Power Systems Homework Help

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 Feeder

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

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.

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.

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.

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.

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?

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)

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.

1 (B) Develop truth tables for the following Boolean expressions: D = AB + BC F = BC + AD

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).

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?

Problems-1: [2x4=8 pts] Write the general equation governing the photogeneration phenomenon in a PN junction diode. In the equation you should have the current term due to the voltage biasing and the photogenerated current term due to incident light. Mark these terms in your provided equation. Also Answer following questions (1) Draw the I-V current relation (I versus V plot) for changing gop (rate of optical generation). (2) Which quadrant of this I-V relation is utilized for solar-cell applications. (mark in your I- V Curve)? (3) Which quadrant of the I-V relation is utilized for photo-detector application (mark in your I-V curve)? (4) Now consider the photogeneration current term. What will be the effect on photogenerated current, if the P and N sides are highly doped in comparison to light doped. (hint: how depletion region width changes. Also, we are only concerned with the photogenerated terms, not the thermal current or voltage biasing term)

Problems-2: [2x4=8pts] We know that the PN junctions, diodes, photodiodes (LEDS and photodetectors) have similar physicalstructure. But +ve and -ve terminals and direction of currents depends on how the device is being operated.Consider following PN junctions with light shining on it, such that hv > Eg. Here Egis the bandgap of thesemiconductor material of the PN junction. A. Answer parts (i) and (ii) for each of the cases (a), (b) and (c). (i) position of positive and negative terminals (by choosing terminals 1 or 2 and assigning + or -ve sign) and (ii) direction of current through the device. (a) when there is no incident light, and PN junction is operated as a diode rectifier. (b) when PN junction is used as a photo-detector. (c) when PN junction is used as solar cell. B. Also answer in which of the above three cases, a battery should be applied to the PN junctions and in which cases we simply use PN junction as a battery.

a) Discuss when it is more economical to use HVDC (High Voltage Direct Current) transmission, and why. Provide a distance / cost diagram, as part of your discussion. Form the admittance matrix (YBUS) for a three-bus system, with the following reactances (X) between buses: Bus (1) to bus (2): X12 = j0.04 p.u. Bus (1) to bus (3): X13 = j0.33 p.u. Bus (2) to bus (3): X23 = j0.98 p.u. Neglect line capacitance. ) A balanced three-phase system has a fundamental current magnitude Ip = 11 A, a third harmonic of magnitude I3 = 1.14 A,and a sixth harmonic of magnitude I6 = 0.324 A. From this information, calculate: The Total Harmonic Distortion (THD) of the system. The current through the neutral.

A 110 km long three-phase transmission line, rated at 275 kV (line-line) / 50 Hz, is fed by a 180 MVA generator. The transmission line has the following characteristics: R=0.05 Ω/km , km.X- 0.47 Ωkm, y = 4.2 x 106 S/km, The transmission line supplies a city with 194.4 MW, at 271 kV anda power factor of 0.88 lagging. The generator has an automaticover-voltage relay that will trip if the voltage gets above 280 kV.Determine: if the relay will trip. (ii)if the generator is over-loaded, and if so, by how much in %. (b) Consider that the generator in 3(a) above has sub-transient reactance of 0.18 p.u. Calculate the fault current and the rating of a suitable circuit breaker, if a fault occurs at the receiving end of the line in 3(a) above. Use a base of 200 MVA for your calculations and ignore the line parallel admittance. (c)Briefly describe a distinct difference of zero-sequence components against positive or negative sequence components.

In Power World Simulator case Problem 2_32 (see Figure 2.28) a 8 MW and 4 Mvar load is supplied at 13.8 kV through a feeder with an impedance of 1 + j2 N. The load is compensated with a capacitor whose out-put, Qcap, can be varied in 0.5 Mvar steps between 0 and 10.0 Mvars.What value of qcap minimizes the real power line losses? What value of Neap minimizes the MVA power flow into the feeder?

For the system from Problem 2.32, assume that half the time the load is 10 MW and 5 Mvar, and for the other half it is 20 MW and 10 Mvar.What single value of Qcap Would minimize the average losses? Assume that Qcap can only be varied in 0.5 Mvar steps.сар