FACULTY OF ENGINEERING

LAB SHEET

EEL4126 Power System Operation and Control I TRIMESTER 2014-2015

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 Gauss-

kpb Page 2 of 16 Power System Operation and Control seidel 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. 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; V i

--(2) y V i1 1

y V i 2 2

I The complex power at bus i is; i

y V --(3) i n n

y i 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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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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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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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 % form the bus admittance matrix warning off lfnewton % Load flow solution by Newton-Raphson method busout % Prints the power flow solution on the screen lineflow % computes and displays the line flow and losses

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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 or delete the row representing line data of line 4-5]. 4. Restore the original line data matrix. Open line 2-5 and check for overloading and voltage limit. 5. Restore the original line data matrix. Open lines 2-4 and 4-5 simultaneously and check for overloading and voltage limit. 6. Restore the original line data matrix. 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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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 improve 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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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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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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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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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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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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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. Print the SIMULINK block diagrams of all the test cases. 2. Print the responses in each case. 3. Give values of peak time, rise time, settling time and percent overshoot in case 1. 4. Compare the performances of cases 3 and 4.

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