6.6. In the power system network shown in Figure 6.5, bus 1 is a slack bus wi V = 1.020° per unit and bus 2 is a load bus with S2 = 280 MW + j60 Mvar. TI line impedance on a base of 100 MVA is Z = 0.02 + j0.04 per unit. (a) Using Gauss-Seidel method, determine Va. Use an initial estimate of V 1.0 + j0.0 and perform four iterations. (b) If after several iterations voltage at bus 2 converges to V, = 0.90 j0.1 determine S, and the real and reactive power loss in the line. %3D Z12 0.02+ j0.04 2 1 S2 = 280 MW +j60 Mvar

6.6. In the power system network shown in Figure 6.5, bus 1 is a slack bus wi V = 1.020° per unit and bus 2 is a load bus with S2 = 280 MW + j60 Mvar. TI line impedance on a base of 100 MVA is Z = 0.02 + j0.04 per unit. (a) Using Gauss-Seidel method, determine Va. Use an initial estimate of V 1.0 + j0.0 and perform four iterations. (b) If after several iterations voltage at bus 2 converges to V, = 0.90 j0.1 determine S, and the real and reactive power loss in the line. %3D Z12 0.02+ j0.04 2 1 S2 = 280 MW +j60 Mvar

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.72P

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following figure shows the one-line diagram of a power system. Bus 1 is selected as a reference bus (slack bus), and bus 2 is load bus. Using the Gauss-Seidel method, determine the value of the voltage at the load bus 2 and perform two iteration. Moreover determine the complex power flow at bus 1 and also active and reactive power in transmission line. The line impedance on a base of 100 MVA. Use an initial estimate of V,º = 1+ j(0) . S1 Z12 = 0.02 + j0.04 2 S2 = 280 MW +j60 Mvar
6.11. In the two-bus system shown in Figure 6.24, bus 1 is a slack bus with V₁ = 1.020° pu. A load of 100 MW and 50 Mvar is taken from bus 2. The line impedance is z12 = 0.12 + j0.16 pu on a base of 100 MVA. Using Newton- Raphson method, obtain the voltage magnitude and phase angle of bus 2. Start with an initial estimate of |V₂|(0) = 1.0 pu and 8₂ (0) two iterations. 0°. Perform 2 *12 = 0 12 + j0.16 Note 100 MW -+-) 50 Myar Perform Second iteration I have problem while solving it 어 V = 1.040° FIGURE 6.24 One-line diagram for Problem 6.11.. U(¹) = 0.8 Pu ops 62 = -1.0 radion
6.11. In the two-bus system shown in Figure 6.24, bus 1 is a slack bus with V₁ = 1.040° pu. A load of 100 MW and 50 Mvar is taken from bus 2. The line impedance is z12 = 0.12 + j0.16 pu on a base of 100 MVA. Using Newton- Raphson method, obtain the voltage magnitude and phase angle of bus 2. Start with an initial estimate of |V₂|(0) 1.0 = 0°. Perform and 62 (0) pu two iterations. 2 100 MW 212 = 0 12 + j0.16 -|- 50 Mvar ot V₁ = 1.040° FIGURE 6.24
6.11. In the two-bus system shown in Figure 6.24, bus 1 is a slack bus with V₁ = 1.020° pu. A load of 100 MW and 50 Mvar is taken from bus 2. The line impedance is 212 0.12 + j0.16 pu on a base of 100 MVA. Using Newton- Raphson method, obtain the voltage magnitude and phase angle of bus 2. Start with an initial estimate of |V₂|(0) 1.0 pu and 5₂ (0) two iterations. 0°. Perform Note 212 0.12 + 30.16 +100 MW nghiệm 50 Mvar Perform Second iteration I have problem Y, while solving it 어 V₁ = 1.040° FIGURE 6.24 One-line diagram for Problem 6.11. V(i) = 0.8 Pu 62") = -1.0 radion
In the power system network shown in Figurebelowbus 1 is a slack bus with V = 1.020° per unit and bus 2 is a load bus with S2 300 MW + 80 Mvar. The line impedance on a base of 100 MVA is Z = 0.01 + j0.02 per %3D unit. (a) Using Gauss-Seidel method, determine V. Use an initial estimate of = 1.0 + j0.0 and perform two iterations. i.e.Deternine(a)V2 and (b)V½? Z12 = 0.01+ j0.0 2 2 S2 300 MW+80 Mvar (a) 0.954 - j0.052 (b) 0.949 - j0.0517 (a) 0.914 - j0.0152 (b) 0.949 - j0.0517 (a) 0.945 - j0.025 (b) 0.994- j0.0571 (a) 0.965 - j0.0255 (b) 0.914 - j0.0529
Q2. 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 MVAR
6.1. A power system network is shown in Figure 47. The generators at buses 1 and 2 are represented by their equivalent current sources with their reactances in per unit on a 100-MVA base. The lines are represented by n model where series reactances and shunt reactances are also expressed in per unit on a 100 MVA base. The loads at buses 3 and 4 are expressed in MW and Mvar. (a) Assuming a voltage magnitude of 1.0 per unit at buses 3 and 4, convert the loads to per unit impedances. Convert network impedances to admittances and obtain the bus admittance matrix by inspection. j0.25 50.25 -j4 j0.4 j0.1 j0.16 j0.2 -j4+3 4 S3 -j4 S4 FIGURE 47 One-line diagram for Problem 6.1. 100 MW +j25 Mvar 200 MW +j50 Mvar
Q4(b) The equivalent circuit of a single phase short transmission line is shown in Figure Q4(b). Here, the total line resistance and inductance are shown as lumped instead of being distributed. i) Sketch the phasor diagram and assess with by labeling the details for the A.C. series circuit shown in Figure Q4(b) for the lagging power factor at load point (Vn). ii) Summarize, what if the load change from low value to high value shown in Figure Q4(b). R XL el Vs Vn Figure Q4(b) Load
A loss less TiL with characteristic impedance of to is terminated in Zr=3Z0. use crank diagram to sketch the voltage versus distance from the load, (Assume vst = 1 volt). @ Repeat the above How for Zv=Zo/3-
6.32 For a two-bus power system, a 0.7 + j0.4 per unit load at bus 2 is supplied by a generator at bus 1 through a transmission line with series impedance of 0.05 + j0.1 per unit. With bus 1 as the slack bus with a fixed per-unit voltage of 1.0/0, use the Gauss-Seidel method to calculate the voltage at bus 2 after three iterations.
How do we handle a PV bus in the Gauss Seidel Method? What will happen to the bus voltage if the reactive power at a PV bus exceeds the upper bound? And why?
The equivalent circuit of a single phase short transmission line is shown in Figure Q4 (b). Here, the total line resistance and inductance are shown as lumped instead of being distributed. i) Sketch the phasor diagram and assess with by labeling the details for the A.C. series circuit shown in Figure Q4 (b) for the lagging power factor at load point (Vn). ii) Summarize, the impact of voltage regulation and efficiency, if the line resistance and line increases are doubled Figure Q4(b). R XL Vs Vn Figure Q4(b) Load