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Variable-Speed Drives by the Numbers

Semiconductors, losses, cooling, life, motors, fans, braking, harmonics and maintenance for the drives that run a factory

How variable-speed drives control induction motors and how to size, cool, apply and maintain them with numbers: switch physics, losses, junction temperature, energy savings and life.

10 chapters · About 100 minutes · Free to read · Intermediate engineering and maintenance

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About this book

Most of the electricity a factory buys is turned into motion by induction motors, and more and more of those motors are fed through variable-speed drives. A drive lets a fan run at the airflow the process needs instead of fighting a damper, lets a conveyor start gently and match its feed to the machine it serves, and lets a pump deliver the flow without a throttling valve. It does this by switching hundreds of volts on and off thousands of times a second in semiconductor devices smaller than a coin, and those devices, their losses, their heat and their ageing decide whether the drive does its job for fifteen years or fails in two.

This book explains drives from the semiconductor up and the machine down. It starts with what a drive does to a motor, then explains how its diodes and transistors block voltage and carry current, where their losses come from, how hot they get and how long they last. It then turns to the machines: the motor at low and high speed, the energy saved on fans and pumps, starting, stopping and braking, harmonics, earth leakage and interference, and finally how to specify, commission and maintain a drive.

It is for mechanical, electrical and maintenance engineers, technicians and plant managers. It assumes engineering or trade training and comfort with power, torque and simple algebra; the semiconductor physics is explained as it is used. Each chapter works the running case with real numbers, includes one plausible mistake and how it was found, links the KEVOS® tools that do the chapter’s calculations, and ends with an exercise and its worked answer.

The running case

Every chapter follows one drive panel. This is an illustration. A plastics recycler in Albury, New South Wales, shreds, washes and granulates used plastic containers into flake for re-use. Its wash line has a drive panel, called DP-4 in this book, feeding three motors:

F-1: the dust and vapour extraction fan for the granulators and wash tanks, a 30 kW, 4-pole, 400 V, 50 Hz induction motor rated at 1,475 rpm, belt-driven. Before the drive it ran at full speed with an outlet damper partly closed.
P-3: the cooling-water pump for the extruder and the granulator bearings, a 22 kW, 2-pole motor rated at 2,950 rpm, sending water up to a cooling tower on the roof.
C-2: the infeed belt conveyor to the shredder, a 7.5 kW, 4-pole geared motor whose speed sets the shredder’s feed rate.

DP-4 holds three drives of matching rating, each with a six-pulse diode rectifier, a DC link of electrolytic capacitors and a three-phase inverter of insulated-gate bipolar transistors (IGBTs) and diodes switching at 4 kHz, in a ventilated steel cabinet in the wash hall, which is warm, humid and dusty with plastic fines.

Ratings, losses, temperatures, prices and failure records are the plant’s working figures or are calculated from stated assumptions. They do not describe KEVOS® work or any real business, drive maker, motor maker or supplier. Prices are in Australian dollars excluding GST, because a GST-registered business claims the GST back on its costs.

How to use the book

Chapters 1 to 5 are about the drive itself, and Chapters 6 to 10 about applying and keeping it. Read Chapter 1 first; the others stand on their own once the case is familiar. Each chapter links the KEVOS® calculators it uses. The tools do the arithmetic; the chapter explains what the inputs mean and where they come from. Every result in the text was checked by calculation, and the numbers in figures match the text.

Limits and responsibility

This book is educational. Drives operate at lethal voltages and store energy in their capacitors after they are switched off. Installation, wiring, protection and maintenance must be carried out by licensed electrical workers to the wiring rules, the drive maker’s instructions and the applicable Australian requirements. Machine safety functions that depend on a drive must be designed and validated by competent people. Standards are named by number and scope only. Datasheet values, losses and costs in the case are illustrations; use the manufacturer’s documents and measured data for real work.

Who this book is for

Mechanical, electrical and maintenance engineers, technicians and plant managers who specify, install, set up, troubleshoot or pay for variable-speed drives on fans, pumps, conveyors and other factory machines.

What you will learn

Explain how a drive's rectifier, DC link and inverter control an induction motor's speed, and how its semiconductor switches block voltage and conduct current.
Estimate a drive's conduction and switching losses, junction temperature and cabinet cooling, and find the cause of an overheating drive.
Estimate the life of a drive's capacitors, fans and power modules, and plan maintenance and spares from it.
Apply drives to fans, pumps and conveyors with the right torque, cooling and speed range, and check the energy saving and the business case.
Set ramps and braking, and deal with harmonics, earth leakage, cable effects and electromagnetic compatibility in a real installation.

Inside this book

Chapters

01What a drive does to an induction motorHow an induction motor's speed follows supply frequency, how a drive's rectifier, DC link and PWM inverter make a variable frequency and voltage, and how to read motor load on and off a drive.

Figure 2Intrinsic carrier density in silicon, and so junction leakage, relative to 25 °C

Junction temperature	Ratio to 25 °C	What it means
25 °C	1	Close to 10¹⁰ carriers per cm³; negligible leakage
75 °C	36.5	A warm drive at part load
125 °C	563	Typical full-load junction temperature in a well-cooled drive
150 °C	1,760	Common maximum continuous rating for silicon IGBTs
175 °C	4,870	Highest rating of modern silicon modules

This is an illustration from the standard expression, with silicon's bandgap narrowing with temperature. The ratio doubles about every 15 K near 125 °C.

Diodes, IGBTs and wide-bandgap switchesHow power diodes, MOSFETs and IGBTs block voltage and carry current, why breakdown, leakage and resistance depend on the semiconductor and temperature, and why silicon carbide is replacing silicon.

Figure 2DP-4 DC link capacitor life from the 105 °C endurance rating, from the Arrhenius acceleration check tool

Core temperature	Acceleration factor	Equivalent service life	10 K rule	Against 90,000 h
55 °C, yearly average	48.47	242,353 h	160,000 h	COVERS TARGET LIFE
65 °C, summer worst	20.35	101,737 h	80,000 h	COVERS TARGET LIFE by the tool; not by the 10 K rule

This is an illustration. E_a = 0.83 eV; endurance 5,000 h at 105 °C; target 90,000 h, fifteen years at the plant's 6,000 running hours a year. The tool's sensitivity table shows the factor at 55 °C ranging from 19.0 at 0.63 eV to 123.5 at 1.03 eV: the activation energy dominates the answer.

Drive life: capacitors, fans and power cyclingHow temperature sets the life of a drive's DC link capacitors and cooling fans, how power cycling wears out power modules, and how to combine the parts into a drive reliability and a maintenance plan.

Figure 1Load torque and a self-cooled motor's continuous torque against speed, per unit of rated

Torque, per unit of rated motor torqueSpeed, % of rated

Load torque and a self-cooled motor's continuous torque against speed, per unit of rated data
Speed, % of rated	Torque, per unit of rated motor torque
20	0.62	0.03	1.42
40	0.70	0.12	0.75
60	0.85	0.26	0.52
80	0.95	0.46	0.41
100	1.00	0.72	0.34

This is an illustration. The motor's continuous torque limit for a standard totally enclosed, fan-cooled motor on a drive, assumed from typical maker curves: 0.55 at 10%, 0.70 at 40%, 0.85 at 60%, 0.95 at 80% and 1.0 at rated speed. A fan's torque, here 0.72 at rated speed, falls with the square of speed; the conveyor's, worked from the conveyor tool's formula with the feeder at 45 t/h, rises at low speed because material piles up on the slower belt: at 20% speed it would exceed rated torque.

The motor at low and high speedHow load torque changes with speed for conveyors, fans and pumps, why a self-cooled motor overheats at low speed under constant torque, and what field weakening gives above rated speed.

Figure 2The supply current of F-1's motor, on the mains and on the drive, at full load

Supply	Real power	Displacement power factor	Current distortion	True power factor	Supply current
Motor direct on the mains	32.05 kW	0.86	negligible	0.86	53.8 A
Drive with DC choke	32.61 kW	0.98	38%	0.916	51.4 A
Drive without choke, typical	32.61 kW	0.97	about 108%	about 0.66	about 71 A

This is an illustration. Harmonic shares with the choke from the drive's data; without a choke, typical shares of 80%, 65%, 25% and 18% at the 5th, 7th, 11th and 13th. The motor on the drive still draws its magnetising current, but from the DC link, not from the supply.

Harmonics, power factor, cables and interferenceHow a drive's rectifier draws harmonic current, true and displacement power factor, how fast switching stresses cables, insulation and bearings, and how screening controls interference.

Figure 1DP-4's drive specifications in brief

Item	F-1 extraction fan	P-3 cooling-water pump	C-2 infeed conveyor
Motor	30 kW, 4-pole, 53.8 A	22 kW, 2-pole, 38.8 A	7.5 kW, 4-pole geared, 14.5 A
Load type	Variable torque	Variable torque with 8 m static head	Constant torque, rising at low speed
Duty rating	Normal duty, 110% for 60 s	Normal duty	Heavy duty, 150% for 60 s, vector control
Speed range	25 to 50 Hz	30 to 50 Hz, minimum set by the lift	10 to 60 Hz, forced-ventilated motor
Stopping	Coast	Ramp, 30 s	Ramp with backstop; no braking needed uphill
Cable and filter	45 m screened, dv/dt filter	30 m screened	20 m screened
Control	Duct pressure, 4–20 mA	Return water temperature	Shredder current, fieldbus

This is an illustration. Each line traces to a chapter: duty and speed range to Chapters 6 and 7, stopping to Chapter 8, cable and filter to Chapter 9. All three drives: 400 V supply, DC choke, EMC category for an industrial site, safe torque off, rated for 45 °C ambient at the chosen switching frequency.

Specifying, commissioning and maintaining drivesHow to write a drive specification from the load and the site, commission a drive step by step, record its settings, plan spares across a fleet, and keep its set-up on replacement.

Apply This in Practice

Use these KEVOS® tools to try the method from this reading with your own numbers.

Applies this method
Arrhenius Acceleration Check (Temperature Acceleration Factor, Equivalent Hours, Test Length)
Turns a DC link capacitor's 105 °C endurance rating into an estimated service life at the cabinet's core temperatures, with the sensitivity to activation energy.
Used in Drive life: capacitors, fans and power cycling
Open the calculator
Applies this method
Belt Conveyor Drive Sizing
Works out an inclined belt conveyor's tension, pulley power and torque at full and reduced belt speed, showing the motor torque rising as material piles up at low speed.
Used in The motor at low and high speed
Open the calculator
Applies this method
Critical Spares Plan (Poisson Failures over the Lead Time, Spares for a Service Level)
Decides how many spare drives to hold for a fleet of 14 drives from their random failure rate, running hours, lead time and a 99% cover target.
Used in Specifying, commissioning and maintaining drives
Open the calculator
Applies this method
Enclosure Cooling Airflow (Heat Load, Wall Losses, Fan Airflow Needed)
Sizes the filter-fan airflow for a cabinet of three variable-speed drives in a warm, dusty hall, and shows how loaded filters or through-panel heatsinks change it.
Used in Junction temperature and cabinet cooling
Open the calculator
Applies this method
Equipment Investment Appraisal (NPV, IRR, Payback, B/C, EUAC)
Appraises variable-speed drives on a fan and a pump from their measured energy savings: NPV, IRR and payback over a 12-year life.
Used in Fans, pumps and energy savings
Open the calculator
Applies this method
Fan Duty, Fan Laws and Belt Drive
Applies the fan laws to slow an extraction fan from damper control to the airflow needed, giving the new speed, pressure and shaft power saved.
Used in Fans, pumps and energy savings
Open the calculator
Applies this method
Induction Motor Load Assessment (Current, Slip, Load, Energy)
Estimates a cooling-water pump motor's load, output, input and yearly energy cost from its measured speed before a variable-speed drive was fitted.
Used in Fans, pumps and energy savings
Open the calculator
Applies this method
Induction Motor Synchronous Speed, Slip and Load
Estimates an induction motor's load from its measured speed and rated slip on the mains, used to find a damper-controlled fan's load before its drive was fitted.
Used in What a drive does to an induction motor
Open the calculator
Applies this method
Pump and Fan Affinity Laws
Gives the affinity-law flow, head and power at reduced pump speed, shown to overstate the saving on a system with static head.
Used in Fans, pumps and energy savings
Open the calculator
Applies this method
Pump Operating Point on the System Curve
Finds a cooling-water pump's operating point and the speed needed for a reduced flow on a system with an 8 m static lift to a cooling tower.
Used in Fans, pumps and energy savings
Open the calculator
Applies this method
RMS Torque for a Motor Duty Cycle
Checks a conveyor motor's RMS torque over a slow and fast duty cycle, and shows why a torque-only check misses a self-cooled motor's heating at low speed.
Used in The motor at low and high speed
Open the calculator
Applies this method
Rotor Run-Up Time (Inertia, Acceleration Time, Start Energy)
Works out a high-inertia fan's run-up time, stored energy and rotor heating for a direct-on-line start, and its run-up time at a drive's current limit.
Used in Starting, stopping and braking
Open the calculator
Applies this method
System Reliability from Weibull Components (Series and Redundancy)
Combines a drive's capacitors, fan and electronics as Weibull blocks in series to find its reliability over five and ten years and its weakest part.
Used in Drive life: capacitors, fans and power cycling
Open the calculator
Applies this method
Three-Phase Motor Power, Current and Torque
Gives a three-phase motor's rated line current, input power, torque and apparent power from its nameplate, compared later with the supply current of its drive.
Used in What a drive does to an induction motor
Open the calculator
Applies this method
Weibull Reliability and B10 Life
Gives a drive cooling fan's reliability and hazard rate at five and ten years from its L10 life with a wear-out Weibull model, supporting planned fan replacement.
Used in Drive life: capacitors, fans and power cycling
Open the calculator

References and source notes

The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 1 November 2026.

J. Singh, Cambridge University Press. Electronic and Optoelectronic Properties of Semiconductor Structures (2003). Copyright work, used only as a map of ideas: doping, intrinsic carrier density and its temperature dependence, carrier mobility and its limitation by lattice scattering, impact ionisation and avalanche breakdown, minority-carrier injection and recombination. No text, equations as set out there, figures or problems are reproduced, and all cases and calculations are KEVOS® originals.
A. Wintrich, U. Nicolai, W. Tursky and T. Reimann, SEMIKRON International. Application Manual Power Semiconductors, second edition (2015). Background for the loss and thermal models of IGBT and diode modules in Chapters 2 to 5: conduction losses from threshold voltage and slope resistance, switching energies scaled with current and voltage, and thermal resistance chains.
B. J. Baliga, Springer. Fundamentals of Power Semiconductor Devices (2008). Background for the ideal drift region, its breakdown voltage and specific on-resistance, and the comparison of silicon and silicon carbide in Chapter 2.
A. Hughes and B. Drury, Newnes. Electric Motors and Drives: Fundamentals, Types and Applications, fifth edition (2019). Background for induction motor operation on a drive, constant flux and field weakening, motor cooling at low speed and braking in Chapters 1, 6 and 8.
Commonwealth of Australia, Federal Register of Legislation, based on Safe Work Australia's model code. Work Health and Safety (Managing Electrical Risks in the Workplace) Code of Practice 2015 (2015). Named in Chapters 1 and 10 for the duty to manage electrical risks, including isolation and the stored energy in a drive's DC link capacitors. Work in New South Wales follows the code of practice approved there; check the current version with the state regulator.

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