Power Systems Analysis - Homework 2
1. Given a transmission line, we perform two tests and obtain the following results:
Open-circuit test (I2 = 0):
Zoc =
V1
= 8006 89
I1
(1)
V1
= 2006 77
I1
(2)
Short-circuit test (V2 = 0):
Zsc =
Find the characteristic i

Power Systems Analysis - Homework 1
1. Consider the circuit:
(a) Write a second-order differential equation describing i(t).
(b) Explain why i(t) can be written as the sum of a vanishing term and and a sinusoidal term.
(c) Find i(t) for R = L = C = 1.
2.

Power Systems Analysis - Homework 5
1. Consider a synchronous generator described by the swing equation:
+ D(t)
+ Pe (t) = Pm
M (t)
where the mechanical power Pm is fixed and the electrical power Pe (t) is given as
Pe (t) = a sin (t) + b sin (2(t) .
(a)

Power Systems Analysis - Homework 3
1. Given symmetric matrices A0 , A1 , . . . , An Rmm , define:
M , cfw_(x1 , . . . , xn ) Rn |A0 + x1 A1 + + xn An 0.
Prove that M is a convex set ( is the positive semidefinite sign).
2. Prove that the following functi

Power Systems Analysis - Homework 4
1. Draw the supply and demand curves corresponding to the following table:
Calculate the production/consumption level and revenue of each company.
2. The 300MW load of a small power system must be supplied at minimum co