Security-constrained stochastic optimal power flow analysis using optimally reduced scenarios for wind generation

Electrical power scheduling typically occurs in two stages: day-ahead (DA) planning and real-time (RT) balancing. In DA scheduling, generation and reserve capacities are set for the next day, with reserves used to balance power in RT under variable conditions. Due to the emerging need for electricity, power systems often operate in marginal states, increasing the probability of equipment failure (contingencies). These uncertainties make potential changes in network topology; this situation becomes even more challenging in the presence of renewable energy sources (RESs) due to their inherent uncertain nature. If this combined effect of uncertainty is not considered explicitly during scheduling, the network may collapse. This paper presents a security-constrained stochastic optimal power flow (SC-SOPF) method to schedule generation and reserves in systems with high wind penetration. The stochastic nature of wind power is modeled through scenario-generation and scenario-reduction techniques by formulating it as a non-convex optimization problem. The proposed scenario-reduction technique ensures that the moments of the reduced scenario set remain the same as the original one while maximizing the distinct features in each scenario. The aforesaid problem was solved using particle swarm optimization (PSO), genetic algorithm, differential evolution, ant colony optimization, and whale optimization techniques. It is found that the value of the objective function obtained by the PSO is at least 21.08% lower than other evolutionary algorithms. The reduced scenarios are used in a two-stage stochastic SC-SOPF model, solved using the benders decomposition technique with group cuts. The effectiveness of the proposed SC-SOPF is evaluated with respect to the expected load not served (ELNS) during real-time operations. Tests on modified IEEE 9-bus and 39-bus systems show that although the DA cost increases on average by 8.07% for the modified 9-bus system and only by 0.18% for the modified 39-bus system due to the larger allocation of reserve capacity by the proposed scheduling technique, consequently ELNS reduces significantly—by 94.74% for the 9-bus system and 47% for the 39-bus system.

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