Electric Power Systems Exam #1: 10/07/2014

1° Part

Exercise 1 A three-phase, six-pole, 50 Hz induction motor is supplied by a line-to-line voltage of V = 400 V. The

windings of the machine are Y-connected and the transformer ratio between the stator and the

rotor windings is m = 1.2. The stator and rotor resistances are = 0.0348 Ω and = 0.0566 Ω,

respectively, while the reactance of the rotor windings computed with respect to the stator

frequency is = 0.3929 Ω.

In no-load operating conditions, the motor absorbs a current = 15 while the measured iron

losses are = 900 .

In normal operating conditions, the mechanical power applied to the machine shaft is = 83.572

kW and the rotor speed is = 945 [/ !"].

Neglecting the voltage drops in the stator phases and the mechanical losses determine:

1. the phasor of the current absorbed by the motor in no-load conditions ($ );

2. the phasor of the rotor current $ in normal operating conditions;

3. the phasor of the stator current $ in normal operating conditions;

4. the electric power absorbed by the motor from the electrical grid and the efficiency of the motor

in normal operating conditions.

Exercise 2 Consider the following electrical network

Generator G An Vn Real power output: PG Operating voltage: VG

[MVA] [kV] [MW] [kV]

G 100 132 60 135

Demand D Vn Absorbed real power: PD Power factor

[kV] [MW] [-]

G 132 87 0.9 - lagging

1 2

3

Ext Grid

L1

L2 L3

G

D

Linea L

[km]

xl

[Ω/km]

Vn

[kV]

L1 30 0.25 132

L2 50 0.38 132

L3 45 0.33 132

After careful examination of the network topology:

1. determine the bus admittance matrix;

2. identify the bus types for Power Flow (PF) computation;

3. choose the starting profile for the iterative process of PF;

4. write the PF system of equations and compute the initial power mismatches (residues);

5. perform one PF iteration using the Gauss method (compute the bus voltage phasors);

2° Part

Answer only one of the two following questions

1. Describe the rotating magnetic field via the various methods to generate it. Provide the

proof of the Galileo Ferraris theorem.

2. Show how to obtain the capability curves for a synchronous generator and comment their

structure.

Answer only one of the two following questions 1. Gauss method: describe the methodology, provide the graphical interpretation of the

method, obtain the canonical form and describe how to apply it for power flow

computations.

2. Primary and secondary frequency control.