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128<br />

J. Anuszczyk, M. Jabłoński<br />

1. INTRODUCTION<br />

At present the majority <strong>of</strong> all the eng<strong>in</strong>eer<strong>in</strong>g mach<strong>in</strong>es are equipped with<br />

drive systems conta<strong>in</strong><strong>in</strong>g <strong><strong>in</strong>duction</strong> <strong>motor</strong>s. It happens so, due to the<br />

adv<strong>an</strong>tages <strong>of</strong> the <strong><strong>in</strong>duction</strong> <strong>motor</strong> itself, as well as th<strong>an</strong>ks to the application <strong>of</strong><br />

the most modern drive systems controlled with the help <strong>of</strong> signal processors<br />

<strong>an</strong>d modern steer<strong>in</strong>g algorithms. These algorithms allow very precise regulation<br />

<strong>of</strong> the rotat<strong>in</strong>g speed <strong>an</strong>d the driv<strong>in</strong>g moment. The application <strong>of</strong> the newest<br />

methods <strong>of</strong> steer<strong>in</strong>g, based on the <strong>field</strong>-<strong>oriented</strong> <strong>motor</strong> description (Fig. 1),<br />

enforces the need <strong>of</strong> know<strong>in</strong>g the parameters <strong>of</strong> the equivalent <strong><strong>in</strong>duction</strong> <strong>motor</strong><br />

scheme. In the realization <strong>of</strong> steer<strong>in</strong>g algorithms, vector control captures its<br />

strategy on the dynamic states <strong>of</strong> the whole drive system, where ma<strong>in</strong>ly control<br />

signals <strong>an</strong>d the signals from closed-loop c<strong>an</strong> be improved by the choice <strong>of</strong><br />

shorter times for computational cycles. These methods at present are st<strong>an</strong>dard<br />

<strong>in</strong> the sphere <strong>of</strong> electrical drives with speed regulation for <strong><strong>in</strong>duction</strong> <strong>motor</strong>s <strong>an</strong>d<br />

are characterized with better reaction <strong>of</strong> the steer<strong>in</strong>g object to the ch<strong>an</strong>ge <strong>of</strong> the<br />

set value <strong>an</strong>d lower powers, start<strong>in</strong>g torques <strong>an</strong>d currents <strong>in</strong> comparison to<br />

scalar algorithms – Fig. 1.<br />

The development <strong>of</strong> digital electronics <strong>an</strong>d energy-electronics also enabled<br />

the implementation <strong>of</strong> the newest methods <strong>of</strong> parameters identification. It has<br />

given rise to the application <strong>of</strong> the new algorithms, which allowed also the<br />

eng<strong>in</strong>eers <strong>an</strong>d researchers to def<strong>in</strong>e the required <strong>motor</strong> parameters, tun<strong>in</strong>g<br />

controllers <strong>an</strong>d the diagnostics <strong>of</strong> the whole steer<strong>in</strong>g system. The drives <strong>in</strong><br />

practice, work <strong>in</strong> frequently ch<strong>an</strong>g<strong>in</strong>g electromech<strong>an</strong>ical conditions, both from<br />

the side <strong>of</strong> load <strong>an</strong>d supply. Higher technical requirements are put aga<strong>in</strong>st these<br />

systems <strong>in</strong> the <strong>field</strong> <strong>of</strong> dynamics <strong>an</strong>d efficiency. In the stage <strong>of</strong> design<strong>in</strong>g it is<br />

therefore necessary to take <strong>in</strong>to account the dynamic characteristics, a useful<br />

tool <strong>in</strong> that area is model<strong>in</strong>g study <strong>an</strong>d simulation <strong>of</strong> the tr<strong>an</strong>sient<br />

electromagnetic processes. Nowadays drives give us completely new<br />

possibilities <strong>of</strong> <strong>an</strong>alysis <strong>of</strong> parameters <strong>an</strong>d dynamic states <strong>of</strong> the <strong>in</strong>vestigated<br />

<strong><strong>in</strong>duction</strong> <strong>motor</strong>s cooperat<strong>in</strong>g with the <strong>in</strong>verter drive system: U/f (scalar), VC<br />

(vector control) <strong>an</strong>d DTC (direct torque control), [4], [6].<br />

PROCEEDINGS OF ELECTROTECHNICAL INSTITUTE, Issue 229, 2006


Representation <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> <strong>in</strong> <strong>field</strong>-<strong>oriented</strong> steer<strong>in</strong>g algorithm ... 129<br />

20<br />

18<br />

16<br />

14<br />

Motor torque [Nm]<br />

Speed <strong>of</strong> <strong>motor</strong> [rot/m<strong>in</strong>]<br />

1500<br />

1350<br />

1200<br />

1050<br />

12<br />

10<br />

Scalar control U/f<br />

Vector control<br />

900<br />

750<br />

8<br />

600<br />

6<br />

450<br />

4<br />

300<br />

2<br />

0<br />

0,0 0,3 0,5 0,7 0,9 1,1 1,3 1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0 3,2<br />

-2<br />

Time [s]<br />

150<br />

0<br />

-150<br />

12<br />

10<br />

8<br />

Motor current I [A]<br />

Scalar control<br />

Vector control<br />

6<br />

4<br />

2<br />

0<br />

-2<br />

-4<br />

-6<br />

-8<br />

-10<br />

Time [s]<br />

-12<br />

0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0 3,2<br />

Fig. 1. Comparison <strong>of</strong> start<strong>in</strong>g curves <strong>of</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> for different steer<strong>in</strong>g algorithms,<br />

[2], [3]


130<br />

J. Anuszczyk, M. Jabłoński<br />

2. MOTOR MODEL AND IDENTIFICATION<br />

OF PARAMETERS<br />

The <strong><strong>in</strong>duction</strong> <strong>motor</strong> itself is a nonl<strong>in</strong>ear, multidimensional object with<br />

coupl<strong>in</strong>gs <strong>of</strong> controll<strong>in</strong>g signals with <strong>in</strong>ternal controlled signals occurr<strong>in</strong>g <strong>in</strong>side,<br />

such as coupled fluxes or electromagnetic torque. The difficulties <strong>in</strong> controll<strong>in</strong>g<br />

such <strong>an</strong> object could be overcome with the use <strong>of</strong> spatial vector theory, <strong>in</strong><br />

a properly chosen coord<strong>in</strong>ate system, for describ<strong>in</strong>g the dynamics <strong>of</strong> the <strong>motor</strong>.<br />

The <strong>motor</strong> model used allows the researchers to execute <strong>in</strong>troductory <strong>an</strong>d <strong>in</strong><br />

progress calculations carried out for the actual conditions, [2], [5].<br />

⎧<br />

dΨ<br />

s<br />

⎪U<br />

s<br />

= Rs<br />

I<br />

s<br />

+ + jΨ<br />

sΩϑ<br />

⎪<br />

dt<br />

⎪ dΨ<br />

r<br />

⎪0 = Rr<br />

I<br />

r<br />

+ + jΨ<br />

r<br />

( Ωϑ<br />

− Ω)<br />

⎪ dt<br />

⎨Ψ<br />

s<br />

= Ls<br />

I<br />

s<br />

+ Lm<br />

I<br />

r<br />

⎪<br />

⎪Ψ<br />

r<br />

= Lr<br />

I<br />

r<br />

+ Lm<br />

I<br />

s<br />

⎪<br />

3 Lm<br />

*<br />

⎪M<br />

= p Im( Ψ<br />

r<br />

I<br />

s<br />

) − M<br />

o<br />

⎪ 2 Lr<br />

⎪⎩<br />

⇒<br />

⎧ dΨ<br />

r<br />

⎪Tr<br />

+ Ψ<br />

r<br />

= LmI<br />

sd<br />

⎪ dt<br />

⎧<br />

⎪ 1<br />

⎨Tr<br />

Ω<br />

r<br />

= LmI<br />

⇒ ⎪Ψ<br />

r<br />

= const;<br />

I<br />

⎨<br />

sq<br />

⎪ Ψ<br />

r<br />

⎪<br />

⎩M<br />

≅ I<br />

sq<br />

⎪ 3 Lm<br />

⎪M<br />

= p Ψ<br />

r<br />

I<br />

sq<br />

⎩ 2 Ψ<br />

r<br />

sd<br />

1<br />

= Ψ<br />

L<br />

m<br />

rz<br />

(1)<br />

Here, the applied <strong>motor</strong> model is the key to use the implemented technology<br />

<strong>of</strong> the <strong>field</strong>-<strong>oriented</strong> steer<strong>in</strong>g. The mathematical model <strong>of</strong> the <strong><strong>in</strong>duction</strong> <strong>motor</strong>, is<br />

lead out from the classical equations with the regard <strong>of</strong> universal, practical<br />

simplifications. The model is described by parameters expressed <strong>in</strong> the system<br />

<strong>of</strong> coord<strong>in</strong>ates connected with the stator, the equivalent schema is presented <strong>in</strong><br />

Fig. 2.<br />

The <strong>in</strong>vestigated drive system uses modern methods <strong>of</strong> identification <strong>of</strong> the<br />

<strong>motor</strong> parameters <strong>an</strong>d control s<strong>of</strong>tware tools, all <strong>of</strong> these is done automatically.<br />

The parameters <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> c<strong>an</strong> be obta<strong>in</strong>ed <strong>in</strong> the start<strong>in</strong>g<br />

"identification run" process that is used to identify the classical equivalent<br />

scheme <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> – Fig. 2. On the basis <strong>of</strong> this "run" we get a lot <strong>of</strong><br />

precious <strong>in</strong>formation to describe the drive: parameters <strong>of</strong> the equivalent scheme<br />

<strong>an</strong>d the sett<strong>in</strong>gs <strong>of</strong> the controllers. This “run” consists <strong>of</strong> several tests,<br />

depend<strong>in</strong>g on the selected k<strong>in</strong>d <strong>of</strong> control (U/f or vector) <strong>an</strong>d the feedback used:<br />

measurement <strong>of</strong> parameters <strong>in</strong> st<strong>an</strong>dstill state, measurement <strong>of</strong> parameters <strong>in</strong><br />

no-load state <strong>an</strong>d optimization <strong>of</strong> controllers (e.g. speed controller, etc.).


Representation <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> <strong>in</strong> <strong>field</strong>-<strong>oriented</strong> steer<strong>in</strong>g algorithm ... 131<br />

Depend<strong>in</strong>g on the utilization <strong>of</strong> the exam<strong>in</strong>ed drive system there is access to the<br />

parameters adjust<strong>in</strong>g the dynamics <strong>of</strong> the supplied <strong><strong>in</strong>duction</strong> <strong>motor</strong> (these<br />

parameters are shown on the functional block diagrams <strong>of</strong> the <strong>in</strong>verter, [2], [3]).<br />

Fig. 2. Equivalent schema <strong>of</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> implemented <strong>in</strong> the exam<strong>in</strong>ed SIEMENS<br />

drive system SIMOVERT MASTERDRIVES VC, [3]<br />

Where: R S – resist<strong>an</strong>ce <strong>of</strong> stator w<strong>in</strong>d<strong>in</strong>gs, R ’ r – resist<strong>an</strong>ce <strong>of</strong> rotor w<strong>in</strong>d<strong>in</strong>gs recalculated to<br />

the stator side, X Sσ – leakage react<strong>an</strong>ce <strong>of</strong> stator, X S – own react<strong>an</strong>ce <strong>of</strong> stator w<strong>in</strong>d<strong>in</strong>gs,<br />

X ’ rσ – leakage react<strong>an</strong>ce <strong>of</strong> rotor recalculated to the stator side, X ’ r – own react<strong>an</strong>ce <strong>of</strong> rotor<br />

w<strong>in</strong>d<strong>in</strong>gs recalculated to the stator side, X m – react<strong>an</strong>ce <strong>of</strong> magnetization, s – slip,<br />

I S – phase current <strong>of</strong> stator, I r ’ – phase current <strong>of</strong> rotor recalculated to the stator side,<br />

I m – current <strong>of</strong> magnetization, n 1 – synchronous speed, n – rotor speed, f 1 – frequency <strong>of</strong><br />

stator EMF, f 2 – frequency <strong>of</strong> rotor EMF, p – pair <strong>of</strong> poles, U ph , E ph – phase voltage <strong>an</strong>d EMF<br />

In the described drive system, the identified parameters are based on the<br />

results <strong>of</strong> measurements executed <strong>in</strong> the system work<strong>in</strong>g only for the need <strong>of</strong><br />

test. Identification takes place on the ground <strong>of</strong> registered curves <strong>of</strong> magnitude,<br />

which are the <strong>an</strong>swer to the given <strong>in</strong>put. The drive system before start<strong>in</strong>g its<br />

duty has to be exactly recognized <strong>an</strong>d parameterized. The properly, wellchosen<br />

by the producer procedure <strong>of</strong> parameterization serves to achieve this<br />

target. Right after <strong>in</strong>putt<strong>in</strong>g the qu<strong>an</strong>tities from the rat<strong>in</strong>g plate <strong>of</strong> the <strong>motor</strong> the<br />

„automation parameterization” is executed, which calculates the basic<br />

parameters for the steer<strong>in</strong>g algorithms <strong>in</strong> open loop <strong>an</strong>d closed loop regulation<br />

<strong>an</strong>d steer<strong>in</strong>g system, tak<strong>in</strong>g <strong>in</strong>to account, among other, the pulse frequency.<br />

Parameters <strong>of</strong> the longitud<strong>in</strong>al br<strong>an</strong>ch <strong>of</strong> the equivalent schema are calculated<br />

on the ground <strong>of</strong> results <strong>of</strong> measurements executed at st<strong>an</strong>dstill (motionless<br />

rotor) – Fig. 3. This dictates requirements for the exploitation, s<strong>in</strong>ce it is really<br />

necessary that rotor <strong>of</strong> <strong>motor</strong> stays motionless dur<strong>in</strong>g the tests. Parameters <strong>of</strong><br />

the tr<strong>an</strong>sverse br<strong>an</strong>ch <strong>of</strong> the equivalent schema are identified <strong>in</strong>stead dur<strong>in</strong>g the<br />

no-load tests <strong>of</strong> the <strong>motor</strong>, <strong>in</strong> the state without load (idle-run measurement).


132<br />

J. Anuszczyk, M. Jabłoński<br />

a)<br />

b)<br />

Fig. 3. The curves obta<strong>in</strong>ed dur<strong>in</strong>g identification <strong>of</strong> parameters <strong>in</strong> „st<strong>an</strong>d still” state:<br />

a) <strong>motor</strong> 1.5 kW, b) <strong>motor</strong> 55 kW<br />

3. STEERING ALGORITHMS OF THE DRIVE<br />

AND ITS MOTOR MODELS<br />

The SIMOVERT MASTERDRIVES (made by SIEMENS) mach<strong>in</strong>e is<br />

a frequency converter for very precise drives with controlled speed <strong>an</strong>d torque.<br />

It is a module-based drive, which c<strong>an</strong> cooperate with a wide r<strong>an</strong>ge <strong>of</strong> <strong>motor</strong>s<br />

<strong>an</strong>d other devices, th<strong>an</strong>ks to its abilities to parameterize. The regulation process<br />

itself <strong>an</strong>d connected with it the process<strong>in</strong>g <strong>of</strong> particular signals is carried out<br />

digitally by the me<strong>an</strong>s <strong>of</strong> the microprocessor system (DSP). On the other h<strong>an</strong>d,<br />

all the other available components <strong>of</strong> the signal route, accord<strong>in</strong>g to which the<br />

steer<strong>in</strong>g takes place, are presented <strong>in</strong> the drive documentation <strong>in</strong> the form <strong>of</strong>


Representation <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> <strong>in</strong> <strong>field</strong>-<strong>oriented</strong> steer<strong>in</strong>g algorithm ... 133<br />

m<strong>an</strong>y pages illustrat<strong>in</strong>g block diagrams <strong>of</strong> the particular parts complet<strong>in</strong>g certa<strong>in</strong><br />

tasks <strong>in</strong> the whole process <strong>of</strong> steer<strong>in</strong>g – Fig. 4.<br />

Equivalent <strong><strong>in</strong>duction</strong><br />

<strong>motor</strong> models<br />

Fig. 4. Function diagram <strong>of</strong> sensorless steer<strong>in</strong>g algorithm <strong>an</strong>d equivalent <strong>motor</strong> models, [3]<br />

For the benefit <strong>of</strong> the users implement<strong>in</strong>g the drive, a new graphic system<br />

has been used <strong>of</strong> represent<strong>in</strong>g the very sophisticated steer<strong>in</strong>g structure. This is<br />

to accelerate <strong>an</strong>d simplify the operation <strong>of</strong> this device. This facility has<br />

orig<strong>in</strong>ated from the use <strong>of</strong> the so-called BICO technology (Fig. 4), which until<br />

now has been the most optimal <strong>representation</strong> <strong>of</strong> the logical connection/l<strong>in</strong>k<strong>in</strong>g<br />

<strong>of</strong> signals. The documentation [3] conta<strong>in</strong>s the normalized numeration <strong>of</strong> the<br />

<strong>in</strong>put / output signals (the so-called connectors) as well as the parameters <strong>of</strong> the<br />

given block. Th<strong>an</strong>ks to this data, there exists a possibility <strong>of</strong> model<strong>in</strong>g the way,<br />

<strong>in</strong> which the steer<strong>in</strong>g is accomplished to meet all the requirements <strong>of</strong> the user.<br />

This is possible after l<strong>in</strong>k<strong>in</strong>g particular block connectors with one <strong>an</strong>other, or<br />

after sett<strong>in</strong>g all the parameters <strong>of</strong> these particular blocks. The tool s<strong>of</strong>tware<br />

DriveMonitor, <strong>in</strong>stalled on the PC, is usually used to configure <strong>an</strong>d set the<br />

parameters <strong>of</strong> the drive <strong>an</strong>d enable the communication with the drives by


134<br />

J. Anuszczyk, M. Jabłoński<br />

me<strong>an</strong>s <strong>of</strong> the typical serial <strong>in</strong>terface. There is also a possibility <strong>of</strong> choos<strong>in</strong>g the<br />

methods <strong>of</strong> exam<strong>in</strong>ation or archivization <strong>of</strong> the time curves obta<strong>in</strong>ed from the<br />

convector (ex: output current, <strong>motor</strong> torque, steer<strong>in</strong>g error signal, speed <strong>of</strong> the<br />

<strong>motor</strong>). The selected k<strong>in</strong>d <strong>of</strong> control is applied <strong>in</strong> every case where the quality <strong>of</strong><br />

control <strong>in</strong>fluences the quality <strong>of</strong> the technological process. The <strong>field</strong> <strong>oriented</strong><br />

control method relies on determ<strong>in</strong><strong>in</strong>g the components <strong>of</strong> the <strong>motor</strong>’s stator<br />

current: component I sd (responsible for flux generation) <strong>an</strong>d component I sq<br />

(responsible for generat<strong>in</strong>g torque). Additionally it is necessary to measure or<br />

evaluate the <strong>an</strong>gular position <strong>of</strong> the coupled flux vector <strong>in</strong> the mach<strong>in</strong>e, where<br />

the <strong>in</strong>formation is required about the status variables <strong>an</strong>d <strong>in</strong>accessible by<br />

measurement (or hardly accessible) <strong>in</strong>formation such as, i.e. the flux <strong>in</strong> the<br />

<strong><strong>in</strong>duction</strong> <strong>motor</strong>’s rotor. Therefore methods were developed, <strong>in</strong> relation to the<br />

algorithms reproduc<strong>in</strong>g the <strong>in</strong>accessible by measurement status variables,<br />

which make it possible to replace <strong>an</strong> actual measurement <strong>of</strong> a physical qu<strong>an</strong>tity<br />

with <strong>an</strong> <strong>in</strong>direct method based on easily measured variables. Every switch<strong>in</strong>g <strong>of</strong><br />

the power section is directly dependent on the electromagnetic condition <strong>of</strong> the<br />

<strong>motor</strong> <strong>an</strong>d is determ<strong>in</strong>ed from the calculations <strong>of</strong> the stator flux <strong>an</strong>d <strong>motor</strong><br />

torque. In Fig. 5a) the zoom <strong>of</strong> function diagram is presented, executed <strong>in</strong> BICO<br />

technology for realization <strong>of</strong> steer<strong>in</strong>g algorithms <strong>in</strong> the r<strong>an</strong>ge <strong>of</strong> operation with<br />

<strong>in</strong>corporation <strong>of</strong> equivalent models. The current model acts to 10 % <strong>of</strong> the set<br />

value (measurement <strong>of</strong> speed necessary) or the arr<strong>an</strong>gement <strong>of</strong> given current<br />

(the sensorless arr<strong>an</strong>gement), however above this value switches <strong>in</strong> the EMF<br />

model (does not require the measurement <strong>of</strong> rotary speed). In Fig. b) area B is<br />

marked, <strong>in</strong> which the process <strong>of</strong> switch<strong>in</strong>g both equivalent models occures.<br />

The phenomena <strong>of</strong> electromagnetic process occurr<strong>in</strong>g dur<strong>in</strong>g start<strong>in</strong>g the<br />

drives with vector-control steer<strong>in</strong>g is the most crucial element <strong>of</strong> function<strong>in</strong>g <strong>of</strong><br />

m<strong>an</strong>y <strong>in</strong>dustrial processes. The time duration <strong>of</strong> the process <strong>of</strong> establish<strong>in</strong>g the<br />

electromagnetic state depends on the rated power <strong>of</strong> applied <strong>motor</strong>. For<br />

example for <strong>motor</strong> <strong>of</strong> rated power P N = 1.5 kW this process is over <strong>in</strong> about total<br />

0.3 s, <strong>an</strong>d for a <strong>motor</strong> <strong>of</strong> rated power P N = 100 kW it lasts almost about 1.8 s<br />

(this time is calculated from the moment the start signal for the application "the<br />

start take-<strong>of</strong>f” was set to the time <strong>of</strong> detect<strong>in</strong>g speed n > 0) – region A on<br />

Fig. 5b). Some relatively large delays occur <strong>in</strong> the start<strong>in</strong>g process after<br />

apply<strong>in</strong>g "the start take-<strong>of</strong>f” signal, what for example, <strong>in</strong> case <strong>of</strong> the cr<strong>an</strong>es<br />

application c<strong>an</strong> make up large technical problem, [1], [2].<br />

PROCEEDINGS OF ELECTROTECHNICAL INSTITUTE, Issue 229, 2006


Representation <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> <strong>in</strong> <strong>field</strong>-<strong>oriented</strong> steer<strong>in</strong>g algorithm ... 135<br />

a)<br />

b)<br />

B<br />

A<br />

Fig. 5. Equivalent schema <strong>of</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong>:<br />

a) <strong>an</strong>d start<strong>in</strong>g curves b) for selected sensorless steer<strong>in</strong>g algorithm


136<br />

J. Anuszczyk, M. Jabłoński<br />

4. THE INFLUENCE OF EQUIVALENT PARAMETERS<br />

OF THE MODEL ON THE PERFORMANCE<br />

OF THE STEERING ALGORITHM<br />

In case <strong>of</strong> vector control, the element <strong>of</strong> large me<strong>an</strong><strong>in</strong>g is the accuracy<br />

<strong>of</strong> determ<strong>in</strong><strong>in</strong>g the value <strong>of</strong> w<strong>in</strong>d<strong>in</strong>g stator resist<strong>an</strong>ce. When the actual value<br />

<strong>of</strong> resist<strong>an</strong>ce is smaller th<strong>an</strong> the one <strong>in</strong>troduced to the model, the control system<br />

is adapt<strong>in</strong>g the parameters <strong>of</strong> the <strong>in</strong>itial stage <strong>of</strong> start<strong>in</strong>g to the given conditions,<br />

suitably enlarges the tension <strong>in</strong> order to compensate the voltage drop on the<br />

resist<strong>an</strong>ce <strong>of</strong> w<strong>in</strong>d<strong>in</strong>gs. In consequence, the speed <strong>of</strong> the rotor <strong>in</strong> the time, when<br />

it beg<strong>in</strong>s its calculation on basis <strong>of</strong> phase currents, shows larger th<strong>an</strong> the<br />

process <strong>of</strong> steer<strong>in</strong>g needs at this po<strong>in</strong>t. The effect <strong>of</strong> this is the negative<br />

impulse, appear<strong>an</strong>ce <strong>of</strong> component Isq <strong>an</strong>d <strong>in</strong> consequence negative driv<strong>in</strong>g<br />

torque. The situation, <strong>in</strong> which the resist<strong>an</strong>ce <strong>in</strong> the model is understated<br />

generate the opposite result, but <strong>in</strong> courses <strong>of</strong> speed less unfavorable.<br />

Therefore <strong>in</strong> case <strong>of</strong> impulse ch<strong>an</strong>ge <strong>of</strong> load torque for <strong>motor</strong> SzJe -24a, the<br />

fluctuations <strong>of</strong> speed are signific<strong>an</strong>tly restricted <strong>an</strong>d establish <strong>in</strong> comparatively<br />

short time.<br />

a) b)<br />

Strumień Flux<br />

n/f<br />

Uwyj.<br />

Strumień Flux Flux<br />

n/f<br />

EMF model<br />

Uout<br />

Moment Torque<br />

EMF model<br />

Uwyj.<br />

Uout<br />

Torque<br />

Moment<br />

The memory <strong>of</strong> drive conta<strong>in</strong> the parameters <strong>of</strong> <strong>motor</strong> model<br />

calculated with classical method<br />

Time [s]<br />

16500= n1 ; 16500 = Un ; 7000 = Mn<br />

150%<br />

150%<br />

c) d)<br />

Start<strong>in</strong>g proces for SzJe24a <strong><strong>in</strong>duction</strong> <strong>motor</strong> with the<br />

parameters calculated <strong>in</strong> classical method<br />

125%<br />

125%<br />

The memory <strong>of</strong> drive conta<strong>in</strong> the parameters <strong>of</strong> <strong>motor</strong> model<br />

used from identification<br />

Time [s]<br />

Start<strong>in</strong>g proces for SzJe24a <strong><strong>in</strong>duction</strong> <strong>motor</strong> with the parameters<br />

from the identification<br />

100<br />

Mo tor to rq u e<br />

Load 100%<br />

10 0 %<br />

Motor torque<br />

Load 100%<br />

Motor voltage about 90%<br />

75 %<br />

Motor voltage above 75%<br />

75 %<br />

50 %<br />

50 %<br />

25%<br />

START<br />

OutputVol ts ,<br />

DCBusVolts,<br />

Isq(act),<br />

MotorTorque,<br />

Isd(act),<br />

Flux(Curve)<br />

Time [s]<br />

25 %<br />

START<br />

OutputVolts ,<br />

DCBusVolts,<br />

Isq(act),<br />

MotorTorque,<br />

Isd(act),<br />

Flux(Curve)<br />

Time [s]<br />

0,0 0,9 1,8 2,7 3,6 4,5 5,4 6,3 7,2 8,1 9,0 9,9 10,8 11,7 12,6 13,5 14,4 15,3 16,2 17,1 18,0<br />

0 ,0 0 ,9 1 ,8 2 ,7 3 ,6 4 ,5 5 ,4 6 ,3 7 ,2 8 ,1 9 ,0 9,9 1 0,8 11 ,7 1 2,6 13 ,5 1 4,4 15 ,3 1 6,2 17 ,1 1 8,0<br />

Fig. 6. Start<strong>in</strong>g curves <strong>of</strong> 1.5 kW <strong><strong>in</strong>duction</strong> <strong>motor</strong>:<br />

a),c) start<strong>in</strong>g process <strong>in</strong> vector control algorithm with the parameters calculated <strong>in</strong> classical method;<br />

b),d) start<strong>in</strong>g process <strong>in</strong> vector control algorithm with the parameters from identification, [2]


Representation <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> <strong>in</strong> <strong>field</strong>-<strong>oriented</strong> steer<strong>in</strong>g algorithm ... 137<br />

The experiment was executed depend<strong>in</strong>g on <strong>in</strong>troduc<strong>in</strong>g to the memory <strong>of</strong><br />

the converter two sets <strong>of</strong> parameters to describe the equivalent model <strong>of</strong> the<br />

<strong>motor</strong> <strong>in</strong> the algorithm <strong>of</strong> control. These were the follow<strong>in</strong>g parameters:<br />

calculated with the classic method procedures – Fig. 6 a) i c) <strong>an</strong>d obta<strong>in</strong>ed from<br />

identification – Fig. 6 b) i d). In Fig. 6, for example, are shown the curves<br />

acquired dur<strong>in</strong>g start<strong>in</strong>g the converter with <strong>motor</strong> SzJe-24a, with parameters<br />

counted with the classic method as well as measured dur<strong>in</strong>g the start<strong>in</strong>g<br />

procedure with parameters got from identification. Essential differences come<br />

out <strong>in</strong> the values <strong>an</strong>d time <strong>of</strong> establish<strong>in</strong>g <strong>of</strong> the magnetic flux. Differences occur<br />

also <strong>in</strong> the tr<strong>an</strong>sient processes <strong>in</strong> the <strong>motor</strong> dur<strong>in</strong>g switch<strong>in</strong>g current <strong>an</strong>d voltage<br />

models, this me<strong>an</strong>s the utilization <strong>of</strong> the sensorless vector control algorithm. In<br />

settled state however, the acquired curves are very similar to each other. If the<br />

ch<strong>an</strong>ge <strong>of</strong> schema parameters has the essential <strong>in</strong>fluence on dynamics (what<br />

we notice <strong>in</strong> shape <strong>an</strong>d time, for example, <strong>of</strong> creat<strong>in</strong>g the current component <strong>of</strong><br />

stator Isq - <strong>in</strong> consequence the torque <strong>of</strong> the <strong>motor</strong>) then it does not cause<br />

essential ch<strong>an</strong>ges <strong>in</strong> operation <strong>of</strong> the speed controller.<br />

5. CONCLUSIONS<br />

The considerations concern<strong>in</strong>g the work <strong>of</strong> a drive arr<strong>an</strong>gement with vector<br />

control steer<strong>in</strong>g algorithm give rise to the follow<strong>in</strong>g conclusion: the vector control<br />

is preferable due to the improved control characteristics e.g. accelerat<strong>in</strong>g along<br />

the current limit <strong>an</strong>d also due to the improved immunity to stall<strong>in</strong>g. Usually the<br />

vector control is also possible, even when several <strong>motor</strong>s are connected to<br />

a s<strong>in</strong>gle drive converter, as normally, the <strong>motor</strong>s are similarly loaded. On the<br />

basis <strong>of</strong> <strong>in</strong>vestigations <strong>of</strong> the model with const<strong>an</strong>t parameters <strong>of</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong><br />

<strong>in</strong> dynamic states we c<strong>an</strong> see, that its behavior is similar to the response <strong>of</strong><br />

a real <strong>motor</strong> despite accept<strong>an</strong>ce <strong>in</strong> model<strong>in</strong>g such simplifications, as the<br />

omission <strong>of</strong> hysteresis, accept<strong>an</strong>ce <strong>of</strong> perm<strong>an</strong>ent saturation <strong>of</strong> magnetic circuit<br />

as well as omission <strong>of</strong> current displacement <strong>in</strong> rotor w<strong>in</strong>d<strong>in</strong>gs for the <strong>motor</strong><br />

Sg-90L4 (differences <strong>in</strong> relation to measurements <strong>of</strong> <strong>in</strong>itial value <strong>of</strong> dynamic<br />

torque amount to about 28 % - difference <strong>in</strong> time <strong>of</strong> duration <strong>of</strong> the process is<br />

near to 0,27 s). It is good to underl<strong>in</strong>e that the area <strong>of</strong> <strong>in</strong>compatibility <strong>of</strong> <strong>in</strong>itial<br />

torque amplitudes from the po<strong>in</strong>t <strong>of</strong> view <strong>of</strong> drive perform<strong>an</strong>ce has no larger<br />

me<strong>an</strong><strong>in</strong>g because it is outside the area <strong>of</strong> limitations specified by the sett<strong>in</strong>gs <strong>of</strong><br />

functional parameters, <strong>an</strong>d also it results from different − subord<strong>in</strong>ated<br />

parameters <strong>of</strong> the drive steer<strong>in</strong>g, form<strong>in</strong>g the electromagnetic phenomena <strong>in</strong>


138<br />

J. Anuszczyk, M. Jabłoński<br />

<strong>motor</strong>. These effects are not considered <strong>in</strong> case <strong>of</strong> start<strong>in</strong>g a <strong>motor</strong> supplied<br />

from network with full voltage. The proportion <strong>of</strong> actual value <strong>of</strong> the w<strong>in</strong>d<strong>in</strong>gs<br />

resist<strong>an</strong>ce <strong>of</strong> the <strong>motor</strong> <strong>an</strong>d the value <strong>of</strong> resist<strong>an</strong>ce <strong>in</strong>troduced to the equivalent<br />

model has large <strong>in</strong>fluence on the course <strong>of</strong> the start<strong>in</strong>g process. Introduction, to<br />

model <strong>of</strong> the <strong>motor</strong>, <strong>of</strong> new sett<strong>in</strong>gs <strong>of</strong> the parameters <strong>of</strong> leakage react<strong>an</strong>ce Xk<br />

(Xk = Xs + Xr’), magnetiz<strong>in</strong>g react<strong>an</strong>ce Xm <strong>an</strong>d magnetiz<strong>in</strong>g current Im,<br />

<strong>in</strong>fluences the ch<strong>an</strong>ge <strong>of</strong> calculated value <strong>of</strong> the torque <strong>an</strong>d ch<strong>an</strong>ge <strong>of</strong> the po<strong>in</strong>t<br />

<strong>of</strong> work <strong>of</strong> the <strong>motor</strong>. The conception <strong>of</strong> EMF model does not require the<br />

measurement <strong>of</strong> rotary speed <strong>of</strong> the <strong>motor</strong> shaft. This model is also less<br />

“sensitive” to the ch<strong>an</strong>ge <strong>of</strong> temperature, particularly to the ch<strong>an</strong>ge <strong>of</strong> rotor<br />

resist<strong>an</strong>ce under ch<strong>an</strong>g<strong>in</strong>g temperature <strong>of</strong> the <strong>motor</strong>. The perform<strong>an</strong>ce <strong>of</strong> the<br />

EMF model strongly depends however on ch<strong>an</strong>ges <strong>of</strong> the stator resist<strong>an</strong>ce <strong>of</strong><br />

<strong>motor</strong> <strong>in</strong> the r<strong>an</strong>ge <strong>of</strong> low frequencies. Utilization <strong>of</strong> this model <strong>in</strong> this case <strong>of</strong><br />

arr<strong>an</strong>gement with closed-loop speed control ensures the more precise<br />

identification <strong>of</strong> parameters <strong>of</strong> the mach<strong>in</strong>e <strong>an</strong>d the possibility <strong>of</strong> generat<strong>in</strong>g<br />

maximum driv<strong>in</strong>g torque already practically at zero rotary speed (for ex: lifts<br />

application).<br />

LITERATURE<br />

1. Anuszczyk J., Jabłoński M.: Method <strong>of</strong> determ<strong>in</strong>ation <strong>of</strong> static torque values for the state <strong>of</strong><br />

motionless shaft <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> under load <strong>in</strong> a converter drive system, Problems <strong>of</strong><br />

Exploitation on Mach<strong>in</strong>es <strong>an</strong>d Electrical Drives, PEMINE’06, KOMEL, Ustroń, 2006.<br />

2. Jabłoński M.: The <strong>an</strong>alysis <strong>of</strong> functional parameters <strong>an</strong>d modification <strong>of</strong> steer<strong>in</strong>g algorithms <strong>in</strong><br />

vector control converter drive with the <strong><strong>in</strong>duction</strong> <strong>motor</strong>, Doctor thesis. Technical University <strong>of</strong><br />

Lodz. Faculty Electrical, Electronic, Computer <strong>an</strong>d Control Eng<strong>in</strong>eer<strong>in</strong>g, Lodz, 2006.<br />

3. Siemens: Compendium for SIMOVRET MASTERDRIVES CUVC, Erl<strong>an</strong>gen, 04.2002.<br />

4. H. Tunia, M. Kaźmierkowski.: Automation <strong>of</strong> converter drive system, PWN, Warsaw 1987.<br />

5. W. Paszek.: Dynamic states <strong>of</strong> AC electrical mach<strong>in</strong>es, WNT, Warsaw 1986.<br />

6. Vas P.: Sensorless vector <strong>an</strong>d direct torque control. Oxford University Press 1998.<br />

M<strong>an</strong>uscript submitted 14.11.2006<br />

Reviewed by Jarosław Zadrożny


Representation <strong>of</strong> <strong>an</strong> <strong><strong>in</strong>duction</strong> <strong>motor</strong> <strong>in</strong> <strong>field</strong>-<strong>oriented</strong> steer<strong>in</strong>g algorithm ... 139<br />

PREZENTACJA SILNIKA INDUKCYJNEGO<br />

PRZEZ POLOWO ZORIENTOWANY ALGORYTM<br />

DLA PRZEMYSŁOWYCH PRZETWORNIKOWYCH<br />

SYSTEMÓW NAPĘDOWYCH<br />

J. ANUSZCZYK, M. JABŁOŃSKI<br />

STRESZCZENIE<br />

Praca omawia wyniki badań i symulację<br />

pracy silnika <strong>in</strong>dukcyjnego współpracującego z przetwornikowym systemem<br />

sterow<strong>an</strong>ia wektorowego dla różnych konfiguracji sterow<strong>an</strong>ia<br />

i algorytmów sterow<strong>an</strong>ia. Ten układ sterow<strong>an</strong>ia stosuje różne równoważne<br />

modele silnika. Zalety i wady bad<strong>an</strong>ego układu napędowego<br />

zostały przedstawione i wyniki mierzonych parametrów dla różnych<br />

algorytmów sterow<strong>an</strong>ia porówn<strong>an</strong>o z obliczeniami.

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