Stochastic Dual Dynamic Programming for Operation of DER Aggregators Under Multi-Dimensional Uncertainty

Abstract

Abstract--The operation of aggregators of distributed energy resources (DER) is highly complex, since it entails the optimal coordination of a diverse portfolio of DER under multiple sources of uncertainty. The large number of possible stochastic realizations that arise, can lead to complex operational models that become problematic in real-time market environments. Previous stochastic programming approaches resort to two-stage uncertainty models and scenario reduction techniques to preserve the tractability of the problem. However, two-stage models cannot fully capture the evolution of uncertain processes and the a priori scenario selection can lead to suboptimal decisions. In this context, this paper develops a novel stochastic dual dynamic programming (SDDP) approach which does not require discretization of either the state space or the uncertain variables and can be efficiently applied to a multi-stage uncertainty model. Temporal dependencies of the uncertain variables as well as dependencies among different uncertain variables can be captured through the integration of any linear multidimensional stochastic model, and it is showcased for a porder vector autoregressive (VAR) model. The proposed approach is compared against a traditional scenario-tree-based approach through a Monte-Carlo validation process, and is demonstrated to achieve a better trade-off between solution efficiency and computational effort.Index Terms--Aggregator, distributed energy resources, multidimensional uncertainty, stochastic dual dynamic programming, vector autoregressive modeling. I. NOMENCLATURE A. IndexesIndex of time periods, running from 1 to . Index of energy storage (ES) units, running from 1 to . Index of flexible loads (FL), running from 1 to . Index of wind turbines (WT), running from 1 to . Index of micro-generators, running from 1 to . B. ParametersEnergy market price at period . Operating cost of micro-generator . Cost of demand shedding. C. VariablesPower sold to (positive)/bought from (negative) the market at period . ,Power output of micro-generator at period . Demand shed at period ., Energy level of ES unit at period . ,Power input (positive) / output (negative) of ES unit at period . , ℎChange of demand of FL at period due to load shifting. ,Demand of FL at period after load shifting., Dispatched wind power output of WT at period . II. INTRODUCTIONA. Background FUNDAMENTAL feature of the emerging Smart Grid paradigm involves the integration of a large number of distributed energy resources (DER) storage units, in order to support the economic operation of the future low-carbon power system [1]- [2]. However, the large number, small individual size and inherent stochasticity characterizing these DER have complicated system scheduling and market coordination. Furthermore, driven by the wide integration of renewable generation in power systems, there is a general consensus to move energy trading as close as possible to real-time [3]- [4], which intensifies the complexity of DER coordination. These challenges have...

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