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Q1:1. Consider a three-phase power system with one-line diagram shown in Figure 1. The three-phase trans- former between CBs 1 and 2 (CB: circuit breaker) nameplate ratings are listed: 5MVA, 13.8A-138.0YkV, the transformer reactance X₁1 = 3.80 (viewed from low voltage side 13.8kV, resistance is negligible). The impedance of the transmission line between CBs 3 and 4 is ZL1 = (10+j100). -(50 pts) (a) Pick up SB = 100MVA for the entire three-phase system, and rated voltage VB = 138.0kV, calculate the per-unit line L1 and transformer impedance values. (b) If an SLG fault occurs at the midpoint of the line (L2) between CBs 5 and 6, which breaker(s) should operate? If the CB 5 or CB 6 does not operate, which breaker(s) will provide the backup protection? (c) List the operating CB(s) for different zones, which are listed in Figure 2. (d) If the second generator is connected at bus 3, the system (generators, buses, and transmission lines) is protected by overcurrent relays R1 to R12. Assuming the directional overcurrent relays are used for three transmission lines, what is the remote backup relay(s) for R7? And why? G Generator mm www Transformer - GSU Bus 1 depending on which breakfas Bus 3 Transmission line L1 Shunt Reactor L3 Shunt Capacitor Figure 1: A three-phase power system. Bus 2 Distribution Transformer FeederSee Answer
Q2: Figure 1 shows a common and simple power circuit breaker control schematic. You are asked to draw an equivalent logic diagram using the well-known symbols shown in Figure 3. In order to complete the scheme, use a simulated representation of the actual circuit breaker as shown in Figure 2. Assume that both, the tripping coil and the closing coil have associated contacts and that they operate over an auxiliary relay (used to simulate the circuit breaker) called 52, which has normally open (52/a) and normally closed (52/b) contacts. CS/T and CS/C are spring self-reset switches as explained in class. a) Explain the scheme shown in Figure 1. Put special emphasis on the function of auxiliary relay Y. b) Draw the logic diagram using logic gates symbols as explained in class See Answer
Q3: The portion of a power system shown by the one-line diagram of Fig. 5, with generating sources back of all three ends, has conventional primary and back-up relaying. In each of the listed cases, a short circuit has occurred and certain circuit breakers have tripped as stated. Assume that the tripping of these breakers was correct under the circumstances. Where was the short circuit? Was there any failure of the protective relaying, including breakers, and if so, what failed? Assume only one failure at a time.Draw a sketch showing the overlapping of primary protective zones and the exact locations of the various faults. Note: This problem was taken from the book “The Art and Science of Protective Relaying, " by C. Mason, recommended in class. Note: Assume that the system has remote back-up only. It does not have local back-up.See Answer
Q4: For the reactance network of Fig. 8.14, find Zpus by direct formulation,bus ) The voltage at each bus, The current drawn by a capacitor having a reactance of 5.0 per unit connected from bus 3 to neutral, (d) The change in voltage at each bus when the capacitor is connected at bus 3 (e) The voltage at each bus after connecting the capacitor.The magnitude and angle of each of the generated voltages may be assumed to remain constant.See Answer
Q5: Figure 1 shows the parameter of s single phase 50 Hz transformer. The transformer rating is10 kVA, 7500/250 V. The high voltage side is connected to a 7500 V supply and a load Z, = 5Z90° Q is connected to the low voltage side. Determine (1)Load voltage (11)Load current (ii1)Voltage regulation (iv)Draw the phasor diagramSee Answer
Q6: A 20 KVA, 240/120 V, 50 Hz distribution transformer supplies a load of 10 kW at 0.9powerfactor lagging. This transformer is connected as an auto transformer to supply a load at 240 V. (a) Determine the maximum kVA the auto transformer can supply to the 240 V circuit (b) Determine the efficiency of the auto transformer for full load at 0.9 power factor lagging.See Answer
Q7: 5. Assume that we have a material with refractive index n,. We input a waveform with an amplitude Eo and frequency w such that the sample length l contains exactly two periods. Assume E = 0 at the edges at time t = 0.Assume another material n, on the right such that the boundary is in short condition. n, is a conductor at the given w. Discuss the necessary mathematical requirements for n2 to force a short condition on the boundary,assuming n, is vacuum. Is this a physically valid refractive index? Hint: is there propagation in n2? See Answer
Q8: or the following questions,figures/circuit diagram/ equations/phasor diagram (if applicable)F WITH YOUR EXPLAINATION (a) Explain the following FACTS Device • Distribution System (b) How can you improve the voltage regulation of distribution system network? Three 415/6350 V, 50 Hz, single phase transformers are used to form a three phase, 415/11000transformer bank. Draw the circuit diagram showing the three phase transformer connection.See Answer
Q9: Consider the following 5-bus system. Assume that the series line impedances are z= 0.0099+ j0.099. Neglect the shunt capacitive impedances of the lines, only consider the shunt capacitors onbuses Four and Five. \text { Build the } Y_{\text {bus }}\left(\text { Hint: } 1 / z_{L}=1-\mathrm{j} 10\right)See Answer
Q10: a) A thyristor in a fully-controlled converter that supplies 66yA to a D.C. load is mounted on a0.5 kg aluminium heat sink. If the forward voltage across the device is 1.5 V, and aluminium has a specific heat capacity of 895 J(kg °C)-1. The ambient temperature is 40 °C maximum and the thyrist or is mounted directly on the heat sink. (i) Calculate the steady state temperature of the thyrist or junction, given that the thermal resistance of the heat sink is 0.15 °C W-1 and that of the device is 0.12°CW-1. (ii) How long does the heat sink take to reach a steady-state temperature? b) Draw a circuit with two transistors, a PNP and NPN, and then determine and prove a formula for la in terms of common base gains. Explain how the circuit operates. c) State an electronic power component and explain how heat dissipation can be modelled.See Answer
Q11: 1 (B) Develop truth tables for the following Boolean expressions: D = AB + BC F = BC + ADSee Answer
Q12: 8. (a) Kron reduce Yus of the circuit of Fig. 7.18 to reflect elimination of node (2) (b) Use the Y - A transformation of Table 1.2 to eliminate node (2) from the circuit of Fig. 7.18 and find YBUS for the resulting reduced network. Compare results of parts (a) and (b).See Answer
Q13: If System A has an expected load of 80 MW in a lead time of 2 hours, what is the unit commitment risk for the system in the lead time?See Answer
Q14: Determine the time dial setting of the phase relays given in the 138 kV system of Figure 1. The numbers within rectangles are the bus numbers. All relays within the loop are directional and have CTR=400/5 and Ipu=5 A. All relays associated with radial lines have CTR=400/5, Ipu=5 A and TD=2. All the relays have the curve t=TD-(5.95/(M²-1)+0.18); and INST=∞ The equivalent impedance of the source is Zsı=j0.2 ohms. Each line has a total impedance ofZL1= 2+j12 ohms. Use a coordination time interval (CI) of 0.4 seconds. See Answer
Q15: System B has exactly the same parameters as System A. It also has three 40-MW generators, and the MTTFS of the generators are the same as the ones listed in Question 1. The load of System Bin a lead time of 2 hours is also 80 Mw .If System A and System B are interconnected, what is the unit commitment risk for system A in the lead time of 2 hours? Assuming the tie line is 100% reliable and has no capacity limit.See Answer
Q16: 4. [15] An RC circuit is excited with a fixed frequency signal. The excitation signal and the response are measured with an oscilloscope. The time traces are shown in the plot below.Note that any DC offsets of the signals may be ignored. Calculate the following: a. The frequency of the excitation signal, b. The magnitude (gain) of the frequency response, and c. The phase of the frequency response. See Answer
Q17: Now let's consider the load forecast uncertainty. In System A, the load forecast for the next 2 hours follows a Normal Distribution. The mean of the Normal Distribution is 80MW, and the standard deviation is 6 MW. What is the expected unit commitment risk for System A in a lead time of 2hours considering the load forecast uncertainty? To calculate the expected unit commitment risk ,please consider 7 possible load scenarios: 62 MW, 68 MW, 74 MW, 80 MW, 86 MW, 92 MW, 98MW.See Answer
Q18: 5. [20] A DC permanent magnet motor develops 35.3 in-lbf of torque when operated at an armature voltage of Va-60 volts and a speed of 1433 RPM. The manufacturer claims that the motor has a no-load speed of 3344 rpm when operated at 60 V. Determine: a) the motor's theoretical "no-load" speed,WNL, b) the motor's theoretical back-EMF constant, ka, c) the motor's theoretical torque constant, ka,d) the motor's theoretical resistance, Ra,e) the motor's efficiency at 1433 RPM when operated at an armature voltage of Va-30 volts. See Answer
Q19: 6. [10] The setup below is used to measure angular velocity of a shaft. In a 1.00 second period, a total of 325 pulses are counted. What is the angular velocity in RPM? See Answer
Q20: 7. [15] Two strain gages are mounted (one on the top, one on the bottom) to a steel beam with a rectangular cross-section, as shown in the figure to the right. Note that the cantilever beam is loaded in bending. Determine the load, P applied to the cantilever beam with the given dimensions and the following nominal parameter values: See Answer

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