AC power
AC systems are widely adopted in modern power systems becauase they can be easily stepped up or down (by transformers), reduces transmission line losses, and produce rotating magnetic fields that spin electric motors (which represent a significant portion of electrical loads).
Root mean square, phasors, complex numbers
RMS, a method to quantify AC waveforms. How to solve: (1)-compute the square of the waveform (so it's always positive); (2)-compute the average of value of (1); (3)-take the square root of (2)
Ideal waveforms in AC are sinusoidal. For a purely resistive load, waveform i_R is in phase with v. For a purely inductive load, the current i_L lags the voltage deg (a negative cosine waveform). For a purely capacitive load, the current i_C is leading the voltage by 90deg (positive cos waveform). For a mixed load (of R, C, L), the phase shift angle $\theta can be any value between +/-90deg.
remember: inductive lag,capacitive lead,resistive inphase
Phasors give info on the magnitude and phase shift of a waveform. HOW TO DRAW
phasor angle theta between v (reference) and i
Complex number analysis is another way to analyze circuits. Represent phasor with a magnitude and angle. Vbar and Ibar. Negative angle for lagging. Complex form also called polar form. To multiply two complex numbers, take product of magnitudes and sum of angles. TODO figure out more math
Complex impedance. Impedance can be composed of any combination of R, L, C. In series, Zbar = Rbar + Xbar_L (sum of elements). In parallel, divide the parallel circuit elements by the current, then add them.
Types of power
Active power (P, also real power, average power) measured in W, is the actual work done. Energy converted to heat, light, mechanical work.
P = V_rms I_rms cos(\phi)
Reactive power (Q), measured in VAR, is power stored and released by inductors and capacitors.
Q = V_rms I_rms sin(\phi)
Apparent power (S), measured in VA, is the total power, a combination of active and reactive power.
S = V_rms I_rms
Complex power (S = P + jQ), measured in VA, combines P and Q in complex form, something something phasors
Instantaenous power (p = vi) is the produce of the the voltage and current at a point in time.
The power triangle relates the different types of power TODOOODOODDODOODOO
POWER FACTOR CORRECTION CONVERSON