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5. A Mixed-Integer SDP Solution Approach to Distributionally Robust Unit Commitment with Second Order Moment Constraints

Author

Zheng, Xiaodong, Chen, Haoyong, Xu, Yan, Li, Zhengmao, Lin, Zhenjia, and Liang, Zipeng

Subjects
Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control
Abstract

A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of stochastic parameters can be inferred from historical data, and then employed to model the set of probability distributions. The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints, and we show that it can be recast as a mixed-integer semidefinite programming (MI-SDP) with finite constraints. The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation. Based on the verification of strong duality of the semidefinite programming (SDP) problems, we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce a SDP relaxation for the feasibility checking problem, which is an intractable biconvex optimization. Experimental results on a IEEE 6-bus system are presented, showing that without any tunings of parameters, the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general, and our method also enjoys higher reliability of dispatch operation.

Published
2019
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6. A Global Solution Method for Decentralized Multi-Area SCUC and Savings Allocation Based on MILP Value Functions

Author

Zheng, Xiaodong, Chen, Haoyong, Xu, Yan, Shen, Feifan, and Liang, Zipeng

Subjects
Electrical Engineering and Systems Science - Systems and Control
Abstract

To address the issue that Lagrangian dual function based algorithms cannot guarantee convergence and global optimality for decentralized multi-area security constrained unit commitment (M-SCUC) problems, a novel decomposition and coordination method using MILP (mixed integer linear programming) value functions is proposed in this paper. Each regional system operator sets the tie-line power injections as variational parameters in its regional SCUC model, and utilizes a finite algorithm to generate a MILP value function, which returns the optimal generation cost for any given interchange scheduling. With the value functions available from all system operators, theoretically, a coordinator is able to derive a globally optimal interchange scheduling. Since power exchanges may alter the financial position of each area considerably from what it would have been via scheduling independently, we then propose a fair savings allocation method using the values functions derived above and the Shapley value in cooperative game theory. Numerical experiments on a two-area 12-bus system and a three-area 457-bus system are carried out. The validness of the value functions based method is verified for the decentralized M-SCUC problems. The outcome of savings allocation is compared with that of the locational marginal cost based method., Comment: 8 pages, 7 figures

Published
2019
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25. A Data-Driven Convex Model for Hybrid Microgrid Operation With Bidirectional Converters

Author

Liang, Zipeng, Dong, Zhaoyang, Li, Chaojie, Wu, Chenye, and Chen, Haoyong

Abstract

Bi-directional converters (BDCs) facilitate the high efficiency of hybrid AC/DC microgrids (HMs). However, the HM operation is rather challenging due to the non-convex system model. This letter develops a data-driven convex model for HM operation involving BDCs. First, a least squares approximation method with data-driven weight functions is proposed to linearize BDC efficiency behavior. Then, the convex linear HM model is formulated by combining this linearized model with an analysis of the conditions ensuring non-simultaneous BDC inverting and rectifying operations. The low approximation error and high computational efficiency of the proposed model are demonstrated based on an analysis of numerical studies.

Published
2023
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