Prepared by

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United Arab Emirates University College of
Engineering Electrical Engineering Department
Automatic Generation Control

• Prepared by
• Abeer ALNuaimi
• Balqees ALDaghar
• Afra Ebrahim
• Lila Abdullah

200203257 200324560 200310882
Project Advisor Dr. Abdulla Ismail
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Contents

• Introduction
• Summary about our project.
• Review GP1 task.
• Gantt chart for GP2
• optimal control
• LFC with PI optimal control
• AVR with PI optimal control

3
Contents

• Combination of LFC and AVR
• LFC with Fuzzy logic control
• LFC with Robust control
• Comparison for three controllers
• PI, Fuzzy Robust
• Conclusion

4
AGC Overview

• The system
• Power Generation system.
• The problems
• Frequency and voltage variations
• The consequences
• Machine damage.
• Blackouts, or outages.

5
GP1 Overview

• The Project
• Automatic Generation Control system
• The Advantages
• Limits the variations.
• Avoide machine damages
• Avoide blackouts
• Enhance the system reliability and security.

6
GP1 Overview
7
GP1 Overview

Gp1
8
Gantt chart GP2 Plan
9
Gantt chart GP2 Plan
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Optimal Linear Control Systems

• optimal control is a set of differential
  equations describing the paths of the control
  variables that concerned with operating a dynamic
  system to minimize the cost functional with
  weighting factors supplied by a engineer.

11
Example for optimal control
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Optimal Linear Control Systems

• Application of optimal control
• Mechanics of motion.
• Economics.
• Medicals.
• Populations.

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The targets for using the optimal linear control
system

• Stable closed-loop system.
• Reduce steady state errors.
• Reach standard performance measures
• Peak Time, Tp.
• Percent of overshoot.
• Percent of under shoot.
• Settling time, Ts.
• Rise time, Tr.

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• Minimization cost equation

State variable
Input
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The LFC with the I and OPC

• Model1 With the integral control.

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The LFC with the I and OPC

• MATLAB Defining the Matrices.
• A-12.5 0 -12.5 -53.33 -3.33 0 00 3.86 -2.70
  00 0 0.87 0
• B12.5000 F00-1.930
• C0 0 1 0
• D0

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The LFC with the I and OPC
SSR t25s
US 4
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The LFC with the I and OPC

• Model1 With the integral control and optimal
  control.

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The LFC with the I and OPC

• MATLAB Defining the Matrices.
• Q10 0 0 0 0 10 0 0 0 0 10 0 0 0 0 10
• R1
• K,P,evlqr(A,F,Q,R)
• AoA-(FK)
• sys1ss(Ao,F,C,D)
• yolsim(Ao,F,C,0,u,t)

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The LFC with the I and OPC
SSR t10s
US 1.5
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The LFC with the I and OPC

• The Integral and the Optimal control Advantages
• Undershoot Reduction from 4 to 1.5
• The steady state response deducted faster
• The integral control helps in enhancing the
  steady state response from t25s to t10s.
• The Optimal control helps in enhancing the
  Transient response.

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System Models (AGC)
Automatic Voltage Regulator (AVR)
Excitation system

Voltage sensor
Gen. field
Steam
Turbine
G
Shaft
Valve Control mechanism
Load frequency control (LFC)
Frequency sensor
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Automatic Voltage Regulation

• For efficient and reliable operation of Power
  Systems, the control of voltage should satisfy
  the following objective
• Voltages at the terminals of all equipment in the
  system are within acceptable limits. Maintaining
  voltages within the required limits is
  complicated due to the fact that
• The power system supplies power to vast number of
  loads and fed from many generating units.

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Automatic Voltage Regulation

• 2) System voltage is closely related to the
  system reactive power which is a reactive loads
  such as inductors and capacitors dissipate zero
  power, yet the fact that they drop voltage and
  draw current gives the deceptive impression that
  they actually do dissipate power.
• 3) The proper selection and coordination of
  equipment for controlling the system voltage and
  the reactive power are among the major challenges
  in power system operation and control.

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Automatic Voltage Regulation

• Reactive Power (QV) is one of the two main
  elements in the power system must be controlled.
  
• Any voltage error in the system is sensed,
  measured, and transformed into reactive-power
  command signal.
• The objective of the AVR is to keep the system
  terminal voltage at the desired value by means of
  feedback control

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Block diagram of AGC model
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AVR Model
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Block diagram of a simple automatic voltage
regulator (AVR)
KE200 TE 0.05KG1 TG 0.2KR0.05 TR
0.05 KA0.15 TA10
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Block diagram of a simple automatic voltage
regulator (AVR)

• Voltage error is improved by controlling the
  rotor field-current generator EMF.
• The steady state voltage error can be eliminated
  using an integral controller.
• The AVR has a substantial effect on transient
  stability when varying the field voltage to
  maintain the terminal voltage constant.

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AVR Model

• Case 1
• AVR without PI (Proportional and Integral )
  controller.
• Case 2
• AVR with PI controller.
• Case 3
• AVR with optimal control.

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Case 1 AVR without PI (Proportional and
Integral ) controller.
Block diagram of AVR model without PI controller
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The output voltage response without controller
Overshoot error
Steady State error
?V
Time (s)
The output voltage response when Ka of the
amplifier is 0.15
The output voltage response when Ka of the
amplifier was changed to 0.1
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Case 2 AVR with PI controller.
Block diagram of AVR model with Ki and Kp gains
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The output voltage response when Ki0.2 and Kp
1.5
The output voltage response with PI controller
V
Time (s)
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Case 3 AVR with optimal control.
Block diagram of AVR model with feedback gains
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Step1 Find the state variables and output
equations

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Step2 Find A,B, C, D matrices

• State differential Equation
• Output Equation
• A-5 5 0 0 0 -20 4000 0 0 0 -0.1 -0.0120 0 0
  -20
• B000.010
• C1 0 0 0
• D0

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Step 3 MATLAB command to find the feedback gains

• MATLAB command
• A-5 5 0 0 0 -20 4000 0 0 0 -0.1 -0.0120 0 0
  -20
• Q5 0 0 0 0 5 0 0 0 0 5 0 0 0 0 5
• B000.010
• R5
• F,P,evlqr(A,B,Q,R)
• Result of running the program  
• F
•  
• -0.0230 0.0582 206.0278 -0.0899
•  
• P
•  
• 1.0e005
•  
• 0.0000 0.0000 -0.0001 0.0000

MATLAB Function
values of feedback gains k1,k2,k3,k4
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The output voltage response with optimal and
integral control
V
Time (s)
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AGC system
AVR
LFC
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AVR and LFC Combination
x3
Load Frequency Control
Auto Voltage Regulator
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AVR and LFC Combination

• Forming A, B, C, D and F Matrices
• State Differential Equation.
• Output Equation.
• MATLAB.
• Tuning K1,K2,K3,K4 and K5 Between 0 and 1
• Trial and Error
• K1 has no affect on either one of the two
  systems.
• K2 has an affect on the LFC response.
• K3 has an affect on both the LFC and the AVR
  system stability.
• K4 and K5 both have an affect on the AVR
  overshoot.

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AVR and LFC Combination

• Tuning K1,K2,K3,K4 and K5 Between 0 and 1
• K at which the responses of both AVR and LFC are
  behaving normally
• K1 1
• K2 0.8
• K3 0.1
• K4 0
• K5 1

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AVR response
AGC response
LFC response
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AVR and LFC Combination
x3
Load Frequency Control
Auto Voltage Regulator
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AVR response
AGC response
LFC response
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AVR response
AGC response
LFC response
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AVR and LFC Combination

• The Combination of both AVR and LFC systems might
  cause slight changes in their responses.
• Fortunately the undershoots and overshoots never
  exceeded 20.
• AVR stand alone system
• Overshoot 2.2
• With the optimal control the overshoot almost
  eliminated.
• AVR within AGC system
• Overshoot 0.2
• LFC stand alone system
• Undershoot 2.8
• LFC within AGC system
• Undershoot 2.5

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Fuzzy logic control

• It is the process of formulating the mapping
  from a given input to an output using fuzzy
  logic. The mapping of FL done based on human
  operators behavior.

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Fuzzy logic control
Cheaper
Flexible
Fuzzy logic
Natural languages
Faster
Model nonlinear function
Easy to understand
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Fuzzy Logic Control Application

• Automatic control
• Data classification
• Decision analysis
• Expert systems
• Computer vision

• Cameras
• washing machines
• microwave ovens
• Industrial process control
• Medical instrumentation

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Fuzzy logic control process

• Fuzzify Inputs
• Apply Fuzzy Operator
• Apply Implication Method
• Aggregate All Outputs
• Defuzzify

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Modeling one area LFC with Fuzzy logic control
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FIS Editor
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Membership Function
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FIS variables
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FIS variables
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Rule Editor
If-And-Then rules
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The response of LFC one area Fuzzy control
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Modeling two area LFC with Fuzzy logic control
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Area Control Error

• Area control error is the difference between the
  actual power flow out of area, and scheduled
  power flow. ACE also includes a frequency
  component.

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The response of LFC two areas Fuzzy control
? F1
? F2
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The response of Tie line for LFC two areas Fuzzy
control
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LFC Model with Robust controller

• What is Robust control ?
• Why we need Robust control in our model
  (AGC)?
• Applications of Robust control
• Robust controller design

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Robust controller

• The dynamic behavior of electric power systems is
  heavily affected by disturbances and changes in
  the operating points.
• An industrial plant such as power systems always
  contains parametric uncertainties.
• In many control applications, it is expected that
  the behavior of the designed system will be
  insensitive (robust) to external disturbance and
  parameter variations

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Applications of Robust control

• Robust control of Temperature
• Disk drive read system
• Mobile ,Remote-Controlled video camera
• Spacecraft
• Control of a(Digital audio tape) DAT player
• Elevator
• Microscope control

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Robust controller design
?Pd(t) load disturbance (P.u. MW) Tg governor
time constant (s) Kg governor gain Tt turbine
time constant (s) Kt Turbine gain Tp
Generator time constant (s) K p Generator
gain R speed regulation due to governor action
(HZ p.u. MW-1) KI Integral control gain
LFC Block diagram of power system
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• Our robust load-frequency controller design
  procedure is as follows
• Step 1 Find the range of the system parameters
• State equation
• Output equation
• Where

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• A
• -1/Tp Kp/Tp 0 0
• 0 -1/Tt 1/Tt
  0
• -1/RTg 0 -1/Tg
  -1/Tg
• K 0 0
  0
• The range of the system parameters is

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• Step 2 Choose the nominal parameters for the
  system and
• decide the bound of the
  uncertainties
• The nominal parameters are from the original
  model of LFC
• And ,

A -2.7030 3.8595 0
0 0 -3.3330 3.3330
0 -31.2500 0 -12.5000
-12.5000 0.8800 0 0
0 B0012.50 F3.8595000

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• Now, let decide the bound of the uncertainties
• Hence, the parametric uncertainties are

A -0.8109 1.1579 0
0 0 -0.9990 0.9999 0
-9.3750 0 -3.7500 -3.7500
0.2640 0 0
0 B006.250 F2.70165000
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• After this change in the system the new matrices
  are as follow

A   -3.5139 5.0174 0
0 0 -4.3320
4.3320 0 -40.6250 0
-16.2500 -16.2500 1.1440 0
0 0 B0018.750 F
6.56115000
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• Step 3 Choose the design constants e and the
  design constant
• matrices Q and R
• And because the algebraic Riccati equation is
  nonlinear equation we use MATLAB program to solve
  it.

• Algebraic Riccati equation

Where , Q gt 0 and R gt 0
e e1 gt 0 , very small value
T U are the rate change of the generation
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• Step 4 Use the algorithm given eq. (1) to solve
  Riccati equation
• and obtain the solution P
• By using the command from the MATLAB we can found
  P as follow

MATLAB Command A-3.5139 5.0174 0 00 -4.332
4.332 0 -40.625 0 -16.25 -16.25 1.144 0 0
0 Q5 0 0 0 0 5 0 0 0 0 5 0 0 0 0
5 B0018.750 R0.01 F,P,evlqr(A,B,Q,R)
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Result of the command   F 9.6166 17.6707
21.6925 21.5108 P 1.1042 0.6104
0.0051 1.7927 0.6104 0.9237 0.0094
1.1636 0.0051 0.0094 0.0116 0.0115
1.7927 1.1636 0.0115 7.7951 ev
1.0e002 -4.1956 -0.0522
0.0168i -0.0522 - 0.0168i -0.0083
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• By using MATLAB the output frequency response was
  drawn without considering the feedback gains

MATLAB Command clc t00.120 u-0.1ones(lengt
h(t),1) x00 0 0 0 A-3.5139 5.0174 0 00
-4.332 4.332 0 -40.625 0 -16.25 -16.25 1.144 0
0 0 eig(A) B0018.750 C1 0 0
0 D0 sysss(A,B,C,D) y,xlsim(sys,u,t,x0)
plot(t,y) Title('The output
frequency respronse') xlabel('Time') ylabel('f')
grid
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The output frequency response with uncertainties
parameters and without feedback gains
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• Step 5 Construct the feedback gain
• Also, by using the same command from MATLAB we
  found the optimal gains
•  

F 9.6166 17.6707 21.6925 21.5108
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LFC Block diagram of power system for the
proposed robust controller
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The output frequency response for the proposed
robust controller
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Comparison between robust and integral controller

Figure 1 With nominal parameters 1/Tp 2.7030,
Kp/Tp 3.8595, 1/TT 3.333, 1/TG 12.5, 1/RTG
31.25, KI 0.88
Figure 2 With 1/Tp1.05, Kp/Tp1.494, 1/TT1.3,
1/TG1.79,1/RTG0.7143,KI1.144
Figure 3 With 1/Tp 0.8, Kp/Tp 1.1424,
1/TT1.031, 1/TG1.52,1/RTG0.61,KI0.88
Figure 4 With 1/Tp 0.033, Kp/Tp 4,
1/TT2.564, 1/TG9.615,1/RTG3.081,KI0.88
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Comparison

• The use of the PID algorithm for control does not
  guarantee
• optimal control of the system or system
  stability, thats why
• in our designs of LFC and AVR we used the optimal
  linear
• control systems.
• The Fuzzy-logic controller can be seen as a
  heuristic and
• modular way of defining nonlinear system but the
  fuzzy
• logic controller failed in considering the
  uncertainties.

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Comparison

• The proposed robust controller is simple,
  effective and can
• ensure that the overall system is asymptotically
  stable for
• all admissible uncertainties.

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Conclusion

• Our goal in the end is to design a control system
  that serves the power network in the UAE for
  better performance and better power services in
  terms of consumption and supplement.
• Enhance our skills and understanding of
  Engineering project design and management.
• Achieve the best as an outcome of a successful
  group work.

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Thank you for your listening