Optimal Control of DERs in ADN Under Spatial and Temporal Correlated Uncertainties

The uncertainties of distribution energy resources (DERs) have significant impacts on active distribution networks (ADNs), and it is necessary to control the DER outputs to hedge the negative impacts of their uncertainties on ADNs. However, DER uncertainties are complicated, containing spatial and temporal correlation, which makes it challenging to design proper control schemes, especially when there exist temporal-correlated units such as energy units (EUs). This paper provides an Itô process model to describe the characteristics of stochastic resources and EUs in a unified way, which makes it easy to evaluate the impacts of stochastic resources on temporal-correlated units. Based the moment form of the Itô process model, a moment optimization (MO) approach is provided to transform the stochastic control (SC) problem into an optimization problem with respect to the first-order and second-order moments of the system variables. The scale of MO is comparable to that of the corresponding deterministic control problem, which means that the computational efficiency of MO is much higher than that of traditional approaches. Case studies also show that the proposed approach outperforms existing approaches in both the performance and computational efficiency, which means that the proposed approach has attractive potential for use in large-scale applications.