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

I1= 8006 − 89◦ (1)

Short-circuit test (V2 = 0):

Zsc =V1

I1= 2006 77◦ (2)

Find the characteristic impedance Zc and γm.

2. In the following figure, the transformer is ideal. Find the (primary) driving-point impedance (at theterminals a-n) for the circuit.

3. For the system shown below, construct Ybus. The parameters for various elements are provided in thetable.

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4. For the system given below, the parameters of the transmission lines are given in the table (resistancehas been ignored). Also,

Bus Capacitor at bus 2: y = j0.30 p.u.

Bus Inductor at bus 3: y = −j0.60 p.u.

Line Series Reactance p.u. Shunt Admittance p.u.1-2 j0.10 j0.242-3 j0.20 j0.263-1 j0.25 j0.30

(a) Determine Ybus for the three-bus system.

(b) Determine Ybus with bus 2 eliminated.

5. Find a solution of the equation cos(x) = x3 using Newton’s method.

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