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| 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 |
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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.
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Received: 12 November 2021
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2023, Vol. 38 
