representation of an induction motor in field-oriented steering ...
representation of an induction motor in field-oriented steering ...
representation of an induction motor in field-oriented steering ...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
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.