Design of Interactive Artificial Bee Colony Based Multiband Power System Stabilizers in MultiMachine

Power System Amit Shrivastava

Electrical Engineering Department Maulana Azad National Institute of Technology,

Bhopal, 462051, INDIA amitshri77@yahoo.com

Manisha Dubey Electrical Engineering Department

Maulana Azad National Institute of Technology, Bhopal, 462051, INDIA md_mact@yahoo.co.in

Yogendra Kumar Electrical Engineering Department

Maulana Azad National Institute of Technology, Bhopal, 462051, INDIA

ykmact@yahoo.com

Abstract— This paper presents the implementation of interactive Artificial Bee Colony algorithms based multiband power system stabilizers in multimachine power system. In the proposed artifical expert system, generator speed deviation and accelerating power are chosen as input signals to multiband power system stabilizer. The problem of selection of optimal parameters of multiband power system stabilizer is converted into an optimization problem and which is solved by IABC algorithm with the Integral of Squared Time Squared Error (ISTSE) based objective function. To demonstrate the robustness of the proposed swarm based multiband power system stabilizer, simulation studies on multimachine system subjected to three-phase fault have been carried out. Simulation results show the superiority and robustness of IABC based multiband power system stabilizer over conventionally tuned controller.

Keywords— Dynamic Stability, Interactive Artificial Bee Colony Algorithms, Multiband Power System Stabilizer.

Introduction

HE power systems are complex non-linear systems, which are often subjected to low frequency oscillations. The application of power system stabilizers for improving

dynamic stability of power systems and damping out the low frequency oscillations due to disturbances has received much attention recently [1]-[3]. Power system is a highly nonlinear system and it is difficult to obtain exact mathematical model of the system. In recent years, adaptive self tuning, variable structure, artificial neural network based PSS, fuzzy logic based PSS, have been proposed to provide optimum damping to the system oscillations under wide variations in operating conditions and system parameters [4]-[6]. Low frequency oscillation problems are very difficult to solve because power systems are very large, complex and geographically distributed. Therefore, it is necessary to utilize most efficient optimization methods to take full advantages in

simplifying the problem and its implementation. From this perspective, many successful and powerful optimization methods and algorithms have been employed in formulating and solving this problem.

These days swarm intelligence has become more and more attractive for the researchers, who work in the relevant research field. It can be classified as one of the branches in evolutionary computing. Swarm intelligence can be defined as the measure introducing the collective behavior of social insect colonies or other animal societies to design algorithms or distributed problem-solving devices. Generally, the algorithms in swarm intelligence are applied to solve optimization problems. Many swarm intelligence algorithms for solving problems of optimization have proposed such as the Cat Swarm Optimization (CSO) , the Parallel Cat Swarm Optimization (PCSO) , the Artificial Bee Colony(ABC) , the Particle Swarm Optimization (PSO) , the Fast Particle Swarm Optimization (FPSO) , and the Ant Colony Optimization (ACO). Moreover, several applications of optimization algorithms based on computational intelligence or swarm intelligence one after another. Karaboga proposed the Artificial Bee Colony (ABC) algorithm based on a particular intelligent behavior of the honeybee swarms in 2005. In addition, the accuracy and the efficiency of the ABC are compared with the Differential Evolution (DE), the PSO and the Evolutionary Algorithm (EA) for numeric problems with multi-dimensions .By observing the operation and the structure of the ABC algorithm, we notice that the operation of the agent, e.g. the artificial bee, can only move straight to one of the nectar sources which are discovered by the employed bees. Nevertheless, this characteristic may narrow down the zones of which the bees can explore and may become a drawback of the ABC.

T

Karaboga(2007) gave IABC ,as in improved version of ABC.we are using interactive strategy in this paper by considering the universal gravitation between the artificial bees for the ABC to retrieve the disadvantages. To test and verify the advantages, which we gain in the proposed method, series of experiments are executed and are compared with the original ABC and the PSO. The experimental results exhibit that the IABC performs the best on solving the problems of numerical optimization. [26-27]

An interactive Artificial Bee Colony (IABC) algorithm is proposed for optimal tuning of MBPSS parameters to improve power system low frequency oscillations damping in this paper. This paper deals with the design method for the stability enhancement of a multi machine power system using MBPSSs whose parameters are tuned using IABC algorithm. The proposed tuning scheme uses a IABC based search that integrates a classical parameter optimization criterion based on Integral of Squared Time Squared Error (ISTSE).

I. SYSTEM MODEL

A.Multi Machine Infinite Bus System For the study in this paper, the two area multi-

machine power system [2] is simulated in the MATLAB/Simulink environment The system contains eleven buses and two areas, connected by a weak tie between bus 7 and 9. Totally two loads are applied to the system at bus 7 and 9. Two shunt capacitors are also connected to bus 7 and 9 as shown in the figure 1. The system has the fundamental frequency 60 Hz. The system comprises two similar areas connected by a weak tie. Each area consists of two generators, each having a rating of 900 MVA and 20 kV. The left half of the system is identified as area 1 and the right half is identified as area 2.

Figure1: Kundur’s two area system The test system consists of two fully symmetrical areas linked together by two 230 kV lines of 220 km length. This system is specifically designed to study low frequency electromechanical oscillations [2] in large interconnected power systems. Three electromechanical modes of oscillation are presented in this system; two intra-area modes, one in each area, and one inter-area low frequency mode.

Despite its small size, it mimics very closely the behavior of typical systems in actual operation. Each area is

Figure 2: Kundur’s two area system Simulink model

equipped with two identical round rotor generators rated 20kV/900MVA. The synchronous machines have identical parameters. Thermal plants having identical speed regulators are further assumed at all locations, in addition to the fast static exciters.

Figure 3: Simulink model of area 1 &2

All generators are producing about 700 MW each. The loads are represented as constant impedances and split between the areas in such a way that there is power transfer of 400 MW from area 1 to area 2.Figure 4 showing the system with fault. and is simulated for a time duration of 20 sec using phasor simulation power GUI of MATLAB/SIMULINK and fault is created at t = 1 sec.

Figure 4:Kundur’s two area system with fault Simulink model B. Multiband power system stabilizer (MBPSS) The main characteristics of the MB-PSS model (IEEE PSS4B) [4] are shown in Figures 5. As for conventional PSS [3], the MB-PSS comprises three main functions, the transducers, the lead-lag compensation and the limiters. Two speed deviation transducers are required to feed the three band structure used as lead-lag compensation. Four adjustable limiters are provided, one for each band and one for the total PSS output.

The low band usually found in the range of 0.05 Hz ,takes care of very slow oscillating phenomena such as common modes found on isolated system. The intermediate band is used for inter-area modes usually found in the range of 0.2 to 1.0 Hz. The high band is dealing with local modes, either plant or inters machines, with a typical frequency range of 0.8 to 4.0 Hz.

The speed deviation transducers are both derived from machine terminal voltages and currents. The first one ΔωL is associated with the first two bands. Its measurement is accurate in the 0 to 2.0 Hz range. ΔωH, the Second transducer, is designed for the high band with a frequency range of 0.8 to 5.0 Hz. The MBPSS also provide two tunable notch filters to reject the high frequency torsional modes originate on turbo-generators. These are tuned for the first two torsional modes of a given machine. Each branch of a differential filter was designed to provide flexibility similar to a conventional PSS.

On the other hand, the differential capabilities of such a filter bring additional possibilities. The most frequent one is the symmetrical band-pass filter that provides inherent dc washout, zero gain at high frequency and phase leading up to the resonant frequency. The band-pass filter can be synthesized with one pair of lead lag blocks. The two other pairs may then be used to introduce additional compensating effects. As an example, the wash-out block might be added to increase dc rejection while the third block may he used to boost or attenuate the signal in a certain range of frequency.

Nevertheless, the simplest and most natural way to use these differential band filters is the symmetrical approach. With a simple and efficient setting method such as the one presented here, it is possible to set the PSS with only two high level parameters per band .Doing so, the whole lead-lag compensation circuit is specified with six parameters. They are the three filter central frequencies FL, FI, FH and gains KL,

KI KH, Being plain band-pass filters, only the first block in each branch is involved. Time constants and gains are derived from simple equations as shown here for the high band case. KHl1 = KH17= 1 (lead-lag blocks)

… (1) TH2 = TH7 =1/(2ΠFH√R)

… (2) T H 1=T H2/ R

… (3) T H 8=T H7x R

… (4) KH1 = KH2 = ( R2 + R) / ( R2 -2R + 1)

… (5) Central time constants TH2 and TH7 are directly derived from the filter central frequency FH while the symmetrical time constants, TH1 and TH8are computed using constant ratio R. Equation (5) is used to derive branch gains KH1 and KH2 to obtain a unit gain for the differential filter. The band gain is therefore equal to KH. This technique allows us to represent the MBPSS in a simplified model as shown in figure 5.

Fig.5 Simulink model of MBPSS III.DESIGN METHODOLOGY

A. Interactive Artificial Bee Colony (IABC)

Artificial Bee Colony (ABC) is a new optimization algorithm proposed by Karaboga and Basturk in 2005 [23-26]. It is derived from the honey bee’s natural behavior which is exhibited by them during search for the sources of best food. A colony of artificial bees in ABC algorithm contains three groups of bees: employed, onlooker and scout bees. Employed bees bear the information about their food sources, distance of

the food source, its direction from the nest, and the nectar amount of the source; scout bees search for the surrounding environment of the nest so that new food sources could be found; and onlooker bees wait in the beehive for finding a food source through the information collected by employed bees.

Interactive Artificial Bee Colony (IABC) directs in the theory of universal gravitation to the movement of onlooker bees in ABC, and it effectively increases the exploitation ability of ABC. In general, the ABC algorithm works well on finding the better solution of the objective function. Nevertheless, the original design of the onlooker bee’s movement only considers the relation between the employed bee, which is selected by the roulette wheel selection, and the one which is selected randomly. Therefore, it is not powerful enough to take full advantage of the capacity of exploitation. The proposed IABC algorithm is an improved version of ABC algorithm [8]. The universal gravitations between the onlooker bee and the selected employed bees are exploited, by employing the Newton law of universal gravitation described in the equation (6).

1 212 2 21

21

m mF G rrΛ= … (6)

2 1

2 121

r rr rr Λ −=

−

… (7) In the equation (6) & (7), 12 represents the gravitational force, starting from the object 1 to the object 2, G is the universal gravitational constant, 1 and 2 are the masses of the objects, 21 symbolizes the separation between the objects and ˆ 21 denotes the unit vector in the direction position 2 to 1.

In the IABC algorithm, the mass 1 is substituted by the parameter ‘θi’ , which is the fitness value of the employed bee which is selected by applying the roulette wheel selection. The mass, 2, is substituted by the fitness value of the arbitrarily chosen employed bee and is represented by the symbol ‘θk’. The universal gravitation in the equation (6) is formed in the vector format. Hence, its values on different dimensions can be taken separately. Therefore, 21 is calculated by considering the difference between the objects only on the currently alarmed dimension and the universal gravitation on each dimension is calculated separately. In other words, the strength of the gravitation on different dimensions is calculated one by one. Thus, the gravitation on the jth dimensions between θi and θk can be formed in the equation (8).

2

( ). ( ) ( ).( )( )

i k kj ijkj

kj ijkj ij

F FFi G θ θ θ θθ θθ θ

−

−−=

…(8) Since the universal gravitation is considered,

enlarging the consideration between the employed bee, that is selected by the onlooker bee, and more than one employed bees is achievable by adding different ik ⋅ [θi − θk] into the

equation (4), therefore, the gravitation plays the role of a weight factor controlling the specific weight of [θi − θk]. The IABC process can be illustrated in 5 steps: Step 1. Initialization: Scatter percentage of the population

into the solution space arbitrarily, and then calculate their fitness values, which are called the nectar amounts, where represents the ratio of employed bees to the total population. Once these populations are positioned into the solution space, they are called the employed bees.

Step 2. Move the onlookers: Compute the probability of selecting a food source by equation (9),

… (9)

Pi : The probability of selecting the ith employed bee; S : The number of employed bees θi : The position of the ith employed bee; F(θi) : The fitness value

Pick a food source to move to by roulette wheel selection for every onlooker bees. Now determine its nectar amount. The movement of the onlookers follows the equation (10). Calculation of the new position:

… (10)

t : The iteration number j : The dimension of the solution Step 3. Move the scouts: If the fitness value of the employed

bees is not improved by a continuous predetermined number of iterations, which is called “ ”, then those food sources are discarded, and the employed bees now become the scouts. The scouts are moved by the equation (11).The movement of the scout bees follows equation (11).

…(11)

r : A random number between 0 & 1,

Step4. Update the best food source found up till now: Memorize the best fitness value and the position, which are found by the bees.

Step 5. Check of the termination criterion: Check if the amount of the iterations satisfy the termination condition. If the termination condition is fulfilled, then terminate the program and store the results as output; otherwise go back to the Step 2.

B.Objective Function

It is worth mentioning that the PSS is designed to minimize the power system oscillations after a small & large disturbance so as to improve the power system stability. These oscillations are reflected in the deviations in power angle, rotor speed and line power. Minimization of any one or all of the above deviations could be chosen as the objective function. In this study IABC based search is used for the optimization of parameters of MBPSS. The IABC based

( )( )∑

=

= S

kk

ii

F

FP

1

θ

θ

( ) ( ) ( ) ( )( )ttttx kjijijij θθφθ −+=+1

( )minmaxmin jjjij r θθθθ −⋅+=[ ]1,0∈r

design integrates the parameter optimization criterion based on Integral of Squared Time Squared Error (ISTSE).

An objective function that reflects small steady state error, small overshoots and oscillations has been selected for the optimization. The performance index J is defined as:

2

1 2 3 40

2 2 2 2st

J dtt ω ω ω ω⎡ ⎤= + + +⎢ ⎥⎣ ⎦∫ Δ Δ Δ Δ

…(12) Where Δω is speed deviation of the each generator.

A total of 7 parameters of MBPSS controller are being tuned to get the optimal response ts is the time range of the simulation. It is aimed to minimize this objective function in order to improve the system response in terms of the settling time and overshoots under different operating condition. The design problem can be formulated as the following constrained optimization problem, where the constraints are the controller parameters bounds, as follow, Minimize J subjected to following constraints:

GGMIN<GG<GGMAX KLMIN <KL< KLMAX FLMIN<FL<FLMAX

KHMIN<KH<KHMAX FHMIN<FH<FHMAX

KIMIN<KI<KIMAX FIMIN<FI<FIMAX

…(13) Table-I Parameter used in IABC

Table-II Optimized Parameter of IABCMBPSS

IV.SIMULATION STUDY Kundur model is developed for Multi machine infinite bus system using MATLAB/SIMULINK R2009b.MMIB system is simulated under the 3 Phase fault condition with and without IABCMBPSS. Figures shows the speed deviation for all for generator We have implemented the stabilizers IEEE PSS4B on all generating units (G1, G2, G3 and G4).in Kundur

test system, The techniques used for optimizing MBPSS are the Phase compensation, ISTSE. The dynamic performance of the system has been investigated under large perturbation. A 3-phase fault was applied at the line at t = 1 sec, for 20 ms duration and the post fault system restores to prefault conditions. The dynamic responses were obtained by simulating the nonlinear model of the system. It is clear from the result that the oscillations are smaller and settling time of oscillations is considerably shorter with MBPSS following a three phase fault for inter area modes of oscillations.

Fig 6: Speed deviation of generators without MBPSS during 3 phase fault (LLLG)

Fig7: Speed deviation of generators with IABCMBPSS during 3 phase

fault (LLLG)

Fig8: Dynamic response for Δω12, 3 phase fault (LLLG) with

IABCMBPSS (local mode)

Figure 9: Dynamic response for Δω13, 3 phase fault (LLLG)with

IABCMBPSS(Inter area mode)

Colony Size 20 Food Num Colony Size/2

Limit 100 Max Cycle 10000 Run Time 1 Stall Gen 50

Para meter

Lower Bound

Upper Bound

ISTSE J=7.7414

66e-003

ITAE J=2.7449

36e-001

IAE J=2.62734

2e-002 GG 1 20 19.3329 19.3329 4.0060

FL 0.1 1 0.9635 0.9635 0.3155 KL 10 30 5.1356 5.1356 29.6056 FI 1.1 10 1.4066 1.4066 1.9789 KI 30 70 60.4328 60.4328 67.8171 FH 10 20 12.2381 12.2381 17.5122 KH 70 200 103.476 103.476 162.1272

Fig10: Dynamic response for Δω34, 3 phase fault (LLLG)

with IABCMBPSS (local mode)

V.CONCLUSIONS This paper presents a systematic approach for the design of IABC based multiband power system stabilizers in a multi machine power system. Simulation studies reveal that the proposed IABCMBPSS can provide good damping characteristics during small disturbance and large disturbances for local as well as inter area modes of oscillations. In this paper, the IABC algorithm has been implemented to optimally tune the MBPSS parameters for the improvement of the relative stability and secure operation of the multi machine power systems. To optimize the parameters of the stabilizers a time domain-based objective for a broad range of operating conditions is introduced and is solved by IABC. Investigations reveal the performance of IABC based multiband power system stabilizers in a multi machine infinite bus system is better in terms of settling time and peak overshoot under fault conditions.

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[22] Amit Shrivastava, Manisha Dubey, Yogendra Kumar “Optimization Techniques Based Power System Stabilizer's: An Overview, International Journal on Emerging Technologies 4(1): 50-54(Dec-2013) ISSN No. (Print): 0975-8364ISSN No. (Online): 2249-3255

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