The electric power system and the water distribution systems (WDS) have several interdependencies which have been recognized and which comprise what is informally referred to as the water-energy nexus. The need to adequately model and study these two systems and their interactions is becoming critically important due to the likelihood of load increases in both systems or due to unforeseen events. From previous studies, it is known that the power system is quite resilient under normal operating conditions as well as under small disturbances due to robust design and planning procedures. However, long-term droughts or wide spread power outages can have a severe effect and are part of a set of high impact, low probability events which need to be studied, understood and if possible, quantified. This paper presents novel performance metrics to aid in assessing the resilience of the power system when subjected to such rare, extreme conditions. The metrics proposed here are based on quantities that are relevant to the power system exclusively as well as on parameters pertaining to its operation in conjunction with the water distribution system. The resilience measures of performance are calculated using appropriate metrics which can be obtained from long-term, time-domain simulations.