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NORTH CAROLINA STATE UNIVERSITYELECTRICAL AND COMPUTER ENGINEERING

ECE 550 HW4 on AGC F14

Note: You need to show all the calculation/derivation steps

in order get full credit for an answer.

Consider the following system

G1 G2

CB1 CB2

P PL1 L2

G1 and G2 are identical unitsrating: 30 MVA, 13.8 kV.M = 300 MW.sec., D = 0.6 MW.

Turbine time const. = 0.5 sec.Gov. time const. = 0.1 sec.

Droop = 5%

Line: x = 10 /ph.

Q1. Consider the case in which CB1 and CB2 are open so that G1 and G2 supply onlytheir own loads, PL1= 20 MW, PL2= 20 MW, respectively. Hence, in this case consider only one

generator for the following:i) Draw the system block-diagram model and derive the transfer function between the frequency

of the unit and the load.ii) Determine the response of the machines (changes in frequency and turbine mechanical power) for a

10% step increase in PL1.

You can use the Simulink tool of Matlab to simulate the associated machine dynamics.iii) Calculate the change in frequency (in Hz) and mechanical power output of the two generators for the

load change in (ii) and verify that these results agree with that of the simulations in (ii).iv) After the load change, you want to restore frequency of the system back to its rated value by changing

manually the governor control setting Pr.

Calculate the required change in Pr.

Also, verify that this action works by simulating it using the Simulink model. In the simulation, youneed to apply the Pr change after the load change and the system settles to the new steady state.

Q2. Repeat Q1(i-iii) with CB1 and CB2 closed.For analysis, neglect line dynamics & use area model.

Q3. Consider the case in Q2 again. This time you use a more detailed model by including the line thatconnects the two machines.

i) Draw the block-diagram for this case.Derive the transfer function between the frequency of the G1 and the loads.

ii) Using Simulink, obtain system response (frequency and the power output of gens) for a 10% step

change in PL1.

iii) Calculate the change in frequency of the units in Hz, i.e, the steady-state value.

Also, calculate how the two Gens share the load. Compare these results with that of Q2.

Q4. Assume that two CBs are closed and the two generators are put under one AGC to regulate thefrequency with controller gains K1= 0.8 and K2= 1.2 Consider a 10% step increase in PL1.

ii) Draw the block-diagram for this case. Use the area model.Derive the transfer function between the frequency of the unit and the load.

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ii) Using Simulink, obtain frequency variation and AGC response (change in reference settings of G1 andG2).

iii) Calculate the change in frequency of the units in Hz, i.e, the steady-state value.

Also, calculate the change in power reference settings of the generators.

Q5. Now, consider that the two generators belong to two different areas, and the line is a tie-lineconnecting the two areas. The two generators are under two different AGCs with

K1= 0.8 K2= 1.2 and B1= B2= 10.so that the frequency of the system and the tie-line power flow can be controlled.

Consider again a 10% step increase in PL1.

i) Draw the block-diagram for this case. Derive the transfer function between the output- power flowover the line, Ptie- and the inputs which are the loads PL1and PL2.

ii) Using Simulink, obtain the frequency variation, AGC response (change in reference settings of G1and G2), and the power flow profile over the line, Ptie.

iii) Calculate the change in Ptie and the change in frequency of the units in Hz.

Also, calculate the change in power reference settings of the generators.