Optimal Corrective Control Method of Electricity and Natural Gas Interconnected Systems Based on Space-Time Orthogonal Collocation
Du Hui1, Lin Tao1, Li Qingyan1, Zhang Xiaoning2, Xu Xialing3
1. School of Electrical Engineering and Automation Wuhan University Wuhan 430072 China; 2. School of Control and Computer Engineering North China Electric Power University Beijing 102206 China; 3. Central China Branch of State Grid Cooperation Wuhan 430077 China
Abstract During the gradual implementation of the national energy transition and achieving the "emission peak and carbon neutral" target, renewable energy supported by fast-ramping gas-fired units and the ongoing global coal-to-gas transformation are effective ways to reduce carbon emissions in a short term. Construction of the electricity-gas interconnected systems (EGIS) promotes energy low-carbon transition. But meanwhile, it causes the potential risk of cascading failures between the coupling systems. Besides, compared to the instantaneous balance of electricity, the transient process of natural gas pipeline flow typically lasts from minutes to hours. Once it characterizes the time-dependent slow dynamic characteristics of the pipe flow, the EGIS optimization model is infinite-dimensional and hard to ensure computational accuracy and efficiency simultaneously. To this end, the paper proposes an EGIS optimal corrective control method based on space-time orthogonal collocation (STOC) for timely eliminating the security-limit violation caused by an N-1 fault in the EGIS. Firstly, the STOC is used to discretize the partial-differential-equation-based infinite dynamic pipe flow model in space-time coordinates and transform it into a set of finite linear algebraic equations at the space-time collocation points. Compared with the traditional differential method, the STOC exhibits high computational accuracy and good numerical stability. Secondly, based on the dynamic pipe flow of the gas network and the steady-state power flow of the power system, security constraints are established. And a security-constrained optimal energy flow (SCOEF) model is constructed to obtain the optimal corrective control strategy with the lowest control cost to eliminate the security-limit violation and restore the safe operation of the EGIS. The computational performances of the STOC in accuracy and efficiency are compared with the Wendroff differential method based on a single section of the gas pipeline. More specifically, the coarse Wendroff model whose space-time differential mesh is 14×6 provides results with the worst accuracy performance after 1.503 5s calculation time. The dense Wendroff model whose space-time differential mesh is 52×18 provides results with the best accuracy performance after 12.734 4s calculation time. While the STOC whose space-time collocation mesh is 14×6 provides results with comparable accuracy performance to the dense Wendroff model after the shortest calculation time as 1.490 6s. In addition, the proposed SCOEF model is applied to solving the optimal corrective control strategy for an EGIS benchmark composed of the IEEE 118-bus power system and the Belgian 20-node gas network. The fault in the gas network causes the outage of pipeline 1-2 from delivering natural gas. The pipe flow of pipelines 1-2 is transferred to the remained parallel pipeline 1-2 and the mass flow rate (MFR) of the remained parallel pipeline 1-2 rapidly increased from 5.456 6Sm3/s to 10.876 4Sm3/s, which causes the inlet pressure rises sharply to 7.167 1MPa, far exceeding the security limit. Via the obtained corrective control strategy, namely generation curtailment of the gas-fired unit G66 in the power system, the MFR of pipeline 2-3 dropped from the original 9.656 0Sm3/s to 8.501 1Sm3/s, mitigating the over-limit gas pressure of the upstream pipeline 1-2 in the gas network. The transient gas pressures of the corresponding pipelines are all within the security limit under the obtained corrective control strategy. Finally, the following conclusions can be drawn from the simulation analysis: (1) Compared with the Wendroff differential method, the STOC method has better computational performance when considering accuracy and efficiency comprehensively. (2) By solving the proposed SCOEF model, the obtained optimal corrective control strategy can effectively eliminate the security-limit violation caused by an N-1 fault in EGIS. Future studies can be carried out on the distributed calculation of the proposed SCOEF model considering independence between the power system and gas network operators and also more refined nonlinear feature modeling of the EGIS coupling components.
Du Hui,Lin Tao,Li Qingyan等. Optimal Corrective Control Method of Electricity and Natural Gas Interconnected Systems Based on Space-Time Orthogonal Collocation[J]. Transactions of China Electrotechnical Society, 2023, 38(7): 1765-1779.
[1] Craig M, Guerra O J, Brancucci C, et al.Valuing intra-day coordination of electric power and natural gas system operations[J]. Energy Policy, 2020, 141: 1-8. [2] 包铭磊, 王可欣, 丁一, 等. 考虑电、气备用协同配置的故障传播影响抑制策略[J]. 电力系统自动化, 2022, 46(5): 40-50. Bao Minglei, Wang Kexin, Ding Yi, et al.Containment strategy of failure propagation impacts considering coordinated allocation of power and natural gas reserve[J]. Automation of Electric Power Systems, 2022, 46(5): 40-50. [3] 林涛, 毕如玉, 陈汝斯, 等. 基于二阶锥规划的计及多种快速控制手段的综合安全校正策略[J]. 电工技术学报, 2020, 35(1): 167-178. Lin Tao, Bi Ruyu, Chen Rusi, et al.Comprehensive security correction strategy based on second-order cone programming considering multiple fast control measures[J]. Transactions of China Electrotechnical Society, 2020, 35(1): 167-178. [4] 陈泽兴, 林楷东, 张勇军, 等. 电-气互联系统建模与运行优化研究方法评述[J]. 电力系统自动化, 2020, 44(3): 11-23. Chen Zexing, Lin Kaidong, Zhang Yongjun, et al.A review of modeling and optimal operation of integrated electricity-gas system[J]. Automation of Electric Power Systems, 2020, 44(3): 11-23. [5] Correa-Posada C M, Sanchez-Martin P. Security-constrained optimal power and natural-gas flow[J]. IEEE Transactions on Power Systems, 2014, 29(4): 1780-1787. [6] 黎晨阳, 张沈习, 程浩忠, 等. 计及相关性的电-气互联区域综合能源系统概率多能流计算[J]. 电力系统自动化, 2020, 44(21): 42-49. Li Chenyang, Zhang Shenxi, Cheng Haozhong, et al.Correlation-based probabilistic multi- energy flow calculation of regional integrated energy system with combined electricity and natural gas[J]. Automation of Electric Power Systems, 2020, 44(21): 42-49. [7] 刘明凯, 王占山, 邢彦丽. 基于强化多目标差分进化算法的电-气互联系统最优潮流计算[J]. 电工技术学报, 2021, 36(11): 2220-2232. Liu Mingkai, Wang Zhanshan, Xing Yanli.Enhanced multi-objective differential evolutionary algorithm based optimal power flow calculation for integrated electricity and gas systems[J]. Transactions of China Electrotechnical Society, 2021, 36(11): 2220-2232. [8] 韩佶, 苗世洪, 李超, 等. 计及相关性的电-气-热综合能源系统概率最优能量流[J]. 电工技术学报, 2019, 34(5): 1055-1067. Han Ji, Miao Shihong, Li Chao, et al.Probabilistic optimal energy flow of electricity- gas-heat integrated energy system considering correlation[J]. Transactions of China Electrotechnical Society, 2019, 34(5): 1055-1067. [9] 陈厚合, 丛前, 姜涛, 等. 多能协同的配电网供电恢复策略[J]. 电工技术学报, 2022, 37(3): 610-622. Chen Houhe, Cong Qian, Jiang Tao, et al.Distribution systems restoration with multi- energy synergy[J]. Transactions of China Electrotechnical Society, 2022, 37(3): 610-622. [10] 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 Electrote-chnical Society, 2022, 37(11): 2800-2812. [11] Shao Chengcheng, Wang Xifan, Shahidehpour M, et al.An MILP-based optimal power flow in multicarrier energy systems[J]. IEEE Transactions on Sustainable Energy, 2017, 8(1): 239-248. [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] Sun Guoqiang, Chen Sheng, Wei Zhinong, et al.Corrective security-constrained optimal power and gas flow with binding contingency identification[J]. IEEE Transactions on Sustainable Energy, 2020, 11(2): 1033-1042. [14] Zhang Yachao, Huang Zhanghao, Zheng Feng, et al.Cooperative optimization scheduling of the electricity-gas coupled system considering wind power uncertainty via a decomposition- coordination framework[J]. Energy, 2020, 194: 1-20. [15] 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. [16] 卫志农, 梅建春, 孙国强, 等. 电-气互联综合能源系统多时段暂态能量流仿真[J]. 电力自动化设备, 2017, 37(6): 41-47. Wei Zhinong, Mei Jianchun, Sun Guoqiang, et al.Multi-period transient energy-flow simulation of integrated power and gas energy system[J]. Electric Power Automation Equipment, 2017, 37(6): 41-47. [17] 梅建春, 卫志农, 张勇, 等. 考虑关键故障筛选的电-气互联综合能源系统混合控制方法[J].电网技术, 2019, 43(1): 23-33. Mei Jianchun, Wei Zhinong, Zhang Yong, et al.Hybrid control of integrated power and gas energy systems based on significant contingency screening[J]. Power System Technology, 2019, 43(1):23-33. [18] Fang Jiakun, Zeng Qing, Ai Xiaomeng, et al.Dynamic optimal energy flow in the integrated natural gas and electrical power systems[J]. IEEE Transactions on Sustainable Energy, 2018, 9(1): 188-198. [19] Bao Zhejing, Zhang Qihong, Wu Lei, et al.Cascading failure propagation simulation in integrated electricity and natural gas systems[J]. Journal of Modern Power Systems and Clean Energy, 2020, 8(5): 961-970. [20] Bao Zhejing, Ye Yangli, Wu Lei.Multi- timescale coordinated schedule of interdependent electricity-natural gas systems considering electricity grid steady-state and gas network dynamics[J]. International Journal of Electrical Power & Energy Systems, 2020, 118(105763): 1-10. [21] Menon E S.Gas pipeline hydraulics[M]. Boca Raton: CRC Press, 2005. [22] Garg D, Patterson M, Hager W W, et al.A unified framework for the numerical solution of optimal control problems using pseudospectral methods[J]. Automatica, 2010, 46(11): 1843-1851. [23] Trefethen L N.Spectral methods in Matlab[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2000. [24] Jie Hao, Yuan Meichen, Hong Weirong.A quasi-sequential algorithm for PDE-constrained optimization based on space-time orthogonal collocation on finite elements[J]. Journal of Process Control, 2021, 98(1): 1-9. [25] 郑重, 苗世洪, 李超, 等. 面向微型能源互联网接入的交直流配电网协同优化调度策略[J]. 电工技术学报, 2022, 37(1): 192-207. Zheng Zhong, Miao Shihong, Li Chao, et al.Coordinated optimal dispatching strategy of AC/DC distribution network for the integration of micro energy internet[J]. Transactions of China Electrotechnical Society, 2022, 37(1): 192-207.
2023, Vol. 38 
