South African households, like households in many other developing countries, are faced with regular power outages. This is a big problem, since the outages that the households experience are both frequent and long in duration. Efficient electricity infrastructure investment decisions are possible only if the welfare loss of electricity blackouts is determined. We estimate a measure for welfare analysis. The surveys were conducted using electronic equipment (gadgets/tablets) instead of the orthodox paper method. We subject respondents to eight power outage scenarios. We use a random parameter panel Tobit model to account for both zero willingness to pay (WTP) and cross-sectional heterogeneity. In addition to exploring more scenarios, this study contributes as it extends basic analysis found in the literature by allowing for a proportion of the sample to have a zero WTP. A zero WTP is in many cases not unrealistic. The picture that emerges is that WTP increases with duration, which was expected. Overall, South African households place a significant value towards avoiding the interruption. The WTP values presented in this paper are as an approximation of the value of supply security. Improving reliability of supply to households requires significant and continuous investment in electricity infrastructure.