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Power factor and capacitors
The electrical power required to drive a motor has three components: reactive power (Pr, kVAR), active power (Pa, kW), and apparent power (Pap, kVA). The active power is the actual amount of work done by the motor and measured for billing purposes. The reactive power is the power required to magnetize the motor winding or to create magnetic flux, and is not recordable. The apparent power is the vector sum of kilowatts and kilovars and is the total amount of energy furnished by the utility company.
The power triangles shown in Fig. 1 illustrate the relationships between these terms.
The power factor (Fp) is the ratio of active power to apparent power:
The power factor is "leading" in loads that are more capacitive and "lagging" in loads that are more inductive (e.g., motor or transformer windings). In a purely resistive load, Fops = 1 (unity), such that Pa = Pap (kW = kVA) and no reactive power is present. When Fp < unity, reactive power is present and more power is required to produce work, as seen in the following equation:
The reactive power of a motor is approximately the same from no load to full load. When a motor is operating at full load, the active/reactive power ratio is high, and thus the power factor of the motor is high. A lightly loaded motor has a low active/reactive power ratio, which causes the power factor to be low. At low power factors, more power will be required from the utility company than actually is needed by the load. This translates into higher energy cost and the need for larger generation units and transformers. Some utility companies charge a substantial penalty to their customers for low power factors (generally < 0.95). Also, low power factors might cause more voltage drop in the system, which causes the motors to operate sluggishly and the lights to dim.
It is essential that the power factor of the system be maintained as high as possible (close to unity). Removing the reactive power from the system can make this possible. Power-factor-correction capacitors are used for this purpose. A motor requires inductive or lagging reactive power for magnetizing. Capacitors provide capacitive or leading reactive power that cancels out the lagging reactive power when used for power-factor improvement. The power triangles in Fig. 2 show how capacitors can improve the power factor for a motor. The improved power factor changes the current required from the utility company, but not the one required by the motor.
Capacitors should not be selected as a means of correcting poor power factors that are the result of oversized motors or unbalanced pumping units. Choosing a capacitor for this purpose might cause overcorrection, which can result in a leading power factor. A leading power factor, in turn, might cause overvoltages that would cause control-component failure or power-cable failure. This potential problem generally is avoided by connecting the capacitors downstream of the motor contactors and switching them on and off, along with the motor contactors.
Power factor correction capacitors could be applied to each individual motor to correct the power factor of that motor, or could be a single unit connected to the main bus of the switchgear. In the latter case, the unit should have power-factor-sensing circuits that automatically determine the amount of capacitance required for maintaining a preset power factor. The required amount of capacitors are automatically added to or removed from the switchgear bus to maintain the required power factor.
The cyclic kW load on a pumping-unit motor can cause the power factor to vary from 1.0 to near zero if excessive adverse pumping conditions exist.
|Fp||=||power factor, cos θ|
|Pa||=||active power, kW|
|Pap||=||apparent power, kVA|
- H.B. Bradley, ed. 1987. Petroleum Engineering Handbook. Richardson, Texas: SPE.
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