Solid oxide cells are an exciting technology for energy conversion. Fuel cells, based on solid oxide technology, convert hydrogen or hydrogen-rich fuels into electrical energy, with potential applications in stationary power generation. Conversely, solid oxide electrolysers convert electricity into chemical energy, thereby offering the potential to store energy from transient resources, such as wind turbines and other renewable technologies. For solid oxide cells to displace conventional energy conversion devices in the marketplace, reliability must be improved, product lifecycles extended, and unit costs reduced. Mathematical models can provide qualitative and quantitative insight into physical phenomena and performance, over a range of length and time scales. The purpose of this paper is to provide the reader with a summary of the state-of-the art of solid oxide cell models. These range from: simple methods based on lumped parameters with little or no kinetics to detailed, time-dependent, three-dimensional solutions for electric field potentials, complex chemical kinetics and fully-comprehensive equations of motion based on effective transport properties. Many mathematical models have, in the past, been based on inaccurate property values obtained from the literature, as well as over-simplistic schemes to compute effective values. It is important to be aware of the underlying experimental methods available to parameterise mathematical models, as well as validate results. In this article, state-of-the-art techniques for measuring kinetic, electric and transport properties are also described. Methods such as electrochemical impedance spectroscopy allow for fundamental physicochemical parameters to be obtained. In addition, effective properties may be obtained using micro-scale computer simulations based on digital reconstruction obtained from X-ray tomography/focussed ion beam scanning electron microscopy, as well as percolation theory. The cornerstone of model validation, namely the polarisation or current-voltage diagram, provides necessary, but insufficient information to substantiate the reliability of detailed model calculations. The results of physical experiments which precisely mimic the details of model conditions are scarce, and it is fair to say there is a gap between the two activities. The purpose of this review is to introduce the reader to the current state-of-the art of solid oxide analysis techniques, in a tutorial fashion, not only numerical and but also experimental, and to emphasise the cross-linkages between techniques.

固体氧化物电池是一种令人兴奋的能量转换技术。基于固体氧化物技术的燃料电池将氢或富氢燃料转化为电能，在固定发电中有潜在的应用。相反，固体氧化物电解槽将电能转换为化学能，从而提供了存储瞬态资源（例如风力涡轮机和其他可再生技术）中的能量的潜力。为了使固体氧化物电池在市场上取代传统的能量转换装置，必须提高可靠性，延长产品生命周期并降低单位成本。数学模型可以在一定长度和时间范围内提供对物理现象和性能的定性和定量洞察力。本文的目的是为读者提供有关固态氧化物电池模型的最新技术的概述。这些范围从：基于集总参数的简单方法（很少或没有动力学），到详细的，随时间变化的三维三维电场势解决方案，复杂的化学动力学和基于有效传输特性的全面运动方程式。过去，许多数学模型都是基于从文献中获得的不正确的属性值，以及过于简单的方案来计算有效值。重要的是要注意可用于参数化数学模型以及验证结果的基础实验方法。在本文中，还介绍了用于测量动力学，电学和传输性质的最新技术。诸如电化学阻抗谱的方法允许获得基本的物理化学参数。此外，基于从X射线断层扫描/聚焦离子束扫描电子显微镜以及渗流理论获得的数字重建，可以使用微型计算机模拟来获得有效的性能。模型验证的基础，即极化或电流-电压图，提供了必要的信息，但不足以证实详细模型计算的可靠性。精确模拟模型条件细节的物理实验结果很少，可以公平地说这两个活动之间存在差距。这篇综述的目的是向读者介绍固态氧化物分析技术的最新技术，