This study presents a formulation of the Superposition Theorem (ST) in the spectrum space, tailored for the analysis of composite events in an active distribution network (ADN). Our formulated ST enables a quantitative analysis on a composite event, uncovering the property of additivity among independent atom events in the spectrum space. This contribution is a significant addition to the existing literature and has profound implications in various application scenarios. To accomplish this, we leverage random matrix theory (RMT), specifically the asymptotic empirical spectral distribution, Stieltjes transform, and R transform. These mathematical tools establish a nonlinear, model-free, and unsupervised addition operation in the spectrum space. Comprehensive details, including a related roadmap,theorems, deductions, and proofs, are provided in this work. Case studies, utilizing field data, validate our newly derived ST formulation by demonstrating a remarkable performance. Our ST formulation is model-free, non-linear, non-supervised, theory-guided, and uncertainty-insensitive, making it a valuable asset in the realm of composite event analysis in ADN.

翻译：本研究提出了一种在频谱空间中针对有源配电网（ADN）复合事件分析的叠加定理（ST）表述。我们构建的叠加定理能够对复合事件进行定量分析，揭示了频谱空间中独立原子事件的可加性特征。这一成果是对现有文献的重要补充，并在多种应用场景中具有深远意义。为实现该目标，我们借助随机矩阵理论（RMT），具体包括渐近经验谱分布、Stieltjes变换和R变换。这些数学工具在频谱空间中建立了一种非线性、无模型且无监督的加法运算。本文提供了完整的技术细节，包括相关路线图、定理、推导与证明。采用现场数据进行的案例研究验证了新推导的叠加定理表述，展示了其优异性能。该叠加定理表述具有无模型、非线性、无监督、理论导向及不确定性不敏感的特点，使其成为ADN复合事件分析领域的重要工具。