1. Fundamental Electrical Power Concepts Instantaneous Power: Average Power: RMS (effective value):

2. Using RMS in Power Calculations The total current through R is i 1 (t)+i 2 (t). The instantaneous power is: p(t) =R(i 1 (t)+i 2 (t)) 2

3. The Average power over interval T is:

4. Given two vectors: How can we determine if the two vectors are perpendicular? Dot Product! If then they are perpendicular!

5. Orthogonal Functions Periodic functions with different periods are orthogonal. All even functions are orthogonal to all odd functions. Functions with non-zero average values are not orthogonal. Any constant (DC) function is orthogonal to any function with zero average value (0-mean, or AC). For 0-mean/AC functions:

6. Parseval’s Thorem +_+_ +_+_ +_+_ R + v(t) _ v 1 (t) v 2 (t) v 3 (t) If v 1 (t), v 2 (t) and v 3 (t) are orthogonal Application #1

7. Application #2 TT t0t0

8. 80 uS 100 uS Application #2 Example 15 a 7 a

9. Application #3 P = 0 if v(t) and i(t) are orthogonal waveforms in the interval T.

10. Application #4 For an inductor, = 0 for any periodic function:

11. AC Power Concepts Source voltage waveform is assumed to be an undistorted sinusoid with zero phase angle. Due to reactance of the load, the current waveform may exhibit a phase shift with respect to the voltage waveform. Current waveforms may contain harmonic distortion components, which increases the RMS value of the current waveform, and hence the apparent power (but not real power).