Optimal integration of solar home systems and appliance scheduling for residential homes under severe national load shedding

Abstract

In developing countries such as South Africa, users experienced more than 1 030 hours of load shedding outages in just the first half of 2023 due to inadequate power supply from the national grid. Residential homes that cannot afford to take action to mitigate the challenges of load shedding are severely inconvenienced as they have to reschedule their demand involuntarily. This study presents optimal strategies to guide households in determining suitable scheduling and sizing solutions for solar home systems to mitigate the inconvenience experienced by residents due to load shedding. To start with, this study predicts the load shedding stages that are used as input for optimal strategies using the K-Nearest Neighbour (KNN) algorithm. Based on an accurate forecast of future load shedding outages, this study formulates inconvenience for residents and loss of power supply during load shedding as the objective function. When solving the multi-objective optimisation problem, four different strategies to fight against load shedding are identified, namely (1) optimal home appliance scheduling (HAS) under load shedding; (2) optimal HAS supported by solar panels; (3) optimal HAS supported by batteries, and (4) optimal HAS supported by the solar home system (SHS) with both solar panels and batteries. Among these strategies, appliance scheduling with an optimally sized 9.6 kWh battery and a 2.74 kWp panel array of five 550 Wp panels, eliminates the loss of power supply probability and reduces inconvenience by 92% when tested in the South African load shedding cases in 2023.

More than 18.5 million households in South Africa are affected by load shedding. This results in a potential of 18.5 million unique load profiles. Creating unique optimal solar home systems for each household without evaluating similarities in their load profiles risks duplicating solar home system strategies. Clustering is an unsupervised machine learning method that can group households based on their inherent similarities, minimising intracluster similarity and maximising intercluster dissimilarity.

K-means clustering is used in a case study of 781 South African households metered for a year, forming representative clusters of energy demand profiles to identify optimal strategies for multiple households that minimise the impact of load shedding. Three load clusters are identified as optimal, using the Davies-Bouldin criterion to minimise the ratio of within- and between- cluster distances. From K-means clustering, 43% of households are clustered in a low-energy demand load profile with an average daily energy consumption of 4.5 kWh, 42% in a medium energy and 15% in a high energy demand profile, with an average daily energy usage of 10.8 kWh and 22.1 kWh, respectively. Additionally, based on a 94.4% accurate, hourly, one-year-ahead prediction of load shedding outages using the KNN algorithm, we formulate each cluster’s inconvenience and loss of power supply due to load shedding as a multiobjective mixed-integer nonlinear optimisation problem. The results show that optimal scheduling of a low, medium and high energy consumption cluster with optimally sized 2.4 kWh and 0.39 kWp, 4.8 kWh and 0.78 kWp and 7.2 kWh and 1.17 kWp, battery and panel arrays, respectively, minimises the loss of power supply and substantially reduces the inconvenience of involuntary rescheduling by 86.8%, 71.1% and 86.4% for clusters 1, 2, and 3, respectively.