论文标题
在地热储能的投入输出行为上：按模型订单降低近似值
On the Input-Output Behavior of a Geothermal Energy Storage: Approximations by Model Order Reduction
论文作者
论文摘要
在本文中，我们考虑了一个地热储能，其中时空温度分布是由带有对流项的热方程建模的。这样的存储通常嵌入到住宅供暖系统中，控制和管理需要了解存储中该温度分布的某些汇总特征。他们描述了存储的投入输出行为和相关的能量流以及它们对充电和放电过程的响应。我们旨在通过低维系统来得出这些特征的有效近似描述。这导致了由于热方程式与线性代数输出方程相结合的半散制而产生的大规模ODES的模型订购降低问题。在第一步中，我们通过线性时间不变的系统近似于非时间不变的ODES系统。然后，我们将lyapunov平衡截断模型降低降低以通过仅几个状态方程的减少订单系统近似输出，但几乎相同的输入输出行为。本文提出了广泛的数值实验的结果，显示了应用模型订购方法的效率。事实证明，只有少数合适的ODE足以产生存储的输入输出行为的良好近似值。
In this paper we consider a geothermal energy storage in which the spatio-temporal temperature distribution is modeled by a heat equation with a convection term. Such storages often are embedded in residential heating systems and control and management require the knowledge of some aggregated characteristics of that temperature distribution in the storage. They describe the input-output behaviour of the storage and the associated energy flows and their response to charging and discharging processes. We aim to derive an efficient approximative description of these characteristics by a low-dimensional system of ODEs. This leads to a model order reduction problem for a large scale linear system of ODEs arising from the semi-discretization of the heat equation combined with a linear algebraic output equation. In a first step we approximate the non time-invariant system of ODEs by a linear time-invariant system. Then we apply Lyapunov balanced truncation model order reduction to approximate the output by a reduced-order system with only a few state equations but almost the same input-output behavior. The paper presents results of extensive numerical experiments showing the efficiency of the applied model order reduction methods. It turns out that only a few suitable chosen ODEs are sufficient to produce good approximations of the input-output behaviour of the storage.
