Low-frequency oscillation damping in the electric network through the optimal design of UPFC coordinated PSS employing MGGP
Introduction
The constant increase in load demand requirement causes power systems to expand in large scale nowadays. But due to the different environmental constraints and resource limitations, systems couldn’t be expanded to meet the requirement. This forces the power system to be heavily loaded which in turn decreases the stability margin. The presence of weak tie lines in the interconnected power networks results in low-frequency oscillation. The frequency range of these LFO is 0.1–3 Hz and they are difficult to detect [1]. If these oscillations are left untreated, they sustain and keep rising to the level that may be sufficient for instability or complete blackout of the electric network. Though power system stabilizers (PSS) are capable of improving network stability by damping out the mentioned oscillations, they may not be effective in the case of any strong disturbances like three-phase fault near generator terminal [2], [3], [4].
However, the advancement of power electronic devices and the applications of FACTS devices in power system have revealed auspicious results for enhancement of electric network stability [5], voltage stability [6], and optimal power flow [7]. Among many second-generation FACTS devices, UPFC is the most popular one that is composed of independent series and shunt FACTS controllers [8]. It can adjust three power system parameters namely voltage of the bus, phase angle, and reactance of the line between two buses. Due to this adjustment capability, UPFC finds its application in the improvement of power transfer through the transmission line, enhancement in the power system stability, voltage stability, and harmonic interaction. These tasks are done by the UPFC controller which causes the system parameters to vary as needed [9], [10], [11]. The coordinated application of UPFC and PSS can ensure system stability and suppress LFO during disturbances. The proper selection of parameter settings of the UPFC coordinated PSS determines its effectiveness in damping out of the LFO of any electric system. Many artificial intelligence techniques have been reported in the literature to find optimum PSS parameters coordinated with UPFC. Since the design problem is nonlinear, different metaheuristic techniques including genetic algorithm [12], differential evolution [13], backtracking search algorithm [14], invasive weed optimization [15], variable neighborhood search algorithm [16], collective decision optimization [17], bat algorithm [18], Firefly algorithm [19], particle swarm optimization [20], and modified particle swarm optimization [21] have been employed to enhance power system stability by damping out LFO. However, most of the presented techniques performed the optimization in offline mode and provided optimized parameters for only a certain operating condition. In addition, the tuning process for these techniques required a significant amount of time and any change of the operating situation requires re-tuning of the parameters. Hence, these techniques are not suitable for real-time operations of the power systems as the operating conditions of the power system networks change continually with varying loads as well disturbances. Consequently, real-time tuning of the PSS parameters with/without coordination of FACTS devices employing neural network [22], support vector regression [23], feedback controller [24], and adaptive neuro-fuzzy inference systems [25] have been reported in the literature. However, to the extent of the author's knowledge, the employment of genetic programming (GP) in the real-time design of the UPFC coordinated PSS parameters is not addressed so far, though GP has been used in other applications of power systems including load forecasting [26] and prediction of wind speed [27].
Consequently, this paper employs a genetic programming approach to estimate the UPFC coordinated PSS parameters in real time that overcomes the disadvantages of the meta-heuristic artificial intelligence techniques. This paper develops mathematical models for the key parameters employing an updated version of GP called multi-gene genetic programming (MGGP) and uses them for estimation of the parameters in real-time for any operating conditions. The obtained results (minimum damping ratio, eigenvalues and time domain analyses) confirm the superiority of the proposed MGGP approach over the fixed gain model and the single-gene genetic programming (SGGP) model. Additionally, the comparison of the obtained results with referenced work [4] demonstrates the compatibility of the proposed technique. The advantage of the proposed model lies in the reduction of the time required for the optimization process. The proposed approach requires less than a cycle of time to estimate the UPFC-PSS parameters that signal the real-time application of the proposed approach. Furthermore, the acceptable values of the standard statistical performance indices also provide confidence on the evolved mathematical models to predict the key parameters.
Section snippets
System modeling
The considered electric network consists of a synchronous generator equipped with PSS and an infinite bus which are interconnected through a transmission line (TL) compensated with UPFC as shown in Fig. 1 [20]. Excitation and boosting transformers (ET and BT) are used for connecting the UPFC with the electric network through the transmission line. The main building blocks of the UPFC are two voltage source converters (VSC-B & VSC-E) connected by the common DC link capacitor.
The parts of UPFC
Optimization problem
The objective function of the proposed problem is a combination of two separate objective functions and both of them are associated with system eigenvalues. The first objective function tries to improve the system damping factor whereas the second one sets the damping ratio to a suitable value. The overall objective function J is the combination of these two functions, J1 and J2 [32]:where index of the eigenvalue is denoted by m; n denotes the system
Genetic Programming (GP)
An intelligent machine learning method known as genetic programming was first proposed by Koza [34]. GP follows the Darwinian principle known as ‘survival of the fittest’. Although GP has similar operators like GA, their problem encoding strategy is completely different [35]. GP provides a solution from a tree structure hence provides a mathematical equation whereas the solution of GA is obtained as a string of numbers. Generally, GP is used for solving regression problems, and others highly
Data processing
At the beginning of this process, a set of one thousand operating conditions were generated randomly from the following ranges.
The operating conditions comprised of terminal voltage (v), real and reactive powers (Pe & Qe) of the synchronous machine. The above-mentioned ranges are given in per units. The appropriate ranges for the real and reactive powers of thermal generators have been demonstrated in [3] and detailed illustration about single machine
Conclusions
This paper investigated the performance of an intelligent technique called MGGP to damp out LFO in electric power system network by tuning UPFC coordinated PSS parameters. The proposed technique outturned different mathematical models for the key parameters of the UPFC-PSS based on the provided training and testing datasets. The evolved mathematical models were employed to estimate the respective values of the key parameters in real time depending on the operating conditions of the power system
Acknowledgement
The authors would like to gratefully acknowledge the support of King Fahd University of Petroleum & Minerals (KFUPM) in conducting this research.
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