Lecture 07 AC POWER POWER FACTOR Lesson Objectives

Lecture 07 AC POWER & POWER FACTOR

Lesson Objectives • Compute and define apparent, reactive, and average power for capacitors, inductors, and resistors. • Compute and draw the power triangle for RC, RL, and RLC circuits. • Define and compute the power factor for RC, RL, and RLC circuits. • Summarize the basic steps to compute AC power in all or part of a circuit.

COMPLEX POWER

COMPLEX POWER • The frequency domain representations of the current and voltage of an element and

Definition of Complex Power

• The magnitude of S is called the Apparent Power:

• Converting the complex power from polar to rectangular form:

Real & Imaginary part of S

AVERAGE POWER, P • The real part of S is called Average Power, P. The unit is Watts.

REACTIVE POWER, Q • The imaginary part of S is called Reactive Power, Q. The unit is Var.

• The complex power may be expressed in terms of the load impedance, Z:

S in terms of Z

AVERAGE POWER

AC AVERAGE POWER where; • Average power is independent of whether v leads i, or i leads v.

Average Power in RESISTOR • Since | |=0 o and cos (0 o) =1

Average Power in L and C • PAV in a capacitor and inductor is 0, since; | C|= | L|= 90 o and cos (90 o) =0.

REACTIVE POWER

REACTIVE POWER, Q • The reactive power, Q is given by:

• Reactive power repeatedly stored and returned to a circuit in either a capacitor or an inductor. or

Q For Various Load • Q = 0 for resistive load • Q > 0 for inductive load • Q < 0 for capacitive load

POWER FACTOR

POWER FACTOR • The factor that has the significant control over the delivered power level is the cos ( ), where: • No matter what level I and V are, if: cos ( )=0, >> the power delivered is zero. cos ( )=1, >> the power delivered is max.

POWER FACTOR • Power Factor equation: • where,

Power Factor Leading or Lagging? • Inductive circuits have lagging power factors. • Capacitive circuits have leading power factors. • Power factors follow the current. • Remember ELI and ICE

Ex. • Find power factor if, Sinusoidal shift to the right Sinusoidal shift to the left

Solution Lagging because current is lagging and ELI.

POWER TRIANGLE

Power Triangle and Apparent Power • The impedance triangle with R, X, and Z may be shown to be similar to the power triangle with P, Q, and S, respectively as components. • Apparent power – A useful quantity combining the vector sum of P and Q.

Recall the Impedance Triangle XL Z R

The Power Phasor I 2 X L I 2 Z I 2 R

The Power Triangle S P QL

Im S +QL (lagging) P -QC (leading) Re

SUMMARY OF POWER

IMPORTANCE OF S • S contains all power of a load. • The real part of S is the real power, P • Its imaginary part is the reactive power, Q. • Its magnitude is the apparent power • The cosine of its phase angle is the power factor, pf.

Review Quiz • Name three types of power. • Q has units of … ? P has units of … ? S has units of … ? • Formula for P, Q, S… ? • Power factor is … ? • T/F: Power factor can never be greater than one or less than zero.