Q1. (a) Discuss briefly the factors that lead to high magnetizing inrush current in a transformer.

(b) Figure above shows a reactor being disconnected from its supply. During the process of opening, the circuit breaker S reignites, but interrupts the re-ignition current at the first zero of high frequency current, trapping the energy in L₂.

(i) Compute the peak voltage subsequently appearing across the reactor as a consequence of this energy trapping.

(ii) Build a circuit in Simulink to simulate the above. To reduce initial transients switch in the circuit when the current passes through a zero, give it some time to reach steady state, and then start the sequence described above; Switch off - restrike (after about 0.0002 s) -interruption at first zero of high frequency current. Use a stiff solver with maximum time step size of 0.00001 s. Submit a snapshot of you circuit and the voltage waveform across the inductor.

Q2. (a) Why does an arcing fault on an ungrounded three-phase system lead to potentially higher escalating voltages? Discuss briefly.

(b) In an arcing ground problem consider that a fault occurs when the potential of A is at negative peak. If the fault clears when the transient current or power current of phase A passes through a zero, then a charge will be trapped on the capacitance to ground causing the neutral to be shifted above ground and hence high transients upon arc restrike.

One of the solutions to prevent the capacitors C₀ from charging during the fault is to connect a "Petersen Coil"; an inductor L₀ between neutral and ground to block (neutralize) the capacitor current.

To find the value of the inductor L₀:

(i) Calculate the total capacitive current to ground at the fault instant using system voltages I_C = V_aωC₀ + V_bωC₀ + V_CωC₀. Remember that V_a = 0.

Equate this current to the Peterson Coil inductive current I_{L_0} = V_N/ωL₀.

(ii) Show that this equality holds true for any general voltages V_b, V_C and V_N while phase A is faulted; i.e. V_a = 0.

(iii) Download the model system "Q2_Exam.mdl" and insert an inductor between neutral and ground equal to the design value (in both systems). Show (provide snapshots of the waveforms in your answer sheet) that the inductor suppresses the fault power frequency current in the first system, and that a slightly higher or lower value of L₀ fails to neutralize this current.

Also show (using the second system) that subsequent voltage restrikes or mitigated with the Petersen coil in place.

Q3. (a) Discuss briefly the different methods used for transient analysis of three phase systems.

(b) Consider the distribution system shown fed from the high voltage level through a step down transformer. The distribution bus has a capacitor bank connected and outgoing cable feeders. The source impedance is represented by inductance L. The capacitor bank is modeled by a capacitance CQ per phase and a neutral to ground capacitance CR. The outgoing cables have a total capacitance of G per phase to ground.

A line-to-line fault occurs on two phase as shown. Draw the sequence network for this fault and place the breaker at the fault location such that it interrupts both sequence currents I₁ and I₂.

(i) Will the resulting high frequency transient have one or two frequency components? Express the transient frequency or frequencies in terms of system parameters. What is the peak transient current in terms of supply voltage E and system parameters? Use the injected current ramp method (ignore capacitances when calculating power-frequency fault current).

(ii) Attempt to solve the same problem again by looking at the network between the poles of the faulted phase breakers. This will be between points P and P' on diagram (both breakers will clear the fault simultaneously since they carry the same current). The injected ramp will be different compared to the symmetrical components method as the interrupted currents are now I_b and I_c rather than sequence currents.

(Help: since the capacitor CR is uncharged it can be bypassed, thereby connecting the Y point of the CQ capacitors to ground).

Q4. (a) Describe the influence of a power circuit on a neighboring communication circuit in terms of inducing an interference voltage in it.

Very briefly, what are the main methods for minimizing the electromagnetic pickup in such circuits?

(b) The two power conductors A and B in above figure carry a transient current of 10 kA peak oscillating at 5 kHz when the circuit is energized, The control circuit nearby (also shown enlarged) is shielded by a copper tube.

(i) Calculate the peak voltage induced per meter length in the control circuit with and without the shield. For copper ρ = 1.72 x 10^-8 Ω.m.

(ii) If the transient current was a step increase of 10 kA instead of a sinusoid, find the induced voltage in the control circuit as a function of time with the copper shield in place.

Q5. (a) For a distributed line connected to a constant voltage source at the beginning, draw waveforms for the voltage and current at both ends when a short circuit is suddenly applied to the termination. Show how the current at beginning and end progresses after the short circuit is applied.

(b) An overhead line has a distributed model. The resistance of the line causes a square wave voltage surge to be attenuated over the total line travel distance to a value of 0.97 of the initial magnitude.

If a square wave voltage surge of 100 kV enters the beginning of the line, when the line termination at the remote end is an open circuit, find

(i) The reflected voltage component upon the first reflection at the open circuit.

(ii) The second reflected voltage components upon the second reflection at the open circuit

(iii) The final value of the voltage at the open circuit terminal after some time assuming the square wave is continuous. (Hint: attempt to express the voltage build up as an infinite series, and find the final value).

Attachment:- Assignment.rar