide bandwidth; isolated from HV.

    • Challenges: Requires precise, stable integration; sensitive to external fields; positioning critical.

  • Shunt Resistors (Current Viewers): Low-inductance, high-power resistors (e.g., manganin) placed in series. Voltage drop across shunt ∝ current.

    • Advantages: Simple, direct measurement.

    • Challenges: Must withstand high energy; introduces resistance/loss; bandwidth limited by inductance; safety isolation.

  • Magnetic Instruments (Hall Effect, Current Transformers): CTs saturate on high DC components of surges. Hall effect sensors can measure DC but have limited bandwidth.

• Key Challenges:

  • Bandwidth: Must capture fast rise-times (nanoseconds to microseconds).

  • Saturation: Magnetic cores saturate, distorting waveform.

  • Energy Withstand: Must survive high fault currents without damage.

  • Isolation & Safety: Must provide safe isolation from HV circuit.

  • Waveform Distortion: Lead inductance and capacitance can distort the measured surge shape.

IV. GASEOUS DIELECTRIC BREAKDOWN

1. Townsend Discharge Theory (Primary & Secondary Ionization)

• Primary Ionization (α-process): Free electrons (from natural radiation) are accelerated by electric field. They collide with neutral gas molecules, ionizing them if kinetic energy > ionization energy. This creates electron avalanches.

  • Townsend's First Ionization Coefficient (α): Number of ionizing collisions per unit length traveled by an electron. Depends on E/p (field strength/pressure).

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

(A, B are gas constants)

• Secondary Ionization (γ-process): Processes that generate new electrons at the cathode, sustaining the discharge.

  • Positive Ion Bombardment (γᵢ): Positive ions accelerated to cathode, knock out electrons.

  • Photon Interaction (γₚ): UV photons from excited atoms/molecules hit cathode, eject electrons (photoelectric effect).

  • Secondary Emission Coefficient (γ): Average number of secondary electrons produced per incident positive ion/photon.

• Breakdown Condition: When the total number of electrons multiplies sufficiently to cause a self-sustaining discharge.

$$ i = i_0 e^{\alpha d} \left[ \frac{1}{1 - \gamma (e^{\alpha d} - 1)} \right] $$

For breakdown (i → ∞), denominator → 0:

$$ \boxed{\gamma (e^{\alpha d} - 1) = 1} \quad \text{or} \quad \alpha d = \ln\left(\frac{1}{\gamma} + 1\right) \approx \ln\left(\frac{1}{\gamma}\right) \quad (\text{if } \gamma \ll 1) $$

This is **Townsend's breakdown criterion**.

2. Streamer Mechanism

• Context: Explains fast breakdown (spark formation) in non-uniform fields where E/p is high in small regions (e.g., point-plane).

• Process:

  1. An electron avalanche develops in a high-field region.

  2. Avalanche head contains many electrons and positive ions. Space charge of ions distorts the electric field, enhancing it ahead of the avalanche.

  3. This enhanced field creates new, secondary avalanches from the tip (streamer head) via photoionization (photons from excited atoms in the original avalanche).

  4. The streamer propagates forward as a self-propagating ionization front, fed by the space charge field.

  5. When streamers from cathode and anode meet, a conducting plasma channel (spark) forms.

• Improvement over Townsend: Explains:

  • Very fast transition from avalanche to spark (nanoseconds).

  • Breakdown in non-uniform fields.

  • Formation of visible branched spark channels.

  • Why breakdown voltage is lower than predicted by Townsend for large gaps in non-uniform fields.

3. Paschen's Law

• Statement: The breakdown voltage (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 (Sketch): From Townsend criterion: $$\displaystyle \alpha d = \ln(1 + 1/\gamma) $$. Substitute $$\displaystyle \alpha = A p e^{-Bp/V_b d} $$. Rearranging gives:

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

For a given gas, γ is roughly constant, so V_b = f(pd).

• Paschen Minimum: The curve V_b vs. pd has a minimum. At this minimum, breakdown occurs at the lowest voltage.

  • For air: Minimum ~ 327 V at pd ≈ 0.567 torr·cm.

  • Implication: There is an optimum gap/pressure for minimum insulation strength. Equipment design avoids operating near this minimum.

• Practical Implications:

  • Insulation Design: For a given voltage, choose d such that pd is far from the Paschen minimum.

  • Gas-Filled Equipment (GIS): Pressure is raised to increase pd well above minimum, significantly increasing breakdown strength.

  • Vacuum Systems: At very low p, pd is small, V_b rises again (but vacuum breakdown mechanisms differ).

4. Time Lags in Breakdown

• Statistical Time Lag (tₛ): Time delay due to the random availability of a primary free electron (from natural radiation) near the cathode at the moment voltage is applied. Depends on radiation level and field strength.

• Formative Time Lag (t_f): Time required for the electron avalanche to develop to a size where space charge effects (streamer formation) cause breakdown. Depends on E/p, gap geometry.

• Total Breakdown Time Lag: $$\displaystyle t_{total} = t_s + t_f $$

• Significance: Crucial for impulse insulation strength. A very fast-rising impulse (steep front) may have a short t_f, but if t_s is long, breakdown may not occur until voltage has already peaked or decayed. This explains why impulse withstand voltage is often higher than 50 Hz AC withstand voltage.

V. BREAKDOWN IN VACUUM AND SOLID DIELECTRICS

1. Vacuum Breakdown

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

  • Field Emission: At high fields (>10⁷ V/m), electrons tunnel from cathode microprotrusions (field enhancement).

  • Microparticle Bridging: Microscopic particles (metal, insulator) are dislodged and accelerated across the gap, impacting and vaporizing, creating a plasma.

  • Cathode Spot: Once a micro-arc initiates, a localized, intense plasma (cathode spot) forms on the cathode, sustaining the arc.

• Causes of Arcing Inside Vacuum:

  • Surface Flashover: Most common. Discharge travels along the surface of an insulator (due to surface charges, imperfections) rather than through the vacuum gap.

  • Desorption: HV causes adsorbed gases on electrode/insulator surfaces to desorb, creating a localized pressure rise and breakdown.

  • Metal Vapor: From electrode erosion during pre-discharges.

• Key Feature: Vacuum has excellent volume insulation strength, but surface flashover is the weak link. Smooth, clean electrodes and high-quality insulators with low secondary emission yield high hold-off voltages.

2. Solid Dielectrics Breakdown

• Intrinsic Strength: Theoretical maximum electric field a perfect, defect-free crystal can withstand before electronic breakdown (~10⁸ - 10⁹ V/m for polymers, higher for ceramics).

• Practical Breakdown Mechanisms (Occur at much lower fields):

  • Electronic (Avalanche) Breakdown: At high fields, electrons gain enough energy between collisions to ionize the lattice (collision ionization), leading to an avalanche. Similar to gas, but in a dense medium. Can lead to thermal runaway.

  • Thermal Breakdown: Localized heating from dielectric losses (conduction, polarization) causes a temperature run-away, melting or carbonizing the material.

  • Discharge (Treeing) Breakdown: Partial discharges in voids or at interfaces erode the material via chemical and physical processes, forming electrically conducting carbonized paths ("trees").

  • Electromechanical Breakdown: Electrostatic forces distort the material, leading to mechanical failure (especially in flexible sheets).

3. Partial Discharge (PD)

• Definition: A localized electrical discharge that only partially bridges the insulation between conductors. Does not immediately cause complete breakdown but is progressive and damaging.

• Causes: Cavities (voids), inclusions, delaminations within or at interfaces of solid insulation. Gas (often air) in the cavity has much lower breakdown strength than the solid dielectric.

• PD in Cables: Test involves applying AC voltage (typically 1.5-2x rated voltage) and detecting PD pulses using:

  • Electrical Detection: Coupling capacitors and high-frequency current transformers (HFCT) or PD detectors.

  • Acoustic Detection: Piezoelectric sensors on cable sheath.

• Fault Location:

  • Time-Domain Reflectometry (TDR): Sends a fast pulse; reflections from PD site (impedance discontinuity) are timed.

  • Acoustic Location: Multiple sensors triangulate the source of acoustic emission from PD.

• Cavity Breakdown Mechanism:

  1. Voltage across cavity increases.

  2. When local field in cavity reaches gas breakdown strength, a micro-discharge occurs.

  3. Discharge erodes cavity walls, produces ozone/acidic byproducts, creates carbon tracks.

  4. Repeated PDs enlarge the cavity/tree, eventually causing complete breakdown.

VI. TESTING OF HIGH VOLTAGE EQUIPMENT AND INSULATION

1. Insulation Testing Methods Comparison

2. Circuit Breaker Tests

• Short-Circuit Test (Making/Breaking Capacity):

  • Objective: Verify the breaker can safely interrupt (break) and close (make) its rated short-circuit current without failure.

  • Procedure: Breaker is connected to a special test circuit (source, current-limiting reactors). A trigger signal closes the breaker against a forced current (making) or opens it under load (breaking). Current is measured, and arc behavior, contact wear, and re-ignition are observed.

• Dielectric Test (Withstand Test):

  • Objective: Verify integrity of main insulation (to ground and across poles) and clearances.

  • Procedure: Apply AC voltage (usually 1 min at rated or higher) or impulse voltage between each pole and ground, and between poles. No breakdown should occur.

3. Insulator Tests

• Mechanical Strength Test:

  • Tensile: For suspension insulators (string).

  • Bending/Torsion: For pin-type, post-type insulators.

  • Objective: Verify mechanical design loads (wind, ice, weight) are withstood without fracture or permanent deformation.

• Puncture Voltage Test:

  • Objective: Determine internal dielectric strength of the insulator material itself.

  • Procedure: Apply voltage between the metal cap and pin (through the insulator body). A very high voltage is needed to puncture the solid dielectric. Failure is a conducting hole through the insulator.

• Flash-Over Voltage Tests:

  • Objective: Determine the voltage at which an arc bridges the surface of the insulator (from cap to pin).

  • Dry & Wet Tests: Wet test (artificial rain) simulates rain, drastically lowering flash-over voltage due to surface conductivity. Tests the creepage distance design.

  • Procedure: Apply slowly rising AC voltage until flash-over occurs. Repeat to get average value.

4. Power Transformer Tests

• High Voltage Test (Induced Voltage Test / Separate Source Voltage Test):

  • Induced: Apply voltage to LV winding at 2-5x rated frequency. This induces overvoltage in HV winding. Tests inter-turn, inter-layer, and major insulation.

  • Separate Source: Apply HV directly from a test transformer to HV winding (LV grounded). Tests insulation to ground and between windings.

  • Necessity: To verify insulation coordination (clearances, creepage distances) and detect manufacturing defects (loose windings, insulation damage, contamination) that routine tests might miss. It's a type test and often a routine test.

5. Insulation Application Techniques (Motor Coils)

• Purpose: Impregnate and encapsulate motor/generator windings with insulating resin/varnish to:

  • Fill voids, improve dielectric strength.

  • Bind windings mechanically, reduce vibration.

  • Provide moisture/chemical barrier.

• Pouring Methods:

  1. Vacuum Pressure Impregnation (VPI): Most effective. Coil is placed in a pressure vessel, evacuated to remove air/moisture, then resin is introduced under vacuum. Pressure is then applied to force resin into all voids. Cures to a solid mass.

  2. Dip and Bake (Trickle Impregnation): Coil is dipped in resin, then baked in an oven. Simpler, but less thorough void filling than VPI.

  3. Resin Pouring (Potting): Liquid resin is poured into a mold containing the pre-wound coil, then cured. Used for smaller stators.

[!TIP] Exam Focus: Be ready to compare tests (HV vs IR, puncture vs flashover, dry vs wet insulator tests). Know the purpose of each major test on transformers and circuit breakers. VPI is the gold standard for motor winding insulation.