South Africa’s Integrated National Electrification Programme provides low-income households with a free 20-Ampere electricity supply connection. Many of these households persist in using solid and liquid fuels like wood, coal and paraffin for heating and to a lesser degree for cooking. It is generally held that the use of dirty, less convenient fuels persists because they are less more affordable, but the restricted electricity connection also limits the type and number of appliances which can be used simultaneously. The implications of these restricted connections are explored in this paper with a mixed integer programming optimization model. Household appliances are ranked according to their priority, and scheduled according to the lifestyle and needs of the household members. Three scenarios encompassing the range of appliance power ratings are considered. It is found that the 20-Ampere electricity supply does indeed restrict the use of appliances with medium and high-power ratings in peak evening periods. There is no such restriction for energy efficient or small appliances. Increasing the electricity connection to a 40-Ampere supply alleviates all restrictions. As low-income households become more affluent, they need to upgrade their electricity connection in order to make use of more diverse energy services.