8. 3 Power Factor Correction 8.1 Power in a Sinusoidal Steady-state Circuit 8.2 Maximum Average Power Transfer Chapter 8 AC Power Analysis 交流功率分析

8.1 Power in a Sinusoidal Steady-state Circuit Let the voltage and current at the terminals of the circuit be The instantaneous power absorbed by the circuit is N0N0 v i + - 瞬时功率

The average power is the average of the instantaneous power over one period. cos  ： power factor 功率因数  =  v -  i ： power factor angle 功率因数角 average power is also called real power (W) 有功功率 ( 瓦） reactive power (VAR ) 无功功率 ( 乏） apparent power (VA) 视在功率 ( 伏安） i leads v : leading power factor 领先的功率因数 i lags v : lagging power factor 滞后的功率因数

 S P Q Power triangle 功率三角形 Similar triangle 相似三角形 Impedance triangle 功率三角形 |Z| R X zz Complex power (VA) 复功率 ( 伏安）  =  Z

Real Power and Reactive Power for R 、 L 、 C P R =VIcos  =VIcos0  =VI P L =VIcos  =VIcos90  =0 P C =VIcos  =VIcos( - 90  )=0 Q R =VIsin  =VIsin0  =0 =I2R=V2/R=I2R=V2/R Q L =VIsin  =VIsin90  =VI Q C =VIsin  =VIsin ( - 90  )= - VI

The complex, real,and reactive powers of the sources equal the respective sums of the complex, real,and reactive powers of the individual loads. but Conservation of AC Power 功率守恒

N0N0 v i + - Solution: Example 8.1 Find P, Q, S and in the circuit.

Example 8.2 In the circuit, f=50Hz ， the readings of voltmeter, ammeter and wattmeter are 50V ， 1A and 30W, respectively. Calculate R and L. Solution: and

8.2 Maximum Average Power Transfer 最大有功功率传输 The Thevenin impedance Z Th and the load impedance Z L are

The maximum average power transfer When That

The process of increasing the power factor without altering the voltage or current to the original load is known as power factor correction. 11 22 8.3 Power Factor Correction 功率因数提高 and

部分电路图和内容参考了： 电路基础（第 3 版），清华大学出版社 电路（第 5 版），高等教育出版社 特此感谢！