Power Electronics Application to Power System (EX-702 (A)) - Unit 3 Short Notes

UNIT 3: POWER ELECTRONICS APPLICATION TO POWER SYSTEM

1.0 HIGH VOLTAGE TECHNOLOGY: FUNDAMENTALS AND SIGNIFICANCE

High Voltage (HV) Technology refers to the generation, measurement, insulation, and application of voltages typically above 1 kV (for AC) or 3 kV (for DC) in electrical power systems and industrial processes.

Significance in Modern Power Systems:

• Efficient Long-Distance Transmission: Reduces current ($$\displaystyle I = P/V $$), minimizing $$\displaystyle I^2R $$ losses and allowing thinner, cheaper conductors.

• Improved System Stability & Capacity: Enables interconnection of distant power grids and increases power transfer capability of existing lines.

• Essential for Key Equipment: Required for transformers, circuit breakers, instrument transformers, and insulation coordination.

Voltage Level Classifications:

Major Applications:

• Power Applications: Overhead transmission lines & substations, HV cables, power transformers, HV switchgear (circuit breakers, isolators).

• Non-Power Applications: Electrostatic precipitators (pollution control), X-ray machines, particle accelerators, high-power lasers, dielectric testing labs.

Need for HV Generation in Laboratories:

• Insulation Testing: To simulate overvoltages (lightning, switching) and test dielectric strength of equipment.

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

• Testing Scenarios:

  • Routine Tests: On every manufactured unit.

  • Type Tests: On prototype to verify design.

  • Research Experiments: To understand fundamental phenomena.

[!TIP] Exam Focus: Be prepared to differentiate between HV, EHV, UHV ranges and cite both power and non-power applications clearly.

2.0 BREAKDOWN MECHANISMS IN DIELECTRICS

2.1 Gaseous Dielectrics

Primary Ionization: Free electron gains energy from electric field, collides with neutral gas molecule, ionizes it (creates new electron + positive ion). Requires electron energy > ionization energy of gas.

Secondary Ionization: Processes that generate new free electrons at the cathode.

1. Positive Ion Impact: Accelerated positive ions strike cathode, ejecting secondary electrons.

2. Photoelectric Effect: UV photons from de-excitation of gas atoms strike cathode, emitting electrons.

3. Thermionic Emission: Cathode heating by ion impact.

Townsend Discharge Theory (First Ionization Stage):

• Townsend's First Ionization Coefficient (α): Number of ionizing collisions produced by one electron per unit path length. Function of $E/p$ (field strength/pressure).

• Townsend's Second Ionization Coefficient (γ): Number of secondary electrons produced per positive ion arriving at cathode.

• Breakdown Condition: When electron multiplication becomes self-sustaining.

$$i = i_0 e^{\alpha d} \quad \text{(current growth)}$$

Breakdown occurs when secondary emission sustains the discharge:

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

For breakdown, denominator $$\displaystyle \rightarrow 0 $$:

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

For $$\displaystyle \gamma (e^{\alpha d}) >> 1 $$, simplified to:

$$\boxed{\alpha d = \text{constant}}$$

This is the **Townsend breakdown criterion**.

Streamer Mechanism (Second Ionization / Practical Breakdown):

• Improvement over Townsend: Explains fast breakdown in non-uniform fields and the formation of visible spark channels.

• Process:

  1. Space charge from avalanche distorts local electric field.

  2. High field at avalanche tip causes photo-ionization in the gas ahead.

  3. New electron avalanches develop from these photo-electrons, creating a self-propagating ionization wave (streamer).

  4. Streamers from cathode and anode meet, forming a conducting spark channel.

Statistical Time Lag ($$\displaystyle t_s $$): Time delay due to random availability of initiating free electron (from natural radiation/background). Follows stochastic distribution.

Formative Time Lag ($$\displaystyle t_f $$): Time for electron avalanche to grow to breakdown after the initiating electron appears. Depends on $E/p$ and $d$.

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

Paschen's Law:

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

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

• Derivation (Simplified): From Townsend criterion $$\displaystyle \alpha d = \text{constant} $$. $\alpha$ is function of $$\displaystyle E/p = V/(pd) $$. So $$\displaystyle V_b/(pd) = \text{constant} \Rightarrow V_b \propto pd $$ at high $pd$. At low $pd$, $$\displaystyle V_b $$ increases due to fewer collisions. Combining gives the Paschen curve.

• Paschen Minimum: The curve has a minimum $$\displaystyle V_{min} $$ at a specific $$\displaystyle (pd)_{min} $$.

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

• Practical Implication: For a given voltage, there is a minimum safe clearance ($$\displaystyle d_{min} $$) at a given pressure. Below this, breakdown voltage increases (vacuum-like behavior).

Breakdown in Deep Vacuum:

• Not due to gas ionization (no gas molecules).

• Mechanisms:

  1. Field Emission: High field at micro-protrusions on electrodes emits electrons (cold cathode).

  2. Microscopic Arcing: Vaporization of electrode material at micro-protrusion tips.

  3. Outgassing: Adsorbed gases on electrode surfaces desorb under field/electron bombardment, providing a medium for discharge.

  4. Microparticle Charging & Acceleration: Charged microparticles gain kinetic energy, strike electrode, cause local heating/vaporization.

2.2 Solid Dielectrics

Intrinsic Strength: Maximum electric field a perfect, defect-free solid dielectric can withstand before electronic breakdown. Very high (100 kV/mm to 1000 kV/mm).

Electronic Breakdown in Solids:

1. Field Ionization: High field directly ionizes atoms/molecules (similar to gas, but requires much higher field).

2. Avalanche Breakdown: High-energy electrons collide and create electron-hole pairs, leading to avalanche multiplication (common in semiconductors).

3. Thermal Breakdown: Localized heating from leakage current or dielectric loss causes thermal runaway, melting/charring.

Cavity Breakdown (Partial Discharge - PD):

• Cause: Gaseous inclusions or voids within the solid dielectric or at interfaces.

• Process:

  1. Void has lower dielectric strength than solid.

  2. Voltage across void reaches its breakdown strength ($$\displaystyle V_b \propto pd $$, but $p$ is low).

  3. Partial Discharge (PD) occurs locally within the void, but does not completely bridge electrodes.

  4. Repeated PD erodes the solid insulation, eventually leading to complete breakdown.

• Significance: PD is a major aging mechanism and a key diagnostic tool for insulation health.

[!TIP] Common Pitfall: Do not confuse streamer (gas, fast, visible spark) with cavity/PD (in solids, localized, often invisible initially). Paschen's Law applies to gaps, not solid thickness directly.

3.0 HIGH VOLTAGE GENERATION METHODS

3.1 Series Resonant Circuit for HV Testing

• Principle: Uses series resonance ($$\displaystyle X_L = X_C $$) to magnify voltage across the test object (capacitor $$\displaystyle C_t $$) while limiting current from the source.

• Circuit: HV transformer (low current) -> Inductive reactor ($L$) -> Test object ($$\displaystyle C_t $$) in series.

• Resonance Condition:

$$\omega L = \frac{1}{\omega C_{eq}} \quad \text{where} \quad C_{eq} = C_t + C_{hv\ transformer}$$

$$\boxed{f_0 = \frac{1}{2\pi\sqrt{L C_{eq}}}}$$

• Advantages:

  • Low power input from source (high $Q$ circuit).

  • Compact, portable reactors possible.

  • Naturally filters harmonics.

3.2 Cockcroft-Walton (CW) DC Generator

• Construction: Cascaded voltage doubler stages. Each stage: 2 diodes + 1 capacitor.

• Working: AC input charges capacitors in parallel during positive half-cycle, connects them in series during negative half-cycle, adding voltages.

• Output Voltage (Ideal, no load): $$\displaystyle V_{out} = 2n V_{peak} $$ (n = number of stages).

• Advantages:

  • No HV transformer needed (uses low-voltage AC source).

  • Portable, no moving parts.

  • High voltage, low current.

• Limitations:

  • High Ripple & Poor Regulation: Voltage drops significantly with load current. $$\displaystyle V_{drop} \propto I \cdot n / fC $$.

  • Capacitor size/voltage rating increases with stages.

3.3 Tesla Coil

• Construction: Two resonant LC circuits (primary & secondary) magnetically coupled. Primary: low inductance, few turns, capacitor. Secondary: high inductance, many turns, toroidal top electrode.

• Working:

  1. Primary circuit spark gap fires, oscillating $$\displaystyle L_1C_1 $$.

  2. Resonant energy transfer to secondary $$\displaystyle L_2C_2 $$.

  3. High-frequency (50-1000 kHz), high-voltage AC generated at secondary.

• Why Current Flows in Nearby Objects (at High Frequency):

  1. Skin Effect: High frequency forces current to flow on conductor's surface, reducing effective cross-section but allowing flow through thin wires/objects.

  2. Capacitive Coupling: High $dV/dt$ creates strong electric fields. Nearby objects act as one plate of a capacitor, the other being the coil. Displacement current flows through dielectric (air, human body) even without direct contact.

3.4 Impulse Generators

• Purpose: Generate standard lightning impulse ($1.2/50 \mu s$) and switching impulse ($250/2500 \mu s$) waveforms.

• Basic Circuit: Charging resistor ($$\displaystyle R_c $$), DC source ($V$), large capacitor bank ($C$), triggering gap, wave-shaping resistors ($$\displaystyle R_s $$, $$\displaystyle R_f $$) and capacitors.

• Triggering using Three-Electrode Gap:

  • Arrangement: Main gap (between electrode 1 & 2) in series with a trigger gap (between electrode 2 & 3). Electrode 2 is common.

  • Process: DC voltage applied across 1-3. Trigger pulse (DC or impulse) applied to trigger electrode 3 initiates breakdown in trigger gap. This rapidly reduces voltage across main gap, causing its breakdown with minimal time delay.

• Why Preferred?

  • Precise Timing: Trigger pulse allows exact synchronization with oscilloscope/recording equipment.

  • Low Jitter: Consistent breakdown time from shot-to-shot.

  • Isolation: Trigger circuit isolated from high-energy main circuit.

• Method of Control Tripping: Using a firing pulse from a control unit to initiate the trigger gap breakdown.

[!TIP] Exam Focus: Know the difference between CW (DC, ripple) and Tesla (HF AC). For impulse generators, draw the three-electrode gap and explain its advantage over a simple two-electrode gap.

4.0 HIGH VOLTAGE MEASUREMENT TECHNIQUES

4.1 Potential Dividers for HV Measurement

• Principle: High voltage $$\displaystyle V_H $$ applied across series impedance $$\displaystyle Z_H $$, low voltage $$\displaystyle V_L $$ measured across known impedance $$\displaystyle Z_L $$: $$\displaystyle V_H = V_L \cdot (Z_H / Z_L) $$.

• Conditions for Impulse Work:

  1. Short Rise Time: $RC$ time constant << impulse front time (e.g., $$\displaystyle < 1 \mu s $$ for $1.2/50 \mu s$ wave).

  2. Critical Damping: To avoid oscillations. Over-damped (slow response) or under-damped (ringing) distorts waveform.

  3. Impedance Matching: Output impedance should be low to drive recording device (oscilloscope) without loading.

• Types & Comparison:

4.2 Standard Sphere Gap

• Construction: Two identical metallic spheres (diameter 6.25 cm to 100 cm) separated by adjustable gap.

• Operation: Breakdown voltage across gap is a function of sphere diameter ($D$) and gap spacing ($S$). Measured peak voltage is read from standardized tables/graphs.

• For AC/DC: Measures peak value (RMS = Peak/√2 for sinusoidal AC).

• For Impulse: Measures peak value directly (waveform independent if gap is uniform).

• Factors Influencing Measurement:

  • Sphere diameter ($D$)

  • Gap spacing ($S$)

  • Humidity: Increases breakdown voltage (water vapor electronegative).

  • Polarity: Positive polarity gives lower breakdown voltage in non-uniform fields (positive streamer).

  • Waveform: For non-standard impulses, correction factors may be needed.

4.3 Electrostatic Voltmeter

• Principle: Attraction force between fixed and moving electrode is proportional to $$\displaystyle V^2 $$. Movement of pointer (via mirror/spring) indicates voltage.

• Construction: Fixed stator, moving vane/plate, spring suspension, damping vane, scale.

• Advantages: True RMS for AC, no loading (infinite impedance), high accuracy.

• Disadvantages: Low power, fragile, expensive, limited range.

4.4 Generating Voltmeter

• Principle for High DC Voltage: Rotating vane (or disc) with radial slots passes between fixed field electrodes. Capacitance between rotating and fixed electrodes varies sinusoidally. This generates an AC current proportional to $$\displaystyle V_{DC} $$. The AC current is integrated (measured) to get $$\displaystyle V_{DC} $$.

• Advantage: Non-contact measurement, high impedance, suitable for very high DC voltages (HVDC).

4.5 Surge Current Measurement

• Methods & Instruments:

  1. Rogowski Coil: Toroidal coil around conductor. $$\displaystyle V_{out} \propto di/dt $$. Integrator needed to get $i(t)$. Advantage: No magnetic core (no saturation), wide bandwidth.

  2. Shunt Resistor: Low-value, non-inductive resistor. $$\displaystyle V_{shunt} = i(t) \cdot R_{shunt} $$. Challenge: Must withstand high surge currents without inductance affecting waveform.

  3. Current Transformers (CTs): For AC components only, may saturate on DC offset.

• Challenges in HV Systems:

  • High $di/dt$: Requires very high bandwidth measurement system.

  • Electromagnetic Interference (EMI): Severe noise from arc/breakdown. Requires heavy shielding, fiber optic links.

  • Safety & Isolation: Measurement circuit must be fully isolated from high voltage ground potential.

  • Bandwidth vs. Range: Trade-off between measuring very fast transients and large magnitudes.

5.0 TESTING OF POWER SYSTEM EQUIPMENT

5.1 Circuit Breakers

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

  • Objective: Verify ability to close onto and interrupt maximum fault current.

  • Method: Test circuit with source, reactor (limits current), breaker under test. Measures: arcing time, re-ignition, current chopping, recovery voltage.

• Dielectric Test (Insulation Withstand):

  • Objective: Verify insulation strength between poles and to ground.

  • Method: Apply power-frequency voltage (1 min) and/or impulse voltage. Checks for flashover, puncture.

5.2 Insulators

• Mechanical Strength Test: Tensile, bending, torsion tests to verify design load withstand.

• Puncture Voltage Test: Voltage applied across the insulator (electrodes on metal parts). Tests internal dielectric strength. Failure is internal puncture (often brittle).

• Flash-Over Voltage Test: Voltage applied between metal cap and pin (normal service condition). Tests surface insulation. Failure is external flashover along wet/dirty surface.

• Necessity: Ensures mechanical integrity under wind/ice, prevents internal failure (puncture), and guarantees surface performance under pollution (flashover).

5.3 Power Transformers

• High Voltage (HV) Test / Withstand Test:

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

  • Objective: Verify major insulation strength (oil, paper, barriers).

• Insulation Resistance (Megger) Test:

  • Applies DC voltage (typically 2.5-5 kV) and measures resistance.

  • Objective: Detect gross insulation deterioration, moisture, contamination. Qualitative (trend monitoring).

• Key Difference:

  • HV Test: Destructive/High Stress. Tests strength under high electric stress. Applied for short duration (1 min AC, few impulses).

  • Insulation Resistance Test: Non-Destructive/Low Stress. Tests quality (leakage current). Applied at lower voltage for longer time. Sensitive to surface moisture.

5.4 Partial Discharge (PD) Tests

• On HV Cables: PD measured during routine testing or in-service monitoring.

• Detection Methods:

  • Electrical: Measure high-frequency current pulses (using HFCT or coupling capacitor).

  • Acoustic: Detect ultrasonic emissions from PD.

  • UHF: Detect electromagnetic waves in cable sheath.

• Fault Location: Using Time Domain Reflectometry (TDR) or pulse-echo method. PD pulses reflect from impedance discontinuities (defects). Time delay of reflected pulse gives distance to fault.

5.5 Insulation Systems for Rotating Machines

• Pouring Methods for Motor Coil Insulating Paint (Varnish):

  1. Dip & Bake: Coil dipped in liquid varnish, then baked. Simple, but voids possible.

  2. Vacuum-Pressure Impregnation (VPI): Most effective. Coil placed in pressure vessel, vacuum removes air/moisture, then varnish forced in under pressure. Eliminates voids, excellent for high voltage/high reliability.

• Relation to Cavity Breakdown & PD: VPI minimizes gaseous voids/cavities within the insulation. Voids are prime sites for partial discharge initiation, which degrades insulation over time.

6.0 HVDC TRANSMISSION SYSTEMS

6.1 Merits and Demerits

6.2 HVDC Converter Station Layout & Equipment

• Converters (Thyristor Valves): Core. Form rectifier (AC->DC) or inverter (DC->AC). Usually 6-pulse or 12-pulse (two 6-pulse bridges in series, phase-shifted).

• Converter Transformers: Provide necessary voltage transformation and phase shift for 12-pulse operation. Often with two secondary windings (star/delta).

• AC & DC Filters: Multi-tuned, high-pass filters to suppress harmonics (see 6.4).

• DC Switchyard: Contains disconnectors, surge arresters, DC current/voltage measuring equipment.

• Control Systems: For firing angle control, current/power regulation, commutation margin control.

6.3 Principle of HVDC System Control

• Basic Objectives:

  • Power Regulation: Maintain scheduled power flow.

  • Current Limiting: Prevent valve/DC line overcurrent.

  • Commutation Margin Control (γ Control): Ensure successful commutation (overlap angle μ, extinction angle γ). Minimum γ (~15-20°) required.

• Converter Control Characteristics:

  • Rectifier Operating Region: Constant Current (CC) control at low power, Constant Extinction Angle (CEA) at high power (to maintain γ).

  • Inverter Operating Region: Constant Current (CC) control at low power, Constant Gamma (CG) control at high power (primary control).

  • Power Reversal: Achieved by changing firing angle α past 90° (inverter operation). Power direction changes, but DC voltage polarity remains same.

6.4 AC and DC Filters in HVDC Systems

• Purpose:

  • Harmonic Suppression: Filter out converter-generated harmonics from AC and DC sides.

  • Reactive Power Compensation: AC filters also supply capacitive reactive power to offset converter consumption.

• Types & Tuning:

  • Tuned Filters: Series L-C-R tuned to specific harmonic frequencies (e.g., 12th, 24th for 12-pulse). High impedance at tuned frequency.

  • High-Pass Filters (C-type, L-type): Provide low impedance for high-order harmonics. Often used for broadband damping.

  • Typical Arrangement: AC side has multiple tuned filters (e.g., 12th, 24th) + high-pass. DC side has a single high-pass filter (DC filter) for ripple.

6.5 Types of Harmonics in HVDC Systems

• Characteristic Harmonics: Determined solely by pulse number ($p$) of converter bridge.

  • Order: $$\displaystyle h = kp \pm 1 $$ (k = integer, 1,2,3...)

  • For 12-pulse: $$\displaystyle h = 11, 13, 23, 25, 35, 37... $$

  • For 6-pulse: $$\displaystyle h = 5, 7, 11, 13, 17, 19... $$

• Non-Characteristic Harmonics: Caused by:

  • Unbalanced AC system voltages.

  • Imperfect transformer tap positions.

  • Firing angle errors.

  • Can include even harmonics (2, 4, 6...) and triplens (3, 9, 15...).

6.6 Types of DC Links in HVDC Systems

1. Point-to-Point: Two converter stations, one DC line. Most common (e.g., interconnections).

2. Back-to-Back: No DC line; rectifier & inverter in same station. Used for asynchronous tying or isolated load.

3. Multi-Terminal DC (MTDC): More than two converter stations connected to common DC bus/line.

6.7 Multi-Terminal DC (MTDC) Systems

• Series MTDC: Converters connected in series on DC side. Current same everywhere, voltage additive. Control: Master station controls voltage, others control current. Complex protection.

• Parallel MTDC: Converters connected in parallel on DC side. Voltage same, current additive. Control: Master station controls power/current, others control voltage. Easier protection.

• Applications:

  • Offshore Wind Integration: Multiple wind farms feed into offshore platform HVDC converter.

  • Large Interconnections: Tapping into existing HVDC links to supply new load centers.

  • Island Supply: Supplying power to multiple islands from a single mainland source.

6.8 Power Reversal in HVDC Systems

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

• Control Implications:

  • Rectifier becomes Inverter: The station that was rectifying (α < 90°) now inverts (α > 90°), and vice versa.

  • DC Voltage: Remains same polarity (e.g., positive on pole 1 relative to pole 2/earth).

  • DC Current: Reverses direction.

  • Firing Angles: Both stations operate with α > 90° (inverter mode). One station (now rectifier) reduces α towards 90°, the other (now inverter) increases α above 90° to control power.

  • Smooth Transition: Requires coordinated control to avoid large transients.

7.0 FACTS (FLEXIBLE AC TRANSMISSION SYSTEMS) CONTROLLERS

7.1 Introduction to FACTS Controllers

• Definition: Power electronics-based systems that provide fast, dynamic control of AC transmission system parameters (voltage, impedance, phase angle).

• Role: Enhance controllability, increase power transfer capability, improve stability (damping oscillations), and optimize power flow.

7.2 Principle of Conventional Reactive Power Compensators

• Shunt Compensation: Adding capacitance (capacitor bank) or inductance (reactor) in parallel with line.

  • Effect: Controls voltage magnitude at the point of connection ($$\displaystyle V \propto Q_{shunt} $$).

• Series Compensation: Adding capacitance in series with line.

  • Effect: Reduces line inductive reactance ($$\displaystyle X_L $$), increasing power transfer $$\displaystyle P \propto V_1V_2 \sin\delta / X_L $$. Also affects power flow distribution.

7.3 SVC (Static Var Compensator)

• Principle: Combines Thyristor-Switched Capacitors (TSC) and Thyristor-Controlled Reactors (TCR).

  • TSC: Capacitor bank switched in/out by thyristor valves (stepwise reactive power).

  • TCR: Reactor with thyristor valve controlling firing angle (continuous reactive power absorption).

• Operation: By combining TSC (capacitive) and TCR (inductive), net reactive power ($Q$) can be continuously controlled from capacitive to inductive.

• Effect: Fast voltage regulation at the point of connection by injecting/absorbing $Q$.

7.4 TCSC (Thyristor Controlled Series Capacitor)

• Principle: A series capacitor ($C$) permanently in line, shunted by a Thyristor-Controlled Reactor (TCR).

• Operation:

  • Varying TCR firing angle changes the effective impedance of the parallel combination ($$\displaystyle Z_{eff} $$).

  • Capacitive Mode: TCR off or minimum conduction → $$\displaystyle Z_{eff} \approx -jX_C $$ (max capacitive boost).

  • Inductive Mode: TCR fully on → $$\displaystyle Z_{eff} \approx -j(X_C X_L / (X_C - X_L)) $$ (less capacitive or slightly inductive).

• Advantages:

  • Damping of power oscillations (PSS function).

  • Increases steady-state power transfer.

  • Can optimize power flow.

• Disadvantages:

  • Sub-Synchronous Resonance (SSR) Risk: Can excite torsional modes in nearby turbine-generators if not properly controlled.

  • Complex control and protection.

  • High cost.

7.5 STATCOM (Static Synchronous Compensator)

• Principle: Voltage Source Converter (VSC) using GTOs/IGBTs, connected to AC bus via coupling transformer.

• Operation:

  • VSC generates a controllable AC voltage $$\displaystyle V_{STATCOM} $$.

  • By controlling magnitude & phase of $$\displaystyle V_{STATCOM} $$ relative to system voltage $$\displaystyle V_{sys} $$:

    • $$\displaystyle |V_{STATCOM}| > |V_{sys}| $$ → Injects capacitive reactive power ($$\displaystyle Q > 0 $$).

    • $$\displaystyle |V_{STATCOM}| < |V_{sys}| $$ → Absorbs inductive reactive power ($$\displaystyle Q < 0 $$).

• Advantages over SVC:

  • Faster response (milliseconds).

  • Better performance at low voltages (can generate $Q$ even when $$\displaystyle V_{sys} $$ is low).

  • Smaller footprint (no large capacitor banks/reactors).

  • No harmonic resonance risk with system.

7.6 SSSC (Static Synchronous Series Compensator)

• Principle: VSC connected in series with transmission line via a coupling transformer.

• Operation:

  • VSC injects a controllable AC voltage $$\displaystyle V_{SSSC} $$ in quadrature with line current.

  • Effectively changes the line's apparent impedance:

    • $$\displaystyle V_{SSSC} $$ leads $I$ → reduces net inductive reactance (series capacitive effect).

    • $$\displaystyle V_{SSSC} $$ lags $I$ → increases net impedance (series inductive effect).

  • Can also regulate power flow by controlling voltage drop across line.

• Use: Power flow control, damping oscillations, mitigating SSR (by counteracting TCSC-induced effects).

7.7 UPFC (Unified Power Flow Controller)

• Principle: Combination of STATCOM (shunt) and SSSC (series) connected via a common DC link.

• Unified Control:

  • Shunt VSC: Controls DC link voltage & can independently inject/absorb $Q$ at the shunt point.

  • Series VSC: Injects a controllable voltage $$\displaystyle V_{SE} $$ with variable magnitude & phase angle in series with line.

• Capabilities:

  • Simultaneous control of active power (via $$\displaystyle V_{SE} $$ phase angle) and reactive power (via both $$\displaystyle V_{SE} $$ magnitude and shunt $Q$).

  • Can regulate voltage, control line power flow, and damp oscillations independently and simultaneously.

  • Most versatile and powerful FACTS controller.

[!TIP] Exam Focus: Be able to draw the UPFC schematic and clearly state the difference between SVC (TCR+TSC, thyristor-based, slower) and STATCOM (VSC-based, faster, better low-voltage performance). For TCSC, emphasize SSR risk.