相量变换在正弦电路功率分析中的应用

The Phasor Transformation Applications in the Sine Circuit Analysis

本文介绍了相量变换原理及其在正弦电路功率分析中的应用。基于复功率等于电压相量与电流相量共轭积的定义,得出了复功率与有功功率和无功功率的关系;建立了有功功率、无功功率、复功率及复交流功率与瞬时功率的关系,进而仅基于瞬时功率的守恒性便证明了上述功率也满足守恒性。由于这些功率守恒性的证明不需要特勒根定理为基础,因而有助于学生在学习特勒根定理之前理解交流电路功率的守恒性。

The phasor transformation and its applications in the AC power analysis are introduced in this paper . The relations between the complex power and the active power as well as the reactive power are obtained based on the fact that the complex power is defined as the multiplication of the voltage phasor and the conjugate of the current phasor. Moreover, the relations between both the active power and the reactive power and the instantaneous power are also achieved at the same time. Therefore, the conservations of complex power and complex alternating power can be demonstrated in the different ways before only based on the conservation of the instantaneous power. One of the advantages of this teaching strategy is that it can promote the students to understand the AC power conservations before they learn the Tellegen＇s theorem.