voltage stabilizer
TRANSCRIPT
Prepared by Abeer ALNuaimi Balqees ALDaghar Afra Ebrahim Lila Abdullah
United Arab Emirates University College of Engineering Electrical Engineering Department
Project AdvisorDr. Abdulla Ismail
200203257 200324560200310882
ContentsContents Introduction
• Summary about our project.• Review GP1 task.• Gantt chart for GP2
optimal control:• LFC with PI & optimal control• AVR with PI & optimal control
ContentsContents Combination of LFC and AVR LFC with Fuzzy logic control LFC with Robust control Comparison for three controllers
• PI, Fuzzy & Robust Conclusion
AGC OverviewAGC Overview• The system:
– Power Generation system.
• The problems:– Frequency and voltage variations
• The consequences:– Machine damage.– Blackouts, or outages.
GP1 OverviewGP1 Overview• The Project:
– Automatic Generation Control system• The Advantages:
– Limits the variations.– Avoide machine damages– Avoide blackouts– Enhance the system reliability and security.
GP1 OverviewGP1 Overview
GP1 OverviewGP1 Overview
Gp1
Gantt chart GP2 PlanGantt chart GP2 Plan
Gantt chart GP2 PlanGantt chart GP2 Plan
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.
Example for optimal control
Optimal Linear Control Systems • Application of optimal control:
– Mechanics of motion.– Economics.– Medicals.– Populations.
The targets for using the optimal linear control system:
1. Stable closed-loop system.2. Reduce steady state errors.3. Reach standard performance
measures:– Peak Time, Tp.– Percent of overshoot.– Percent of under shoot.– Settling time, Ts.– Rise time, Tr.
• Minimization cost equation:
0,0)()()()(21
2121)(
min
RRdttuRtutxRtxJif
io
TT
tu
State variable Input
The LFC with the I and OPC
l
f1
0.875
scontroller
1
0.3s+1Turbine
PL
1
0.08s+1Governor
1.428
0.37s+1Generator
0.4
Gain
• Model1: With the integral control.
The LFC with the I and OPC• MATLAB: Defining the Matrices.
– A=[-12.5 0 -12.5 -5;3.33 -3.33 0 0;0 3.86 -2.70 0;0 0 0.87 0];– B=[12.5;0;0;0]; F=[0;0;-1.93;0];– C=[0 0 1 0];– D=[0];
The LFC with the I and OPC
0 5 10 15 20 25 30-0.045
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0Model1 output respronse without integral controller
Time (s)
df/d
t (H
z)
US: 4%
SSR: t=25s
The LFC with the I and OPC• Model1: With the integral control and optimal control.
f2
f1
-0.4s-0.875
scontrol ler1
-0.875
s
control ler
1
0.3s+1Turbine1
1
0.3s+1
Turbine
PL1
PL
1
0.08s+1Governor1
1
0.08s+1
Governor
1.428
0.37s+1Generator1
1.428
0.37s+1
Generator
-K-
Gain4
-K-
Gain3
-K-
Gain2
-K-
Gain1
-K-Gain
du/dt
Derivative
-K-
-1.143
The LFC with the I and OPC• MATLAB: Defining the Matrices.
– Q=[10 0 0 0; 0 10 0 0 ;0 0 10 0 ;0 0 0 10];% – R=1;– [K,P,ev]=lqr(A,F,Q,R)– Ao=A-(F*K)– sys1=ss(Ao,F,C,D);– yo=lsim(Ao,F,C,0,u,t);
The LFC with the I and OPC
0 5 10 15 20 25 30-0.045
-0.04
-0.035
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0Model1 output respronse without integral controller(Blue) and Optimal control(green)
Time (s)
df/d
t (H
z) US: 1.5%
SSR: t=10s
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 t=25s to t=10s.– The Optimal control helps in enhancing the Transient response.
System ModelsSystem Models (AGC)(AGC)
Valve Control mechanism
Load frequency control (LFC)
Frequency sensor
Voltage sensor
Automatic Voltage Regulator (AVR)
Excitation system
Gen. field
Turbine
GP
Steam
tieP
VP
GG QP ,
G
Shaft
Automatic Voltage RegulationAutomatic 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:
1) The power system supplies power to vast number of loads and fed from many generating units.
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.
Automatic Voltage RegulationAutomatic 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
Automatic Voltage RegulationAutomatic Voltage Regulation
Block diagram of AGC model
AVR Model
Block diagram of a simple automatic voltage regulator (AVR)
KKEE=200=200 T TEE =0.05 =0.05KKGG=1=1 T TGG =0.2 =0.2KKRR=0.05=0.05 T TRR =0.05 =0.05KA=0.15 TA=10KA=0.15 TA=10
• 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.
Block diagram of a simple automatic voltage regulator (AVR)
31
AVR Model
Case 1: AVR without PI (Proportional and Integral ) controller.
Case 2: AVR with PI controller.
Case 3: AVR with optimal control.
Case 1: AVR without PI (Proportional and Integral ) controller.
Block diagram of AVR model without PI controller
The output voltage response without controller
Steady State errorOvershoot error
Time (s)
∆V
Overshoot
Steady state error
The output voltage response when Ka of the amplifier was changed to 0.1
The output voltage response when Ka of the amplifier is 0.15
Case 2: AVR with PI controller.
Block diagram of AVR model with Ki and Kp gains
The output voltage response when Ki=0.2 and Kp= 1.5
Overshoot
Time (s)
V
The output voltage response with PI controller
Case 3: AVR with optimal control.
Block diagram of AVR model with feedback gains
4)( xsU 3x
)(01.001.01.03 43 tuxxx
2x
32 4000202 xxx
3x
2x1x
211 55 xxx
4x
144 2020 xxx
1x
Step1: Find the state variables and output equations:
State differential Equation:
Output Equation:
A=[-5 5 0 0; 0 -20 4000 0; 0 0 -0.1 -0.01;20 0 0 -20] B=[0;0;0.01;0]C=[1 0 0 0]D=[0]
)()()( tuBtxAtx mnnn
)()()( tuDtxCty mpnp
Step2: Find A,B, C, D matrices
Step 3: MATLAB command to find the feedback gains
MATLAB command
A=[-5 5 0 0; 0 -20 4000 0; 0 0 -0.1 -0.01;20 0 0 -20] Q=[5 0 0 0; 0 5 0 0; 0 0 5 0; 0 0 0 5]B=[0;0;0.01;0]R=5[F,P,ev]=lqr(A,B,Q,R)
Result of running the program:
F = -0.0230 0.0582 206.0278 -0.0899 P = 1.0e+005 * 0.0000 0.0000 -0.0001 0.0000 0.0000 0.0000 0.0003 0.0000 -0.0001 0.0003 1.0301 -0.0004 0.0000 0.0000 -0.0004 0.0000 ev = -20.6225 + 3.4261i -20.6225 - 3.4261i -2.9577 + 3.1290i -2.9577 - 3.1290i
values of feedback gains k1,k2,k3,k4
MATLAB Function
The output voltage response with optimal and integral control
Time (s)
V
AVR
LFC
AGC system
x7x6x5
x9
x8
x1 x2 x3
x4
df/dt
Vref (s)
V(t) + df/dt
V(t)
1
0.3s+1Turbine
1
0.05s+1Sensor
PL
1.5
Kp
0.2
sKI
1K5
0 K4
0.1K3
1 K2
0.8K1
0.875
sIntegral control 1
0.08s+1Gov ernor
1
0.2s+1Generator1
1.428
0.37s+1Generator
200
0.05s+1Exciter
0.1
10s+1Amplifier
0.4
1/R
x3
Load Frequency Control
Auto Voltage Regulator
AVR and LFC Combination
• Forming A, B, C, D and F Matrices:– State Differential Equation.State Differential Equation.– Output Equation.Output Equation.– MATLAB.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.
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
AVR and LFC Combination
0 5 10 15 20 25 30-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005Model1(reordered) output respronse with the integral controller
Time (s)
df/d
t (H
z)
LFC response
AVR response
AGC response
0 100 200 300 400 500 600 700 800 900 10000
20
40
60
80
100
120
x7x6x5x9
x8
x1 x2 x3
x4
df/dt
Vref (s)
V(t) + df/dt
V(t)
1
0.3s+1Turbine
1
0.05s+1Sensor
PL
0
Kp
0.09
sKI
-K-
K9
-K-
K8
-K-
K7
-K-
K6
1K5
0 K4
0.1K3
1 K2
-K-
K10
0.8K1
0.875
sIntegral control 1
0.08s+1Governor
1
0.2s+1Generator1
1.428
0.37s+1Generator
200
0.05s+1Exciter
0.1
10s+1Amplifier
0.4
1/R
x3
Load Frequency Control
Auto Voltage Regulator
AVR and LFC Combination
0 5 10 15 20 25 30-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005Model1(reordered) output respronse with the integral controller
Time (s)
df/d
t (H
z)
LFC response
AVR response
AGC response
0 50 100 150 200 250 300 350 400 450 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Model1 output respronse with integral and optimal controllers
Time (s)
Vol
ts (v
)
0 1 2 3 4 5 6 7 8 9 10-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
Model1yv and ydf output respronse in an AVR & LFC combination
Time (s)
Vol
t/Df/d
t (vs
)
0 5 10 15 20 25 30-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005Model1(reordered) output respronse with the integral controller
Time (s)
df/d
t (H
z)
LFC response
AVR response
AGC response
0 50 100 150 200 250 300 350 400 450 5000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Model1 output respronse with integral and optimal controllers
Time (s)
Vol
ts (v
)
• 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%
AVR and LFC Combination
Fuzzy logic controlFuzzy 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
operator’s behavior.
Fuzzy logic controlFuzzy logic control
FuzzFuzzy y
logiclogicNatural language
s
Model nonlinear function
Cheaper
Faster
Flexible
Easy to understand
Fuzzy Logic Control Fuzzy Logic Control ApplicationApplication
• Automatic control • Data classification• Decision analysis• Expert systems• Computer vision
• Cameras• washing machines• microwave ovens• Industrial process control• Medical instrumentation
Fuzzy logic control processFuzzy logic control process
• Fuzzify Inputs• Apply Fuzzy Operator• Apply Implication Method• Aggregate All Outputs• Defuzzify
Modeling one area LFC with Modeling one area LFC with Fuzzy logic controlFuzzy logic control
FIS EditorFIS Editor
Membership FunctionMembership Function
FIS variablesFIS variables
de\e LN MN SN VS SP MP LP
LP VS SP MP LP LP LP LP
MP SN VS SP MP MP LP LP
SP MN SN VS SP SP MP LP
VS MN MN SN VS SP MP MP
SN LN MN SN SN VS SP MP
MN LN LN MN MN SN VS SP
LN LN LN LN LN MN SN VS
FIS variablesFIS variables
Variables Linguistic Term Range of linguistic term
Near +0.05 LP (large positive) [+0.04 +0.05 +0.05]
Near -0.05 LN (large negative) [-0.05 -0.05 -0.04]
So far from +0.05 MP (medium positive) [+0.025 +0.035 +0.045]
So far from -0.05 MN (medium negative) [-0.045 -0.035 -0.025]
Very far from +0.05 SP (small positive) [+0.005 +0.015 +0.03]
Very far from -0.05 SN (small negative) [-0.03 -0.015 -0.005]
∆f=0 VS (very small) [-0.007 0 +0.007]
Rule EditorRule Editor
If-And-Then rules
The response of LFC one The response of LFC one area Fuzzy controlarea Fuzzy control
Modeling two area LFC with Modeling two area LFC with Fuzzy logic controlFuzzy logic control
Area Control ErrorArea 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.
fff
PPP
PPP
sch
tieschtietie
gschgg
The response of LFC two The response of LFC two areas Fuzzy controlareas Fuzzy control
∆ F1
∆ F2
The response of Tie line for The response of Tie line for LFC two areas Fuzzy controlLFC two areas Fuzzy control
LFC Model with Robust controllerLFC Model with Robust controller
What is Robust control ?
Why we need Robust control in our model (AGC)?
Applications of Robust control
Robust controller design
Robust controllerRobust 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
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
Robust controller designRobust controller design
∆Pd(t) : load disturbance (P.u. MW)Tg : governor time constant (s)Kg : governor gainTt : turbine time constant (s)Kt : Turbine gainTp : Generator time constant (s)K p : Generator gainR : speed regulation due to governor action (HZ p.u. MW-1)KI: Integral control gain
LFC Block diagram of power system
Our robust load-frequency controller design procedure is as follows:
Step 1:Step 1: Find the range of the system parametersFind the range of the system parameters• State equation:
• Output equation:
• Where :
)()()( tuDtxCty mpnp
)](),(),(),([)( 4321 txtxtxtxtx
)()()()( tPFtButAxtx d
14 xKx I
1x
143 )(31 xRT
ktu
Tk
xTgkgx
Tx
g
g
g
g
g
3221 x
Tkx
Tx
t
t
t
d
P
P
P
P
P
PTkx
Tkx
Tx 211
1
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:
0,/1,0,0 GTB
0,0,0,/ PP TKF
],[/1
],[/1
],[/1
],[/
],[/1
55
44
33
22
11
aaRT
aaT
aaT
aaTK
aaT
G
G
T
PP
P
]639.10,081.3[/1]857.17,615.9[/1
]762.4,564.2[/1]12,4[/
]1.0,033.0[/1
G
G
T
PP
P
RTTT
TKT
Step 2:Step 2: Choose the nominal parameters for the system andChoose the nominal parameters for the system and decide the bound of the uncertaintiesdecide the bound of the uncertainties
• The nominal parameters are from the original model of LFC:
And ,
)()()()()( tuBBtxAAtx
AAA BBB
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
B=[0;0;12.5;0]
F=[3.8595;0;0;0]
• Now, let decide the bound of the uncertainties:
• Hence, the parametric uncertainties are:
AA
BB FF
7.0&5.0,3.0
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
B=[0;0;6.25;0]
F=[2.70165;0;0;0]
• After this change in the system the new matrices are as follow:
AAA BBB
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
B=[0;0;18.75;0]
F=[6.56115;0;0;0]
Step 3:Step 3: Choose the design constants εChoose the design constants ε and the design constant and the design constant matrices matrices Q Q and and RR
And because the algebraic Riccati equation is nonlinear equation we use MATLAB program to solve it.
)1(....01121
1
1 EqQUPTBRBPPAAP TT
Where , Q > 0 and R > 0
ε & ε1 > 0 , very small value
• Algebraic Riccati equation:
T & U are the rate change of the generation
Step 4:Step 4: Use the algorithm given eq. (1) to solve Riccati Use the algorithm given eq. (1) to solve Riccati equationequation
and obtain the solution and obtain the solution PP• By using the command from the MATLAB we can found P as
follow:MATLAB Command MATLAB Command
A=[-3.5139 5.0174 0 0;0 -4.332 4.332 0; -40.625 0 -16.25 -16.25; 1.144 0 0 0]Q=[5 0 0 0; 0 5 0 0; 0 0 5 0; 0 0 0 5]B=[0;0;18.75;0]R=0.01[F,P,ev]=lqr(A,B,Q,R)
Result of the command Result of the command F = 9.6166 17.6707 21.6925 21.5108P = 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 7.7951ev = 1.0e+002 * -4.1956 -0.0522 + 0.0168i -0.0522 - 0.0168i -0.0083
• By using MATLAB the output frequency response was drawn without considering the feedback gains:
MATLAB CommandMATLAB Commandclct=[0:0.1:20];u=-0.1*ones(length(t),1);x0=[0 0 0 0];A=[-3.5139 5.0174 0 0;0 -4.332 4.332 0; -40.625 0 -16.25 -16.25; 1.144 0 0 0];eig(A)B=[0;0;18.75;0];C=[1 0 0 0];D=[0];sys=ss(A,B,C,D);[y,x]=lsim(sys,u,t,x0); plot(t,y)Title('The output frequency respronse');xlabel('Time');ylabel('f');grid
0 2 4 6 8 10 12 14 16 18 20-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01The output frequency respronse
Time(s)
Del
ta f
(HZ)
The output frequency response with uncertainties parameters and without feedback gains
Step 5:Step 5: Construct the feedback gainConstruct 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
LFC Block diagram of power system for the proposed robust controller
The output frequency response for the proposed robust controller
Comparison between robust and integral controller
With proposed robust controller
With Integral controller
With proposed robust controller
With 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/Tp=1.05, Kp/Tp=1.494, 1/TT=1.3, 1/TG=1.79,1/RTG=0.7143,KI=1.144
With proposed robust controller
With Integral controller
Figure 3 : With 1/Tp = 0.8, Kp/Tp= 1.1424, 1/TT=1.031, 1/TG=1.52,1/RTG=0.61,KI=0.88
With proposed robust controller
With Integral controller
Figure 4: With 1/Tp = 0.033, Kp/Tp= 4, 1/TT=2.564, 1/TG=9.615,1/RTG=3.081,KI=0.88
Comparison Comparison The use of the PID algorithm for control does not guaranteeoptimal control of the system or system stability, that’s whyin our designs of LFC and AVR we used the optimal linearcontrol systems.
The Fuzzy-logic controller can be seen as a heuristic andmodular way of defining nonlinear system but the fuzzylogic controller failed in considering the uncertainties.
Comparison Comparison The proposed robust controller is simple, effective and canensure that the overall system is asymptotically stable forall admissible uncertainties.
ConclusionConclusionOur 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.