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newSchoolWorks.com › VoTechWorks › Manufacturing & Marine › Robotics / Mechatronics › Motor Drives: AC/DC Motors, Variable-Frequency Drives, and Motion Control › Lesson 5
MFG-MECH15-05 · Lesson 5 · 12 clock hours · theory

Variable-Frequency Drive (VFD) Principles: V/Hz, Volts-per-Hertz, and PWM

Objective. Students will explain how a VFD rectifies, filters, and inverts AC power using pulse-width modulation to vary motor speed, and describe V/Hz ratio and why it is maintained constant below base speed.

⚠ Pending professional review

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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What a VFD Does and Why It Matters

A variable-frequency drive (VFD) lets you control the speed of an AC induction motor by changing both the frequency and the voltage of the power supplied to it. Instead of running a motor at one fixed speed, a VFD allows smooth ramp-up, precise speed control, and energy savings — critical capabilities in automated manufacturing and marine systems. Understanding how a VFD works internally makes you a more effective technician when you need to commission, troubleshoot, or safely service one.

The Three Stages of a VFD

Every VFD converts power in three sequential stages. Trace the power flow from left to right through these blocks.

Stage 1 — Converter (Rectifier): Incoming three-phase AC (typically 480 V, 60 Hz in US industrial plants) enters a bridge rectifier made of diodes. The diodes allow current to flow in only one direction, converting the alternating waveform into a pulsating DC voltage. The result is not yet smooth — it ripples at six times the line frequency for a three-phase, full-wave bridge (360 Hz ripple on 60 Hz supply).

Stage 2 — DC Bus (Capacitor Bank): Large electrolytic capacitors smooth the pulsating DC into a relatively steady DC bus voltage. On a standard 480 V AC drive, the DC bus sits at roughly 650–680 V DC under normal conditions. This bus is the energy reservoir the inverter draws from. A pre-charge resistor (or pre-charge circuit) is connected in series with the bus during power-up to limit the inrush of current that would otherwise surge into the uncharged capacitors and damage them or blow fuses. Once the capacitors are charged to near full voltage, a contactor bypasses the resistor and normal operation begins. The DC bus test points are the measurement locations you will use with a meter to confirm bus voltage — always treat these points as energized even after the drive is powered off, because capacitors store lethal charge.

Stage 3 — Inverter (IGBT Switches): Insulated-gate bipolar transistors (IGBTs) are arranged in three pairs (one pair per output phase). By switching each IGBT on and off thousands of times per second under control of the drive's microprocessor, the inverter reconstructs a synthetic AC output whose frequency and voltage are both adjustable. This switching technique is called pulse-width modulation (PWM).

Pulse-Width Modulation (PWM)

PWM works by varying the width of each voltage pulse while keeping the DC bus voltage fixed. The average voltage seen by the motor over many switching cycles approximates a sine wave. If you look at the raw output on an oscilloscope, you see a series of rectangular pulses at DC bus voltage levels, not a true sine wave. The motor's own inductance acts as a low-pass filter and smooths the current into something close to sinusoidal. The rate at which the IGBTs switch is called the carrier frequency (also called switching frequency), typically 2–16 kHz. Higher carrier frequencies produce quieter motor operation (less audible whine) but generate more heat in the drive and in the motor, and cause greater stress on motor insulation — especially over long cable runs.

V/Hz Ratio: Keeping Flux Constant

An AC induction motor develops torque through electromagnetic flux in its core. The flux is proportional to voltage divided by frequency (V/Hz). If you reduce frequency to slow the motor but do not also reduce voltage by the same proportion, the core saturates, draws excessive current, overheats, and can be damaged. If you reduce voltage too much relative to frequency, flux weakens and torque drops.

The solution is to maintain a constant V/Hz ratio at all speeds below base speed (the nameplate frequency, typically 60 Hz). For example, a 460 V / 60 Hz motor has a V/Hz ratio of approximately 7.67 V/Hz. At 30 Hz, the drive outputs roughly 230 V — half the voltage at half the frequency. The ratio stays constant, flux stays constant, and rated torque capability is maintained.

Above base speed, voltage cannot increase beyond the drive's supply limit, so the drive holds voltage constant while continuing to raise frequency. In this field-weakening region, flux and torque decrease. Most general industrial applications stay at or below base speed.

Why Long Cable Runs Require Derating

When PWM pulses travel down a long motor cable, the cable's capacitance and inductance cause voltage reflections. These reflections can produce voltage spikes at the motor terminals significantly higher than the DC bus voltage, stressing the motor's winding insulation. Drive manufacturers publish derating guidelines and maximum cable length specifications. For long runs, output reactors or dV/dt filters are added between the drive and motor.

Safety: Work Near VFDs

VFDs present serious electrical hazards.

Key terms10

Variable-Frequency Drive (VFD)An electronic power converter that controls AC motor speed by varying the frequency and voltage of the output power supplied to the motor.
Rectifier (Converter)The first stage of a VFD; a diode bridge that converts incoming AC to pulsating DC.
DC BusThe intermediate DC voltage rail inside a VFD, smoothed by a capacitor bank, from which the inverter stage draws power.
IGBT (Insulated-Gate Bipolar Transistor)A high-speed power switching device used in VFD inverter stages to chop the DC bus voltage into PWM pulses.
Pulse-Width Modulation (PWM)A switching technique in which the width of each output voltage pulse is varied so that the average voltage approximates a desired sine wave at a controlled frequency.
V/Hz Ratio (Volts-per-Hertz)The ratio of output voltage to output frequency maintained constant by a VFD below base speed to keep motor flux — and therefore torque capability — at rated levels.
Carrier Frequency (Switching Frequency)The rate, in kHz, at which the VFD's IGBTs switch on and off; higher values reduce audible noise but increase drive and motor heating.
Pre-charge ResistorA resistor placed in series with the DC bus during VFD power-up to limit inrush current into the uncharged capacitor bank, protecting components from damage.
Field WeakeningOperation above base speed in which the drive holds voltage constant while increasing frequency, causing flux and maximum torque to decrease.
Base SpeedThe motor's nameplate speed corresponding to rated voltage and rated frequency (typically 60 Hz); the upper limit of the constant V/Hz region.

Worked examples4

1. A motor nameplate reads 460 V, 60 Hz. The VFD is commanded to run the motor at 45 Hz using constant V/Hz control. What output voltage should the drive produce?
  1. Step 1 — Find the V/Hz ratio at nameplate conditions: V/Hz = 460 V ÷ 60 Hz = 7.667 V/Hz.
  2. Step 2 — Multiply the ratio by the commanded frequency: V_out = 7.667 V/Hz × 45 Hz = 345 V.
  3. Step 3 — Confirm the ratio is preserved: 345 V ÷ 45 Hz = 7.667 V/Hz. ✓
Answer: The drive should output approximately 345 V at 45 Hz.
2. The same 460 V / 60 Hz motor is slowed to 20 Hz. What is the required output voltage to maintain constant V/Hz?
  1. Step 1 — Use the same V/Hz ratio: 7.667 V/Hz.
  2. Step 2 — Calculate output voltage: V_out = 7.667 × 20 Hz = 153.3 V.
  3. Step 3 — Check: 153.3 V ÷ 20 Hz = 7.667 V/Hz. ✓
Answer: The drive should output approximately 153 V at 20 Hz.
3. A technician measures 648 V on the DC bus of a 480 V (line-to-line) VFD. Is this reading reasonable? Explain using the relationship between AC RMS and rectified DC.
  1. Step 1 — For a three-phase full-wave rectifier, the theoretical no-load DC bus voltage equals the AC line-to-line RMS voltage multiplied by √2: V_DC ≈ 480 V × 1.4142 = 679 V (theoretical peak).
  2. Step 2 — Under load and accounting for diode drops and line impedance, actual bus voltage typically falls in the 640–680 V range.
  3. Step 3 — 648 V falls within the expected range for a 480 V supply.
Answer: Yes, 648 V is a normal DC bus reading for a 480 V drive; the rectifier produces roughly 650–680 V DC from a 480 V AC source.
4. A VFD datasheet states the carrier frequency can be set to 4 kHz or 8 kHz. A motor is located 300 feet from the drive. Which carrier frequency setting is generally preferred for this installation, and why?
  1. Step 1 — Higher carrier frequencies increase the rate of voltage change (dV/dt) in the output pulses.
  2. Step 2 — Long cables amplify voltage reflections caused by impedance mismatches; higher switching frequencies combined with long runs produce higher peak voltages at the motor terminals.
  3. Step 3 — Lower carrier frequency (4 kHz) reduces the severity of voltage reflections and reduces drive heating, making it the preferred setting for long cable runs, though an output reactor or dV/dt filter should also be considered per the manufacturer's guidance.
Answer: The lower carrier frequency (4 kHz) is generally preferred for a 300-foot cable run to reduce voltage reflections and motor insulation stress.

The math in this lesson2

Learners hold constant volts per hertz to find VFD output voltage at 45 Hz and 20 Hz.
6.RP.3N-RN.2
In class: Lecture with block diagram: trace power flow through converter (rectifier), DC bus (capacitor bank), and inverter (IGBT switches); instructor shows oscilloscope waveform of PWM output vs. pure sine. · Students draw their own VFD block diagram from memory, label each stage, and annotate where DC bus voltage is measured and where a pre-charge resistor limits inrush. · Video analysis: students watch a manufacturer training clip on IGBT switching and answer a guided worksheet on switching frequency, carrier frequency effects on motor heating, and why derating is required for long cable runs.
Materials: Whiteboard and markers, VFD block diagram posters, oscilloscope (or oscilloscope screenshot printouts), VFD training unit (any brand with exposed DC bus test points, de-energized), manufacturer technical manual excerpt, guided worksheet
Check: Block-diagram drawing scored on six labeled stages and correct signal flow; worksheet graded for accuracy. Pass = 80% on both with V/Hz explanation correct.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Motor and Motor Controls
1. In a VFD, which stage converts incoming AC power to pulsating DC?
Motor and Motor Controls
2. Why is a pre-charge resistor included in a VFD's DC bus circuit?
Motor and Motor Controls
3. A VFD maintains a constant V/Hz ratio below base speed primarily to:
Motor and Motor Controls
4. A motor is rated 230 V / 60 Hz. Using constant V/Hz control, what voltage should the VFD output at 30 Hz?
Motor and Motor Controls
5. Which switching devices in the VFD inverter stage generate the PWM output waveform?
Electrical Safety / OSHA Compliance
6. A technician is about to open a VFD enclosure after turning off the upstream disconnect. According to safe practice and OSHA 29 CFR 1910.147, what must be done before touching internal components?
Motor and Motor Controls
7. Increasing a VFD's carrier frequency from 4 kHz to 12 kHz will most likely:
Motor and Motor Controls
8. When a VFD operates a motor above its base speed (above 60 Hz on a standard motor), what happens to motor flux and maximum available torque?
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