Under the guidance of
Dr. Abraham T. Mathew
Submitted by: Avdesh Mehra
M170250EE
ICS
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Objective
Automatic Voltage Regulator System
Modeling and Simulation
PID tuning Algorithms
Genetic Algorithm
Particle Swarm Optimization
Results
Work to be done
References
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To model and analyze the synchronous power generator
in MATLAB.
To design an optimum PID controller for Automatic
voltage regulator (AVR) system.
Applying Particle Swarm Optimization (PSO) and
Genetic Algorithm (GA) for the specified problem
statement.
To analyze, apply and compare the PSO and GA for
best performance of the system.
To test different Fitness Functions and compare for best
results.

It is used with the synchronous generators in the power
plants.

Controls the voltage of the system nearer to the steady state
stability.

The automatic voltage regulators reduce the over voltages
which occur because of the sudden loss of load on the
system.

It increases the excitation of the system under fault
conditions so that the maximum synchronizing power exists
at the time of clearance of the fault.
Power transmission:
SIMULINK MODEL OF AVR SYSTEM:
STEP RESPONSE WITHOUT PID:
Genetic Algorithm (GA):
 GA is a search based optimization technique based on
the principle of natural genetics and natural
selection.
 It finds the optimal solution
 Genetic algorithms are a particular class of
evolutionary algorithms that use techniques inspired by
evolutionary biology such as inheritance, mutation,
selection, and crossover (also called recombination).
1.
A 50x3 gain chromosome population is generated.
𝐾𝑝1 𝐾𝑖1 𝐾𝑑1
⋮
⋮
⋮
𝐾𝑝50 𝐾𝑖50 𝐾𝑑50
50×3
2.
3.
4.
Fitness value is calculated for each gain vector using
the fitness function.
𝑧 = 1 − 𝑒 −𝑏 × (𝑀𝑝 +𝐸𝑠𝑠 ) + 𝑒 −𝑏 × 𝑡𝑠 − 𝑡𝑟
where b=1
Best individuals will be selected according to The
Roulette Wheel Selection Method.
Crossover and Mutation will occur and the original
population will be updated.
Selected Best Parent Gain Chromosomes (A and B):
A
0.1
0.2
0.3
B
0.4
0.5
0.6
C
0.4
0.2
0.3
0.9
0.3
Crossover Gain Chromosome (C)
D
0.4
Mutated Gain Chromosome (D)
SELECTION:
• Roulette Wheel Selection Method is used.
• Gains having the minimum fitness value will get selected more
number of times.
• A new 50x3 gain matrix will be formed using the best gain values.
Kp
Ki
Kd
Fitness
Function
A
0.231
0.123
0.215
0.02
0.5
A
0.231
0.123
0.215
0.02
0.365
0.2
A
0.231
0.123
0.215
0.02
0.211
0.341
0.6
C
0.159
0.247
0.365
0.1
0.917
0.782
1.2
C
0.159
0.247
0.365
0.1
Kp
Ki
Kd
Fitness
Function
A
0.231
0.123
0.215
0.02
B
0.516
0.314
0.786
C
0.159
0.247
D
0.412
E
0.952
Initial Population
Selected Best Gains
CROSSOVER:
Child1 = beta1*Parent1+(1-beta1)*Parent2
Child2 = beta2*Parent1+(1-beta2)*Parent2
Where beta value will be decided by:
betas=rand(2,1)*(1+2*alpha)-(0.5+alpha)
And alpha=2.
Crossover is responsible for the convergence of the algorithm.
Kp
Ki
Kd
Fitness
Function
A-A
0.231
0.123
0.215
0.02
A-A
0.231
0.123
0.215
0.02
A-C
0.231
0.123
0.365
0.1
A-C
0.231
0.123
0.365
0.1
C-C
0.159
0.247
0.365
0.2
MUTATION:
Mutation will modify the gain chromosomes randomly
and generate a new population with new fitness function values.
Kp
Ki
Kd
P
0.231
0.399
0.215
Q
0.231
0.123
0.563
R
0.832
0.123
0.365
S
0.231
0.412
0.365
T
0.741
0.247
0.365
TERMINATION OF LOOP :
Termination can be achieved in 3 ways:
• When there has been no improvement in the population for X iterations.
• When we reach an absolute number of generations.
• When the objective function value has reached a certain pre-defined value.
The second type of termination condition is being used in the program.
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑃𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑠𝑖𝑧𝑒 × 20 + 10
In this case population size =50, maximum generations=70.
Fitness function value for each iteration:
GA algorithm flow chart:
Particle Swarm Optimization Algorithm (PSO):

PSO is a search based optimization technique based on
the principle of swarm intelligence.

Inspired from the natural social behavior and dynamic
movements with communications of insects, birds and
fish.
1.
A 50x3 gain particle population is generated, initialised and
their fitness value is calculated.
𝐾𝑝1 𝐾𝑖1 𝐾𝑑1
⋮
⋮
⋮
𝐾𝑝50 𝐾𝑖50 𝐾𝑑50
50×3
For Example:
Kp
Ki
Kd
Fitness
Function
A
0.231
0.123
0.215
0.8
B
0.516
0.314
0.786
0.5
C
0.159
0.247
0.365
0.2
D
0.412
0.211
0.341
0.6
E
0.952
0.917
0.782
1.2
Where Kp,Ki,Kd are the uniform random values
generated within the specified range of [0 0 0] to [1.5 1 1]
2.
Initialize the Global Best and Personal Best fitness function values
to infinite and Direction Matrix to zeros.
gBest=0 and pBest=0
Example of direction Matrix:
A
0
0
0
B
0
0
0
C
0
0
0
D
0
0
0
E
0
0
0
3.
Update the Gains and Direction of the 𝑡 𝑡ℎ particle according to
the following equations.
particle(t).Direction = w*particle(t).Direction
+ c1*rand(VarSize).*(particle(t).Best.Gain - particle(t).Gain)
+ c2*rand(VarSize).*(GlobalBest.Gain - particle(t).Gain)
particle(t).Gain = particle(t).Gain + particle(t).Direction;
where,
c1,c2=2,
maximum weight=0.9, minimum weight = 0.4
After 𝑡 𝑡ℎ iteration:
Kp
Ki
Kd
Fitness
Function
A
0.231
0.123
0.215
1.500
B
0.516
0.314
0.786
0.200
C
0.396
0.610
0.186
0.077
D
0.412
0.211
0.341
0.121
E
0.952
0.917
0.782
1.200
gBest=0.2,pBest=0.2
Best Gains will be 𝐾𝑝 = 0.396 , 𝐾𝑖 = 0.610 , 𝐾𝑑 = 0.186
TERMINATION OF LOOP :
Termination can be achieved in 2 ways:
• When we reach an absolute number of generations.
• When the objective function value has reached a certain pre-defined value.
The second type of termination condition is being used in the program.
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 100
Fitness function value for each iteration:
PSO algorithm flow chart:

Original objective function: 𝑊 𝑘 = 1 − 𝑒 −𝛽 × 𝑀𝑃 + 𝐸𝑆𝑆 +
𝑒 −𝛽 (𝑡𝑠 − 𝑡𝑟 )

Where 𝛽 is constant.

Modified Objective Function 1: 𝐹 𝑘 = 𝛼 × 𝑀𝑃 + 𝐼𝑆𝐸 + 𝛽 𝑡𝑠 + 𝑡𝑟

Where, 𝛼 𝑎𝑛𝑑 𝛽 are constants and 𝐼𝑆𝐸 =

Integral time squared error: 𝐼𝑇𝑆𝐸 =

Integral Time Absolute Error: 𝐼𝑆𝐴𝐸 =

Integral Absolute Error: 𝐼𝐴𝐸 =
𝑡𝑠𝑖𝑚
0
𝑡𝑠𝑖𝑚
𝑡
0
𝑡𝑠𝑖𝑚 2
𝑒 (𝑡)𝑑𝑡
0
× 𝑒 2 (𝑡)𝑑𝑡
𝑡𝑠𝑖𝑚
𝑡
0
𝑒(𝑡) 𝑑𝑡
× 𝑒(𝑡) 𝑑𝑡


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Coding and general analysis of PSO and GA
algorithms.
Modification of algorithms for single objective PID
controller for the AVR system.
Genetic algorithm is applied with the following fitness
functions: Original, ITSE, ITAE, ISE, IAE, Modified
PSO algorithm is applied for the following objective
functions: Original, ITSE, ITAE, ISE, IAE.
Results are obtained and compared.
FITNESS
FUNCTION
Rise Time
Settling
Time
% Peak
Overshoot
Steady State
Error
GA (Original)
0.3232
0.5022
0
0.0038
GA (ITSE)
0.1238
0.7189
21.7142
0.0033
GA (ITAE)
0.1348
0.7529
19.1245
0.0053
GA (ISE)
0.0904
3.5078
24.5994
0.0002277
GA (IAE)
0.1257
0.7264
21.5095
0.0117
GA (Modified)
0.2034
1.9503
1.000
0.0042
Table 1: For different Fitness functions with GA algorithm
FITNESS
FUNCTION
Rise Time
Settling
Time
%
PeakOvershoot
Steady State
Error
PSO (Original)
0.3335
0.5213
0
0.0038
PSO (ITSE)
0.1065
1.7390
42.3452
0.0091
PSO (ITAE)
0.1196
1.2043
32.7725
0.0044
PSO (ISE)
0.1000
1.6650
44.7595
0.0013
PSO (IAE)
0.1046
1.5689
43.5791
5.9365e-04
Table 2: For different Fitness functions with PSO algorithm
GA bar graphs:
Rise Time
Settling Time
Rise Time
Settling Time
3.5078
0.3232
0.1238
GA
0.1348
GA (ITSE) GA (ITAE)
0.0904
GA (ISE)
0.1257
GA (IAE)
(Original)
0.5022
0.7189
0.7529
GA
GA (ITSE)
GA (ITAE)
GA (IAE)
Steady State Error
% PeakOvershoot
21,7142
24,5994
19,1245
Steady State Error
0.0117
21,5095
0.0038
0.0033
0.0053
0.000227
7
0
(Original)
GA (ISE)
(Original)
% Peak Overshoot
GA
0.7264
GA (ITSE) GA (ITAE)
GA (ISE)
GA (IAE)
GA
(Original)
GA (ITSE) GA (ITAE)
GA (ISE)
GA (IAE)
GA ALGORITHM RESULT PLOTS:
GA STEP RESPONSE Fitness
Function: Original
GA STEP RESPONSE Fitness
Function: ITSE
GA STEP RESPONSE Fitness
Function: ITAE
GA STEP RESPONSE Fitness
Function: ISE
GA STEP RESPONSE Fitness
Function: IAE
GA STEP RESPONSE Fitness
Function: Modified
PSO ALGORITHM RESULT PLOTS:
PSO STEP RESPONSE Fitness
Function: Original
PSO STEP RESPONSE Fitness
Function: ITSE
PSO STEP RESPONSE Objective
Function: ITAE
PSO STEP RESPONSE Objective
Function: ISE
PSO STEP RESPONSE Objective
Function: IAE
SIMULINK MODEL FOR GA-PSO COMPARISION
SIMULINK OUTPUT:

Applying new optimization algorithms like Fire fly algorithm,
Krill herd algorithm, Fish for hash algorithm, Cuckoo search
algorithm for better results.

Applying these algorithms and designing PID controller for
MULTI-OBJECTIVE PERFORMANCE CRITERIA to search
efficiently the optimal PID controller parameters of an AVR
system.

Taking into consideration, the non-linearity of the AVR system
and further analyzing the system using optimization methods.

Applying the dq method for controlling the field voltage of
Synchronous Machine.
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Controller in AVR System,” IEEE Transactions on Energy Conversion, Vol. 19, pp. 384-394
(2004).
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AVR System”, Tamkang Journal of Science and Engineering, Vol. 12, No. 3, pp. 259-270
(2009)
[3] Olle L. Elgerd, Electric Energy Systems Theory, 2 ed. Tata McGraw Hill, 2006.
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Conference on Emerging Technologies and Factory Automation. ETFA (1996)
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Applications, pp. 141 – 145 (1995)
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ICNN'95 - International Conference on Neural Networks, Volume: 4, Page s: 1942 – 1948,
(1995)
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System Using Particle Swarm Optimization Algorithm”, 24th Canadian Conference on Electrical and Computer Engineering(CCECE), pp. 337-340 (2011)
[8] Sheikh Abid Hossain ; Sourav Roy ; Animesh Karmaker ; Md. Rafiqul Islam, “Performance
improvement of PID controller for AVR system using Particle Swarm Optimization”, International
Conference on Advances in Electrical Engineering (ICAEE), pp. 243 - 246 (2015)
[9] G. Shabib, A. G. Moslem,and A. M. Rashwan, “Optimal Tuning of PID Controller for AVR System
Using Modified Particle Swarm Optimization”, Recent Advance in Neural Networks, Fuzzy Systems
and Evolutionary Computing, pp. 104-110, 2005.
[10] Rosy Pradhan, Santosh Kumar Majhi, Bibhuti Bhusan Pati, "Design of PID controller for
automatic voltage regulator system using Ant Lion Optimizer", World Journal of Engineering, Vol. 15
Issue: 3, pp.373-387 (2018)
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