6 Variable Frequency Drives Rev 4 100417

Chapter 6: Variable Frequency Drives Electrical Drives 0903582

Copyright held by the author 2010: Dr. Lutfi R. Al-Sharif Page 1 of 14

Chapter 6 Variable Frequency Drives (Revision 4.0, 17/4/2010)

1. Principle of Operation of Variable Frequency Drives As discussed earlier, the principle of operation of variable voltage AC drives, is that the rms value of the voltage is varied by varying the firing angle. This leads to a different speed-torque curve, and thus a variation in speed. This is summarised in Figure 1.

Speed torque characteristic at various voltages.

0

500

1000

1500

2000

2500

3000

3500

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

Speed (rpm)

Torq

ue (N

.m) V=100%

V=75%

V=50%

V=25%

Figure 1: Principle of speed regulation in variable voltage drives.

It is important to note that in variable voltage AC systems, the frequency is constant. If it is possible to vary the frequency of the voltage fed to the motor, then the synchronous speed is varied, and the whole of the speed torque curve moves accordingly. This is the principle of the variable frequency drives. The concept is summarised in Figure 2.



f 0f 1f 2f 3Torque

Speed

Figure 2: Principle of speed control in the variable frequency drives.

3f.2 Calculation of Torque in Variable Voltage Variable Frequency Systems In an ideal drive system driving a constant torque load, it should attempt to keep the torque constant throughout the speed range. This is what a variable voltage variable frequency drive does. In order to keep the torque constant, the ratio of voltage to frequency has to be kept constant. Thus, as lower speeds are needed, the frequency drops, and the voltage drops at the same time.

vf constant

However, before we discuss this concept any further, we need to be able to calculate the torque produced at any speed. The formula for torque in an induction motor, at a fixed frequency can be calculated as follows:

)1(..........3

2

21

2

21

2

2

NmXX

SRR

SRV

T synch



Where: V is the rms value of the voltage per phase; R1 is the primary resistance; R2 is the secondary resistance; X1 is the primary reactance at rated frequency; X2 is the secondary reactance at rated frequency; S is the slip; synch is the synchronous speed in rad/s. Using the above formula, for a 75kW motor single cage rotor, the torque can be calculated against speed. The result is shown in Figure 3. Note that within variable voltage variable frequency drives, a standard single cage rotor motor can be used, which is not the case with variable voltage AC drives.

Speed torque characteristic for a 75 kW SCIM motor

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700 800 900 1000

Speed (rpm)

Torq

ue (N

m)

Strating torque

Pull out torque

Rated torque

Figure 3: Speed torque curve for a 75kW motor.

Note also on the diagram, the three points highlighted: the starting torque point; the pull out torque (which the maximum torque the motor can produce) and the rated torque. This formula for calculating the torque can be used to calculate the values of torque at different frequencies. It is necessary to note the following:

As the frequency drops, the voltage drops by the same ratio, to keep the flux constant.

As the frequency drops, the value of the reactance drops by the same ratio. The value of resistance and the value of the number of poles remain

constant.



As the frequency drops, the synchronous speed drops by the same ratio. The slip is always calculated based on the value of the synchronous speed

for the specific frequency. 3f.3 Voltage to Frequency Ratio By using the method outlined in the last sub-section for deriving the torque value at different frequencies, and keeping the v/f ratio constant, several s-t curves can be derived. These are shown in Figure 4, for frequencies of 80%, 60%, 40% and 20% of the rated frequency 50Hz. Although the v/f ratio has been kept constant, the rated torque has dropped for the same slip.

Reduction of torque at low speeds

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700 800 900 1000

Speed (rpm)

Torq

ue (N

m)

Figure 4: Reduction of torque at low speed with a constant v to f ratio.

The reason for this is as follows. At slow speeds, keeping the v to f ratio constant is not sufficient to keep the torque constant. This is to do with the internal primary resistance within the motor model. To counteract this effect, the voltage needs to be boosted at low speed above the constant ratio level. This is best illustrated by an example. Example 1 A motion control system is to be driven at one quarter of its rated speed at inching. This is done by keeping the v/f ratio constant, using an induction motor fed from a variable voltage frequency inverter. Calculate the ratio of the torque at 25% speed to the torque at rated speed, and suggest the necessary voltage boost as a percentage.

The induction motor has a ratio of XR1

of 5.

Solution



By differentiating equation (1) against s, we can get the value of the maximum torque (pull-out torque):

T

pVR

f XR

Nmm

34

1 1

2

2

1

11

2

..........( )

At one quarter the rated speed, R1 is still the same value, X has one quarter the value (as the frequency is lower), the voltage is one quarter of its value at rated

speed, and XR1

is 1.25. Thus the ration of the torque at quarter speed to torque at

top speed is:

586.01.61

6.225.025.0

5114

3

25.11125.0425.0

32

2

1

2

2

1

2

%100

%25

fR

Vpf

RVp

TT

m

m

If the v/f ratio is kept constant, the pull-out torque achieved will only be 59% of the rated torque. Thus, the voltage has be more than just 0.25 of its value at rated speed. In fact it should be:

10 586

0 25 0 326.

. .

So, whereas the frequency should be reduced to 25% of its rated speed value, the voltage should only be reduced to 32.6% of its rated speed value. This is a necessary voltage boost to keep the maximum torque constant.

3. Block Diagram of a VVVF Inverter The basic sections of a variable voltage variable frequency drive are shown in Figure 5. The main components of such a drive are:

The rectifier (DC source). The DC link (for storage of charge). The inverter (to convert DC to AC).



M

DC Link

Rectifier Inverter

3 phase supply

Figure 5: Block diagram a VVVF system.

These three components will be discussed in more detail in the following sections. 4. Generation of DC The first section of any inverter is a rectifier section, which will provide a DC supply to the inverter. This is usually implemented by the use of a rectifier. Two types exist, and are discussed below. 4.1 Voltage Source Inverter (VSI) This type of inverter is sometimes called voltage fed inverter. It consists of a six diode uncontrolled rectifier, feeding a capacitor, which acts as a voltage charge. This is shown in Figure 6.

+

-

RST

AC Supply

To inverterV

Figure 6: Rectifier section of voltage fed inverter.

This can be modelled as a fixed voltage source in parallel of a capacitor, as shown in Figure 7.



+

-

V

+

-To inverterConstant

voltagesource

V

Figure 7: Model of voltage feeding section as a constant voltage source with a capacitor.

The VSI is the most widely used type with drives driving motors. 4.2 Current Source Inverter (CSI) This type is sometimes called a current fed inverter. It is composed of a half controlled three phase bridge rectifier, in series with an inductor.

RST

AC Supply

To inverter

I

Figure 8: Half controlled rectifier, in series with an inductor as a current source inverter feeder.

It can be modelled as a variable voltage source in series with an inductor. It

effectively forms a current source. It does not have any serious application in motor control, and is sometimes used when feeding resonant circuits for heating applications.



To inverter

I+

-

VVariableVoltageSource

Figure 9: Model of a current source inverter feeder, as a variable voltage source in series with

an inductor.

5. The Inverter Section The inverter section is made of six switches connected as shown in Figure 10. The switching sequence of transistors (in this case) would connect any of the three output lines to the motor to the positive rail or the negative rail. The transistor number sequence indicates the sequence of switching of the transistors.



U V W

+

-

+

-T

1

T4

T3

T6

T2

T5

VDC

VDC

Figure 10: Inverter section, using six bipolar transistors.

Two types of switching methods exist for the switching of the transistors:

Switching two transistors on at the same time out of the six transistors. Switching three transistors on at the same time out of the six transistors.

The phase and line voltages for both method of switching are shown in Figure 11 for the case of three transistors switching at the same time, and in Figure 12 for the case of two transistors switching on at the same time.



VAN

VBN

VCN

VAB

VBC

VCA

+VDC

-VDC

+2VDC

-2VDC

Figure 11: Phase and line waveforms for the system with three transistors conducting at the

same time.



VAN

VBN

VCN

VAB

+VDC

-VDC

+2VDC

-2VDC

Figure 12: Phase and line waveforms for the system with two transistors conducting at the

same time.

6 Pulse Width Modulation The waveforms produced in the large section are far from sinusoidal, and thus will induce currents which contain significant levels of harmonics. Harmonics do not produce any useful torque, and cause heating in the motor. Pulse width modulation is used to produce a voltage which will make the current nearer to a sinusoidal shape. 6.1 The triangulation method (sinusoidal modulation with natural sampling) The method is based on the concept of switching the voltage at a high rate. The inductance of the motor filters out the high switching, and a nearly sinusoidal current flows. The method of generating the waveform switching sequence is achieved by using a modulation method. A triangular waveform of a frequency higher than the required sinusoid is overlaid on the sinusoid. The ratio of the frequency of the triangular waveform to the frequency of the sinusoid is denoted as p.



At each intersection point between the triangular waveform and the sinusoidal waveform, the positive transistor of a specific phase is switched off, and the negative transistor is switched on. At the next intersection, the state is reversed, and the negative transistor is switched off and the positive transistor switched on.

Figure 13: Sinusoidal modulation with p=3.

Figure 13 shows an example for p=3. In order to reduce the ripple in the current and approach a better sinusoid, higher values of p are used. Another example for p=6 is shown in Figure 14. The limitation on the value of p is the switching speed of the switching devices and the switching losses.



Figure 14: Sinusoidal modulation with p=6.

This switched voltage, when imposed on the windings of the motor, causes a nearly sinusoidal waveform to flow. Although the switched voltage shown is only a phase voltage, and is not the actual waveform at the terminals of the motor winding, it can be used to show how the motor filters out the high frequencies in the waveform. Figure 15 shows an estimate of the current waveform for p=6. As the value of p is increased, the ripple in the current waveform is reduced.

Figure 15: Current waveform for p=6.

7 Practical applications of VF drives Due to the complexity of the processing required in VVVF systems, they are invariably implemented in digital format (using microprocessors, and even dedicated digital signal processing (DSP) integrated circuits). This is in sharp contrast to the variable voltage AC systems, which were mainly implemented in analogue op-amp technology. All systems are invariably implemented as Voltage Source Inverters (VSI). The use of IGBT (insulted gate bipolar transistor) allows higher switching frequencies which reduces the harmonic content of the voltage waveform to the motor.



Three distinct types of inverters exit: the standard pulse width modulation (PWM) inverter; the flux vector control (FVC) inverter and the so-called direct torque control (DTC).

The PWM attempts to feed a sinusoidal current to the motor by switching the output voltage on and off at a very high switching frequency. This inductance of the motor coupled with the high switching frequency results in a nearly sinusoidal current being fed to the motor.

The FVC system attempts to control the flux alignment of the rotor with that of the stator to achieve optimum interaction and thus indirectly control the torque. This is achieved by feeding back the position and the speed of the motor by the use of a shaft encoder fitted to the motor.

The DTC control is a new method which controls the torque directly.

References & Bibliography Lander, C.W., 1993, Power Electronics, Third Edition, McGraw Hill, 1993. Shepherd, W., Hulley, L.N. & Liang, D.T.W., 1995, Power electronics and motor

control, Second Edition, Cambridge University Press. Problems 1- By using equation (2), repeat example 1, and calculate the pull out torque when

the frequency is: (a) 30% of its rated value. (b) 5% of its rated value. 2- Sketch the gating waveform for the six transistors, shown in Figure 10, for the

two transistor conduction system and the for the three transistor conduction system.

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6 Variable Frequency Drives Rev 4 100417