The available delivery capability (ADC) of a power distribution network with respect to a power transaction is evaluated in real-time. The power transaction involves simultaneous power deliveries from power sources in a source area to loads in a sink area. First, a list of contingencies are ranked in the power distribution network with respect to static security constraints to obtain a subset of top-ranked contingencies. For each top-ranked contingency in the subset, a representation of the power transaction in a steady state of the power distribution network, in a form of parameterized three-phase power flow equations, is solved to obtain a corresponding power delivery capability (PDC) and a corresponding binding constraint among the static security constraints. The reliability of the power transaction in the power distribution network is then evaluated based on, at least in part, a first contingency PDC which is a smallest PDC among obtained corresponding PDCs.