Fast Probabilistic Energy Flow Calculation for Natural Gas Systems: A Convex Multiparametric Programming Approach

Probabilistic energy flow (PEF) calculation is a fundamental task for the operation and planning of both natural gas systems (NGSs) and integrated energy systems considering uncertainties. Traditional Monte Carlo simulation (MCS) based PEF approach requires repeated energy flow calculations based on a large number of random samples, leading to a huge computation burden. Hence, this paper proposes a convex multiparametric programming (MPP) based fast PEF calculation method for NGSs. First, we develop an energy function based convex optimization model whose optimal solution is equivalent to the solution of deterministic energy flow equations. Then, we propose a convex MPP model with uncertain boundary conditions (such as the gas injections/loads) as the parameters. A multiparametric quadratic approximation algorithm is further introduced to solve the proposed MPP and obtain the analytical energy flow expression. This analytical expression characterizes the mapping relationship between the energy flow solution and uncertain parameters. Finally, we establish an online PEF calculation framework, in which the repeat energy flow calculations can be efficiently performed by merely substituting the uncertain parameters into the analytical energy flow expression obtained offline. Case studies on multiple NGSs verify the effectiveness of the proposed method. Note to Practitioners—This paper introduces a novel approach for efficient PEF calculation in NGSs that addresses the computational challenges posed by traditional methods. Conventional MCS-based PEF approaches involve numerous energy flow calculations with massive stochastic scenarios, resulting in significant computational burdens. The key contribution of our work is to equivalently reformulate the original PEF problem as an energy function based convex MPP model, which incorporates uncertain boundary conditions (e.g., gas injections/loads) as its parameters. Then, a multiparametric quadratic approximation algorithm is suggested to obtain the parametric solution of this MPP, which is essentially an analytical expression of the energy flow solution as a function of uncertain parameters. This allows for efficient repeated energy flow calculations by simply substituting uncertain parameters into the pre-determined expression obtained offline. Thus, the online PEF computational efficiency can be significantly improved. We conduct case studies on several benchmark NGSs to validate the effectiveness and scalability of the proposed method. Numerical results show that the online PEF computation efficiency of the proposed method is approximately 2-3 orders of magnitude faster than that of the NR-MCS method.