Data-Driven Chance-Constrained Optimal Gas-Power Flow Calculation A Bayesian Nonparametric Approach
Abstract : This paper proposes a data-driven chanceconstrained optimal gas-power flow (OGPF) calculation method without any prior assumption on the distribution of uncertainties of wind power generation. The Gaussian mixture model is employed to fit the uncertainty distribution, where the Bayesian nonparametric Dirichlet process is adopted to tune the component number. To facilitate the online application of the proposed methods, an online-offline double-track distribution construction approach is established, where the frequency of training the relatively time-consuming Dirichlet process Gaussian mixture model can be reduced.On account of the quadratic gas consumption expression of gas-fired generators as well as the linear decision rule based uncertainty mitigation mechanism, the chance constraints would become quadratic ones with quadratic terms of uncertainties, which makes the proposed model more intractable. An equivalent linear separable counterpart is then provided for the quadratic chance constraints, after which the intractable chance constraints could be converted into traditional linear ones. The convex-concave procedure is used to crack the nonconvex Weymouth equation in the gas network and the auxiliary quadratic equalities. Simulation results on two test systems validate the effectiveness of the proposed methods.
? On the basis of the above discussion on effort directions, this paper aims to summarize the existing work of each aspect in IES operation optimization and give our insights to inspire future researches.
? At present, the selection of the optimization algorithm for a concrete operation optimization problem often relies on expert knowledge or production experiences and existing previous research.
? With the increasing penetration of renewable resources in IES, more renewable energy generation units with different power generation characteristics in time and space scale may be integrated in the system, and these existing PDFs are not fairly applicable and sufficiently accurate.
? Optimal gas-power flow (OGPF) is one of the most fundamental problems in the area of IEGS operation, which has been addressed by many inspiring works.
? A steady-state OGPF model was proposed in, where the computational challenging Weymouth equations were replaced with their mixed integer linear program (MILP) based approximation.
? In, the simplified gas flow dynamics was incorporated in the OGPF model, which can still be converted into a tractable problem by employing the mixed integer based piecewise linearization.
? In, DPMM is adopted to set the component numbers for basic uncertainty sets in the robust unit commitment problem.
• To reduce pollutant emission and faced with the fossil energy crisis, the installed capacity of renewable energy is rapidly growing worldwide, and an RE-dominated system is proposed for the future.
• The experiments showed that the proposed method was one to two orders more efficient than Monte Carlo-based estimates. However, it faced a curse-of-dimensionality challenge.
• It is obvious that the prediction error is getting smaller as time goes on.
• Multi-stage operation optimization is therefore proposed to successively mitigate uncertainty of RE at different time scales and then reduce adverse influence on the IES optimal operation
? It can be observed that the solution becomes a feasible one after three iterations, reflecting the well convergence performance of the devised algorithm.
? As aforementioned, GMM could be adopted to generate a candidate distribution for the uncertainties. However, the component number for GMM training, which is a crucial parameter on the performance of the training results, has to be predetermined.
? The fitting time of the DPGMM is the longest, as its component number is 7. The costs of the decisions and their aftermath are gathered in the third and fourth columns of Table II, where the performances of the DPGMM and the Gaussian distribution are the best and the worst, respectively.
|