三相三线电路中的多端电路瞬时功率理论推导

Deduction of instantaneous power theory of multi-terminal circuit in three-phase three-wire circuit

针对在电压电流畸变情况下基于相电压定义的传统功率理论已失去其有效性的问题,提出了多端电路的理念。将三相三线制电路作为三端电路处理,给出了端电压和端电流的定义。并且利用瞬时端电压和瞬时端电流定义了瞬时有功和无功功率。文中分别在电压电流均正弦对称、电压正弦对称电流畸变不对称以及电压电流均畸变不对称三种情况下推导了在三端电路中瞬时有功功率和瞬时无功功率的表达式,该表达式与基于瞬时功率理论推导得出的表达式一致。据此给出了三端电路中瞬时有功功率和瞬时无功功率的定义。

In view of the traditional power theory based on the definition of phase voltage is no longer valid under the circumstance of distorted voltage and current,the concept of multi-terminal circuit is proposed. Take the threephase three-wire circuit as an example,which is treated as the three-terminal circuit. Definitions of its terminal voltage and current are proposed in this paper while the instantaneous active power and reactive power are defined using instantaneous terminal voltage and current. The expressions of instantaneous active power and reactive power are deduced under three conditions respectively,which both the current and voltage are sinusoidal and symmetric,the voltage is sinusoidal and symmetrical while the current is distorted and asymmetric and both the current and voltage are distorted and asymmetric. The results of them are the same as the expressions deduced under the instantaneous power theory. According to this,the definitions of instantaneous active power and instantaneous reactive power of three-terminal circuit are given.