PracticeFinalExam - Spring 2009 EE 422/522 Final Exam NAME STUDENT NUMBER 1 Power flow solutions – Fast Decoupled Newton-Raphson algorithm(20

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Unformatted text preview: Spring 2009 EE 422/522: Final Exam NAME: STUDENT NUMBER: 1. Power flow solutions – Fast Decoupled Newton-Raphson algorithm (20 points): Perform one interation using the fast decoupled Newton-Raphson 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 Newton-Raphson method. BE SURE TO SHOW YOUR WORK. 4. Fault current calculations (25 points): Consider two generators in parallel connected through wye-wye 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 line-line 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 Off-Peak Load Monday-Friday 160 MW 75 MW Saturday-Sunday 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 pre-fault, during fault and post-fault conditions. (b) Sketch the power angle curves labeling them as pre-fault, during fault or post-fault 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.

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