天然气流动方程的统一性和MI-SOCP求解器
Natural Gas Flow Equations: Uniqueness and an MI-SOCP Solver
摘要：
燃气发电厂在补偿可再生能源发电方面的关键作用增加了天然气管网（GN）的运行可变性。为了开发更可靠和有效的计算工具GN监测，控制和规划，这项工作认为，解决非线性方程的稳态流量和压力在GN的任务。它首先表明，如果气体流动方程是可行的，他们享有唯一的解决方案。据我们所知，这是第一个结果证明在整个可行域的气体注入的稳态气体流量的解决方案的唯一性。为了找到这个解决方案，我们提出了一个混合整数二阶锥规划（MI-SOCP）的求解器依赖于松弛的气体流动方程。这种松弛在特定的网络拓扑下是可证明的。与现有的替代方案不同，所设计的求解器不需要适当的初始化或预先知道气体流动方向，并且可以处理具有压缩机的气体网络。对随机气体注入的树状和网状网络的数值试验表明，即使不满足导出的条件，松弛也是精确的。
英文摘要：
The critical role of gas fired-plants to compensate renewable generation has increased the operational variability in natural gas networks (GN). Towards developing more reliable and efficient computational tools for GN monitoring, control, and planning, this work considers the task of solving the nonlinear equations governing steady-state flows and pressures in GNs. It is first shown that if the gas flow equations are feasible, they enjoy a unique solution. To the best of our knowledge, this is the first result proving uniqueness of the steady-state gas flow solution over the entire feasible domain of gas injections. To find this solution, we put forth a mixed-integer second-order cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow equations. This relaxation is provably exact under specific network topologies. Unlike existing alternatives, the devised solver does not need proper initialization or knowing the gas flow directions beforehand, and can handle gas networks with compressors. Numerical tests on tree and meshed networks with random gas injections indicate that the relaxation is exact even when the derived conditions are not met.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
