8. AC POWER CIRCUITS by Ulaby & Maharbiz

Overview

Linear Circuits at ac Instantaneous power Average power Power at any instant of timeAverage of instantaneous power over one period  Power delivery (utilities)  Electronics (laptops, mobile phones, etc.)  Logic circuits Power is critical for many reasons: Note: Power is not a linear function, cannot apply superposition

Instantaneous Power for Sinusoids Power depends on phases of voltage and current Trig. Identity: Constant in time (dc term) ac at 2 

Average Value Sine wave Truncated sawtooth

Average Value for These properties hold true for any values of φ 1 and φ 2

Effective or RMS Value Equivalent Value That Delivers Same Average Power to Resistor as in dc case For current given by Effective value is the (square) Root of the Mean of the Square of the periodic signal, or RMS value Hence: Similarly,

Average Power Note dependence on phase difference

Average Power Sinceand a similar relationship applies to I, Power factor angle: 0 for a resistor = 90 degrees for inductor ‒ 90 degrees for capacitor

ac Power Capacitors Capacitors (ideal) dissipate zero average power = 0

ac Power Inductors Inductors (ideal) dissipate zero average power = 0

Complex Power Phasor form defining “real” and “reactive” power

Power Factor for Complex Load Inductive/capacitive loads will require more from the power supply than the average power being consumed Power supply needs to supply S in order to deliver P av to load Power factor relates S to P av

Power Factor

Power Factor Compensation Introduces reactive elements to increase Power Factor

Example 8-6: pf Compensation

Maximum Power Transfer Max power is delivered to load if load is equal to Thévenin equivalent Max power transfer when Set derivatives equal to zero

Example 8-7: Maximum Power Cont.

Example 8-7: Maximum Power

Three Phase

Y & Delta

Y-Source Connected to a Y-Load

Multisim Measurement of Power

Multisim Measurement of Complex Power Complex Power S

Summary