Sascha Stegen

School of Electrical Engineering,

Griffith University, Australia

Electrical Machines and Drives

Motors

Generators

Power Electronics and Drives

Open-loop inverter-fed

General arrangement of speed-controlled drive

General arrangement of inverter-fed variable-frequency induction motor speed-controlled drive.

Most low and medium power inverters use MOSFET or IGBT devices, and may modulate at ultrasonic frequencies, which naturally result in relatively quiet operation.

The majority of inverters are 3-phase input and 3-phase output.

Single-phase input versions are available up to about 5 kW, and some very small inverters (usually less than 1 kW) are specifically intended for use with single-phase motors.

Torque–speed curves for inverter-fed induction motor with constant voltage–frequency ratio

Typical torque–speed curves for inverter-fed induction motor with low-speed voltage boost, constant voltage–frequency ratio from low speed up to base speed, and constant voltage above base speed.

Constant torque, constant power and high-speed motoring regions

If the magnitude of the flux wave in an induction: ◦ motor is kept constant, the torque in the normal

operating region is directly proportional to the slip speed. (We should recall that ‘normal operating region’ means low values of slip, typically a few per cent of synchronous speed.)

◦ So the parameter that must be controlled in order to

control torque is the slip speed. But the only variable that we can directly vary is the stator frequency (and hence the synchronous speed); and the only variable we can measure externally is the actual rotor speed.

These three quantities (see Figure ) are represented by the following analogue voltages:

Schematic diagram of closed-loop inverter-fed induction motor speed controlled drive with tacho feedback.

Schematic diagram of speed-controlled d.c. motor drive.

The current at the end of each pulse is the same as at the beginning, so it follows that the average voltage across the armature inductance (L) is zero.

We can therefore equate the average applied voltage to the sum of the back emf (assumed pure DC because we are ignoring speed fluctuations) and the average voltage across the armature resistance, to yield

which is exactly the same as for operation from a pure DC supply.

This is very important, as it underlines the fact that we can control the mean motor voltage, and hence the speed, simply by varying the converter delay angle.

Armature voltage (a) and armature current (b) waveforms for continuous current operation of a DC motor supplied from a single-phase fully-controlled thyristor converter, with firing angle of 60deg.

Steady-state torque–speed curve for a synchronous motor supplied at constant frequency

Equivalent circuit for synchronous machine

Self-synchronous motor–inverter system. In large sizes this arrangement is sometimes referred to as a ‘synchdrive’; in smaller sizes it would be known as a brushless DC motor drive.

Open-loop inverter-fed synchronous motor drives

Scheme of a cross section for a 6/4 switched reluctance machine

Driver scheme for a 6/4 switched reluctance machine

pulse width modulation (PWM) (Chopper)

the efficiency is close to 100%

There are several switching components on the market:

Bipolar junction transistor (BJT),

Metal oxide semiconductor field effect

transistor (MOSFET), Insulated gate bipolar

transistor (IGBT).

BJT, on/off-state

Circuit symbols for self-commutating devices ◦ Bipolar junction transistor (BJT)

◦ Metal oxide semiconductor field effect transistor (MOSFET)

◦ Insulated gate bipolar transistor (IGBT)

◦ Gate turn-off thyristor (GTO)

http://www.ewh.ieee.org/soc/es/May2001/02/Begin.htm

http://what-when-how.com/permanent-magnet-motor/brushless-

motors-of-special-construction-permanent-magnet-motor/

When an inductance L carries a current I, the energy stored in the magnetic field (W) is given by

The voltage and current in an inductance are related by the equation

Chopper with a freewheel diode

When the transistor is on, current (I) flows through the load, but not through the diode, which is said to be reverse-biased.

When the transistor is turned on, the current through it and the battery drops very quickly to zero. But the stored energy in the inductance means that its current cannot suddenly disappear.

So, since there is no longer a path through the transistor, the current diverts into the only other route available, and flows upwards through the low-resistance path offered by the diode, as shown in Figure (b).

How is the output voltage controlled?

What does the converter output voltage look like?

Will there be any problem if the voltage is not pure DC?

How does the range of the output voltage relate to AC mains voltage?

Thyristor

Single-pulse rectifier

As soon as a firing pulse is delivered to the gate-

cathode circuit the device turns on, the voltage

across it falls to near zero, and the load voltage

becomes equal to the supply voltage.

When the supply voltage reaches zero, so does

the current. At this point the thyristor regains its

blocking ability, and no current flows during the negative half-cycle.

The conventional way of drawing the circuit

Redrawn circuit to assist understanding

The load voltage therefore consists of rectified chunks of the mains voltage. It is much smoother than in the single-pulse circuit, though again it is far from pure DC

◦ Output voltage waveforms of single-phase fully-controlled rectifier

with resistive load, for firing angle delays of 45deg. and 135deg.

The maximum output voltage (Vdo) is obtained with α=0 degree.

The thyristor can be seen as a diode, so the forward voltage can be calculated with:

where Vrms is the rms (root mean square) voltage.

The variation of the mean DC voltage with α is given by

with a resistive load the DC voltage can be varied from a maximum of Vdo down to zero by varying a from 0 degree to 180 degree.

Motor loads are inductive, and we have seen earlier that the current cannot change instantaneously in an inductive load.

We must therefore expect the behaviour of the converter with an inductive load to differ from that with a resistive load, in which the current can change instantaneously.

Firing angle delays of 15

degree

Firing angle delays of 60

degree

The main DC voltage is now related to the angel α by

This equation indicates that we can control the mean output voltage by controlling α, though this equation shows that the variation of mean voltage with α is different from that for a resistive load.

a resistive load

Single-phase inverter ◦ Inverter circuit for single-phase output.

◦ Inverter output voltage waveforms – resistive load

Inverter output voltage and frequency control with pulse-width modulation

Forward motoring in quadrant 1

Forward braking in quadrant 2

Reverse motoring in quadrant 3

Reverse braking quadrant 4

Caution! Sometimes the quadrants are counterclockwise

http://www.globalspec.com/reference/42927/203279/four-quadrant-

operation-and-regenerative-braking

http://www.lme.ntua.gr/ele_dynamometer.html

http://www.lme.ntua.gr/ele_dynamometer.html

𝑉𝑎 = 𝛿V

𝐼𝑎 =𝛿V − 𝐸

𝑅𝑎

Motoring operation:

Regenerative operation:

Non-load operation:

𝑉𝑎 = 𝛿V 𝐼𝑎 =𝛿V − 𝐸

𝑅𝑎

𝛿 = (𝐸/V)

𝛿 < (𝐸/V)

𝛿 > (𝐸/V)

The conventional way of drawing the circuit

Redrawn circuit to assist understanding

Three-phase inverter power circuit

Returning to the six-pulse converter, the mean output voltage can be shown to be given by

We note that we can obtain the full range of output voltages from +Vdo to -Vdo, so that, as with the single-phase converter, regenerative operation will be possible.

The Magneto resistive forces (mmfs), are produced by the phase currents

𝐹𝑎𝑠 = 𝐹𝑎𝑠 sin𝜔𝑡

𝐹𝑏𝑠 = 𝐹𝑏𝑠 sin(𝜔𝑡 − 120°)

𝐹𝑐𝑠 = 𝐹𝑐𝑠 sin(𝜔𝑡 − 240°)

For identical magnitudes of the three phase mmfs, the overall force can be expressed as:

The stator mmf vector is:

𝐹𝑠𝑠 =

3

2𝐹𝑎𝑠

𝑠

𝑒(𝜔𝑡−9𝑜°)

𝐹𝑠𝑠 = 𝐹𝑎𝑠

𝑠𝑒𝑗𝑜°+𝐹𝑏𝑠𝑠𝑒𝑗120°+𝐹𝑐𝑠

𝑠𝑒𝑗24𝑜°

𝑅′𝑟 = 𝑅𝑟𝑎𝑇12

𝑋′𝑟 = 𝑋𝑟𝑎𝑇12

𝑍𝑠 = 𝑅𝑠 + 𝑗𝐿𝑠𝜔

𝑍𝑚 = 𝑗𝐿𝑚𝜔

𝑍𝑟 =𝑅′𝑟𝑠

+ 𝑗𝐿𝑟𝜔

𝑍 = 𝑍𝑠 +𝑍𝑚𝑍𝑟

𝑍𝑚 + 𝑍𝑟

𝐼𝑠 =𝑉

𝑍

𝐼′𝑟 =𝑍𝑚

𝑍𝑚 + 𝑍𝑟𝐼𝑠

𝑃𝑒𝑙𝑒𝑐 = 3𝐼′𝑟2𝑅′𝑟𝑠

𝑃𝑚𝑒𝑐ℎ = 𝑃𝑒𝑙𝑒𝑐 − 3𝐼′𝑟2𝑅′𝑟

𝜔𝑚 = 𝜔(1 − 𝑠)2

𝑃

𝑇 =𝑃𝑚𝑒𝑐ℎ

𝜔𝑚

http://www.online-

engineering.biz/uploads/pics/Antriebssimulation_01.jpg

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J. L. Kirtley, “Electric Power Principles”, Wiley, 2010, T. Wildi, Electrical Machines, Drives, and Power

Systems, Fourth Edition, Prentice Hall, 2000 Austin Hughes, “Electric Motors and Drives -

Fundamentals, Types and Applications,” Elsevier www.wikipedia.de http://www.patchn.com C. C. Chan, “The state of the art of electric, hybrid

vehicles, and Fuel Cell Vehicles,” Proc. IEEE, 2010 http://www.moeller.net Modern Electric, Hybrid Electric, and Fuel Cell Vehicles:

Fundamentals, Theory, and Design, ISBN-13: 978-1420053982