Bio-inspired fuzzy logic based tuning of power system stabilizer

Expert Systems with Applications 36 (2009) 9281–9292

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Bio-inspired fuzzy logic based tuning of power system stabilizer S.P. Ghoshal a, A. Chatterjee b, V. Mukherjee b,* a b

Department of Electrical Engineering, National Institute of Technology, Durgapur, West Bengal, India Department of Electrical Engineering, Asansol Engineering College, Asansol, West Bengal 713 304, India

a r t i c l e

i n f o

Keywords: Bacteria foraging optimization Conventional power system stabilizer Dual-input power system stabilizer Genetic algorithm Sugeno fuzzy logic

a b s t r a c t In this paper, bacteria foraging optimization (BFO) – a bio-inspired technique, is utilized to tune the parameters of both single-input and dual-input power system stabilizers (PSSs). Conventional PSS (CPSS) and the three dual-input IEEE PSSs (PSS2B, PSS3B, and PSS4B) are optimally tuned to obtain the optimal transient performances. A comparative performance study of these four variants of PSSs is also made. It is revealed that the transient performance of dual-input PSS is better than single-input PSS. It is, further, explored that among dual-input PSSs, PSS3B offers superior transient performance. A comparison between the results of the BFO and that of genetic algorithm (GA) is conducted in this study. The comparison reveals that BFO is more effective than GA in finding the optimal transient performance. For on-line, off-nominal operating conditions Sugeno fuzzy logic (SFL) based approach is adopted. On real time measurements of system operating conditions, SFL adaptively and very fast yields on-line, off-nominal optimal stabilizer parameters. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Electromechanical oscillation of low frequency is inherent in power system, which may be attributed as a setback due to the usage of fast acting, high gain automatic voltage regulator (AVR) in modern generator excitation system. Transfer of bulk power across weak transmission lines; any disturbance such as sudden change in loads, change in transmission line parameters, fluctuation in the output of the turbine and faults etc have invited the problem of low frequency oscillations (typically in the range of 0.2–3.0 Hz) under various sorts of system operating conditions and configurations. The very common and widely accepted solution prevailing in the utility houses to address this problem is the usage of power system stabilizer (PSS). The PSS adds a stabilizing signal to AVR that modulates the generator excitation. Its main task is to create a damping electrical torque component (in phase with rotor speed deviation) in turbine shaft, increasing the generator damping. A practical PSS must be robust over a wide range of operating conditions and capable of damping the oscillation modes in power system. From this perspective, the conventional singleinput PSS (machine shaft speed (Dxr ) as single-input to PSS) design approach based on a single-machine infinite bus (SMIB) linearized model in the normal operating condition has some deficiencies:

* Corresponding author. Tel.: +91 0341 2253057; fax: +91 0341 2256334. E-mail addresses: [email protected] (S.P. Ghoshal), nirsha_apurba@ rediffmail.com (A. Chatterjee), [email protected] (V. Mukherjee). 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.12.004

(i) There are uncertainties in the linearized model resulting from the variation in the operating configuration since the linearization coefficients are derived typically at normal operating condition. (ii) Various techniques like PID, artificial neural network, GAfuzzy, hybrid neuro-fuzzy, adaptive fuzzy logic, simulated annealing, pole-shifting etc have been tested to achieve tuning under various operating conditions for the single-input PSS. But even after that the single-input PSS suffers from robustness in a multi-machine power system. The two inputs to dual-input PSS, unlike the conventional single-input (Dxr ) PSS, are Dxr and DT e . The processed output of the PSS is DV pss that acts as an excitation modulation signal and the desired damping electrical torque component is produced. Modeling of PSS2B, PSS3B and PSS4B are reported in IEEE Digital Excitation System Subcommittee Report (1996) and those models are taken in the present study. With the objectives of optimal tuning, improved performances, adaptive real time tuning and robustness; extensive research works in the past and relatively recent have been carried out. To mention a few among these numerous works, time to time reported in the literature, fuzzy (Hiyama, Kugimiya, & Satoh, 1994), GA-fuzzy (Abido & Abdel-Magid, 1997), neuro-fuzzy (Abido & Abdel-Magid, 1998), pole-shifting (El-Sherbiny, Hasan, El-Saady, & Yousef, 2003) may be recalled. Most of these techniques are centered on angular speed deviation (Dxr ) as single-input feedback to PSS. Some of these techniques suffer from complexity of computational algorithm, heavy computational burden, memory storage problem and non-adaptive

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Nomenclature cmax, cmin positive constants dattract, drepelent positive constants positive constants d1 ; d2 field voltage ed infinite bus voltage EB generator’s LT side bus voltage Et 0 voltage behind X 0d E fd field winding H inertia constant, MW-s/MVA thyristor exciter gain Ka damping torque coefficient, pu torque/pu speed deviaKD tion maxchemo maximum chemotactic cycle maxcycles maximum number of iteration cycle (k) maxdispersal maximum dispersal cycle maxreprod maximum reproduction cycle maxswim maximum swim length (integer value) numBact total number of bacteria overshoot of change in rotor speed, pu osh first objective function OF 1 ðÞ second objective function OF 2 ðÞ P active power, pu probability of elimination Ped Q reactive power, pu rand() random number in the interval [0, 1] selection ratio sr execution time, s tex settling time of change in rotor speed, s tst

tuning under various system operating conditions and configurations. Some suffer from robustness because of choice of limited number of control parameters of PSS, limited number of optimization functions and on-line real time necessity for fast changing PSS parameters. Some algorithms like GA, simulated annealing (SA) suffer from settings of algorithm parameters and give rise to repeated revisiting of the same suboptimal solutions. Bacteria foraging optimization (BFO) – a bio-inspired technique, has been reported by Mishra, Tripathy, and Nanda (2007) to establish the potential application of BFO technique as a soft computing intelligence in power system optimization arena. The main focus of this article is the tuning of single-input PSS installed in multi-machine power system. But what about the tuning of dual-input PSS? A comparison among single-input PSS and dual-input PSSs is yet to address. Thus, it is very much pertinent to explore a comparative study between these two configurations of PSSs with the assistance of BFO technique (Mishra et al., 2007; Passino, 2002). GA may be taken as a standard algorithm accepted by the researchers. A fuzzy logic system (Mukherjee & Ghoshal, 2007) based PSS can adjust its parameters on-line according to the environment in which it works and can provide good damping over a wide range of operating conditions. The PSS ultimately derived from this paper proves to be the most robust model in damping all electromechanical modes of generator’s angular speed oscillations for all off-line and on-line conditions, step changes of mechanical torque inputs (DT m ), reference voltage inputs (DV ref ) and during/after clearing of system faults. Thus, the objectives of this paper may be documented as follow:  to compare single-input PSS with dual-input PSS,  to contrast the generator’s angular speed oscillations for dualinput PSS (namely PSS2B, PSS3B, and PSS4B) equipped system model,

T0 Trr ush var

system constant terminal voltage transducer time constant, s undershoot of change in rotor speed, pu number of problem variables (depends on specific application) variables’ upper limits varmax variables’ lower limits varmin wattract, wrepelent positive constants equivalent transmission line reactance Xe k eigenvalue xd damped frequency, rad/s xn undamped natural frequency, rad/s x0 rated speed = 2pf0, elect rad/s wfd field flux linkage n damping ratio DT e incremental change in electromagnetic torque, pu DT m incremental change in mechanical torque, pu Dv 1 incremental change in terminal voltage, pu DV pss incremental change in power system stabilizer output voltage, pu DV max maximum value of incremental change in PSS output pss voltage, pu DV min minimum value of incremental change in PSS output pss voltage, pu DV ref incremental change in reference voltage, pu Dd rotor angle deviation, pu Dxr speed deviation = xrx0x0 , pu d ðDxr ) time derivative of change in rotor speed dt

 to present the potential benefit of BFO over GA, as optimizing technique,  to explore the suitability of fuzzy logic based controller for online real time environment, and  to critically examine the best type of PSS for practical implementation under any sort of system disturbances. The rest of the paper is organized as follows. In Section 2, SMIB system and various PSSs under investigation is presented. Mathematical problem for the present study is formulated in Section 3. Bacteria foraging optimization technique as implemented for optimal PSS tuning is described in Section 4. SFL as applied for on-line tuning of PSS parameters is narrated in Section 5. Input control parameters of the simulation are given in Section 6. Section 7 documents the simulation results. Finally, concluding remarks and scope of future work are outlined in Section 8. 2. SMIB system and various PSS under investigation An SMIB (Kundur, 2006) model, as considered in the present work, is shown in Fig. 1. The theoretical basis of the PSS representation may be found out from the work of El-Zonkoly (2006). As the purpose of PSS is to introduce damping torque component, speed deviation is used as logical signal to control generator excitation for CPSS. On the other hand, speed deviation and torque deviation are taken as the best pair of inputs for dual-input PSS (Mukherjee & Ghoshal, 2006). The block diagram of SMIB system with AVR, thyristor high gain exciter, synchronous generator and PSS is shown in Fig. 2. The generator including AVR, excitation system and transmission-circuit reactance is represented by a two-axis, fourth order model. IEEE type ST1A model of the static excitation system is considered. The block diagrams of different stabilizers under study are shown in Figs. 3–6.

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Fig. 1. Single-machine infinite bus test system.

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In practice, a PSS is formed with a gain block, one or two leadlag networks (that give the desired phase compensation between input and electrical torque at the generator shaft) and a washout filter. In PSS2B, there are two washout blocks represented by (T w1  T w4 ) along with transducer time constants (T 6  T 7 Þ and transducer gain constant (K s3 Þ. A torsional filter (Time constants T 8  T 9 ) is provided. Finally, lead-lag network blocks represented by (T 1 ; T 2 ; T 3 ; T 4 ; T 5 ; T 10 with limits) yield the stabilizer output, DV pss . In other models (PSS3B and PSS4B), the time constants T1 and T3 represent the transducer time constants. The washout time constants are T2 and T4. The transducer gain constant, K s1 is negative and another transducer gain constant, K s2 is positive. In PSS3B model, the stabilizing signal DV pss results from the vector summation of processed signals for Dxr and DT e . The significant difference in PSS4B model is that there is a conditioning network consisting of

Fig. 2. Block diagram representation of SMIB system with AVR, thyristor high gain exciter, synchronous generator and PSS.

Fig. 3. Block diagram representation of CPSS.

Fig. 4. Block diagram representation of dual-input PSS2B.

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Fig. 5. Block diagram representation of dual-input PSS3B.

Fig. 7. D-shaped sector in the negative half of s plane.

oscillation occurs for the particular parameters of PSS. These particular PSS parameters will be rejected during the optimization technique. So, first multi-objective optimization function is formulated as in Eq. (1).

OF 1 ðÞ ¼ 10OF 11 þ 10OF 12 þ 0:01OF 13 þ OF 14

Fig. 6. Block diagram representation of dual-input PSS4B.

start-up time constant, T0; inertia time constant, Mð¼ 2HÞ for the combined turbine-generator shaft system. The generator with AVR and excitation system along with CPSS/PSS2B/PSS3B/PSS4B is represented by eight/seventeenth/eighth/eleventh order state transition matrices, respectively. 3. Mathematical problem formulation The parameters of the PSS (for CPSS: K pss , T d1 , T d2 , T d3 , T d4 , T d5 , T d6 ; for PSS2B: K s1 , T1, T2, T3, T4, T5; for PSS3B: K s1 , K s2 , T d1 , T d2 , T d3 , T d4 ; for PSS4B: K s1 , K s2 , T1, T2, T3, T4) are to be so tuned that some degree of relative stability and damping of electromechanical modes of oscillations, minimized undershoot ðush ), minimized overshoot ðosh Þ and lesser settling time ðtst Þ of transient oscillations of Dxr are achieved. So, to satisfy all these requirements, two multi-objective optimization functions, OF 1 ðÞ and OF 2 ðÞ which are to be minimized in succession are designed in the following way: P OF 11 ¼ i ðr0  ri Þ2 if r0 > ri , ri is the real part of the ith eigenvalue. The relative stability is determined by r0 . The value of r0 is taken as 6.0 for the best relative stability and optimal transient performance. P OF 12 ¼ i ðn0  ni Þ2 , if (imaginary part of the ith eigenvalue) > 0.0, ni is the damping ratio of the ith eigenvalue and ni < n0 . Minimum damping ratio considered, n0 ¼ 0:3. Minimization of this objective function will minimize maximum overshoot. P OF 13 ¼ i (imaginary part of ith eigenvalue)2, if ri P r0 . High value of imaginary part of ith eigenvalue to the right of vertical line r0 is to be prevented. Zeroing of OF 13 will increase the damping further. OF14 = an arbitrarily chosen very high fixed value (say, 106), which will indicate some ri values P0.0. This means unstable

ð1Þ

The weighting factors ‘10’ and ‘0.01’ are chosen to impart more weights to OF 11 , OF 12 and to reduce high value of OF 13 , to make them mutually competitive during optimization. By optimizing OF 1 ðÞ, closed loop system poles are consistently pushed further left of jx axis with simultaneous reduction in imaginary parts also, thus, enhancing the relative stability and increasing the damping ratio above n0 . Finally, all closed loop system poles should lie within a D-shaped sector (Fig. 7) in the negative half plane of jx axis for which ri << r0 ; ni >> n0 . Selection of such low negative value of r is purposefully chosen. The purpose is to push the closed loop system poles as much left as possible from the jx axis to enhance stability to a great extent. Thorough computation shows that optimization of OF 1 ðÞ is not sufficient for sharp tuning of PSS parameters. So, it is essential to design second multi-objective optimization function, for sharp tuning of PSS parameters. Thus, the second multi-objective optimization function OF 2 ðÞ is formulated as in Eq. (2).

 2  2 OF 2 ðÞ ¼ osh  106 þ ush  106 þ ðt st Þ2  2 d þ ðDxr Þ  106 dt

ð2Þ

In Eq. (2); osh , ush , t st , dtd ðDxr Þ are all referred to the transient response of Dxr . The constrained optimization problem for the tuning of PSSs is, thus, formulated as follows: Minimize OF 1 ðÞ and OF 2 ðÞ in succession with the help of any optimization technique to get optimal PSS parameters, subject to the limits (IEEE Digital Excitation System Subcommittee Report, 1996; Kundur, 2006):  175:0 6 K pss 6 230:0 (a) For CPSS: 0:001 6 T di 6 1:0; i ¼ 1 to 6 8 < 10 6 K s1 6 30 (b) For PSS2B: 0:01 6 T i 6 1:0; i ¼ 1 to 5 : T 10 ¼ 0:0001 Other parameters are fixed.  100:0 6 K s1 6 10:0; 10:0 6 K s2 6 100:0 (c) For PSS3B: 0:005 6 T di 6 2:0; i ¼ 1 to 4 No fixed parameters are required.  100:0 6 K s1 6 10:0; 10:0 6 K s2 6 100:0 (d) For PSS4B: 0:005 6 T i 6 2:0; i ¼ 1 to 4; T 0 ¼ 0:2

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4. Bacteria foraging optimization Natural selection favors propagation of genes of those animals that have efficient foraging strategies (method of finding, handling and taking in food) and eliminate those animals that have weak foraging strategies. As the efficient foraging strategy allows the animals to ingest better and quality food, only animals having better food searching strategy are allowed to enjoy reproductive cycle, in turn, producing better species. Poor foraging strategies are either shaped into good ones or eliminated after many generations. With their own physiological (e.g. cognitive and sensing capabilities)

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and environmental (e.g. physical characteristics of the search space, density of prey, risk and hazards from predators) constraints, animals try to maximize the consumption of energy per unit time interval. Such evolutionary idea has bred the concept of BFO (Passino, 2002) as an optimization algorithm. It is, gradually, being utilized by the interested research groups as an optimization algorithm to solve a range of non-linear optimization problems. Four processes can explain the foraging strategy of Escherichia bacteria present in human intestine. These are chemotaxis, swarming, reproduction and elimination-dispersal.

Fig. 8. Pseudo code of bacteria foraging optimization.

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Fig. 8 (continued)

A set of relatively rigid flagella helps the bacteria in locomotion. Its characteristics of movement for searching of food can be in two different ways, i.e. swimming and tumbling together known as

chemotaxis. Its movement in a predefined direction is termed as swimming (running), where as tumbling is the movement in altogether different direction. During its entire lifetime, it alternates

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The BFO algorithm, as adopted in the present work, is detailed in Fig. 8.

5. SFL as applied for on-line tuning of PSS parameters The behavior of a synchronous generator connected to a network depends on, among other things, its position in this network, the operating conditions (in particular, the reactive power flow and the voltage map), the network topology and the generation schedule. For on-line tuning of the parameters of PSS, very fast acting SFL is adopted in the present work. The whole process of SFL (Mukherjee & Ghoshal, 2007) involves three steps as Fig. 9. Fuzzification of input operating conditions (P, Q, Xe and Et).

between these two modes of operation. Clockwise rotation of its flagella results in tumble, where as, anticlockwise rotation yields swim. Likelihood of increased search for nutrient concentration, enhanced capability to gang up on a large prey to kill and digest it, group protection of the individual from predators are the highlighting objectives and motivations of social and intelligent foraging strategy. Successful foraging for food of each and individual of the group result from grouping, communication mechanism and collective intelligence. To attract the other bacteria towards the optimal convergence direction, it is necessary to pass on the information about the nutrient concentration (optimal point) to other bacteria. This is called swarming. To achieve this, a penalty function based upon the relative distances of each bacterium from the fittest bacterium till that search duration, is added to the original optimization function. This penalty function becomes zero when all the bacteria have merged into the desired solution point. After getting evolved through several chemotactic stages, the original set of bacteria is allowed for reproduction. Biological aspect of their conjugation process is splitting of one into two identical bacteria. It is mimicked in the optimization process by replacing the poorer half (having higher objective function value for minimization problem and vice versa) with weaker foraging strategy by the healthier half, which is eliminated owing to their poorer forging strategy, maintaining the total number of population bacteria constant in the process of evolution. Elimination and/or dispersal of a set of bacteria to a new position result(s) in drastic alteration of smooth biological process of evolution. The underlying concept behind this step is to place a newer set of bacteria nearer to the food location to avoid stagnation (to avoid premature trapping into local optima).

(a) Fuzzification: The first step is fuzzification of input operating conditions as active power (P), reactive power (Q), equivalent transmission line reactance (Xe) and Generator’s LT side bus voltage (Et) in terms of fuzzy subsets (Low, Medium, High). These are associated with overlapping triangular membership functions. SFL rule base table is formed, each composed of four nominal inputs and corresponding nominal optimal PSS parameters as outputs determined by any of the optimizing techniques dealt with. The respective nominal central values of the input subsets of P are (0.2, 0.7, 1.2), those of Q are (0.2, 0.6, 1.0), those of Xe are (0.4752, 0.77, 1.08) and those of Et are (0.5, 0.8, 1.1), respectively, at which membership values are unity (Fig. 9). These are nominal input conditions also. Sugeno fuzzy rule base table consists of 34(=81) logical input conditions or sets (SFL tables calculated for different PSS structures investigated), each composed of four nominal inputs. Each logical input set corresponds to nominal optimal PSS parameters as output. (b) Sugeno fuzzy inference: For on-line imprecise values of input parameters, firstly their subsets in which the values lie are determined with the help of ‘‘IF”, ‘‘THEN” logic and corresponding membership values are determined from the membership functions of the subsets. From Sugeno fuzzy rule base table, corresponding input sets and nominal PSS parameters are determined. Now, for each input set being satisfied, four membership values like lP , lQ , lXe and lEt and their minimum lmin are computed. For the input logical sets that are not satisfied because parameters do not lie in the corresponding fuzzy subsets, lmin will be zero. For the non-zero lmin values only, nominal PSS parameters corresponding to fuzzy sets being satisfied are taken from the Sugeno fuzzy rule base table.

Table 1 GA and BFO based comparison of OF 2 ðÞ values for CPSS, PSS2B, PSS3B and PSS4B based systems. Value of OF 2 ðÞ (107)

Sl. No.

Operating conditions (P, Q, Xe, Et; all are in pu)

Algorithms

CPSS

PSS2B

PSS3B

PSS4B

1

0.2,0.2, 0.4752,1.1

GA–SFL BFO–SFL

7.45 4.91

6.23 4.02

1.42 1.01

2.90 1.62

2

0.5, 0.2, 0.4752, 1.0

GA–SFL BFO–SFL

7.85 4.87

7.33 4.14

2.47 1.21

3.17 1.52

3

0.75, 0.50, 0.4752, 0.50

GA–SFL BFO–SFL

7.16 3.97

5.18 3.17

2.71 1.01

3.88 1.45

4

0.95, 0.30, 0.4752, 0.5

GA–SFL BFO–SFL

7.29 3.15

5.85 2.17

2.02 1.42

4.58 1.96

5

1.2, 0.6, 1.08, 0.5

GA–SFL BFO–SFL

8.96 5.16

8.72 4.83

3.74 2.57

4.39 2.43

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Fig. 10. Comparative BFO based transient response profiles of CPSS, PSS2B, PSS3B and PSS4B for 0.01 pu simultaneous change in DT m and DV ref (P = 1.2, Q = 0.6, Xe = 0.4752, Et = 0.5).

(c) Sugeno defuzzification: It yields the defuzzified, crisp output for each parameter of PSS. Final crisp PSS parameter output is given by Eq. (11).

P K crisp ¼

i

lðiÞ min  Ki ðiÞ i lmin

ð11Þ

P

where, i correspond to input logical sets being satisfied among 81 input logical sets, Ki is corresponding nominal PSS parameter. ðiÞ K crisp is crisp PSS parameter. lmin is the minimum membership value corresponding to ith input logical set that is satisfied. 6. Input control parameters For simulation step perturbation of 0.01 pu is applied either in reference voltage or in mechanical torque. The simulation is implemented in MATLAB 7.1 software on a PC with PIV3.0 G CPU and 512 M RAM. The followings are the different input control parameters. (a) For SMIB system: Inertia constant, H = 5, M = 2H, nominal frequency, f0 = 50 Hz, 0.995 6 j Eb j 6 1.0, the angle of Eb ¼ 0 , 0.2 6 P 6 1.2,0.2 6 Q 6 1.0, 0.4752 6 Xe 6 1.08, 0.5 6 Et 6 1.1. At t = 0, it is assumed that Dd = 5 = 0.0857 rad is the state perturbation, Dxr = 0.0 and other state deviations are also zero. In the block diagram representation of generator with exciter and AVR; Trr = 0.02 s, K a ¼ 200:0.

Fig. 11. Comparative BFO based convergence profiles of OF 1 ðÞ for CPSS, PSS2B, PSS3B and PSS4B (P = 0.5, Q = 0.2, Xe = 0.4752, Et = 1.0).

(b) For GA: Number of parameters depends on problem variables (PSS configuration), number of bits = (number of parameters)*8 (for binary coded GA, as considered for the present work), population size = 50, maximum number of iteration cycles = 200, mutation probability = 0.001, crossover rate = 80%. (c) For BFO: Number of problem variables depends upon the PSS structure under investigation. All the parameters of the algorithm are given in Fig. 8.

7. Simulation and results Optimized PSS parameters determined by any of the optimization technique are substituted in MATLAB–SIMULINK model of the system to obtain the transient response profiles. Final values of OF 1 ðÞ and OF 2 ðÞ are already obtained from the end of optimization. Final eigenvalue, final undamped and damped frequencies and final damping ratio are all determined by the optimization technique at the end of optimization. Sugeno fuzzy rule base tables (not shown) are obtained by applying each optimization technique for distinct 81 number nominal input operating conditions. The outputs are 81 distinct nominal optimal PSS parameters sets. For the optimization, BFO technique is adopted. GA is utilized for the sake of comparison. The major observations of the present work are documented below. (a) Analytical transient response characteristics: Table 1 depicts the comparative GA and BFO based optimal transient

Table 2 BFO based comparison of OF 1 ðÞ values under different operating conditions for CPSS, PSS2B, PSS3B and PSS4B. Operating conditions (P, Q, Xe, Et; all are in pu)

Type of PSS

PSS parameters

OF 1 ðÞ

tex (s)

1.2, 0.6, 0.4752, 0.5

CPSS PSS2B PSS3B PSS4B

175.00, 0.005, 0.005, 0.001, 0.001, 0.352, 0.001 10.00, 0.097, 0.010, 0.113, 0.01, 0.25 10.00, 10.00, 0.271, 0.005, 0.005, 0.334 10.00, 10.00, 0.273, 0.005, 0.138, 0.005

1455.62 1251.60 291.30 311.52

330.65 639.21 344.78 420.73

1.0, 0.6, 0.93, 0.5

CPSS PSS2B PSS3B PSS4B

175.00, 0.005, 0.005, 0.001, 0.001, 0.165, 0.001 10.00, 0.01, 0.253, 0.158, 0.01, 0.01 10.00, 10.00, 2.00, 2.00, 0.005, 0.099 10.00, 10.00, 0.005, 0.153, 0.249, 0.005

1448.61 1243.00 290.88 378.87

350.09 632.93 334.89 411.90

1.0, 0.2, 1.08, 0.5

CPSS PSS2B PSS3B PSS4B

230.00, 0.005, 0.005, 0.029, 0.001, 0.001, 0.001 10.00, 0.01, 0.126, 0.01, 0.393, 0.204 10.00, 10.00, 0.171, 0.005, 0.139, 0.131 10.00, 10.00, 0.005, 0.168, 0.237, 0.005

1491.69 1444.20 267.77 372.49

345.16 638.75 335.89 415.62

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response characteristics (in terms of OF 2 ðÞ value) of different PSS equipped system model. From this table, it may be inferred that the transient stabilization performance of dual-input PSS equipped system model is better than single-input counter part. Comparing dual-input PSSs, it is also observed that the transient stabilization performance of PSS3B equipped system model is superior to that of others.

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PSS3B equipped system model offers lesser values of osh , ush , t st , dtd ðDxr Þ and, thereby, lesser values of OF 2 ðÞ. It may also be observed that the BFO based optimization technique offer lesser value of OF 2 ðÞ than GA based one. Thus, BFO based optimization technique offers better results than GA based one. Fig. 10 depicts that the comparative optimal transient performance of the different PSS equipped power

Fig. 12. Comparative BFO and GA based transient response profiles of CPSS, PSS2B, PSS3B and PSS4B for 0.01 pu simultaneous change in DT m and DV ref ; (P = 0.2, Q = 0.2, Xe = 0.4752, Et = 1.0).

Fig. 13. Comparative BFO and GA based transient response profiles of CPSS, PSS2B, PSS3B and PSS4B for 0.01 pu simultaneous change in DT m and DV ref ; (P = 0.2, Q = 0.2, Xe = 0.4752, Et = 1.0).

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Fig. 14. MATLAB–SIMULINK based transient response profiles of Dxr and Dv 1 under different perturbation conditions for generator equipped with PSS3B.

system model corresponding to an operating condition of P = 1.2, Q = 0.6, Xe = 0.4752, Et = 0.5 (all are in pu) for 0.01 pu simultaneous change in DT m and DV ref . From this figure, it is noticed that the transient stabilization performance of dual-input PSS is better than that of single-input one. Among the dual-input PSSs, the performance of PSS3B is established to be the best one. (b) Analytical eigenvalue based system performance analysis: BFO based comparison of OF 1 ðÞ values of CPSS, PSS2B, PSS3B and PSS4B are shown in Table 2 for different system operating conditions. From Table 2, it is observed that the value of OF 1 ðÞ is the least for PSS3B, establishing the performance of PSS3B to be the best one. For PSS3B equipped system model, majority of the eigenvalues are within D-shaped sector (Fig. 7) which yield lesser values of OF 11 ðÞ, OF 12 ðÞ and OF 13 ðÞ. Hence, the value of OF 1 ðÞ is very less for PSS3B equipped system model. On the other hand, majority of the eigenvalues for PSS2B based system are outside the Dshaped but very close to and right side of (r0 , j0) point. This yields higher values of OF 11 ðÞ, OF 12 ðÞ and OF 13 ðÞ. The value of OF 1 ðÞ is more for this system. Thus, from the eigenvalue analysis it may be concluded that a considerable improvement has occurred in the transient performance for the PSS3B based system.

(c) Convergence profiles: The comparative BFO based convergence profiles of OF 1 ðÞ for CPSS, PSS2B, PSS3B and PSS4B are depicted in Fig. 11 corresponding to an operating condition of P = 0.5, Q = 0.2, Xe = 0.4752, Et = 1.0 (all are in pu). From these figures, the objective function value, OF 1 ðÞ corresponding to PSS3B is found to converge faster than the others. (d) Comparative optimization performance of the optimization techniques: With regard to optimization performances of the optimizing algorithms, as depicted in Table 1, it may be concluded that the BFO based approach offers the lower values of OF 2 ðÞ for the same input operating conditions. Comparative transient performances of Dxr and convergence profiles of OF 1 ðÞ for BFO and GA based optimization for all the four PSS modules (CPSS, PSS2B, PSS3B, and PSS4B) are depicted in Figs. 12 and 13, respectively. These figures assist to conclude that the transient stabilization performance and convergence profile of BFO based optimization are better than those of GA based one. Though the execution time of BFO (Table 1) is more than GA (not shown in the present work), BFO offers much better optimal performance. Thus, BFO may be accepted as a true optimizing algorithm for the power system based application as considered in the present work.

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(e) Transient performance study under different perturbations: Fig. 14 displays MATLAB–SIMULINK based transient response profiles of Dxr and Dv 1 for PSS3B equipped generator. This figure helps to conclude that PSS3B damps the oscillations of Dxr and Dv 1 very quickly under any form of system perturbations. Real parts of some eigenvalues for CPSS/PSS2B are always either equal to, or greater than r0 in the negative half plane of jx axis. A few eigenvalues are always outside D-shaped sector (Fig. 7) for any operating condition. So, objective function values (OF 1 ðÞ) are always higher (Table 2). Much lower negative real parts of eigenvalues of PSS3B and PSS4B (not shown) cause higher relative stability than CPSS/PSS2B. Larger reductions of xn and xd for some electromechanical oscillations are due to higher damping ratios ni >> n0 for those particular modes, in case of PSS3B and PSS4B (Table 3). (f) Simulation of fault: It is revealed that PSS3B is offering the best transient performance in damping all electromechanical modes of generator’s angular speed oscillations for all

nominal and off-nominal system conditions, step changes of mechanical torque inputs (DT m Þ, reference voltage inputs (DV ref Þ. LT bus fault of duration 220 ms at the instant of 2.0 s is simulated for PSS3B equipped system model and the corresponding comparative transient response profiles of Dxr for both GA–SFL and BFO–SFL based responses are plotted in Fig. 15 (Fig. 15a corresponds to Fault 1 and Fig. 15b corresponds to Fault 2). A look into these figures show that after the creation of the fault the BFO–SFL based response recovers from this abnormal situation with much lesser fluctuation in angular speed as compared to that of GA–SFL based one. Table 4 depicts the system model parameters as determined by SFL. Thus, BFO–SFL based model exhibits better response having lesser amplitude of angular speed deviation under fault and subsequent clearing condition yielding better dynamic robust transient performance than GA–SFL based one. PSS3B proves to be much less susceptible to faults because PSS3B settles all the state deviations to zero much faster than any other PSSs.

Table 3 GA, and BFO based results of eigenvalue analysis corresponding to operating conditions (P = 0.95, Q = 0.30, Xe = 1.08, Et = 0.5; all are in pu). Damping ratio (n)

Undamped natural frequency (xn ), rad/s

Corresponding damped frequency (xd ), rad/s

Lowest

Highest

Lowest

Lowest

Highest

0.16 0.38

0.57 0.65

0.38 0.59

2.45 1.45

0.42 0.45

0.59 4.31

GA–SFL BFO–SFL

0.26 0.49

0.97 1.00

0.48 0.63

3.33 13.42

0.32 0.56

0.79 7.79

PSS3B

GA–SFL BFO–SFL

0.36 0.72

0.98 0.98

0.17 0.47

1.93 0.96

0.15 0.33

1.8 0.38

PSS4B

GA–SFL BFO–SFL

0.2 0.37

0.95 0.95

0.55 0.34

1.22 2.97

0.54 0.28

0.36 2.98

Type of PSS

Algorithms-SFL

CPSS

GA–SFL BFO–SFL

PSS2B

Highest

Fig. 15. Comparative GA–SFL and BFO–SFL based transient response profiles of Dxr for the generator equipped with PSS3B under change in operating conditions.

Table 4 Off-nominal operating conditions, simulation of faults, algorithms-SFL, and optimal PSS3B parameters. Fault No.

Off-nominal operating conditions (P, Q, Xe, Et; all are in pu)

Algorithms-SFL

PSS3B parameters

Fault 1

0.95, 0.3, 0.4752, 1.0

BFO–SFL GA–SFL BFO–SFL GA–SFL BFO–SFL GA–SFL

13.50, 83.26, 0.529, 0.051, 0.008, 1.566 59.57, 59.22, 0.558, 0.013, 0.317, 0.169 No change in parameters

BFO–SFL GA–SFL BFO–SFL GA–SFL BFO–SFL GA–SFL

10.88, 26.40, 1.279, 0.369, 0.070, 0.140 10.00, 53.24, 1.618, 0.192, 0.410, 0.254 No change in parameters

LT bus fault of duration 220 ms and subsequent clearing 0.95, 0.3, 1.08, 1.0 Fault 2

1.0, 0.6, 0.4752, 1.1 LT bus fault of duration 220 ms and subsequent clearing 0.2, 0.2, 0.4752, 1.1

12.34, 83.67, 1.608, 0.239, 0.326, 0.473 14.22, 66.25, 0.208, 0.013, 0.161, 0.099

13.07, 39.00, 1.322, 1.816, 1.006, 0.088 15.27, 12.11, 1.805, 0.893, 0.137, 0.005

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8. Conclusion The present work concludes the following: (i) Transient performance of dual-input PSS is better than single-input counter part. (ii) In the dual-input PSS family (namely PSS2B, PSS3B, and PSS4B), transient performance of dual-input PSS3B shows lesser undershoot, lesser overshoot and lesser settling time as compared to those of PSS2B and PSS4B. (iii) Results obtained from the analysis of PSS3B equipped system configuration shows that the dynamic stabilization offered by PSS3B is better with change in operating conditions and configurations, faulted or post fault conditions. (iv) System perturbations can be very quickly damped out by the PSS3B equipped system model. (v) Between the two optimization techniques considered, bacteria foraging optimization is better than genetic algorithm. (vi) For real time determination of optimal PSS parameters; fast, on-line manipulator Sugeno fuzzy logic is very suitable. The computational burden is low. Its practical implementation is easy. Thus, the practical applicability of dual-input PSS, especially PSS3B, may be established for SMIB system. Its more rigorous testing for multi-generator system is under consideration for future work.

References Abido, M. A., & Abdel-Magid, Y. L. (1997). A genetic based fuzzy logic power system stabilizer for multimachine power systems. In Proceedings of IEEE conference. pp. 329–334. Abido, M. A., & Abdel-Magid, Y. L. (1998). A hybrid neuro-fuzzy power system stabilizer for multimachine power systems. IEEE Transaction on Power Systems, 13(4), 1323–1330. El-Sherbiny, M. K., Hasan, M. M., El-Saady, G., & Yousef, A. M. (2003). Optimal pole shifting for power system stabilization. Electric Power Systems Research, 66(3), 253–258. El-Zonkoly, A. M. (2006). Optimal tuning of power system stabilizers and AVR gains using particle swarm optimization. Expert Systems with Applications, 31(3), 551–557. Hiyama, T., Kugimiya, M., & Satoh, H. (1994). Advanced PID type fuzzy logic power system stabilizer. IEEE Transaction on Energy Conversion, 9(3), 514–520. IEEE Digital Excitation System Subcommittee Report (1996). Computer models for representation of digital-based excitation systems. IEEE Transaction on Energy Conversion, 11(3), 607–615. Kundur, P. (2006). Power system stability and control. India: Tata McGraw-Hill. Mishra, S. M., Tripathy, S. C., & Nanda, J. (2007). Multi-machine power system stabilizer design by rule based bacteria foraging. Electric Power Systems Research, 77(12), 1595–1607. Mukherjee, V., & Ghoshal, S. P. (2007). Intelligent particle swarm optimized fuzzy PID controller for AVR system. Electric Power Systems Research, 77(12), 1689–1698. Mukherjee, V., & Ghoshal, S. P. (2006). Towards input selection and fuzzy based optimal tuning of multi-input power system stabilizer. In Proceedings of fourteen national power system conference (NPSC 2006), Paper No. 51, IIT Roorkee, India. Passino, K. M. (2002). Biomimicry of bacteria foraging for distributed automation and control. IEEE Control System Magazine, 52–67.