Dynamic Hydrogen Injection in Integrated Electricity-Gas Systems: A PDEs-Embedded Flexible Operation Strategy

Integrated electricity-gas systems (IEGS) with hydrogen injection has emerged as a crucial pathway to decarbonize energy systems. By coordinating the flexibility of the gas system and hydrogen blending, the accommodation of large-scale renewable energy integrated in power systems can be further improved. However, the time-varying nature of dynamic hydrogen injection, influenced by stochastic renewable energy, can lead to fluctuations in gas concentrations in the gas network, threatening the secure operation of IEGS. This paper focuses on the low-carbon flexible operation strategy for IEGS with dynamic hydrogen injection. First, a flexible operation strategy of hydrogen-mixed gas turbine is developed with a detailed correlation characterization of carbon emission, combustion thermoldynamics, and chemical reaction kinetics under dynamic hydrogen ratios. Second, an optimal IEGS dispatch strategy is formulated in which the joint dynamics of the system component and the gas flow is captured to accurately track the time-varying concentrations of hydrogen in the gas network. Third, a set of discretized partial differential equations (PDEs) is utilized to model mixed gas flows, leading to a PDEs-constrained optimization model. Finally, Taylor series expansions for PDE linearization and McCormick envelope for bilinear terms are employed, enabling tractable algebraic representations. A sequential linear programming (SLP) algorithm with adaptive penalty factors is developed to drive relaxation tightening more efficiently. Numerical results on a 24-bus-20-node system and a practical 197-bus-171-node system in Northwest China illustrate the effectiveness of the proposed model.