Scholarly article on topic 'A hybrid firefly algorithm and pattern search technique for SSSC based power oscillation damping controller design'

A hybrid firefly algorithm and pattern search technique for SSSC based power oscillation damping controller design Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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{"Power system stability" / "Static Synchronous Series Compensator (SSSC)" / "Firefly Algorithm (FA)" / "Pattern Search (PS)"}

Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Srikanta Mahapatra, Sidhartha Panda, Sarat Chandra Swain

Abstract In this paper, a novel hybrid Firefly Algorithm and Pattern Search (h-FAPS) technique is proposed for a Static Synchronous Series Compensator (SSSC)-based power oscillation damping controller design. The proposed h-FAPS technique takes the advantage of global search capability of FA and local search facility of PS. In order to tackle the drawback of using the remote signal that may impact reliability of the controller, a modified signal equivalent to the remote speed deviation signal is constructed from the local measurements. The performances of the proposed controllers are evaluated in SMIB and multi-machine power system subjected to various transient disturbances. To show the effectiveness and robustness of the proposed design approach, simulation results are presented and compared with some recently published approaches such as Differential Evolution (DE) and Particle Swarm Optimization (PSO). It is observed that the proposed approach yield superior damping performance compared to some recently reported approaches.

Academic research paper on topic "A hybrid firefly algorithm and pattern search technique for SSSC based power oscillation damping controller design"

Ain Shams Engineering Journal (2014) xxx, xxx-xxx

Ain Shams University Ain Shams Engineering Journal

www.elsevier.com/locate/asej www.sciencedirect.com

ELECTRICAL ENGINEERING

A hybrid firefly algorithm and pattern

search technique for SSSC based power oscillation

damping controller design

Srikanta Mahapatra a, Sidhartha Panda b'*, Sarat Chandra Swain a

a Department of Electrical Engineering, KIIT University, Bhubaneswar, Odisha, India b Department of Electrical and Electronics Engineering, VSSUT, Burla, Odisha, India

Received 21 March 2014; revised 9 June 2014; accepted 5 July 2014

KEYWORDS

Power system stability; Static Synchronous Series Compensator (SSSC); Firefly Algorithm (FA); Pattern Search (PS)

Abstract In this paper, a novel hybrid Firefly Algorithm and Pattern Search (h-FAPS) technique is proposed for a Static Synchronous Series Compensator (SSSC)-based power oscillation damping controller design. The proposed h-FAPS technique takes the advantage of global search capability of FA and local search facility of PS. In order to tackle the drawback of using the remote signal that may impact reliability of the controller, a modified signal equivalent to the remote speed deviation signal is constructed from the local measurements. The performances of the proposed controllers are evaluated in SMIB and multi-machine power system subjected to various transient disturbances. To show the effectiveness and robustness of the proposed design approach, simulation results are presented and compared with some recently published approaches such as Differential Evolution (DE) and Particle Swarm Optimization (PSO). It is observed that the proposed approach yield superior damping performance compared to some recently reported approaches.

© 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

1. Introduction

With growing power transfer, transient and dynamic stability is of increasing importance for secure operation of power

Corresponding author. Tel.: +91 9438251162. E-mail addresses: msrikanta@gmail.com (S. Mahapatra), panda_ sidhartha@rediffmail.com (S. Panda), scs_132@rediffmail.com (S.C. Swain).

Peer review under responsibility of Ain Shams University.

systems. Recently developed Flexible AC Transmission System (FACTS) controllers have the potential to significantly improve the transient and dynamic stability margin [1]. FACTS controllers are capable of controlling the network condition in a very fast manner. FACTS controllers enable increased utilization of existing networks closer to their thermal loading capacity, thus avoiding the need to construct new transmission lines. Static Synchronous Series Compensator (SSSC) is one of the important members of series FACTS controller. SSSC is very effective in controlling power flow in a transmission line with the capability to change its reactance characteristic from capacitive to inductive independently of the magnitude of the line current [2]. SSSC is also immune to classical network resonances. An auxiliary damping

http://dx.doi.org/10.1016/j.asej.2014.07.002

2090-4479 © 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

controller can be designed for SSSC to damp the power system oscillations [3].

A conventional lead-lag controller structure is preferred by the power system utilities because of the ease of on-line tuning and also lack of assurance of the stability by some adaptive or variable structure techniques. The problem of FACTS controller parameter tuning is a complex exercise. A number of conventional techniques have been reported in the literature pertaining to design problems of conventional power system stabilizers namely: the eigenvalue approach, pole placement technique and frequency domain optimization technique, etc. But, the conventional techniques suffer from heavy computation burden and the search process is likely to be trapped in local minima as the optimal solution may not be obtained.

The growth in size and complexity of electric power systems along with the increase in power demand has necessitated the use of intelligent systems that combine knowledge, techniques and methodologies from various sources for the real-time control of power systems. In the recent years, new artificial intelligence-based approaches have been proposed to design a FACTS-based supplementary damping controller. These approaches include Particle Swarm Optimization (PSO) [4], Genetic Algorithm (GA) [5], Differential Evolution (DE) [6], multi-objective evolutionary algorithm [7], etc.

In [8], design of bacterial foraging optimization-based (BFO) SSSC controller for damping low frequency oscillations in a single - machine infinite - bus power system has been presented. The design of lead-lad controller is formulated as an optimization problem to minimize a time domain based objective function by employing BFO technique. Gravitational Search Algorithm (GSA) is employed in [9,10] to design a supplementary lead-lag structured damping controller for a SSSC for power system dynamic performance enhancement. The linear model of power system has been used for design and analysis purpose. A hybrid approach involving PSO and BFOA is presented for the design of SSSC based damping controller in [11] where the parameters of the lead-lag structured SSSC controller as well as the gains of AC and DC voltage regulator are optimized. Coordinated design of SSSC with Power System stabilizers by hybrid PSO and BFOA [12] and Improved Lozi map based Chaotic Optimization Algorithm (ILCOA) is proposed in [13]. A multi-objective GA approach is presented in [14] to design the SSSC based damping controller to improve the transient performance of a power system subjected to a severe disturbance by minimizing the power angle, terminal voltage and power flow time trajectory deviations with respect to a post-contingency equilibrium point for a power system installed with a SSSC. An Adaptive Neuro-Fuzzy Inference System (ANFIS) method based on the ANN was presented in [15] to design a SSSC based controller for the improvement of transient stability where the ANFIS structures were trained using the generated database by the fuzzy controller of the SSSC. It is clear from literature review [4-14] that, the lead-lag structured controller is preferred by the power system utilities due to its simplicity and the favorable ration between cost and benefits. It is also observed that remote speed deviation signal [4,7-14] and line active power [5-6] are used as the control input signal to the SSSC based damping controller.

It obvious from literature survey that, the performance of the power system depends on the artificial techniques employed, controller structure and control input signal as

well as chosen objective function. Hence, proposing and implementing new high performance heuristic optimization algorithms with new control structure/signals to real world problems are always welcome. Recently, a new biologically-inspired meta-heuristic algorithm, known as the Firefly Algorithm (FA) has been developed by Yang [16,17]. FA is a population based search algorithm inspired by the flashing behavior of fireflies. FA is simple, flexible and versatile, which is very efficient in solving a wide range of diverse real-world problems. The characteristics of FA algorithm are as follows [18]:

• FA can automatically divide its population into subgroups, due to the fact that local attraction is stronger than long distance attraction. Hence, FA can deal with highly nonlinear, multi-modal optimization problems naturally and efficiently.

• FA does not use past individual best, and there is no explicit global best either. This avoids any potential draw-backs of premature convergence as those reported in PSO.

• FA has an ability to control its modality and adapt to problem landscape by controlling its scaling parameter.

FA has been successfully employed to solve the nonlinear and non-convex optimization problems [19-21]. Recent research shows that FA is a very efficient and could outperform other metaheuristic algorithms. The superiority of FA over Artificial Bee Colony (ABC) Algorithm, PSO and Bacteria Foraging (BF) Algorithm has also been reported in the literature [20,22-23]. In [20], FA has been applied to optimize the classical controller parameters. A binary real coded firefly algorithm has been applied to a static problem of power system in [22] and the results are compared with GA and PSO. In [23] FA is used for clustering on benchmark problems and the performance of the FA is compared with other two nature inspired techniques such as Artificial Bee Colony (ABC), PSO.

To achieve good performance by any meta-heuristic algorithm, a good balance between exploitation and exploration should be maintained during the search process. FA being a global optimizing method is designed to explore the search space and most likely will give an optimal/near-optimal solution if used alone. On the other hand, local optimizing methods such as Pattern Search (PS) are designed to exploit local areas, but they are usually not good at exploring wide area and hence not applied alone for global optimization [24,25]. Due to their respective strength and weakness, there is motivation for the hybridization of FA and PS.

In view of the above, a maiden attempt has been made in this paper for the application of a hybrid Firefly Algorithm and Pattern Search (h-FAPS) approach for the design of a SSSC based damping controller. In the design of a robust damping controller, selection of the appropriate input signal is a main issue. Input signal must give correct control actions when a disturbance occurs in the power system. Most of the available literatures on damping controller design are based on either local signal or remote signal [4-14]. For local input signals, line active power, line reactive power, line current magnitude and bus voltage magnitudes are all candidates to be considered in the selection of input signals for the FACTS power oscillation damping controller. Among these possible local input signals, active power and current are the most

commonly employed in the literature. Similarly, generator rotor angle and speed deviation can be used as remote signals. However rotor speed seems to be a better alternative as input signal for FACTS based controller. It has also been reported in the literature that from power system stability improvement point of view remote speed deviation signal is a better choice than the local line active power signal [6]. But, to avoid additional costs associated with communication and to improve reliability, input signal should preferably be locally measurable. But the drawback of using the remote signal is that they may impact reliability of the controller as the signal will be unavailable in case of failure of communications. Moreover, when remote signals are used, synchronization and efficient PMUs are required to achieve the proper damping based on wide area measurement systems (WAMS). Further, remote control signals are associated with time delays due to signal transmission and this may further degrade the capability of the controller. In order to take the advantage of remote signal and at the same time to avoid its drawbacks, a modified signal equivalent to the remote speed deviation signal is derived from the locally measurable line active power signal and used as the input signal to the SSSC-based controller in this paper.

In stability studies, the overall accuracy is primarily decided by how correctly the system is modeled. Over the years, several SSSC models have been developed and used by the researchers depending on the applications. Traditionally, for the small signal stability studies, linear models are used for years, providing reliable results. However, linear models cannot properly capture complex dynamics of the system, especially during major disturbances. The behavior underlying the performance of a synchronous machine during major disturbances is represented by a set of non-linear differential equations. In addition to these, other equations describing different constraints introduced by the loads and/or network, the excitation system, mechanical control system, and installed FACTS controller, etc., are included. Thus the complete mathematical description of a power system becomes exceedingly difficult. Linearized models give satisfactory results under small disturbance conditions. This presents difficulties for designing the FACTS controllers in that, the controllers designed to provide desired performance at small signal condition do not guarantee acceptable performance in the event of major disturbances. As large-disturbance stability improvement is of main concern here, tuning of the control parameters is performed via simulations of severe fault conditions using non-linear model of power system with SSSC controller.

The aim of the present work was twofold. A remote control signal is constructed from the locally measureable line active power to improve the reliability. A novel hybrid technique taking the advantage of global Firefly Algorithm and local Pattern Search technique is proposed. The design problem of SSSC-based controller to improve power system transient stability is transformed into an optimization problem and proposed h-FAPS technique is employed to search for the optimal controller parameters. The performances of the proposed controller are evaluated in two test systems subjected to various transient disturbances. To show the effectiveness and robustness of the proposed design approach, simulation results are presented and compared with some recently published approaches.

The power systems studied in this paper are Single Machine Infinite Bus (SMIB) and two area four machine systems. Even

though, the studied multi-machine power system is a simple two-area system, the structure and parameters are realistic. The system is ideally suitable for studies related to the stability and control of local and inter-area modes, without the overwhelming complexity of actual inter-connected power systems for stability studies [25]. By studying the above simple systems, the basic characteristics of the controller can be assessed and analyzed, and conclusions can be drawn to give an insight for the implementation of SSSC in a large realistic power system.

2. Materials and methods

2.1. Single-machine infinite bus power system with SSSC

In order to design the SSSC-based damping controller, as well as to assess its performance, a Single-Machine Infinite-Bus (SMIB) power system depicted in Fig. 1 is considered at the first instance. The system comprises a synchronous generator connected to an infinite-bus through a step-up transformer and a SSSC followed by a double circuit transmission line. The generator is equipped with hydraulic turbine and governor (HTG), excitation system and a power system stabilizer. The HTG represents a nonlinear hydraulic turbine model, a PID governor system, and a servomotor. The excitation system consists of a voltage regulator and DC exciter, without the exciter's saturation function as recommended in IEEE Recommended Practice for Excitation System Models for Power System Stability Studies [25]. In Fig. 3, T represents the transformer; VT and VB are the generator terminal and infinite-bus voltages respectively; V1 and V2 are the bus voltages; VDC and Vcnv are the DC voltage source and output voltage of the SSSC converter respectively; I is the line current and PL and PL1 are the total real power flow in the transmission lines and that in one line respectively.

2.2. Modeling of Static Synchronous Series Compensator (SSSC)

A SSSC is a solid-state voltage sourced converter (VSC), which generates a controllable AC voltage, and connected in series to power transmission lines in a power system. SSSC provides the virtual compensation of transmission line impedance by injecting the controllable voltage (Vq) in series with the transmission line. The injected voltage Vq is in quadrature with the line current, and emulates an inductive or a capacitive reactance so as to influence the power flow in the transmission lines. The virtual reactance inserted by Vq influences electric power flow in

Figure 1 Single machine infinite bus power system with SSSC.

the transmission lines independent of the magnitude of the line current [2]. The variation of Vq is performed by means of a VSC connected on the secondary side of a coupling transformer. The compensation level can be controlled dynamically by changing the magnitude and polarity of Vq and the device can be operated in both capacitive and inductive mode. The VSC uses forced commutated power electronic devices to produce an AC voltage from a DC voltage source. A capacitor connected on the DC side of the VSC acts as a DC voltage source. To keep the capacitor charged and to provide transformer and VSC losses, a small active power is drawn from the line. As presented by authors [4-7] VSC using IGBT-based PWM inverters is used in the present study. The single-line block diagram of control system of SSSC is shown in Fig. 2. The control system consists of [27]:

• A phase-locked loop (PLL) to synchronize on the positive-sequence component of the current I. The output of PLL is used to compute the direct-axis and quadrature-axis components of the three-phase voltages and currents.

• Measurement systems to measure the q-axis components of positive-sequence of current I (Iq), voltages Vi and V2 (Viq and V2q) and the DC voltage VDC.

• Two voltage regulators which compute the two components of the converter voltage (Vdcnv and Vqcnv) which is fed to the Pulse Width Modulator (PWM) to calculate the VSC pulses to obtain the desired DC voltage (VDCref) and the injected

voltage (Vqref).

VSC using IGBT-based pulse-width modulation (PWM) inverters is used in the present study. However, as details of the inverter and harmonics are not represented in power system stability studies, a GTO-based model can also be used. This type of inverter uses PWM technique to synthesize a sinusoidal waveform from a DC voltage with a typical chopping frequency of a few kilohertz. Harmonics are canceled by connecting filters at the AC side of the VSC. This type of VSC uses a fixed DC voltage VDC. The converter voltage Vcnv is varied by changing the modulation index of the PWM modulator.

2.3. Modeling of machine

The dynamics of the stator, field, and damper windings are included in the model. All stator and rotor quantities are expressed in the two-axis reference frame (two-axis d-q frame). All rotor parameters and electrical quantities are referred to stator and are represented by primed variables. The mathematical equations are given by [26]:

d Vd = Rsld + Jt Uq - XRUq (l)

d Vq = Rslq + -Jt Uq + XRUd (2)

Vfd = R'fdfd + dt Ufd (3)

Vkd ~ Rkd'kd + ft Ukd (4)

Vkql ~ Rkql 'kql + ft Ukql (5)

Vkq2 ~ Rkq2^kq2 + dt Ukq2 (6)

where Ud = Ldid + Lmdifd + 4d); Uq = Lqiq + Lmq + ^ Ufd Z Lfdifd + Lmd{id + ikd); Ukd — Lkdikd + Lmd{id + ifd), u'kqi — Lkqiikqi~ Lmqiq; 9kq2 — Lkq2ikq2 + Lmqiq.

In the above equations, the subscripts:

d and q represents d-axis and q-axis quantities R and S represents rotor and stator quantities f and k represents field and damper winding l and m represents leakage and magnetizing inductance

The mechanical equations are given by: 1

7 xr j (Pe FrWr Pm

Figure 2 Single-line diagram of the SSSC control system.

— h — rnr dt

where xr and h angular velocity and angular position of the rotor respectively, Pe and Pm represents electrical and mechanical power respectively, J and Fr represents inertia and friction of rotor respectively. The machine speed is determined by the machine inertia constant and by the difference between the mechanical torque, resulting from the applied mechanical power, and the internal electromagnetic torque and so the responses are obtained considering the inertia. Further, the gate limits are also considered in the analysis.

3. The proposed approach

3.1. Structure of SSSC-based controller

The commonly used lead-lag structure as shown in Fig. 3 is chosen in this study as a SSSC-based controller. The structure consists of a gain block with gain KS, a signal washout block and two-stage phase compensation block. The phase compensation block gives the suitable phase-lead characteristics to compensate for the phase lag between input and the output signals. The signal washout block acts as a high-pass filter to allow signals associated with oscillations in input signal to pass unchanged. Without it steady changes in input would modify

Block Block lead-lap; Block

Figure 3 Structure of SSSC-based damping controller.

the output. The value of wash out time constant TW is not critical and may be in the range of 1-20 s [26]. The phase compensation block (time constants T1S, T2S, T3S and T4S) provides the appropriate phase-lead characteristics to compensate for the phase lag between input and the output signals. Vqref represents the reference injected voltage as desired by the steady state power flow control loop. The steady state power flow loop acts quite slowly in practice and hence, in the present study Vqref is assumed to be constant during large disturbance transient period. The required value of compensation is obtained according to the variation in the SSSC injected voltage AVq which is added to Vqref.

3.2. Selection of input signal

damping coefficient respectively; and x represents the rotor speed. As M and D are used to predict the equivalent speed deviation signal, these constants are assumed as tunable parameters.

So the rotor speed can be expressed as:

Aw = J([AP - D(w - 1)]/M)

The block diagram representation of Eq. (10) is given in Fig. 4. Am of Fig. 4 is the derived speed deviation signal which is fed to the lead-lag structured SSSC based controller shown in Fig. 3.

3.3. Problem formulation

In the design of an effective and robust controller, selection of the appropriate input signal is a fundamental issue. Input signal must give correct control actions when a disturbance occurs in the power system. Also, the oscillation modes to be damped should be 'observable' in the input signal for which mode observability analysis can be performed to select the most effective signal to damp out the critical modes under consideration. Both local and remote signals can be used as control input. To avoid additional costs associated with communication and to improve reliability, input signal should preferably be locally measurable. However, local control signals, although easy to get, may not contain the desired oscillation modes. So, compared to wide-area signals, they are not as highly controllable and observable. In a wide-area monitoring system, global positioning system synchronized time-stamped data are used. However, it has been reported in literature that, in today's technology with dedicated communication channels, have around 50-ms delay for the transmission of measured signals in the worst scenarios [6].

The relation between active power and speed is given by:

X =[Pm - Pe - D(W - 1)]/M

where Pm and Pe are the input and output powers of the generator respectively; M and D are the inertia constant and

In lead-lag structured controllers, the washout time constant TW is usually pre-specified [4-6]. In the present study, TW = 10 s is used. The controller gain KS and the time constants time constants T1S, T2S, T3S and T4S are to be determined. Also, the imaginary inertia constant M and damping coefficient D are to be determined. During steady state conditions AVq and Vqref are constant. During dynamic conditions the series injected voltage Vq is modulated to damp system oscillations. The effective Vq in dynamic conditions is given by:

Vq = Vqref + DVq (11)

It is worth mentioning that the SSSC-based damping controller helps in minimizing the power system oscillations after a large disturbance so as to improve the power system stability. It may be recalled that the oscillations occur due to the mismatch between input mechanical power and output electrical power and the deference of power enters into/drawn from the rotor causing its speed to change. Minimization of rotor speed deviations could be chosen as the objective. In the present study, an integral time absolute error of the speed deviations is taken as the objective function as given by Eq. (12).

J = \Aw\- t ■ dt

Figure 4 Block diagram representation for input signal.

where Am is the speed deviation; and t is the time range of the simulation. For objective function calculation, the timedomain simulation of the power system model is carried out for the simulation period. It is aimed to minimize this objective function in order to improve the system response in terms of the settling time and overshoots. The problem constraints are the SSSC controller parameter bounds.

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

Minimize J

Subject to

KT 6 Ks 6 K™

T-min ^ n-< ^ T^max T1S 6 T 1S 6 T1S

T-mm ^ rp ^ T--max T3S 6 T 3S 6 T3S

T-min ^ n-< ^ T^max

T 4S 6 T 4S 6 T 4S

Dmin 6 D 6 Dmax Mmin 6 M 6 Mmax

4. Proposed optimization technique

4.1. Firefly Algorithm

The Firefly Algorithm (FA) is a population-based algorithm developed by Yang [16]. Fireflies are characterized by their flashing light produced by biochemical process bioluminescence. The flashing light may serve as the main courtship signals for mating. It is based on the following three idealized behavior of the flashing characteristics of fireflies [17]:

(a) All fireflies are unisex and are attracted to other fireflies regardless of their sex.

(b) The degree of the attractiveness of a firefly is proportional to its brightness. Their attractiveness is proportional to their light intensity. Thus for any two flashing fireflies, less bright firefly moves toward the brighter one. As brightness is proportional to distance, more brightness means less distance between two fireflies. If any two flashing fireflies have the same brightness, then they move randomly.

(c) The brightness of a firefly is determined by the objective function to be optimized.

For proper design of FA, two important issues need to be defined: the variation of light intensity (I) and the formulation of attractiveness (b). The attractiveness of a firefly is determined by its light intensity or brightness and the brightness is associated with the objective function. The light intensity I(r) varies with the distance r monotonically and exponentially

I(r) = V-

where I0 is the original light intensity and y is the light absorption coefficient.

As a firefly's attractiveness is proportional to the light intensity seen by adjacent fireflies, the attractiveness ß of a firefly is defined as:

ß = ßoe-yrl (16)

where ß0 is the attractiveness at r = 0.

The distance between any two fireflies st and Sj is expressed as Euclidean distance by the base firefly algorithm as:

rj = Ils- - S'il = \jXlSl(Sik " Sjk)2 where n denotes the dimensionality of the problem.

The movement of the ith firefly is attracted to another more attractive firefly j. The movements of fireflies consist of three terms: the current position of ith firefly, attraction to another more attractive firefly, and a random walk that consists of a randomization parameter a and the random generated number 8t from interval [0; 1]. The movement is expressed as:

Si = Si + ßoe yru (s- - Sj)

4.2. Fine tuning by Pattern Search algorithm

The Pattern Search (PS) optimization technique is a derivative free evolutionary algorithm suitable to solve a variety of optimization problems that lie outside the scope of the standard optimization methods. It is simple in concept, easy to implement and computationally efficient. It possesses a flexible and well-balanced operator to enhance and adapt the global search and fine tune local search [28]. The Pattern Search (PS) algorithm computes a sequence of points that may or may not approaches to the optimal point. The algorithm starts with a set of points called mesh, around the initial points. The initial points or current points are provided by the FA. The mesh is created by adding the current point to a scalar multiple of a set of vectors called a pattern. If a point in the mesh is having better objective function value, it becomes the current point at the next iteration [25].

The Pattern search begins at the initial point X0 that is given as a starting point by the FA algorithm. At the first iteration, with a scalar = 1 called mesh size, the pattern vectors or direction vectors are constructed as [01], [10], [—10] and [0 — 1]. The direction vectors are added to the initial point X0 to compute the mesh points as X0 + [01], X0 + [10], X0 + [—10] and X0 + [0 — 1] as shown in Fig. 2. The algorithm computes the objective function at the mesh points in the same order. The algorithm polls the mesh points by computing their objective function values until it finds one whose value is smaller than the objective function value of X0. Then the poll is said to be successful when the objective function value decreases at some mesh point and the algorithm sets this point equal to X1. After a successful poll, the algorithm steps to iteration 2 and multiplies the current mesh size by 2. As the mesh size is increased by multiplying by a factor i.e. 2, this is called the expansion factor. So in 2nd iteration, the mesh points are: X1 + 2 * [01], X1 + 2 * [10], X1 + 2 * [—1 0] and X1 + 2 * [0 — 1] and the process is repeated until stopping criteria is met. Now if in a particular iteration, none of the mesh points has a smaller objective function value than the value at initial/current point at that iteration, the poll is said to be unsuccessful and same current point is used in the next iteration. Also, at the next iteration, the algorithm multiplies the current mesh size by 0.5, a contraction factor, so that the mesh size at the next iteration is smaller and the process is repeated until stopping criteria is met.

5. Results and discussions

5.1. Application of h-FAPS algorithm

The model of the system under study is developed in MAT-LAB/SIMULINK environment. For objective function calculation, the developed model is simulated considering a severe

disturbance. Simulations were conducted on a Pentium 4,

3 GHz, 504 MB RAM computer, in the MATLAB 7.0.1 environment. The equivalent speed deviation signal is generated from the local signal i.e. the line active power of nearest bus where SSSC is located.

FA is controlled by three parameters: the randomization parameter a, the attractiveness b, and the absorption coefficient c. These parameters are generally chosen in the range 0-1. Additionally, the number of fireflies and maximum generation should be properly chosen so as to get the satisfactory performance of the algorithm with minimum computational efforts. A series of experiments were conducted to properly choose these control parameters of FA. The tunned control parameters are: number of fireflies = 5; maximum generation = 100; b = 0.2; a = 0.5 and c = 0.5. Simulations were conducted on an Intel, core i-3core cpu, of 2.4 GHz and

4 GB RAM computer in the MATLAB 7.10.0.499 (R2010a) environment. The optimization was repeated 50 times and the best final solution among the 50 runs is chosen as final controller parameters. Pattern Search (PS) is then employed to fine tune the best solution provided by FA. The final values

of controller parameters obtained by FA are taken as the initial points for PS algorithm. The PS is executed with a mesh size of 1, mesh expansion factor of 2 and mesh contraction factor of 0.5. The maximum number of objective function evaluations and generations are set to 10 each. The flow chart of proposed h-FAPS approach is shown in Fig. 5. The results of proposed h-FAPS algorithm over 20 independent runs are shown in Table 1. The individual result of FA algorithm is also provided in Table 1 for comparison. The minimum, maximum, mean and standard deviations of objective function values obtained in 20 runs are also given in Table 1 for better illustration of evolution process,. It is clear from Table 1 that the minimum objective function value (ITAE value) obtained by FA algorithm is 88.768 x 10~4 and the same decreases to 84.784 x 10~4 by proposed by the proposed h-FAPS approach. It is also evident from Table 1 that computationally proposed h-FAPS is superior to original FA as better minimum, maximum, mean and standard deviation values are obtained with h-FAPS compared to FA.

To assess the effectiveness and robustness of the proposed controller, three different operating conditions (nominal, light

Figure 5 Flow chart of proposed h-FAPS technique.

Table 1 Simulation results, over 20 independent runs of FA and h-FAPS algorithms.

Technique/parameters Ks Tis T2S T3S T4S D M Min. x10~4 Ave. x10~4 Max. x10~4 St. dev. x10~4

h-FAPS 51.991 0.171 0.232 0.793 0.748 18.851 6.994 84.784 90.965 94.201 2.198

FA 67.146 0.614 0.253 0.233 0.528 16.324 11.088 88.768 91.767 94.716 2.248

Figure 6 System response under 5 cycle 3-phase fault at bus 2 cleared by 5 cycle line outage with nominal loading: (a) speed deviation, (b) power angle, (c) tie-line power and (d) SSSC injected voltage.

and heavy) are considered. Simulation studies are carried out under different fault disturbances and fault clearing sequences. The response with proposed h-FAPS optimized SSSC-based damping controller with modified local input signal is shown with solid lines, the response with DE optimized SSSC-based

damping controller with local input signal [6] is shown with dotted lines and the response with PSO optimized SSSC-based damping controller with remote input signal [4] is shown with dashed lines. A signal transmission delay of 50 ms [6] is assumed for remote signal.

5.1.1. Nominal loading (Pe = 0.85 p.u., d0 = 51.5°)

The behavior of the proposed controller is verified at nominal loading condition under severe disturbance. A 5-cycl, 3-phase fault is applied in the transmission line near Bus2 at t = 1.0 s. The fault is cleared by tripping the faulted line and the faulty line is restored after 5-cycles. The original system is restored after the fault clearance. The system response under this severe disturbance is shown in Fig. 6(a)-(d). The plots in (a), (b), (c) and (d) are, speed deviation Am in per unit, power angle d in degree, real power flow in the transmission line PL in MW, and the SSSC injected voltage Vq in per unit respectively. It can also be seen from the Fig. 6(a)-(d) that the proposed h-FAPS optimized SSSC based controller with modified local input signal provides a better damping characteristic compared to both DE optimized SSSC based controller with local input signal [6] and PSO optimized SSSC based controller with remote input signal [4]. For better illustration of advantage of proposed approach, performance comparison with different input signals/techniques is given in Table 2. The comparison is done using various error criterions (ITAE, ISE, ITSE and IAE) and settling time of speed deviations following the above disturbance. It is evident from Table 2 that the propose approach provides a better performance compared to some recently published approaches.

5.1.2. Light loading (Pe = 0.4p.u., d0 = 22.9°)

To test the robustness of the controller to operating condition and location of the fault, the generator loading is changed to light loading condition and a 5-cycle, 3-phase fault is applied at the end of one transmission line connecting Bus2 and Bus3, near Bus3 at t = 1.0 s. The fault is cleared by tripping of the faulted line and the faulty line is restored after 5-cycles. The original system is restored after the fault clearance. The system response under this contingency is shown in Fig. 7 which clearly depicts the robustness of proposed controller for changes in operating condition and type of disturbance. Also, h-FAPS optimized SSSC controller with proposed modified signal provides better transient response compared to DE and PSO optimized SSSC controller with local tie-line power deviation signal and remote speed deviation signal respectively.

5.1.3. Heavy loading (Pe = 1.0p.u., d0 = 60.7°)

The robustness of the proposed controller is also tested at heavy loading condition under another severe disturbance. A 5-cycle 3-phase fault is applied near Bus2 at t = 1.0 s. the fault

Table 2 Performance comparison with different input signals/techniques.

Signal Technique ITAE x10~4 ISE x10~6 ITSE x10~6 IAE x10~4 Settling time (s)

Proposed modified signal h-FAPS 84.784 29.505 4.198 54.129 2.23

Proposed modified signal FA 88.768 29.916 4.244 54.829 2.31

Local signal DE [4] 97.933 31.141 4.558 58.917 2.43

Remote signal PSO [6] 102.285 38.966 5.771 64.116 2.82

I ° < -1

1 ..........Local signal: DE -----Remote signal: PSO -Proposed signal: h-FAPS

Time (sec)

CL 600

..........Local signal: DE -----Remote signal: PSO -Proposed signal: h-FAPS "

ivrV ■■ * \ / ""• V V (b,

Time (sec)

Figure 7 System response under 5 cycle 3-phase fault at bus 3 cleared by 5 cycle line outage with light loading: (a) speed deviation and (b) tie-line power.

Figure 8 System speed deviation response under 5 cycle 3-phase fault at bus 2 cleared by 5 cycle line outages (both lines) and load removal (for 100 ms) with heavy loading.

is cleared removing both the transmission lines for 5-cycles. Also the load near Bus1 is disconnected for 100 cycles. Fig. 8 shows the system speed deviation response for the above interruption from which it is clear that the propose approach outperforms the other recently published approaches.

5.2. Extension to multi-machine power system

The proposed approach of designing and optimizing the parameters of a SSSC based damping controller is also extended to a two-area four-machine [26,29,30] power system shown in Fig. 9. The system consists of four generators divided in to two subsystems and are connected via an intertie. Following a disturbance, the two subsystems swing against each other resulting in instability. To improve the stability the line is sec-tionalized and a SSSC is assumed on the mid-point of the tieline. The relevant data for the system is given in Appendix A.

For a system of N machines, the number of electromechanical oscillating modes is (N — 1) mode. So for a large practical system, the objective function can be expressed as the sum of all oscillating modes. In the present study, the objective function for multi-machine system is expressed as:

J = J|A«l|+£|A«i|). t . dt

where AwL and Aw7 are the speed deviations of local and inter-area modes of oscillations respectively and t is the time range of the simulation. The same approach as explained earlier for single-machine infinite bus power system is followed to optimize the SSSC-based damping controller parameters in the multi-machine system. The optimized values of the controller are shown in Table 3. For comparison, the corresponding values with local input signal (tie-line power) are also given in Table 3.

The behavior of the proposed controller is verified under various severe disturbances. A self clearing 3-phase fault is applied in the transmission line near Bus9 at t = 1 s. The fault is cleared after 5-cycles and the original system is restored. The variations of the local mode of oscillation, inter-area mode of oscillation and tie line active power flow are shown in

Figure 9 Two-area four-machine power system with SSSC.

Table 3 SSSC-based controller parameters obtained by h-FAPS algorithms for multi-machine power system.

Signal/parameters Ks T1S T2S T3S T4S D M Objective function value x10 4

Local signal (line active power) Proposed signal (modified line active power) 17.072 38.974 0.305 0.317 0.492 0.463 0.379 0.187 0.931 0.219 2.792 17.682 3.77 19.127 422.442 215.169

(a) î

■ No control

- Local signal

- Proposed signal

2 3 4 5 6 "Time (sec)

^ 2 S o

s" < -2

1300 1200 1100 1000 900

(b) A A

ÄV; / I A A

!u A1 '-A' W

IJ « /f v ;

\ / '•„• V

; \j ..........No control

-----Local signal

-Proposed signal

1 2 3 4 5 6 7 8 Time (sec)

(C) A A \\ / \ / \ M i i ; >. liL-V - A ; ' -----No control -----Local signal -Proposed signal -

; \ ! \ / \ ' » / » / \ / \

1 ~kt~ T \ " V / ; l î \ i »

/ \ ! 1 ' \ 1 / \ / \J '

[/ V ■

3 4 5 Time (sec)

0.15 0.1

sT 0.05

■ No control

■ Local signal

■ Proposed signal

012345678 Time (sec)

Figure 10 System response for line outage disturbance: (a) inter-area mode of oscillation, (b) local mode of oscillation, (c) tie-line power response and (d) SSSC injected voltage.

Fig. 10(a)-(c) respectively for the above severe disturbance. From these figures it can be seen that, both inter-area and local modes of oscillations are highly oscillatory in the absence of SSSC-based damping controller and the proposed controller significantly improves the power stability by damping these oscillations by suitable modulating the SSSC injected voltage. It can also be seen from the Fig. 10(a)-(c) that in all cases the transient response with h-FAPS optimized SSSC-based damping controller with modified local input signal is better compared to same with local input signal.

To test the robustness of the proposed approach another severe disturbance is considered. One of the parallel transmission line connecting Bus8B and Bus9 is removed for 10-cycles

Figure 11 System response for 3-phase fault disturbance cleared by 5-cycle outage: (a) local mode of oscillation, (b) inter-area mode of oscillation and (c) tie-line power response.

at t = 0 s. Fig. 11(a)-(c) show the variations of the inter-area mode of oscillation, local mode of oscillation and tie-line power response for the above contingency. It is evident from Fig. 11(a)-(c) that the transient response in all the cases are better with proposed h-FAPS optimized SSSC-based damping controller using modified local input signal is better compared to local input signal.

The objective of this work is to evaluate the damping capability of h-FAPS optimized SSSC controller. In this connection, various disturbances like self clearing 3-phase fault and 3-phase fault cleared by line outage are considered but fault ride through (FRT) operation is not considered. For the analysis purpose, a phasor model of SSSC is employed which does not include detailed representations of the power electronics i.e. details of the inverter and harmonics are not represented. The total capacitance value of the DC link is related to the SSSC converter rating and to the DC link nominal voltage. The energy stored in the capacitance in joules divided by the converter rating is a time duration which is usually a fraction of a cycle at nominal frequency. For fault ride through operation of SSSC, proper FRT technique should be applied to protect the converter. A widely adopted solution for FRT is to use a DC chopper on the DC link to limit the sever over voltages on the DC link during bolted faults.

6. Conclusion

An attempt has been made for the first time to apply a hybrid Firefly Algorithm (FA) and Pattern Search (PS) technique to design a SSSC based power oscillation damping controller. The input signal to the SSSC-based controller is derived from the locally measurable line active power. The design problem is formulated as an optimization problem and h-FAPS technique is employed to optimize the controller parameters. The effectiveness of the proposed SSSC controller in improving the power system stability is demonstrated for both single machine infinite bus and two-area four-machine power systems under various severe disturbances. To show the superiority of the proposed design approach, simulation results are presented and compared with recently reported approaches such as DE and PSO. It is observed that the proposed controller with modified local input signal exhibits a superior damping performance in comparison to both remote and local input signals.

Appendix A

A complete list of parameters used appears in the default options of SimPowerSystems in the User's Manual [27]. All data are in per unit unless specified otherwise.

Single-machine infinite bus power system

Generator: SB = 2100 MVA, H = 3.7 s, VB = 13.8 kV, f = 60 Hz, RS = 2.8544e—3, Xd = 1.305, XJ = 0.296, XJ' = 0.252, Xq = 0.474, XJ = 0.243, XJ' = 0.18, Td = 1.01 s, TJ = 0.053 s, TqO' = 0.1 s. Load at Bus2: 250 MW.

Transformer: 2100 MVA, 13.8/500 kV, 60 Hz, R1 = R2 = 0.002, Li = 0, L2 = 0.12, D1/Yg connection, Rm = 500, Lm = 500.

Transmission line: 3-Ph, 60 Hz, Length = 300 km each, Rl = 0.02546 X/km, R0 = 0.3864 X/km, Ll = 0.9337e-3 H/km, L0 = 4.1264e—3 H/km, C1 = 12.74e-9 F/km, C0 = 7.751e—9 F/km.

Hydraulic turbine and governor: Ka = 3.33, Ta = 0.07, Gmin = 0.01, Gmax = 0.97518, Vgmin = -0.1 pu/s, Vgmax = 0.1 pu/s, Rp = 0.05, Kp = 1.163, K = 0.105, Kd = 0, Td = 0.01 s, b = 0, Tw = 2.67 s.

Excitation system: TLP = 0.02 s, Ka = 200, Ta = 0.001 s, Ke =1, Te = 0, Tb = 0, Tc = 0, Kf = 0.001, Tf = 0.1 s,

Four-machine power system

Generators: Sn = Sm = Sb3 = Sb4 = 2100 MVA, H = 3.7 s, VB = 13.8 kV, f =60 Hz, RS = 2.8544e—3, Xd = 1.305, XJ = 0.296, XJ' = 0.252, Xq = 0.474, XJ = 0.243, XJ' = 0.18, Td = 1.01 s, TJ = 0.053 s, Tq,

0.1 s.

Loads: Load 1: P = 11670 MW, QL = 1000 MVAR, QC = 3070 MVAR; Load 2: P = 92350 MW, QL = 1000 MVAR, QC = 5370 MVAR.

Transformers: SBti = SBT2 = SBT3 = SBT4 = 2100 MVA, 13.8/500 kV, f =60 Hz, Ri = R2 = 0.002, Li = 0, L2 = 0.12, Dx/Yg connection, Rm = 500, Lm = 500.

Transmission lines: 3-Ph, 60 Hz, Line lengths: Li = 50 km, L2 = 20 km, L3 = 220 km, Ri = 0.02546 X/km, R0 = 0.3864 X/km, Li = 0.9337e-3 H/km, L0 = 4.i264e-3 H/km, Ci = I2.74e-9 F/km, C0 = 7.75ie-9 F/km.

SSSC: Converter rating: Snom = 100 MVA; System nominal voltage: Vnom = 500 kV; Frequency: f =60 Hz; Maximum rate of change of reference voltage (Vqref) = 3 pu/s; Converter impedances: R = 0.00533, L = 0.16; DC link nominal voltage: VDC = 40 kV; DC link equivalent capacitance CDC = 375 x 10-6 F; Injected Voltage regulator gains: KP = 0.00375, Ki = 0.1875; DC Voltage regulator gains: KP = 0.1 x 10-3, K = 20 x 10-3; Injected voltage magnitude limit: Vq = ±0.2.

Initial operating conditions: Machine I: Pei = 1567.5 MW (0.7464 p.u.); Qei = 115.2MVAR (0.05486 p.u.), Machine 2: Pe2 = 1567.8 MW (0.7466 p.u.); Qe2 = 146.96 MVAR (0.06998 p.u.), Machine 3: Pe3 = 1576.6 MW (0.7507 p.u.); Qe3 = 3i6.5i MVAR (0.1507 p.u.), Machine 3: Pe4 = 1735 MW (0.8262 p.u.); Qe3 = 305.88 MVAR (0.1457 p.u.).

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Srikanta Mahapatra is working as an Assistant Professor in the Department of Electrical Engineering, School of Technology, KIIT, University, Bhubaneswar, Orissa, India. He is working toward his PhD in KIIT University in the area of application of computational intelligent techniques to power system problems. His area of research includes optimization techniques, power system stability.

Sidhartha Panda is a Professor at Veer Surendra Sai University of Technology (VSSUT), Burla, Orissa, India. He received his PhD from Indian Institute of Technology, Roorkee, India in 2008, ME in Power Systems Engineering in 2001 and BE in Electrical Engineering in 1991. Earlier, he worked as a Professor at National Institute of Science and Technology (NIST), Berhampur, Orissa and as an Associate Professor in KIIT University, Bhubaneswar, India. His areas of research include power system transient stability, power system dynamic stability, FACTS, optimization techniques, distributed generation and wind energy.

Sarat Chandra Swain received his PhD from KIIT University, Bhubaneswar in 20i0, and ME from UCE Burla in 200i. Currently, he is working as an Associate Professor in the Department of Electrical Engineering, School of Technology, KIIT, University, Bhubane-swar, Orissa, India. His area of research includes optimization techniques, power system stability, FACTS and economic operation of power system.