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systems analysis design
Questions and Answers of
Systems Analysis Design
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
Repeat Problem 11.10, except assume there is a three-phase-to-ground bolted short circuit at bus five.Problem 11.10For the five bus system from Example 6.9, assume the transmission lines and
The generator in Figure 11.4 is initially operating in the steady-state condition given in Example 11.3 when circuit breaker B12 inadvertently opens. Use the equal-area criterion to calculate the
The generator in Figure 11.4 is initially operating in the steady-state condition given in Example 11.3 when a temporary three-phase-to-ground short circuit occurs at point F. Three cycles later,
If breakers B13 and B22 in Problem 11.13 open later than 3 cycles after the fault commences, determine the critical clearing time.Problem 11.13The generator in Figure 11.4 is initially operating in
Building upon Problem 11.11, assume a \(60 \mathrm{~Hz}\) nominal system frequency, that the bus fault actually occurs on the line between buses five and two but at the bus two end, and that the
Analytically determine whether there is a critical clearing time for Problem 11.15.Problem 11.15Building upon Problem 11.11, assume a \(60 \mathrm{~Hz}\) nominal system frequency, that the bus fault
Consider the first order differential equation, \(\frac{d x_{1}}{d t}=-x_{2}\), with an initial value \(x(0)=10\). With an integration step size of 0.1 seconds, determine the value of \(x(0.5)\)
The following set of differential equations can be used to represent that behavior of a simple spring-mass system, with \(x_{1}(t)\) the mass's position and \(x_{2}(t)\) its velocity:\(\frac{d
A \(60 \mathrm{~Hz}\) generator is supplying \(400 \mathrm{MW}\) (and 0 Mvar) to an infinite bus (with 1.0 per unit voltage) through two parallel transmission lines. Each transmission line has a per
Open PowerWorld Simulator case Problem 11_20. This case models the Example 11.4 system with damping at the bus 1 generator, and with a line fault midway between buses 1 and 2 . The fault is cleared
Open PowerWorld Simulator case Problem 11_21. This case models the Example 11.4 system with damping at the bus 1 generator, and with a line fault midway between buses 2 and 3. The fault is cleared by
Consider the six-bus power system shown in Figure 11.29, where all data are given in per-unit on a common system base. All resistances as well as transmission-line capacitances are neglected. (a)
Modify the matrices Y11,Y12Y11,Y12, and Y22Y22 determined in Problem 11.22 for(a) the case when circuit breakers B32 and B51 open to remove line 3-5; and(b) the case when the load PL3+jQL3PL3+jQL3 is
Open PowerWorld Simulator case Problem 11_24, which models the Example 6.9 with transient stability data added for the generators. Determine the critical clearing time (to the nearest 0.01 second)
With PowerWorld Simulator using the Example 11_9 case determine the critical clearing time (to the closest 0.01 second) for a transmission line fault on the transmission line between bus 44 (PEACH69)
PowerWorld Simulator case Problem 11_26 duplicates Example 11.10, except with the synchronous generator initially supplying \(75 \mathrm{MW}\) at unity power factor to the infinite bus.(a) Derive the
PowerWorld Simulator case Problem 11_27 duplicates the system from Problem 11.24, except the generators are modeled using a two-axis model, with the same \(\mathrm{X}_{d}^{\prime}\) and
PowerWorld Simulator case Problem 11_28 duplicates Example 11.11 except the wind turbine generator is set so it is initially supplying \(100 \mathrm{MW}\) to the infinite bus at unity power
Redo Example 11.12 with the assumption the generator is supplying \(100+j 10\) MVA to the infinite bus.Example 11.12For the system from Example 11.3, assume the synchronous generator is replaced with
The block-diagram representation of a closed-loop automatic regulating system, in which generator voltage control is accomplished by controlling the exciter voltage, is shown in Figure 12.14.
The Automatic Voltage Regulator (AVR) system of a generator is represented by the simplified block diagram shown in Figure 12.15, in which the sensor is modeled by a simple first-order transfer
Open PowerWorld Simulator case Problem 12_3. This case models the system from Example 12.1 except with the rate feedback gain constant, \(\mathrm{K}_{\mathrm{f}}\), has been set to zero and the
An area of an interconnected \(60-\mathrm{Hz}\) power system has three turbinegenerator units rated 200,300, and 500 MVA. The regulation constants of the units are \(0.03,0.04\), and 0.05 per unit,
Each unit in Problem 12.5 is initially operating at one-half its own rating when the load suddenly increases by 100 MW. Determine(a) the steadystate decrease in area frequency, and(b) the MW increase
Each unit in Problem 12.5 is initially operating at one-half its own rating when the frequency increases by 0.005 per unit. Determine the MW decrease of each unit. The reference power setting of each
Repeat Problem 12.7 if the frequency decreases by 0.005 per unit. Determine the MW increase of each unit.Problem 12.7Each unit in Problem 12.5 is initially operating at one-half its own rating when
An interconnected \(60-\mathrm{Hz}\) power system consisting of one area has two turbine-generator units, rated 500 and \(750 \mathrm{MVA}\), with regulation constants of 0.04 and 0.06 per unit,
Open PowerWorld Simulator case Problem 12_10. The case models the system from Example 12.4 except 1) the load increases is a \(50 \%\) rise at bus 6 for a total increase of \(250 \mathrm{MW}\) (from
Open PowerWorld Simulator case Problem 12_11, which includes a transient stability representation of the system. Each generator is modeled using a two-axis machine model, an IEEE Type 1 exciter and a
Repeat Problem 12.11 except first double the \(\mathrm{H}\) value for each of the machines. This can be most easily accomplished by selecting Stability Case Info, Transient Stability Case Summary to
For a large, \(60 \mathrm{~Hz}\), interconnected electrical system assume that following the loss of two \(1400 \mathrm{MW}\) generators (for a total generation loss of \(2800 \mathrm{MW}\) ) the
A \(60-\mathrm{Hz}\) power system consists of two interconnected areas. Area 1 has \(1200 \mathrm{MW}\) of generation and an area frequency response characteristic \(\beta_{1}=400 \mathrm{MW} /
Repeat Problem 12.14 if \(\mathrm{LFC}\) is employed in area 2 alone. The area 2 frequency bias coefficient is set at \(\mathrm{B}_{f 2}=\beta_{2}=600 \mathrm{MW} / \mathrm{Hz}\). Assume that LFC in
Repeat Problem 12.14 if \(\mathrm{LFC}\) is employed in both areas. The frequency bias coefficients are \(\mathrm{B}_{f 1}=\beta_{1}=400 \mathrm{MW} / \mathrm{Hz}\) and \(\mathrm{B}_{f
Rework Problems 12.15 through 12.16 when the load in area 2 suddenly decreases by \(300 \mathrm{MW}\). The load in area 1 does not change.Problem 12.15Repeat Problem 12.14 if \(\mathrm{LFC}\) is
On a 1000-MVA common base, a two-area system interconnected by a tie line has the following parameters:The two areas are operating in parallel at the nominal frequency of \(60 \mathrm{~Hz}\). The
From the results of Example 13.2, plot the voltage and current profiles along the line at times \(\tau / 2, \tau\), and \(2 \tau\). That is, plot \(v(x, \tau / 2)\) and \(i(x, \tau / 2)\) versus
Rework Example 13.2 if the source voltage at the sending end is a ramp, \(e_{\mathrm{G}}(t)=\mathrm{E} u_{-2} \mathrm{M}=\mathrm{E} t u_{-1}(t)\), with \(\mathrm{Z}_{\mathrm{G}}=2
Referring to the single-phase two-wire lossless line shown in Figure 13.3, the receiving end is terminated by an inductor with \(2 \mathrm{~L}_{\mathrm{R}}\) henries. The source voltage at the
Rework Problem 13.3 if \(Z_{\mathrm{R}}=Z_{c}\) at the receiving end and the source voltage at the sending end is \(e_{\mathrm{G}}(t)=\mathrm{E} u_{-1}(t)\), with an inductive source impedance
Rework Example 13.4 with \(\mathrm{Z}_{\mathrm{R}}=5 \mathrm{Z}_{c}\) and \(\mathrm{Z}_{\mathrm{G}}=\mathrm{Z}_{c} / 3\).Example 13.4At the receiving end, \(\mathrm{Z}_{\mathrm{R}}=\mathrm{Z}_{c} /
The single-phase, two-wire lossless line in Figure 13.3 has a series inductance \(\mathrm{L}=(1 / 3) \times 10^{-6} \mathrm{H} / \mathrm{m}\), a shunt capacitance \(\mathrm{C}=(1 / 3) \times 10^{-10}
The single-phase, two-wire lossless line in Figure 13.3 has a series inductance \(\mathrm{L}=2 \times 10^{-6} \mathrm{H} / \mathrm{m}\), a shunt capacitance \(\mathrm{C}=1.25 \times 10^{-11}
The single-phase, two-wire lossless line in Figure 13.3 has a series inductance \(\mathrm{L}=0.999 \times 10^{-6} \mathrm{H} / \mathrm{m}\), a shunt capacitance \(\mathrm{C}=1.112 \times 10^{-11}
Draw the Bewley lattice diagram for Problem 13.5.Problem 13.5Rework Example 13.4 with \(\mathrm{Z}_{\mathrm{R}}=5 \mathrm{Z}_{c}\) and \(\mathrm{Z}_{\mathrm{G}}=\mathrm{Z}_{c} / 3\).Example 13.4At
Rework Problem 13.9 if the source voltage is a pulse of magnitude \(\mathrm{E}\) and duration \(\tau / 10\); that is, \(e_{\mathrm{G}}(t)=\mathrm{E}\left[u_{-1}(t)-u_{-1}(t-\tau / 10)ight]\).
As shown in Figure 13.32, a single-phase two-wire lossless line with \(Z_{c}=\) \(400 \Omega, v=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\), and \(1=100 \mathrm{~km}\) has a \(400-\Omega\) resistor,
The junction of four single-phase two-wire lossless lines, denoted A, B, \(\mathrm{C}\), and \(\mathrm{D}\), is shown in Figure 13.13. Consider a voltage wave \(v_{\mathrm{A}}^{+}\)arriving at the
Referring to Figure 13.3, the source voltage at the sending end is a step \(e_{\mathrm{G}}(t)=\mathrm{Eu}_{-1}(t)\) with an inductive source impedance \(\mathrm{Z}_{\mathrm{G}}(s)=s
As shown in Figure 13.33, two identical, single-phase, two-wire, lossless lines are connected in parallel at both the sending and receiving ends. Each line has a \(400-\Omega\) characteristic
As shown in Figure 13.34, an ideal current source consisting of a 10-kA pulse with \(50-\mu\) s duration is applied to the junction of a single-phase, lossless cable and a single-phase, lossless
For the circuit given in Problem 13.3, replace the circuit elements by their discrete-time equivalent circuits and write nodal equations in a form suitable for computer solution of the sending-end
Repeat Problem 13.18 for the circuit given in Problem 13.13. Assume \(\Delta t=0.03333 \mathrm{~ms}\).Problem 13.18For the circuit given in Problem 13.3, replace the circuit elements by their
For the circuit given in Problem 13.7, replace the circuit elements by their discrete-time equivalent circuits. Use \(\Delta t=100 \mu \mathrm{s}=1 \times 10^{-4} \mathrm{~s}\). Determine and show
For the circuit given in Problem 13.8, replace the circuit elements by their discrete-time equivalent circuits. Use \(\Delta t=50 \mu \mathrm{s}=5 \times 10^{-5} \mathrm{~s}\) and \(\mathrm{E}=\)
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