Fuzzy vs. Probabilistic Techniques to Address Uncertainty for Radial Distribution Load Flow Simulation ()
1. Introduction
Current time power distribution systems, especially in developing countries, are steadily approaching towards its maximum operating limits and voltage stability is a major concern. Voltage instability leads to blackouts and makes the system unreliable. It is important to have a reliable power distribution system, which maintains voltages within the permissible range and ensure a high quality of output.
The voltage instability can be addressed using the various techniques e.g. reconfiguration, addition of capacitor banks etc., however need an efficient simulation of load flow and a mathematical method which address the uncertainty efficiently especially the uncertainty associated with input parameters. Distribution system uncertainties are due to error in measurement of feeder parameters, variation in expected values of the demands with time etc. and are main causes of uncertain simulation outputs.
Uncertainty can be analyzed and addressed using several techniques. In past, many solution methods have been developed on Load Flow distribution networks using Fuzzy and probabilistic models.
D. M. Falcao describes the conceptual basis and preliminary results of a load estimation based on the application of neural network and fuzzy set techniques [1]. Chi-Wen Liu presents a neurofuzzy network for voltage security monitoring [2]. I. J. Ramirez-Rosado, Dominguez-Navarro, presents a new possibilistic (fuzzy) model for the multiobjective optimal planning of power distribution networks [3]. Vikas kumar presents a comparison between probalistic and Fuzzy alpha cut techniques in general [4]. A. J Abebe presents a comparison of two methods (fuzzy alpha cut and Monte Carlo simulation) of analysis of uncertainty arising from uncertain model parameters [5]. However none have been found comparing two methods and addressing importance of each other for radial distribution system calculations.
This paper presents a comparison of “Monte-Carlo simulation method (MCS)” a technique based on probability and “Fuzzy alpha cut method (FAC)” a technique based on Fuzzy. The MCS technique treats uncertain parameter as random variable that obeys a given probabilistic distribution and model output is then a random variable. The fuzzy analysis is based on fuzzy logic and fuzzy set theory, which is widely used in representing uncertain knowledge. Uncertain model parameters are treated as fuzzy numbers with a membership function.
2. Methodology
2.1. Steps & Input Data
For simulation purpose this paper uses a load flow algorithm, based on concept described by R. Raina, M Thomas, R. Ranjan [6]. The algorithm calculates the total real and reactive system power loss of the radial distribution network. The algorithm considers input parameters as random variables for Monte Carlo simulation and as fuzzy numbers with a given membership function for fuzzy logic.
This simulation is run on a typical 19 bus distribution system from the D. Thukram, H. M W. Banda and J. Jerome [7] shown in Figure 1.
Input connected load data for the feeder are given in Table 1, Conductor data for the feeders are given in Table 2 and Table 3.
Figure 2 shows the Typical Load Flow calculation chart used for Fuzzy and Monte Carlo simulation. The details of formulas and computing method are in [6].