Swarm and Bacterial Foraging based Optimal Power System Stabilizer for Stability Improvement Prakash K. Raya, Shiba R. Paitala, Asit Mohantyb ,T. K. Panigrahia, Manish Kumara, Harishchandra Dubeyc a Department of Electrical Engineering, IIIT Bhubaneswar, India. (e-mail: pkrayiiit@gmail.com, shiba.paital@gmail.com, tapas@iiit-bh.ac.in, manishdxsy@gmail.com) bDepartment of Electrical Engineering, CET Bhubaneswar, India. (e-mail: asithimansu@gmail.com) cDepartment of Electrical Engineering, The University of Texas at Dallas, USA (e-mail: harishchandra.dubey@utdallas.edu) Abstract—This paper presents a robust power system stabilizer (PSS) based PID controller for study of stability in a single-machine-infinite-bus (SMIB) power system. The PID controller gains are optimized by bacterial foraging optimization (BFO) and particle swarm optimization (PSO) for improvement of system stability in SMIB system. The robustness of the controller was tested under different operating conditions and their performances are being compared with the conventional PSS-PID controller. In addition, their effectiveness are also investigated through the performance indices like Integral Squared Error (ISE), peak overshoot and settling time. Further, stability of the power system is evaluated by bode plot and mean squared error curve of the proposed optimization techniques. It is observed from the simulated results that PSO based PSS-PID controller provide better performance and stability as compared to BFO optimized PSS-PID and conventional PSS-PID controllers under different operating scenarios. Keywords— Bacterial foraging optimization (BFO), particle swarm optimization (PSO) power system stabilizer, singlemachine-infinite-bus (SMIB), stability. I. INTRODUCTION Due to the increase in power demand, the modern electric power systems are being forced to operate near their stability limits. This may lead to some power quality issues [1-2] and low frequency oscillations in the order of 0.2 Hz–3.0Hz under sudden disturbance conditions. These low frequency oscillations are produced due to variation in loading conditions, fault disturbances and can cause sustained oscillations in the voltage and frequency of the system and may also reduce power transfer capability of the system. In order to damp these low frequency power system oscillations in the system and to improve the transient stability, power system stabilizers (PSS) are extensively used due to its simplest structure, ease of implementation and its ability to damp out these oscillations by supplying necessary stabilization signals effectively and economically [3-7]. Power system stabilizers (PSSs) must be versatile and flexible enough so that it can damp these oscillations quickly over wide range of operating conditions and disturbances. Proportional-Integral-Derivative (PID) controllers are being used broadly in process control industries due to its simplicity and high performance since several decades [8]. Conventionally the parameters of Power system stabilizers with wash-out, lead-lag compensator gain, PSS gain etc. are tuned manually on hit-and-trial basis. But, due to the increase in complexity of the power system, the parameters are c 978-1-5090-2597-8/16/$31.00 2016 IEEE tuned with some artificial intelligence techniques like Particle Swarm Optimization (PSO) [9] and Neural Networks (NN) [10-11] in order to obtain improved performances. In [12-13] Genetic algorithm (GA), Fuzzy logic [14-15] etc. are used for tuning the parameters of PID controller and the power system stabilizer. In this proposed research, PID based PSS controllers have been designed based on BFO, PSO and are incorporated with a SMIB system to damp the transient stability oscillations produced due to load disturbances. The performance of the proposed controller is simulated via Matlab /Simulink and compared with the other conventional methods such as PSSPID. It has been proved that the proposed controller gives superior performance in terms of enhancing power system stability than the conventional controllers. II. POWER SYSTEM MODELING In this proposed research, a single machine infinite bus system is considered as shown in Fig. 1 for the stability study. The system is linearized based on Phillips–Heffron model as shown in Fig. 2 to simplify the small-signal stability study. Of course, though the linearization may affect for large disturbance study, but is affected to lesser amount in case of small-signal study this considers a lower range of variation in load demand. For the analysis, a fourth order model of synchronous machine was taken for study with conventional PSS, and PSS-PID based controller is illustrated in Fig.2 [1617]. The mathematical modeling of the power system was represented by third order model given by [16]; 1916 δ = ωb (ω − 1) (1) Tm − Te − D (ω − 1) M (2) E fd − ( xd − xd′ ) id − Eq′ E q′ = Td′0 (3) ω = E fd = K A ( vref − vt ) − E fd Te = vqiq + vd id TA (4) (5) Where, Tm and Te are the mechanical torque and electrical torque respectively; Ȧ and Ȧb are the rotor speed and base speed respectively; M and D are the machine inertia and damping coefficient respectively; į is the rotor angle, Efd and E'q are the generator field voltage and transient axis generator internal voltage respectively; xd and x'd are the d-axis reactance and transient reactance respectively; vd, id and vq, iq are d-axis and q-axis voltage and current respectively; vref is the reference voltage, KA and TA are the gain and time constant of the excitation system respectively; T'do is the open-circuit transient time constant [17-18]. § sTw ·§ 1 + sT1 ·§ 1 + sT3 U ( s ) = K PSS ¨ ¸¨ ¸¨ © 1 + sTw ¹ © 1 + sT2 ¹© 1 + sT4 · ¸ Δω ( s ) ¹ (6) B. PID based PSS In PID based PSS, the parameters of power system stabilizers and PID controller are tuned on hit-and-trial method in order to compensate the phase lag between electrical torque and the exciter input. The stabilizing signal as output of PSS-PID controller is proportional to speed [18]. The mathematical given by, ª § sTw U ( s ) = « K PSS ¨ © 1 + sTw ¬« modelling of the given PSS-PID is º · § 1 + sT1 · § 1 + sT3 · ¸¨ ¸¨ ¸ Δω ( s ) » ¹ © 1 + sT2 ¹ © 1 + sT4 ¹ ¼» (7) Ki ª º « K p + s + K d s » Δω ( s ) ¬ ¼ IV. OBJECTIVE FUNCTION The objective function for optimizing the parameters of the proposed controller considered in the present study is Integral Squared Error (ISE), which is expressed as follows: tsim J = ISE = Fig. 1. Schematic representation of SMIB system with various approaches. K1 Power System stabilizer (PSS) § sTw ·§ 1 + sT1 ·§ 1 + sT3 · K PSS ¨ ¸¨ ¸¨ ¸ © 1 + sTw ¹ © 1 + sT2 ¹© 1 + sT4 ¹ ΔTm + ¦ - 1 sM + D Δω Δδ BFO/PSO s 1 sTd′0 + 1 ¦ + - ΔE fd (8) 0 Where change in speed (ǻȦ) is taken as error which is given as input to the controller. The design problem can be formulated as the following optimization problem where the parameters are optimized by BFO and PSO. Minimize J Subject to K imin ≤ K i ≤ K imax K5 KA sTA + 1 2 K pmin ≤ K p ≤ K pmax K4 K2 ΔE 'q ωb PID Controller ³ e ( t ) dt ¦ - K + min d ≤ Kd ≤ K (9) max d UPSS K6 Fig. 2. Heffron–Phillips model for SMIB power system with PSS-PID. III. STRUCTURE OF PROPOSED STABILIZER A. Conventional Powrer System stabilizer Power system stabilizers are the power system devices used to improve the transient stability oscillations in the power system. The control structure of power system stabilizer consists of gain of PSS (KPSS), high pass filter time constant as wash-out (Tw), lead-lag phase compensation time constants (T1, T2, T3 and T4). The input to the power system stabilizer is the deviation in synchronous speed (ǻȦ) and U(s) be the output of the power system stabilizer. The mathematical modeling of the PSS is given by, V. OPTIMIZATION TECHNIQUES This section presents the optimization techniques such as bacterial foraging optimization (BFO) and particle swarm optimization (PSO) for tuning the gains of the PID controller. The details are explained below: The transfer function of PID controller Laplace domain is represented by TFPID ( s ) = K p + Ki + Kd s s (10) The output of PID controller in time domain is given by t u ( t ) = K p e ( t ) + K i ³ e ( t )dt + K d 0 d e (t ) dt (11) Where u(t) is the control signal and e(t) is the error signal. 2016 IEEE Region 10 Conference (TENCON) — Proceedings of the International Conference 1917 A. PSO-PID Controller Particle Swarm Optimization (PSO) is an evolutionary algorithm designed based on the behavior of swarms when searching food in a search space based on own as well as group experience [19]. PSO is efficiently used for tuning of PID controllers due to its simplest structure. The optimal values (Kp, Ki & Kd) is obtained using PSO based on updating the local best position (pbest) and velocity to global position (gbest) and velocity as shown in Fig. 3. The steps of Particle Swarm Optimization can be summarized as follows: Step 1: Initialize the particle population size, dimension of the search space with random position and velocity. chemotaxis, swarming, reproduction and eliminationdispersal. The algorithm of Bacteria Foraging Optimization is as follows; Step 1: Initialize all the variables Step 2: Evaluate the objective function for the optimization process. Step 3: (i) Start of the swimming or tumbling operation, (ii). Start of the elimination-dispersal loop, (iii). Start the reproduction loop, (iv). Start the chemotaxis loop. Step 4: Update the fitness of each bacteria based on their health. Step 5: If the stopping criteria are met, stop the search, otherwise, repeat step 1 to step 4 until criteria are met. Step 2: Calculate fitness function of each particle. Step 3: Based on the fitness of each particle being compared with the best fitness value, update the fitness value, position and velocity. Step 4: Based on the fitness of each particle being compared with the global best fitness value, update global best fitness value, position and velocity of each particle using the equations (12) and (13). Step 5: Then, the procedure from step 2 onwards is repeated till termination criteria is satisfied. The velocity and position of each particle is updated using the following equations: v dj ( t + 1) = w ( t ) v dj ( t ) + C1r1 ( pbest dj − x dj ( t ) ) + C2 r2 ( g best dj − x dj ( t ) ) g best dj = x dj + v dj ( t + 1) (12) (13) Where ˜୨ୢ ሺ–ሻ is the jth particle in the dth dimension at iteration t, š୨ୢ (t) is the current position of particle, C1 and C2 are acceleration coefficients, r1 and r2 represents random numbers within [0,1]. VI. SIMULATION RESULTS AND DISCUSSIONS This section describes the simulation results for the stability study in single machine connected to infinite bus (SMIB) power system which is simulated in Matlab/Simulink environment. The system is modeled as linearized transfer functions because of small-signal stability study due to small disturbances in load. A. Stability test under step decrease in load demand The load in the system is decreased by 20 % by switching off some electric equipments/devices. The real and reactive power is observed to be 0.8 and 0.7 p.u. respectively when subjected to a load change. During this disturbance the proposed BFO-PSS-PID, PSO-PSS-PID and the conventional PSS-PID controller is tested for verification of the system stability and performance. It is observed that when the system is operated with the above set of controllers, the voltage and the frequency of the system oscillates around the nominal value of 1 p.u. It is shown in Figs 4 (a) and (b). It is clearly noticed that because of heuristic nature of the conventional PSS-PID controller, the oscillations are more in terms of peak overshoot as well as the settling time when compared with PSO-PSS-PID and BFOPSS-PID. Of course, in case of PSO-PSS-PID, the oscillation is minimum as compared to the other two controllers. B. Stability test under step increase in load demand ¦ Fig. 3. Block diagram of proposed PSO-PID technique. B. BFO-PID Controller Bacteria foraging optimization (BFO) [20] is proposed by passino and is based on the foraging behavior of Escherichia coli (e.coli) bacteria for solving the real world optimization problems. It simulates the process of locating food by a group of E.coli bacteria in the human body. The bacterial foraging process consists mainly of four sequential mechanisms namely 1918 Again, the stability performance of PSS-PID in SMIB is tested under step increase in loading condition. The variation in load cause the variation in real and reactive power as: Step increase in load demand (P, Q, V) = (1.2, 1.3, 1.15) pu; It is observed that PSS with PID controller, PSO-PSS-PID and BFO-PSS-PID controllers stabilize the voltage and frequency of the SMIB as shown in Fig. 5 (a) and (b) respectively about the nominal voltage of 1 p.u. It is again observed that both PSO and BFO are stabilizing the voltage and frequency fairly better than the conventional PID controller and the PSO show the best possible result as compared to the other two. Also the decreased in settling times and peak overshoots are as reflected from the figures. 2016 IEEE Region 10 Conference (TENCON) — Proceedings of the International Conference 1 .6 PSO-PSS 1 .4 BFO =P S S PSS Magnitude (pu) 1 .2 1 0 .8 0 .6 0 .4 0 .2 0 0 10 20 (a) 30 40 50 60 70 80 T im e ( s e c ) 0.02 PSO-PSS-PID BFO-PSS-PID 0 -0.01 -0.02 (a) 0 20 40 Time (sec) 60 2.5 80 Mean square error Magnitude(pu) PSS-PID 0.01 (b) Fig. 4 Stability study for step decrease in load (a) voltage and (b) angular frequency in SMIB C. Stability performance of PSO and BFO techniques Further, stability test based on bode plot is performed to know the performance from the magnitude and phase plots. The performances of the conventional and optimal PSS are reflected from Fig. 6 (a). It is observed that both PSO and BFO based PSS perform better stability as compared to the conventional PSS. Also the mean square error is calculated for PSO as well as BFO and is shown in Fig. 6 (b). It is analyzed here that PSO gives little bit less error as compared to the BFO. Magnitude (pu) 1 0 .5 P S O - P S S - P ID B F O - P S S - P ID P S S - P ID 0 10 (a) 20 T im e 30 Magnitude (pu) [2] -0.01 20 40 Time (sec) 4 6 No of iterations 8 10 REFERENCES PSO-PSS-PID PSS-PID BFO-PSS-PID 0 2 40 0 -0.02 0 VII. CONCLUSION [1] 0.01 0.5 Fig. 6 Performance of PSO in terms of accumulative fitness and probability (s e c) 0.02 1 In this paper, study of power system stability is improved by the design of PSS based on PID controller under different operating conditions. The PID controller in PSS is optimized by PSO and BFO to obtain better stability performance. It is observed from the case studies that PSO and BFO optimized PSS-PID controller provide better stability and minimize low frequency oscillations as compared to the conventional PSSPID controller. 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