Introducing FOPLC Based TCSC in Coordination with AGC to Improve Frequency Stability of Interconnected Multi-source Power System M. Tarafdar Hagh, J. Morsali, K. Zare
K. M. Muttaqi
Faculty of Electrical and Computer Engineering University of Tabriz, Iran
[email protected],
[email protected],
[email protected]
School of Electrical, Computer and Telecommunications University of Wollongong, Australia
[email protected]
Abstract—Fractional order phase lead-lag controller (FOPLC) is a generalization of classical phase lead-lag controller (CPLC) using fractional calculus. Nowadays, fractional order controllers (FOC) have found wide applications in various aspects of power system control and operation. In this paper, FOPLC are used in structure of flexible ac transmission system (FACTS) based frequency stabilizer to enhance the dynamic performance of automatic generation control (AGC) system. So, Thyristor controlled series capacitor (TCSC) based damping controller with FOPLC structure is proposed in coordination with secondary integral load frequency controller (LFC). The controller is optimized via an improved particle swarm optimization (IPSO) algorithm. The dynamic performance of the proposed controller is compared with CPLC using eigenvalue analysis and time domain simulations. An interconnected multi-source realistic power system with TCSC in series with the tie-line is investigated considering the nonlinearity effects of generation rate constraint (GRC) and governor dead band (GDB). Simulation results reveal that FOPLC based TCSC damping controller achieves superior dynamic performance under various load perturbation patterns in terms of decreased performance index, settling time and amplitude of oscillations. Furthermore, the robustness of the proposed controller has been tested for large uncertainties in system parameter and loading condition.
categories of the FOC i.e., TID (tilted proportional and integral) controller, CRONE controller (CRONE is a French abbreviation which means fractional order robust control), fractional order proportional-integral-derivative (FOPID) controller, and fractional order phase lead-lag compensator (FOPLC) are compactly surveyed. In [3], it is claimed that the FOPLC should have its equal value compared to the CRONE or FOPID (so called PIȜD) controllers. The similarities between the FOPLC and the FOPID controller in the frequency domain are studied in [4]. The FOPLC is the generalized version of the CPLC employing fractional calculus. It is one of well-established kinds of the FOCs that has received remarkable attention from control engineering society and is investigated in details in [4, 5]. In [6], a procedure for achieving rational-order approximations for the FOPLC is proposed in which, the exponentially stable infinite-dimensional state-space representation of the FOPLC is extracted from the Taylor series expansion.
Keywords— Fractional order controller (FOC); classical phase lead-lag controller (CPLC); Fractional order phase leadlag controller (FOPLC); TCSC-AGC; FOMCON; frequency stability
I.
INTRODUCTION
Lately, fractional calculus has received considerable attention in engineering researches with a growing interest in applying fractional order controllers (FOC) [1, 2]. Fractional calculus extends the ordinary differential equations to fractional order differential equations, i.e. those having non-integer powers of differentials and integrals. Theoretically, fractional calculus can comprise both modeling of a system with fractional order dynamics and control of an integer order dynamic system by FOC. Often, the main issue is to employ the FOC in feedback systems to improve the performance of control system. In [3], four
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Recently, utilization of FOC has received more attention in electrical power engineering issues, specifically for power system control, due to the progress in computational power that permits simulation and implementation of the fractional order controller with sufficient accuracy. In [710], FOPID controller is designed as an automatic voltage regulator (AVR) system. It is shown that greater dynamic performance and robustness can be obtained by using FOC in comparison with the integer order PID controller (IOPID). In [11-14], the FOPID is used as secondary load frequency controller (LFC). It is demonstrated that the FOC outperforms the integer order controller (IOC) in enhancing of the power system frequency stability. Sensitivity analysis shows that the FOC based LFC can provide better robustness than the IOC under large uncertainty scenarios. In [15], the authors introduce the FOPID based power system stabilizer (FOPID-PSS) to improve the dynamic stability of multi-machine power system. They also claim the superiority of this stabilizer compared to both IOPIDPSS and conventional PSS (CPSS) with the classical leadlag structure. Automatic generation control (AGC) is an important function in frequency regulation of modern power Systems. Application of AGC in presence of various flexible ac
transmission system (FACTS) devices is an interesting issue that has received much attention in recent published papers [16-20]. Literature survey shows that the classical phase lead-lag controller (CPLC) has been used widely in design of the FACTS based damping controllers [17, 19, 20]. It is possible to extend the CPLC to its generalized fractionalorder case known as the FOPLC which was studied comprehensively in [4]. However, surprisingly to the best of the authors' knowledge, the FOPLC structure has not been employed in design of FACTS based damping controllers applicable in the frequency stability or even the rotor angle stability studies [21], till now. Recently, a novel modeling and control method for application of TCSC in AGC of an interconnected realistic multi-source power system is presented in [20]. The CPLC is employed in the structure of the TCSC based damping controller so that the TCSC-AGC coordinated controller can contribute effectively in damping the area frequency and tie-line power oscillations of the realistic interconnected multi-source power system [20]. A widely-employed approach for time domain simulation of systems containing non-integer order controllers is to approximate the FOC with an integer order rational transfer function and then perform the simulation [7-10]. Nowadays, the computations and simulations associated with the FOC issues can be carried out easily using MATLAB/SIMULINK based toolboxes which are dedicated to fractional order control such as the CRONE toolbox [22], Ninteger toolbox [23], or FOMCON toolbox [24, 25]. The FOMCON is a fractional order modeling and control toolbox developed for MATLAB software to analyze fractional systems and controllers in both time domain and frequency domain. The goal of this toolbox is to provide a user friendly, suitable and accurate means to design FOCs for a wide range of practical applications [26, 27]. In this paper, TCSC based damping controller with FOPLC is introduced to stabilize effectively the area frequency and tie-line power oscillations in AGC of an interconnected power system. The realistic multi-source power system of [20] with the TCSC in the tie-line is regarded as the benchmark test system in all simulations. The coordinated design of proposed FOPLC based TCSC damping controller and integral type LFC is formulated as a nonlinear optimization problem. The adjustable parameters are optimized concurrently via an improved particle swarm optimization (IPSO) algorithm. The objective is to minimize the integral of time multiplied squared error (ITSE) performance index. The performance of the proposed controller is compared with CPLC based TCSC damping controller, in coordination with integral AGC, from the standpoint of dynamic performance and system robustness against various uncertainties. Simulations are performed using the FOMCON toolbox version 0.3-alpha, which is run on a laptop with an Intel Core™ 2 Duo of 2.66 GHz and 4 GB DDR3 RAM.
II.
FOPLC BASED TCSC FOR FREQUENCY STABILITY
A. A review to fractional calculus Fractional calculus is a generalization of integer order integral and differential to a fractional order operator a Dtα , where a and t denote the limits of the operation and Į denotes the fractional order which is a complex number [1]. The fractional order operator is defined as:
dα , ℜ(α ) > 0 dt α ° ° α (1) ℜ(α ) = 0 1, a Dt = ® ° t α ° ³a (dτ ) , ℜ(α ) < 0 ¯ There are various definitions and approximations for fractional derivative and integral. The widely used Riemann–Liouville (R-L) definition for fractional order differential is given by [11]: t
1 dn (t − τ )n −α −1 f (τ )dτ (2) Γ(n − α ) dt n ³a where n-1 Į < n; n is an integer number; and ī(·) is Euler’s gamma function. Also, the fractional order integral is given by: α a Dt f (t ) =
t
1 (t − τ )α −1 f (τ )dτ (3) Γ(α ) ³a For simplicity, Laplace transform is routinely employed to explain the fractional or integer order differentiation. For fractional order of Į (0
