Power Electronics Application to Power System (EX-702 (A)) - Unit 1 Short Notes

UNIT 1: HIGH VOLTAGE ENGINEERING & POWER ELECTRONICS APPLICATIONS IN POWER SYSTEMS

I. INTRODUCTION TO HIGH VOLTAGE TECHNOLOGY

Definition and Significance

• High Voltage (HV) Technology deals with the generation, measurement, testing, and application of voltages significantly higher than those used in standard power distribution (typically > 1000 V AC or 1500 V DC).

• Significance in Modern Power Systems:

  • Efficiency: Reduces current ($$\displaystyle I = P/V $$) for same power, minimizing $$\displaystyle I^2R $$ losses in transmission lines.

  • Long-Distance Transmission: Enables economical transmission over hundreds of kilometers.

  • System Interconnection: Facilitates linking of large, distant generation sources to load centers.

Voltage Classification

Applications

• Power Applications:

  • Transmission: EHV/UHV AC & HVDC lines.

  • Distribution: HV sub-transmission and distribution networks.

  • Generation: Step-up transformers in power plants.

• Non-Power Applications:

  • Medical: X-ray machines, CT scanners, radiation therapy.

  • Industrial: Particle accelerators, electrostatic precipitators, food processing.

  • Research: High-energy physics experiments, plasma generation.

Laboratory Requirements

High voltage generation in labs is essential for:

1. Insulation Coordination Studies: Determining dielectric strength of equipment.

2. Equipment Certification: Type tests, routine tests (e.g., on transformers, cables, circuit breakers).

3. Research & Development: Studying new insulating materials, breakdown phenomena, and testing prototypes.

[!TIP] Exam Focus: Be prepared to differentiate between HV, EHV, UHV ranges and list at least 3 power and 3 non-power applications.

II. BREAKDOWN MECHANISMS IN DIELECTRICS

A. Gaseous Dielectrics

Ionization Processes

• Primary Ionization: Free electrons gain energy from an electric field, collide with neutral gas molecules, and ionize them. Described by Townsend's first ionization coefficient (α), the number of ionizing collisions per unit length.

$$ \alpha = A p e^{-B(p/E)} $$

Where $p$ = pressure, $E$ = electric field, $A$, $B$ = gas constants.

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

Condition for Breakdown (Townsend Criterion)

Breakdown occurs when the total number of electrons multiplies sufficiently. The self-sustaining discharge condition is:

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

Where $d$ = gap distance.

Breakdown Theories

1. Townsend Breakdown Theory:

   • Mechanism: Electron avalanche growth via α and γ.

   • Limitation: Cannot explain the rapid current rise and time lag observed in practical breakdowns, especially in non-uniform fields.

2. Streamer Mechanism (Improvement):

   • Formation: In a dense electron avalanche, space charge distorts the electric field. The field at the avalanche head becomes high enough to cause ionization without electron drift, forming a streamer (a highly ionized channel).

   • Propagation: Streamers propagate through photo-ionization (UV photons from the avalanche ionize gas ahead) and electron drift. Explains fast breakdown in non-uniform fields.

Time Lags

• Statistical Time Lag ($$\displaystyle t_s $$): Time for the initial electron to appear from natural background radiation or field emission. Random.

• Formative Time Lag ($$\displaystyle t_f $$): Time for the electron avalanche to grow and form a conducting channel after the first electron appears. Depends on $E/p$ and $d$.

  Total Breakdown Time Lag: $$\displaystyle t = t_s + t_f $$

B. Solid, Liquid, and Vacuum Dielectrics

• Solid Dielectrics:

  • Intrinsic Strength: Theoretical maximum electric field a perfect, defect-free material can withstand (~10⁶ V/cm).

  • Electronic Breakdown: At very high fields, electrons are ripped from atoms (avalanche/streamer similar to gases).

  • Thermal Breakdown: Localized heating from dielectric losses exceeds dissipation, leading to thermal runaway and carbonization.

• Vacuum Breakdown:

  • Cavity Breakdown: Micro-protrusions on electrode surfaces cause intense local field emission of electrons. These electrons bombard the anode, releasing vapor/micro-particles that cause a vacuum arc.

  • Key Factor: Surface cleanliness and smoothness of electrodes.

C. Paschen's Law

Derivation and Concept

Breakdown voltage $$\displaystyle V_b $$ in a gas is a unique function of the product of gas pressure ($p$) and electrode gap ($d$), assuming uniform field.

$$ V_b = f(pd) $$

For a given gas, experimental data fits:

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

Paschen Minimum

• The curve $$\displaystyle V_b $$ vs. $pd$ has a minimum.

• Minimum Breakdown Voltage ($$\displaystyle V_{b,min} $$) occurs at an optimal $pd$ product.

• For air, $$\displaystyle V_{b,min} \approx 327 $$ V at $pd \approx 0.567$ Torr·cm.

Practical Implications

1. Insulation Design: For a given gap $d$, there is a minimum safe operating pressure (or vice-versa). Explains why small gaps in low-pressure systems (e.g., vacuum interrupters) can withstand high voltage.

2. Clearance Selection: Guides minimum required clearance distances in air at standard conditions for a given voltage level.

3. Gas-Filled Equipment: Design of gas-insulated switchgear (GIS) uses SF₆ at specific pressures to achieve high dielectric strength in compact spaces.

[!TIP] Exam Focus: You must be able to state Paschen's Law, sketch the $$\displaystyle V_b $$ vs. $pd$ curve showing the minimum, and explain its significance for equipment design.

III. HIGH VOLTAGE GENERATION

A. AC High Voltage Generation: Tesla Coil

• Construction: Resonant air-core transformer. Primary: few turns of heavy wire. Secondary: many turns of fine wire. capacitor across primary, spark gap in series with primary.

• Working Principle: LC resonance. Capacitor charges from supply, discharges through spark gap, creating damped oscillations in primary. Energy transfers magnetically to secondary, which resonates at a much higher frequency (100s kHz to MHz).

• Why Current Flows in Nearby Objects: High frequency causes skin effect (current flows on surface) and strong capacitive coupling to nearby objects, allowing them to light up without direct contact.

B. DC High Voltage Generation: Cockcroft-Walton Generator

• Circuit: Voltage multiplier using diodes and capacitors in a cascaded ladder network.

• Operation: AC input (from transformer) is rectified and multiplied stage by stage. Output voltage ≈ $$\displaystyle 2nV_{peak} $$ (for n stages) under no-load.

• Advantages: No need for high-voltage transformer, portable, produces high DC voltage from low-voltage AC.

• Limitations: Significant voltage drop and ripple under load, size becomes impractical for very high voltages (> 1 MV), poor regulation.

C. Impulse Voltage Generation: Marx Circuit

• Circuit Configuration: Multiple capacitor stages charged in parallel via resistors to a DC voltage. At triggering, they are connected in series via spark gaps to generate a high-voltage impulse (standard lightning impulse: 1.2/50 μs).

• Triggering Mechanism: Three-Electrode Gap:

  • Arrangement: Each stage has a main spark gap (between two electrodes). A third, smaller "trigger" electrode is placed near the main gap's cathode.

  • Principle: A DC voltage is applied to the trigger electrode via a high-value resistor. A triggering pulse (from a separate source) applied to the trigger electrode initiates a discharge across the main gap.

  • Why Preferred: Provides precise, simultaneous triggering of all stages, ensuring a clean, undistorted impulse waveform. More reliable than self-breakdown of main gaps.

D. Series Resonant Circuit for Testing

• Principle: An inductor ($L$) and capacitor ($C$) in series with the test object (represented by its capacitance $$\displaystyle C_t $$). The circuit is driven by a variable-frequency source.

• Resonance Condition: When driving frequency $\omega$ equals the natural resonant frequency:

$$ \omega_0 = \frac{1}{\sqrt{L(C + C_t)}} \quad \text{or} \quad \omega_0 L = \frac{1}{\omega_0 C_{eq}} \quad \boxed{} $$

Where $$\displaystyle C_{eq} = C \parallel C_t $$.

• Application: At resonance, the circuit impedance is minimal (purely resistive), and the voltage across the test object ($$\displaystyle C_t $$) is magnified by the quality factor $$\displaystyle Q = \omega_0 L / R $$ (where $R$ is circuit resistance). This allows generation of very high test voltages from a low-power source.

[!TIP] Exam Focus: Draw and explain the Marx circuit with three-electrode triggering. Derive the resonance condition for a series resonant test circuit.

IV. HIGH VOLTAGE MEASUREMENT

A. Voltage Measurement Techniques

Sphere Gap

• Construction: Two identical, highly polished, spherical electrodes with adjustable gap.

• Operation: Breakdown occurs at a critical gap distance for a given peak voltage. The peak value of AC, DC, or impulse voltage is read from standardized tables based on sphere diameter and gap.

• Influencing Factors: Sphere diameter, gap distance, atmospheric conditions (temperature, pressure, humidity - corrected by air density factor), polarity (for DC).

Potential Dividers

• Purpose: Scale down high voltage to a measurable low voltage for oscilloscopes or meters.

• Types:

  | Type | Construction | Advantages | Disadvantages | Best For | | :--- | :--- | :--- | :--- | :--- | | Resistance | Series resistors | Simple, good for DC/PF | High power loss, poor HF response | DC, Power Frequency | | Capacitance | Series capacitors | Low loss, excellent HF response | Needs buffer amp, sensitive to stray C | Impulse, HF | | Mixed RC | R & C in parallel per stage | Good damping, wide bandwidth | More complex, calibration needed | Impulse Voltages |

• Conditions for Impulse Work: Proper damping to prevent oscillations, frequency response covering impulse spectrum (kHz to MHz), minimal inductance.

Generating Voltmeter

• Principle: Rotating vane (or disc) in electric field acts as a variable capacitor. Charge $$\displaystyle Q = CV $$ flows to/from the vane, integrated over time gives a current proportional to $V$. A current meter reads this.

• Use: Direct reading, portable instrument for high DC voltages (kV to 100s kV).

Electrostatic Voltmeter

• Principle: Electrostatic force between fixed and moving vanes causes deflection. Torque $$\displaystyle \propto V^2 $$.

• Construction & Use: Handles both AC and DC high voltages. Requires no external power. Accuracy depends on calibration.

B. Surge Current Measurement

• Methods & Instruments:

  • Rogowski Coil: Air-cored toroidal coil around conductor. Output voltage $$\displaystyle v = M di/dt $$. Requires integration for $i(t)$. Excellent for high $di/dt$, no saturation.

  • Magnetic Links: Record peak current magnetically (e.g., on a plastic sheet). Used for lightning/strike current peaks.

  • Shunt Resistors: Low-inductance, high-power resistor (e.g., carbon pile). Voltage drop measured by oscilloscope. Must withstand high energy.

• Challenges:

  • Extremely high magnitude (kA to 100s kA) and fast rise time (μs).

  • Severe electromagnetic interference (EMI).

  • Insulation and safety requirements for the measuring circuit.

  • Bandwidth limitation of measuring instruments.

V. HIGH VOLTAGE TESTING OF EQUIPMENT

A. Circuit Breaker Tests

• Short-Circuit Test: Verifies ability to break maximum fault current. Measures arcing time, current chopping, re-ignition.

• Dielectric Test: Verifies insulation strength. Includes power-frequency withstand voltage and impulse voltage (lightning & switching) tests.

B. Insulator Tests

• Mechanical Strength Test: Tests tensile, compressive, bending, and torsional strength. Crucial for withstanding line tensions and environmental loads.

• Puncture Voltage Test: Determines voltage at which insulator material itself breaks down internally (through the body). Indicates material quality.

• Flash-Over Voltage Test: Determines voltage at which an arc forms over the surface of the insulator. Depends on creepage distance, surface condition, and pollution.

C. Transformer Tests

• High Voltage Test (Withstand Test): Applies voltage higher than rated to main insulation (winding-to-ground, winding-to-winding) for a specified time (e.g., 1 min at power frequency). Checks for insulation weakness.

• Insulation Resistance (IR) Test: Applies moderate DC voltage (e.g., 2.5 kV) and measures resistance (MΩ/GΩ). Comparison:

  • IR Test: Diagnostic, qualitative, checks moisture/contamination, low voltage.

  • HV Test: Destructive/acceptance test, verifies dielectric strength, high voltage.

D. Cable Tests

• Partial Discharge (PD) Tests:

  • Procedure: Apply voltage, detect electrical pulses (PD pulses) emitted from localized insulation defects using couplers and sensitive instruments. Measure PD inception/extinction voltages.

  • Fault Location: Time-Domain Reflectometry (TDR): Sends a fast-rising voltage step, reflects from impedance discontinuities (faults). Time delay gives distance. PD Mapping: Locating PD sources along cable length using multiple sensors.

E. Isolator (Disconnector) Tests

• Electrical Tests:

  • Contact Resistance Measurement: Ensure low, stable resistance.

  • Dielectric Withstand Test: Across open contacts.

  • Operational Tests: Speed, interlocking, mechanical endurance.

VI. POWER ELECTRONICS APPLICATIONS: HVDC AND FACTS

A. HVDC Transmission Systems

Overview & Comparison

Converter Station Layout

Types of DC Links

1. Point-to-Point: Two converter stations, one link. Most common.

2. Back-to-Back: No DC line; converters at same site. Used for asynchronous tie or frequency conversion.

3. Multi-Terminal (MTDC):

   • Series: Stations in series on DC line. Power control is difficult.

   • Parallel: Stations in parallel. Easier control, more common.

Control Principles

• Basic Objectives: Control DC current (to limit overload) and extinction angle (γ) (to ensure commutation).

• Converter Control Characteristics: For a rectifier, characteristic is a curve of DC voltage ($$\displaystyle V_d $$) vs. DC current ($$\displaystyle I_d $$). Control variable is firing angle (α). Decreasing α increases $$\displaystyle V_d $$.

$$ V_d = V_{d0} \cos \alpha - \frac{3}{\pi} X_c I_d $$

Where $$\displaystyle V_{d0} $$ = open-circuit voltage, $$\displaystyle X_c $$ = commutating reactance.

> **Power Reversal:** Achieved by changing firing angle α > 90° (inversion mode). Necessary for bidirectional power flow (e.g., in back-to-back or MTDC systems).

Filters and Harmonics

• AC Filters: Tuned LC filters (12-pulse, 24-pulse) to absorb characteristic harmonics (12th, 24th...). C-type filters for lower harmonics (5th, 7th) with lower losses.

• DC Filters: LC filters on DC side to smooth ripple and suppress radio interference (from low-frequency harmonics).

• Harmonics: Characteristic (determined by pulse number, e.g., 12k±1 for 12-pulse), Non-characteristic (from unbalance, control imperfections).

B. FACTS Controllers

Introduction to FACTS

• Definition: Flexible AC Transmission Systems. Power electronics-based devices that enhance controllability, increase power transfer capability, and improve stability of AC systems.

Conventional Reactive Power Compensator: SVC

• Static VAR Compensator (SVC): Uses thyristors to switch/reactors (TCR) and capacitors (TSC).

• Characteristics: Provides continuous, fast reactive power (VAr) control. Acts as a variable shunt impedance. Improves voltage profile and damping.

Thyristor-Based FACTS

• Thyristor Controlled Series Capacitor (TCSC):

  • Construction: A series capacitor bank shunted by a thyristor-controlled reactor (TCR).

  • Operation: By controlling TCR firing angle, net series reactance ($$\displaystyle X_{net} = X_C \parallel X_L $$) is varied continuously from capacitive to inductive.

  • Advantages: Increases transfer capability, damps power oscillations, mitigates subsynchronous resonance (SSR).

  • Disadvantages: Generates harmonics, complex control, high losses in reactor.

• Static Synchronous Series Compensator (SSSC):

  • Operation: A voltage-source converter (VSC) connected in series with the line via a transformer. Injects a controllable AC voltage ($$\displaystyle V_{inj} $$) in quadrature with line current, effectively changing line impedance.

  • Use: Power flow control, loop flow management, oscillation damping. Can also inject negative sequence for fault current limitation.

VSC-Based FACTS

• Static Synchronous Compensator (STATCOM):

  • Operation: A VSC shunt-connected to the bus. By controlling the magnitude and phase of its output voltage ($$\displaystyle V_{stat} $$), it generates or absorbs reactive power.

    • $$\displaystyle V_{stat} > V_{bus} $$ → Supplies VAr ( capacitive).

    • $$\displaystyle V_{stat} < V_{bus} $$ → Absorbs VAr ( inductive).

  • Advantage over SVC: Better performance at low voltages, smaller footprint, faster response, less harmonics.

• Unified Power Flow Controller (UPFC):

  • Schematic: Two VSCs (series and shunt) coupled via a common DC capacitor.

  • Functions: Can independently control line voltage (shunt VSC), line impedance (series VSC magnitude), and phase angle (series VSC phase). The most versatile FACTS controller for comprehensive power flow control.

[!TIP] Exam Focus: Be able to sketch and label the UPFC. Differentiate between TCSC (thyristor-based, series capacitor) and SSSC (VSC-based, series voltage injection). Know the primary function of STATCOM (dynamic voltage support).

VII. SPECIAL TOPICS AND COMPARISONS

• Partial Discharge in Cables: (Covered in V.D). A non-destructive test to detect and locate insulation voids/defects by measuring high-frequency current pulses.

• Insulation Techniques (Motor Coils): Common pouring/impregnation methods: Dip & Bake (simple), Vacuum Pressure Impregnation (VPI) (best, removes voids, complete penetration), Resin Rich (pre-impregnated).

• Test Comparisons:

  • High Voltage Test vs. Insulation Resistance Test:

    | Feature | High Voltage Test | Insulation Resistance Test | | :--- | :--- | :--- | | Purpose | Verify dielectric strength | Check insulation quality (moisture, contamination) | | Voltage | High (above rated) | Low (DC, typically 0.5-5 kV) | | Duration | Short (1 min) | Short (1 min) or absorption ratio | | Interpretation | Pass/Fail (no breakdown) | Resistance value (MΩ/GΩ) and absorption index |

• Intrinsic Strength of Solid Dielectrics: The theoretical maximum electric field a flawless, homogenous solid can withstand before electronic breakdown (avalanche of electrons accelerated to ionizing energies). In practice, breakdown occurs at much lower fields due to impurities, voids, and thermal effects.

END OF UNIT 1 NOTES