Download Study of Excitation Control System Responses

FACULTY OF ENGINEERING
LAB SHEET
EET4126 Power System Operation
and Control
II TRIMESTER 2011-2012
PSOC 1 – Contingency analysis of power systems
PSOC 2 – Study of excitation control system responses
*Note: On-the-spot evaluation may be carried out during or at the end of the experiment. Students
are advised to read through this lab sheet before doing experiment. Your performance, teamwork
effort, and learning attitude will count towards the marks.
Power System Operation and Control
EET4126 Power System Operation and Control
Instruction
1. Before coming to the laboratories read the lab sheet carefully and understand the
procedure of performing the experiments.
2. Handle the PC with care.
3. Only use that software, which is necessary for your experiment.
4. Do not use any diskette, CD or pen-drive without the permission of the lab staff.
Marking Scheme
Lab Report Writing: (The report should consists of Results and Answers for all questions,
Discussion and Conclusion) ------------------------------------------ 7 marks
Spot evaluation (Oral assessment at the end of lab) --------------- 3 marks
Experiment # I
Contingency analysis of power systems
Objectives
* To assess the necessity of contingency analysis
* To perform the load flow analysis by using MATLAB software
* To evaluate the effect of line outage in a power system
* To evaluate the effect of generator outage in a power system
Introduction
The major security function in a power system is contingency analysis. The results of
contingency analysis allow systems to be operated defensively. The majority of the
problems that occur on power system can cause serious trouble within such a quick time
period that the operator could not take action fast enough. This is often the main reason
of cascading failures. Hence, the computers in modern power system operation control
centers are equipped with the contingency analysis programs that model the possible
systems troubles before they arise. These programs are based on a model of the power
system and are used to study outage events and alarm the operators to any potential
overloads or out-of-limit voltages. For example, the simplest form of contingency
analysis can be put together with the procedures to set up the power-flow data for each
outage to be studied by the power-flow program. Several variations of this type of
contingency analysis scheme involve fast solution methods, automatic contingency event
selection, and automatic initializing of the contingency power flows using actual data and
state estimation procedures.
Newton-Raphson (N-R) Power Flow Solution
The most widely used power flow solution employs Newton-Raphson technique. Because
of its quadratic convergence, Newton's method is mathematically superior to the Gaussseidel method and is less prone to divergence with ill-conditioned problems. For large
power systems, the Newton-Raphson method is found to be more efficient and practical.
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Power System Operation and Control
The number of iterations required to obtain a solution is independent of the system size,
but more functional evaluations are required for each iteration. Since in the power flow
problem real power and voltage magnitude are specified for the voltage-controlled buses,
the power now equation is formulated in polar form. For the typical bus of the power
system shown in Figure 1, the equation can be written in terms of the bus admittance
matrix as;
---(1)
In the above equation, j includes bus i. Expressing this equation in polar form, we have;
Vi
--(2)
yi1
V1
yi 2
The complex power at bus i is;
V2
Ii
yi n
--(3)
Vn
yi 0
Figure 1
Substituting from (2) for Ii in (3);
---(4)
---(5)
---(6)
Equations (5) and (6) constitute a set of nonlinear algebraic equations in terms of the
independent variables, voltage magnitude in per unit, and phase angle in radians. We
have two equations for each load bus, given by (5) and (6), and one equation for each
voltage-controlled bus, given by (5). Expanding (5) and (6) in Taylor's series about the
initial estimate and neglecting all higher order terms results in the following set of linear
equations.
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Power System Operation and Control
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Power System Operation and Control
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Power System Operation and Control
MATLAB Simulation
To solve the power flow problem with the help of a computer, MATLAB software may be
used. [Refer the book ‘Power System Analysis’ by Hadi Saadat and go through the source
programs for power flow study.]
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Power System Operation and Control
Note: If necessary, appropriate values of minimum and maximum Mvar of generation
may be chosen. In the absence of shunt compensation in any bus the injected Mvar at that
bus becomes zero.
MVA base. The last column is for transformer tap setting; for lines, 1 and for transformer
off-nominal turns ratio must be entered in this column.
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Power System Operation and Control
Generation and loads are as given in the data prepared for use in the MATLAB
environment in the matrix defined as busdata. Code 0, code 1 and code 2 are used for
load buses, the slack bus and voltage-controlled buses, respectively. The control
commands required are lfybus, lfnewton and lineflow. Command lfybus computes the
bus admittance matrix using linedata, and lineflow computes the power flow through
each line after the power flow solution.
lfnewton: This program obtains the power flow solution by the Newton-Raphson
method and requires the busdata and the linedata files. It is designed for the direct use
of load and generation in MW and Mvar, bus voltages in per unit, and angle in degrees.
Loads and generation are converted to per unit quantities on the base MVA selected. A
provision is made to maintain the generator reactive power of the voltage-controlled
buses within their specified limits. The violation of reactive power limit may occur if the
specified voltage is either too high or too low. In the second iteration, the var calculated
at the generator buses are examined. If a limit is reached, the voltage magnitude is
adjusted in steps of 0.5 percent up to ±5 percent to bring the var demand within the
specified limits.
Formats of busdata and linedata are given below.
Bus Bus Voltage Angle ---Load----- -----Generator---------- Injected
No code Mag. Degree MW Mvar MW Mvar Qmin Qmax Mvar
busdata=[
];
Bus bus R
X 1/2 B line code
nl nr p.u. p.u. p.u.
linedata=[
];
The steps to enter the data and command are given below.
clear
basemva = 100; accuracy = 0.001; maxiter = 10;
busdata=[
linedata=[
lfybus
warning off
lfnewton
busout
lineflow
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];
];
% form the bus admittance matrix
% Load flow solution by Newton-Raphson method
% Prints the power flow solution on the screen
% computes and displays the line flow and losses
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Power System Operation and Control
TEST SYSTEM
Each line is rated for 65 MVA and the bus1 generator rating is 100 MVA. The allowable
voltage variation in load buses is 1.05pu to 0.95pu. Assume minimum and maximum
Mvar for each generator to be 10 and 50 Mvar.
1. Compute linedata and busdata matrices.
2. Perform the power flow study. Print the results and check for overloading and
voltage limit.
3. Open line 4-5 and check for overloading and voltage limit. [Increasing its
impedance to a very high value may simulate opening of a line.]
4. Open line 2-5 and check for overloading and voltage limit.
5. Open lines 2-4 and 4-5 simultaneously and check for overloading and voltage
limit.
6. Open generator 3 and check for overloading and voltage limit. [Changing it to be
a load bus with generated MW and Mvar to be zero may simulate opening of a
generator.]
EXERCISE
1. Print and submit all your results.
2. Assume the rating of line 2-5 to be 75 MVA. Is it overloaded in case 5? Compute
the compensation required in bus 5 to keep its voltage within 1.02 to 0.98 pu.
3. Compare N-R method with decouple method of power flow study.
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Power System Operation and Control
Experiment # II
Study of Excitation Control System Responses
Objectives
*
*
*
*
*
To classify the function of excitation control system
To construct the models of amplifier, exciter, generator etc. of the excitation system
To design the SIMULINK block diagram of the control system
To appraise the step response of the excitation control system
To stabilize the control system responses
Synchronous Generator Excitation System
The generator excitation system maintains generator voltage and controls the reactive
power flow. The generator excitation of older systems may be provided through slip rings
and brushes by means of dc generators mounted on the same shaft of the rotor of the
synchronous machine. However, modern excitation systems usually use ac generators
with rotating rectifiers, and are known as brushless excitation. Recently Static Excitation
System is increasingly used. Static rectifier, controlled or uncontrolled, supplies the
excitation current directly to the field of the main alternator through its slip rings. The
supply of power to the rectifiers is from the main generator or the station auxiliary bus
through a transformer to step down the voltage to an appropriate level.
It is well known that a change in the real power demand affects essentially the frequency,
whereas a change in the reactive power affects mainly the voltage magnitude. The
sources of reactive power are generators, capacitors, and reactors. The generator reactive
power is controlled by field excitation. Other supplementary methods of improving the
voltage profile on electric transmission systems are transformer load-tap changers,
switched capacitors, step-voltage regulators, and static var control equipment. The
primary means of generator reactive power control is the generator excitation control
using automatic voltage regulator (AVR). The role of an (AVR) is to hold the terminal
voltage magnitude of a synchronous generator at a specified level. The schematic
diagram of a simplified AVR is shown in Figure1.
A drop in the terminal voltage magnitude accompanies an increase in the reactive power
load of the generator. The voltage magnitude is sensed through a potential transformer on
one phase. This voltage is rectified and compared to a dc set point signal. The amplified
error signal controls the exciter field and increases the exciter terminal voltage. Thus, the
generator field current is increased, which results in an increase in the generated emf. The
reactive power generation is increased to a new equilibrium, raising the terminal voltage
to the desired value. We will look briefly at the simplified models of the component
involved in the AVR system.
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Power System Operation and Control
Amplifier Model
The excitation system amplifier may be a magnetic amplifier, rotating amplifier, or
modern electronic amplifier. The amplifier is represented by a gain KA and a time
constant τA, and the transfer function is
----(1)
Typical values of KA are in the range of 10 to 400. The amplifier time constant is very
small, in the range of 0.02 to 0.1 second, and often is neglected.
Exciter Model
There is a variety of different excitation types. However, modern excitation systems uses
ac power source through solid-state rectifiers such as SCR. The output voltage of the
exciter is a nonlinear function of the field voltage because of the saturation effects in the
magnetic circuit. Thus, there is no simple relationship between the terminal voltage and
the field voltage of the exciter. Many models with various degrees of sophistication have
been developed and are available in the IEEE recommendation publications. A
reasonable model of a modern exciter is a linearized model, which takes into account the
major time constant and ignores the saturation or other nonlinearities. In the simplest
form, the transfer function of a modern exciter may be represented by a single time
constant τE and a gain KE, i.e.,
---(2)
The time constant of modern exciters are very small.
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Power System Operation and Control
Generator Model
The synchronous machine generated emf is a function of the machine magnetization
curve, and its terminal voltage is dependent on the generator load. In the linearized
model, the transfer function relating the generator terminal voltage to its field voltage can
be represented by a gain KG and a time constant τG and the transfer function is
---(3)
These constants are load-dependent, KG may vary between 0.7 to 1, and τG between 1.0
and 2.0 seconds from full-load to no-load.
Sensor Model
The voltage is sensed through a potential transformer and, in one form, it is rectified
through a bridge rectifier. The sensor is modeled by a simple first order transfer function,
given by
---(4)
τR is very small, and we may assume a range of 0.01 to 0.06 second. Utilizing the above
models the AVR block diagram is shown in Figure 2.
The open-loop transfer function of the block diagram in Figure 2 is
---(5)
and the closed-loop transfer function relating the generator terminal voltage Vt(s) to the
reference voltage Vref(s) is
---(6)
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Power System Operation and Control
or
---(7)
For a step input Vref(s) = 1/s, using the final value theorem, the steady-state response is
---(8)
TEST MODEL
The AVR system of a generator has the following parameters
Substitution of the system parameters in the AVR block diagram of Figure 2 results in the
block diagram shown in Figure 3.
The SIMULINK block diagram of the test AVR system, with KA = 10, is given in Fig 4.
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Power System Operation and Control
Excitation System Stabilizer - Rate Feedback
It is observed for higher values of KA the system become unstable, and a value exceeding
12.5 results in an unbounded response. Thus, we must increase the relative stability by
introducing a controller, which would add a zero to the AVR open-loop transfer function.
On way to do this is to add a rate feedback to the control system as shown in Figure 5. By
proper adjustment of KF and τF, a satisfactory response can be obtained.
Excitation System Stabilizer - PID Controller
One of the most common controllers available commercially is the proportional integral
derivative (P1D) controller. The PID controller is used to improve the dynamic response
as well as to reduce or eliminate the steady-state error. The derivative controller adds a
finite zero to the open-loop plant transfer function and improves the transient response.
The integral controller adds a pole at origin and increases the system type by one and
reduces the steady-state error due to a step function to zero. The PID controller transfer
function is
---(9)
The block diagram of an AVR compensated with a PID controller is shown in figure 6.
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Power System Operation and Control
Construction of SIMULINK Model
To create a SIMULINK block diagram presentation of Figure 4 select new... from the File
menu. This provides an untitled blank window for designing and simulating a dynamic
system. You can copy blocks from within any of the seven block libraries or other
previously opened windows into the new window by depressing the mouse button and
dragging. Open the Source Library and drag the Step Input block to your window.
Double click on Step Input to open its dialog box. Set the step time to a large value and
set the Initial Value and the Final Value to represent the step input. Open the Linear
Library and drag the Sum block to the right of the Step Input block. Open the Sum dialog
box and enter + - under List of Signs. Using the left mouse button, click and drag from
the Step output port to the Summing block input port to connect them. Drag a copy of the
Transfer Function block from the Linear Library and connect it to the output port of the
Sum block. Click on the Transfer Function block once to highlight it. Use the Edit
command from the menu bar to copy and paste copies of the Transfer Function. Open the
Transfer Function dialog box and enter values of gains and time constants to represent the
correct transfer function. Put appropriate names to the blocks. Highlight the Sensor block,
and from the pull-down Options menu, click on the Flip Horizontal to rotate the Sensor
block by 180 degree. Connect all the blocks as shown in Figure 4 by connecting the
output to input ports. Finally, get one Auto-scale Scope from the Sink Library and
connect it to the output of the Generator block.
Before starting simulation, you must set the simulation parameters.
Pull down the Simulation dialog box and select Parameters. Use default values for the
Start and Stop Time, and Maximum Step Size. Leave the other parameters at their default
values. Press OK to close the dialog box.
If you don’t like some aspect of the diagram, you can change it in a variety of ways. You
can move any of the icons by clicking on its center and dragging. You can move any of
the lines by clicking on one of its corners and dragging. You can change the size and the
shape of any of the icons by clicking and dragging on its corners. You can remove any
line or icon by clicking on it to select it and using the cut command from the edit menu.
You should now have exactly the same system as shown in Figure 4. Pull down the File
menu and use Save as to save the model in a file. Make sure to delete this file at the end
of your experiment.
SIMULINK enables you to construct and simulate many complex systems, such as
control systems modeled by block diagram with transfer functions including the effect of
nonlinearities. In addition, SIMULINK provides a number of built-in state variable
models and subsystems that can be utilized easily.
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Power System Operation and Control
Test Results
1. Start the simulation. SIMULINK will create the Figure windows and display the system
responses. Save the system response. Find out the time domain performance
specifications, namely, peak time, rise time, settling time and percent overshoot. If
necessary, you may write and run a simple MATLAB program for this.
2. Change the value of KA to 20 and check whether the system is stable. Save the
response.
3. Draw the SIMULINK block diagram and construct the SIMULINK model of Fig 5.
Assume KF and τF to be 2 and 0.04 respectively. Record the step response and check
the stability of the system.
4. Draw the SIMULINK block diagram and construct the SIMULINK model of Fig 6.
Assume KP, KI and KD to be 1.0, 0.25 and 0.28 respectively. Record the step
response and check the stability of the system.
EXERCISE
1.
2.
3.
4.
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Print the SIMULINK block diagrams of all the test cases.
Print the responses in each case.
Give values of peak time, rise time, settling time and percent overshoot in case 1.
Compare the performances of cases 3 and 4.
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