Example 1: Using gaussian elemination , solve the nodal equation bellow to find the bus voltages. At each step of elimination find the equivalent circuit of the reduced matrix. 2) (3 4. -j16.75 jl1.75 | j2.50 j2.50 jl1.75 --j19.25 j2.50 j5.00 V2 1.00/ - 90° 0.68/ – 135° 3. j2.50 j2.50 -j5.80 0.00 V3 4 j2.50 j5.00 0.00 -j8.30 V4

Example 1: Using gaussian elemination , solve the nodal equation bellow to find the bus voltages. At each step of elimination find the equivalent circuit of the reduced matrix. 2) (3 4. -j16.75 jl1.75 | j2.50 j2.50 jl1.75 --j19.25 j2.50 j5.00 V2 1.00/ - 90° 0.68/ – 135° 3. j2.50 j2.50 -j5.80 0.00 V3 4 j2.50 j5.00 0.00 -j8.30 V4

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 6.2MCQ: For an NN square matrix A, in (N1) steps, the technique of Gauss elimination can transform into an...

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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. -61.75MW
7. In the circuit below write the loop equations and set up (not solve) the matrix equation for the load current. Wiso 150 75 28 100
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
By using Gauss-Siedal method, the voltage of the bus 2 after two iteration is Your answer By using Gauss-Siedal method the voltage of the bus 3 after two iteration is Your answer For a system consist from 3 buses and bus 1 is the slack bus. The data of the system are:- 0.25 -0.2 -0.05 Ybus j -0.2 0.225 -0.025 p.u. -0.05 -0.025 0.075 V₁=1+j0 p.u., P₂+jQ2-0.6+j0.25 p.u., P3+jQ=0.8+j0.5 p.u.
Following 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
Solve numerical : Following 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 δ2, power flows and line losses by using Fast decoupled power flow method. All the values are given in per unit on 100MVA base. Use a tolerance of 0.001 for power mismatch.
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
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…
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
please solve for nodal stress method. (if it is possible to apply supernodes)
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
State True or false a- The DC load flow study is a linear analysis b- In a load frequency control, a generator unit equipped with a governor can be assumed to be a controlled unit.