1
AGC of multi-area interconnected power systems by considering different cost
2
functions and Ant Colony Optimization technique based PID controller
3
Corresponding Author: K.Jagatheesan,
4
Dept. of Electrical & Electronics Engg.
5
Mahendra Institute of Engg. & Tech.
6
Namakkal, Tamil nadu, India
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[email protected]
8 9
Co-Authors: B.Anand Dept. of Electrical & Electronics Engg.
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Hindusthan college of Engg. & Tech.
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Coimbatore, Tamilnadu, India.
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Nilanjan Dey
13
Dept. of CSE, Techno India College of Technology, West Bengal, India.
14
[email protected]
15
M.Omar
16
Faculty of Engineering at shoubra
17
Benha University, Egypt
18
[email protected]
19
Valentina E. Balas
20
Faculty of Engineering, Aurel Vlaicu University of Arad, ROMANIA.
21
[email protected]
22 23 24
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Abstract—Automated industries require high quality of power supply for better performance. Therefore,
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power generating units play crucial role. In this work, multi-area power system incorporates six area
3
thermal power systems with different steam configuration is investigated with Automatic Generation
4
Control (AGC). The investigated system included non-reheat thermal power system in area 1 and 2, while
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area 3 and 4 are single reheat thermal power system and area 5 and 6 are double reheat thermal power
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system. All areas are interconnected through tie-line. A Proportional-Integral-Derivative (PID) controller is
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proposed as a secondary controller to provide the necessary control signal during sudden load demand. To
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achieve optimal PID controller performance, the controller gain values are optimized by considering nature
9
inspired meta-heuristic algorithm, namely the Ant Colony Optimization (ACO) technique using different
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objective functions. Time domain specification analysis is considered to evaluate the performance of
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investigated power system, where the power system is designed and modeled under Matlab/Simulink
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environment. Finally, simulation results established that Integra Time Absolute Error (ITAE) objective
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function based PID controller provided superior performance compared to other objective function based
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PID controller.
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Keywords - Automatic Generation Control; Multi-area power systems; Objective function; Proportional-
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Integral-Derivative.
18 19
1. Introduction
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Nowadays, industries are modernized through which powers are reduced by replacing suitable drives to
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improve the overall efficiency and quality. This is achieved based on the power quality, where the drive’s
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performance depends on the good quality power. The consistency in frequency and voltage decides the
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quality of the power supply. To guarantee stable power generating unit and to maintain power system’s
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parameters within the specified value, many control theory has been developed for the past few decades.
2
1
The developed control theory was concerned with single or multi-area interconnected power systems. The
2
first Load Frequency Control (LFC) was published and discussed by chon [1]. Many different control
3
techniques are proposed by researcher to balance power generation with load demand to maintain system
4
stability.
5
The control techniques are: classical control techniques and soft computing/Artificial Intelligence
6
techniques. Automatic generation control of interconnected power system was discussed with Parameter-
7
plane technique in [2]. The LFC of non linear reheat thermal power system parameters were optimized by
8
using Lyapunov Technique [3]. The AGC of interconnected hydrothermal power system was discussed by
9
considering generation rate constraint non linearity and continuous and discrete mode optimization
10
technique in [4]. Optimal control theory was applied into the hydro thermal power system in [5]. Adaptive
11
controller was designed for load frequency control of power system [6]. Das et al. [7] discussed the AGC
12
issue in interconnected reheat thermal power system with Variable Structure Controller (VSC).
13
Chidambaram and Paramasivam [8] presented load frequency control of decentralized interconnected power
14
system by considering energy storage unit and TCPS units. The PID controller parameters in AGC of
15
interconnected power system were optimized by using Artificial Bee Colony (ABC) in [9]. Bacterial
16
foraging technique was applied to tune the fuzzy PID controller parameters in interconnected hydrothermal
17
power system [10]. The PID controller parameters in single area thermal power system were optimized by
18
using Stochastic Particle Swarm Optimization technique [11]. The PI controller parameters were optimized
19
by using conventional tuning method and PID controller parameters are optimized by using Ant Colony
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Optimization technique in multi-area hydro thermal power system with mechanical and electric governor
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[12]. The LFC issue of multi-area interconnected power system was discussed by implementing firefly
22
algorithm in [13]. Dash et al. [14] discussed the AGC of multi-area power system by considering two-
23
degree of freedom (2DOF) controllers and FACTS with Cuckoo Search optimization technique. Fuzzy PID
3
1
controller parameters in AGC of multi-area power system were discussed with Teaching Learning Based
2
Optimization technique in [15]. The recent work related to AGC is illustrated in Table 1.
3
It is clear from the preceding literatures that the main contribution of the current work is:
4 5 6 7 8 9
To design the simulink model of six area transfer function model of investigated multi-area interconnected power system under SIMULINK model. To design the appropriate PID controller for the investigated power system in order to regulate the frequency of the system and tie-line power between interconnected power system. To optimize the controller gain values using ACO technique during one percent Step Load Perturbation (1% SLP) in area 1.
10
The remaining sections of the work are organized as follows. The proposed system model and different
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components of investigated power system is given in the section 2. The design of proper controller using
12
tuning optimization approach is discussed in section 3. The open loop response of proposed system and
13
results obtained with different objective functions are presented in section 4. Finally, the conclusion of the
14
proposed system with proposed optimization technique and performance of different objective functions is
15
introduced in section 5.
16 17
2. Methodology
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Six area interconnected power system is investigated in the current study, which consists of six thermal
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power systems and schematic diagram is shown in fig.1. In the investigated power system area 1 and 2 are
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non reheat turbine equipped thermal power system, area 3 and 4 are single reheat turbine equipped thermal
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power system and area 5 and 6 are double reheat turbine equipped thermal power system. Detailed
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description of the mentioned power system’s areas is given as follows.
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In the investigated power system, when load disturbance occurs in any one of interconnected power system
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it affects the output of corresponding power generating unit and stability of the whole system. In order to
4
1
overcome this issue, power is exchanged between control areas through tie-line. The performance of
2
proposed system is modeled under MATLAB/SIMULINK environment and transfer function model of six
3
area power system shown in fig.2. In figure 2, R1, R2, R3, R4, R5 and R6 are the self regulation parameters
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for the governor in p.u. Hz; Tg1, Tg2, Tg3, Tg4, Tg5 and Tg6 represent the speed governor time constants
5
in sec.; Tr1, Tr2, Tr3, Tr4, Tr5 and Tr6 are the reheat time constants in sec.; Kr1, Kr2, Kr3, Kr4, Kr5 and
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Kr6 are the reheater gain; Tt1, Tt2, Tt3, Tt4, Tt5 and Tt6 are the steam chest time constant in sec.; Tp1,
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Tp2, Tp3, Tp4, Tp5 and Tp6 are the power system time constant in sec. ( Tp 2 H / f * D ); Kp1, Kp2, Kp3,
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Kp4, Kp5 and Kp6 are the power system gain ( Kp 1 / D ); B1, B2, B3, B4, B5 and B6 are the frequency
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bias parameters; delPtie is the incremental tie-line power change; delF1, delF2, delF3, delF4, delF5 and
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delF6 are the incremental frequency deviations in Hz; ACE1, ACE2, ACE3, ACE4, ACE5, and ACE6
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stand for area control error in pu. The optimal parameters of investigated power system parameters are taken
12
from [16-22].
13 14
2.1 Non reheat thermal power system
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In the case of non reheat thermal power plant, turbine consists of two pressure stages. High Pressure (HP)
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steam stage and Low Pressure (LP) steam stage. The input of the turbine is HP steam and output of the
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turbine is LP steam. This type of turbine is called as non-reheat turbine [19].
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The transfer function of non-reheat turbine is given by
19
GT (s )
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Where, S is the Laplace function and Tt is the turbine time constant.
1 1 sTt
(1)
21 22
2.2 Single reheat thermal power system
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1
In reheat thermal power system, it is available different types of turbine models such as, single stage reheat
2
turbine and double stage reheat turbine. The single stage reheat turbine consists of three different steam
3
stages, like high pressure steam, intermediate pressure steam and low pressure steam stages. The input of
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turbine is high pressure steam and output is intermediate pressure steam. It is given into the turbine as an
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input and output is low pressure steam [19].
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The transfer function of single stage reheat turbine is given by
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GT ( s)
8
Where, α is the reheater co-efficient, Tr is the reheater time constant and Tt is the turbine time constant.
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2.3 Double reheat thermal power system
1 1 sTt
1 sTr 1 sTr
(2)
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Double stage reheat turbine consists of four different steam pressure stages, namely the Very High Pressure
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(VHP) steam, High Pressure (HP) steam, Intermediate Pressure (IP) steam and Low Pressure (LP) steam
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stage. The VHP steam is given to the input of turbine and output steam is HP steam. It is given in to the HP
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stage before entering into the LP stage of the steam turbine [19].
14
The transfer function of double stage reheat turbine is given by
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GT (s )
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Α and β are the reheater co-efficient, Tr is the reheater time constant and Tt is the turbine time constant.
(Tr1Tr 2 .s Tr 2 .s s (Tr 2 Tr1) 1) (1 s.Tr1 )(1 s.Tr 2 )(1 s.Tt )
(3)
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3. Proposed System
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3.1 Proportional-Integral-Derivative controller
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1
Proportional-Integral-Derivative controller (PID) is a most commonly used industrial closed loop feedback
2
controller. The proposed PID controller calculates an error value based on the difference between a
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measured value and desired output value. The schematic diagram of proposed controller is shown in fig.3.
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The controller comprises of three basic terms, namely the proportional term, integral term and derivative
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term. Proportional term in the controller increases the loop gain to make the system less sensitive during
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load disturbance, while the integral term vanish the steady state errors in the response of system and the
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derivative term of the controller increase stability of the system. The area control error (ACE) is given as an
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input to the controller, which is defined as combination of change in frequency deviation and tie-line power
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flow deviations [16-22]. The ACE expression for each area is given as follows:
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ACE1 B1 .F1 Ptie1
(4)
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ACE2 B2 .F2 Ptie2
(5)
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ACE 3 B3 .F3 Ptie3
(6)
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ACE 4 B4 .F4 Ptie4
(7)
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ACE5 B5 .F5 Ptie5
(8)
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ACE 6 B6 .F6 Ptie6
(9)
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Based on the controller’s error input, it generates suitable control output signal and given to the power
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system as an input or reference signal. This control signal is given to power system having the ability to
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satisfy sudden load demand. The expression for control signals of each controller in each area is given in the
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following expression [16-22].
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21
U 1 K P1 . ACE1 K i1 . ACE1 dt K d 1 .
dACE 1 dt
U 2 K P 2 . ACE 2 K i 2 . ACE 2 dt K d 2 .
dACE 2 dt
(10)
(11)
7
1
2
3
4
U 3 K P 3 . ACE 3 K i 3 . ACE 3 dt K d 3 .
dACE 3 dt
(12)
dACE 4 dt
(13)
U 4 K P 4 . ACE 4 K i 4 . ACE 4 dt K d 4 .
U 5 K 5 . ACE 5 K i 5 . ACE 5 dt K d 5 .
dACE 5 dt
U 6 K P 6 . ACE 6 K i 6 . ACE 6 dt K d 6 .
dACE 6 dt
(14)
(15)
5
In power system, the controller proper design is mainly based on the selection suitable objective function,
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which is designed based on the desired constraint and specifications. From the literature, it is clearly
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indicated that four different objective functions are commonly used, namely the integral Square Error (ISE),
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integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE) [16-
9
22], where the ITSE objective function is expressed by:
J te(t ) 2 dt 10 11
0
(16)
The ISE objective function is given by:
J e(t ) 2 dt 12 13
0
(17)
The IAE objective function is given by:
J | e(t ) | dt 14 15
0
(18)
While, the ITAE objective function is expressed by:
J t | e(t ) | dt 16
0
(19)
17
These objective functions are then used with the optimization algorithm to identify the optimal PID
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controller parameter values.
8
1 2
3.2 Ant Colony Optimization (ACO) techniques
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The desirable characteristics such as the versatile, robust and population based search, of heuristic
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algorithms are inspired by researchers for solving many combinatorial optimization problems. In this work,
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ACO approach is used for the optimization of PID controller parameters in LFC issue of interconnected
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power systems [20-22].
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The ACO technique has foraging behavior of some natural real ant species. The real ants’ behavior was
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inspired by many researchers to develop and implement many applications in the early nineties [20-22]. The
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natural behavior of ants during food searching process are deposit the pheromone chemical trial on the
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ground in order to mark the favorable path and shortest path and it is more helpful for other ants from the
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same colony to identify. The ants are finding their shortest path between their colony to source without any
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visual cues. The information about shortest path is communicated to others ants from the colonies via
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pheromone trial. The ACO technique has three main phases for solving optimization problem, namely
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initialization, constructing ant solutions and updating pheromone concentration. It is used to tune the
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controller gain values proportional gain (KP), integral gain (KI), derivative gain (KD) gain values
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simultaneously with in the specified constraint. During the initialization phase, number of nodes, number of
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iterations, pheromone quantity and number of iterations area specified. The values of the variable are selected
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to give good results.
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Consequently, the proposed system flow for optimization of PID controller parameters is given by:
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Step 1: Start the simulation
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Step 2: Initialization of ACO algorithm Parameters
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Number of Iterations, Evaporation rate, Number of ants, Pheromone, Probability
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Step 3: Run the Simulink model and Evaluate cost function
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Step 4: Update pheromone and probability
9
1
Step5: Calculate the optimal value of PID controller parameters and fitness value
2
Step 6: Check maximum iteration is reached or not
3
If yes, then stop the process
4
If No, go to step 3 and Repeat the procedure
5
Step 7: Stop
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Thus, from the previous steps the ACO algorithm is used based on the objective (fitness) function to
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determine the optimal PID parameters to guarantee better controller performance. In the present work, the
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initialization parameters (Number of ants, pheromone (τ), evaporation rate (ρ), and number of iterations) were
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selected to give better result as provided by Omar et al. in [20-22]. The parameter values were chosen as: Number of
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ants=50, pheromone (τ) =0.6, evaporation rate (ρ) =0.95 and number of iterations=100.
11 12
4. Simulation Results and Discussions
13 14
The transfer function model of investigated six area interconnected thermal power system with PID
15
controller is designed under MATLAB/SIMULINK environment. The investigated power system is
16
simulated for a simulation time of 120sec., however for clear comparison performance and measurement of
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supremacy purpose graph drawn only up to 20 sec. The controller parameters are optimized by using the
18
four different objective functions, namely the ISE, ITSE, IAE and ITAE with one percent Step Load
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Perturbation in area 1. The open loop frequency deviations and tie-line power flow deviations comparisons
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are depicted in figs. 4 and 5. The performance of ACO- PID controller with different objective functions is
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shown in the figs. 6-14.
22 23
4.1 Open loop response
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1
The open loop frequency deviations and tie-line power flow deviations in area 1, area 3 and area 5 with 1%
2
SLP in area 1 and zero load demand conditions are shown in figs 4 and 5; respectively. In the response,
3
solid lines, dashed lines, dotted lines and the solid bold lines represented the response frequency deviation
4
and tie-line power flow deviation in Area 1 with 1% SLP in area1, Area 3 with 1% SLP in area1, in Area
5
5with 1% SLP in area1 and the load demand =0; respectively.
6
The numerical values are given in the Table 2. It evident that, during nominal or zero loading conditions the
7
parameters of the power system does not affect. When load demand occurs in the power system, it affects
8
system performance and stability with more damping oscillations with large steady state error.
9
The aforementioned issue in power system is solved by implementing proper controller. In this work, the
10
PID controller is implemented as a secondary controller given in section 3.
11 12
4.2 Response of ACO-PID controller with different objective functions
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The closed loop transfer function model of investigated power system with PID controller given in section 2
14
and 1% SLP in applied to the power system at time t=0sec are to be employed. The control parameters KP,
15
KI and KD are optimized by ACO optimization technique and responses are shown figs. 6-14.
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The solid lines denoted the response of ISTE objective function based PID controller response, dashed lines
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represented the ISE based PID controller response, dotted lines illustrated the IAE based PID controller
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response and solid bold lines illustrated the response of ITAE based PID controller response.
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Figs.6-8 demonstrated the frequency deviation comparisons of area 1, area 3 and area 5 with different
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objective functions. The deviations in frequency are effectively reduced and settled fast as soon as possible
21
with ITAE based PID controller compared to other objective function based controller response in the same
22
investigated power system. It is obvious that using the ITAE fitness function is superior to using ISE, IAE
23
or ISTE functions, to obtain the optimal controller parameters.
11
1
The numerical values of different response of power system with different objective function are given in
2
the Table 3 and a comparison chart is shown in fig.15. All power system response with ITAE based PID
3
controller yield less settling (DelF1: 22.03>20.39>11.89>10.29;
4
ACE1:12.19>16.22>10.23>6.647) time with minimal damping oscillations compared other objective based
5
controller response.
6
The preceding results established the efficiency of using the proposed ACO-PID approach to achieve better
7
controller performance using ITAE objective function.
DelPtie1:
12.84>16.59>10.59>9.94;
8 9 10
5. Conclusion
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The current work proposed the design of ACO-PID controller for the thermal power system. The
12
investigated power system is six area interconnected thermal power. The gain values of PID controller,
13
namely the KP, KI, KD were optimized using ACO technique with four different objective functions and
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one percent Step Load Perturbation (1% SLP). The objective functions are ISE, ITSE, IAE and the ITAE.
15
These four functions based designed PID controllers are equipped in power systems to study and analysis
16
the effect of objective functions in the design of controller.
17
The AGC of six area interconnected thermal power system has been successfully designed and investigated
18
with PID controller under MATLAB/SIMULINK environment. The controller parameters, namely the
19
proportional gain, integral gain and derivative gain are optimized by using Artificial intelligence based ACO
20
technique by considering different objective functions. Finally, the simulation results established that the
21
ITAE objective function based PID controller provide better controlled response compared to other
22
objective
23
(DelF1:22.03>20.39>11.89>10.29) compared to ISE, ITSE and IAE based PID controller performance in
24
the same investigated power system.
functions
in
terms
of
minimal
damping
oscillations
with
fast
settled
response
12
1 2 3 4 5 6
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Table 1 Literature survey related to proposed work
1
Size of the power S.No
Year
Author
Technique
Controller system Emotional learning
Farhangi et al. 1
2012
Emotional Learning
Two area thermal
based intelligent
[23] controller Proportional – Differential 2
2013
Rout et al. [24]
Two area thermal
Integral (PI)
Evolution algorithm controller Differential 3
2013
Sahu et al. [25]
2-Degree Of Freedom Two area thermal
Evolution algorithm
(DOF) PID controller
Imperialist Shabani et al. 4
2013
Competitive
Three area
PID controller
[26] Algorithm Imperialist Fractional Order PID 5
2014
Taher et al. [27]
Competitive
Three area (FOPID)
Algorithm Self Adaptive Khooban and 6
2015
Proportional – Four area hydro
Modified Bat Niknam [28]
Integral (PI) thermal
Algorithm
controller Proportional-Integral-
Anwar and Pan 7
2015
Direct Synthesis
Single area
Derivative (PID)
[29] controller
18
8
Sharma and
Grey Wolf
Three area solar
Saikia [30]
Optimizer Algorithm
thermal
2015
Classical controllers
Pradhan et al. 9
2015
Multi area multiFirefly Algorithm
[31]
Fuzzy-PID controller source
Craziness based Arya and 10
2015
Two area multiparticle swarm
Kumar [32]
PI controller source
optimization 1
19
1
Table 2 Performance of Open loop response of system Steady Settling time Response
State error (s) (p.u.)
DelF1
62.54
-0.00384
DelF3
66.98
-0.00384
DelF5
44.36
-0.00384
DelPtie1
42.58
-0.00833
DelPtie3
41.7
0.00169
DelPtie5
49.32
0.00165
0
0
DelF1 with load demand = 0% 2 3
20
1
Table 3 Comparisons of settling time with different objective functions Response
Settling time
/ Objective
ISE
ITSE
IAE
ITAE
DelF1
22.03
20.39
11.89
10.29
DelF3
18.38
16.71
11.3
10.06
DelF5
30.64
33.8
17.5
11.07
DelPtie1
12.84
16.59
10.59
9.94
DelPtie3
22.67
33.39
25.53
19.32
DelPtie5
28.87
27.19
24.9
19.7
functions
ACE1
12.19
16.22
10.23
6.647
ACE3
24.43
25.46
22.79
19.32
ACE5
28.72
26.94
24.99
19.56
2 3
21
1
2 3
Fig.1 Schematic diagram interconnected six area thermal power systems
4 5
Fig.2 Transfer function model of ith control area in six area interconnected thermal power system
6
22
1
Fig.3 Schematic diagram of PID controller 0.002
delF(Hz)
0.000 -0.002 -0.004 -0.006 -0.008 -0.010
Area 1 with 1% SLP in area 1 Area 3 with 1% SLP in area 1 Area 5 with 1% SLP in area 1 Load demand = 0
-0.012 -0.014 0
10
20
30 40 Time (s)
50
60
2 3
Fig.4 Comparisons of open loop frequency deviations 0.004 delPtie(p.u. MW)
0.000
Area 1 with 1% SLP in area 1 Area 3 with 1% SLP in area 1 Area 5 with 1% SLP in area 1 Load Demand = 0
-0.004 -0.008 -0.012 0
4 5
10
20
30 40 Time (s)
50
60
Fig.5 Comparisons of open loop tie-line power deviations
23
0.002
delF1(Hz)
0.000 -0.002 -0.004
ITSE - PID ISE - PID IAE - PID ITAE - PID
-0.006 -0.008 0
5
10
15
20
Time (s) 1 2
Fig.6 Comparison of delF1 with ACO-PID controller considering different objective functions
delF3(Hz)
0.002
0.000
ITSE - PID ISE - PID IAE - PID ITAE - PID
-0.002
-0.004 0 3 4
5
10
15
20
Time (s)
Fig.7 Comparison of delF3 with ACO-PID controller considering different objective functions
24
0.002
delF5(Hz)
0.001 0.000 -0.001 ITSE - PID ISE - PID IAE - PID ITAE - PID
-0.002 -0.003 -0.004 0
5
10
20
Time (s)
1 2
15
Fig.8 Comparison of delF5 with ACO-PID controller considering different objective functions
delPtie1(p.u. MW)
0.001 0.000 -0.001 -0.002 -0.003
ITSE - PID ISE - PID IAE - PID ITAE - PID
-0.004 -0.005 -0.006 0
5
10
20
25
30
Time (s)
3 4
15
Fig.9 Comparison of delPtie1 with ACO-PID controller considering different objective functions 0.0015 delPtie3(p.u. MW)
ITSE - PID ISE - PID IAE - PID ITAE - PID
0.0010 0.0005 0.0000
-0.0005 0 5
5
10
15
20
25
30
Time (s)
25
1
Fig.10 Comparison of delPtie3 with ACO-PID controller considering different objective functions 0.0015 delPtie5(p.u. MW)
ITSE - PID ISE - PID IAE - PID ITAE - PID
0.0010 0.0005 0.0000
-0.0005 0
5
10
20
25
30
Time (s)
2 3
15
Fig.11 Comparison of delPtie5 with ACO-PID controller considering different objective functions
4
ACE1(p.u.)
0.000 -0.002 -0.004
ITSE - PID ISE - PID IAE - PID ITAE - PID
-0.006 -0.008 0 5 6
5
10
15
20
25
30
Time (s)
Fig.12 Comparison of ACE1 with ACO-PID controller considering different objective functions
26
0.001
ACE3(p.u.)
0.000 ITSE - PID ISE - PID IAE - PID ITAE - PID
-0.001
-0.002 0
5
10
15
20
25
30
Time (s) 1 2
Fig.13 Comparison of ACE3 delPtie1 with ACO-PID controller considering different objective functions) 0.002 ITSE - PID ISE - PID IAE - PID ITAE - PID
ACE5(p.u.)
0.001
0.000
-0.001 0
5
15
20
25
30
Time (s)
3 4
10
Fig.14 Comparison of ACE5 with ACO-PID controller considering different objective functions ISE ITSE IAE ITAE
Settling Time (s)
20
15
10
5
0
DelF1
5
DelPtie1 Response
ACE1
27
1
Fig.15 settling time comparisons with different objective functions
28
