A DC Optimal Power Flow problem is to be solved for a 3-bus network. The per-unit reactances of the lines interconnecting the buses are as follows: X12 = 0.25 pu, X13 = 0.15 pu and X23 = 0.2 pu. There is a generator at each bus. The loads at buses 1, 2 and 3 are 125 MW, 300 MW and 100 MW respectively. Bus 1 is taken as the reference bus, and SBase = 100 MVA. Which one of the below is NOT a constraint of the DCOPF problem? Select one: Oa. -400 02 - 666.67 03 = P1 - 125 O b. None of these O c. -500 02 - 1166.67 03 = P3 - 100 O d. 900 02 - 500 03 = P2 - 300
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- Equipment ratings for the five-bus power system shown in Figure 7.15 are as follows: Generator G1:    50 MVA, 12kV, X=0.2 per unit Generator G2: 100 MVA, 15 kV, X=0.2 per unit Transformer T1: 50 MVA, 10 kV Y/138kVY,X=0.10 per unit Transformer T2: 100 MVA, 15 kV /138kVY,X=0.10 per unit Each 138-kV line: X1=40 A three-phase short circuit occurs at bus 5, where the prefault voltage is 15 kV. Prefault load current is neglected. (a) Draw the positive-sequence reactance diagram in unit on a 100-MVA, 15-kV base in the zone of generator G2. Determine (b) the ThĂ©venin equivalent at the fault, (c) the subtransient fault current in per unit and in kA rms, and (d) contributions to the fault from generator G2 and from transformer T2.With the same transformer banks as in Problem 3.47, Figure 3.41 shows the oneline diagram of a generator, a step-up transformer bank, a transmission line, a stepown transformer bank, and an impedan load. The generator terminal voltage is 15 kV (line-to-line). (a) Draw the per-phase equivalent circuit, aounting for phase shifts for positive-sequence operation. (b) By choosing the line-to-neutral generator terminal voltage as the reference, determine the magnitudes of the generator current, transmiss ion-line current, load current, and line-to-line load voltage. Also, find the three-phase complex power delivered to the load.A DC Optimal Power Flow problem is to be solved for a 3-bus network. The per-unit reactances of the lines interconnecting the buses are as follows: X12 = 0.1pu, X13 = 0.12 pu and X23 = 0.2 pu. There is a generator at each bus. The loads at buses 1, 2 and 3 are 150MW, 200mw, and 100MWrespectively. Bus 1 is taken as the reference bus, and SBase = 100 MVA. Which one of the below is a constraint of the DCOPF problem? Select one: O a. None of these O b. -500 0₂-1000 03 = P3 - 110 O c. 1500 0₂-500 03 = P₂ - 220 O d. 1500 0₂-500 03 = P₂ - 200 O e. -500 0₂-1000 03 = P3 - 150 O f. -1500 8₁-1000 03 = P₁ - 150
- A network consisting of a set of generator and load buses is to be modeled with a DC power flow, for the sake of conducting a contingency analysis. The initial flows calculated with the DC power flow give the following information: f°2-4 = - 65.3 MW and fº4-5 = 13.6 MW. The following values of LODF and PTDF factors are given: PTDF54,2-4 = -0.2609, LODF2-4,4-5 = -0.6087. Calculate the contingency flow on line 2-4 due to outage of line 4-5. Select one: O a. -75.5MW O b. None of these O c. -68.85MW O d. -73.58MW O e. 75.5MW O f. -61.75MWQ2. Figure Q2 shows the single-line diagram. The scheduled loads at buses 2 and 3 are as marked on the diagram. Line impedances are marked in per unit on 100 MVA base and the line charging susceptances are neglected. a) Using Gauss-Seidel Method, determine the phasor values of the voltage at load bus 2 and 3 according to second iteration results. b) Find slack bus real and reactive power according to second iteration results. c) Determine line flows and line losses according to second iteration results. d) Construct a power flow according to second iteration results. Slack Bus = 1.04.20° 0.025+j0.045 0.015+j0.035 0.012+j0,03 3 |2 134.8 MW 251.9 MW 42.5 MVAR 108.6 MVARFollowing figure shows the one-line diagram of a two bus system. Take bus 1 as slack bus, bus 2 as load (PQ) bus. Neglect the shunt charging admittance. Obtain the bus admittance matrixYBUs and find V₂ and 62, power flows and line losses using FDLF method. All the values are given in per unit on 100MVA base. Use a tolerance of 0.001 for power mismatch. 1 Z12= 0.12+10.16 Slack bus V₁ 1.0/0⁰ pu 2 PL2=1.0pu Q12=0.5pu
- The figure below shows the one-line diagram of a four- bus power system. The voltages, the scheduled real power and reactive powers, and the reactances of transmission lines are marked at this one line diagram (The voltages and reactances are in PU referred to 100 MW base. The active power P2 in MW is the last three digits (from right) of your registration number (i.e for the student that has a registration number 202112396, P2 =396). [10] Starting from an estimated voltage at bus 2, bus 3, and bus 4 equals V2 (0) = 1.15<0°, V3 = 1.15 < 0°, V4 1.1< 0°. 1- Specify the type of each bus and known & unknown quantities at each bus. 2- Find the elements of the second row of the admittance matrix (i.e. [Y21 Y22 Y23 Y24]). 3- Using Gauss-Siedal fınd the voltage at bus 2 after the first iteration. 4- Using Newton-Raphson, calculate: |- The value of real power (P2), at bus 2 after the first iteration. Il- The second element in the first row of the Jacobian matrix after the first iteration. 2 P2…1. FIGURE 52 shows the one-line diagram of a simple three-bus power system with generation at bus I. The voltage at bus l is V1 = 1.0L0° per unit. The scheduled loads on buses 2 and 3 are marked on the diagram. Line impedances are marked in per unit on a 100 MVA base. For the purpose of hand calculations, line resistances and line charging susceptances are neglected a) Using Gauss-Seidel method and initial estimates of Va 0)-1.0+)0 and V o)- ( 1.0 +j0, determine V2 and V3. Perform two iterations (b) If after several iterations the bus voltages converge to V20.90-j0.10 pu 0.95-70.05 pu determine the line flows and line losses and the slack bus real and reactive power. 2 400 MW 320 Mvar Slack 0.0125 0.05 300 MW 270 Mvar FIGURE 52A DC Optimal Power Flow problem consists of a 3-bus network. The per-unit reactances of the lines interconnecting the buses are as follows: X₁2 = 0.35 pu, X₁3 = 0.25 pu and X23 = 0.1 pu. Bus 2 is taken as the reference bus, and SBase = 125 MVA. The power flow limit on transmission line 2-3 is 500 MW. Which one of the below is the constraint that needs be incorporated in the DCOPF problem to account for line 2-3 transmission capacity limit? Select one: O a. 03 -0.6 rad O b. 03 = -0.4 rad О с. 500 (0₁.03) 500 O d. 03 -0.5 rad О е. ņ 1000 (0₂.03) = 500 Of. None of these 27 201
- The one-line diagram of a simple power system is shown in Figure below. The neutral of each generator is grounded through a current-limiting reactor of 0.25/3 per unit on a 100-MVA base. The system data expressed in per unit on a common 100-MVA base is tabulated below. The generators are running on no-load at their rated voltage and rated frequency with their emfs in phase. G Stark Item Base MVA Voltage Rating X' x² 20 kV 20 kV 20/220 kV 20/220 kV 100 0.05 0.15 0.15 0.10 0.10 220 kV 0.125 0.125 0.30 0.15 0.25 025 0.7125 0.15 100 100 0.15 0.05 0.10 0.10 0.10 100 0.10 100 100 Lu La 220 kV 0.15 220 kV 0.35 100 A balanced three-phase fault at bus 3 through a fault impedance Zf= jo.I per unit. The magnitude of the fault current in amperes in phase b for this fault is: Select one: A. 345.3 B. 820.1 C. 312500 3888888 产产Problem 2 Two shunt generators A and B operate in parallel and their load characteristics maybe taken as straight lines. The voltage falls from 240V at no load to 200V at200A, while that of B falls from 245V at no load to 220V at 150A. Determine the bus bar voltage when supplying 66.9KW load. How is the load divided between two generators?Q2) The bus-bar (A) and (B) are linked by a bus-bar reactor of 1000 KVA with 10% reactance on bus-bar (A). The system has 2 generators each one of 5000 KVA with 5 % reactance, and on bus-bar (B) two motors each one of 5000 KVA with 12% reactance. Find the steady state apparent power (MVA) given to the symmetrical short circuit occurred on bus-bar (B) in the circuit shown below. Ма Mi B Gi A G₂ Xr m