Solving Large-Scale AC Optimal Power Flow Problems Including Energy Storage, Renewable Generation, and Forecast Uncertainty

Abstract

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 proposed algorithm improves on techniques in prior work, as it does not rely upon model approximations and maintains scalability with respect to the number of scenarios considered in the OPF problem. The optimality of the proposed method is assessed using the lower bound from the solution of an SOCP relaxation and is shown to be sufficiently close to the globally optimal solution. Moreover, the reliability of the OPF solution is validated via Monte Carlo simulation and is demonstrated to fall within acceptable violation levels. Timing results are provided to emphasize the scalability of the method with respect to the number of scenarios considered and demonstrate its utility for real-time applications.

Several extensions of this stochastic OPF are then developed for both operational and planning purposes. The first is to include the cost of generator reserve capacity in the objective of the stochastic OPF problem. The need for the increased accuracy provided by the AC OPF is highlighted by a case study that compares the reliability levels achieved by the AC-QP algorithm to those from the solution of a stochastic DC OPF. Next, the problem is extended to a planning context, determining the maximum wind penetration that can be added in a network while maintaining acceptable reliability criteria. The scalability of this planning method with respect not only to large numbers of wind scenarios but also to moderate network size is demonstrated. Finally, a formulation that minimizes both the cost of generation and the cost of reserve capacity while maximizing the wind generation added in the network is investigated. The proposed framework is then used to explore the inherent tradeoff between these competing objectives. A sensitivity study is then conducted to explore how the cost placed on generator reserve capacity can significantly impact the maximum wind penetration that can be reliably added in a network.