IMPLEMENTATION ON DIFFERENTIAL EQUATION OF MILNE-SIMPSON FOR PREDICTION FOR APPARENT POWER USAGE IN PLN (PERSERO) UIW NTB

Abstract

Electricity is one of the essential forms of energy required by humans in modern society. Consequently, the demand for electricity supply will continue to increase over time. Irregular or fluctuating electricity consumption can affect the readiness of power generation units to provide an adequate supply of electricity to consumers or the public. By predicting apparent power (VA), power companies can optimize generation efficiency, ensure grid stability, and reduce losses. This study applies the logistic equation model using annual apparent power usage data obtained from PT PLN (Persero) UIW NTB for the 2011–2024 period. The model parameters (growth rate r and carrying capacity K) were estimated directly from the historical data, and the differential equation was solved numerically using the Milne-Simpson method with initial values generated by the fourth-order Runge-Kutta approach. The logistic model is chosen for its ability to represent nonlinear growth toward a saturation capacity. Simulation results show a gradually increasing trend in VA usage that slows down as it approaches the saturation phase around 2030. Model validation, performed by comparing the numerical predictions with the actual historical data, shows very small relative errors ranging from 10⁻⁵ to 10⁻⁷, confirming that the Milne-Simpson method possesses high accuracy and stability.