UNIT 2: Power System Protection - Comprehensive Short Notes

1.0 FAULT ANALYSIS & SYMMETRICAL COMPONENTS

1.1 Types of System Faults

• Symmetrical (Three-phase) Fault: All three phases short-circuited. System remains balanced. Highest fault current but least frequent.

• Unsymmetrical Faults: System becomes unbalanced.

  • Single Line-to-Ground (LG): Most common (~70%).

  • Line-to-Line (LL): ~15%.

  • Double Line-to-Ground (LLG): ~10%.

  • Three-phase (LLLG): Symmetrical, ~5%.

• Fault Level / Fault MVA: The maximum power (in MVA) that can be delivered at a point during a fault. It determines the required breaking capacity of circuit breakers and the short-time withstand current of equipment.

  Fault MVA = $$\displaystyle \sqrt{3} \times V_{LL} \times I_{fault} $$

1.2 Symmetrical Components Theory

• Significance: Any set of three unbalanced phasors can be resolved into three balanced sets: Positive Sequence (V₁, I₁), Negative Sequence (V₂, I₂), Zero Sequence (V₀, I₀).

• Mathematical Relationships (for voltages):

$$ \begin{bmatrix} V_a \\ V_b \\ V_c \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 \\ 1 & a^2 & a \\ 1 & a & a^2 \end{bmatrix} \begin{bmatrix} V_0 \\ V_1 \\ V_2 \end{bmatrix} $$

where $$\displaystyle a = 1\angle120^\circ $$.

Inverse: $$\displaystyle V_0 = \frac{1}{3}(V_a + V_b + V_c) $$, etc.

• Sequence Networks:

  • Positive Sequence: Source voltage $$\displaystyle E_a $$ behind $$\displaystyle Z_1 $$ (usually $$\displaystyle X_d'' $$ for generators).

  • Negative Sequence: No voltage source, impedance $$\displaystyle Z_2 \approx X_2 $$.

  • Zero Sequence: No voltage source, impedance $$\displaystyle Z_0 $$ depends on grounding (e.g., transformer connection, ground wire presence).

1.3 Fault Current Calculations (General Procedure)

1. Draw individual sequence networks for the fault location.

2. Interconnect them based on fault type (see diagrams below).

3. Solve for sequence currents ($$\displaystyle I_0, I_1, I_2 $$).

4. Obtain phase currents from sequence currents.

5. Fault current expressions assume solid ground ($$\displaystyle Z_f=0 $$) unless specified.

Sequence Network Interconnection Diagrams (at generator terminals):

• LG Fault: All three networks in series.

$$\displaystyle I_f = I_a = 3I_0 = 3I_1 = 3I_2 $$

$$\displaystyle \boxed{I_{LG} = \frac{3E_a}{Z_1 + Z_2 + Z_0}} $$

• LL Fault: Positive & Negative networks in parallel, Zero open.

$$\displaystyle I_f = I_a = -I_b $$, $$\displaystyle I_c=0 $$

$$\displaystyle \boxed{I_{LL} = \frac{\sqrt{3}E_a}{Z_1 + Z_2}} $$

• LLG Fault: Positive & (Negative || Zero) networks in parallel.

$$\displaystyle I_f = I_a + I_b $$

$$\displaystyle \boxed{I_{LLG} = 3I_1 = \frac{3E_a}{Z_1 + \frac{Z_2Z_0}{Z_2+Z_0}}} $$

• LLLG Fault: Only Positive Sequence network (balanced).

$$\displaystyle \boxed{I_{LLLG} = \frac{E_a}{Z_1}} $$

Effect of Fault Impedance ($$\displaystyle Z_f $$): Add $$\displaystyle Z_f $$ in series with the faulted phase(s) in the sequence network connection. For LG fault: $$\displaystyle I_{LG} = \frac{3E_a}{Z_1+Z_2+Z_0+3Z_f} $$.

2.0 PROTECTIVE RELAYS: OPERATING PRINCIPLES & CHARACTERISTICS

2.1 Relay Fundamentals

• Requirements: Selectivity (minimum outage), Speed (minimum damage), Sensitivity (minimum fault current), Reliability (operate when needed, not otherwise), Economy.

• Classification:

  • Electromechanical: Moving parts (magnetic/induction).

  • Static (Analog): Solid-state (transistors, op-amps).

  • Microprocessor-based (Numerical): Digital signal processing.

• Key Terms:

  • Pick-up Value: Minimum input to cause operation.

  • Reset Value: Maximum input to return to original state.

  • Overrun: Disc movement beyond reset point after fault clears.

  • Time Dial Setting (TDS): Adjusts time-current characteristic slope.

  • Plug Setting (PS): Adjusts current pick-up (e.g., 0.8, 1.0, 1.2 of rated current).

2.2 Electromechanical Relays

• Electromagnetic Attraction Type:

  • Construction: solenoid/plunger or attracted armature.

  • Operation: AC/DC magnetic force attracts armature. Used for overcurrent, differential, under-voltage.

• Induction Disc Relay (Shaded-Pole / Watt-hour meter type):

  • Construction: Aluminum disc in air-gap between two electromagnets (fluxes 90° apart).

  • Operation: Eddy currents in disc produce torque $$\displaystyle T \propto \phi_1 \phi_2 \sin\theta $$. Drives disc to close contacts.

  • Minimizing Overrun: Use backstop, permanent magnet (dashpot), or gravity.

• Induction Cup Relay:

  • Construction: Stationary electromagnets induce currents in a hollow cylindrical cup (instead of disc). Lighter, less inertia.

  • Operation: Similar torque principle, faster, more sensitive.

  • Reset-to-Pickup Ratio: 0.9 - 0.95 (better than disc's ~0.85). Excellent for differential protection.

2.3 Static Relays

• Advantages: No moving parts, fast, multiple characteristics, low burden.

• Functional Building Blocks:

  • Level Detector: Outputs "1" if input > set value. (Functional diagram: Comparator + Filter + Output driver).

  • Comparator: Compares two inputs (amplitude or phase).

    Conversion: Phase comparator can be made from two amplitude comparators using a 90° phase-shift network.

2.4 Relay Characteristics & Plots

• Overcurrent Relays:

  • Definite Time (DT): Fixed time after pickup.

  • Inverse Definite Minimum Time (IDMT): Time inversely proportional to fault current.

  • Standard Curves: Standard Inverse (SI), Very Inverse (VI), Extremely Inverse (EI).

  • Operating Time Formula (IEC Standard):

$$ t = \frac{\beta}{(PSM)^\alpha - 1} + \gamma \quad \text{(where PSM = } \frac{I_f}{I_{pick-up}} \text{)} $$

    For **Standard Inverse**: $$\displaystyle \alpha=0.02 $$, $$\displaystyle \beta=0.14 $$, $$\displaystyle \gamma=0 $$ (or use tables).

*   **Problem Solving:** $$\displaystyle t = TMS \times t_{curve} $$ (from standard time dial curve at given PSM).

• Directional Relay (R-X Plane):

  • Principle: Operates only for power flow in one direction (e.g., into bus).

  • Characteristic: Offset circle (diameter not through origin) or directional circle (semi-circle). Maximum torque angle $$\displaystyle \theta_m $$ (usually $$\displaystyle 30^\circ $$ or $$\displaystyle 45^\circ $$ lead of $V$).

• Distance / Impedance Relays:

  • Impedance Relay (MHO Relay): Voltage/Current comparison. Characteristic: Circle passing through origin on R-X plane. $$\displaystyle |Z| < Z_{set} $$ operates.

  • Offset MHO Relay: Circle offset from origin. Used for reach adjustment (e.g., to avoid load encroachment). Applied in Zone 2/3 of distance protection.

2.5 Microprocessor-Based / Numerical Relays

• Block Schematic:

  Analog Inputs (CT/VT) → Anti-aliasing Filter → A/D Converter → CPU (DSP) → Output (Trip/Close) → Communication Port

• Advantages: Multiple functions in one unit, adaptive settings, self-monitoring, fault recording, communication (IEC 61850), digital filtering.

3.0 PROTECTION SCHEMES FOR POWER SYSTEM EQUIPMENT

3.1 Transformer Protection

• External Faults: Overcurrent (primary/secondary side), Buchholz (for through-faults).

• Internal Faults:

  • Differential Protection (Merz-Price):

    • Principle: Compare $$\displaystyle I_{in} $$ and $$\displaystyle I_{out} $$. Under normal/through-fault, $$\displaystyle I_1 = I_2 $$. Internal fault: $$\displaystyle I_1 \neq I_2 \rightarrow $$ operate.

    • Star-Delta CT Connection: HV side (Wye) CTs in Delta, LV side (Delta) CTs in Wye to compensate for 30° phase shift of transformer.

    • CT Ratio Selection (Star-Delta):

$$ \frac{CT_{ratio, HV}}{CT_{ratio, LV}} = \frac{\sqrt{3} \times V_{HV}}{V_{LV}} \times \frac{I_{LV}}{I_{HV}} $$

        (Where $$\displaystyle V_{HV}, V_{LV} $$ are line voltages).

    *   **Percentage Differential with Bias Slope:** `(I1 - I2)` vs `(I1 + I2)/2` plot. **Slope** set to allow for CT errors & inrush during external faults.

    *   **Inrush Current:** Differentials **5-10×** rated current, **contains 2nd harmonic** → **harmonic restraint** used to block relay.

*   **Buchholz Relay:**

    *   **Construction:** Gas-filled dome on transformer pipe, with two floats.

    *   **Operation:**

        1.  **Gas Accumulation (minor fault):** Gas bubbles rise → lower float drops → **alarm**.

        2.  **Oil Surge (major fault):** Oil rushes towards conservator → upper float closes → **trip**.

    *   **Application:** **Oil-immersed transformers** only. Protects tank faults (inter-turn, core).

3.2 Alternator / Generator Protection

• Stator: Percentage Differential (same as transformer, but CTs on all three phases).

• Rotor: Loss of Excitation (impedance relay), Field Suppression (discharge field via resistor).

• Other: Reverse Power (turbine motoring), Over/Under Frequency, Overvoltage, Stator Earth Fault (via VT secondary).

3.3 Busbar Protection

• Requirements: High speed, absolute selectivity.

• Schemes:

  • Differential (High-Impedance): All busbar CTs in parallel, with high series impedance & stabilizing resistor. Requires identical CTs & short, low-impedance leads. Fast, but sensitive to CT saturation during external faults.

  • Frame Leakage: CT surrounds the busbar frame/duct. Current flows in CT only during internal bus fault (when fault current returns via earth). Simple, used in metal-clad switchgear.

3.4 Transmission Line Protection

• Protection Zones: Primary (100% line), Backup (remote/near, 100%+ next line).

• Pilot Protection Schemes: Use communication channel (pilot) for simultaneous tripping at both ends.

  • Power Line Carrier Current (PLCC):

    • Implementation: HF signal (30-500 kHz) coupled to line via coupling capacitor & line trap.

    • Merits: Uses existing line, fast.

    • Demerits: Affected by line attenuation, switching transients, needs tuning.

  • Phase Comparison: Compares phase angles of currents at both ends. Operates if phase difference > 30° (internal fault).

• Distance Protection: Primary/backup using MHO (Zone 1) & Offset MHO (Zone 2/3) relays. Three-zone scheme common.

• Auto-reclosing: Purpose: Restore supply after transient faults (80% of faults). Types: Single-pole (for single line-ground) or three-pole.

4.0 CIRCUIT BREAKERS: THEORY, TYPES & SELECTION

4.1 Arc Phenomena & Interruption Theory

• Arc Formation: Ionization of contact gap by high temperature (~10,000 K) from initial contact separation.

• Arc Quenching Methods:

  • Oil: Decompose to gas (H₂) for cooling & blast.

  • Air Blast: High-pressure air cools & sweeps arc.

  • SF₆: Excellent dielectric & arc-quenching (electronegative gas).

  • Vacuum: High dielectric strength, arc extinguishes at current zero (no thermal ionization).

• Theory of Current Interruption: Energy Balance Concept. At current zero, arc energy input (from arc column) must be less than energy removed (by cooling/expansion) for successful interruption.

• Recovery Voltage: System voltage that appears across CB contacts after arc extinction. Rate of Rise of Recovery Voltage (RRRV) critical for success.

• Restriking Voltage: Transient voltage across contacts during de-ionization. Amplitude & frequency depend on system L/C.

4.2 Circuit Breaker Ratings & Selection

• Breaking Capacity: RMS value of symmetrical current it can break at rated voltage. Often expressed in MVA.

  • Asymmetrical Breaking Capacity: Must handle DC offset (first half-cycle). Related to X/R ratio.

• Making Capacity: Peak current it can close onto a fault (1.8× symmetrical breaking current for CBs).

• Selection Factors: Rated voltage/current, fault level at point, duty cycle (O-0.3s-CO-3min-CO), location (indoor/outdoor), reliability, cost.

• Testing: Type tests (design), routine tests (each unit), commissioning tests.

4.3 Types of Circuit Breakers

• Explosion Pot (in OCB): Bush-type (solid walls, gas pressure builds) & Cross-jet (arc drawn across jets). Function: contain & cool the arc gases.

5.0 SUPPORTING DEVICES & ADVANCED CONCEPTS

5.1 Current Limiting Reactors

• Need: Limit fault current to within CB breaking capacity during faults (e.g., when system expanded).

• Types: Air-core (no saturation, linear), Iron-core (smaller size, may saturate), Oil-immersed.

• Location: Busbar reactors (between bus sections) or feeder reactors (in series with feeder).

5.2 Fuses

• HRC (High Rupturing Capacity) Fuse:

  • Construction: Cercelain body, silver wire element, quartz sand filling.

  • Operation: Element melts (I²t characteristic), sand quenches arc by cooling & chemical reaction.

  • Application: LT switchgear, transformer protection, motor protection.

5.3 Buchholz Relay (See 3.1)

5.4 Security, Reliability & Software

• Security: No unwanted trip during normal operation/load. Ensured by: proper setting, CT saturation detection, harmonic restraint, logic blocking.

• Reliability: Trip when required. Ensured by: redundancy (dual systems), self-supervision (watchdog, hardware/software checks), regular testing.

• Software Development for Protection:

  • Role: Configuration (IED settings), coordination studies (TMS calculation), security management (password, access levels), event analysis (COMTRADE files).

  • Tools: PSCAD/EMTDC for simulation, DIGSI/Siemens, CSC/ABB configuration software.

6.0 KEY FORMULAS & NUMERICALS (Quick Reference)

1. IDMT Relay Operating Time:

$$ t = TMS \times \frac{0.14}{(PSM)^{0.02} - 1} \quad \text{(Standard Inverse)} $$

where $$\displaystyle PSM = \frac{\text{Fault Current}}{\text{Relay Pick-up Current}} $$.

2. CT Ratio for Star-Delta Transformer Differential:

$$ \frac{CT_{HV}}{CT_{LV}} = \frac{\sqrt{3} \times V_{HV}}{V_{LV}} $$

3. Percentage Differential Relay Check:

   • Bias Slope = $$\displaystyle \frac{I_{operate}}{I_{restrain}} \times 100\% $$

   • Will it trip? If $$\displaystyle (I_1 - I_2) > \text{Slope} \times \frac{(I_1 + I_2)}{2} $$.

4. Per-Unit Conversion:

$$ Z_{pu(new)} = Z_{pu(old)} \times \frac{(MVA_{new}/MVA_{old})}{(kV_{new}/kV_{old})^2} $$

5. Fault Current from Symmetrical Components:

   • LG: $$\displaystyle I_f = \frac{3E_a}{Z_1+Z_2+Z_0} $$

   • LLL: $$\displaystyle I_f = \frac{E_a}{Z_1} $$

Exam Tip: Always draw sequence network diagrams for unsymmetrical faults. For transformer differential, explicitly state HV CT in Delta, LV CT in Star. For IDMT problems, compute PSM first using CT ratio. For MHO relay, remember characteristic is a circle through origin; Offset MHO is shifted for Zone 2/3.