Addressing the issues of inadequate exploitation of hydrogen energy collaboration potential and the challenge in balancing accuracy and efficiency of probabilistic solution algorithms, this paper proposes a calculation method for the probabilistic optimal energy flow of electricity-hydrogen systems based on compressed sparse arbitrarily polynomial chaos expansions (CS-aPCE).
Firstly, to harness the spatial-temporal collaboration potential of hydrogen energy, a modeling approach for electricity-hydrogen optimal energy flow is introduced incorporating peer-to-peer (P2P) hydrogen collaboration between on-site and off-site hydrogen refueling stations (HRSs). Considering the P2P coupling of inter-station hydrogen flows and bidirectional electricity flows, a P2P collaboration mechanism is proposed for between on-site and off-site HRSs and the power distribution network. Based on Nash bargaining theory, a probabilistic optimal electricity-hydrogen energy flow model is constructed, which incorporates time-delay and discreteness constraints for inter-station hydrogen P2P transactions. This model coordinates multi-stakeholder benefit allocation and electricity-hydrogen price decisions, enhancing feasibility and fairness.
Secondly, a probabilistic optimal energy flow solution algorithm for on-site and off-site HRSs and power distribution networks is proposed based on CS-aPCE, aiming to improve the efficiency and accuracy of high-dimensional probability calculations. The core of this algorithm lies in leveraging historical data to drive the collocation points, subsequently calculating key statistical metrics such as expectations and standard deviations through analytical methods, without reliance on prior probabilistic information. To further optimize computational performance, the CS-aPCE algorithm integrates Gaussian quadrature rules to construct high-frequency collocation points and incorporates compressed sparse grid techniques. Effective compression criteria are proposed, and the dimensionality reduction effect and computational accuracy of the algorithm are theoretically proven, ensuring its efficiency and robustness under high-dimensional randomness.
The effectiveness of the proposed method is validated through numerical examples, leading to the following conclusions: firstly, the CS-aPCE algorithm presented in this paper can solve high-dimensional and probabilistic electricity-hydrogen energy flow problems rapidly and with high precision. The computation time is merely 10% of that required by the Monte Carlo simulation method, while the errors in expected values and standard deviations are below 4.21%. Furthermore, the computational accuracy for higher-order moments is improved by 60.28% to 156.98% compared to the traditional aPCE method. Secondly, the stationarity threshold exerts a certain influence on the accuracy and efficiency of the CS-aPCE algorithm. A reasonable threshold should be selected by comprehensively considering the stationarity distribution characteristics of random variables. Finally, the electricity-hydrogen optimal energy flow model considering P2P hydrogen collaboration between stations can mobilize the coordination potential of flexible resources within the distributed hydrogen supply network, coordinate the distribution of inter-station hydrogen flows, and achieve fair allocation of benefits among multiple stakeholders.