The use of geometric algebra in circuit analysis and its impact on the definition of power

Milton Castro-Núñez, Róbinson Castro-Puche, E. Nowicki
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引用次数: 18

Abstract

Geometric algebras of the Euclidean 2-dimensional and 3-dimensional spaces have been used to analyze electric circuits with linear and harmonic generating loads (HGLs). It is shown in this paper that with both loads, time domain signals may be transformed to the Gn domain such that the resulting multivectors permit circuit analysis through rotations and dilation-contractions of the excitation signal. The power equation, in particular, is created by applying the geometric product of the voltage and current multivectors and is suitable for linear and nonlinear loads. This is in contrast to commonly used frequency analysis methods where the reactive power cannot be obtained in correspondence with its definition in the time domain and it fails at providing a unified power equation for linear and HGLs. We interpret the proposed power equation in the frequency and time domains and introduce an analogous quantity to the reactive power Q, the CN-power, for circuits with nonlinear loads. A power factor equation applicable to both loads is also presented. The resulting one-to-one correspondence between the time domain and the Gn domain avoids eliminating any component from the power equation in the time domain. Single-phase circuit examples are provided.
几何代数在电路分析中的应用及其对功率定义的影响
利用欧几里得二维和三维空间的几何代数分析了具有线性和谐波发电负载的电路。本文表明,在这两种负载下,时域信号都可以转换到Gn域,从而通过激励信号的旋转和扩张-收缩,得到的多向量可以进行电路分析。特别是,功率方程是通过应用电压和电流多矢量的几何乘积创建的,适用于线性和非线性负载。这与常用的频率分析方法相反,这些方法无法获得与时域定义相对应的无功功率,并且无法为线性和hgl提供统一的功率方程。我们在频域和时域中解释了所提出的功率方程,并引入了一个与非线性负载电路的无功功率Q (n -功率)类似的量。并给出了适用于两种负载的功率因数方程。时域和Gn域之间的一对一对应避免了从时域的功率方程中消除任何分量。提供了单相电路示例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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