Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN: 9781305632134
Author: J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher: Cengage Learning
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Chapter 6, Problem 6.37P
To determine
The value of
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The symmetrical components the value of(1+a^2+a^2)
Q1
A three bus system has the following bus power and voltage specifications:
Bus
Real
Reactive
Generated Generated
Voltage
Bus type
Power
Power
Real
Reactive
(p.u.)
Demand
Demand
Power
Power
(p.u.)
(p.u.)
(p.u.)
(р.и.)
0.4
0.25
unspecified unspecified
1.05 + j0.0
Slack
1.5
0.9
unspecified
P-Q
3
1
unspecified
1.02
Р-V
(magnitude)
Angle unspecified
The Ybus matrix is shown as follows:
[542-68° 22Z116°
Y = 22/116°
312108°
582-63° 33Z107° p.u.
bus
312108°
33/107° 672-67°
(a)Determine the voltages at bus 2 and bus 3 after first iterations using Gauss Seidel. Use flat
start voltage.
(b) If the final value of voltage at buses 2 and 3 are 12-5.13° p.u. and 1.02Z-8.32° p.u.
respectively, calculate the following;
(i) Real and reactive power generated at bus 1
(ii) Power losses in branch (2-3)
1.
2.
Find the bus admittance matrix for the following power system
network.
Z-0.3+j0.5
Zı=0.6+j4
Z-0.4+j0.3
Slack
Z13=6.5+j7
Z3=8.5+j9
PQ bus
3
Z-0.5+j0.4
Chapter 6 Solutions
Power System Analysis and Design (MindTap Course List)
Ch. 6 - For a set of linear algebraic equations in matrix...Ch. 6 - For an NN square matrix A, in (N1) steps, the...Ch. 6 - Prob. 6.9MCQCh. 6 - Prob. 6.11MCQCh. 6 - Using Gauss elimination, solve the following...Ch. 6 - Prob. 6.9PCh. 6 - Determine the bus admittance matrix (Ybus) for the...Ch. 6 - Prob. 6.34PCh. 6 - Prob. 6.37PCh. 6 - Prob. 6.38P
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- Determine the bus admittance matrix (Ybus) for the three-phase power system shown in Figure 6.23 with input data given in Table 6.11 and partial results in Table 6.12. Assume a three-phase 100 MVA per unit base. TABLE 6.11 Bus input data for Problem 6.20 TABLE 6.12 Partially Completed Bus Admittance Matrix (Ybus) for Problem 6.30arrow_forwardThe units of admittance, conductance, and susceptance are siemens. (a) True (b) Falsearrow_forward2. For the 3-bus network shown in figure, the impedances indicated are in per unit. a) Draw pu admittance diagram and obtain the bus admittance matrix Ybus for the network. b) Find the source voltages Eai and Ecz so that buses 1 and 2 have the voltages V = 120°, V2 = 1.05490° X= 0.20 pu X = 0.20 pu X= 0.36 pu Xo = 0.36 pu Xo 0.15 pu X p= 0.36 pu X- 0.36 pu X - 0.3 pu Load %3Darrow_forward
- 3. The incremental cost function for generation units in a power system presented below. Write matrix equation for first iteration in second order gradient method. (IC) = 4.7 +0,007 P (IC)₂ = 4.2+0.004 P₁₂ (IC)₂ = 5.1 +0.012 P (IC) = 3.8+0.015₁ Consider unit 2 as P₁ = 300 MW dependent unit and initial = 200 MW P=250 MW guess as P₁ =100 MWarrow_forwardQ3) in pu Consider 4-bus 5 line Power System shown below. All indicated values are admittances Y12 =2-j6 Y13 =1-j3 Y23 =0.666-j2 Y24 =1-j3 Y34 =2-j6 Y4 =j0.2: a. Develop the Y-bus matrix (i.e., the admittance matrix).arrow_forwardDraw the single line diagram and determine the Y bus matrix for the given data. All admittances are given in pu. Bus Line Admittance in PU From To 1 2 -j1.0 3 -j2.5 4 -j5 3 4 -j5 3. -j1.25arrow_forward
- The order of the matrix increases during the formulation of Z bus , when a new branch is added between the existing bus and new bus True Falsearrow_forwardQuestion 7 1 point In which of the following matrix construction or building will consume more time ? Why of Justify ? (i) Z bus Matrix (ii) Y bus Matrixarrow_forwardA three bus system has the following bus power and voltage specifications: Bus Real Reactive Generated Generated Voltage Bus type Power Power Real Reactive (р.u.) Demand Demand Power Power (р.и.) (р.u.) (р.и.) (р.u.) 1 0.4 0.25 unspecified unspecified 1.05 + j0.0 Slack 1.5 0.9 unspecified P-Q 3 1 unspecified 1.02 P-V (magnitude) Angle unspecified The Ybus matrix is shown as follows: [542-68° 22Z116° 312108° 222116° 582-63° 33Z107° p.u. 31Z108° 33/107° 672-67° ] (a)Determine the voltages at bus 2 and bus 3 after first iterations using Gauss Seidel. Use flat start voltage. (b) If the final value of voltage at buses 2 and 3 are 12-5.13° p.u. and 1.022-8.32° p.u. respectively, calculate the following; (i) Real and reactive power generated at bus 1 (ii) Power losses in branch (2-3) 2.arrow_forward
- Write a matrix equation that determines the loop currents. 39 V 2023 29 V+ ≤452 4 32 m 3652, 24 V 11 V 492 For each matrix, let row 1 correspond to loop 1, row 2 correspond to loop 2, and so on. Also, enter positive values for positive voltages and negative values for negative voltages.arrow_forwardIn a 3-bus system that consists of one generator (slack) bus and two PQ (load) busses, the data were obtained: Bus 3 Bus 2 Load 0.9471L-2.13 pu 1.2 pu 0.5 pu Bus 1 Load 0.9857L-3.61• pu 0.9 pu Slack Туре Voltage Real power Reactive Power 1 L0o pu P1 Q1 0.3 If the lines are purely resistive and have the following resistances: R12 = 1 pu, R13 0.75 pu and R23 0.6 pu Find the following: 1) The values of Pi and Q1. 2) The bus admittance matrix of the system.arrow_forwardQuestion 2 Draw the per-unit reactance diagram for the system shown below. Transformers 1 and 3 are identical. Transformers 2 and 4 are identical too. 1) Choose a base of 11 KV, 100 MVA in the generator side. Calculate the current in each transmission line. I 2) Choose a base of 11 KV, 100 MVA in the Motor side. Calculate the current in each transmission line. j25 || kv 100 MVA 9% F उही T₁ T Bet 11.5/115 kv бо MVA 8% ى وال T₁=T and te T₂ Tu +38 11516-640 70 M/A 10% T₂ =T4 6.6 kv 80 MVA 18%arrow_forward
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