发表机构
The University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非正弦条件下无功功率的标量定义选择问题，证明在特定假设下唯一得到Iliovici型度量，并量化了标量化带来的信息损失与电流模糊性维度。
AI 中文摘要
无功功率是交流电力系统中的一个基本概念，在单频正弦稳态条件下定义明确。然而，在非正弦条件下，多种无功功率定义并存且可能产生不同的标量值，表明传统的$Q$并非唯一扩展。本文通过追问哪些附加假设能选择出标量无功功率度量，以及在该降维过程中丢失了哪些信息，重新审视了这一问题。在连续有限谐波空间上，在常见时间平移下不变的实双线性、交替标量读出允许不同的谐波加权。要求该度量对每个光滑、严格单调、时不变无记忆电阻器都为零，迫使权重与谐波阶数成正比；通过基频校准，这产生了经典的导数型（即Iliovici型）度量。该要求与在每个谐波上独立复现传统无功功率不相容。本文的贡献在于在所声明的观测类别内给出这一逆向刻画，而非微分功率公式本身。本文还量化了标量化造成的信息损失，并推导出剩余电流模糊性的精确维度。这些结果阐明了选择标量无功功率定义所需的假设，以及该标量量所保留的电流信息的极限。
英文摘要
Reactive power is not uniquely defined for nonsinusoidal voltage and current waveforms because different scalar readouts can assign different values to the same measured voltage--current waveform pair. This paper characterizes which scalar readouts are selected by specific measurement and physical requirements, and quantifies the current information lost through scalarization. The scalar readout is first restricted by requiring bilinearity, alternation, and invariance to the measurement time origin. Requiring it to vanish for all smooth, strictly monotone, time-invariant memoryless resistors then forces the harmonic weights to be proportional to harmonic order. With consistency across harmonic cutoffs and fundamental-frequency calibration, this uniquely yields the classical derivative, or Iliovici-type, scalar within the stated class. The selected weighting is also incompatible with conventional reactive-power calibration independently at every harmonic. Furthermore, for known nonzero voltage, active power and a finite set of skew scalar readouts leave an affine family of compatible currents of exact dimension \(d-1-r_v\). These results establish explicit selection and information-loss limits for scalar reactive-power measurements under nonsinusoidal conditions.
