Fast Estimation Method for Selection of Optimal Distributed Generation Size Using Kalman Filter and Graph Theory Ahmed Al Ameri and Cristian Nichita Groupe de Recherche en Electrotechnique et Automatique GREAH Lab., University of Le Havre Le Havre, France ahamedsaad@yahoo.com, nichita@univ-lehavre.fr Hilal Abbood and Ali Al Atabi Electrical Engineering and Electronics Department University of Liverpool Liverpool, UK abbood@liverpool.ac.uk, aliataby@liverpool.ac.uk Abstract - This paper presents a linearised model for a Distributed Generation (DG) network with the aim of estimating optimal size of DG using Kalman filter and graph theory. Relationships between the active power and voltage angle and between the reactive power and voltage magnitude are utilised to determine the minimum real power loss and voltage profile of the distributed network. A 2-stage method is suggested to estimate the best size of DGs. In the first stage, the graph flow method is used to generate the incident matrix to build the linear model and in the second stage, a Kalman filter algorithm is applied to obtain the optimal size of the DG at each bus system. The proposed method has been implemented and tested on standard IEEE 5-bus test system. Simulation results showed that the proposed method is of a significant time saving when compared to an existing method based on load flow. Keywords- distributed generation; Kalman filter algorithm; graph theory; power system analysis; linear load flow. I. INTRODUCTION Electric utility companies are striving to install the renewable Distributed Generation (DG) as an energy resource, to meet growing customer load demand. Renewable energy sources in DG can take various forms including fuel cell, photovoltaic and wind power. In recent years, the installation of renewable DG on the electrical network has provided numerous benefits: preclusion of required system upgrades, improved power quality, reduction of energy losses, improved reliability, and increased efficiency [1], [2]. Poor choice of location or inaccurate sizing DG would increase power losses in the network more than when there is no renewable DG at all. Many researchers have therefore considered and proposed different approaches for selection of optimal DG size in electrical networks [3]-[11]. The impact of connecting DGs to the power grid has been studied with reference to voltage profile, system protection, loss of the power grid, system restoration and other network-related parameters [1]. Numerous studies have been reported in literature to solve the problems associated to DGs connection to the power grid [2]. These studies involved implementation of (i) conventional analytical approaches [3] – [5] using sensitivity factors obtained from quantities such as system bus impedance and admittance matrices, and the exact loss formula and (ii) different optimisation methods based on soft computing techniques [8] – [11]. These techniques were proposed to select optimal size and/or of a single or multiple DGs. In [8], a Genetic Algorithm (GA) was proposed to investigate the impact of DGs connection on voltage stability of the power grid. A fuzzy of evolutionary programming was suggested to obtain optimal size of two types of DG with the aim of minimising total prospective payments levied during compensation issues attributable to system losses [9]. The Artificial Neural Network (ANN) was also proposed in [10] to reduce line losses and beneficially increase the voltage profile. In [11], an Artificial Bee Colony (ABC) algorithm was suggested to determine the optimal size the DG as well as the power factor, and location with the ultimate goal of minimising the total real-power loss. Kalman filtering algorithm has also been of interest in selection of optimal sizes of multiple DGs [12], [13]. It has been proposed in the context of generalised generation distribution factors to select the optimal location of the DGs. The work reported in [12] was then extended in [13] to consider the power loss sensitivity in obtaining the optimal location of the DG. However, most of these techniques do not focus on the computation speed which is of particular importance in improving system stability, reliability, and economy. Most of these studies have also dealt with generalised generation distribution factors to select the optimal location for DGs using power loss or power loss sensitivity as an optimal location index. High levels of variable electricity generation produced by renewable resources require fast control decisions to improve stability, reliability and economy [14]. A parallel algorithm for DG placement design has been proposed in [15] to reduce the power loss and increase system’s stability with less computation time. This paper suggests a 2-stage method is suggested to estimate the best size of DGs in a distributed power grid. In the first stage, the graph flow method is used to generate the incident matrix to build the linear model and in the second stage, a Kalman filter algorithm is then applied to obtain the optimal size of the DG at each bus system with a substantial reduction in the computation speed as compared to an existing method based on load flow. The remainder of this paper is organised as follows: Section II presents the power flow and graph theory model of the DG network under study. The proposed DG power 2015 17th UKSIM-AMSS International Conference on Modelling and Simulation 978-1-4799-8713-9/15 $31.00 © 2015 IEEE DOI 10.1109/UKSim.2015.105 420