Explain what happens if r was chosen to be linear use the

Question

Marking scheme

The student should provide some explanation of how he/she arrives at an answer. This explanation can be in the form of an equation that the student states or it could be in the form of a brief description of his/her reasoning

For each part of a question:

The student will score full marks if he/she gives the right answer together with correct explanation (or equation).

For each part the student can lose up to 35% of the marks if the answer is right, but no explanation is given or the explanation is inadequate.

For each part the student will be able to score up to 80% of the marks if the answer is wrong but the explanation is correct cc partly correct.

Question 1

Refer to the above one-line diagram

V1 =bus 1 nominal operating voltage

V2 = bus 2 nominal operating voltage

Z+ = positive sequence reactance of transmission line Z

Z⁰= zero reactance of transmission line

Z1+ = positive sequence reactance of transformer T1

Z2+ = positive sequence reactance of transformer T2

R1 = neutral earthing resistor of transformer T1

R2 = neutral earthing resistor of transformer T2

R_f = fault resistance

(values for the above will be provided via the StudyDesk)

a. For a bolted balanced three-phase fault at location C, calculate the magnitude and phase of the transmission line currents flowing away from bus B and line currents flowing towards the transformer for both transformers. Use the given line to neutral voltage at bus I as the reference

b. For single phase fault at location C, calculate the magnitude and phase of the transmission line currents flowing away from bus B and line currents flowing towards the transformer for both transformer. Use the given line to neutral voltage at bus I as the reference. Assume phase 'a' is faulted fault resistance is Re

c For phase to phase fault at location C, calculate the magnitude and phase of the transmission line currents flowing away from bus B and line currents flowing towards the transformer for both transformers Use the given line to neutral voltage at bus 1 as the reference. Assume phases 'b' and 'c' are faulted and fault resistance is zero.

d. For phase to phase to ground fault at location C, calculate the magnitude and phase of the transmission line currents flowing away from bus B and line currents flowing towards the transformer for both transformers Use the given line to neutral voltage at bus 1 as the reference. Assume phases 'b' and ' c' are faulted and fault resistance is zero.

Question 2

Refer to the above diagram. The three CTs and resistance R represent a high impedance protection system for the the bus.

i_t =current in line 1 flowing towards the bus

i₂ =current in line 2 flowing towards the bus

i₃ =current in line 3 flowing towards the bus

R₁ = CT secondary winding resistance of CT1

R₂ = CT secondary winding resistance of CT2

R₃ = CT secondary winding resistance of CT3

R = equivalent resistance of overvoltage relay branch

Expressions for currents it, i2, and i3 and values for the resistance will be given via the StudyDeslc Piecewise linear magnetising curves for the CTs and the piecewise linear voltage-current characteristic of resistance R will also be provided.

a. Prove that even in the presence of CT saturation of one of the relays, the protection system is secure against a through fault. Use the given values of resistances, line currents under the close-in through fault, CT ratios and relay setting

b. Explain what happens if R was chosen to be linear? Use the given values of resistances, line currents under the bus fault, CT ratios and relay setting.

c. Explain what happens if, during normal operation (that is if there are no primary side faults), the secondary terminals of one of the CTs are shorted. Use the given values of resistance; line currents at maximum demand, CT ratios and relay setting.