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systems analysis design

Questions and Answers of Systems Analysis Design

At the end of a transmission line with the characteristic impedance of \(\mathbf{Z}_{\mathbf{C}}=(1-j) \Omega\), a load with the impedance of \(\mathbf{Z}_{\mathbf{L}}=(1+j) \Omega\) has been
As is shown in Fig. 5.1, a medium transmission line has been presented by its \(\mathrm{T}\) model. Calculate the charging current of the line ( \(\mathbf{I}_{\text {Charging). }}\) ).1) Only
Figure 5.2 shows the single-line diagram of a short transmission line. Determine its transmission matrix.1) \(\left[\begin{array}{cc}1+\mathbf{Y Z} & 1 \\ \mathbf{Z} &
Determine the characteristic impedance of a transmission line that the relation below is true for its parameters:\[\frac{R}{L}=\frac{G}{C}\]1) \(\frac{R}{L}\).2) \(\infty\).3) 0 .4) It is equal to
Figure 5.3 shows the single-line diagram of a short transmission line that a resistor with the resistance of \(R\) has been installed in its middle point. Determine its transmission matrix.1)
Calculate the characteristic impedance of a long transmission line that its transmission matrix is as follows:\[[T]=\left[\begin{array}{cc}\frac{1}{2} & j \\\frac{3}{4} j &
Calculate the charging current ( \(\mathbf{I}_{\text {Charging }}\) ) of a long transmission line.1) \(\frac{\mathbf{V}_{\mathrm{s}} \tanh (\gamma l)}{\mathbf{Z}_{\mathrm{c}}}\)2)
In a long transmission line, consider the definitions below, and choose the correct relation between \(\mathbf{Z}_{\mathbf{C}}, \mathbf{Z}_{\text {S.C. }}\), and \(\mathbf{Z}_{\text {O.C. }}\).
In a long transmission line, the impedance measured from the beginning of the line, when its end is open circuit, is the reciprocal of the impedance measured from the beginning of the line, when its
In a no-load and lossless transmission line, which one of the following relations is correct? Herein, \(\mathbf{V}_{\mathbf{R}}, \mathbf{V}_{\mathbf{S}}, \beta, \gamma\), and \(l\) are the voltage of
A factory is supplied by an ideal transformer through a short transmission line. At the bus of the factory, a shunt capacitor has been installed to correct its power factor. Which one of the
For the power system illustrated in Fig. 7.1, determine \(Z_{22}\) of the network impedance matrix ([ \(\left.Z_{\text {Bus }}ight]\) ).1) \(j 0.6 \Omega\)2) \(j 0.06 \Omega\)3) \(j 0.4 \Omega\)4)
The network impedance matrix ( \(\left[\mathrm{Z}_{\mathrm{Bus}}ight]\) ) and the result of load flow simulation problem are presented in the following. If a capacitor with the reactance of \(3.4 p .
In a three-bus power system, the voltage of the second bus is about \(\left(1.2 \angle 0^{\circ}ight) p . u\), and the network impedance matrix is as follows. If an inductor with the reactance of
For the power system shown in Fig. 7.2, determine the network admittance matrix ([ \(\left.\mathrm{Y}_{\text {Bus }}ight]\) ).1) \(j\left[\begin{array}{ccc}-20 & 15 & 15 \\ 15 & -25 &
For the power system shown in Fig. 7.3, determine the network impedance matrix \(\left(\left[Z_{\text {Bus }}ight]ight.\) ).1) \(j\left[\begin{array}{cc}\frac{2}{30} & \frac{1}{30} \\
For the power system shown in Fig. 7.4, determine the detriment of the network impedance matrix ([Z \(\left.\mathrm{Z}_{\text {Bus }}ight]\) ).1) -0.5 2) 0.5 3) -0.2 4) 0.2 jp.u. j0.5 p.u. 0101
For the power system shown in Fig. 7.5, determine the value of \(\frac{Z_{12}}{Z_{22}}\), belonging to \(\left[Z_{\text {Bus }}ight]\), if the base voltage in the transmission line and the base MVA
In a three-bus power system shown in Fig. 7.6, determine the sum of the diagonal components of the network admittance matrix ( \(\left[\mathrm{Y}_{\text {Bus }}ight]\) ).1) \(-j 60\) p. и.2) \(-j 20
The impedance diagram of a three-phase four-bus power system is shown in Fig. 7.7.If the lines of 2-4 and 1-3 are removed from the system, the network admittance matrix can be presented in the form
The network admittance matrix of a four-bus power system is presented in the following. Determine the updated network admittance matrix if the second and the third buses are
The network admittance matrix of a power system is presented in the following. There are two parallel similar lines between the buses. If one of them is disconnected from bus 1 and then grounded,
In a load flow problem, which type of the bus has a known active power?1) Load bus 2) Voltage-controlled bus 3) All buses except slack bus 4) None of them.
To speed up the algorithm of Gauss-Seidel load flow, an accelerating factor \((\alpha)\) is usually used. Which one of the following relations presents that?1) \(\mathbf{V}_{\mathbf{i}, \mathbf{A c
Which one of the following choices is correct about the DC load flow (DCLF), Decoupled Load flow (DLF), and Newton-Raphson load flow (NRLF)?1) DLF is faster than DCLF, and DCLF is faster than NRLF.2)
Use DC load flow to determine the active power flowing through the line. Herein, \(S_{B}=100\) MVA.1) \(32.2 \mathrm{MW}\)2) \(85.6 \mathrm{MW}\)3) \(41.7 \mathrm{MW}\)4) \(65.4 \mathrm{MW}\) 8-25
In the power system, shown in Fig. 9.2, determine \(\delta\). Do not use DC load flow approximation.1) \(60^{\circ}\)2) \(30^{\circ}\)3) \(90^{\circ}\)4) \(0^{\circ}\) V-1/8 p.u. j0.05 p.u. V-1/0
Calculate \(P_{12}\) by using DC load flow. Herein, assume \(\pi \equiv 3\).2) \(2 p . u\).3) \(3 p . u\).4) \(3.5 \mathrm{p} . u\). Vil 30 p.u. j0.3 p.u j0.5 p.u. jo.4 p.u. Val-30 p.u.
Use DC load flow to determine \(P_{G 2}\). Herein, assume \(\pi \equiv 3\).1) 0.2 p.u.2) \(0.25 p . u\).3) \(0.6 \mathrm{p} . u\).4) \(0.75 p \cdot u\). Vil 20 p.u. j0.5 p.u. IVlZ-12 p.u. P-1 p.u.
Determine the inverse matrix of Jacobian matrix considering the following terms:\[\left\{\begin{array}{l}P_{2}=\delta_{2}+3\left|\mathbf{V}_{2}ight| \\Q_{2}=0.1
Use DC load flow to determine the phase angle of bus 4. Herein, assume \(\pi \equiv 3\).1) \(-45^{\circ}\)2) \(-36^{\circ}\)3) \(-30^{\circ}\)4) \(-15^{\circ}\) 2 1 p.u. jo.1 p.u. 3 -1/0 p.u. jo.1
In a power plant, the power loss coefficients for the two power generation units are \(L_{1}=\$ 1.5 / M W, L_{2}=\$ 1.8 / M W\). Calculate the total generation of the units if Lagrange Multiplier
In a power plant, the generation cost functions of the units are as follows:\[\left\{\begin{array}{l}C_{1}=0.0075 P_{G 1}^{2}+50 P_{G 1}+1000 \\C_{2}=0.005 P_{G 2}^{2}+45 P_{G
In a power plant, the generation cost functions of the units are as follows:\[\left\{\begin{array}{c}C_{1}=0.05 P_{G 1}^{2}+50 P_{G 1}+1500 \\C_{2}=0.075 P_{G 2}^{2}+40 P_{G
In a power plant, the generation cost functions of the units are as follows:\[\left\{\begin{array}{l}C_{1}=135 P_{G 1}^{2}+100000 P_{G 1} \\C_{2}=115 P_{G 2}^{2}+85000 P_{G 2}\end{array}ight.\]Solve
The single-line diagram of a power system is shown in Fig. 9.7.The voltage of bus 1 is about \(\left(1 \angle 0^{\circ}ight) p . u\). and \(S_{B}=100\) MVA. Calculate \(\mathbf{V}_{\mathbf{2}}\)
Use Newton-Raphson load flow (NRLF) to determine the voltage of load bus after one iteration.1) \(0.952) \(0.983) \(0.934) \(0.9 V=1/0 p.u. jo.1 p.u. (1 + j0.5) p.u.
What is the phasor representation of the voltage signal of \(\sqrt{2} \cos (t)\) ?1) \(1 \mathrm{~V}\)2) \(\left(1 \angle 90^{\circ}ight) \mathrm{V}\)3) \(0 \mathrm{~V}\)4) \(\left(1
Represent the current signal of \(\sqrt{2} \sin (t)\) in phasor domain.1) \(1 \mathrm{~A}\)2) \(\left(1 \angle 90^{\circ}ight) \mathrm{V}\)3) \(0 \mathrm{~A}\)4) \(\left(1 /-90^{\circ}ight)
Define the signal of \(\cos \left(2 t+30^{\circ}ight)\) in phasor domain.1) \(1 \angle 30^{\circ}\)2) \(2 \angle-30^{\circ}\)3) \(\frac{1}{\sqrt{2}} \angle 0^{\circ}\)4) \(\frac{1}{\sqrt{2}} \angle
Represent the signal of \(10 \sin \left(t-60^{\circ}ight)\) in phasor form.1) \(10 /-150^{\circ}\)2) \(10 /-60^{\circ}\)3) \(5 \sqrt{2} /-150^{\circ}\)4) \(10 / 60^{\circ}\)
In the single-phase power system of Fig. 1.1, the voltage and current are as follows:\[\begin{aligned}v(t) & =110 \cos \left(\omega t+30^{\circ}ight) V \\i(t) & =0.5 \cos \left(\omega
In the single-phase power system of Fig. 1.1, the voltage and current are given as follows:\[\begin{gathered}v(t)=100 \sqrt{2} \cos (t) V \\i(t)=\sqrt{2} \cos \left(t-30^{\circ}ight)
The impedance of a generator, with the rated specifications of \(20 \mathrm{kV}\) and 200 MVA, is \(\mathbf{Z}=j 0.2 p\). \(u\). Determine its reactance in percent if \(21 \mathrm{kV}\) and \(100
The reactance of a generator, with the nominal specifications of \(14 \mathrm{kV}\) and \(500 \mathrm{MVA}\), is \(1.1 p . u\). Determine its impedance in percent if \(20 \mathrm{kV}\) and \(100
In the power bus of Fig. 1.2, determine the \(i_{3}(t)\) if we know that \(i_{1}(t)=10 \cos (10 t) A, i_{2}(t)=10 \sin (10 t) A\), and \(i_{4}(t)=10 \sqrt{2} \cos \left(10 t+45^{\circ}ight) A\).1)
In the single-phase power bus of Fig. 1.3, \(V_{r m s}=200 \mathrm{~V}\) and the equivalent impedance of the loads are \(\mathbf{Z}_{\mathbf{1}}=(8-j 6) \Omega\) and \(\mathbf{Z}_{2}=(3+j 4)
Calculate the instantaneous power of a single-phase power system that its voltage and current are \(v(t)=\) \(110 \sqrt{2} \cos (120 \pi t) V\) and \(i(t)=2 \sqrt{2} \cos \left(120 \pi
In the single-phase power system of Fig. 1.4, calculate the active and reactive powers transferred from bus 1 to bus 2. Consider the following data:\[\mathbf{V}_{\mathbf{1}}=\left(10 \angle
In the power system of Fig. 1.5, \(\mathbf{E}_{\mathbf{1}}=200 \angle-30^{\circ} \mathrm{V}, \mathbf{E}_{2}=200 \angle 0^{\circ} V, \mathbf{Z}=j 5 \Omega\). Which one of the following choices is
In the power bus of Fig. 1.6, the base voltage and power are \(20 \mathrm{kV}\) and \(100 \mathrm{MVA}\), respectively. If a reactor is connected to this bus, determine its reactance in per unit
Figure 1.7 shows the single-line diagram of a power system with the following specifications. Calculate the resistance of the load in per unit (p.u.) if the nominal quantities of the generator are
Figure 1.8 illustrates the single-line diagram of a power system with the given information. Calculate \(P\) and \(Q\) in per unit (p.u.). In this problem, assume that \(\sin \left(15^{\circ}ight)
Calculate the complex power delivered to a factory that includes two loads with the following specifications:\[\begin{gathered}\text { Inductive Load : } P_{1}=60 \mathrm{~kW}, Q_{1}=660
Figure 1.9 shows the single-line diagram of a balanced three-phase power system, in which a synchronous generator has been connected to a no-load transmission line through a transformer.Calculate the
For the three-phase power system of Fig. 1.10, the following specifications have been given. Determine the voltage drop of the line in percent:Line : \(\mathbf{Z}=(10+j 40) \Omega /\) phase Load :
In the power system of Fig. 1.11, calculate the impedance of the load in per unit (p.u.) for the following specifications. In this problem, \(20 \mathrm{kV}\) (in the generator side) and 3 MVA are
In the single-phase power bus of Fig. 1.12, the characteristics of the loads are as follows. Determine the total power factor of the bus:\[\begin{gathered}\text { Load } 1: P_{1}=25 k W, Q_{1}=25 k V
In the single-phase power bus of Fig. 1.13, determine the capacitance of the shunt capacitor that needs to be connected to the bus to adjust its power factor at one for the following
In the single-phase power system of Fig. 1.14, three loads have been connected to the power bus in parallel. Determine the capacitance of the shunt capacitor that needs to be connected to the bus to
In the power system of Fig. 1.15, determine the reactive power of the shunt capacitor to keep the voltage of its bus at 1 p.u. In this problem, assume that \(\cos \left(\sin ^{-1}(0.1)ight) \equiv
In the three-phase power system of Fig. 1.16, two balanced three-phase loads with the star and delta connections have been connected to a three-phase power supply. Calculate the line voltage of the
In the power system of Fig. 1.17, \(\delta=15^{\circ}\). If the value of \(\delta\) increases and \(E_{1}\) and \(E_{2}\) are kept constant, which one of the following choices is correct? In this
Three loads with the following specifications, resulted from the load flow simulation, have been connected to the power bus shown in Fig. 1.18. If all the loads are modeled by an admittance,
At the end of a three-phase power system, \(400 \mathrm{~V}, 50 \mathrm{~Hz}\), three capacitor banks (with triangle configuration) have been connected to the system. Determine the capacitance of
The single-line diagram of a balanced three-phase power system is shown in Fig. 1.19. In this problem \(S_{B}=100 M V A\) and \(V_{B}=22 \mathrm{kV}\) in the first bus. Calculate the impedance seen
In the power system of Fig. 1.20, calculate the current of the load in per unit (p.u.) for the following specifications. In this problem, \(100 \mathrm{~V}\) (in the generator side) and \(1
For a set of linear algebraic equations in matrix format, \(\mathbf{A x}-\mathbf{y}\), for a unique solution to exist, \(\operatorname{det}(\mathbf{A})\) should be ___________.
For an \(N \times N\) square matrix \(\mathbf{A}\), in \((N-1)\) steps, the technique of Gauss elimination can transform into an ___________ matrix.
For the iterative solution to linear algebraic equations \(\mathbf{A x}-\mathbf{y}\), the \(\mathbf{D}\) matrix in the Jacobi method is the Gauss-Siedel is the __________ portion of \(\mathbf{A}\).
Is convergence guaranteed always with Jacobi and Gauss-Siedel methods, as applied to iterative solutions of linear algebraic equations?(a) Yes(b) No
For the iterative solutions to nonlinear algebraic equations with the Newton-Raphson method, the Jacobian matrix \(\mathbf{J}(i)\) consists of the partial derivatives. Write down the elements of
For the Newton-Raphson method to work, one should make sure that \(\mathbf{J}^{-1}\) exists.(a) True(b) False
The Newton-Raphson method in four steps makes use of Gauss elimination and back substitution.(a) True(b) False
The number of iterations required for convergence is dependent/independent of the dimension \(N\) for Newton-Raphson method. Choose one.
The swing bus or slack bus is a reference bus for which \(\mathrm{V}_{1} / \delta_{1}\), typically \(1.0 \angle 0^{\circ}\) per unit, is input data. The power flow program computes __________. Fill
Most buses in a typical power flow program are load buses, for which \(\mathrm{P}_{k}\) and \(\mathrm{Q}_{k}\) are input data. The power flow program computes __________.
For a voltage-controlled bus \(k\), __________ are input data, while the power flow program computes __________.
When the bus \(k\) is a load bus with no generation and inductive load, in terms of generation and load, \(\mathrm{P}_{k}=\) __________, and \(\mathrm{Q}_{k}=\) __________.
Starting from a single-line diagram of a power system, the input data for a power flow problem consists of __________, __________, and __________.
Nodal equations \(\boldsymbol{I}=\boldsymbol{Y}_{\text {bus }} \boldsymbol{V}\) are a set of linear equations analogous to \(\boldsymbol{y}=\boldsymbol{A x}\).(a) True(b) False
Because of the nature of the power flow bus data, nodal equations do not directly fit the linear-equation format, and power flow equations are actually nonlinear. However, the Gauss-Siedel method can
The Newton-Raphson method is most well suited for solving the nonlinear power flow equations.(a) True(b) False
By default, PowerWorld Simulator uses __________ method for the power flow solution.
Prime-mover control of a generator is responsible for a significant change in __________, whereas excitation control significantly changes __________.
From the power flow standpoint, the addition of a shunt-capacitor bank to a load bus corresponds to the addition of a positive/negative reactive load. Choose the right word.
Tap-changing and voltage-magnitude-regulating transformers are used to control bus voltages and reactive power flows on lines to which they are connected.(a) True(b) False
A matrix, which has only a few nonzero elements, is said to be __________.
Sparse-matrix techniques are used in Newton-Raphson power flow programs in order to reduce computer __________ and __________ requirements.
Reordering buses can be an effective sparsity technique in power flow solutions.(a) True(b) False
While the fast decoupled power flow usually takes more iterations to converge, it is usually significantly faster than the Newton-Raphson method.(a) True(b) False
The "dc" power flow solution, giving approximate answers, is based on completely neglecting the \(\mathrm{Q}-\mathrm{V}\) equation and solving the linear real-power balance equations.(a) True(b) False
Using Gauss elimination, solve the following linear algebraic equations:\[\begin{aligned}-25 x_{1}+10 x_{2}+10 x_{3}+10 x_{4} & =0 \\5 x_{1}-10 x_{2}+10 x_{3} & =2 \\10 x_{1}+5 x_{2}-10 x_{3}+10
Using Gauss elimination and back substitution, solve 8 2 1 4 6 2 3 4 14 X X 3 4 2
Rework Problem 6.2 with the value of 8 changed to 4.Problem 6.2Using Gauss elimination and back substitution, solve 8 2 1 4 6 2 3 4 14 X X 3 4 2
What is the difficulty in applying Gauss elimination to the following linear algebraic equations?\[\begin{aligned}-5 x_{1}+5 x_{2} & =5 \\10 x_{1}-10 x_{2} & =-5\end{aligned}\]
Show that, after triangularizing \(\mathbf{A x}=\mathbf{y}\), the back substitution method of solving \(\mathbf{A}^{(N-1)} \mathbf{x}=\mathbf{y}^{(N-1)}\) requires \(N\) divisions, \(N(N-1) / 2\)
Solve Problem 6.2 using the Jacobi iterative method. Start with \(x_{1}(0)=\) \(x_{2}(0)=x_{3}(0)=0\), and continue until (6.2.2) is satisfied with \(\varepsilon=0.01\).Eq (6.2.2)Problem 6.2Using
Repeat Problem 6.6 using the Gauss-Seidel iterative method. Which method converges more rapidly?Problem 6.6Using the Jacobi iterative method. Start with \(x_{1}(0)=\) \(x_{2}(0)=x_{3}(0)=0\), and
Express the following set of equations in the form of (6.2.6), and then solve using the Jacobi iterative method with \(\varepsilon=0.05\) and with \(x_{1}(0)=1\), and \(x_{2}(0)=1, x_{3}(0)=0\).Eq

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