Individuals experience varying levels of social vulnerability to power grid outages caused by disasters. Neglecting social vulnerability in energy resilience strategies can lead to uneven recovery, which has become a major concern in the U.S. However, few studies consider environmental and infrastructural factors in their social vulnerability analysis. Here we introduce a conceptual Power Outage-Risk integrated Social Vulnerability Index (PO-RSVI) to assess vulnerability of small residential communities to prolonged outages. The proposed index comprises dimensions of prolonged outage susceptibility, community coping capacity, and community accessibility, each with indicators evaluating social hardship during power outages. Additionally, an extensive analysis investigates the relationship between PO-RSVI and willingness to pay for emergency power supplies during such event. Through an extensive analysis of three Texas communities using survey and online datasets, PO-RSVI effectively highlights disparities missed by conventional assessments and provides valuable insights for policymakers and energy resilience planners.