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systems analysis design

Questions and Answers of Systems Analysis Design

The switch in Figure P10-20 has been in position A for a long time and is moved to position \(\mathrm{B}\) at \(t=0\). Transform the circuit into the s domain and solve for \(I_{\mathrm{L}}(s),
The switch in Figure P10-22 has been in position A for a long time and is moved to position \(\mathrm{B}\) at \(t=0\). Transform the circuit into the s domain and solve for \(I_{\mathrm{C}}(s),
The switch in Figure P10-22 has been in position \(\mathrm{B}\) for a long time and is moved to position A at \(t=0\). Transform the circuit into the s domain and solve for \(V_{\mathrm{C}}(s),
Transform the circuit in Figure P10-24 into the \(\mathrm{s}\) domain and find: \(I_{\mathrm{L}}(s)\) and \(I_{\mathrm{L}}(t)\), when \(v_{1}(t)=V_{\mathrm{A}} e^{-1000} t\), \(R=200 \Omega, L=200
The switch in Figure P10-26 has been in position A for a long time and is moved to position \(\mathrm{B}\) at \(t=0\).(a) Transform the circuit into the \(s\) domain and solve for \(I_{\mathrm{L}}\)
The circuit in Figure P10-28 is in the zero state. The network function \(K=V_{\mathrm{O}}(s) / I_{1}(s)\) for the circuit is (a) Select \(R\) and \(C\) so that there is a pole at \(-1000
The initial conditions for the circuit in Figure P10-29. are \(v_{\mathrm{C}}(\mathrm{O})=\mathrm{O}\) and \(i_{\mathrm{L}}(\mathrm{O})=I_{\mathrm{O}}\). Transform the circuit into the \(s\) domain
The initial conditions for the circuit in Figure P10-29. are \(v_{\mathrm{C}}(\mathrm{O})=\mathrm{o}\) and \(i_{\mathrm{L}}(\mathrm{O})=I_{\mathrm{O}}\). Transform the circuit into the \(s\) domain
There is no energy stored in the capacitor in Figure P1032 at \(t=0\). Transform the circuit into the \(s\) domain and use current division to find \(v_{\mathrm{O}}(t)\) when the input is
Repeat Problem 10-32 when \(i_{\mathrm{S}}(t)=10\) sin \(1000 t u(t) \mathrm{mA}\).Data From Problem 10-32There is no energy stored in the capacitor in Figure P1032 at \(t=0\). Transform the circuit
For the circuit of Figure P10-34:(a) Find the Thévenin equivalent circuit that the \(R_{X}\) load resistor sees when \(v_{\mathrm{C}}(\mathrm{o})=V_{\mathrm{O}} \mathrm{V}\).(b) If the output
(a) The circuit in Figure P10-35 is in the zero state. Find the Thévenin equivalent to the left of the interface.(b) A \(0.22-\mu \mathrm{F}\) capacitor is connected across the interface in Figure
Select a value of \(C\) in Figure P10-3 3 so that \(V_{\mathrm{O}}(s) /\) \(V_{\mathrm{S}}(s)\) has a natural pole at \(s=-10 \mathrm{Mrad} / \mathrm{s}\).
Find the required impedance \(Z_{\mathrm{X}}(s)\) that needs to be inserted in series as shown in Figure P10-37. to make the output voltage equal to V(s) = s(s+1000) s + 2000s + 106 V(s)
The equivalent impedance between a pair of terminals is(a) A voltage \(v(t)=20 e^{-1000 t} u(t)\) is applied across the terminals. Find the resulting current response \(i(t)\).(b) Plot the pole-zero
There is no initial energy stored in the circuit in Figure P10-39. Use circuit reduction to find the output network function \(V_{2}(s) / V_{1}(s)\). Then select values of \(R\) and \(C\) so that the
Refer to the dependent-source circuit in Figure \(\underline{\mathrm{P} 10-40}\).(a) Find \(V_{\mathrm{O}}(s)\) in terms of the input and the elements for the zero state.(b) Locate the natural poles
There is no initial energy stored in the circuit in Figure P10-41.(a) Transform the circuit into the \(s\) domain and formulate mesh-current equations.(b) Show that the solution of these equations
There is no initial energy stored in the circuit in Figure P10-41.(a) Transform the circuit into the \(s\) domain and formulate node-voltage equations.(b) Show that the solution of these equations
There is no initial energy stored in the circuit in Figure P10-43 .(a) Transform the circuit into the \(s\) domain and formulate node-voltage equations.(b) Solve these equations for \(V_{2}(s)\) in
There is no initial energy stored in the circuit in Figure P10-43 . The Thévenin equivalent circuit to the left of point A when a unit step is applied isSelect values for \(R_{2}\) and \(C_{2}\)
There is no initial energy stored in the bridged-T circuit in Figure P10-45 .(a) Transform the circuit into the \(s\) domain and formulate node-voltage equations.(b) Use the node-voltage equations to
For the dependent source circuit in Figure P10-4 \(\underline{6}\) write a set of node-voltage equations. But first do a source conversion for the capacitors (they have the same value but different
There is no initial energy stored in the circuit in Figure P10-4.7.(a) Find the zero-state mesh currents \(i_{\mathrm{A}}(t)\) and \(i_{\mathrm{B}}(t)\) when \(v_{1}(t)=25 u(t) \mathrm{V}\).(b) Find
There is no external input in the circuit in Figure P10\(4 \underline{8}\).(a) Find the zero-input node voltages \(v_{\mathrm{A}}(t)\) and \(v_{\mathrm{B}}(t)\), and the voltage across the capacitor
Use mesh-current equations to find the three mesh currents in Figure P10-4.9. Find \(V_{\mathrm{X}}(s)\) and \(I_{\mathrm{X}}(s)\). Repeat the problem using node-voltage analysis. Which analysis
The circuit in Figure P10-50 is in the zero state. Use mesh-current equations to find the circuit determinant. Select values of \(R, L\), and \(C\) so that the circuit has(a) \(\omega_{0}=40
What is the main purpose of conductors bundling in transmission lines?1) Decreasing inductive reactance of transmission line 2) Decreasing resistance of transmission line 3) Decreasing Corona power
Determine the Geometrical Mean Radius (GMR) of the conductors with the arrangements shown in Fig. 3.1. The Geometrical Mean Radius (GMR) of each conductor is \(r^{\prime}\).1) \(r^{\prime}
Which one of the following choices is correct about the effect of bundling of conductors of a transmission line on its inductance, capacitance, and characteristic impedance?1) Decrease, decrease, no
Determine the Geometrical Mean Radius (GMR) of the conductors with the arrangements shown in Fig. 3.2. The Geometrical Mean Radius (GMR) of each conductor is \(r^{\prime}\).1) \(\sqrt[8]{2 r^{6}
Determine the Geometrical Mean Radius (GMR) of the conductors with the arrangements shown in Fig. 3.3.The radius of each conductor is \(r\).1) \(1.722 r\)2) \(1.834 r\)3) \(1.725 r\)4) \(1.532 r\)
Figure 3.4 shows a single-phase transmission line including two conductors (" 1 " and " 3 ") for sending power and one conductor ("2") for receiving power. The Geometrical Mean Radius (GMR) of each
Figure 3.5 shows a single-phase transmission line. Herein, conductor " 1 " is for sending power, and conductors " 2 " and " 3 " are for receiving power. The Geometrical Mean Radius (GMR) of each
What difference can we see in the capacitance of a transmission line if we change the conductor arrangements from the two-bundling to the three-bundling, as can be seen in Fig. 3.6? The Geometrical
Figure 3.7 illustrates two single-phase transmission lines. The Geometrical Mean Radius (GMR) of each conductor is \(r^{\prime}\). In Fig. 3.7 (b), conductors " 2 " and " 3 " are for sending power,
Figure 3.8 shows a single-phase line including two conductors ("2" and " 3 ") for sending and one conductor (" 1 ") for receiving power. The Geometrical Mean Radius (GMR) of each conductor is
Figure 3.9 illustrates two three-phase transmission lines. The Geometrical Mean Radius (GMR) of each conductor is \(r^{\prime}\) and \(r^{\prime}1) \(d=\frac{r^{\prime}}{\sqrt{2}}\).2) \(d=2
Which one of the arrangements of a three-phase transmission line, shown in Fig. 3.10, has the least inductance and the most capacitance? The Geometrical Mean Radius (GMR) of each conductor is
What difference can we see in the inductance of a transmission line if we change the conductor arrangements from the two-bundling to three-bundling, as can be seen in Fig. 3.11? The Geometrical Mean
Which one of the parameters below can be ignored for a short transmission line?1) Resistance 2) Inductance 3) Reactance 4) Capacitance.
Based on Ferranti effect, which one of the following terms is correct?1) The voltage in the receiving end increases when the transmission line is operated in no-load or low-load conditions.2) The
Which one of the matrices below belongs to a transmission matrix of a real transmission line?1) \(\left[\begin{array}{cc}j & 1 \\ 0 & -j\end{array}ight]\)2) \(\left[\begin{array}{ll}1 & j \\ 2 &
Two power systems have the transmission matrices below. If these systems are cascaded, determine their equivalent transmission matrix:\[\left[T_{1}ight]=\left[\begin{array}{cc}1 & j 2 \\0 &
Calculate the characteristic impedance of a long lossless transmission line that has the inductance and capacitance of about \(1 \mathrm{mH} / \mathrm{meter}\) and \(10 \mu \mathrm{F} /
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

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