Stochastic Optimization for Discrete Overcurrent Relay Tripping Characteristics and Coordination

The inverse-time operating characteristic of overcurrent relays is the primary protective element in distribution system protection schemes and has been utilized for several decades. As the distribution system becomes increasingly complex due to the growth of distributed generation, the protection task based on existing methodologies will become more difficult. Faster relay operating times while maintaining selectivity is critical. In this paper, a stochastic mixed-integer linear program is formulated to minimize a relay's tripping time at discrete fault current intervals and considers the cost of tripping a relay as the objective function. The formulation takes into account the probabilistic nature of the fault current observed at each relay, which can be impacted by fault location, fault resistance, device failure, and DG output. Monte Carlo simulation is used to determine the empirical probabilities of each relay observing a particular fault current. Probabilistic fault scenarios are simulated on the IEEE 34-node test feeder. The proposed approach shows a decrease in expected energy loss due to faults up to 11.5% compared to conventional TCC curves for 10 000 Monte Carlo fault scenarios.