Chapter 8
AC Power

m8.4 The Power Factor

The circuit shown in Figure m8.4 is a “scale model” of two industrial electric motors and a heating unit connected to a manufacturing plant power distribution network. The resistor/inductor combinations R1-L1 and R2-L2 model the winding resistance and magnetic fields of the motors. Resistor R3 models the heater coils. C represents the power factor compensation equipment – essentially a capacitor bank with high power capacity.

  1. Determine the power factor of the uncompensated load, and draw its power triangle to scale.
  2. Determine the value of the compensation capacitor C required to improve the load power factor to 0.90 lagging.
  3. Available power factor compensation capacitors include 0.1 μF, 1.0 μF, and 10 μF; the cost of compensation equipment increases with capacitance. Choose the least expensive compensation capacitor closest to C and then determine the power factor and power triangle (also drawn to scale) of the compensated load.

Component values are: R1 = 10 Ω, R2 = 100 Ω, R3 = 100 Ω, L = 3.3 mH, L = 33 mH, and V SRC = 1 V at 2500 Hz (actual industrial motors operate at hundreds of volts and 50 Hz to 60 Hz frequency)

PIC


Figure m8.4: Circuit for Problem m8.4

NI Multisim Measurements

Enter the circuit of Figure m8.4 with an AC_VOLTAGE source, setting its peak value and frequency according to the values specified in the problem statement. Place a SPST switch to conveniently engage or disengage the power factor compensation capacitor. Connect a wattmeter to measure the power factor of the combined load and capacitor.

IMPORTANT: Reduce the interactive simulation maximum time step TMAX to 1e-006 seconds; find this parameter at Simulate → Interactive Simulation Settings. The default time step does not produce sufficient sample points per period at the operating frequency in this problem to allow the wattmeter to produce an accurate power factor measurement.

  1. Measure the power factor of the uncompensated load (switch open).
  2. Close the switch to engage the compensation capacitor.
  3. Measure the power factor of the compensated load.
NI Multisim video tutorials:

NI myDAQ Measurements

Build the circuit of Figure m8.4. Do not place resistors R1 and R2, as these simply model the finite winding resistances of the two inductors.

Activate the circuit with the NI ELVISmx Function Generator on AO0, and place an op amp voltage follower between AO0 and the remaining circuit; the voltage follower boosts the current drive of the analog output beyond its limit of 2 mA.

Use the NI ELVISmx Oscilloscope to display the load voltage on AI0. Place a 10 Ω shunt resistor between the op amp output and the remaining circuit; display the voltage across this shunt resistor on AI1, and recognize that its voltage is proportional to the load current.

  1. Measure the power factor of the uncompensated load.
  2. Place your selected compensation capacitor into the circuit.
  3. Measure the power factor of the compensated load.

Additional helpful tips:

NI myDAQ video tutorials:

Further Exploration with NI myDAQ

Long-haul electrical energy distribution networks rely on transformers to boost the voltage to hundreds of thousands of volts while simultaneously reducing the current to very low levels – remember that power is the product of voltage and current, hence a given power can be transferred with low voltage and high current or vice versa. Reducing the current reduces the resistive losses in the transmission wires and improves efficiency.

Experience how power factor compensation impacts the amount of current that the utility must supply to the customer’s equipment:

  1. Measure and record the RMS voltage and current as displayed on the oscilloscope for the uncompensated load.
  2. Repeat these measurements for the compensated load.
  3. Discuss which values remain similar and which values change significantly. Comment on the value of power factor compensation as far as energy transmission efficiency is concerned.