A Lotka-Volterra approach to modelling revenue and consumer dynamics in electricity distribution: a case study of KEDCO

Abstract

This study presents a two-equation predator-prey model to capture the nonlinear interactions between consumer growth and revenue dynamics in electricity distribution systems. Drawing on the classical Lotka-Volterra framework, total active consumers are modelled as the “prey” population sustaining revenue, while revenue generation functions as the “predator,” exerting feedback effects through pricing signals and service delivery. The model is calibrated using Kano Electricity Distribution Company (KEDCO)’s operational data, formatted as quarterly time-series data from 2015 to 2023. Parameters were initially estimated using Nonlinear Least Squares Regression (NLSR), and the system was numerically solved using the Runge-Kutta 4th Order (RK4) method. However, the NLSR approach produced unstable forecasts with economically unrealistic equilibria, highlighting its limitations for complex, nonlinear, and large-scale systems. As a result, parameters were subsequently refined using Differential Evolution with logarithmic transformation to ensure numerical stability and economic plausibility. In contrast, these refined parameters generated stable and accurate forecasts, achieving mean absolute percentage errors of  for consumers and  for revenue. Equilibrium and Sensitivity analysis were conducted which confirmed neutrally stable centres characteristic of Lotka-Volterra systems, but crucially, only the refined model yielded economically plausible equilibria. The Sensitivity analysis further highlighted the model’s responsiveness to operational inefficiencies and pricing policies, revealing that consumer growth is most influenced by intrinsic growth and interaction rates while revenue dynamics depend strongly on decay and consumer contribution rates. This proposed framework demonstrates its utility as a robust, policy-informing tool for optimizing revenue sustainability and demand management in electricity distribution networks.