High-Order Taylor Expansion-Based Nonlinear Value Function Approximation for Stochastic Economic Dispatch of Active Distribution Network

The stochastic economic dispatch (SED) problem of active distribution network (ADN) is computationally intractable for traditional algorithms due to the randomness, nonlinearity, and nonconvexity. To solve this problem, we decompose it into a sequence of tractable subproblems, and then employ the high-order Taylor expansion (HTE)-based value functions to estimate the interaction among these subproblems. Compared with traditional value function approximation (VFA) techniques, the proposed HTE-based VFA technique extends the approximate value function from the low-order form to the arbitrarily high-order form, which facilitates describing the nonlinear characteristics. Furthermore, different from commonly used Monte Carlo-based expectation calculation (EC) techniques, which require to re-execute calculation procedures in numerous scenarios, the proposed HTE-based EC technique leverages the nature of HTE to directly obtain the expectation of value function according to the distributions of random variables. Such that the computational burden can be reduced significantly. Finally, the aforementioned two techniques are combined to form an HTE-based economic dispatch algorithm, and then applied to several ADN systems. The numerical simulations fully demonstrate the effectiveness of the proposed algorithm.