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An Improved Benders Dual Decomposition Method to Solve the Optimal Sizing Problem of Power-to-Ammonia Plants
  • Wang Shunchao
Wang Shunchao

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Converting renewable electricity into green ammonia has emerged as a new solution for cross-sector decarbonization and an important source of flexibility for power systems. Power-to-Ammonia (PtA) plants are an integration of various electro-chemical-mechanical processes and multiple storage facilities. Optimal sizing of these modules is an important but challenging optimization problem at the engineering stage. It is a two-stage decision-making program, involving both discrete and continuous variables at two stages, and requiring a large number of scenarios to accurately capture the stochasticity in renewable energy generation. We formulate this problem as a general stochastic mixed-integer programming (SMIP). We use the Benders Dual Decomposition (BDD) method as an algorithmic framework for this problem, which enables scenario decomposition and computation parallelization. To reduce the duality gap of the BDD method, we derive a new type of optimality cut, the Strengthened Lagrangian Cut (SLC), based on dissimilarity random scenario bundling. We prove that the SLC is tighter than the Lagrangian cut, and the resulting master problem provides tighter lower bound and high-quality feasible solutions for upper bound calculations. We develop an Improved Benders Dual Decomposition (IBDD) method based on SLCs. Numerical results show that the traditional BDD method can produce acceptable results for the PV-powered PtA case but not for the wind-powered PtA case. In comparison, the IBDD method produces satisfactory results for both cases and outperforms the BDD method. The IBDD method is demonstrated to be capable of solving large-scale SMIPs (containing more than 95,000 mixed-integer variables and 141,000 constraints in the extensive form) by achieving low relative gaps (< 1%) within manageable computational time (< 1200s) on a standard Laptop.
25 May 2024Submitted to TechRxiv
03 Jun 2024Published in TechRxiv