Load Frequency Control of two Area Power System using PID1 Controller

Load Frequency Control of two Area Power System using PID1 Controller

D. Khamari*,J. K.Rout, B. K.Singh, D. Bhoi, L. K. Patel

Department of Electrical and Electronics Engineering Vikash Institute of Technology,

Bargarh, Odisha, India

Abstract:- This paper presents a load frequency control (LFC) of two equal area power system. Initially non-reheat thermal system is considered in each area with modified proportional plus integral plus derivative (PID1) controller. In the next step firefly algorithm is employed to tune the optimum gain of the PID1 controller. Then the superiority of the proposed approach is demonstrated by comparing the result with some recently published technique such as genetic algorithm (GA) based PI, bacteria foraging optimization algorithm (BFOA) based PI controllers for the same interconnected power system. Investigations reveal on comparison that modified proportional integral derivative controller (PID1) provides much better response in terms of settling time, peak over shoot and peak under shoot compared to proportional integral (PI) controllers.

Keywords:- Load frequency control (LFC), Two-area power system, Firefly algorithm (FA), proportional plus integral (PI) modified proportional plus integral plus derivative (PID1) controller

1. INTRODUCTION:

   An electric energy system must be maintained at a desired operating level characterized by nominal frequency and voltage profile and this is achieved by close control of real and reactive powers generated through the controllable source of the system. Therefore, the control issue in power systems can be decoupled into two independent problems. One is about the active power and reactive power and voltage control [1]. The active power and frequency control is referred to as LFC. A large frequency deviation can damage equipment, degrade load performance, cause the transmission lines to be over loaded and can impede with system protection schemes, ultimately leading to an unstable condition for power system [2]. Thus, the primary job of LFC is to maintain the frequency constant against the arbitrarily varying active power loads, which also referred to unknown external disturbance. Another job of

   the LFC is to regulate the tie-line power exchange error. A typical large-scale power system is composed of several areas of generating units. To reduce the cost of electricity and to improve reliability of power supply, these generating units are connected via tie lines [1]. The usage of tie-line power imports a new error into the control problem, i.e., tie-line power exchange error. When a sudden active power load exchange occurs to an area, the area will obtain energy via tie-lines from other areas. But eventually, the area that is subject to the load change should balance it without external supports; otherwise there would be economic conflicts between the areas. Hence, each area requires a separate load frequency controller to regulate the tie-line power exchange error so that all the areas in an interconnected power system can set their set- point differently [3,4]. In [5] Ali and abd-Elazim employed a BFOA to optimize the PI controller parameters and shown its superiority over GA in a two-area non-reheat thermal system. In [6] author were employed modified classical controller structure such as structure 1 and 2 of PID controller (PID1) and structure 2(PID2) were applied and their performances was compared for an automatic generation control (AGC) system. In [7] author were demonstrated the superiority of Firefly Algorithm tuned PI/PID controller of two area interconnected power system for AGC.

2. POWER SYSTEM MODEL

1. LFC model

   The Load Frequency Control (LFC) for two-area interconnected non-reheat thermal power system is shown in Figure 1. Each area has two outputs and three inputs. The inputs are the controller input Pref, tie-line power error PTie and load

   B1 1

   R1

   + –

   PD1

   –

   AEC1

   +

   PG1

   1 1 sTG1

   1 1 sTG1

   PI/PID1

   Controller

   PI/PID1

   Controller

   +

   a

   PT 1

   1 1 sTT 1

   1 1 sTT 1

   +

   –

   a12

   PTie

   a12

   a12

   T12 S

   F1

   KPS 1

   1 sT PS 1

   KPS 1

   1 sT PS 1

   +

   –

   AEC2

   PI/PID1

   Controller

   PI/PID1

   Controller

   + 1

   PG 2

   P21

   1 1 sTT 2

   1 1 sTT 2

   PT 2-

   KPS 2

   1 sT PS 2

   KPS 2

   1 sT PS 2

   F 2

   1 s

   TG 2+

   –

   B2

   B2

   – PD 2

   1

   R2

   (Fig- 7, Block diagram of two area non reheat thermal power system)

   disturbance PD. The outputs are the generator frequency f and area control error (ACE) given by Eq. (1).

   AEC = B f + PTie (1)

   Where B represents the frequency bias parameter.

   To simplicity the frequency-domain analysis, transfer functions are used to model each component of the area. Turbine is represented by the transfer function [2]:

   Input

   KP

   Proportional gain

   KD

   Derivative gain

   KP

   Derivative

   du dt

   Output

   () = () = 1

   (2)

   () 1+

   Integral gain

   From [2], the transfer function of a governor is:

   Integrator

   () = () =

   ()

   1

   1+

   (3)

   KI 1

   S

   The speed governing system has two inputs and

   1

   1

   with one output () given by [4]

   Fig. 2 Block diagram of PID1 controller structure

   () = () () (4)

   () =

   = +

   (7)

   1

   1 1 1

   The generator and load is represented by the transfer function [5]

   2() = 2 = 22 (8)

   () =

   1+

   1

   2

   (5)

   In this paper ITAE is used as objective function to properly design the proposed PI/PD1 controller. The expression for Integral Time Absolute Error (ITAE) objective function is

   Where Kps= and Tps =

   The generation load system has two inputs

   () () with one output () given by

   given in equation (9):

   = = (|

   | + |

   | ). . (9)

   0

   () = ()[ () ()] (6)

2. Controller Structure and Objective Function

To control the frequency PI/PID1 controller are provided in each area. The structure of the PID1 controller is show in figure2 where KP1, KP2, KI1, KD1, are the proportional, integral &derivative gains respectively. The error input to the controllers is the respective ACE given by,

In the above equations,is the incremental change in frequency of area m, is the incremental change in the tie line power connecting between area m and n, and tsim is the time range simulation.

Therefore, the design problem can be formulated as the following optimization problem.

Minimize J (10)

Subject to

1 1 1 ,

,

,

2 2 2

(11)

The minimum and maximum values of PID controller parameters are chosen as -2.0 and 2.0 respectively.

1. SIMULATION RESULT AND DISCUSSION

   The load frequency control (LFC) for two-area interconnected non-reheat thermal power system in shown fig-1. Each are has two output and three inputs the inputs are the controller input tie line power error Ptie and load disturbance PD the output are the generated frequency f. The controller parameter values are shown in table 1.

   Table 1 PI/PID1 Controller Parameter

   Parameter	GA:PI[5]	BFOA:PI[5]	FA:PID1
   KP1	0.2346	0.4207	0.9176
   KI	0.2662	0.2795	1.9963
   KD	–	–	0.6002
   KP2	–	–	0.6020

   A 10% step increase in load demand is applied in area-1 at t=0 sec and the system performance with the PI/PID1 controller is shown in table 2. It is clear from table 2 that better system performance in terms of settling time in frequency and tie line power deviation with ITAE error is achieved with FA tuned PID1 controller compare to GA tuned PI [5] and BFOA tuned PI [5] approaches as mentioned in table 2.

   Table 2 Comparative performance values for 10% step load charge in area-1

   Techniques/ parameters	Settling times (2% band)Ts			ITAE
   	F1	F2	Ptie
   GA:PI[5]	10.59	11.39	9.37	2.7475
   BFOA:PI[5]	5.52	7.09	6.35	1.7975
   FA:PID1	0.70	0.63	0.60	0.1464

   Case A: step load change in area-1

   Initially, a step increase in load of 10% in area -1 is considered and system dynamic response i.e. the deviation in frequency of the area -1, area-2 and deviation in tie-line power are shown in figures 3-5. It is clear from figures 3-5 that stability is improved and frequency error, tie-line power deviation and settling time get reduced.

   (Fig.3. Change in frequency of area-1 for 10% SLP in area-1)

   (Fig.4. Change in frequency of area-2 for 10% SLP in area-1)

   (Fig.5. Change in tie-line power for 10% SLP in area-1)

   Case B: Step load change in area-2

   In this case, a step increases in load of 10% in area 2 is considered and the system dynamic response i.e. the deviation in frequency of area-1, area-2 and deviation in tie-line power are shown in figures 6-8. From these figures it can be seen that the maximum under shoot, over shoot are also reduced which improves the stability of the power system.

   (Fig.6.Change in frequency of area-1 for 10% SLP in area-2)

   (Fig.7.Change in frequency of area-2 for 10% SLP in area-2)

   (Fig.8. Change in tie-line power for 10% SLP in area-2)

   Case C: Simultaneously step load change of 20% in area-1 and 10% in are-2.

   In this case step increase in load of 10% in area-1 and 20% in area-2 simultaneously are considered and system dynamic responses are shown in figure 9-11 that the best dynamic performance is achieved by firefly algorithm tuned PID1 controller compare to the Genetic algorithm tuned PI controller, Bacteria foraging optimization algorithm tuned PI controller for the similar two area power system.

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   (Fig.9.Change in frequency of area-1 for 20% SLP in area-1 and 10% SLP in area-2)

   (Fig.10. Change in frequency of area-2 for 20% SLP in area-1 and 10% SLP in area-2)

   (Fig.11.Change in tie-line power for 20% SLP in area-1 and 10% SLP inarea-2)

   4. CONCLUSION

   In this work an attempt has been taken to apply firefly algorithm based modified proportional Integral Derivative controller (PID1) for load frequency control of two area interconnected power system. Simulation result show that better system performances in terms of ITAE objective function minimum setting time in frequency and tie line power deviations is achieved with firefly Algorithm optimized modified proportional integral derivative controller (FA PID1) compare to genetic algorithm optimize proportional integral controller (GA PI) and Bacteria foraging optimization algorithm optimized proportional integral controller (BFOA PI). This concludes that FA PID1 outperform GA PI and BFOA PI.

   APPENDIX

   Nominal parameters of the two-area system investigated are [5]

   B1=0.425;B2=0.425;R1=2.4;R2=2.4;Tg1=0.08;Tg2=0.08; Tt1=0.3;Tt2=0.3;Kps1=120;Kps2=120;Tps1=20;Tps2=20; T12=0.545;a12=-1;

   REFERENCES

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   2. Hassan Bevrani.: Robust Power System Frequency Control, Springer, (2009)

   3. Kundur P.: Power System Stability and Control, New Delhi: Tata McGraw Hill ,(2009)

   4. L.C. Saikia, J.Nanda, and S. Mishra.: Performance comparison of several classical controllers in AGC for multi-area interconnected thermal system. International Journal of Electrical Power & Energy SystemsVol. 33,(2011) 394401

   5. Ali ES., Abd-Elazim S M.,Bacteria forging optimization algorithm based load frequency controller for interconnected power system, int. J. Elect. Power Energy Syst.,Vol. 33, pp. 633- 638, 2011.

   6. D.Khamari,L.Mishra,S.Sahu,P.Gartia,B.P.Gouda,M.Dash,: Automatic generation control of an interconnect power system using modified classical control. Int.journal of Eng.Research and Technology Vol.6 (2017) 303-312.

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