HVDC & FACTS (EX-702 (B)) - Unit 2 Short Notes

UNIT 2: HVDC & FACTS (with High Voltage Engineering Fundamentals)

1. High Voltage Technology and Breakdown in Gaseous Dielectrics

1.1. High Voltage Technology: Concept, Significance, and Voltage Classifications

• Concept: Technology concerned with the generation, measurement, transmission, and application of voltages significantly above standard distribution levels (typically > 1000 V AC or 1500 V DC).

• Significance:

  • Power Transmission: Enables long-distance, high-capacity power transfer with reduced line losses ($$\displaystyle P_{loss} \propto I^2R $$; higher voltage $\Rightarrow$ lower current for same power).

  • Testing: Essential for testing insulation strength of power equipment (transformers, cables, circuit breakers) to ensure reliability.

  • Industrial Applications: Used in particle accelerators, X-ray generation, electrostatic precipitators, ozone generation, and food preservation.

• Voltage Classifications (as per IEC/IEEE):

  | Acronym | Range (AC) | Range (DC) | Typical Application | | :--- | :--- | :--- | :--- | | HV | 1 kV - 35 kV | 1.5 kV - 50 kV | Distribution, industrial | | EHV | 35 kV - 230 kV | 50 kV - 300 kV | High-power transmission | | UHV | > 230 kV (often > 800 kV) | > 300 kV (often > 600 kV) | Very long-distance, bulk power |

[!TIP] Exam Focus: Be prepared to quote exact voltage ranges and cite both power and non-power applications. Common pitfall: Confusing HV/EHV/UHV ranges for AC vs. DC.

1.4. Ionization Processes in Gaseous Dielectrics

• Primary Ionization: Impact ionization by free electrons accelerated by the electric field. An electron gains enough kinetic energy between collisions to ionize a neutral gas molecule, creating a new electron-ion pair.

  • ** Townsend's First Ionization Coefficient ($\alpha$):** Number of ionizing collisions produced by one electron per unit length of drift. $$\displaystyle \alpha = A p e^{-Bp/E} $$, where $p$=pressure, $E$=field, $A,B$=gas constants.

• Secondary Ionization: Processes that generate additional electrons at the cathode, sustaining the discharge beyond the initial avalanche.

  • Mechanisms:

    1. Positive Ion Impact: Positive ions strike cathode, releasing secondary electrons (coefficient $\gamma$).

    2. Photon Interaction: UV photons from the avalanche excite gas atoms; emitted photons hit cathode, ejecting electrons (photoelectric effect).

    3. Metastable Atoms: Excited but non-radiating atoms collide with cathode, releasing electrons.

[!TIP] Key Distinction: Primary ionization creates electron avalanches in the bulk gas. Secondary ionization provides the "feedback" mechanism at the electrode to make the discharge self-sustaining.

1.5. Townsend's Theory: Breakdown Condition

• Theory: Describes the transition from a non-self-sustaining discharge to a self-sustaining spark breakdown.

• Breakdown Condition: When the total number of electrons reaching the anode equals the initial number of electrons multiplied by the combined effect of primary and secondary ionization.

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

where $$\displaystyle n_a $$ = electrons at anode, $$\displaystyle n_0 $$ = initial electrons, $\alpha$ = first ionization coefficient, $d$ = gap distance.

For self-sustenance: $$\displaystyle n_0 = \gamma (n_a - n_0) $$, where $\gamma$ = secondary ionization coefficient.

**Final Townsend Breakdown Criterion:**

$$1 = \gamma (e^{\alpha d} - 1) \quad \text{or} \quad e^{\alpha d} = 1 + \frac{1}{\gamma}$$

For large $\alpha d$: $$\displaystyle \boxed{e^{\alpha d} \approx \frac{1}{\gamma}} $$

1.6. Streamer Mechanism of Breakdown in Non-Uniform Fields

• Limitation of Townsend: Fails to explain rapid breakdown in non-uniform fields (e.g., point-plane) and the formation of visible spark channels.

• Streamer Theory:

  1. An initial electron avalanche develops a dense space charge of positive ions.

  2. The space charge distorts the local electric field, enhancing it at the avalanche head.

  3. The enhanced field causes further ionization ahead of the avalanche, creating a streamer—a highly ionized, self-propagating channel.

  4. Streamers from cathode and anode can merge, leading to complete breakdown.

• Significance: Explains the fast propagation of spark channels and the lower breakdown voltage observed in non-uniform fields compared to Townsend's prediction.

1.7. Paschen's Law

• Statement: The breakdown voltage ($$\displaystyle V_b $$) of a uniform field gap is a unique function of the product of gas pressure ($p$) and gap distance ($d$), independent of their individual values, for a given gas and electrode material.

$$V_b = f(pd)$$

• Derivation (Simplified): Combines Townsend's criterion ($$\displaystyle e^{\alpha d} = 1/\gamma $$) with $$\displaystyle \alpha = A p e^{-Bp/E} $$. Assuming $\gamma$ constant and $$\displaystyle E = V_b/d $$, solving yields $$\displaystyle V_b $$ as a function of $pd$.

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

• Practical Implications:

  • Insulation Design: For a given voltage, there is an optimum $pd$ (pressure-distance product). Too low $p$ (vacuum) or too high $p$ (dense gas) increases $$\displaystyle V_b $$.

  • High-Altitude Equipment: Lower atmospheric pressure ($p \downarrow$) reduces breakdown strength; equipment must be derated.

  • SF₆ Circuit Breakers: Operate at high pressure to achieve very high dielectric strength.

[!TIP] Crucial Formula: Remember the Paschen Minimum value for air (~327V) and its $pd$ product. This is a frequent numerical question.

1.8. Statistical and Formative Time Lags

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

$$T = T_s + T_f$$

• Statistical Time Lag ($$\displaystyle T_s $$): Time for the first free electron to appear (from natural background radiation/ionization). Random/variable. Depends on voltage level (higher voltage $\Rightarrow$ shorter $$\displaystyle T_s $$).

• Formative Time Lag ($$\displaystyle T_f $$): Time for the electron avalanche to develop into a spark channel after the first electron appears. Deterministic. Depends on gap geometry, gas, and overvoltage.

• Importance: Critical for switching surge insulation coordination and impulse testing. The 50% breakdown voltage is defined for a standard impulse wave where $$\displaystyle T_s $$ is significant.

2. Breakdown in Other Media and Partial Discharges

2.4. Partial Discharge (PD) Tests on High-Voltage Cables

• Principle: PD are localized electrical discharges that only partially bridge the insulation. They indicate incipient faults.

• Procedure (for cables):

  1. Cable sample is placed in a test tank with water as a ground electrode.

  2. AC voltage (typically 1.5-2x rated voltage) is applied.

  3. PD pulses are detected using a PD detector (coupling capacitor, filter, measuring instrument).

  4. PD magnitude (pC) and PD inception/extinction voltages are recorded.

• Fault Location (Time Domain Reflectometry - TDR):

  • A fast voltage step (or PD pulse itself) is injected at one end.

  • The reflected pulse from the impedance discontinuity (fault/PD site) is measured.

  • Fault Distance = (Wave velocity $\times$ Time delay) / 2.

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

[!TIP] Exam Focus: Know the basic TDR principle. PD tests are non-destructive and used for quality control/condition monitoring, unlike withstand tests.

3. High Voltage Generation Methods

3.1. Series Resonant Circuits

• Principle: Uses resonance in an LC circuit to generate high AC voltages from a low-voltage source.

• Circuit: Low-voltage AC source ($$\displaystyle V_s $$) $$\displaystyle \rightarrow $$ Inductor ($L$) $$\displaystyle \rightarrow $$ Capacitor ($C$, the test object) $$\displaystyle \rightarrow $$ back to source. A tuning capacitor ($$\displaystyle C_t $$) is often in parallel with $C$.

• Operation: At series resonance ($$\displaystyle \omega L = 1/(\omega C_{total}) $$), the circuit impedance is minimum (purely resistive). Current $$\displaystyle I = V_s / R $$ (R = circuit resistance) is maximum.

• Voltage Magnification: $$\displaystyle V_C = I \cdot X_C = I / (\omega C_{total}) $$. Since $I$ is large at resonance, $$\displaystyle V_C \gg V_s $$.

• Resonance Condition Derivation:

  Impedance $$\displaystyle Z = R + j(\omega L - 1/(\omega C)) $$. At resonance, imaginary part = 0.

$$\left. \omega L - \frac{1}{\omega C} = 0 \quad \Rightarrow \quad \boxed{\omega_0 = \frac{1}{\sqrt{LC}}} \right.$$

where $C$ is total capacitance.

3.2. Cockcroft-Walton (CW) Generator

• Construction: Cascaded voltage doubler stages. Each stage has 2 diodes ($$\displaystyle D_1, D_2 $$) and 2 capacitors ($$\displaystyle C_1, C_2 $$). Driven by a high-frequency AC source ($$\displaystyle V_{ac} $$).

• Working (1 Stage):

  • Negative half-cycle: $$\displaystyle D_1 $$ conducts, $$\displaystyle C_1 $$ charges to $$\displaystyle V_{ac} $$.

  • Positive half-cycle: $$\displaystyle D_2 $$ conducts. $$\displaystyle C_1 $$ (now at $$\displaystyle V_{ac} $$) in series with $$\displaystyle V_{ac} $$ charges $$\displaystyle C_2 $$ to $$\displaystyle 2V_{ac} $$.

  • Cascading $n$ stages gives $$\displaystyle V_{out} \approx 2n V_{ac} $$ (no load).

• Advantages: Simple, no transformer needed, produces smooth DC, portable.

• Limitations: Poor regulation (voltage drops with load), high ripple, limited current, requires high-frequency AC source.

  | Parameter | Expression (Ideal, No Load) | | :--- | :--- | | Output Voltage | $$\displaystyle V_o \approx 2n V_{ac} $$ | | Ripple Voltage | $$\displaystyle \Delta V \approx \frac{I}{f C} (3n + 1) $$ | | Regulation | Poor (voltage sag $\propto$ load current) |

3.3. Tesla Coil

• Construction: 1) Primary Circuit: Low-voltage, high-frequency AC source $$\displaystyle \rightarrow $$ Primary coil (few turns, heavy wire) $$\displaystyle \rightarrow $$ spark gap (SG). 2) Secondary Circuit: Large number of turns of fine wire on a cylindrical form, with a toroidal top load (terminal). Primary and secondary are magnetically coupled but not electrically connected.

• Working:

  1. Capacitor in primary charges from source.

  2. When voltage across capacitor exceeds SG breakdown, it sparks, dumping energy into primary LC circuit.

  3. Primary oscillates at its resonant frequency $$\displaystyle f_1 = 1/(2\pi\sqrt{L_1 C_1}) $$.

  4. Energy is transferred magnetically to secondary LC circuit (resonant freq $$\displaystyle f_2 $$). For maximum transfer, $$\displaystyle f_1 \approx f_2 $$.

  5. Secondary voltage builds up to very high values (MV) due to turns ratio.

  6. High-frequency, high-voltage output appears at the toroid.

• High-Frequency Effect on Nearby Objects: The intense, rapidly alternating electric field causes dielectric breakdown of air at lower voltages (due to skin effect, reduced ionization time). It can light fluorescent tubes or cause corona from pointed objects without contact.

[!TIP] Key Point: Tesla coil is a resonant air-core transformer. Its high frequency is key to the "wireless" lighting effect.

4. Impulse Generation and Triggering

4.1. Impulse Generator Triggering Using Three-Electrode Gap

• Method: A third electrode (triggering electrode) is placed between the main spark gaps (charging electrode and ground).

  1. Generator capacitors are charged to DC voltage $$\displaystyle V_c $$.

  2. A triggering pulse (from a separate pulse generator) is applied to the middle electrode.

  3. This creates a local field enhancement, initiating a spark at the first main gap (between charging electrode and trigger electrode).

  4. The spark rapidly propagates through all series gaps, discharging the capacitor bank.

• Why Preferred:

  • Precise Timing: Triggering is independent of the random statistical time lag of spontaneous breakdown.

  • Synchronization: Allows perfect synchronization with oscilloscopes or other test equipment.

  • Consistency: Produces identical impulse waves for repeated testing.

  • Control: Enables triggering at a desired phase of a superimposed AC voltage (for switching impulse tests).

5. High Voltage Measurement Techniques

5.1. Potential Dividers

• Principle: A known fraction of the high voltage is measured using a low-voltage instrument (oscilloscope, DVM). $$\displaystyle V_{HV} = V_{meas} \times (R_1+R_2)/R_2 $$ (for resistive) or similar ratio for capacitive.

• Types & Comparison:

  | Type | Construction | Frequency Response | Use Case | Pros | Cons | | :--- | :--- | :--- | :--- | :--- | :--- | | Resistance Divider | Series resistors (high stability, low temp coeff.) | Poor at high freq (parasitic C) | DC, Power-frequency AC | Simple, accurate for DC/50Hz | Loading, heating, poor impulse response | | Capacitance Divider | Two capacitors (low loss, e.g., compressed gas) | Excellent (up to MHz) | Impulse & HF | Minimal loading, good transient resp. | Bulky, sensitive to stray C, calibration complex | | Mixed RC (R-C) Divider | Series resistor + shunt capacitor at each stage | Optimized for impulse | Standard for Impulse | Good damping, accurate impulse response | More complex design, needs careful matching |

[!TIP] Golden Rule: For impulse voltage measurement, a properly designed RC (or R-C) divider is mandatory to avoid oscillations.

5.2. Conditions for Potential Dividers in Impulse Work

1. Transient Response: The divider's step response must be critically damped or overdamped to avoid oscillations that distort the impulse wave.

2. High-Frequency Behavior: Parasitic inductances and capacitances must be minimized and matched. The divider's natural frequency should be much higher than the impulse wave's dominant frequency.

3. Matching: The characteristic impedance of the coaxial cable connecting the divider to the recorder must match the divider's output impedance to prevent reflections.

4. Screening: Entire divider and connecting cable must be shielded to reject EMI.

5.3. Sphere Gap for HV Measurement

• Construction: Two precisely machined, identical metal spheres of diameter $D$ (e.g., 25 cm, 50 cm, 100 cm, 150 cm). Gap distance $S$ is adjustable.

• Operation:

  • A high voltage is applied across the spheres.

  • The voltage at which a spark jumps the gap is the 50% breakdown voltage.

  • This voltage is looked up in standard tables (IEC 60052) based on $D$ and $S/D$ ratio to get the peak value of the applied voltage.

• For AC/DC: Measures peak value (rms = peak/√2 for AC sine).

• For Impulse: Measures peak value directly (standard tables for standard lightning impulse).

• Influencing Factors:

  • Sphere diameter ($D$)

  • Gap distance ($S$) and $S/D$ ratio

  • Polarity (for DC/Impulse, positive vs. negative breakdown differs)

  • Surrounding objects (must be > 2D away)

  • Atmospheric conditions (pressure, temperature, humidity - corrections applied)

[!TIP] Critical: Sphere gap is a primary standard. It is non-destructive for AC/DC but destructive for impulse (erodes spheres). Always cite the need for atmospheric correction.

6. Surge Current Measurement

6.1. Methods and Instruments

• Rogowski Coil: A toroidal, air-core coil placed around the conductor. The surge current $i(t)$ induces a voltage $$\displaystyle v(t) = M \frac{di}{dt} $$ (M = mutual inductance). Requires an integrator to get $i(t)$. Advantages: No saturation, linear, no direct contact.

• Shunt Resistor (Current Viewing Resistor - CVR): A low-value, non-inductive resistor (e.g., special alloy) in series. Voltage drop $$\displaystyle v(t) = i(t) \times R_{shunt} $$ is measured. Must have very low inductance.

• Current Transformer (CT) for Surges: Special high-frequency CT with wide bandwidth and no core saturation. Less common for very high surges.

6.2. Challenges in Measuring Surge Currents

• Extreme Magnitude & dI/dt: Can be hundreds of kA with rise times of μs. Requires instruments with very high bandwidth and dynamic range.

• Electromagnetic Interference (EMI): The surge generates strong EMI that can corrupt the measurement signal.

• Inductance & Reflections: Lead inductance in the measurement circuit can cause significant voltage spikes (L di/dt) and signal ringing.

• Saturation: Magnetic core devices (CTs, iron-cored Rogowski) can saturate, distorting the waveform.

• Safety & Isolation: Measurement circuit must provide high isolation from the high-voltage system.

• Calibration: Difficult to generate a known, repeatable surge current for calibration.

7. High Voltage Testing of Power Equipment

7.1. Circuit Breaker Testing

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

  • Objective: Verify the breaker can safely interrupt (break) and close onto (make) the maximum fault current it is rated for.

  • Procedure: Breaker is connected to a special synthetic test circuit that replicates the transient recovery voltage (TRV) and current conditions of a real short-circuit. Tests are done at rated voltage and current.

• Dielectric Test (Withstand Test):

  • Objective: Verify the integrity of the main insulation (contacts-to-ground, phase-to-phase) under overvoltage stress.

  • Procedure: Apply a power-frequency voltage (typically 1 min) or impulse voltage (standard lightning/switching impulse) at a specified level (e.g., 1.5x rated voltage for power-frequency). No breakdown should occur.

7.2. Insulator Testing

• Mechanical Strength Test: Applies a specified mechanical load (tension, compression, bending) to verify the insulator's structural integrity. Necessary to prevent mechanical failure in service (e.g., under wind/ice load).

• Puncture Voltage Test: Voltage applied across the insulator (e.g., from pin to cap). Tests the bulk dielectric strength of the insulator material itself. Necessary to ensure the insulator material is free of internal voids/defects.

• Flash-Over Voltage Test: Voltage applied along the insulator surface (from line to ground pin). Tests the surface insulation under wet/dry conditions. Necessary to ensure adequate creepage distance and surface hydrophobicity to prevent surface flashover in contaminated/wet conditions.

[!TIP] Distinguish: Puncture = through the material (internal). Flashover = along the surface (external). Both are dielectric tests but target different failure modes.

7.3. Transformer Testing: High Voltage Test vs. Insulation Resistance Test

• High Voltage Test (Withstand Test):

  • Applies overvoltage (AC or impulse) between windings and ground, or between windings.

  • Purpose: To verify the insulation strength can withstand transient overvoltages (lightning, switching) without breakdown. It's a destructive test at a high stress level.

• Insulation Resistance (IR) Test (Megger):

  • Applies DC voltage (typically 2.5-5 kV) and measures leakage current to calculate resistance (in GΩ or MΩ).

  • Purpose: To detect gross insulation deterioration (moisture, contamination, major cracks). It's a non-destructive, routine test. Does not prove strength against high transient voltages.

• Comparison:

  | Feature | High Voltage Test | Insulation Resistance Test | | :--- | :--- | :--- | | Voltage Type | AC or Impulse (high) | DC (low) | | Primary Purpose | Verify dielectric strength | Check insulation quality (dryness, contamination) | | Stress Level | Very high (near breakdown) | Low | | Nature | Destructive (if failed) | Non-destructive | | Information | "Will it survive a surge?" | "Is it generally healthy?" |

8. HVDC Transmission Systems

8.1. Merits and Demerits of HVDC Transmission

• Merits:

  1. Long Distance/Underwater: Lower cost for very long lines (>~600 km overhead, >~50 km submarine cable) due to no reactive power, lower line losses, and smaller conductors.

  2. Asynchronous Interconnection: Can connect two AC systems with different frequencies or that are not synchronized.

  3. Controllable Power Flow: Power flow is precisely and rapidly controllable by converter firing angle, independent of system phase angles. Helps stabilize AC networks.

  4. No Skin Effect: DC current distributes uniformly in conductor, better utilization of cross-section.

  5. Lower Right-of-Way: Requires narrower corridor for same power.

• Demerits:

  1. High Converter Cost: Expensive converter stations (AC/DC & DC/AC) with complex valves, controls, and filters.

  2. Reactive Power Requirement: Converters consume large amounts of reactive power (≈ 40-60% of active power), requiring large shunt capacitors/filters.

  3. Harmonics Generation: Produces characteristic harmonics (12-pulse: 12, 24, 36...) that pollute both AC and DC sides, requiring expensive filters.

  4. Lack of Overload Capability: DC lines cannot use the short-term overload capability of AC lines (limited by converter thermal limits).

  5. Multi-terminal Complexity: Control and protection of multi-terminal DC (MTDC) systems are more complex than AC.

8.2. HVDC Converter Station: Layout and Equipment

• Layout (Single-Line): AC Bus $$\displaystyle \rightarrow $$ AC Filter/Shunt Capacitor $$\displaystyle \rightarrow $$ Converter Transformer (with on-load tap changer) $$\displaystyle \rightarrow $$ Converter Valve (in valve hall, 6-pulse or 12-pulse) $$\displaystyle \rightarrow $$ DC Smoothing Reactor $$\displaystyle \rightarrow $$ DC Filter $$\displaystyle \rightarrow $$ DC Bus/Line $$\displaystyle \rightarrow $$ (Polarity reversal switches) $$\displaystyle \rightarrow $$ Neutral Bus (ground return).

• Key Equipment:

  • Converter Transformers: Step-up/down AC voltage, provide phase shift for harmonic cancellation (12-pulse).

  • Valves: Thyristor-based stacks (in series for voltage rating, in parallel for current rating). The core of the converter.

  • AC & DC Filters: Tuned LC circuits to absorb harmonics and provide capacitive reactive power.

  • Smoothing Reactor: Large inductor on DC side to limit ripple current and provide inertia for control.

  • Control System: Firing angle control, voltage regulation, protection.

  • Switchyard: AC/DC circuit breakers, disconnectors, surge arresters.

8.3. Types of DC Links

8.4. Principle of Control of HVDC System

• Core Idea: Control the firing angle ($\alpha$) of the thyristor valves to control the average DC output voltage $$\displaystyle V_d $$.

• Basic Equation (6-pulse bridge, no overlap):

$$V_d = V_{do} \cos \alpha - \frac{3}{\pi} \omega L_c I_d$$

where $$\displaystyle V_{do} $$ = open-circuit DC voltage (max at $$\displaystyle \alpha=0 $$), $$\displaystyle L_c $$ = commutating reactance (transformer leakage), $$\displaystyle I_d $$ = DC current.

• Control Modes:

  • Constant Current (CC) Mode: $\alpha$ adjusted to keep $$\displaystyle I_d $$ constant (primary control).

  • Constant Voltage (CV) Mode: $\alpha$ adjusted to keep $$\displaystyle V_d $$ constant (often at the receiving end).

  • Constant Power (CP) Mode: $$\displaystyle P = V_d I_d $$ is regulated by controlling both $$\displaystyle V_d $$ and $$\displaystyle I_d $$ (master control).

• Hierarchy: Master (power) $$\displaystyle \rightarrow $$ Current/Voltage (local) $$\displaystyle \rightarrow $$ Firing Pulse.

8.5. Converter Control Characteristics

• Definition: The steady-state relationship between DC voltage $$\displaystyle V_d $$ and DC current $$\displaystyle I_d $$ for a given AC system voltage and firing angle.

• Inverter Characteristic: $$\displaystyle V_d = V_{do} \cos \alpha - \frac{3}{\pi} \omega L_c I_d $$. Slope is $$\displaystyle -\frac{3}{\pi} \omega L_c $$.

• Rectifier Characteristic: Similar equation but with negative $$\displaystyle I_d $$ (current direction). Slope is $$\displaystyle +\frac{3}{\pi} \omega L_c $$.

• Operating Point: Determined by intersection of rectifier and inverter characteristics. The current margin ($\Delta I$) is set to ensure stable operation (rectifier in CC, inverter in constant extinction angle $\gamma$ mode).

[!TIP] Visualize: The two sloping lines (rectifier positive slope, inverter negative slope) crossing. The intersection is the steady-state $$\displaystyle I_d, V_d $$. Current margin is the vertical gap between inverter CC line and its actual $\gamma$-controlled line.

8.6. AC and DC Filters in HVDC Control

• Purpose: Mitigate harmonic pollution and provide/consume reactive power.

• AC Filters: Connected to the AC bus of the converter station.

  • Tuned to characteristic harmonics (e.g., 12th, 24th for 12-pulse).

  • Provide capacitive reactive power to compensate converter consumption.

  • Types: Single-tuned, double-tuned, C-type.

• DC Filters: Connected in the DC bus (between pole and neutral/earth).

  • Tuned to even-order harmonics (2nd, 4th) that pass through the converter bridge.

  • Do not provide significant reactive power.

  • Crucial for reducing ripple on DC line and interference with telephone lines.

8.7. Types of Harmonics in HVDC Systems

• AC Side Harmonics: Characteristic odd harmonics (for 6-pulse: 5,7,11,13,...; for 12-pulse: 11,13,23,25,...). Non-characteristic harmonics can arise from unbalances.

• DC Side Harmonics: Characteristic even harmonics (for 6-pulse: 2,4,6,...; for 12-pulse: 2,4,8,10,...). The fundamental (50/60 Hz) is also present on DC side due to voltage ripple.

• Telephone Interference: Low-frequency DC harmonics (especially 2nd) induce voltages in nearby telephone lines (TPI - Telephone Influence Factor).

8.8. Power Reversal in HVDC Systems

• Concept: Reversing the direction of active power flow without changing the physical polarity of the DC line conductors.

• Method: Simply reverse the firing angle control.

  • Normal (Rectifier Mode): $\alpha$ between 0° and 90° (usually 15°-20°). $$\displaystyle V_d > 0 $$, power flows from AC1 to AC2.

  • Reversal (Inverter Mode): $\alpha$ between 90° and 180° (usually 160°-170°). $$\displaystyle V_d < 0 $$, power flows from AC2 to AC1.

• Advantage: Fast (within milliseconds) and convenient for changing power flow direction (e.g., for asynchronous power exchange, black start).

8.9. Multi-terminal DC (MTDC) Systems

• Definition: A DC system with more than two converter stations connected to the same DC bus/line.

• Types & Comparison:

  | Feature | Series MTDC | Parallel MTDC | | :--- | :--- | :--- | | Connection | Converters connected in series on DC side. | Converters connected in parallel to common DC bus. | | Current | Same current flows through all converters. | Same voltage at all converters; currents divide. | | Voltage | Voltage is sum of individual converter voltages. | Voltage is common; controlled by one "slack" station. | | Control | Complex. Power sharing by controlling individual voltages. Easier if one is voltage controller. | Simpler. Similar to parallel AC generators. One station controls voltage, others control power/current. | | Fault Impact | A converter fault interrupts entire line current. | A converter fault only removes its own current; others continue. | | Insulation | DC line insulation must withstand sum of all station voltages. | Line insulation rated for maximum system voltage. |

• Applications:

  • Offshore Wind Integration: Multiple wind farms connect to a common HVDC platform (parallel MTDC).

  • Large Interconnections: Connecting multiple cities/regions to a central HVDC hub.

  • Grid Access for Remote Generation: (e.g., hydro, solar farms) feeding into a main DC corridor.

  • Asynchronous Interconnection of Multiple AC Grids.

9. FACTS Controllers

9.1. FACTS Controllers: Definition and Overview

• Definition: Flexible AC Transmission Systems. Power electronics-based devices that provide fast, dynamic control of AC transmission system parameters (voltage, impedance, phase angle) to enhance controllability and increase power transfer capability.

• Overview: Based on Voltage Source Converters (VSC) or Thyristor-based switches. They act as controllable impedances or voltage sources in series/shunt with the line.

9.2. Conventional Reactive Power Compensators: Principle

• Principle: Use fixed or switched shunt capacitors/inductors (or SVC) to inject/absorb reactive power (Q).

• Effect: Controls voltage magnitude at the point of connection.

  • Capacitors ($+Q$) $\Rightarrow$ Voltage rise.

  • Inductors ($-Q$) $\Rightarrow$ Voltage drop.

• Goal: Maintain voltage within limits, improve stability, reduce losses. Slow (mechanical switches) or moderately fast (thyristor-switched).

9.3. Static Var Compensator (SVC)

• Principle: A thyristor-controlled reactor (TCR) in parallel with thyristor-switched capacitors (TSC). Provides continuously variable reactive power.

• Operation:

  • TCR: Thyristor pair in series with reactor. By controlling firing angle ($\alpha$), the reactor current (and thus its inductive VAR consumption) is smoothly controlled from maximum to zero.

  • TSC: Thyristor switches connect/disconnect capacitor banks in steps. Provides capacitive VARs in discrete steps.

  • Combined, SVC can continuously generate/absorb reactive power over a wide range.

• Characteristics: Slope in V-I characteristic (voltage regulation). Fast response (ms).

9.4. Static Synchronous Compensator (STATCOM): Operation in Compensation

• Principle: A Voltage Source Converter (VSC) with a DC capacitor, connected in shunt via a coupling transformer. Acts as a synchronous condenser (rotating machine) but static.

• Operation:

  • VSC generates a controlled AC voltage ($$\displaystyle V_{STATCOM} $$) at its terminals.

  • By controlling the magnitude and phase of $$\displaystyle V_{STATCOM} $$ relative to the system voltage ($$\displaystyle V_{sys} $$), it can inject/absorb both reactive and active power.

  • Reactive Power Control: $$\displaystyle Q \propto (V_{STATCOM} - V_{sys}) \times V_{sys} / X $$. If $$\displaystyle V_{STATCOM} > V_{sys} $$, it injects $+Q$ (capacitive). If $$\displaystyle V_{STATCOM} < V_{sys} $$, it absorbs $-Q$ (inductive).

  • Active Power: Drawn from/returned to the DC capacitor (small losses).

• Advantages over SVC: Faster response, better performance at low voltages (more VARs at low $$\displaystyle V_{sys} $$), smaller footprint, harmonic generation lower.

9.5. Static Synchronous Series Compensator (SSSC): Operation and Use

• Principle: A VSC with DC capacitor connected in series with the transmission line via a coupling transformer.

• Operation:

  • VSC injects a controlled AC voltage ($$\displaystyle V_{SSSC} $$) in quadrature with the line current ($$\displaystyle I_L $$).

  • The injected voltage acts as a variable series impedance: $$\displaystyle Z_{SSSC} = V_{SSSC} / I_L $$.

  • Since $$\displaystyle V_{SSSC} \perp I_L $$, it behaves as a pure reactance ($$\displaystyle X_{SSSC} $$), either capacitive (boosting voltage) or inductive (bucking voltage).

• Uses:

  1. Power Flow Control: By changing line impedance ($$\displaystyle X_{line} + X_{SSSC} $$), power flow $$\displaystyle P \propto \frac{V_1 V_2}{X_{line} + X_{SSSC}} \sin\delta $$ is controlled.

  2. Damping Oscillations: Rapid modulation of $$\displaystyle X_{SSSC} $$ can damp power swings.

  3. Load Sharing: Balance power between parallel lines.

9.6. Thyristor Controlled Series Capacitor (TCSC): Detailed Discussion

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

• Construction: Fixed capacitor in series with line. Parallel to capacitor: a reactor ($L$) with a thyristor pair (TCR).

• Operation & Control:

  • Total Impedance: $$\displaystyle Z_{TCSC} = \frac{1}{j\omega C} \parallel j\omega L_{TCR}(\alpha) $$.

  • By varying the TCR firing angle $\alpha$, the effective inductive current through $L$ changes.

  • This changes the net capacitive reactance seen by the line: $$\displaystyle X_{TCSC} = X_C - X_L(\alpha) $$.

  • Modes:

    • Bypass Mode ($\alpha \approx 90°$): TCR fully on, $$\displaystyle X_L \approx X_C $$, net $X \approx 0$. Used for fault current limitation or during start-up.

    • Control Mode ($$\displaystyle \alpha < 90° $$): Net capacitive reactance $$\displaystyle X_{TCSC} > 0 $$ (but less than $$\displaystyle X_C $$). Used for power flow control.

    • Blocking Mode ($$\displaystyle \alpha > 90° $$): TCR off, pure capacitor $$\displaystyle X_C $$.

• Advantages:

  • Fast, continuous control of line impedance.

  • Improves system stability (damping).

  • Increases transfer capability.

  • Can mitigate subsynchronous resonance (SSR) by dynamically changing $$\displaystyle X_{TCSC} $$.

• Disadvantages:

  • Complex control (needs to handle harmonics, resonance).

  • Requires protection against overvoltages during faults.

  • Slower than SSSC (due to LC resonance time constant).

  • Can introduce low-order harmonics.

9.7. Unified Power Flow Controller (UPFC): Schematic Diagram

• Principle: Combines the functions of SSSC (series voltage injection) and STATCOM (shunt reactive/active power) in one unit, with a common DC link.

• Schematic:

  
  AC System Bus
  
      |
  
      |-----[Shunt Coupling Transformer]-----[VSC1]----[DC Capacitor]----[VSC2]-----[Series Coupling Transformer]----|-> To Transmission Line
  
      |                                                                                                           |
  

|-----------------------------------------------------------------------------------------------------------|

```

*   **VSC1 (Shunt):** Connected via shunt transformer. Controls **bus voltage** (reactive power) and **supplies/absorbs active power** to/from the DC link.

*   **VSC2 (Series):** Connected via series transformer. Injects a **controlled voltage** ($$\displaystyle V_{inj} $$) in series with the line. The magnitude and phase of $$\displaystyle V_{inj} $$ are independent.

*   **DC Link:** Common capacitor links the two VSCs. Active power balance between them.

• Capabilities: Simultaneously controls line impedance (via $$\displaystyle V_{inj} $$), bus voltage (via shunt VSC), and power flow ($P, Q$) in the line. The most versatile FACTS controller.

[!TIP] UPFC is the "Swiss Army Knife" of FACTS. Remember it has two VSCs sharing a DC capacitor, one in shunt, one in series. It can do everything SVC, SSSC, and TCSC can, plus more.

END OF UNIT 2 NOTES