Power System Protection (EX-701) - Unit 3 Short Notes

UNIT 3: POWER SYSTEM PROTECTION

I. FUNDAMENTALS OF FAULT ANALYSIS & SYMMETRICAL COMPONENTS

1. Types of Power System Faults

• Symmetrical (Balanced) Fault: Only Three-Phase Fault (LLL). All three phases short-circuited. System remains balanced. Least frequent but most severe.

• Unsymmetrical (Unbalanced) Faults:

  • Single Line-to-Ground (LG): One phase to neutral/ground. Most common (~70%).

  • Line-to-Line (LL): Two phases short-circuited.

  • Double Line-to-Ground (DLG): Two phases to ground.

• Causes: Insulation failure, lightning, wind, ice, human error, equipment failure.

• Effects: Large fault currents, voltage dip, instability, equipment damage, fire hazard.

2. Concept of Symmetrical Components

• Significance: Simplifies analysis of unbalanced 3-phase systems by resolving unbalanced phasors into three balanced sets:

  1. Positive Sequence: A₁, a²A₁, aA₁ (balanced, phase sequence A-B-C).

  2. Negative Sequence: A₂, a²A₂, aA₂ (balanced, phase sequence A-C-B).

  3. Zero Sequence: A₀, A₀, A₀ (all in phase, no phase displacement).

• Operator 'a': $$\displaystyle a = 1 \angle 120^\circ = -\frac{1}{2} + j\frac{\sqrt{3}}{2} $$, $$\displaystyle a^2 = 1 \angle -120^\circ $$, $$\displaystyle a^3 = 1 $$, $$\displaystyle 1 + a + a^2 = 0 $$.

• Transformation Matrix:

$$\begin{bmatrix} A_0 \\ A_1 \\ A_2 \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \\ 1 & a & a^2 \\ 1 & a^2 & a \end{bmatrix} \begin{bmatrix} A_a \\ A_b \\ A_c \end{bmatrix}$$

Inverse transformation is similar with matrix transpose (since matrix is symmetric).

3. Sequence Network Representation

• Positive Sequence Network: Similar to steady-state equivalent, EMF = $$\displaystyle E_a $$ (pre-fault voltage), impedance = $$\displaystyle Z_1 $$ (sub-transient/transient reactance for generators).

• Negative Sequence Network: No EMF source, impedance = $$\displaystyle Z_2 $$ (usually ≈ $$\displaystyle Z_1 $$ for syn. machines).

• Zero Sequence Network: No EMF source, impedance = $$\displaystyle Z_0 $$. Path depends on grounding (e.g., solidly grounded gen: $$\displaystyle Z_0 $$ in series with neutral impedance $$\displaystyle Z_n $$).

• Interconnection for Faults at Generator Terminals (Unloaded):

  | Fault Type | Sequence Network Connection | Fault Current Expression (Phase 'a') | |-----------------|-----------------------------------|-------------------------------------| | Three-Phase (LLL) | Only Positive Sequence | $$\displaystyle I_{f,a} = \frac{E_a}{Z_1} $$ | | Single LG | All 3 sequences in parallel | $$\displaystyle I_{f,a} = 3I_0 = \frac{3E_a}{Z_1+Z_2+Z_0} $$ | | Line-to-Line (LL) | Positive & Negative in parallel, Zero open | $$\displaystyle I_{f,a} = -I_{f,b} = \frac{\sqrt{3}E_a}{Z_1+Z_2} $$ | | Double LG (DLG) | Positive & Negative in parallel, this combo in series with Zero | $$\displaystyle I_{f,a} = \frac{3E_a}{Z_1 + \frac{Z_2Z_0}{Z_2+Z_0}} $$ |

4. Fault Current & Voltage Calculations

• Key Formulas (Terminal Fault, Unloaded Gen):

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

  • DLG Fault Current: $$\displaystyle I_{DLG} = \frac{\sqrt{3}E_a}{Z_1 + \frac{Z_2Z_0}{Z_2+Z_0}} $$

  • LLL Fault Current: $$\displaystyle I_{LLL} = \frac{E_a}{Z_1} $$

• Fault Level / Fault MVA: $$\displaystyle S_{fault} = \sqrt{3} V_{pre-fault} I_{fault} $$. Represents short-circuit MVA at the fault point.

• Effect of Fault Impedance (Z_f): Add $$\displaystyle Z_f $$ to the series combination of sequence networks in the fault path.

  • LG with Z_f: $$\displaystyle I_{f} = \frac{3E_a}{Z_1+Z_2+Z_0+3Z_f} $$

• Line-to-Line Voltages during Fault: Can be found using sequence voltages: $$\displaystyle V_a = V_0 + V_1 + V_2 $$, etc.

5. Per Unit System & Reactance Diagram

• Base Conversion: $$\displaystyle Z_{pu,new} = Z_{pu,old} \times \frac{(MVA_{new}/MVA_{old})}{(kV_{new}/kV_{old})^2} $$

• Procedure for Multi-Machine System:

  1. Choose a common system base (MVA, kV).

  2. Convert each generator's reactance to this base.

  3. Draw all reactances on a single line diagram referred to a common voltage level (using transformer turns ratios).

Example (Nov 2023): Three generators on a common bus. Convert each to 200 MVA, 35 kV base, then draw pu reactance diagram.

II. PROTECTIVE RELAYS: PRINCIPLES & CHARACTERISTICS

1. Relay Operating Principles

2. Relay Characteristics & Settings

• Time-Current Characteristics (IDMT):

$$t = \frac{TMS \times \beta}{(PSM^n - 1)}$$

Where:

*   $t$ = operating time (s)

*   $TMS$ = Time Multiplier Setting (0-1)

*   $PSM$ = Plug Setting Multiplier = $$\displaystyle \frac{\text{Fault Current}}{\text{Relay Rated Current} \times \text{Plug Setting}} $$

*   $\beta, n$ = constants depending on curve type:

    *   **Standard Inverse:** $$\displaystyle \beta=0.14 $$, $$\displaystyle n=0.02 $$

    *   **Very Inverse:** $$\displaystyle \beta=13.5 $$, $$\displaystyle n=1 $$

    *   **Extremely Inverse:** $$\displaystyle \beta=80 $$, $$\displaystyle n=2 $$

Exam Tip: Always compute PSM first. For DT relays, $$\displaystyle t = TMS \times \text{time dial setting} $$.

• R-X Diagram Representation:

  • Impedance Relay: Circular characteristic. Operates when $$\displaystyle Z = \frac{V}{I} < Z_{set} $$. Offset circles for directional or to avoid 3rd zone issues.

  • MHO Relay (Admittance): Directional. Circle passing through origin. Operates when $$\displaystyle |Y| > |Y_{set}| $$ or $$\displaystyle Z < Z_{set} \cos(\theta - \theta_{char}) $$. More stable for long lines.

  • OFF-SET MHO: Two circles. Inner (reach) for Zone 1, outer (offset) for Zone 2/3. Prevents tripping for load impedance.

  • Directional Relay: Semicircle in R-X plane (e.g., for power relay, operates when $$\displaystyle \cos\phi > \cos\theta_{setting} $$).

3. Static Relays

• Advantages: No moving parts, fast, accurate, multi-function, self-test, communication capable.

• Functional Blocks:

  • Level Detector: Outputs 1 if input > setting. (e.g., Schmitt trigger).

  • Comparator: Compares two inputs.

    • Amplitude Comparator: $$\displaystyle |A| > |B| $$? (e.g., for overcurrent).

    • Phase Comparator: $$\displaystyle \angle(A-B) < \delta $$? (e.g., for directional).

  • Logic Circuits: AND, OR, NOT to combine outputs (e.g., trip = overcurrent AND directional).

  • Timer: Provides time delay (RC or digital).

• Conversion: An amplitude comparator can be converted to phase comparator by passing one input through a 90° phase-shift network. Vice-versa using vector summation.

4. Microprocessor-Based / Numerical Relays

• Block Schematic:

  
  CT/VT → Analog Input (filter, attenuator) → Sampler → A/D Converter → CPU (DSP) → Output (trip, alarm, comm)
  
  

• Functions:

  • Protection: Implements all relay characteristics (IDMT, impedance, differential) via software.

  • Measurement: Records V, I, P, Q, frequency.

  • Monitoring: CT saturation, breaker status, health.

  • Communication: IEC 61850, SCADA integration.

• Software Development: Focus on security (avoid nuisance trips), reliability (fail-safe), speed (real-time), self-check.

Exam Tip: Logic circuits in numerical relays replace hardware comparators. E.g., IF (I > Iset) AND (dir = forward) THEN trip.

III. CIRCUIT BREAKERS: THEORY, TYPES & SELECTION

1. Arc Phenomenon & Interruption Theory

• Arc Formation: When contacts separate, ionization of medium creates low-resistance path.

• Arc Quenching: Must cool & de-ionize arc column rapidly to prevent re-strike.

• Recovery Voltage ($$\displaystyle v_r $$): System voltage across contacts after current zero. Transient Recovery Voltage (TRV): High-frequency oscillation superimposed on power-frequency recovery voltage. Critical for interruption.

• Restriking Voltage: Voltage across contacts during arcing. High di/dt causes high restriking voltage.

• Theory of Current Interruption: Energy Balance Concept – Arc extinguishes if rate of heat removal > rate of heat generation. At current zero, if dielectric strength of medium > recovery voltage, arc won't re-strike.

2. Types of Circuit Breakers

3. Ratings & Selection Criteria

• Breaking Capacity: Max rms symmetrical current it can break at rated voltage. Asymmetrical breaking current = $$\displaystyle \sqrt{2} \times I_{sym} \times (1 + e^{-t/\tau}) $$ (where τ = L/R time constant).

• Making Capacity: Max peak current it can close against (includes DC offset). Usually 1.8× symmetrical breaking current peak.

• Selection Factors: Rated voltage/current, breaking/making capacity, duty cycle (O-0.3s-CO-3min-CO), application (transmission vs. distribution), TRV withstand, environmental conditions.

• Testing: Type tests (thermal, dielectric, mechanical), routine tests.

IV. PROTECTION SCHEMES FOR POWER SYSTEM EQUIPMENT

1. Generator / Alternator Protection

• Faults:

  • Stator: Phase-phase, phase-ground (LG). Protected by % Differential.

  • Rotor: Field winding ground, loss of excitation. Protected by field ground relay, loss-of-excitation relay (impedance).

  • Abnormal: Overcurrent, overvoltage, negative seq. (overheating), overheating (RTD), out-of-step.

• Stator % Differential Protection:

  • Principle: Compare currents entering/leaving stator winding. $$\displaystyle I_{op} = |I_1 - I_2| $$, $$\displaystyle I_{rest} = |I_1 + I_2| $$. Trip if $$\displaystyle \frac{I_{op}}{I_{rest}} > \text{slope} $$.

  • Slope (bias): 15-30%. Prevents maloperation during through faults (CT mismatch, magnetizing current).

  • Numerical Check (Dec 2024): Slope = 15%. $$\displaystyle I_{CT1}=400A $$, $$\displaystyle I_{CT2}=320A $$. $$\displaystyle I_{op}=80A $$, $$\displaystyle I_{rest}=360A $$. Ratio = 22.2% > 15% → TRIP.

• Generator-Transformer Unit Protection: Treat gen + transformer as one unit. One differential relay covers both. CTs on gen neutral and transformer HV side.

• Buchholz Relay: Gas-actuated relay in transformer/generator oil conservator.

  • Incipient Faults: Minor overheating/arcing → gas bubbles → float operation → alarm.

  • Severe Faults: Oil surge → flap operation → trip.

2. Transformer Protection

• Internal vs. External: Differential for internal; overcurrent/backup for external.

• Merz-Price (Percentage Differential) for Star-Delta Transformer:

  • CT Ratio Selection: Must compensate for current magnitude (turns ratio) and phase shift (star-delta connection).

  • Formula: $$\displaystyle \frac{I_{HV}}{I_{LV}} = \frac{V_{LV}}{V_{HV}} \times \sqrt{3} $$ (due to delta-star).

  • CT Ratio Calculation (Dec 2025, Nov 2023):

    Given: Transformer 0.4/11 kV star-delta. LV CT ratio = 500/5. Find HV CT ratio.

$$I_{LV} = \frac{S}{\sqrt{3} \times 0.4}, \quad I_{HV} = \frac{S}{\sqrt{3} \times 11}$$

$$\frac{I_{HV}}{I_{LV}} = \frac{0.4}{11} = \frac{1}{27.5}$$

    LV CT secondary = 5A. For balance: HV CT secondary should also be 5A.

$$\text{HV CT ratio} = \frac{I_{HV}}{5} = \frac{I_{LV} / 27.5}{5} = \frac{500/5}{27.5} = \frac{100}{27.5} \approx 3.636$$

    So HV CT ratio ≈ **364/5 A** (or nearest standard).

• Other Protections:

  • Restricted Earth Fault (REF): Sensitive earth fault protection for star-connected winding with grounded neutral.

  • Overfluxing: $V/f$ relay for geomagnetic storms or overvoltage.

  • Temperature: Oil temperature, winding temperature (RTDs).

3. Busbar Protection

• Importance: Busbar fault → total station shutdown.

• Differential Protection:

  • Principle: Sum of currents entering bus = 0 under normal. Fault → differential current.

  • Challenges: CT saturation during through faults → false differential. Use high-ratio CTs, high-impedance scheme.

• Frame Leakage Protection:

  • Principle: Busbar enclosed in earthed metal frame. CT on frame earth connection. Fault → current flows through frame → earth CT operates.

  • Application: Simple, used for small substations.

• High-Impedance Differential: Series-connected high resistor stabilizes against CT saturation.

• Biased Differential: Similar to generator % diff, with slope to avoid through-fault maloperation.

4. Transmission Line Protection

• Protection Zones (Distance Relay):

  • Zone 1: 80-90% of line length. No time delay (instantaneous).

  • Zone 2: Covers full line + 50% of next line. Time delay (0.3-0.5s) to coordinate with next line's Zone 1.

  • Zone 3: Backup for next two lines. Longer delay.

• Distance Relays on R-X Diagram: Use impedance characteristics (MHO, offset MHO) to define zones as circles/quadrilaterals.

• Pilot Protection Schemes:

  • Concept: Pilot = communication channel between line ends for fast, selective tripping.

  • Types:

    | Pilot Type | Medium | Range | Merits | Demerits | |------------|--------|-------|--------|----------| | Wire Pilot | Twisted pair | < 40 km | Simple, cheap | Susceptible to induced voltages, maintenance | | Carrier Current (PLCP) | Power line itself (40-500 kHz) | Up to 400 km | No extra wires, uses existing line | Filtering needed, limited to one channel, prone to interference | | Microwave | Radio link | Long | High speed, independent | Expensive, line-of-sight | | Fiber Optic | Optical fiber | Very long | High bandwidth, immune to EMI | Cost, fragility |

  • Power Line Carrier Protection (PLCP): Voltage range: 66 kV and above. Merits: Fast (≤ 30 ms), selective. Demerits: Requires tuning, blocking during switching, limited to one signal per line.

  • Phase Comparison Scheme (Carrier): Compare phase angles of currents at both ends. If both ends see fault in same direction → trip. Blocking type (trip if no blocking signal) more common.

• Overcurrent Protection: For distribution lines (radial). Uses IDMT/DT relays with time-grading.

V. SPECIAL DEVICES & SYSTEM CONSIDERATIONS

1. Current-Limiting Reactors

• Types:

  • Air-Core: No iron, linear inductance. Used in series with generators/feeders to limit fault current.

  • Iron-Core: With iron core, saturates at high current → less effective limiting.

• Principle: Series reactance limits $$\displaystyle I_{fault} = \frac{E}{X} $$.

• Location: Generator terminal, feeder inlet, busbar sections.

• Application: Limit fault current to within breaker rating, protect equipment from mechanical/thermal stress.

2. Fuses

• HRC (High Rupturing Capacity) Fuse:

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

  • Working: Fault → element melts → arc in sand → sand quenches arc by cooling & high pressure.

  • Applications: LT switchgear, motor starters, transformers, capacitor banks. Replaceable element.

3. System Security & Reliability

• Security: Avoid unwanted trips (maloperation). Ensured by:

  • Redundancy (dual systems).

  • Diversity (different technologies).

  • High-quality CTs/VTs, proper settings.

  • Blocking logic (e.g., in pilot schemes).

• Reliability: Trip when required (correct operation). Ensured by:

  • Regular testing & maintenance.

  • Self-monitoring features in numerical relays.

  • Quality assurance in design/manufacture.

  • Adequate backup protection.

4. Protection of Specific Systems

• Motor Protection:

  • Faults: Overload, short-circuit (phase-phase, phase-ground), single phasing.

  • Schemes: Thermal overload relay (bimetal), instantaneous overcurrent for short-circuit, negative sequence relay for unbalanced supply, under-voltage.

• Feeder Protection: Overcurrent (radial), distance (transmission), pilot (important feeders).

KEY NUMERICAL PROBLEM AREAS - QUICK REFERENCE

1. Fault Current Calculation:

   • Use sequence network interconnection.

   • $$\displaystyle I_{LG} = \frac{3E_a}{Z_1+Z_2+Z_0} $$ (with $$\displaystyle Z_f $$: add $$\displaystyle 3Z_f $$).

   • $$\displaystyle E_a $$ usually = 1 pu pre-fault voltage.

2. CT Ratio for Transformer Differential (Star-Delta):

   • HV CT ratio = $$\displaystyle \frac{I_{HV}}{I_{sec}} $$; LV CT ratio = $$\displaystyle \frac{I_{LV}}{I_{sec}} $$.

   • $$\displaystyle \frac{I_{HV}}{I_{LV}} = \frac{V_{LV}}{V_{HV}} \times \sqrt{3} $$.

   • Set $$\displaystyle I_{sec} $$ same for both sides (usually 5A or 1A).

3. IDMT Relay Operating Time:

   • $$\displaystyle PSM = \frac{I_f}{I_{pickup}} $$, where $$\displaystyle I_{pickup} = \text{Relay rating} \times \text{Plug Setting} $$.

   • $$\displaystyle t = \frac{TMS \times \beta}{(PSM^n - 1)} $$ (use correct $\beta,n$ for curve).

4. % Differential Relay Stability Check:

   • $$\displaystyle I_{op} = |I_1 - I_2| $$, $$\displaystyle I_{rest} = |I_1 + I_2| $$.

   • Trip if $$\displaystyle \frac{I_{op}}{I_{rest}} \times 100\% > \text{slope}\% $$.

5. Per Unit Conversion (Multi-Machine):

   • $$\displaystyle Z_{pu,new} = Z_{pu,old} \times \frac{MVA_{new}}{MVA_{old}} \times \left( \frac{kV_{old}}{kV_{new}} \right)^2 $$.

   • Convert all to common base before drawing diagram.

6. Fault Level (MVA):

   • $$\displaystyle S_{fault} = \sqrt{3} \times V_{base} \times I_{fault} $$ (use base voltage and calculated fault current in pu or actual).

Final Exam Strategy: For derivation questions (e.g., DLG fault current), start with sequence networks, write KVL for each, solve for $$\displaystyle I_1 $$, then $$\displaystyle I_f $$. Always draw sequence network diagrams. For numerical problems, state assumptions (neglect resistance, unloaded system).