AI 中文总结
本文针对延迟下即插即用DER系统的设计问题，提出PDOG框架，推导得可连接DER单元容许范围随延迟非单调变化，为相关系统设计提供明确指南。
AI 中文摘要
本文研究即插即用分布式能源资源（DER）系统的基础设计问题，该系统作为可扩展解决方案，正通过用户驱动的模块化单元连接方式整合分布式发电。此类系统中，连接单元数量并非固定，而是随用户操作及系统条件动态变化，因此需在一系列系统规模下保证稳定性与运行约束，而非仅针对单一配置。为应对该挑战，本文提出即插即用DER协调电网（PDOG），并基于归一化延迟与总回路增益构建归一化分析框架。该公式可明确表征稳定性边界，同时结合无反向功率约束推导得到下界，定义系统运行的可行区域。通过将该可行性条件映射至DER单元数量，可得到可连接单元的容许范围作为延迟的函数。分析揭示了一个基本权衡：理论稳定性极限随归一化延迟增加而提升，但实现过程中的增益放大会降低实际接纳能力。因此，容许系统规模对延迟呈现非单调依赖关系，且可能出现可行性边界，超出该边界则不存在容许系统规模。上述结果为在延迟与实现约束下确定DER单元数量提供了明确的设计指南，建立了明确约束并设计系统可扩展性的新范式。
英文摘要
This paper addresses the fundamental design problem of plug-and-play distributed energy resource (DER) systems, which are emerging as a scalable solution for integrating distributed generation through user-driven connection of modular units. In such systems, the number of connected units is not fixed but dynamically varies due to user operation and system conditions, requiring stability and operational constraints to be guaranteed over a range of system sizes rather than for a single configuration. To address this challenge, we propose the Plug-in DER Orchestrated Grid (PDOG) and develop a normalized analytical framework in terms of normalized delay and aggregate loop gain. This formulation enables explicit characterization of the stability boundary together with a lower bound derived from the no-reverse-power constraint, defining a feasible region for system operation. By mapping this feasibility condition into the number of DER units, the admissible range of connectable units is obtained as a function of delay. The analysis reveals a fundamental trade-off: while the theoretical stability limit increases with normalized delay, implementation-induced gain amplification reduces the practical hosting capacity. As a result, the admissible system size exhibits a non-monotonic dependence on delay, and a feasibility boundary may emerge beyond which no admissible system size exists. These results provide explicit design guidelines for determining the number of DER units under delay and implementation constraints, establishing a new paradigm in which system scalability is explicitly constrained and engineered.
