The thesis focuses on developing a data-driven algorithm, based on machine learning, to solve the stochastic alternating current (AC) chance-constrained (CC) Optimal Power Flow (OPF) problem. Although the AC CC-OPF problem has been successful in academic circles, it is highly nonlinear and computationally demanding, which limits its practical impact. The proposed approach aims to address this limitation and demonstrate its empirical efficiency through applications to multiple IEEE test cases. To solve the non-convex and computationally challenging CC AC-OPF problem, the proposed approach relies on a machine learning Gaussian process regression (GPR) model. The full Gaussian process (GP) approach is capable of learning a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertain inputs. The proposed approach uses various approximations for GP-uncertainty propagation. The full GP CC-OPF approach exhibits highly competitive and promising results, outperforming the state-of-the-art sample-based chance constraint approaches. To further improve the robustness and complexity/accuracy trade-off of the full GP CC-OPF, a fast data-driven setup is proposed. This setup relies on the sparse and hybrid Gaussian processes (GP) framework to model the power flow equations with input uncertainty.

翻译：本论文聚焦于开发一种基于机器学习的数据驱动算法，求解随机交流机会约束最优潮流问题。尽管交流机会约束最优潮流问题在学术界已取得成功，但其高度非线性和计算复杂性限制了实际应用价值。所提方法旨在克服这一局限，并通过多个IEEE测试案例验证其经验效率。为解决非凸且计算困难的机会约束交流最优潮流问题，该方法依赖机器学习中的高斯过程回归模型。完整高斯过程能够学习交流潮流方程的简单但非凸数据驱动近似形式，可处理含不确定性输入的情况。该方法采用多种高斯过程不确定性传播近似方案。完整高斯过程机会约束最优潮流方法展现出极具竞争力且前景可观的结果，优于当前最先进的基于样本的机会约束方法。为进一步优化完整高斯过程机会约束最优潮流方法的鲁棒性与复杂度/精度权衡，本文提出一种快速数据驱动框架，该框架基于稀疏与混合高斯过程模型对含输入不确定性的潮流方程进行建模。