Example 6.2 Figure 6.5 shows the one-line diagram of a simple four-bus system. Table 6.1 gives the line impedances identified by the buses on which these terminate. The shunt admittance at all the buses is assumed negligible. (a) Find Yaus assuming that the line shown dotted is not connected. (b) What modifications need to be carried out in Yaus if the line shown dotted is connected. Fig. 65 Sample system for Example 6.2 Table 6.1 Line, bus to bus X, pu R, pu 1-2 0.05 0.15 1-3 0.10 0.30 2-3 0.15 0.45 on 0.30 0.15 2-4 0.10 3-4 0.05 Table 6.2 Line G, pu B, pu 1-2 2.0 -6.0 1-3 1.0 -3.0 2-3 0.666 -2.0 2-4 1.0 -3.0 3-4 2.0 -6.0

Example 6.2 Figure 6.5 shows the one-line diagram of a simple four-bus system. Table 6.1 gives the line impedances identified by the buses on which these terminate. The shunt admittance at all the buses is assumed negligible. (a) Find Yaus assuming that the line shown dotted is not connected. (b) What modifications need to be carried out in Yaus if the line shown dotted is connected. Fig. 65 Sample system for Example 6.2 Table 6.1 Line, bus to bus X, pu R, pu 1-2 0.05 0.15 1-3 0.10 0.30 2-3 0.15 0.45 on 0.30 0.15 2-4 0.10 3-4 0.05 Table 6.2 Line G, pu B, pu 1-2 2.0 -6.0 1-3 1.0 -3.0 2-3 0.666 -2.0 2-4 1.0 -3.0 3-4 2.0 -6.0

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 6.36P

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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
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
Figure 6.12 shows the one-line diagram of a simple three-bus power system with generators at buses 1 and 3. The magnitude of voltage at bus 1 is adjusted to 1.05 pu. Voltage magnitude at bus 3 is fixed at 1.04 pu with a real power generation of 200 MW. A load consisting of 400 MW and 250 Mvar is taken from bus 2. Line impedances are marked in per unit on a 100 MVA base, and the line charging susceptances are neglected. Obtain the power flow solution by the Gauss-Seidel method including line flows and line losses. 1 2 0.02 + j0.04 400 MW 0.01 + j0.03 0.0125 + j0.025 250 Mvar Slack Bus 3 V = 1.0520° 200 MW | V3 = 1.04 Figure 6.12
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.
For the system in Figure 4 with given generation and load dispatch determine the voltages after two itterations of Gauss-Seidel method. Assume the initial voltage to be 1.01 at angle of 0◦ pu at bus 1, 1.015 at angle of 0◦ pu at bus 2, and 1.0 at angle of 0◦ pu at bus 3. All line impedances are in per unit on a common base, and charging is neglected. Take base power of 100 MVA.
6.6. In the power system network shown in Figure 6.5, bus 1 is a slack bus with V = 1.020° per unit and bus 2 is a load bus with S2 = 280 MW + j60 Mvar. The 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 j0.10, determine S, and the real and reactive power loss in the line. %3D S1 Z12 0.02+ j0.04 2 1 S2 280 MW +j60 Mvar
6.5. A three phase 50 Hz transmission line has impedance of (25.3 + j66.5) ohms and a shunt admittance of 4.42 x 10 mho per phase. If it delivers a load of 50 MW at 220 kV at 0.8 power factor lagging, determine the sending end voltage (a) by short line approximation (b) nominal II method (c) exact transmission line equations. Ans. (a) 233.8 2.2° kV, (b) 232.2 2.33°, (c) 230.52 2.50° kV,
Problem 6.5: A 1-phase, 36 kVA, 480/120 V transformer has series impedance Z= 5% stated on its nameplate. Determine Z in ohms looking (a) from HV side source when connected as a step-down transformer, and (b) from LV side source when connected as a step-up transformer.
Example 6.1: For the simplified system shown, the generators are connected at all the three buses. In addition, loads are connected at Buses 2 and 3. Values of real and reactive powers are listed on the table provided. All other buses other than the Slack Bus are PQ type. Assuming a Flat Voltage Start, find the bus voltages and its corresponding bus voltage angles at the two other buses at the end of the first iteration. 5- j16 YBUS =|-8 + j2.65 -8 + j2.65 2.8 - j20 -3 + j6.5 -3.33 + j5.2 -3 + j6.5 -3.33 + 5.2 4.5 – j25 Bus Pi, pu Qi, pu Vi, pu Remarks 1 1.0520° Slack Bus 2 0.7 -0.4 PQ Bus 3 -1.2 0.6 PQ Bus
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 52
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