瞬时功率理论

标签（空格分隔）： 电力电子

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瞬时功率理论最先由日本的Akagi教授在1983年的在日本举行的一次国际会议中提出。瞬时功率理论是电力系统的无功补偿的基础，只有知道三相系统的瞬时有功和无功，才能进行无功补偿，补偿无功电流，进行系统功率因素的校正和减小电力系统中的线路损耗。

Instantaneous Reactive Power Compensators Comprising Switching Devices without Energy Storage Components
Hirofumi Akagi , Yoshihira Kanazawa

1. Abstract

传统的无功功率都是定义在稳态为正弦波的单相或者三相电压电流的平均值的基础上的。而瞬时功率理论是定义在任意电压电流波形的瞬时值的基础上的，所以不止是在稳态满足，在瞬态条件下也能计算瞬时功率，在该理论的基础上可以设计一个单纯使用开关器件而不需要使用储能元件来进行无功补偿。

2.Introduction

传统的无功功率补偿装置都只补偿了稳态条件下的基波成分的无功功率，没有考虑瞬态情况和谐波成分的无功功率。
本文提出了一个新的电量，虚功率（imaginary power）。瞬时无功功率通过使用前面提到的虚功率，定义了唯一的一个表示任意三相电压和电流波形包括畸变波形的无功功率的值。

3.Instantaneous reactive power theory

3.1 Definition of instantaneous imaginary power

In a-b-c coordinates,the a,b, and c axes are fixed on the same plane,apart from each other by 2⋅π3,as shown in Fig.1.The instantaneous space vectors,eaandiaare set on the αaxis,and their amplitude and (+、-)direction vary with the passage of time.In the same way,ebandibare on the baxis,and ec and ic are on the c axis.The space vectors are easily transformed into
α−β coordinates as follows:

[vαvβ]=23−−√[10−1/2sqrt(3)/2−1/2−sqrt(3)/2]⎡⎣⎢vavbvc⎤⎦⎥(1)

[iαiβ]=23−−√[10−1/2sqrt(3)/2−1/2−sqrt(3)/2]⎡⎣⎢iaibic⎤⎦⎥(2)

where the α and β axes are the orthogonal coordinates.Necessarily,eα andiα are on the alpha axis , and eβ and iβ are on the β axis.

The conventional instataneous power on the three phase circuit can be defined as follows:

p=eα⋅iα+eβ⋅iβ(3)

where p is equal to the conventional equation:

p=va⋅ia+vb⋅ib+vc⋅ic(4)

In order to define the instantaneous reactive power ,the authors introduce the instantaneous imaginary power space vector defined by

q=eα×iβ+eβ×iα(5)

This space vector is the imaginary axis vector and is perpendicular(垂直) to the real plane on the α−βcoordinates,to be in compliance（遵循）with the right-hand rule.
The conventional instantaneous power ,p and the instantaneous imaginary power q,which is the amplitude of q,are expressed by

[pq]=[vαvβvβ−vα][iαiβ](6)

3.2 Definition and physical meaning of instantaneous reactive powr