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systems analysis design

Questions and Answers of Systems Analysis Design

Equipment ratings for the four-bus power system shown in Figure 7.14 are given as follows:Generator G1: \(\quad 500 \mathrm{MVA}, 13.8 \mathrm{kV}, \mathrm{X}_{d}^{\prime \prime}=\mathrm{X}_{2}=0.20,
Faults at bus \(n\) in Problem 9.5 are of interest (the instructor selects \(n=1\), 2,3 , or 4). Determine the Thévenin equivalent of each sequence network as viewed from the fault bus. Prefault
Determine the subtransient fault current in per-unit and in kA during a bolted three-phase fault at the fault bus selected in Problem 9.6.Problem 9.6Faults at bus \(n\) in Problem 9.5 are of interest
Equipment ratings for the five-bus power system shown in Figure 7.15 are given as follows:Generator G1: \(\quad 50 \mathrm{MVA}, 12 \mathrm{kV}, \mathrm{X}_{d}^{\prime \prime}=\mathrm{X}_{2}=0.20,
Faults at bus \(n\) in Problem 9.8 are of interest (the instructor selects \(n=\) 1, 2, 3, 4, or 5). Determine the Thévenin equivalent of each sequence network as viewed from the fault bus. Prefault
Determine the subtransient fault current in per-unit and in kA during a bolted three-phase fault at the fault bus selected in Problem 9.9.Problem 9.9Faults at bus \(n\) in Problem 9.8 are of interest
Consider the system shown in Figure 9.18.(a) As viewed from the fault at \(F\), determine the Thévenin equivalent of each sequence network. Neglect \(\Delta-Y\) phase shifts.(b) Compute the fault
Equipment ratings and per-unit reactances for the system shown in Figure 9.19 are given as follows:Synchronous generators:\(\begin{array}{lllll}\text { G1 } & 100 \text { MVA } & 25
Consider the oneline diagram of a simple power system shown in Figure 9.20. System data in per-unit on a 100-MVA base are given as follows:Synchronous generators:G1 & 100 MVA & \(20
Determine the subtransient fault current in per-unit and in kA, as well as the per-unit line-to-ground voltages at the fault bus for a bolted single line-to-ground fault at the fault bus selected in
Repeat Problem 9.14 for a single line-to-ground arcing fault with arc impedance \(Z_{\mathrm{F}}=15+j 0 \Omega\).Problem 9.14Determine the subtransient fault current in per-unit and in kA, as well as
Repeat Problem 9.14 for a bolted line-to-line fault.Problem 9.14Determine the subtransient fault current in per-unit and in kA, as well as the per-unit line-to-ground voltages at the fault bus for a
Repeat Problem 9.14 for a bolted double line-to-ground fault.Problem 9.14Determine the subtransient fault current in per-unit and in kA, as well as the per-unit line-to-ground voltages at the fault
Repeat Problems 9.1 and 9.14 including \(\Delta-Y\) transformer phase shifts. Assume American standard phase shift. Also calculate the sequence components and phase components of the contribution to
(a) Repeat Problem 9.14 for the case of Problem 9.4 (b).(b) Repeat Problem 9.19 (a) for a single line-to-ground arcing fault with arc impedance \(Z_{\mathrm{F}}=(15+j 0) \Omega\).(c) Repeat Problem
A 500-MVA, 13.8 -kV synchronous generator with \(\mathrm{X}_{d}^{\prime \prime}=\mathrm{X}_{2}=0.20\) and \(\mathrm{X}_{0}=0.05\) per unit is connected to a \(500-\mathrm{MVA}, 13.8 -\mathrm{kV}
Determine the subtransient fault current in per-unit and in kA, as well as contributions to the fault current from each line and transformer connected to the fault bus for a bolted single
Repeat Problem 9.21 for a bolted line-to-line fault.Problem 9.21Determine the subtransient fault current in per-unit and in kA, as well as contributions to the fault current from each line and
Repeat Problem 9.21 for a bolted double line-to-ground fault.Problem 9.21Determine the subtransient fault current in per-unit and in kA, as well as contributions to the fault current from each line
Determine the subtransient fault current in per-unit and in \(\mathrm{kA}\), as well as contributions to the fault current from each line, transformer, and generator connected to the fault bus for a
Repeat Problem 9.24 for a single line-to-ground arcing fault with arc impedance \(Z_{\mathrm{F}}=0+j 0.1 \) per unit.Problem 9.24Determine the subtransient fault current in per-unit and in
Repeat Problem 9.24 for a bolted line-to-line fault.Problem 9.24Determine the subtransient fault current in per-unit and in \(\mathrm{kA}\), as well as contributions to the fault current from each
Repeat Problem 9.24 for a bolted double line-to-ground fault.Problem 9.24Determine the subtransient fault current in per-unit and in \(\mathrm{kA}\), as well as contributions to the fault current
As shown in Figure 9.21 (a), two three-phase buses \(a b c\) and \(a^{\prime} b^{\prime} c^{\prime}\) are interconnected by short circuits between phases \(b\) and \(b^{\prime}\) and between \(c\)
Repeat Problem 9.28 for the two-conductors-open fault shown in Figure 9.21 (b). The fault conditions in the phase domain are \[ I_{b}=I_{b^{\prime}}=I_{c}=I_{c^{\prime}}=0 \text { and } V_{a
For the system of Problem 9.11, compute the fault current and voltages at the fault for the following faults at point \(\mathrm{F}\) :(a) a bolted single line-to-ground fault;(b) a line-to-line fault
For the system of Problem 9.12, compute the fault current and voltages at the fault for the following faults at bus 3:(a) a bolted single line-toground fault,(b) a bolted line-to-line fault,(c) a
For the system of Problem 9.13, compute the fault current for the following faults at bus 3:(a) a single line-to-ground fault through a fault impedance \(Z_{\mathrm{F}}=j 0.1 \) per unit,(b) a
For the three-phase power system with single-line diagram shown in Figure 9.22, equipment ratings and per-unit reactances are given as follows:Machines 1 and 2: \(\quad 100\) MVA \(20 \mathrm{kV}
At the general three-phase bus shown in Figure 9.7 (a) of the text, consider a simultaneous single line-to-ground fault on phase \(a\) and lineto-line fault between phases \(b\) and \(c\), with no
Thévenin equivalent sequence networks looking into the faulted bus of a power system are given with \(Z_{1}=j 0.15, Z_{2}=j 0.15, Z_{0}=j 0.2\), and \(E_{1}=1 \angle 0^{\circ}\) per unit. Compute
The single-line diagram of a simple power system is shown in Figure 9.23 with per unit values. Determine the fault current at bus 2 for a three-phase fault. Ignore the effect of phase shift.Figure
Consider a simple circuit configuration shown in Figure 9.24 to calculate the fault currents \(I_{1}, I_{2}\), and \(I\) with the switch closed.(a) Compute \(E_{1}\) and \(E_{2}\) prior to the fault
The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system areDetermine the per-unit fault current and per-unit voltage at bus 2 for a bolted
Repeat Problem 9.38 for a bolted single line-to-ground fault at bus 1.Problem 9.38The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system
Repeat Problem 9.38 for a bolted line-to-line fault at bus 1.Problem 9.38The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system areDetermine the
Repeat Problem 9.38 for a bolted double line-to-ground fault at bus 1.Problem 9.38The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system
(a) Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.1. Use a base of \(1000 \mathrm{MVA}\) and \(765
The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system areDetermine the per-unit fault current and per-unit voltage at bus 2 for a bolted
Repeat Problem 9.43 for a bolted single line-to-ground fault at bus 1.Problem 9.43The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system
Repeat Problem 9.43 for a bolted line-to-line fault at bus 1.Problem 9.43The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system areDetermine the
Repeat Problem 9.43 for a bolted double line-to-ground fault at bus 1.Problem 9.43The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system
Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 4(a). Use a base of \(1000 \mathrm{MVA}\) and \(500
Using the bus impedance matrices determined in Problem 9.47.Problem 9.47Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given
Compute the \(4 \times 4\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.5. Use a base of \(1000 \mathrm{MVA}\) and \(20
Using the bus impedance matrices determined in Problem 9.42.Problem 9.42(a) Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system
Compute the \(5 \times 5\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.8. Use a base of 100 MVA and \(15 \mathrm{kV}\) in the zone
Using the bus impedance matrices determined in Problem 9.51.Problem 9.51Compute the \(5 \times 5\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given
The positive-sequence impedance diagram of a five-bus network with all values in per-unit on a 100-MVA base is shown in Figure 9.25. The generators at buses 1 and 3 are rated 270 and 225 MVA,
For the five-bus network shown in Figure 9.25, a bolted single-line-toground fault occurs at the bus 2 end of the transmission line between buses 1 and 2. The fault causes the circuit breaker at the
A single-line diagram of a four-bus system is shown in Figure 9.27 . Equipment ratings and per-unit reactances are given as follows.On a base of \(100 \mathrm{MVA}\) and \(345 \mathrm{kV}\) in the
The system shown in Figure 9.28 except that the transformers are now \(\mathrm{Y}-\mathrm{Y}\) connected and solidly grounded on both sides. (a) Determine the bus impedance matrix for each of the
The results in Table 9.5 show that during a phase \(a\) single line-to-ground fault the phase angle on phase \(a\) voltages is always zero. Explain why we would expect this result.Table 9.5
The results in Table 9.5 show that during the single line-to-ground fault at bus 2 the \(b\) and \(c\) phase voltage magnitudes at bus 2 actually rise above the prefault voltage of 1.05 per unit. Use
Plot the variation in the bus 2 phase \ (a, b, c\) voltage magnitudes during a single line-to-ground fault at bus 2 as the fault reactance is varied from 0 to 0.30 per unit in 0.05 per-unit steps the
Determine the fault current in amps, except with a line-to-line fault at each of the buses. Compare the fault currents with the values given in Table 9.4.Table 9.4 Single Line-to-Ground Fault Fault
Determine the fault current in amps, except with a bolted double line-to-ground fault at each of the buses. Compare the fault currents with the values given in Table 9.4.Table 9.4 Single
Re-determine the Example 9_8 fault currents, except with a new line installed between buses 2 and 5. The parameters for this new line should be identical to those of the existing line between buses 2
Re-determine the Example 9_8 fault currents, except with a second generator added at bus 3. The parameters for the new generator should be identical to those of the existing generator at bus 3. Are
Using PowerWorld Simulator case, calculate the perunit fault current and the current supplied by each of the generators for a single line-to-ground fault at the ORANGE69 bus. During the fault, what
The primary conductor in Figure 10.2 is one phase of a three-phase transmission line operating at \(345 \mathrm{kV}, 700 \mathrm{MVA}, 0.95\) power factor lagging. The CT ratio is \(1200: 5\), and
A CO-8 relay with a current tap setting of 5 amperes is used with the 100:5 CT in Example 10.1. The CT secondary current I' is the input to the relay operating coil. The CO-8 relay burden is shown in
An overcurrent relay set to operate at \(10 \mathrm{~A}\) is connected to the \(\mathrm{CT}\) in Figure 10.8 with a 500:5 CT ratio. Determine the minimum primary fault current that the relay will
Given the open-delta VT connection shown in Figure 10.38, both VTs having a voltage rating of \(240 \mathrm{kV}: 120 \mathrm{~V}\), the voltages are specified as \(V_{\mathrm{AB}}=230 \angle
A CT with an excitation curve given in Figure 10.39 has a rated current ratio of 500:5 A and a secondary leakage impedance of \(0.1+j 0.5 \Omega\). Calculate the CT secondary output current and the
The CT of Problem 10.5 is utilized in conjunction with a currentsensitive device that will operate at current levels of \(8 \mathrm{~A}\) or above. Check whether the device will detect the 1300-A
The input current to a CO-8 relay is \(10 \mathrm{~A}\). Determine the relay operating time for the following current tap settings (TS) and time dial settings (TDS): (a) \(\mathrm{TS}=1.0,
The relay in Problem 10.2 has a time-dial setting of 4 . Determine the relay operating time if the primary fault current is \(400 \mathrm{~A}\).Problem 10.2A CO-8 relay with a current tap setting of
An RC circuit used to produce time delay is shown in Figure 10.40. For a step input voltage \(\mathrm{v}_{\mathrm{i}}(\mathrm{t})=2 \mathrm{u}(\mathrm{t})\) and \(\mathrm{C}=10 \mu \mathrm{F}\),
Reconsider case (b) of Problem 10.5. Let the load impedance \(4.9+j 0.5 \Omega\) be the input impedance to a \(\mathrm{CO}-7\) induction disc time-delay overcurrent relay. The CO-7 relay
Evaluate relay coordination for the minimum fault currents in Example 10.4. For the selected current tap settings and time dial settings, (a) determine the operating time of relays at B2 and B3 for
Repeat Example 10.4 for the following system data. Coordinate the relays for the maximum fault currents.Example 10.4Data for the \(60-\mathrm{Hz}\) radial system of Figure 10.16 are given in Tables
Using the current tap settings and time dial settings that you have selected in Problem 10.12, evaluate relay coordination for the minimum fault currents. Are the fault-to-pickup current ratios
An \(11-\mathrm{kV}\) radial system is shown in Figure 10.42. Assuming a CO-7 relay with relay characteristic given in Figure 10.41 and the same power factor for all loads, select relay settings to
Rework Example 10.5 for the following faults:(a) a threephase, permanent fault on the load side of tap 3;(b) a single line-to-ground, permanent fault at bus 4 on the load side of the recloser; and(c)
A three-phase \(34.5-\mathrm{kV}\) feeder supplying a 3.5-MVA load is protected by \(80 \mathrm{E}\) power fuses in each phase, in series with a recloser. The time-current characteristic of the 80E
For the system shown in Figure 10.44, directional overcurrent relays are used at breakers B12, B21, B23, B32, B34, and B43. Overcurrent relays alone are used at \(\mathrm{B} 1\) and \(\mathrm{B}
Draw the protective zones for the power system shown in Figure 10.45. Which circuit breakers should open for a fault at(a) \(\mathrm{P}_{1}\),(b) \(\mathrm{P}_{2}\), (c) \(\mathrm{P}_{3}\) ? O 81
Figure 10.46 shows three typical bus arrangements. Although the number of lines connected to each arrangement varies widely in practice, four lines are shown for convenience and comparison. Note that
Three-zone mho relays are used for transmission line protection of the power system shown in Figure 10.25. Positive-sequence line impedances are given as follows.Rated voltage for the high-voltage
Line impedances for the power system shown in Figure 10.47 are \(Z_{12}=Z_{23}=3.0+j 40.0 \Omega\), and \(Z_{24}=6.0+j 80.0 \Omega\). Reach for the zone 3 B12 impedance relays is set for \(100 \%\)
Consider the transmission line shown in Figure 10.48 with series impedance \(Z_{\mathrm{L}}\), negligible shunt admittance, and a load impedance \(Z_{\mathrm{R}}\) at the receiving end. (a) Determine
A simple system with circuit breaker-relay locations is shown in Figure 10.49. The six transmission-line circuit breakers are controlled by zone distance and directional relays, as shown in Figure
Select \(\mathrm{k}\) such that the differential relay characteristic shown in Figure 10.34 blocks for up to \(20 \%\) mismatch between \(I_{1}^{\prime}\) and \(I_{2}^{\prime}\).Figure 10.34 1/2 Trip
Consider a protected bus that terminates four lines, as shown in Figure 10.51. Assume that the linear couplers have the standard \(X_{m}=5 \mathrm{~m} \Omega\) and a three-phase fault externally
A single-phase, 5-MVA, 20/8.66-kV transformer is protected by a differential relay with taps. Available relay tap settings are 5:5, 5:5.5, 5:6.6, 5:7.3, 5:8, 5:9, and 5:10, giving tap ratios of 1.00,
A three-phase, \(500-\mathrm{MVA}, 345 \mathrm{kV} \Delta / 500 \mathrm{kV}\) Y transformer is protected by differential relays with taps. Select CT ratios, CT connections, and relay tap settings.
For a \(\Delta\)-Y connected, 15-MVA, \(33: 11 \mathrm{kV}\) transformer with differential relay protection and \(\mathrm{CT}\) ratios shown in Figure 10.52, determine the relay currents at full load
Consider a three-phase \(\Delta-Y\) connected, \(30-\mathrm{MVA}, 33: 11 \mathrm{kV}\) transformer with differential relay protection. If the CT ratios are 500:5 A on the primary side and 2000:5 A on
Determine the CT ratios for differential protection of a three-phase, \(\Delta-\mathrm{Y}\) connected, 10-MVA, \(33: 11 \mathrm{kV}\) transformer, such that the circulating current in the transformer
A three-phase, \(60-\mathrm{Hz}, 500-\mathrm{MVA}, 11.8-\mathrm{kV}\), 4-pole steam turbine-generating unit has an \(\mathrm{H}\) constant of 5 p.u.-s. Determine:(a) \(\omega_{\text {syn }}\) and
Calculate \(\mathrm{J}\) in \(\mathrm{kg}-\mathrm{m}^{2}\) for the generating unit given in Problem 11.1.Problem 11.1A three-phase, \(60-\mathrm{Hz}, 500-\mathrm{MVA}, 11.8-\mathrm{kV}\), 4-pole
Generator manufacturers often use the term \(\mathrm{WR}^{2}\), which is the weight in pounds of all the rotating parts of a generating unit (including the prime mover) multiplied by the square of
The generating unit in Problem 11.1 is initially operating at \(p_{m \text { p.u. }}=p_{\text {ep.u. }}=\) 0.7 per unit, \(\omega=\omega_{\text {syn }}\), and \(\delta=12^{\circ}\) when a fault
How would the value of \(\mathrm{H}\) change if a generator's assumed operating frequency is changed from \(60 \mathrm{~Hz}\) to \(55 \mathrm{~Hz}\) ?
Repeat Example 11.1 except assume the number of poles is changed from 32 to \(16, \mathrm{H}\) is changed from 2.0 p.u.-s to 1.5 p.u.-s, and the unit is initially operating with an electrical and
Given that for a moving mass \(W_{\text {kinetic }}=1 / 2 \mathrm{Mv}^{2}\), how fast would a \(80,000 \mathrm{~kg}\) diesel locomotive need to go to equal the energy stored in a \(60-\mathrm{Hz}\),
The synchronous generator in Figure 11.4 delivers 0.8 per-unit real power at 1.05 per-unit terminal voltage. Determine: (a) the reactive power output of the generator; (b) the generator internal
The generator in Figure 11.4 is initially operating in the steady-state condition given in Problem 11.8 when a three-phase-to-ground bolted short circuit occurs at bus 3. Determine an equation for
For the five bus system from Example 6.9, assume the transmission lines and transformers are modeled with just their per unit reactance (e.g., neglect their resistance and B shunt values). If bus one

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