The circuit analysis approach based on geometric algebra and \(\varvec{M}\), the power definition based on the geometric product between the voltage and the current multivectors, are used here to demonstrate the shortcomings of the traditional definition of the non-sinusoidal apparent power S. The shortcomings of S are illustrated in three ways. Firstly, by showing an example of how the norm of \(\varvec{M}\) contains S. Secondly, through six experiments that involve compliance with: Kirchhoff’s circuit laws, Tellegen’s theorem, the principle of conservation of energy, the equivalency of two terminal networks and the concept of reactive power compensation. Lastly, by showing how the use of S leads the current’s physical component power theory astray. The experiments show contradictions between the aforementioned circuit theory fundamentals and the results attained with S but a compelling harmony with the results attained with \(\varvec{M}\). The evidence reveals two unprecedented discoveries: (1) that mathematical models aimed at explaining energy flow in non-sinusoidal circuits shouldn’t be based on the decomposition of S—as traditionally done— and, (2) the inappropriateness of extrapolating definitions from sinusoidal conditions to non-sinusoidal settings.

这里使用基于几何代数和\(\varvec{M}\)的电路分析方法，即基于电压和电流多向量的几何乘积的功率定义，来说明传统非-正弦视在功率S。S的缺点体现在三个方面。首先，通过展示\(\varvec{M}\)的范数如何包含S的示例。其次，通过六个实验，涉及到：基尔霍夫电路定律、泰勒根定理、能量守恒原理、两端网络等效性和无功补偿的概念。最后，通过展示如何使用S导致当前的物理组件功率理论误入歧途。实验表明上述电路理论基础与S所获得的结果之间存在矛盾，但与\(\varvec{M}\)所获得的结果之间存在令人信服的和谐。证据揭示了两个前所未有的发现：（1）旨在解释非正弦电路中能量流的数学模型不应该像传统那样基于S的分解，以及（2）从正弦曲线外推定义的不恰当性条件为非正弦设置。