论文标题
Wasserstein双向机会限制，并应用于最佳功率流量
Wasserstein Two-Sided Chance Constraints with An Application to Optimal Power Flow
论文作者
论文摘要
作为建模系统安全条件的一种自然方法，机会限制（CC）试图以很高的可能性来满足一组不确定的不平等现象。尽管联合CC提供了更强的可靠性证书，但比单个CCS相比，计算的挑战更大。通过最佳功率流的应用，我们研究了一个特殊的关节CC，称为两侧CC。我们通过以高斯分布为中心的Wasserstein Ball对不确定的参数进行建模，并基于二阶圆锥约束得出保守近似的层次结构，可以通过现成的商业求解器有效地计算出来。此外，我们显示了这些近似值的渐近一致性，并在仅采用有限层次结构时得出其近似保证。我们证明了基于IEEE 118-BUS和3120-BUS系统的案例研究中所提出的模型的样本外部性能和可扩展性。
As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate, it is oftentimes much more challenging to compute than individual CCs. Motivated by the application of optimal power flow, we study a special joint CC, named two-sided CC. We model the uncertain parameters through a Wasserstein ball centered at a Gaussian distribution and derive a hierarchy of conservative approximations based on second-order conic constraints, which can be efficiently computed by off-the-shelf commercial solvers. In addition, we show the asymptotic consistency of these approximations and derive their approximation guarantee when only a finite hierarchy is adopted. We demonstrate the out-of-sample performance and scalability of the proposed model and approximations in a case study based on the IEEE 118-bus and 3120-bus systems.
