This chapter discusses sinusoidal steady state power calculations. Numerical integration is used to obtain the rms value, average power and quadrature power. | Attia John Okyere. AC Analysis and Network Functions. Electronics and Circuit Analysis using MATLAB. Ed. John Okyere Attia Boca Raton CRC Press LLC 1999 1999 by CRC PRESS LLC CHAPTER SIX AC ANALYSIS AND NETWORK FUNCTIONS This chapter discusses sinusoidal steady state power calculations. Numerical integration is used to obtain the rms value average power and quadrature power. Three-phase circuits are analyzed by converting the circuits into the frequency domain and by using the Kirchoff voltage and current laws. The unknown voltages and currents are solved using matrix techniques. Given a network function or transfer function MATLAB has functions that can be used to i obtain the poles and zeros ii perform partial fraction expansion and iii evaluate the transfer function at specific frequencies. Furthermore the frequency response of networks can be obtained using a MATLAB function. These features of MATLAB are applied in this chapter. STEADY STATE AC POWER Figure shows an impedance with voltage across it given by v t and current through it i t . Figure One-Port Network with Impedance Z The instantaneous power p t is P t v t t If v t and i t are periodic with period T the rms or effective values of the voltage and current are 1999 CRC Press LLC where V rms 1 rms V rms I rms 1 T - f v2 t dt T f 1T - fi2 t dt f is the rms value of v t is the rms value of i t The average power dissipated by the one-port network is 1T P TIv t i t dt T 0 The power factor pf is given as P pf rms rms For the special case where both the current i t and voltage v t sinusoidal that is v t Vm cos wt ev and i t Im cos wt 6I the rms value of the voltage v t is V Vm rms 2 are both and that of the current is 1999 CRC Press .
