Problem 2 Consider a single-machine infinite-bus (SMIB). The phasor voltage at the infinite bus and the internal generator node are denote by E20 and VZ8, respectively (E and V are constant). XL is the line reactance. The mechanical power input into the machine is denoted by p(t), while the frequency w(t) d8(t)/dt denotes the rate of change of the phase angle 8(t). The SMIB dynamics is EZO given by: = VZ8 oÏÏ ooo XL G $(t) = w(t) w(t)=2w (t) + p(t) - (EV/XL) 8(t) Assume zero initial conditions, i.e., 8(0) = 0, w(0) = 0, and V = E = 1, XL = 0.1. a) In transient stability analysis, one needs to closely monitor and control the phase angle 8(t) of the plant, with the help of the mechanical power input p(t). From the above dynamics equations, using p(t) as input and 8(t) as output, show that the input-output transfer function is: H(s) = 1 A(s) P(s) s² + 2s + 10 = where A(s) and P(s) denote, respectively, the Laplace transforms of 8(t) and p(t). b) Assume a unit step input, i.e., p(t) = u(t). Use inverse Laplace transform (and partial fractions expansion) to compute 8(t) (in time-domain). Hint: You may find the above tip useful.

Problem 2 Consider a single-machine infinite-bus (SMIB). The phasor voltage at the infinite bus and the internal generator node are denote by E20 and VZ8, respectively (E and V are constant). XL is the line reactance. The mechanical power input into the machine is denoted by p(t), while the frequency w(t) d8(t)/dt denotes the rate of change of the phase angle 8(t). The SMIB dynamics is EZO given by: = VZ8 oÏÏ ooo XL G $(t) = w(t) w(t)=2w (t) + p(t) - (EV/XL) 8(t) Assume zero initial conditions, i.e., 8(0) = 0, w(0) = 0, and V = E = 1, XL = 0.1. a) In transient stability analysis, one needs to closely monitor and control the phase angle 8(t) of the plant, with the help of the mechanical power input p(t). From the above dynamics equations, using p(t) as input and 8(t) as output, show that the input-output transfer function is: H(s) = 1 A(s) P(s) s² + 2s + 10 = where A(s) and P(s) denote, respectively, the Laplace transforms of 8(t) and p(t). b) Assume a unit step input, i.e., p(t) = u(t). Use inverse Laplace transform (and partial fractions expansion) to compute 8(t) (in time-domain). Hint: You may find the above tip useful.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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