Solving Large-Scale AC Optimal Power Flow Problems Including Energy Storage, Renewable Generation, and Forecast Uncertainty
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Renewable generation and energy storage are playing an ever increasing role in power systems. Hence, there is a growing need for integrating these resources into the optimal power flow (OPF) problem. While storage devices are important for mitigating renewable variability, they introduce temporal coupling in the OPF constraints, resulting in a multiperiod OPF formulation. This work explores a solution method for multiperiod AC OPF problems that combines a successive quadratic programming approach (AC-QP) with a second-order cone programming (SOCP) relaxation of the OPF problem. The solution of the SOCP relaxation is used to initialize the AC-QP OPF algorithm. Additionally, the lower bound on the objective value obtained from the SOCP relaxation provides a measure of solution quality. Compared to other initialization schemes, the SOCP-based approach offers improved convergence rate, execution time and solution quality.
A reformulation of the the AC-QP OPF method that includes wind generation uncertainty is then presented. The resulting stochastic optimization problem is solved using a scenario based algorithm that is based on randomized methods that provide probabilistic guarantees of the solution. This approach produces an AC-feasible solution while satisfying reasonable reliability criteria. The scalability, optimality and reliability achieved by the proposed method are then assessed. This algorithm improves on other techniques, as it does not rely upon model approximations and maintains scalability with respect to the number of scenarios considered. Several extensions of this stochastic OPF are then developed. The first is to include the cost of generator reserve capacity into the stochastic AC-QP OPF. Next, the problem is extended to a planning context, determining the maximum wind penetration that can be added in a network while maintaining reliability criteria. Finally, a formulation that minimizes the cost of generation and cost of reserve capacity while maximizing the wind generation added in the network is investigated.