 Open Access
 Authors : Nishchitha V A , Monisha Pattnaik , Sushmita Deb
 Paper ID : IJERTV10IS040319
 Volume & Issue : Volume 10, Issue 04 (April 2021)
 Published (First Online): 04052021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Load Frequency Control of a FourArea Interconnected ThermalHydroNuclearWind Power System with NonLinearity using Fuzzy Logic PID Controller
Nishchitha V A*1, Monisha Pattnaik*2 Electrical and Electronics Engineering PES University
Bangalore, India
Mrs.Susmita Deb Associate Professor PES University Bangalore, India
AbstractThis paper illustrates the load frequency control of a fourarea interconnected thermalhydronuclearwind power plant system using fuzzy PID controller. The settling time undershoot, and overshoot of the power system is observed with fuzzyPID controller. The thermal system is fused with boiler dynamics and generation rate constraints [13]. The controlling approach assures that the frequencies and interchange of tieline powers are kept in given limitations [8]. From the results it is clear that the peak overshoot and settling time for fuzzyPID controller is better than conventional controller and fuzzy controller when nonlinearity's is taken into consideration. It can also be observed that due to wind which is a nonconventional power system the settling time of the system increases as a whole. Time domain simulations are used to analyze the performance of the power system. The implementation of the fourarea system is done in MATLAB/SIMULINK package.
KeywordsBoiler dynamics, Generation constraint, Load frequency control, fuzzy PID controller and Tieline power

INTRODUCTION
Load frequency control is done in an electric power system to maintain consistent frequency. During loaded conditions the interconnected plants share power through tieline control. Tie line is used between power systems to allow by directional flow of power. Load frequency control becomes a necessity for power system because if the error in frequency exceeds more than 2% the blades of the turbine are likely to get damaged. The frequency and tieline power will be fluctuated if any load variation happens which will further reduce system performance and can damage load, therefore it is mandatory to maintain frequency at stated limits.
Most of the research conducted in this field neglect non linearity's, for example boiler dynamics and generation rate constraints in the thermal power plant for simplicity and better results [7] [9]. But if we go for practical solution, we need to incorporate these effects. In this paper we have taken non linearity into consideration for our fourarea interconnected system.
In literature controllers based on fuzzy, conventional PID and neural networks [11] are proposed [9]. There are various studies about different controlling mechanism having certain pros and cons. In most of the papers a LFC using a conventional PID controller is exercised and it is highlighted
that the performance of this controller is better than others [12]. However, if nonlinearity in a power system is taken into consideration then conventional controllers fail to give an optimum result. Intelligent controllers can be replaced with PID controllers for quick and better dynamic responses. Fuzzy logic controller is usually more useful than conventional controllers because it is faster and more productive in nonlinear applications. Fuzzy logic controller is used to reduce variations on system outputs. In this paper LFC of thermalhydronuclear wind power system is implemented using fuzzyPID controller.

FOURAREA POWER SYSTEM
Power systems mostly comprise of multiple areas which may consist of nonlinear behavior [4]. These areas are interconnected to each other by tieline which need controlling of power flow and frequency [5]. Fig. 1, demonstrates a four area interconnected power system used in our research.
Fig. 1 fourarea interconnected power system
Area 1 encompasses a thermal power plant consisting of a speed governor, steam turbine, electric generator and a single stage reheater. In order to develop a realistic model all non linearity's related to the system is incorporated. Nonlinear mostly relates to how valve position are uninterrupted with respect to change in speed [1]. Boiler dynamics on the other hand relates to how reheater can actively receive steam from boiler.

MATHEMATICAL MODELLING OF FOURAREA POWER SYSTEM
(1)
where A is system matrix, B is input matrix, F is disturbance matrix, x is state vector given in equation (2), u is control vector given in equation is disturbance vector given in equation (4) [3].
(2)
(3)
(4)
State vectors of matrix 2 is given below [3],

NONLINEARITY

Boiler Dynamics
In this paper a drum type boiler is incorporated. Pressure control, boiler storage and fuel system transfer functions are considered in the boiler leading or turbine modes of operation. The Fig. 2 shows the simulated model of boiler [13].
Control signals of matrix 3 is given as [3],
where , , , is given below,
(5)
(6)
(7)
(8)
(9)
Fig. 2 Boiler

Generation rate constraint
In practical system due to mechanical and thermal restriction the rate at which output power can be adjusted has a limit specified to it [2]. This limit is termed as Generation rate constraint. Fig. 3 shows the simulated model of Generation rate constraint [13].
Fig. 3 Generation rate constraint
where,
(10)


COMPLETE SIMULINK MODEL OF FOUR AREA POWER SYSTEM
Fig. 4 Input1 membership function
Fig. 5 Input2 membership function
Fig. 6 Output membership function
TABLE 1: RULE TABLE WITH 5 MEMBERSHIP FUNCTIONS
ACE
ACE
N
S
Z
P
B
N
N
N
N
S
Z
S
N
N
S
Z
P
Z
N
S
Z
P
B
P
S
Z
P
B
B
B
Z
P
B
B
B
ACE
ACE
N
S
Z
P
B
N
N
N
N
S
Z
S
N
N
S
Z
P
Z
N
S
Z
P
B
P
S
Z
P
B
B
B
Z
P
B
B
B

CONTROLLERS

PID Controller
A PID controller continuously evaluates an error value as the difference between a desired signal and a measured process variable and resultant error is multiplied with the proportional constant ). Integral mode is used to remove the steady state error which could not be removed by proportional mode, ) [10] is the integral constant. Derivative mode in the controller improves stability of the system and increases gain and decreases time constant thereby increasing speed of thecontroller response, ) is the derivative constant.

Fuzzy controller
If we further want to improve the transient response and settling time we go for intelligent techniques such as fuzzy logic. This controller works on the basis of sets, these sets are represented by membership function [16] and output is based on degree of membership function. Therefore, the Fuzzy logic controller is used to get optimal result.

FuzzyPID controller
It the combination of fuzzy logic and conventional PID controller, which gives better transient response and setting time. Fig. 4, Fig. 5, Fig. 6 shows the input output membership functions for this controller. Table 1 shows the rule table [11] of fuzzy logic where inputs are ACE and ACE.


SIMULATION AND RESULTS Simulations were performed with the parameters given in
the appendix, with conventional PID controller, FLC and FuzzyPID controller for the fourarea system. Simulation was carried out for step load change of 10% given simultaneously for each area. The GRC for thermal system is considered for 1%. The change in frequency of the system with PID, Fuzzy and fuzzyPID is given in Fig. 7, the settling time, undershoot and overshoot are observed and tabulated in Table
2. Fig. 8 shows the frequency response of three area (thermalhydronuclear) which are conventional systems with FuzzyPID controller. Fig. 9 shows the frequency response of four area with wind incorporated which is a non conventional system. Table 3 shows the comparison table of conventional system with a nonconventional system. It is observed that for a fourarea system as compared to fuzzy and PID, fuzzyPID controller gives better response based on time domain parameters and maintains the system frequency. Also, the result shows that by introducing wind system the settling time increases but maintains the system frequency and is in constant steady state value.
Fig. 7 Output response for PID, Fuzzy and FuzzyPID
Fig. 8 Output response of conventional system
Fig. 9 Output response with nonconventional system

CONCLUSION
In this paper load frequency control of four area interconnected thermalhydronuclearwind power plant system is performed using FuzzyPID controller. From results we can analyze the settling time, overshoot and undershoot of FuzzyPID is better as compared to PID and Fuzzy controllers, Fuzzy PID controller gives the best response when uncertainty and nonlinearity are considered.
TABLE 2: COMPARISION FOR 3 AREA AND 4 AREA
Settling time (s)
Overshoot (%)
Undershoot (%)
PID
68.18
0.24
0.04
Fuzzy
100.7
–
–
FuzzyPID
30.542
0.46
0.0165
It can also be seen that when wind system is included the settling time, overshoot and undershoot of the area increases signifying that when nonconventional system is added it disturbs the time domain parameters to a certain extent.
TABLE 3: COMPARISION FOR 3 AREA AND 4 AREA
Area 3
Area 4
Areas
Settling time(s)
Over shoot (%)
Under shoot (%)
Settling time(s)
Over shoot (%)
Under shoot(%)
Thermal
53.175
0.1179
0.1648
79.95
0.77
0.12
Hydro
53.175
0.13
0.08
79.95
0.808
0.15
Nuclear
53.175
0.24
0.26
79.95
0.230
0.838
Wind
–
–
–
79.951
0.0519
0.1615
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APPENDIX Boiler – T1 = 53.82
T2 = 3.15
T3 = 0.030
= 200
= 10
= 69.2
thermal = 0.000005225
= 1
= 0.000019605
= 1
= 0.08
= 1
= 0.3
= 3.33
= 10
hydro – = 0.000006127
= 1
= 0.000019605
= 1
= 0.487
= 0.513
= 10
= 1
= 0.5
Nuclear – = 0.0000043
= 0.04
= 0.0000012
= 0.08
= 2
= 0.08
= 0.3
= 0.5
= 7
= 6
<>= 10
= 0.08
wind – = 0.000001149
= 0.00006
= 0.000028278
= 0.041
= 7.5
= 1.25
= 1
= 1.4
= 1
K1 = k3 = k5 = k7 = 0.429 k2 = k4 = k6 = k8 = 0.4156
= = = = = = 0.07064
= = = = 120
= = = = 20 [15] [6][10] [14]