CH2 Power computations 2-1 Introduction

1. CH2 Power computations 2-1 Introduction ˙Power computations are essential in analyzing and designing power electronics circuits. ˙Particular emphasis for circuits with no sinusoidal voltages and current.

2. 2-2 Power and energy Instantaneous power : p(t) = ; Fig.2-1 Energy (work) : W=

3. Average (real or active) power : P= T : period of the power waveform P =

4. 2-3 Inductor and capacitor For periodic function For inductor ( L ): The stored energy in inductor at the end of one period is the same as at the beginning. → average power by the inductor.

5. for periodic current. For capacitor ( C ): The stored energy is the same at the end of a period as the beginning. → average power absorbed by the capacitor is for periodic voltages.

6. 2-4 Energy recovery Circuit efficiency can be improved if stored energy can be transferred to the load or to the source rather than dissipated in circuit resistance. Fig.2-4

8. Without the diode-resistor path, the transistor could be destroyed when it is turned off because a rapid decrease in inductor current would result in excessively high inductor and transistor voltage. Transistor on : 0 ＜ ＜ increases linearly when the transistor on, ＜ Transistor off : ＜ (Diode on) ＜ ＜ ＜

9. Average power supplied by dc source All power supplied by the source must be absorbed by the resistor Peak energy stored in the inductor

10. Power absorbed by the resistor The function of the resistor in this circuit of Fig.2-4(a) is to absorb the stored energy in the inductance and protect the transistor a power loss. Another way to remove the stored energy in the inductor is shown in Fig.2-5.

13. Transistor on : 0 ＜ ＜ source current increases linearly Transistor off : ＜ ＜ ＜ ＜ ， decreases and becomes zero at

14. The source is absorbing power when the source current is negative. Average source current is zero, resulting in an average source power of zero. The source supplies power while the transistors are on, and the source absorbs power while the transistors are off and the diode are on. Therefore, the energy stored in the inductor is recovered by transferring it back to the source. Higher efficiency occurs in this circuit.

15. 2-5 Effective root mean square values or

16. : periodic function periodic function and are orthogonal (such as and are sinusoid of If different frequencies), then

17. periodic function，all orthogonal , , ………, periodic function similarly，

18. 2-6 Apparent power and power factor Apparent power : Power factor : Pf = In sinusoidal AC circuit , Pf =

19. 2-7 Power computation for sinusoidal ac circuits For linear circuits which have sinusoidal source, all steady-state voltages and currents are sinusoids. Average power is

20. Pf = Reactive power : By convention，inductors absorb positive reactive power and capacitor absorb negative reactive power complex power : apparent power :

21. 2-8 Power computation for non-sinusoidal periodic waveforms The Fourier series can be used to describe non-sinusoidal periodic waveforms in terms of a series of sinusoids.

22. or rms value of f(t) :

23. Average (real or active) power : or The average of voltage and current products at different frequency is zero.

24. Non-sinusoidal source and linear load: Using Fourier series for source and superposition method to solve the circuit. Fig.2-10.

25. Sinusoidal source and Non-linear load: The current waveform will not be sinusoidal but can be represented as a Fourier series Average power absorbed by the load : The only nonzero power term is at the frequency of the applied voltage.

26. . Distortion factor : DF

27. Total harmonic distortion (THD) : used to quantify the non-sinusoidal property of a waveform. If dc term ( ) is zero ,

28. The only nonzero term for reactive power is at the voltage frequency : Apparent power : Distortion volt-amps: Form factor = Crest factor =