Abstract Precise determination of the chemical equilibrium state is important for electrochemical and thermodynamic modeling of a molten carbonate fuel cell (MCFC). One method for determining the equilibrium state of a MCFC with internal reforming is to compute the total Gibbs free energy of the system (G) and minimize it by adjusting the molar amounts of each substance. Multi-dimensional optimization algorithms can be used for this purpose. The Lagrange method of undetermined multipliers as a powerful analytical solution is used in the present work to estimate chemical equilibrium state. Under this condition, the effects on voltage losses, output voltage, stack power, efficiency and molar portions of the exhaust chemical species at the anode and cathode are investigated, separately of such parameters as current density, reaction temperature, stack pressure as well as fuel and carbon dioxide utilization ratios. A simulation of a MCFC stack performance by the Lagrange method at a specified state, results in an efficiency of 50.3% and output power of 554.3 kW.

中文翻译：

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使用不确定乘数的拉格朗日方法对具有内部蒸汽重整的 MCFC 进行电化学和热力学建模的 Gibbs 能量最小化

摘要 精确确定化学平衡状态对于熔融碳酸盐燃料电池 (MCFC) 的电化学和热力学建模非常重要。确定具有内部重整的 MCFC 平衡状态的一种方法是计算系统 (G) 的总吉布斯自由能，并通过调整每种物质的摩尔量将其最小化。为此可以使用多维优化算法。待定乘数的拉格朗日方法作为一种强大的解析解被用于目前的工作来估计化学平衡状态。在此条件下，分别研究了对电压损失、输出电压、堆功率、效率和阳极和阴极处废气化学物质摩尔部分的影响，这些参数分别包括电流密度、反应温度、烟囱压力以及燃料和二氧化碳利用率。在指定状态下通过拉格朗日方法对 MCFC 堆性能进行仿真，得到 50.3% 的效率和 554.3 kW 的输出功率。