On the Decomposition of Locational Marginal Hydrogen Pricing−Part II: Solution Approach and Numerical Results

In Part I of this two-part article series, we proposed the locational marginal hydrogen price (LMHP) decomposition theorem and derived analytical expressions for LMHP components. Notably, the application of the LMHP decomposition theorem is based on the premise of obtaining optimal solution for the hydrogen market. Due to the existence of the Weymouth equation, which is used to characterize pipeline hydrogen flow, the hydrogen market clearing model is strongly nonconvex and difficult to solve directly. Although the literature has investigated solution algorithms for the Weymouth equation, improving the calculation efficiency while ensuring the accuracy of the solution remains a challenge. To address this knowledge gap, Part II of this two-part article series proposes an improved second-order cone programming (SOCP) algorithm with umbrella constraint identification to solve the hydrogen market. The hydrogen market clearing model is transformed into a mixed-integer SOCP problem, which can be solved iteratively. Before iteration, redundant constraints are removed to minimize the representation of the hydrogen market clearing model, thereby improving computational efficiency. Case studies based on the Belgium-20 node system and a 90-node system verify the effectiveness of the proposed LMHP decomposition theorem and solution algorithm for the hydrogen market.