The growing frequency of power grid disruptions demands innovative solutions to enhance supply resilience. Electric vehicle (EV) fleets, as mobile energy storage units, offer a sustainable response to prolonged outages by forming an EV-based virtual electricity network (EVEN), which transfers electricity from functioning to affected areas. Unlike existing studies focusing on individual EVs as backup, this paper addresses this gap by developing a generic model for the EVEN solution and a method for coordinating electricity delivery via EVs. The model features a central emergency hub which functions during main grid failures and EV-equipped households. Using a real-world system in Sweden, the EVEN model is evaluated for resilience metrics, including days without energy deficits, electricity delivery, and battery degradation. Additionally, seven key parameters-energy supply, demand, EV configuration, and renewable energy systems-are analyzed to identify optimal conditions. Results indicate that the EVEN solution significantly enhances power supply resilience, particularly for small energy users, with small battery degradation, and is most effective when households are near the central hub. This study advances understanding of EVs in strengthening grid resilience, offering a resource-efficient, scalable and sustainable solution for future energy security.