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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 indicate that the relaxation is exact even when the derived conditions are not met.
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Inexactness of Second Order Cone Relaxations for Calculating Operating Envelopes
As the number of distributed energy resources participating in power networks increases, it becomes increasingly more important to actively manage network constraints to ensure safe operation. One proposed method that has gained significant attention and implementation, particularly in Australia, is the use of dynamic operating envelopes. Operating envelopes represent net export limits set by the system operator on every node in the distribution network that change as system conditions change. They are calculated using an optimal power flow problem, frequently using a linearization or relaxation of the nonlinear power flow equations. This paper presents two case studies and some numerical analysis to explain why a second order cone relaxation of the power flow equations will lead to ineffective operating envelopes. A modification to the objective function which allows the second order cone relaxation to nearly recover the solution to the nonlinear formulation is also presented.
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- Award ID(s):
- 1845093
- PAR ID:
- 10486457
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids
- ISBN:
- 978-1-6654-5556-5
- Page Range / eLocation ID:
- 1 to 6
- Format(s):
- Medium: X
- Location:
- Glasgow, United Kingdom
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/SmartGridComm57358.2023.10333939
