1 / 22

Chapter 11

Chapter 11. AC power analysis. rms value. The RMS value is the effective value of a varying voltage or current. It is the equivalent steady DC (constant) value which gives the same effect. effective value or DC-equivalent value.

iden
Download Presentation

Chapter 11

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 11 AC power analysis SJTU

  2. rms value The RMS value is the effective value of a varying voltage or current. It is the equivalent steady DC (constant) value which gives the same effect. effective value or DC-equivalent value The rms value of a periodic function is defined as the square root of the mean value of the squared function. SJTU

  3. If the periodic function is a sinusoid, then What do AC meters show, is it the RMS or peak voltage? AC voltmeters and ammeters show the RMS value of the voltage or current. What does '6V AC' really mean, is it the RMS or peak voltage? If the peak value is meant it should be clearly stated, otherwise assume it is the RMS value. SJTU

  4. AC power analysis Instantaneous Power Suppose: i(t) v(t) N Invariable part Sinusoidal part SJTU

  5. E page415 figure 10.2 SJTU

  6. WLav Stored energy In the sinusoidal steady state an inductor operates with a current iL(t)=IAcos(wt). The corresponding energy stored in the element is Average stored energy SJTU

  7. Stored energy In the sinusoidal steady state the voltage across a capacitor is vc(t)=VAcos(wt). The energy stored in the element is Average stored energy WCav SJTU

  8. Average power The average power is the average of the instantaneous power over one period.-------real power Note : There are other methods to calculate P. 1) 1) 2) SJTU

  9. Resistor case Average power Pav=0.5Vm*Im Pav=vrms*irms Inductor case Pav = 0 Instantaneous power, real power Instantaneous power waveforms for a voltage of 2V peak and a current of 1.5A peak Flowing separately in a resistor, a capacitor and an inductor SJTU Capacitor case Pav = 0

  10. Apparent power S=VrmsIrms (VA) Power factor current leads voltage or current lags voltage <0 or  >0 SJTU

  11. To any passive single port network Reactive power (VAR) Resistor: Q=0 Inductor: Q=VrmsIrms Capacitor: Q=-VrmsIrms SJTU

  12. The power triangle S Q  P SJTU

  13. EXAMPLE Find the average power delivered to the load to the right of the interface in Figure 8-64. Fig. 8-64 SOLUTION: SJTU

  14. Complex power Complex power is the complex sum of real power and reactive power =P+jQ So =VI* Where V is the voltage phsor across the system and I* is the complex conjugate of the current phasor. The magnitude of complex power is just apparent power SJTU

  15. Are these equations right? SJTU

  16. Maximum power transfer Fig. 8-66: A source-load interface in the sinusoidal steady state. SJTU

  17. the maximum average power Let XL=-XT then we know P is maximized when RL=RT where |VT| is the peak amplitude of the Thevenin equivalent voltage SJTU

  18. EXAMPLE (a) Calculate the average power delivered to the load in the circuit shown in Figure 8-67 for Vs(t)=5cos106t, R=200 ohm, and RL=200 ohm. (b) Calculate the maximum average power available at the interface and specify the load required to draw the maximum power. SOLUTION: (a) SJTU

  19. SJTU

  20. (b) Question: If the load must be a resistor, how get the maximum power on it? SJTU

  21. Maximum power transfer when ZL is restricted • RL and XL may be restricted to a limited range of values. • In this situation, the optimum condition for RL and XL is to adjust XL as near to –XT as possible and then adjust RL as close to as possible • the magnitude of ZL can be varied but its phase angle cannot. • Under this restriction, the greatest amount of power is transferred to the load when the magnitude of ZL is set equal to the magnitude of ZT SJTU

  22. Note: • If the load is a resistor, then what value of R results in maximum average-power transfer to R? what is the maximum power then? • If ZL cannot be varied but ZT can, what value of ZT results in maximum average-power transfer to ZL? SJTU

More Related