Computational Intelligence and Neuroscience

Volume 2018, Article ID 6381610, 17 pages

https://doi.org/10.1155/2018/6381610

## STATCOM Estimation Using Back-Propagation, PSO, Shuffled Frog Leap Algorithm, and Genetic Algorithm Based Neural Networks

Electrical and Electronics Engineering Department, University of Gaziantep, Şahinbey, 27310 Gaziantep, Turkey

Correspondence should be addressed to Hamed Atyia Soodi; moc.liamg@77celedemah

Received 18 October 2017; Revised 28 February 2018; Accepted 21 March 2018; Published 26 April 2018

Academic Editor: Carlos A. V. Sakuyama

Copyright © 2018 Hamed Atyia Soodi and Ahmet Mete Vural. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Different optimization techniques are used for the training and fine-tuning of feed forward neural networks, for the estimation of STATCOM voltages and reactive powers. In the first part, the paper presents the voltage regulation in IEEE buses using the Static Compensator (STATIC) and discusses efficient ways to solve the power systems featuring STATCOM by load flow equations. The load flow equations are solved using iterative algorithms such as Newton-Raphson method. In the second part, the paper focuses on the use of estimation techniques based on Artificial Neural Networks as an alternative to the iterative methods. Different training algorithms have been used for training the weights of Artificial Neural Networks; these methods include Back-Propagation, Particle Swarm Optimization, Shuffled Frog Leap Algorithm, and Genetic Algorithm. A performance analysis of each of these methods is done on the IEEE bus data to examine the efficiency of each algorithm. The results show that SFLA outperforms other techniques in training of ANN, seconded by PSO.

#### 1. Introduction

The power systems are the backbone of any country’s economic and social sectors, without which a country cannot excel in the industrial and social development. But the power systems face the ever-growing load demand as more industrial and housing units are established, which makes the job of power system managing challenging. Recently, the increase of nonlinear loads has badly affected the power quality, due to inherent voltage fluctuations in these types of loads, and has also raised question on the long-term stability of the power systems and their associated instruments [1, 2]. Hence, more research studies have been dedicated to improving the power quality and efficiency through variety of different techniques. The total power in the system contains both real and reactive power, which implies that if the reactive power of the system is improved, the overall system can benefit from this improvement.

A family of different devices which can control the reactive power at designated buses is given the name Flexible AC Transmission Systems (FACTS). These devices have the capability to dynamically adjust different system parameters to enhance the performance and quality [2]. The FACTS are actually controllers which can improve the system stability in terms of voltages, reactive power, and phase angles in the steady-state operation. One of the important FACTS devices which we have focused on in this research is called the Static Synchronous Compensator (STATCOM). A STATCOM is used to control the bus voltage or reactive power injection/absorption at the bus and is connected in shunt with the designated bus.

The STATCOM when used as a voltage regulator draws controllable reactive currents from the buses. Since it is an expensive device, the selection of the optimal bus for the installation is of prime importance. When installed at an ideal location, the STATCOM can improve the efficiency of the power systems significantly [3–6]. However, the STATCOM must be installed on a load bus only, since the generator buses do not need voltage regulation [7–9]. Several authors have reported the use of STATCOM for the voltage and reactive power regulation with different configurations. For example, in larger power systems involving hundreds of buses, multipulse inverters based controllers are used because they provide lower harmonic distortion [5, 10, 11].

The planning, implementation, control, and maintenance of power systems initiate with the power flow calculations which constitute the crux of any power system. Over the past few decades, many different solutions have been proposed for the load flow problems. The most important of these techniques have been reviewed in [12]. At any instant, the power systems experience varying operating conditions and the power flow calculations ensure that the operation of the system is within the bounds of the stability criterion. The power flow equations are complex nonlinear algebraic equations which are usually written in computer programs, which are run over the course of the operation for dynamic analysis. Usually, these equations are solved in multiple iterations and hence require substantial processing and memory requirements [13, 14]. One of the primary methods used for the solutions of nonlinear equations is Newton-Raphson method [15], which is widely known for its quadratic convergence features. However, the conventional load flow studies do not account for the presence of STATCOM device(s) in the system and hence the method must be redesigned for the STATCOM buses. In this paper, we have briefly explained the method to modify the existing load flow equations to incorporate the STATCOM parameters such as reactive powers and voltage sources using Newton-Raphson method as done in [16]. Many research studies have been dedicated to the development of modified models for the STATCOM such as [16–19].

Despite all the benefits of Newton-Raphson method, this method is a complex one and requires large memory and processing capabilities. In real time power systems, power systems analysis including economic load dispatch must be done as frequently as every 5 to 15 minutes [20], which becomes very difficult with classical mathematical approaches. The situation is further aggravated as the huge power systems undergo parameters shifting very rapidly. In order to tune the control parameters of STATCOM, the NR method needs to be run countless times in a system as the system passes through different operational states. This makes the whole calculations hectic and time-consuming. We propose an alternative approach to this method which is based on machine learning algorithms. More specifically, we propose the use of Artificial Neural Network (ANN) for estimating the STATCOM parameters such as voltages, phase angles, and reactive powers. ANN is a very powerful tool which can be used for the data fitting operations as well as classification problems. ANN has been successfully used in different fields [21] which involve use of datasets, such as medical and biomedical applications [22–24], business, finance, stock markets, and foreign exchange [25–28], and power applications [29, 30]. The ANN can be trained to capture the nuances in the input data and to produce estimated outputs accordingly, which in this case would be the estimated voltages and reactive powers. The ANN can be used efficiently in real time power systems to do the load flow analysis much faster than the NR method, thus saving cost of computation power and making shrewd decisions at the right moment.

Three separate ANNs have been developed which take the real and reactive powers of the STATCOM bus and predict three different outputs. First ANN is used to estimate the voltage magnitude and the second uses ANN to find phase angle of the STATCOM bus, while the third and last ANN is used to estimate the reactive power of the STATCOM bus. In order to generate a data set of real and reactive powers of the STATCOM bus, the real and reactive powers of all the load buses in the system were perturbed by gradually increasing their values and the corresponding voltages, angles, and reactive powers at the output were recorded. This data is then fed to both of the ANNs for their respective tasks.

Usually, the Back-Propagation (BP) method is the primary method for training the neural networks; however, this method is prone to get stuck in the local minima and also experiences slower convergence rate towards the optimal solution [33]. Alternative approach to the training of neural network for the optimal weight setting is to use metaheuristic techniques to avoid local minima and slow convergence problems. We have used multiple metaheuristic techniques in this study to tune the weights of the ANN with promising results. A survey of different randomized techniques for the training of neural networks is presented in [34]. First one is the Particle Swarm Optimization technique which is based on stochastic optimization. This technique is based on the mimicking of social behavior of swarm of birds flying over an area in search for food. The birds represent the solutions and the total area over which the birds are flying is the search space, while the food represents the optimal solution in the whole search space [35]. PSO performs better than Back-Propagation for training the neural network in terms of rate of convergence [36–38]. PSO can be applied to improve various aspects of the neural network such as weights assigned to different layers and the number of layers. Several works in literature have used PSO for the purpose of training neural networks including [38], which has used neural network for nonlinear channel equalization. In [39], PSO trained neural network is used to predict structure failure in multistoried RC buildings. Similarly [40] presents a review of different PSO trained ANNs which are used in wind energy systems. In [26], PSO based neural networks are used for the forecasting of foreign exchange rates. Another effort is the use of PSO trained neural network in ground water management, which is used to minimize the operational cost of pumps and pipelines connected to the wells [41]. In geology, PSO based ANN is used to estimate the compressive strength of rock samples [42].

Furthermore, we have also applied Shuffled Frog Leap Algorithm (SFLA) [43] for parameter tuning of the ANN. SFLA is another memetic algorithm inspired by the cooperative search metaphor of frogs. The population (solutions) called frogs is divided into different memeplexes each carrying its own meme. The frogs search for local optima in each memeplex using an evolution method which is comparable to the PSO. In the next stage, the frogs are reshuffled to likely a different memeplex based on their global ranking which is comparable to the shuffled complex evolution algorithm. This ensures that global optima is achieved by the frogs. The SFLA has been proved to be an effective tool in the optimization problems. There are several examples of using SFLA for the training of different types of neural networks such as [44] which uses SFLA to train neural networks which are used in channel equalization and estimation problem. Similarly, [45] has used SFLA to propose three novel techniques for scheduling problem. The authors solve multiprocessor problem in grid environment by using SFLA directly, followed by training the ANN and Radial Basis Function Neural Network (RBFNN) using SFLA. SFLA is also used in acoustics such as [46], which has trained wavelet neural network to locate the source of acoustic emission in rotating machinery to diagnose the friction fault source. In [47], the authors have proposed a combination of Improved SFLA (ISFLA) and Back-Propagation to train the neural network to diagnose early faults in rolling bearings.

At last, but not the least, Genetic Algorithm [48] is also applied for the parameter tuning of the ANN. Genetic Algorithm is another efficient method of optimization which has been vastly used for different problems pertaining to the optimization of different parameters. Genetic Algorithm is based on the Darwinian concept of survival and involves natural selection and natural genetics. The algorithm consists of binary strings which are evolved during the run, on the basis of their probabilities and minimal cost. The algorithm consists of certain operations such as mutation, crossover, and reproduction. Genetic Algorithm is used in literature to provide training to the neural network parameters. This includes [49], which has used GA based ANN to model slump of Ready Mix Concrete (RMC) based on its five ingredients. A combination of GA and ANN is used in [50] to solve the inverse kinematics problem of a six-joint Stanford robotic manipulator. The authors have used three different networks training networks using different training sets. Time series forecasting is an efficient way to analyze the impact of future decisions, both in organizational and individual capacities. The time series has been forecasted using GA based ANN in [51], where automatic design of Artificial Neural Networks (ADANN) is used. In [52], GA and ANN have been used to model and optimize the removal of methylene blue using activated carbon.

In terms of similar work, that is, the use of Newton-Raphson and ANN for estimation of different parameters of power systems, there are several instances. For example, [53] has used PSO tuned ANN to estimate operating conditions of the STATCOM. Specifically, the authors have developed two separate neural networks to estimate the STATCOM voltage and reactive power. Both the neural networks are trained using PSO. The authors perturbed the real and reactive powers to produce larger dataset, used Newton-Raphson method to calculate the voltages and reactive powers, and used ANN to estimate voltages and reactive powers. Quite similarly, the authors of [54] have presented an optimal power flow study using two methods, Newton-Raphson based iterative method and Back-Propagation ANN. The outputs to be estimated include voltages amplitudes, phases, and other parameters.

Further works include [55], which has used ANN for the calculation of causation of anomalies in input data on the outputs in power systems. Specifically, ANN is used to calculate the state of power system based on the input data, which is taken as the real and reactive powers, while the outputs are upper and lower limits of voltage magnitudes and phase angles. In [56], the proper size of STATCOM is calculated in both normal and contingency cases, using Newton-Raphson method.

#### 2. Modeling of Power Systems

Each power system consists of several buses interconnected with each other through transmission lines. The buses can either be load or generator buses. The interconnection of different buses can be represented by the admittance matrix or the -matrix. The -matrix is a better representation of the transmission lines because most of the entries in this matrix are zero, as compared to the reactance matrix. However, the -matrix does not incorporate the admittances associated with the load connected to the buses and STATCOM controller. This representation is shown in Figure 1. The steady-state model of the system is represented by the static load flow equations for the real and reactive powers of the buses along with the equality constraints of the transmission network. The static load flow equations of a specific bus are written in terms of voltage magnitudes and phase angles of all the buses connected to this bus. That is, the load flow equations for real () and reactive power () of bus “” are written asIn these equations, is the magnitude of the voltage at bus “” and is the voltage magnitude of “th” bus connected to the bus “,” while “” represents the corresponding phase angle of the voltage and is the total number of buses in the system. and are magnitude and phase angle of the admittance between buses “” and “”. can be calculated from the admittance matrix of the bus system, which is given asHere is the negative of line admittance from bus to bus , containing the real and imaginary part. is calculated aswhere “” is the conductance of the line and “” is the susceptance ( and being the resistance and reactance). The self-admittance terms can be calculated asFor each of the load busses, there are two equations for the corresponding real and reactive powers, while there are four unknown variables of voltages and phase angles. Hence, these equations need to be solved using nonlinear iterative methods. The most common method is the Newton-Raphson method, which requires the Jacobian of the equations. The Jacobian of the above equations can be represented asIn the above equation, sub-Jacobian entries are defined as , , , and . With the addition of STATCOM, the equations of the bus connected to the STATCOM are slightly modified, which are presented and justified in the next section.