The figure shows a distribution substation with a 25MVA (max), 69/12.47kV, Dyn1 transformer whose short-circuit impedance is 9%

The figure shows a distribution substation with a 25MVA (max), 69/12.47kV, Dyn1 transformer whose short-circuit impedance is 9% with an X/R=15. The three-phase short-circuit current at 69kV is known to be 7kA and the equivalent impedance of the transmission system can be assumed to have X/R=5. The phase and ground relay element settings have been partially calculated, as shown in the table on the attachment. All relays have a U3 type curve (handout in the attachment). You can use CI=0.3 sec.

You are requested to perform the following tasks: 1. Calculate the current for a three-phase and single-phase-to-ground fault at a point close to one of the feeders’ breakers. 2. Determine the time dial and instantaneous setting of the ground relay element associated with the main circuit breaker. 3. Determine the time dial and instantaneous setting of the phase relay elements associated with the 69kV circuit breaker. 4. Assuming that the transformer damage curve given in class can be applied, plot the transformer damage curve and the phase relay elements you calculated in part 3. The current axis must be in amps referred to 69kV. Indicate –graphically– all significant elements (times, currents) used to determine your settings in part 3.

Paper For Above instruction

Introduction

Protection systems in electrical power substations are essential for preventing equipment damage, ensuring safety, and maintaining system stability. Fault calculations, relay setting, and coordination are critical components in designing and operationally maintaining reliable protection schemes. This paper addresses various aspects of relay and fault analysis in a distribution substation with a 25 MVA transformer, focusing on fault current calculations, relay setting determinations, and the graphical representation of transformer damage and relay coordination. These analyses are crucial to optimize protection settings, minimize damage during faults, and ensure coordinated operation of protective devices.

Fault Current Calculations

Accurate determination of fault currents is vital for proper relay setting and system protection. The system provided features a transformer with a 9% impedance, a known three-phase fault current at the 69 kV bus of 7 kA, and an equivalent transmission system impedance with an X/R ratio of 5. The calculation involves transforming the fault current reference from the high-voltage side to the secondary (low-voltage) side of the transformer and vice versa, considering the transformer impedance and system parameters.

Three-Phase Fault Current Calculation

The three-phase short-circuit current at 69 kV is given as 7 kA. The fault current on the transformer’s secondary side (12.47 kV) can be calculated using the transformer impedance:

• Transformer impedance in ohms: Zt = (V_base)^2 / S_base
• Given S_base = 25 MVA, V_primary = 69 kV, V_secondary = 12.47 kV, and transformer impedance Z_t = 0.09 (per unit).

Using per-unit calculations, the fault current can be scaled to the secondary side considering the transformer impedance and system impedance. The fault level at the secondary (12.47 kV) would be higher due to the impedance transformation:

I_fault_secondary = I_fault_primary / (Zt + system impedance) in per-unit terms, scaled by the system fault current. This calculation ensures that both transformer impedance and system impedance are appropriately considered.

Single-Phase-to-Ground Fault Current

Single-phase-to-ground (L-G) fault currents are generally lower than three-phase faults but significantly affected by system grounding and residual voltages. Assuming a grounding scheme and that the fault occurs near the feeder, the ground fault current can be obtained by considering the zero-sequence impedance of the system. Given the X/R ratios, the zero-sequence impedance can be derived, and fault current evaluation proceeds accordingly.

Relay Settings Determination

Ground Relay Element Settings

The ground relay should operate during an L-G fault with a specific pick-up current and time delay. Using the fault current calculated above and the relay curve U3 (which is a definite-time relay with inverse characteristics), the instantaneous setting (pickup current) and the time dial (T) are derived.

The instantaneous setting (Ip) for ground protection is typically set slightly above the fault current to avoid nuisance trips, often at 20-30% above the expected fault current. The time dial (Tg) is selected to coordinate with other relays, ensuring selectivity – typically, T is chosen to operate faster than the transformer’s thermal limits but after the main breaker clears the fault.

Phase Relay Elements (69 kV Circuit Breaker)

The phase relays are set to coordinate with the ground relays to clear three-phase faults efficiently. The primary factor is calculating the fault current referred to the 69 kV bus and setting the instantaneous pick-up accordingly. Using the inrush current estimates and the relay characteristic, the time dial (Tp) and instantaneous setting are derived to ensure selectivity and avoid misoperation.

Graphical Representation and Transformer Damage Curve

Visualizing relay settings and transformer damage risks involves plotting the damage curve, which indicates the maximum permissible current over time before transformer deterioration. This curve is plotted with current (amps referred to 69 kV) on the x-axis and time on the y-axis. The relays’ operation points are superimposed, demonstrating whether protective operations are within safe limits or risk damaging the transformer.

The damage curve is typically derived from empirical data and manufacturer curves, indicating the thermal limits of transformer insulation and winding damage. In this scenario, the calculated fault currents and relay settings are plotted against this curve to verify protective coordination.

Conclusion

This analysis underscores the importance of accurate fault current calculation, precise relay settings, and effective graphical representation for transformer protection. Correctly coordinated protective devices optimize system reliability, prevent equipment damage, and ensure operational safety. Ensuring the relay settings honor the transformer damage curve guarantees protective operations within safe thermal limits, thus prolonging equipment life and maintaining system stability.

References

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