0013 13 villamos hajtasok-en

7/30/2019 0013 13 Villamos Hajtasok-En

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Activities:

Draw the block diagrams of the transformations between the coordinate systems, a few

indicated parts of the speed control loop of self-controlled synchronous motors, the structure

of the resolver and its output signals, and a diagram showing the effect of the field weakening

in function of the velocity.They should note the content of the listed diagrams, the operating principle of the resolver up

to the determination of the angles, and the necessity and solution of field weakening in

permanent magnet synchronous motors.

As it could be seen earlier, in order to be able to provide a current vector control, conversions

between the coordinate systems and determination of the resultant vector of three-phase

currents, assumed as symmetric, are needed, in order that the three phase currents can be

characterised by one current vector value in any phase angle.

These operations must be done also inversely, in order that the three phase currents can be

obtained from the actual rotor angle position α, from the reference signals of the prescribed

currents id and iq, as well as from vector components ix and iy, obtained after the conversion.

The following series of operations (figure 1.) show transformation calculations required in

two directions. Operations done to determine currents ia, i b, ic from reference signals id-iq (or

voltages necessary for getting them through) are in figure 1., and in the other block diagram,

figure 2., the momentary current values d-iq to be determined from the measured signals of

currents ia, i b, ic can be seen as sequence of operations calculating current control signals.

Both calculations include

- conversions from an orthogonal to polar coordinate system,

- calculations of vectors shifted by three times 120 degrees from the orthogonal position

(Clark or Clark -1

transformations) for the individual stator coils,

- angle α of the angular motion and

- value υ p of the torque-angle

The first series of operations, supplemented by voltage signal outputs, is shown in figure

9.170 in the upper row, since it produces inverter voltage signals for the currents.

The second series of operations can be found lumped into one block at the bottom right part of

the control loop, it calculates quantities ide-iqe and the control signals for the longitudinal and

crosswise currents from the measured currents and through considering angular displacement

α s.

dq coordinates stem

standing coordinate system



Figure 1. Determination of the individual phase currents from actual demands of id-iq, using

them as reference signals

The second series of operations can be found lumped into one block at the bottom right part of

the control loop, it calculates quantities i de-iqe and the control signals for the longitudinal and

crosswise currents from the measured currents and through considering angular displacementα .

Figure 2. Generation of control signals from phase currents in order to determine actual values

id-iq

2. Sensing the angular displacement

Resolvers are often used for sensing the angular displacement since this instrument is of

absolute nature within one turn and its angular resolution basically depends on the accuracy

of the voltage measurements of sinusoidal and cosinusoidal output signals only. In robot

drives, the angular values reset from resolver output signals are needed for the internal

calculations of the robot, which is not necessary in vehicles, therefore less fine angular

resolution is sufficient here for the control of the motors. Robot drives require at least 16-bit

angular resolution, even if there are mechanical ratios resulting in further improvement. The

resolution has increased to 32 bits recently, approximately since 2000, due to the demands on

enhanced accuracy.

As it can be seen in figure 3. the voltage induced in two stator coils at 90 degrees to each

other changes according to the rotor angle position but the signal shapes of the voltage

induced in both coils are identical with that of the voltage carried to the rotor. In general,

supply through slip rings is alternating voltage with an effective value of 5 V and with a

frequency from 4 to 10 kHz. The voltage signal usually has a sinusoidal shape but another

periodical signal, for example, square waves can also be applied whose generation is simpler.

Figure 3. The principle of the resolver

dq coordinates stem

standing coordinate system



Since the two coils are at 90 degrees to each other, the voltage can be measured on the first

coil according to the sinusoidal function and on the second coil according to the cosinusoidal

function of angle α:

Uk1= U be K 1 sin α,

Uk2= U be K 2 cos α,

where coupling coefficient K is determined by measurement.

The voltage signals can be seen in figure 4. in function of the angle position α.

There are several methods to calculate the angle positions; the simplest way is to consider the

measured voltage as a value of a trigonometric function and to determine the angle using

inverse sinusoidal - cosinusoidal functions, then to perform the check according to the

identities of the trigonometric functions, since two independent function values are producedduring the measurement.

The resolver is an absolute measuring device until the first turn, however further turns 2π

must be counted so this is also an incremental device. Its noise immunity is high since the

voltage - time field of the individual output signals are not modified by needle-shaped signals.

It is insusceptible to changes in the speed and the power-supply voltage. Its disadvantage is

that the device, including signal processing, is expensive, therefore, angle determination has

been solved by means of incremental devices supplemented with Hall transmitters. In this

case two Hall transmitters provide the position of 90 degrees, thus, the signal processing is

supported by absolute, i.e., not incremental values.

Figure 4. The individual voltage signals in function of angle position α

Figures 5. show the factory test curves of the resolver.



Figure 5 a) The applied input signal

Figure 5 b) The shape of the output signal obtained for two full turns, at a speed of

20,000/minute.

Figure 5c.) The photograph of a resolver The outer diameter of the stator is approx. 25 mm.

3. Structure and block diagram of the regulation

In the case of high torques required for shorter time in vehicles and servo drives, operation υ p

= υ pom is more advantageous from an energetic point of view than the operation υ p = 90o, if

the difference between the inductivities is (Lq-Ld)> 0.2. In the case of minor differences theyhave no considerable effect.



On the basis of Figure 4 Lesson 2 it is clear that in relative quantities I=3 belongs to M = 3

beside υ p = 90o

(by this, I2

= 9). Beside υ p = υ pom, in the case of Lq-Ld = 0.2, the required

value of the current is only I = 2.68, and I2

≈7.18. At a difference of Lq-Ld = 0.4, I≈2.35,

since the square of the current is only I2

≈ 5.52, the latter enables a 40 % drop in the copper -

loss in the same coil, considering M = 3 that is it is a triplicate torque level.

Control υ p = υ pom, is more advantageous also for the inverter since it has lower current.The operation adjusted in this way will receive a signal with minimal current.

Figure 6 shows the general block scheme of a speed-controlled synchronous motor drive.

Figure 6 A control loop realising current vector control with modules for torque-angle

calculation on the left side.

The construction of the control loop enables to set the operation with a minimal current, that

is, calculations required for this, in other words, calculations for the position of the maximum

torque, depending also on the current and the calculation of the υ pom torque-angle obtained

therewith.

Ia absolute value of Ia’ output signal of SZW speed controller will be the reference signal for

the I amplitude of the current vector. Sziq transversal and szid longitudinal current regulators

are subordinated to the szω controller. Calculating unit υ po calculates torque-angle υ po,

providing minimum current, as well as sinυ po, cos υ po function values.The transversal and longitudinal current reference signals are calculated by multiplicators:

iqa=Ia sinυ po, and ida=Ia cos υ po.

Filters F1 and F2 removes the components corresponding to the carrier frequency of the

PWM control.

When measuring single phase currents it will be sufficient to measure any two of them, in this

case ia and ic, if the system can be considered a symmetric and three-phase system; in this

case the algebraic sum of the phase currents is zero and the difference between the two values

will be ic.



The lumped block of the coordinate transformations (d,q/a,b,c and a,b,c/d,q) contains the

series of blocks shown in figure...., as it was mentioned previously. This operation also needs

signal α of the rotor angular motion. The actual values of υ p are generated by the calculations

of the reference signal.

The figure includes a speed control loop, which is to be supplemented with the possibility to

specify α path set point to the position control of robots and a block for changing the open -loop gain and possibilities to limit signals.

In vehicle drives, which rarely run in a speed-controlled operation, the motor is not regulated

but controlled from the aspect of the reference signal. The loop in figure 9.170 changes as

follows:

- the feedback of speed signal is omitted,

- the SZW block, adjusting speed control behaviour, functions as a controller or limiter of

current or the running-up of the torque, other functions can remain unchanged, refer to

figure 7 The effect of the operation without feedback is sensed and assessed by the

controlling persons, who will form a judgement on the situation, similarly to handling theaccelerator of a car.

Figure 7 The principle of the current vector control for producing controlled torque values

without speed control function

If a vehicle is capable of a speed controlled operation, through realising this, the functions of

the original control loop will be reset.

For a thorough study and better understanding of this control a PMSM model is available in

the directory of MATALB Simulink showing also possible run-ups and modification changes

for the motor.

4 Extending velocity range, field weakening

As it has been explained in chapter 1.2, in order to extend the speed range, i.e., in the case of

motor variants applied to levels considerably above the nominal velocity, field weakening is

required in order to limit the internal voltage. The validity of voltage equation U

b = 4,44 f N Φ ξ



and it does not depend on the speed so the increase in the internal voltage is speed-

proportional and also above the achieved nominal design speed.

While the flux of an asynchronous motor begins to decrease under constant terminal voltage

at a increased speed range, the flux of the magnetic field generated by the permanent magnets

does not change in PM synchronous motors. Up to reaching the nominal velocity the terminalvoltage must be increased in proportion to the frequency i.e., in proportion to the speed if the

supply is intended to be performed by unchanged current.

If no reserves have been designed the current and the torque will decrease rapidly at a speed

above the nominal value but without further increase in the terminal voltage, the motor cannot

be used for an increase in velocity, only with a considerably decreased torque at the best.

In figure 8 the dashed line shows the changes in the power and the voltage in function of ω.

In the case of ωn nominal, the values of the flux and the torque are constant just as in

asynchronous motors. In a range above ωn, only the power can remain constant applying a

supply with constant voltage, on the other hand, the flux and the torque decrease in a

hyperbolic way, if this intention can be realised.

If we intend to increase the velocity considerably at the nominal value of the terminal voltage,

while I=const (refer to the upper line of the figure), the difference between the terminal and

internal voltage must be maintained also above ωn. However, the increase in the internal

voltage must be prevented for this to happen; applying any of the methods for reducing flux.

Figure 8 Possibilities and requirements of increasing velocity. The flux is marked with Ψ

(The labels in the above figure: constant torque, flux, constant power, field weakening)

This not an easy task, if the machine has been built up with permanent magnets. Flux

reduction has been realised in DC motors constructed with exciting coils since 1870 and it is

being applied even today for increasing velocity at a supply with specified voltage by

decreasing the current flowing in the coil:

ω = U b/k Φ,

according to which, reduction of flux until a limit deteriorating commutation and brush

discharge to a still tolerable extent will essentially increase speed. In the case of applying

permanent magnets their flux must be reduced using some applicable solution.



In general figure 2, lesson 2.(… 9.164) shows that the component id of the resultant vector of

the stator current of synchronous motors with current vector control is in the opposite

direction to the direction of Φ generated by the permanent magnets . The flux reducing effect

of this is low, since only the constituent with direction q takes part in torque generation, and,

if difference (Lq-Ld) is significant the deviation from 90 degrees will result in a considerable

surplus for the resultant torque.

On turning the current vector ahead, the value of id increases and the flux begins to decrease

considerably. Increasing velocities require varying adjustment with an increasing rate for

component id (figure 9), which can also be calculated analytically and can be tested by

calculations based on motor simulations.

Figure 9 Turning the current vector forward and further increase in υ p leads to the lengthening

of constituent id to the left, which reduces the effect of the main flux pointing to the right and

marked with ψ p1, from algebraic aspect.

Thus, field weakening must be realised in a speed range above the nominal value. At aterminal voltage, which can no longer be increased, υ p must be turned farther ahead, up to 150

to 160 degrees, so that component with id direction can increase and can reduce the flux

generated by the built-in permanent magnets in this way.

Thus, variability of υ p requires the extendibility of the current control, therefore it must be

already decided when designing the motor and the drive if an implicate increase in the

complexity of the system can return mainly in the decrease in the motor weight.

It must be noted that certain motor constructions with different magnet arrangements will give

various responses to the intended field weakening and to a remarkable turn of the current

vector. According to simulation tests, owing to the different magnetic resistances anddifferent inductivities, variants may give good or poor responses; in the different cases of

various arrangements of the buried magnets. Some of them may be suitable for an operation

with 300 % speed at nominal terminal voltage.

5. MATLAB model-tests for permanent magnet synchronous motor drives

In the newer MATLAB-Simulink programme-packages several permanent magnet

synchronous motor drive-model can be found, from which we examine the simulation tests of

an engine model with AC6 IPMSM signal, applied in today’s electric cars, having amaximum rpm of 12500/min and 100 kW power,



Main features of the model

The model also contains a current vector-control, suitable for field reduction. The longitudinal

and transversal inductivities of the synchronous motor are different, this makes the motor

suitable for building reluctance-moment.The mechanical system is substituted with first order lag element, which’s time constant can

be varied.

The output of the model effect skeleton - having originally moment-base sign – was changed

to speed-base sign. The results of this can be seen, after the ones, belonging to the original

version.

The drive consists of four main parts: engine, inverter, current-vector controller, speed control

circle

The electric motor is a PMSM motor with an inverter, fed by a 288 V DC circle,

having 100 kW power, with 8 poles and deep laid magnets, significant inductivity-

difference in order to establish reluctance moment. The three-phase voltage-inverter has PWM control, and uses the block of the

MATLAB universal bridge-model.

The current vector control controls to the minimum current at the nominal value of the

flux and - according to the reluctance moment formation - alters the angle position of

the current vector. By increasing the – d direction current component, applies reduction

of flux and field at speeds, higher, than the nominal.

Through changes, the speed control can be turned to moment control circle.

Introduction to the principal details of the MATLAB-Simulink programme of the model

In the following Figures the purpose of the main blocks of the programme will be looked over

Figure 1. shows the input sign of the drive, and the output sign-sources (with the diagram

typers), connected to the measuring system.

The drive is marked with AC6 sign. In the input side the DC voltage-source, substituting the

DC interim circle, the accelerating effect of the electric motor moment on the first order lag

element, symbolizing the driven system, and the time function of the speed-base sign.

The connected oscilloscopes make visible the time functions of the driving moment, the speed

and performance, as well as the alterations of the absolute, longitudinal and transversal values

of current- and voltage vectors.



Figure 1 Main figure of the drive model for synchronous motors with a permanent

magnet.

Moment set point of the original model got modified by a speed-dependent limitation, which

is indicated in Figure 2. Use of the speed or moment set point depends on the intended use of

the drive – position control of machine tools, robot, etc. – and position adjustments include

speed control with current or moment limitation.

Figure 2 Moment set point and its speed dependent limitation can be edited by opening themoment-limiting block. Data of the function-curve can be written in tabular form.



Vehicle drives essentially operate in moment-adjusted or moment value controlled mode with

optional speed limitation, incidence of the speed-controlled applications is lower. In this

model, edit of the speed-controlled or moment-adjusted feature can be performed after

opening the speed-control block shown in Figure 3.

Main units of the opened drive control are shown in Figure 3 below.

Figure 3 Main units of the opened drive control: inverter, speed controller that can be

edited to moment control, the controller of the current vector, and the synchronous motor

at bottom right.

By opening the speed control block the selectable control task and its limitations can be set,

see Figure 4.

Figure 4 Opened speed control block with the selectable control task and its adjustable

limitations. In the window, moment limit values of the original program’s moment control

circuit are shown. In the real process sampling time is set to 140 μs.



By opening the current control block (Figure 5), then opening the motor block, we can enter

or edit some important data of the motor. Ratio of longitudinal to transversal inductivity

values of the synchronous motor is apparently nearly two. Inverter can be adjusted up to 20

kHz switching frequency.

Figure 5: Original engine parameters of the synchronous motor joined to the circuit control

cycle are shown after opening the motor block

In case of speed-controlled feature, the model was equipped with a related set point

adjustment possibility (Figure 6). According to the task, to enable examination of changeover

to the braking operational mode, we specified an initial speed of 3000/min from t=0, then

1000/min from t=1s.



Figure 6 Setting up the speed set point in any detail is possible in tabulated form after opening

the speed set point block at the top left part of the figure.

Types of Model Run

In torque control mode and reduced mode the acceleration of the motor and the connectedsystem takes 2 s, during which period the prescribed torque values vary according to the

torque-speed function presented in the above figure 2.

The type of the acceleration process is defined by the time constant of the first-order lag

element set in this case to 2 s and the torque reduction function prescribed in relation with

acceleration. The time function graphs may be followed on the two graph drawers shown in

Figure 7.

Speed reaches the nominal 3000/min value within about 0,1 s due to low mass load, after

which a process of distinct field reduction may be observed in the variation of the linear and

cross current vector values.

By increasing the torque angle, and by rotating and advancing the resultant vector in relationto axis d, the decrease of the q direction component and the increase of the – d direction

component of the current vector of the same length are obtained.

Shortening of the q direction component results in torque reduction even though the flux

remains constant, but the increase of the – d component counteracts and reduces the flux

generated by permanent magnets. Thus, under the double effect, torque value is reduced, and

it presents the decreasing values of the torque graph shown on the upper left hand graph of

figure 7.

Figure 7: Time function figures of torque control mode: torque, speed, mechanical power output on the left. On the right, amplitude values of current vectors Id and Iq, with I as



resultant vector, marked with capitals in the programme, followed by amplitude values of the

voltage vectors ud and uq, marked with small letters, with u as the resultant vector.

The voltage component curves display a speed-proportional increase until nominal speed is

reached, which, in the above figure, represents an increase in speed becoming constant in time

due the approximately constant acceleration, therefore, the variation of the voltage curvewithin the initial 0-0.1 s field is represented by a straight line.

Speed is 10600/min at 0.75 s, i.e. more than three times higher than the nominal speed value,

nevertheless the engine power is practically constant, as shown in the figure below, reaching

about 100 kW. This value is obtained by the inversely proportional hyperbolic variation of the

speed increase, which does not maintain its hyperbolic character on the time function figure

due to the exponentially decreasing acceleration. Given the sustained increase of the number

of rotations, the tendency cannot be maintained, and it turns into a prolonged process of

torque reduction, indicated by the continuous decrease of the q direction component.

Chart 8. illustrates the first 0,1 s length phase of the starting process. Technically, the three- phase system that is produced by the engine driving inverter can be practically considered

symmetric; the algebraic sum of the current of the three coils is zero.

The current regulator seems to work well, since the values of the phase currents during the

acceleration are of the same amplitudes, in spite of that on increasing speeds the values of the

phase voltages on the coils increase respectively and the angular position according to the

calculated momentum angle of the resultant current is handled with higher priority than the

rotor’s d axis rotation from the vertical symmetry axis of the stator.

Chart 8. The time functions of the phase currents under the start in the first 0,1 s. The chart is part of chart 12, on which the starting currents are significantly greater than those in chart 7.

The two statuses with different momentum differ only in their current values.

We can realize speed control by rewriting the controlling task, by typing the data accordant to

chart 6. According to these the speed-reference signal is 3000/min in the beginning and

starting from the end of 1 s it is -1000/min, that contains an intense acceleration then an

intensive slowdown at shifting, which latter aims to achieve -1000/min with opposite

direction acceleration.

The running results can be seen in chart 9. To the left/center we can see the realized speed-

time function in the model. Its nearly linear entering/leaving sections can be achieved by

nearly constant accelerating-braking momentum.



On its mechanical performance curve we can see that the performance of the traversing curve

on zero speed is zero as well.

Considering the speed’s specified, nominal value of 3000/min, no field reduction will occur.

Figure 9. Current vector speed control mode without field reduction

In Figure 10, the time functions of phase currents led in the stator-coil are shown, closely

tracing the change character of current vectors I d and Iq.

Figure 10. Time functions of phase currents led in the stator-coils

In Figure 11, the change in current direction at t=1.3s allowing a counter-rotating speed-up

may be observed. The generator brake operation lasted until zero speed, from where the motor



operation that was able to exert a counter-rotating torque begun. At a speed of 1000/min,

torque will drop to a level close to idle condition.

Figure 11. Polarity reversal when switching from generator braking to inverse motor

operation.

If being proportional to the moment of inertia, the time constant of the mechanical system

coupled to the axle is increased from 2s to 6.5s, then the speed control will nearly

proportionally increase the stator current and so the moment of inertia to keep acceleration

time from any increase. Details are shown in Figure 12.

Figure 12. An increase in the mechanical time constant will result in an increase in moment,

current, and voltage to keep the start-up and braking period from any increase.

The increase of phase current amplitudes are shown in Figures 12 and 13.



Figure 12. To keep the period of an acceleration process unchanged, the mechanical time constantand so the driving moment may be increased against an increase in related phase currents.

Phase current curves of the start are shown in Figure 8. Details of the change in sign of the

speed at t=1.3s are magnified.

occurring at t = 1.3 seconds, upon changing from generator-driven breaking to engine-drive

mode with a reversed sign of velocity, takes place in a way similar to the previous case, yet

current values are higher.

Details of deceleration breaking followed by reversal are shown on Figure 14. The condition

prior to breaking is close to idle run, with a near zero Id value, the value of the I current vector

resulting in effect from the Iq component.

During breaking, while in generator-driven mode, the high value negative moment is

determined by the Iq component, carrying a negative sign. Component Id is nearly equal to

that seen in engine-drive mode, referring to Figure 12.

Looking at voltage, the value of terminal voltage – assigned with a capital V in the application – is near zero at a velocity of zero, increasing in proportion to the gain in velocity with the



opposite sign. The tendency of the voltage component required for cross current supply

remains constant, as rotation was reversed at t=1.3 seconds, causing the sign inversion

vectors.

After reaching a velocity of 1000/min, in almost idle run, the sign of current- and voltage

components, as well vectors have changed altogether in respect of the reversed sense of rotation, relative to the ones seen in the previous, 3000/min velocity idle run state.

Figure 14. Detailed presentation of Figure 12. in the area of reversal

0013 13 villamos hajtasok-en

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