Evaluating the accuracy of the beta probability density function for a changed socio-economic electrification load profile in the Free State

Abstract

Accurate estimation of After Diversity Maximum Demand (ADMD) is essential for the reliable and cost-effective planning of low-voltage distribution networks in areas undergoing rapid socio-economic change. When ADMD values are misestimated, planners risk either under-built infrastructure that leads to operational constraints or over-designed systems that incur unnecessary capital expenditure. South Africa’s widely used standard, SANS 507-1:2019, derives residential ADMD values from a Beta probability density function calibrated on historical datasets. Whether these values still reflect present-day consumption patterns in electrifying Free State communities remains uncertain, and addressing this uncertainty is vital to maintaining sound planning practice. This study evaluates the applicability and reliability of the SANS 507-1:2019 ADMD values, and their underlying Beta-PDF model, within socio-economically diverse electrification settings across the Free State. The aim is to determine whether the standard continues to provide dependable design guidance or whether contextual adjustment is warranted as community load profiles evolve. Historical transformer-zone load data were processed using documented quality controls, including the exclusion of implausibly low loads, to derive observed ADMD values defined as the 99.5th-percentile load for each consumer class and supply category. These were compared with the standard’s theoretical ADMDs, and deviations were evaluated against a ±12% planning-tolerance threshold. The analysis shows that only 6 of 52 class-by-case comparisons fall within this tolerance, indicating that standard ADMD values often diverge from observed demand. Larger deviations align with regional distinctions recognised in SANS 507-1:2019, demonstrating that geographic and socio-economic context materially influence demand behaviour. The evidence therefore shows that, in several Free State settings, the Beta-PDF-based standard no longer consistently reflects actual ADMD. The study contributes an auditable and reproducible procedure for deriving and validating ADMD in changing socio-economic electrification environments. It further recommends targeted refinement of standard ADMD parameters and supports future recalibration efforts grounded in empirical, region-specific load data to improve the accuracy and relevance of national planning frameworks.