基于相序变换的三相系统瞬时功率定义

Defining the three-phase system instantaneous power components based on the phase-mode transformation

瞬时无功功率理论(p-q理论)应用克拉克变换把不含零序分量的三相三线系统中线性相关的三相电量变换为线性独立的两个分量,构成两维向量,继而基于向量运算法则提出了瞬时功率定义,被广泛应用于有源滤波及无功补偿等工程领域。指出三相三线制p-q理论只是FBD功率理论的特例,继而指出p-q理论应用于三相四线制系统时并不能实现线损最小的最优补偿目标。基于相序变换的数学原理,提出了一种线性变换方法,可把三相四线制系统中的四个线性相关的电量变换为线性独立的三个变量,构成三维正交坐标系中的三维空间向量,继而应用向量运算法则提出了瞬时功率定义方法,具有定义简洁、计算简单直观、物理意义清晰的特点。此外,在三相三线制系统中,该定义与三相三线制p-q理论、FBD功率理论达到了统一,在三相四线制系统中该定义与FBD功率理论也是一致的。

The instantaneous reactive power theory （p-q theory） based on Clarke transformation transforms three linearly dependent electrical quantities to two linearly independent quantities constructing two dimension space-vector for three-phase three-wire systems without zero-sequence component, then a set of instantaneous power definition that is widely applied in active filter and reactive power compensation domains is proposed. This paper indicates the p-q theory of three-phase three-wire system is a special case of FBD power theory, and the p-q theory applied in three-phase four-wire system can not realize the objective of the optimized compensation for the lowest line loss. A linear transformation method based on the mathematical principle of phase-mode transformation is proposed, which can transform the four linearly dependent quantities in three-phase four-wire to three linearly independent quantities constructing three dimension space-vector of three dimension orthogonal coordinate system, then a set of instantaneous power definition based on the principle of vector operation is proposed. The method has the advantage of simple definition, brief graphic computation and clear physics significance. In addition, in the three-phase three-wire systems, this method has achieved agreement with p-q theory and FBD power theory on the definition of the three-phase instantaneous reactive power, and also shows consistency in defining the instantaneous reactive power with FBD power theory in the three-phase four-wire system.