High-temperature electrolysis (HTE) is a promising technology for achieving high-efficiency power-to-gas, which mitigates the renewable curtailment while promoting decarbonization by transforming wind or solar energy into fuels. Different from low-temperature electrolysis, a considerable amount of the input energy is consumed by auxiliary equipment in an HTE system for maintaining the temperature, so the studies on systematic energy 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 operating states without performing nonlinear programming by further investigating the optimization method. In the case study, a numerical case of an HTE system is employed to validate the proposed operation model and optimization method, which proves that the proposed operation strategies not only improve the overall conversion efficiency but also significantly enlarge the load range of the HTE system. A 24-h case with fluctuant power input is also simulated to validate the beneficial effects of the proposed operation strategies on producing more hydrogen from a specific profile of surplus electricity. At last, some results comparisons with existed papers and possible research extensions are discussed briefly.