A Logistic Differential Equation Model Rendition of Customers’ Consumption of Electrical Energy
Emile Kpakpo Adotey
Electricity Company of Ghana, Takoradi, Ghana.
John Awuah Addor *
Department of Mathematics and Statistics, Takoradi Polytechnic, P.O.Box 256, Takoradi, Ghana.
Sarah-Lynn Mensah
Department of Mathematics and Statistics, Takoradi Polytechnic, P.O.Box 256, Takoradi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
This paper presents a logistic differential equation model of customers’ consumption of electrical energy in Ghana. The objective is to model the industrial and commercial consumption of electrical energy of customers of the Electricity Company of Ghana in the Sekondi-Takoradi Metropolis of the Western Region. The paper applies a model based on the Logistic Differential Equation. The consumption data of customers were obtained through an Automatic Meter Reading System which enables a remote reading from customer’s energy meter.
The rate of change of energy consumption has been expressed in the form of the Logistic Differential Equation. Analytical solution has been obtained and constants estimated by fitting a historical energy consumption data to a linear regression equation. The carrying capacity of the Logistic equation referred to as the Optimal Asymptote in this paper has been obtained using the Fibonacci Search Technique. All computations were done based on algorithms which were implemented using the C# Programming Language.
A forecast of a customer’s electricity consumption has been done. The forecast consumption was compared with the actual historical consumption in order to ascertain the level of disparity of the forecast from the actual. The Mean Absolute Percentage Error, which measures the forecasting accuracy or predictive power of the model, has been estimated to be ±6.77%. Practically, the model has predicted correctly to the precision of a maximum of 10% above and a minimum of 2% below the historical energy consumption data.
Keywords: Automatic meter reading system, Fibonacci search technique, industrial energy consumption, linear regression, logistic differential equation, mean absolute percentage error, optimal asymptote