Robust data-driven sparse estimation of distribution factors considering PMU data quality and renewable energy uncertainty - Part II: Scalability and applications

This two-part paper proposes a data-driven, robust, and scalable sparse estimation framework of distribution factors (DFs). Part I proposes a novel Adaptive M -Lasso estimator with theoretically guaranteed robustness. For solving this estimator, common algorithms are not scalable to large-scale systems since they often fail to converge under parallelism. This is addressed in Part II, where a novel Online Parallel Stochastic Coordinate Descent algorithm with theoretically guaranteed scalability is proposed. It can simultaneously update massive DF estimates by stochastic parallelism with fast convergence. It also works recursively under a multi-core setting and does not need step-size tuning, which is applicable for cloud-computing-based online parallel estimation. Convergence bounds of this algorithm are theoretically proven, and its speedup and maximum parallel core number are derived. These guide practical computational resource allocation for high efficiency. The benefits of the framework are showcased in real-time market operations under locational marginal pricing (LMP) and financial transmission right (FTR) mechanisms for congestion management. Thanks to its sparsity-promoting effect, robustness, and scalability, it allows for correctly and fast solving LMPs, congestion patterns, and FTR revenues against uncertainties. Test results on IEEE 300- and European 9241-bus systems via Alibaba Cloud validate the high scalability of this algorithm and benefits of the proposed framework to system applications.