UNIT 5: Power System Protection - Exam-Focused Short Notes

I. FAULT ANALYSIS & SYMMETRICAL COMPONENTS

Types of Faults & Characteristics

• Symmetrical (Balanced) Fault: Three-phase short circuit (L-L-L). System remains balanced; analyzed using only positive sequence network.

• Unsymmetrical (Unbalanced) Faults:

  • Single Line-to-Ground (L-G): Most common (~70%). Requires all three sequence networks in series.

  • Line-to-Line (L-L): No ground involvement. Positive & negative sequence networks in parallel.

  • Double Line-to-Ground (L-L-G): All three sequence networks in parallel.

  • Causes: Insulation failure, weather, human error, equipment damage.

  • Effect: System unbalance, voltage collapse, stability threat, high mechanical stress.

Fault Current Calculation (Generator Terminal)

For an unloaded generator with solidly grounded neutral:

1. L-G Fault:

$$I_f = \frac{3E}{X_1 + X_2 + X_0}$$

> [!TIP] **Key Point:** Zero sequence path exists only if neutral is grounded.

2. L-L-G Fault:

$$I_f = \frac{\sqrt{3}E}{X_1 + \frac{X_2 X_0}{X_2 + X_0}}$$

3. L-L Fault:

$$I_f = \frac{\sqrt{3}E}{X_1 + X_2}$$

4. L-L-L Fault:

$$I_f = \frac{E}{X_1}$$

Fault Level / Fault MVA:

$$\text{Fault MVA} = \sqrt{3} \times V_{\text{base}} \times I_{\text{fault}}$$

. It's the maximum short-circuit power a breaker must interrupt at a point.

Symmetrical Components Theory

• Purpose: Decouple unbalanced 3-phase system into three balanced 3-phase systems (Positive, Negative, Zero Sequence).

• Sequence Networks: Equivalent impedance diagrams for each sequence.

  • Positive Sequence: Normal rotation (A-B-C). All generators have synchronous (Xd), transient (X'd), sub-transient (X"d) reactances.

  • Negative Sequence: Reverse rotation (A-C-B). Reactance ≈ X"d for generators; for transformers, same as positive sequence but phase-shifted.

  • Zero Sequence: All phases in phase (A+A+A). Path requires grounded neutral. For transformers: zero seq. impedance depends on winding connection (star/delta) and grounding.

Per-Unit System & Reactances

• Convert all impedances to common base MVA & base kV.

$$Z_{\text{p.u.}}^{\text{new}} = Z_{\text{p.u.}}^{\text{old}} \times \frac{(\text{MVA}_{\text{base}}^{\text{new}} / \text{MVA}_{\text{base}}^{\text{old}})}{(kV_{\text{base}}^{\text{new}} / kV_{\text{base}}^{\text{old}})^2}$$

• Reactance Significance:

  • X"d (Sub-transient): Fault current initial value (first 1-2 cycles). Used for protection sizing.

  • X'd (Transient): Fault current after sub-transient decay (up to ~0.5 sec). Used for stability studies.

  • Xd (Synchronous): Steady-state fault current. Rarely used for protection.

  • X2 (Negative): ≈ X"d for generators.

  • X0 (Zero): Often < X1 for generators with grounded neutral; critical for L-G fault magnitude.

II. PROTECTIVE RELAYS: TYPES, PRINCIPLES & CHARACTERISTICS

Fundamental Relay Operating Principles

• Electromagnetic Attraction Type: AC/DC. Plunger attracted to solenoid. Used for overcurrent, under-voltage.

• Induction Type Relays (AC only):

  • Induction Disc Relay:

    • Construction: Aluminum disc in magnetic field from two electromagnets (fluxes 90° apart).

    • Torque Equation: $$\displaystyle T = K \phi_1 \phi_2 \sin \theta $$. Disc rotates until spring torque balances.

    • Application: Overcurrent, directional, distance relays.

    • Minimize Overrun: Use brake magnet (permanent magnet) to create retarding torque proportional to speed.

  • Induction Cup Relay:

    • Construction: Hollow cylindrical cup (Al/Cu) instead of disc. Faster, more sensitive.

    • Reset-to-Pickup Ratio: Very high (0.9-0.95). Disc relay: low (~0.85). Cup relay preferred for differential protection where high reset ratio prevents unwanted operation on through-fault CT saturation.

Relay Characteristics & Plots (R-X Plane)

Distance Relay Zones:

• Zone 1: 80-90% of line length. Instantaneous.

• Zone 2: 100-120% of line + next line's 50%. Time-delayed.

• Zone 3: 100-120% of line + next line + backup. Longest time delay.

Time-Current Characteristics: IDMT

• Principle: Operating time inversely proportional to fault current magnitude.

• Standard Equation (IEC):

$$t = \frac{\text{TMS} \times \beta}{(I_f / I_{\text{ps}})^\alpha - 1}$$

Where:

*   $$\displaystyle I_f $$ = Fault current

*   $$\displaystyle I_{\text{ps}} = (\text{Plug Setting}) \times \text{Relay Rated Current} $$

*   TMS = Time Multiplier Setting (0.1 to 1.0)

*   $\alpha, \beta$ = Standard constants (for normal inverse: $$\displaystyle \alpha=0.02, \beta=0.14 $$; very inverse: $$\displaystyle \alpha=1, \beta=13.5 $$; extremely inverse: $$\displaystyle \alpha=2, \beta=80 $$)

IDMT Calculation Steps:

1. Find $$\displaystyle I_{\text{ps}} $$ from plug setting % and relay CT primary rating.

2. Compute $$\displaystyle (I_f / I_{\text{ps}}) $$.

3. Use standard TMS curve equation or graph to find $t$.

Static & Numerical Relays

• Static Relays (Electronic):

  • Advantages: No moving parts, fast, adjustable characteristics, low burden, can implement complex logic.

  • Functional Blocks:

    • Level Detector: Outputs 1 if input > set value. Functional Diagram: Comparator + hysteresis ( Schmitt Trigger).

    • Comparator: Compares two inputs.

      • Amplitude Comparator: $$\displaystyle |A| > |B| $$? Output = 1.

      • Phase Comparator: $$\displaystyle \angle A - \angle B < \theta $$? Output = 1.

      • Conversion: Use quadrature transformer to convert phase comparison to amplitude comparison (and vice versa).

• Microprocessor-Based / Numerical Relays:

  • Block Schematic:

    Analog Inputs → Filter & Anti-alias → ADC (Sampling) → CPU (DSP) → Output Logic → Trip Signal

  • Functions: All EM relay functions + fault location, communication, self-monitoring, event recording.

  • Software Development: Follows IEC 61850 standards for interoperability, security (cyber), and reliability (redundancy, watchdogs).

III. PROTECTION SCHEMES FOR POWER SYSTEM ELEMENTS

Generator / Alternator Protection

• Percentage Differential Protection (Stator):

  • Slope: 15-30%. Higher slope for larger generators.

  • Operation: $$\displaystyle I_{\text{operating}} = |I_1 - I_2| $$, $$\displaystyle I_{\text{restraint}} = \frac{|I_1|+|I_2|}{2} $$. Trip if $$\displaystyle I_{\text{op}} > \text{Slope} \times I_{\text{res}} + I_{\text{min}} $$.

  Problem: Given CT currents, slope, and $$\displaystyle I_{\text{min}} $$, decide trip.

• Buchholz Relay:

  • Location: In conservator pipe between tank & conservator.

  • Operation:

    1. Incipient Fault: Gas bubbles rise → float lowers → alarm contact.

    2. Severe Fault: Oil surge → baffle plate deflects → trip contact.

  • Detects: Turn-to-turn faults, core hot spots, oil level fall.

Transformer Protection

• Merz-Price (Percentage Differential) for Transformer:

  • Challenge: Star-Delta connection causes phase shift & CT ratio mismatch.

  • Solution: Choose CT ratios so that secondary currents are equal in magnitude and phase under normal conditions.

  • CT Ratio Calculation (Star-Delta):

$$\text{CT Ratio}_{\text{Star}} = \frac{\text{Transformer kV}_{\text{Star}}}{\text{Base kV}} \times \frac{\text{Transformer MVA}}{\text{Base MVA}} \times \frac{\text{CT secondary}}{\text{Relay CT rating}}$$

$$\text{CT Ratio}_{\text{Delta}} = \frac{\text{Transformer kV}_{\text{Delta}}}{\text{Base kV}} \times \frac{\text{Transformer MVA}}{\text{Base MVA}} \times \frac{\sqrt{3} \times \text{CT secondary}}{\text{Relay CT rating}}$$

    > **Key:** Delta side CTs are connected in **star** (or vice versa) to compensate for vector group.

• Other Protections:

  • Restricted Earth Fault (REF): Sensitive ground fault protection for transformer neutral zone.

  • Buchholz: For oil-filled transformers.

  • Overcurrent/Overfluxing: External backup.

Transmission Line Protection

• Distance Protection: Primary. Uses impedance relays. Three zones with time-graded coordination.

• Pilot Protection Schemes: Fast, selective for entire line length. Requires communication channel (pilot).

  • Power Line Carrier (PLC):

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

    • Voltage Range: Typically 33 kV to 220 kV.

    • Merits: No separate wire, uses existing line.

    • Demerits: Attenuation, noise, requires line filters, not for EHV (>400 kV).

    • Phase Comparison Scheme: Compare phase angles of currents at both ends. Trip if both ends see fault (internal). Block if only one end sees fault (external).

Busbar Protection

• Differential Protection: All incoming/outgoing CTs sum to zero under normal/external fault. Any imbalance → trip. Requires CTs with same ratio & characteristic.

• Frame Leakage Protection:

  • Principle: CT surrounds busbar support frame. Under bus fault, current flows through frame to ground → operates relay.

  • Application: Simple, used for small, important busbars.

Current Limiting Reactors

• Purpose: Limit fault current magnitude to within breaker capacity during faults.

• Types: Air-core (dry, no saturation) or iron-core.

• Application: Connected in series with generators, feeders, or bus sections.

• Location: Often in generator leads to limit fault current from that generator.

IV. CIRCUIT BREAKERS: THEORY, TYPES & SELECTION

Arc Phenomenon & Interruption Theory

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

• Arc Quenching: Critical for interruption. Methods: High pressure, cooling, lengthening, dielectric strength increase.

• Theory of Current Interruption (Energy Balance):

  • Before Current Zero: Power input from source = Power loss in arc ($$\displaystyle I^2R $$) + Rate of energy storage in arc ($dW/dt$).

  • At Current Zero: $dW/dt$ must be negative (arc loses energy) for thermal reignition to be avoided.

  • After Current Zero: Dielectric strength of medium must rise faster than recovery voltage across contacts.

• Recovery Voltage vs. Restriking Voltage:

  • Restriking Voltage: Transient voltage appearing across contacts immediately after current zero. High-frequency oscillation. Dangerous (can cause re-ignition).

  • Recovery Voltage: Steady-state voltage across CB after transient dies down. Must be withstood by CB.

Circuit Breaker Ratings & Selection

• Breaking Capacity: Max symmetrical RMS current it can interrupt at rated voltage. Based on first-cycle (sub-transient) fault current.

$$\text{Breaking Capacity (MVA)} = \sqrt{3} \times V_{\text{rated}} \times I_{\text{breaking}}$$

> Must be > **maximum fault level** at installation point.

• Making Capacity: Max peak current it can close onto a 3-phase bolted fault. Higher than breaking capacity (includes DC component).

$$\text{Making Capacity (kA peak)} = \sqrt{2} \times [1 + e^{-t/\tau}] \times I_{\text{sym}}$$

Where $t$ = closing time, $\tau$ = time constant of circuit.

• Selection Criteria: Rated voltage/current, fault level, duty (number of operations), application (transmission, distribution, industrial), environment.

Types of Circuit Breakers & Comparison

Explosion Pot (Oil CB):

• Plain/Cross-jet: Simple, limited breaking capacity.

• Self-Blast: Uses arc energy to generate pressure. More efficient.

• Oil Turbine: Uses mechanical turbine to blast oil.

V. ADVANCED & MISCELLANEOUS TOPICS

Security & Reliability in Protection Systems

• Security: No tripping for non-faults (dependability inverse). Ensured by:

  • Redundancy (dual systems, voting logic).

  • Supervision (watchdog timers, self-checks).

  • Proper coordination (settings, zones).

• Reliability: Tripping for all faults (security inverse). Ensured by:

  • Diversity (different operating principles).

  • High-quality components (CTs, relays).

  • Regular testing & maintenance.

Specific Relay Applications Summary

Integrated System Concepts

• Role of Protection: First line of defense for system stability. Must be fast, selective, reliable.

• Software Development for Protection:

  • Lifecycle: Requirements → Design → Coding (IEC 61131-3/61850) → Testing (hardware-in-loop) → Validation → Maintenance.

  • Security: Cyber-security protocols, secure communication (IEC 62351).

  • Reliability: Redundant processors, watchdog timers, fail-safe design.

Logic Circuits in Relays: Improve functions by implementing timers, latches, voting (2-out-of-3), blocking signals to enhance security and selectivity.

END OF UNIT 5 NOTES