Distributed energy supply systems are most efficiently designed by mathematical optimization. However, optimization models often assume availability of all components at any time. In practice, security of energy supply is crucial; thus, reliability is mandatory but often neglected in optimization and only implemented subsequently employing expensive rules of thumb.

In this work, we propose an exact optimization approach to identify ($n-1$)-reliable designs for energy systems. The approach guarantees energy supply during the failure of 1 component at any time and is independent of probabilities and the selection of scenarios. ($n-1$)-reliability is also necessary to allow for maintenance of components. For problems with high computational effort, we propose the inexact but computationally efficient ($n-1^{\max }$)-reliability approach which also guarantees energy supply but allows overproduction. A real-world case study shows that both approaches identify reliable designs at only a small increase of the total annualized costs compared to the unreliable base case.

通过数学优化可以最有效地设计分布式能源供应系统。但是，优化模型通常会随时假设所有组件的可用性。实际上，能源供应的安全至关重要。因此，可靠性是必不可少的，但在优化中常常被忽略，只有随后采用昂贵的经验法则才能实现。

在这项工作中，我们提出了一种精确的优化方法来识别（$ñ-\mathrm{1个}$）可靠的能源系统设计。该方法可确保在1个组件发生故障时随时提供能量，并且与概率和方案选择无关。（$ñ-\mathrm{1个}$可靠性也是保证组件维护所必需的。对于计算量大的问题，我们提出了不精确但计算效率高的问题（$ñ-{\mathrm{1个}}^{\mathrm{最大限度}}$（）可靠的方法，它还保证了能源供应，但允许生产过剩。实际案例研究表明，与不可靠的基本案例相比，这两种方法仅以总年度成本的小幅增长就能确定可靠的设计。