Using a contingent valuation survey, we elicit Swedish households' willingness to pay (WTP) to avoid power outages. In the study respondents are asked to state their WTP for avoiding nine different types of outages. We therefore apply a random parameter Tobit model since there is cross-sectional heterogeneity and a proportion of zero responses. Based on the estimations, we find that the WTP depends positively on the duration of the outages, and that WTP is significantly higher for unplanned outages. The overall variation in the WTP due to observed heterogeneity in housing and socio-economic variables is small compared to the pure effects of power outages. Policy implications of those findings are discussed.