适用能源互联网非线性气流方程组的线性优化求解模型

A Linear Program to Nonlinear Gas Equations in Context of Energy Internet

能源互联网通过多能源互补、协调优化实现能源高效利用和可再生能源消纳提升,具有重要的经济和环保意义。天然气、氢气等作为能源互联网的重要元素可通过管网进行传输,其传输过程需满足一定的非线性物理方程限制(如,Weymouth方程、Panhandle A方程、Panhandle B方程)。然而,非线性的气流方程给多能流的求解计算带来一定挑战。该文将非线性气流方程组精确同构成凸优化模型,从而使凸优化的最优解精确满足管道气流方程组,进一步采用分段线性化的方法将其转化为线性规划模型进行求解。选取多个天然气、氢气系统进行算例分析,给出的数值优化结果验证了模型的可行性与有效性,并在此基础上分析了不同分段数的选取对模型的求解精度与计算效率的影响。

Energy internet can improve the energy efficiency and promote renewable energy accommodation by complementarily utilizing multiple energy resources and coordinating optimization, which is of great economic and environmental significance. Natural gas, hydrogen and etc., the core elements of energy internet, can be transferred through pipelines under the physical regulation(such as Weymouth equation, Panhandle A equation, Panhandle B equation). However, the nonlinear gas equations bring some challenges to the energy flow computation. To address this issue, the nonconvex nonlinear gas equations were isomorphic to a tractably convex optimization model, whose optimal solution can precisely satisfy the gas flow equations of pipelines and pressure equations of compressors. Furthermore, a piecewise linearization technique was used to linearize the nonlinear objective function of the model, thus transforming the original model into a linear programing model. Multiple natural gas networks and hydrogen networks were selected as the test cases. The optimal solutions were given to verify the feasibility and effectiveness of the model. The number of segments on the accuracy and efficiency of the solution was analyzed.