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  The frequency domain representations of the current and voltage of an element and Amplitude or peak values

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

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  P AV in a capacitor and inductor is 0, since; |  C |= |  L |= 90 o and cos (90 o ) =0.

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  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,  cos p effeff P F VI 

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

Example #1  Find power factor if,

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  XLXL R Z

The Power Phasor  I2RI2R I2ZI2Z I2XLI2XL

The Power Triangle  S P QLQL

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 … ? P has units of … ? S 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.