Abstract
Distributed generators providing auxiliary service are an important means of guaranteeing the safe and economic operation of a distribution system. In this paper, considering an energy storage system (ESS), switchable capacitor reactor (SCR), step voltage regulator (SVR), and a static VAR compensator (SVC), a two-stage multi-period hybrid integer second-order cone programming (SOCP) robust model with partial DGs providing auxiliary service is developed. If the conic relaxation is not exact, a sequential SOCP is formulated using convex–concave procedure (CCP) and cuts, which can be quickly solved. Moreover, the exact solution of the original problem can be recovered. Furthermore, in view of the shortcomings of the large computer storage capacity and slow computational rate for the column and constraint generation (CCG) method, a method direct iteratively solving the master and sub-problem is proposed. Increases to variables and constraints to solve the master problem are not needed. For the sub-problem, only the model of each single time period needs to be solved. Then, their objective function values are accumulated, and the worst scenarios of each time period are concatenated. As an outcome, a large amount of storage memory is saved and the computational efficiency is greatly enhanced. The capability of the proposed method is validated with three simulation cases.
Highlights
According to the literatures review, we find that, in the existing robust optimization with partial DGs providing ancillary services, switchable capacitor reactor (SCR), step voltage regulator (SVR), static VAR compensator (SVC) and energy storage system (ESS) are not taken into account
The computing rate of the two-stage multi-period mixed integer second-order cone programming (SOCP) of the proposed method is compared with the column and constraint generation (CCG) method
The objective function values of the proposed method fit that of the improved CCG method very close for different —that is, the precision of the proposed method is high enough
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. For the distribution network with radial topology, if the objective function is convex, strictly increasing with line loss, not increasing with load, independent of the active and reactive power flow of lines, the SOCP relaxation will be exact as long as the original OPF is feasible [9,10]. In this paper, considering ESS, SCR, SVR, and SVC, a two-stage multi-period hybrid integer SOCP robust model with partial DGs providing auxiliary service is developed. Compared with [24], the main contributions of this paper are as follows: (1) The optimization model is extended to multi-period, in which the coordination of ESS, SCR, SVR, and SVC with partial DGs providing ancillary services is formulated.
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