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.
罗清局, 朱继忠. 基于改进交替方向乘子法的电-气综合能源系统优化调度[J]. 电工技术学报, 2024, 39(9): 2797-2809.
Luo Qingju, Zhu Jizhong. Optimal Dispatch of Integrated Electricity and Gas System Based on Modified Alternating Direction Method of Multipliers. Transactions of China Electrotechnical Society, 2024, 39(9): 2797-2809.
[1] 孙宏斌, 潘昭光, 郭庆来. 多能流能量管理研究: 挑战与展望[J]. 电力系统自动化, 2016, 40(15): 1-8, 16. Sun Hongbin, Pan Zhaoguang, Guo Qinglai.Energy management for multi-energy flow: challenges and prospects[J]. Automation of Electric Power Systems, 2016, 40(15): 1-8, 16. [2] 余晓丹, 徐宪东, 陈硕翼, 等. 综合能源系统与能源互联网简述[J]. 电工技术学报, 2016, 31(1): 1-13. Yu Xiaodan, Xu Xiandong, Chen Shuoyi, et al.A brief review to integrated energy system and energy Internet[J]. Transactions of China Electrotechnical Society, 2016, 31(1): 1-13. [3] 刘英培, 黄寅峰. 考虑碳排权供求关系的多区域综合能源系统联合优化运行[J]. 电工技术学报, 2023, 38(13): 3459-3472. Liu Yingpei, Huang Yinfeng.Joint optimal operation of multi-regional integrated energy system considering the supply and demand of carbon emission rights[J]. Transactions of China Electrotechnical Society, 2023, 38(13): 3459-3472. [4] 吴孟雪, 房方. 计及风光不确定性的电-热-氢综合能源系统分布鲁棒优化[J]. 电工技术学报, 2023, 38(13): 3473-3485. Wu Mengxue, Fang Fang.Distributionally robust optimization of electricity-heat-hydrogen integrated energy system with wind and solar uncertainties[J]. Transactions of China Electrotechnical Society, 2023, 38(13): 3473-3485. [5] 严思韵, 王晨, 周登极. 含氢能气网掺混输运的综合能源系统优化研究[J]. 电力工程技术, 2021, 40(1): 10-16, 49. Yan Siyun, Wang Chen, Zhou Dengji.Optimization of integrated electricity and gas system considering hydrogen-natural-gas mixture transportation[J]. Electric Power Engineering Technology, 2021, 40(1): 10-16, 49. [6] Zhu Jizhong, Zhu Haohao, Zheng Weiye, et al.Cooperation mechanism design for integrated electricity-heat systems with information asymmetry[J]. Journal of Modern Power Systems and Clean Energy, 2023, 11(3): 873-884. [7] 耿健, 杨冬梅, 高正平, 等. 含储能的冷热电联供分布式综合能源微网优化运行[J]. 电力工程技术, 2021, 40(1): 25-32. Geng Jian, Yang Dongmei, Gao Zhengping, et al.Optimal operation of distributed integrated energy microgrid with CCHP considering energy storage[J]. Electric Power Engineering Technology, 2021, 40(1): 25-32. [8] 朱浩昊, 朱继忠, 李盛林, 等. 电-热综合能源系统优化调度综述[J]. 全球能源互联网, 2022, 5(4): 383-397. Zhu Haohao, Zhu Jizhong, Li Shenglin, et al.Review of optimal scheduling of integrated electricity and heat systems[J]. Journal of Global Energy Interconnection, 2022, 5(4): 383-397. [9] Duan Jiandong, Yang Yao, Liu Fan.Distributed optimization of integrated electricity-natural gas distribution networks considering wind power uncertainties[J]. International Journal of Electrical Power & Energy Systems, 2022, 135: 107460. [10] Chen Sheng, Wei Zhinong, Sun Guoqiang, et al.Optimal power and gas flow with a limited number of control actions[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 5371-5380. [11] He Chuan, Wu Lei, Liu Tianqi, et al.Robust co-optimization scheduling of electricity and natural gas systems via ADMM[J]. IEEE Transactions on Sustainable Energy, 2017, 8(2): 658-670. [12] Wang Cheng, Wei Wei, Wang Jianhui, et al.Convex optimization based distributed optimal gas-power flow calculation[J]. IEEE Transactions on Sustainable Energy, 2018, 9(3): 1145-1156. [13] Yang Lun, Xu Yinliang, Sun Hongbin.A dynamic linearization and convex relaxation-based approach for a natural gas optimal operation problem[J]. IEEE Transactions on Smart Grid, 2020, 11(2): 1802-1804. [14] He Yubin, Yan Mingyu, Shahidehpour M, et al.Decentralized optimization of multi-area electricity-natural gas flows based on cone reformulation[J]. IEEE Transactions on Power Systems, 2018, 33(4): 4531-4542. [15] Chen Sheng, Conejo A J, Wei Zhinong.Gas-power coordination: from day-ahead scheduling to actual operation[J]. IEEE Transactions on Power Systems, 2022, 37(2): 1532-1542. [16] Wen Yunfeng, Qu Xiaobin, Li Wenyuan, et al.Synergistic operation of electricity and natural gas networks via ADMM[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 4555-4565. [17] Chen Sheng, Conejo A J, Sioshansi R, et al.Unit commitment with an enhanced natural gas-flow model[J]. IEEE Transactions on Power Systems, 2019, 34(5): 3729-3738. [18] 徐玉琴, 方楠. 基于分段线性化与改进二阶锥松弛的电-气互联系统多目标优化调度[J]. 电工技术学报, 2022, 37(11): 2800-2812. Xu Yuqin, Fang Nan.Multi objective optimal scheduling of integrated electricity-gas system based on piecewise linearization and improved second order cone relaxation[J]. Transactions of China Electrotechnical Society, 2022, 37(11): 2800-2812. [19] 史守圆, 瞿凯平, 余涛, 等. 计及大气污染物时空扩散的电-气能流分散协同优化[J]. 电工技术学报, 2019, 34(23): 4957-4971. Shi Shouyuan, Qu Kaiping, Yu Tao, et al.A distributed algorithm for optimal power-gas flow considering space-time diffusion of atmospheric pollutants[J]. Transactions of China Electrotechnical Society, 2019, 34(23): 4957-4971. [20] He Chuan, Zhang Xiaping, Liu Tianqi, et al.Distributionally robust scheduling of integrated gas-electricity systems with demand response[J]. IEEE Transactions on Power Systems, 2019, 34(5): 3791-3803. [21] Tomasgard A, Rømo F, Fodstad M, et al.Optimization models for the natural gas value chain[M]//Hasle G, Lie KA, Quak E. Geometric Modelling, Numerical Simulation, and Optimization. Berlin, Heidelberg: Springer, 2007: 521-558. [22] Borrelli F, Bemporad A, Morari M.Predictive Control for Linear and Hybrid Systems[M]. Cambridge, UK: Cambridge University Press, 2017. [23] Massol O, Banal-Estanol A.Market power and spatial arbitrage between interconnected gas hubs[J]. Energy Journal, 2018, 39: 67-95. [24] Borraz-Sánchez C, Ríos-Mercado R Z. Improving the operation of pipeline systems on cyclic structures by tabu search[J]. Computers & Chemical Engineering, 2009, 33(1): 58-64. [25] Wu Suming, Ríos-Mercado R Z, Boyd E A, et al. Model relaxations for the fuel cost minimization of steady-state gas pipeline networks[J]. Mathematical and Computer Modelling, 2000, 31(2/3): 197-220. [26] Qiu Jing, Yang Hongming, Dong Zhao yang, et al. A linear programming approach to expansion co-planning in gas and electricity markets[J]. IEEE Transactions on Power Systems, 2016, 31(5): 3594-3606. [27] Stephen B, Neal P, Eric C, et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers, 2017, 3(1): 1-12. [28] Figshare. Data of test systems[DB/OL]. [2022-12-15]. https://doi.org/10.6084/m9.figshare.21724619.v1. [29] Zhang Guoqiang, Heusdens R.Distributed optimization using the primal-dual method of multipliers[J]. IEEE Transactions on Signal and Information Processing Over Networks, 2018, 4(1): 173-187.
2024, Vol. 39 
