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 ||=0o and cos (0o) =1

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

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 q R

The Power Phasor I2XL I2Z q I2R

The Power Triangle S QL q P

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

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 the 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.