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Unformatted text preview: Spring 2009
EE 422/522: Final Exam
NAME:
STUDENT NUMBER:
1. Power flow solutions – Fast Decoupled NewtonRaphson algorithm (20 points):
Perform one interation using the fast decoupled NewtonRaphson algorithm assuming a
flat start. Line admittances are given in the diagram.
Bus 1
(slack bus) Bus 2
P2=2.0 Bus 3
P3=4.0 Q3=1.0
(PQ bus)
2. Transient stability (25 points): A generator is connected to a transmission lines as
sketched below. A fault occurs at the location indicated in the diagram (next to the bus).
The fault is temporary so that when it clears the line remains in service. Find the critical
clearing angle and time to ensure stability. All values are given in per unit. j0.2 j0.8 V=1.0
Ea=1.25∠δ
Pm=0.75
H=3.0 Fault 3. Iterative equations (15 points): It is desired to find the solution to the equation
below. (a) Assume a starting guess of x=0.75π and perform one iteration using the
NewtonRaphson method. BE SURE TO SHOW YOUR WORK. 4. Fault current calculations (25 points): Consider two generators in parallel connected
through wyewye transformers and then connected through transmission lines serving a
load at bus 3. Find the fault current for a bolted fault (fault impedance zero): a) 3 phase to
ground fault at bus 3; and b) a lineline fault at bus 3. The various parameters are as
follows:
x1
0.20
0.20
0.05
0.05
0.10
0.25
0.20 Item
G1
G2
T1
T1
L12
L13
L23 x2
0.20
0.20
0.05
0.05
0.10
0.25
0.20 x0
0.10
0.10
0.05
0.05
0.30
0.65
0.60 5. Power system reliability (20 points): For the system described below find (a) the
LOLE on a yearly basis, i.e., the expected number of days/year, and (b) EUE on a yearly
basis, i.e., the expected MWh/year. (For simplicity, assume exactly 52 weeks per year so
364 days).
Generation Data
Unit Capacity FOR 1 150 MW 0.05 2 120 MW 0.05 Load Data  Assume on peak lasts for 12 hours and off peak lasts for 12 hours each day.
Day Daily Peak
Load Daily OffPeak
Load MondayFriday 160 MW 75 MW SaturdaySunday 75 MW 60 MW 6. Load frequency control (20 points): Consider a two area power system. Both areas
have two generating units. The governors are adjusted for a 5% droop in area A and 7.5%
in area B. The unit capacities and area load are given below:
Area A
G1=200 MW
G2=400 MW
Load = 300 MW Area B
G1=100 MW
G2=500 MW
Load=200 MW Initially, there is a 100 MW load transfer from Area A to Area B and the system is
operating at 60 Hz. If the load increases by 150 MW in area A, find:
a) the initial change in system frequency,
b) the area control error (ACE) in both areas assuming the bias is 40 MW/0.1 Hz in both
A and B. Indicate whether the ACE signal indicates an increase or a decrease is
needed in that area.
7. Admittance matrix and load flow equations (20 points): Consider the three bus
power system as sketched below. The line parameters shown are admittances.
Bus 1
(slack bus) Bus 2
P2=2.0 Q2=0.25 Bus 3
P3=2.5 Q3=0.5
(PQ bus)
a. Find the Ybus matrix.
b. Write the load flow equation at bus 2 for the real power injection substituting
all known values.
c. Identify the unknown and known variables for this system in the load flow
equations. 8. Swing Equation (15 points): A generator is connected to parallel transmission lines as
sketched below. A fault occurs at the location indicated in the diagram. When the fault is
cleared this line is taken out of service. (a) Find the swing equation for the prefault,
during fault and postfault conditions. (b) Sketch the power angle curves labeling them as
prefault, during fault or postfault as appropriate. j0.2 j1.0 j0.75 j0.25
Ea=1.1∠δ
Pm=0.5
H=3.0 s Fault V=1.0 9. Short answer (20 points):
a) Consider a small system with two areas, say area A and area B. Both systems are
running properly adjusted load frequency control. Area B experiences a 100 MW
increase in load. What is the Area Control Error (ACE) for area A? b) On a long transmission line, is the maximum power flow limited by “static stability” or
thermal limitations? c) Is bus voltage angle most closely related to real power or reactive power flows? d) Sketch the voltage profile along a lossless transmission line of say 500 km length with
a load equal to the characteristic impedance (surge impedance loading). e) In the power system security framework, what is meant by a secure operating point?
(Be specific.) ...
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This note was uploaded on 07/14/2011 for the course ECE 522 taught by Professor Tomsovic during the Summer '10 term at University of Florida.
 Summer '10
 Tomsovic
 Electrical Engineering

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