Power System Analysis & Design
6th Edition
ISBN: 9781305636187
Author: Glover, J. Duncan, Overbye, Thomas J. (thomas Jeffrey), Sarma, Mulukutla S.
Publisher: Cengage Learning,
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Chapter 4, Problem 4.23MCQ
For a completely transposed three-phase line identical conductors, each with GMR denoted
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Consider the system
dx
ax+u.
dt
Compute the exponential response of the system and use this to derive the transfer
function from u to x. Show that when s = a, a pole of the transfer function, the
response to the exponential input u(t) = est is x(t) = eat x(0) + teat.
For solving the system with u = eat
eat you can't use the
transfer function because the denominator is zero. Try
using the convolution integral solution with initial
conditions set as x(t) =
eat x (0) + fo g(t − T)u(T)dT
-
g(t) is the impulse response of the system.
dny
dn-1y
dn-1u
dn-24
+a1
+
+ Any
=
bi
+b₂-
+ +bnu.
dtn
dtn-1
dtn-1
dtn-2
a) Let be a root of the characteristic equation
1
sn+a1sn-
+
+an
= : 0.
Show that if u(t) = 0, the differential equation has the solution y(t) = e\t.
b) Let к be a zero of the polynomial
b(s) = b₁s-1+b2sn−2+
Show that if the input is u(t)
equation that is identically zero.
=
..
+bn.
ekt, then there is a solution to the differential
dny
dn-1y
dn-1u
dn-24
+a1
+
+ Any
=
bi
+b₂-
+ +bnu.
dtn
dtn-1
dtn-1
dtn-2
a) Let be a root of the characteristic equation
1
sn+a1sn-
+
+an
= : 0.
Show that if u(t) = 0, the differential equation has the solution y(t) = e\t.
b) Let к be a zero of the polynomial
b(s) = b₁s-1+b2sn−2+
Show that if the input is u(t)
equation that is identically zero.
=
..
+bn.
ekt, then there is a solution to the differential
Chapter 4 Solutions
Power System Analysis & Design
Ch. 4 - ACSR stands for Aluminum-clad steel conductor...Ch. 4 - Overhead transmission-line conductors are bare...Ch. 4 - Alumoweld is an aluminum-clad steel conductor....Ch. 4 - EHV lines often have more than one conductor per...Ch. 4 - Shield wires located above the phase conductors...Ch. 4 - Conductor spacings, types, and sizes do have an...Ch. 4 - A circle with diameter Din.=1000Dmil=dmil has an...Ch. 4 - An ac resistance is higher than a dc resistance....Ch. 4 - Prob. 4.9MCQCh. 4 - Transmission line conductance is usually neglected...
Ch. 4 - Prob. 4.11MCQCh. 4 - Prob. 4.12MCQCh. 4 - For a single-phase, two-wire line consisting of...Ch. 4 - For a three-phase three-wire line consisting of...Ch. 4 - For a balanced three-phase positive-sequence...Ch. 4 - A stranded conductor is an example of a composite...Ch. 4 - lnAk=lnAk True FalseCh. 4 - Prob. 4.18MCQCh. 4 - Expand 6k=13m=12Dkm.Ch. 4 - Prob. 4.20MCQCh. 4 - For a single-phase two-conductor line with...Ch. 4 - In a three-phase line, in order to avoid unequal...Ch. 4 - For a completely transposed three-phase line...Ch. 4 - Prob. 4.24MCQCh. 4 - Does bundling reduce the series reactance of the...Ch. 4 - Does r=e14r=0.788r, which comes in calculation of...Ch. 4 - In terms of line-to-line capacitance, the...Ch. 4 - For either single-phase two-wire line or balanced...Ch. 4 - Prob. 4.29MCQCh. 4 - Prob. 4.30MCQCh. 4 - Prob. 4.31MCQCh. 4 - Prob. 4.32MCQCh. 4 - Prob. 4.33MCQCh. 4 - Prob. 4.34MCQCh. 4 - The affect of the earth plane is to slightly...Ch. 4 - When the electric field strength at a conductor...Ch. 4 - Prob. 4.37MCQCh. 4 - Prob. 4.38MCQCh. 4 - Considering two parallel three-phase circuits that...Ch. 4 - The Aluminum Electrical Conductor Handbook lists a...Ch. 4 - The temperature dependence of resistance is also...Ch. 4 - A transmission-line cable with a length of 2 km...Ch. 4 - One thousand circular mils or 1 kcmil is sometimes...Ch. 4 - A 60-Hz, 765-kV, three-phase overhead transmission...Ch. 4 - A three-phase overhead transmission line is...Ch. 4 - If the per-phase line loss in a 70-km-long...Ch. 4 - A 60-Hz, single-phase two-wire overhead line has...Ch. 4 - Prob. 4.9PCh. 4 - A 60-Hz, three-phase three-wire overhead line has...Ch. 4 - Prob. 4.11PCh. 4 - Find the inductive reactance per mile of a...Ch. 4 - A single-phase overhead transmission line consists...Ch. 4 - Prob. 4.14PCh. 4 - Find the GMR of a stranded conductor consisting of...Ch. 4 - Prob. 4.16PCh. 4 - Determine the GMR of each of the unconventional...Ch. 4 - A 230-kV, 60-Hz, three-phase completely transposed...Ch. 4 - Prob. 4.19PCh. 4 - Calculate the inductive reactance in /km of a...Ch. 4 - Rework Problem 4.20 if the bundled line has (a)...Ch. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - For the overhead line of configuration shown in...Ch. 4 - Prob. 4.26PCh. 4 - Figure 4.34 shows double-circuit conductors'...Ch. 4 - For the case of double-circuit, bundle-conductor...Ch. 4 - Prob. 4.29PCh. 4 - Figure 4.37 shows the conductor configuration of a...Ch. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - Prob. 4.34PCh. 4 - Prob. 4.35PCh. 4 - Prob. 4.36PCh. 4 - Prob. 4.38PCh. 4 - Calculate the capacitance-to-neutral in F/m and...Ch. 4 - Prob. 4.40PCh. 4 - Prob. 4.41PCh. 4 - Prob. 4.42PCh. 4 - Three ACSR Drake conductors are used for a...Ch. 4 - Consider the line of Problem 4.25. Calculate the...Ch. 4 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - The capacitance of a single-circuit, three-phase...Ch. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Approximately how many physical transmission...Ch. 4 - Prob. BCSQCh. 4 - Prob. CCSQCh. 4 - Prob. DCSQ
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- For step a), use equations (2) to find the equation for the input impedance equations (2) are V1 = jwL1I1 + jwMI2 and V2 = jwMI1 + jwL2I2 equation for the input impedance: Z1 = V1/I1 = jwL1 + (wM)2/(jwL2 + ZL)arrow_forwardL (a) Find currents i, and b₂ 2 2 (b) Find the dependent source voltage given as Find voltages V, and (c) V₂ 5i2 (d) For each circuit element in the circuit and the two Sources, state whether they are ABSORBING OF SUPPYING Power and how much power is absorbed or Supplied. + V - 5A +lov- C/E₂ + C/E4 Vz い 5+2 + 1A C/E 5V + シュ 2A + 10Varrow_forward4) A circuit is given as shown. (a) Find currents i, and i2. (b) Find the dependent source voltage given as 5i2 (c) Find voltages V, and V₂ 2 (d) For each circuit element in the circuit and the two Sources, State whether they are ABSORBING, OF SUPPLYING POWER and how much power is absorbed or supplied. + 10V - + 4 CIES C/E + V L₁ 4 1A Y T5A GE -5V + CIES iz 2A 2 52 2 +arrow_forward
- Determine the eigenvalues and eigenvectors of using A = ( 1 -3 3 3 -5 3 6-64 Gauss eliminationarrow_forward5) A circuit is given as shown (a) Find currents i₁, L2 and is . (6) Find voltages V, V2, V3 and Vy (c) For each circuit element in the circuit and the two sources, state whether they are ABSORBING SUPPLYING POWER and how much power is absorbed or supplied. + V₁ CIE, 1A +2V- C/E AS 1A + - 4A Vy+ CES CIES 2A4 + IOV +- + + V2 1 434 12V GVarrow_forwardDetermine the eigenvalues and eigenvectors of using Gauss A = -3 322 20 132 -3° 10 -2 4 eliminationarrow_forward
- Can you please help me with this problem?arrow_forwardConsider the following transformer circuit assuming an ideal transformer. In this circuit the signal generator will provide a 10-Volt peak-to-peak sinusoidal signal at a frequency of 1.0 kHz. Assume that L₁ = 0.65 H, L2 = 0.00492 H (=4.92 mH) and that the coupling constant = 0.99925. + VG1( R1 1k N1:N2 11.5:1 12 V1 N1 N2 V2 R2 8.2 1) Find the following using the theory presented in the prelab reading: a) Start with Equations (2) of the prelab reading and show that the input impedance to an ideal transformer is given by the equation for Z1 (=V1/11) in Equations (4) of the prelab reading. Equations (2) are: V₁ = joLI₁ + jœMI₂ and V₂ = j@MI₁ +j@L₂I₂ The equation for the input impedance is: Z₁ = 1½ = jwL₁ + (WM)² jwL₂+ZL b) Assuming that Z is a real impedance, find the equations for the real and imaginary parts of Z1. c) Use your equations from part (b) to calculate the value of the input impedance (Z) at an operating frequency of 200 Hz. Assume that the load impedance is 8.2 Ohms…arrow_forwardUse: R1 = 1.5K, R2 = 5K, R3 = 1K, R4 = 2K, R5 = 2K, R6 = 1K. 40%: Find the value for Vs (in V) such as IR2 = 1mA. 40%: Find the voltage VD. 20%: simulate the circuit in Falstad (attach the link). A 1,5k B R1 Vs L 5k P2 R2 R6 E C R3 С IR2= 1mA D H4 R4 2k 2k R5arrow_forward
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