Objective. Students will calculate true power, reactive power, apparent power, and power factor for a motor load, explain how a VFD improves system efficiency at partial load, and estimate annual energy savings when replacing a throttled valve or damper with variable-speed drive control.
This lesson, its worked examples and its practice questions has not yet been verified by a licensed engineer or certified journey-level tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.
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Industrial motors account for a large share of electrical energy consumed in manufacturing and marine facilities. Understanding how to measure that consumption accurately—and how variable-frequency drives (VFDs) reduce it—is a core skill for every mechatronics technician.
In an AC circuit with reactive loads such as motors and transformers, electrical power has three related quantities.
True power (P) is the power that does real work—turning a shaft, pumping fluid, moving air. It is measured in kilowatts (kW).
Reactive power (Q) is the power that flows back and forth between the source and the magnetic fields of inductive loads. It does no useful work but must be supplied by the utility. It is measured in kilovolt-amperes reactive (kVAR).
Apparent power (S) is the total power the utility must deliver. It is the vector sum of true and reactive power, measured in kilovolt-amperes (kVA).
These three quantities form a right triangle:
where θ is the angle between voltage and current.
Power factor (PF) is the ratio of true power to apparent power:
> PF = P / S = kW / kVA
A power factor of 1.0 (or 100%) means all current delivered does useful work. A power factor of 0.80 means 20% of the apparent current produces no useful output. Utilities often charge demand penalties when power factor falls below a threshold (commonly 0.90), so improving power factor saves money directly.
Displacement power factor describes the phase angle between the fundamental (60 Hz) voltage and current waveforms. A lightly loaded induction motor has a poor displacement power factor because its magnetizing current is relatively large compared with its load current.
True power factor (also called total power factor) accounts for both displacement and harmonic distortion. A VFD draws current from the utility in pulses, creating harmonic currents (primarily 5th and 7th harmonics). These harmonics add to the reactive burden seen by the utility even when the displacement power factor looks acceptable. For this reason, true power factor = distortion factor × displacement power factor, and true power factor is always ≤ displacement power factor when harmonics are present.
Line-side harmonic filters or active front-end VFDs can mitigate harmonic content.
Power-factor correction capacitors are sometimes installed at motor terminals to supply reactive power locally, reducing reactive current drawn from the utility. This is acceptable practice for motors run across the line.
However, capacitors must never be connected to the output terminals of a VFD. The VFD output is a pulse-width-modulated (PWM) waveform, not a sinusoidal voltage. Capacitors on the output create resonance, overcurrent trips, and can destroy both the capacitor bank and the VFD output transistors. Capacitors for power-factor correction belong on the line (input) side of the VFD, or at the service entrance, never between the VFD and the motor.
For centrifugal pumps and fans, the affinity laws describe how flow, pressure (head), and power change with shaft speed:
| Quantity | Relationship |
|---|---|
| Flow (Q) | Q₂/Q₁ = N₂/N₁ |
| Head (H) | H₂/H₁ = (N₂/N₁)² |
| Power (P) | P₂/P₁ = (N₂/N₁)³ |
The cubic relationship for power is the key insight. Reducing speed to 75% of full speed reduces power demand to (0.75)³ = 0.422, or about 42% of full-load power. That means a 58% reduction in power consumption at 75% speed—a dramatic saving compared with throttling a valve or damper, which wastes energy as pressure drop while the motor still runs at full speed.
Traditional flow control with a throttle valve or discharge damper keeps the motor at full speed and full (or near-full) power while restricting flow mechanically. A VFD matches motor speed to the actual flow requirement, so only the energy needed is consumed.
To estimate annual savings, compare full-speed power (with throttling) to reduced-speed VFD power, then multiply by operating hours and the utility rate:
> Annual savings (kWh) = (P_full − P_VFD) × hours_per_year
> Annual savings ($) = annual savings (kWh) × $/kWh
On a ship, HVAC fans often run continuously to maintain air quality and thermal comfort for crew and cargo. At full speed around the clock the energy cost is significant. Installing a VFD allows fan speed to be modulated with demand—lower at night, higher in tropical ports. Even a modest average speed reduction to 80% yields (0.80)³ = 0.512, saving roughly 49% of fan energy. Over a year at sea this translates to measurable fuel savings, reduced engine hours, lower maintenance costs, and reduced emissions—a compelling business case for retrofit.
Before working on any motor or drive:
Answer each question, then check it. Nothing is recorded; this is your own practice.
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