  High-temperature electrolysis (HTE) is a promising technology for achieving
high-efficiency power-to-gas, which mitigates the renewable curtailment by
transforming wind or solar energy into fuels. Different from low-temperature
electrolysis, a considerable amount of the input energy is consumed by
auxiliaries in an HTE system for maintaining the temperature, so the studies on
systematic description and parameter optimization of HTE are essentially
required. A few published studies investigated HTE's systematic optimization
based on simulation, yet there is not a commonly used analytical optimization
model which is more suitable for integration with power grid. To fill in this
blank, a concise analytical operation model is proposed in this paper to
coordinate the necessary power consumptions of auxiliaries under various
loading conditions of an HTE system. First, this paper develops a comprehensive
energy flow model for an HTE system based on the fundamentals extracted from
the existing work, providing a quantitative description of the impacts of
condition parameters, including the temperature and the feedstock flow rates. A
concise operation model is then analytically proposed to search for the optimal
operating states that maximize the hydrogen yield while meeting the desired
system loading power by coordinating the temperature, the feedstock flows and
the electrolysis current. The evaluation of system performance and the
consideration of constraints caused by energy balances and necessary stack
requirements are both included. In addition, analytical optimality conditions
are obtained to locate the optimal states without performing nonlinear
programming by further investigating the optimization method. A numerical case
of an HTE system is employed to validate the proposed operation model, which
proves to not only improve the conversion efficiency but also enlarge the
system load range.
