tailieunhanh - Ebook Electric circuits: Part 2

Part 2 book “Electric circuits” has contents: AC power, the laplace transform, three-phase systems, circuit analysis in the s-domain, magnetically coupled circuits, first- and second-order analog filters, analog filter design, fourier transform, fourier series, two-port circuits. | Chapter 11 AC Power Introduction In this chapter, alternating current (ac) power is discussed. The definitions of instantaneous power p(t), average power P, reactive power Q, complex power S, apparent power |S|, and power factor pf are given. The instantaneous power p(t) is the power as a function of time. It is the product of the voltage v(t) and the current i(t). The average value of the instantaneous power is P. The instantaneous power is the sum of the average power P and the time-varying component. The reactive power is the power exchanged between the source and the reactive components (., inductors and capacitors) of the load. The average value of the reactive power is zero. The complex power is defined as S 5 Vrms I*rms. It can be shown that the real part of the complex power is the average power P, and the imaginary part of the complex power is the reactive power Q. The magnitude of the complex power |S| 5 |Vrms| |Irms| is called the apparent power. A right triangle formed by two sides P (horizontal) and Q (vertical) and hypotenuse |S| is called a power triangle. The phase of S is the difference of phase v of the voltage v(t) and the phase i of current i(t). The angle is the angle made by P and S. The power factor is cos( ); that is, pf 5 cos( ). If the reactive power Q is increased, the angle is increased, and the power factor pf is decreased. The reactive power does not contribute to the real power delivered to the load. It contributes to the power loss on the transmission lines. The power factor correction refers to the reduction in the reactive power by connecting a parallel capacitor to the inductive load to offset the Q value of the load. Instantaneous Power, Average Power, Reactive Power, Apparent Power Let v(t) be the voltage across a circuit and i(t) be the current through the circuit from the positive terminal to the negative terminal [as shown in Figure ]. The circuit can be an element, an .