基于改进交替方向乘子法的电-气综合能源系统优化调度

doi:10.19595/j.cnki.1000-6753.tces.230292

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Abstract It is challenging for distributed optimal dispatch of integrated electricity and gas systems due to the nonlinear and nonconvex Weymouth equation. At present, many studies use the second-order cone to relax the Weymouth equation, which is relatively complicated. On the other hand, the mainstream distributed algorithm alternating direction method of multipliers (ADMM) is not computationally efficient. In this paper, an exact approximate Weymouth equation linearization model and a multi-parameter programming modified ADMM algorithm are proposed to address the aforementioned two concerns.
The Weymouth equation linearization model is based on Taylor expansion, which uses a cluster of tangents to relax the Weymouth equation and replaces the curve with tangents approximately. In particular, a penalty term is added to tighten the slack gap, and the number of tangents is reduced by variable substitution. Then an effective tangent selection method is given to obtain an accurate approximation of the Weymouth equation linearization model.
The multi-parameter programming modified ADMM algorithm improves ADMM by multi-parameter programming, to improve the computational efficiency of distributed optimal dispatch. In the ADMM subproblem, the analytical expression of the optimal solution of the subproblem is obtained by multi-parameter programming. During the iteration, as long as the parameters fall in the critical regions, the parameters can be directly substituted into the analytic equation of the optimal solution to obtain the optimal solution of the subproblem without solving the subproblem, to improve the iteration speed. In addition, this paper also deals with the unavoidable degradation problem in multi-parameter programming by the method based on QR decomposition, which enhances the generality of the multi-parameter programming modified ADMM algorithm.
The simulation results of the small-scale system show that the average relative error of the Weymouth equation linearization model is 0.49%, and the maximum relative error is 2.75%, which achieves a good approximation effect. Compared with the piecewise linearization method, the proposed linearization method has higher accuracy and computational efficiency. In the distributed optimal dispatch, the number of iterations of the multi-parameter programming modified ADMM algorithm and classic ADMM is the same, but the time consumption of the proposed algorithm is only 63.43% of classic ADMM, which is equivalent to a 57.66% increase in computational efficiency. For the varying penalty parameter ADMM, although the number of iterations of the varying penalty parameter ADMM is one less than that of the proposed algorithm, the time consumption of the proposed algorithm is still less than that of the varying penalty parameter ADMM, and the computational efficiency can also be improved by 44.53%. In addition, the simulation results of the large-scale system also verify the accuracy of the Weymouth equation linearization model and the efficiency of the multi-parameter programming modified ADMM algorithm.
Through simulation analysis, the following conclusions can be drawn: (1) The Weymouth equation linearization model can accurately describe the pipeline gas flow, and it has advantages in computational efficiency. (2) The multi-parameter programming modified ADMM algorithm improves the efficiency of distributed optimal dispatch of the integrated electricity and gas system, which is conducive to real-time dynamic economic dispatch.

Key words： Integrated electricity and gas system distributed optimal dispatch Weymouth equation linearization multi-parameter programming alternating direction method of multipliers

Received: 14 March 2023

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	Luo Qingju
	Zhu Jizhong

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Luo Qingju,Zhu Jizhong. Optimal Dispatch of Integrated Electricity and Gas System Based on Modified Alternating Direction Method of Multipliers[J]. Transactions of China Electrotechnical Society, 2024, 39(9): 2797-2809.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.230292 OR https://dgjsxb.ces-transaction.com/EN/Y2024/V39/I9/2797

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