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Nr 62
Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych
Politechniki Wrocławskiej
Nr 62
Studia i Materiały
Nr 28
2008
induction slip-ring motor, losses minimization,
efficiency optimization, scalar control,
optimal supply voltage
Henryk BANACH*
METHOD OF SUPPLY VOLTAGE SELECTION
FOR POWER LOSSES MINIMIZATION
IN AN INDUCTION SLIP-RING MOTOR
The minimizing of total losses in a slip-ring induction motor can be achieved by voltage control.
For every load exists an optimal value of voltage which reduces the losses. This optimal voltage can
be determined by using an analytical method, which was worked out by author. The application
of this method requires knowledge of core and mechanical losses, magnetization characteristic,
voltage drops on brush contacts, resistances and reactances of motor windings. The investigation
of proposed method was made for a small motor with rated data: PN = 0,9 kW and nN =905 rev/min.
For this motor two control characteristics Uopt =f(Ts) were prepared; first one through laboratory
measurements and second one using the analytical method. The both characteristics made for five
selected frequencies 10, 20, 30, 40, 50 Hz are compared in Fig. 1. The comparison shows the close
similarity of both characteristics. These results proved usefulness of the proposed analytical method
for calculation of optimal voltage.
1. INTRODUCTION
The minimization of the total losses in an induction motor at variable load can
be achieved by the voltage control. The voltage control of an inverter can be realized by
using adequate strategies with different criteria. The most described criteria of search
strategies are: minimum of input power or minimum of stator current. These optimal
energy strategy can be realized by optimizing controllers which change suitably the
output voltage of the inverter, according to the load changes. The main disadvantages of
these adaptive strategies are [5]:
– difficulty to minimize the input power because the minimum is shallow,
__________
* Katedra Maszyn Elektrycznych Wydziału Elektrotechniki i Informatyki, Politechnika Lubelska,
ul. Nadbystrzycka 38 A, 20-618 Lublin.
159
– difficulty to find the minimum of the input power while the load and the supply
voltage are changing.
The major advantage is, that a search controller does not require knowledge of any
motor parameters. In consideration of these disadvantages, will be often used a control
strategy based on the losses model. This losses model permits to derive an approach for
voltage determination for each load. The model uses all expressions which describe
losses. Applying the calculus of optimization we can find the optimal value of voltage.
Unfortunately the considerations that can be encountered in the literature are made with
many simplifications such as [1–5]:
– linearization of a magnetization characteristic,
– using of an electric torque instead a torque on the shaft,
– neglecting of stray losses.
The results of calculations for these simplifications were different then in reality.
In that case it was necessary to create a precise losses model of induction motor and
on base of this model to derive an analytical method for determining of an optimal
voltage value for given output power. The analytical method can be worked out for
a squirrel-cage motor as well as a slip-ring motor. This article presents the results
of prepared method for an induction slip-ring motor of small power.
2. METHOD DESCRIPTION
The precise losses model construction was made under following assumptions:
– an actual magnetization characteristic is used,
– power on the shaft is given,
– constant frequency of supply voltage,
– sinusoidal supply voltage and motor currents.
On base of the losses model can be derived a condition of the total losses minimum
for a given output power. This condition could be described as a losses equation:
 1

 3

3 Rs  Rr  I r2  ln I r   Ub I r  ln I r   3Rs I m2  ln I m   PFe  ln PFe 
2
2
where:
3(Rs +Rr)Ir2 – the losses in stator and rotor windings caused by rotor current,
Ir – the rotor current referred to stator,
Im – the magnetizing current,
PFe – the iron losses,
ΔUb – the voltage drops on the brushes referred to stator,
3ΔUbIr – the brush contact loss,
3RsIm2 – the loss in stator winding caused by the magnetizing current,
(1)
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ln Ir  – the derivative of the natural logarithm of rotor current,
ln I m  – the derivative of the natural logarithm of magnetizing current,
ln PFe  – the derivative of the natural logarithm of iron loss.
Based on the equation (1), an analytical method for determining of optimal
voltage was developed. The derivations of this method are very complicated and need
many transformations therefore they are not presented. The algorithm for determining
optimal voltage has very complicated form and must be solved numerically.
The application of this method requires knowledge of following parameters
of an induction slip-ring motor:
– iron loss,
– magnetization characteristic,
– stator and rotor windings resistances,
– mechanical loss.
It is clear that the application of method requires to make many laboratory studies
to determinate those parameters. The accuracy of this method depends mainly
on windings resistances determination.
The method verification was done on the induction slip-ring motor with ratings:
– Typ 2SUDf 100 L-6A
– PN = 0,8 kW
– UN = 380 V
– IN = 3,0 A
– cosN = 0,61
– nN = 905 obr/min
– continuous running S1
For five selected frequencies fs = 10,20,30,40,50 Hz were all necessary parameters
tested, which were useful to investigate the method. The calculations allowed
to prepare five steering characteristics of the optimal voltage Uopt versus the torque
on the shaft Ts, Uopt = f(Ts). The next five characteristics were obtained from laboratory tests on the machines set; an induction slip-ring motor and separately excited
d.c. generator. These all control characteristics were put on the same diagram, Fig.1,
that enables to compare the accuracy of the calculated characteristics. The diagram
shows all characteristics as a function on the shaft torque. The analysis of the diagram
confirms that differences between the calculated and testing characteristics are small
and accuracy of optimal voltage determination is enough good. For all frequencies
the testing characteristics lie above the calculated characteristics. The prepared method allows to determinate an optimal value of supply voltage even for no-load operation.
161
U opt [V]
400
350
300
250
200
Uopt.cal. fs=50Hz
Uopt.test. fs=50Hz
150
Uopt.cal. fs=40Hz
Uopt.test. fs=40Hz
Uopt.cal. fs=30Hz
100
Uopt.test. fs=30Hz
Uopt.cal. fs=20Hz
50
Uopt.test. fs=20Hz
Uopt.cal. fs=10Hz
Uopt.test. fs=10Hz
0
0
1
2
3
4
5
6
7
8
9
10
Ts [Nm]
Fig. 1. Comparison of control characteristics obtained from measurements (solid line )
and from calculations (dash line )
Rys. 1. Porównanie charakterystyk sterowania uzyskanych na podstawie pomiarów (linia ciągła )
oraz na podstawie obliczeń (linia przerywana ).
3. CONCLUSIONS
The presented considerations of optimal voltage selection to minimize the total
losses in an induction slip-ring motor lead to following conclusions:
– the developed method for determination of optimal voltage for given load proved
its usefulness for technical applications,
– the advantage of the method is its high accuracy,
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– the method accuracy is significant depending on assumed for calculation winding resistances; the resistances should come from present motor load,
– the certain disadvantage of described method is necessity of laboratory test to
measure iron losses, mechanical losses, a magnetization characteristic, windings resistance, and leakage reactance of stator winding,
– the described method was developed under assumption, that currents and voltages were sinusoidal,
– the verification of the method was made on a small induction slip-ring motor
supplied with sinusoidal voltage from 3-phase synchronous generator.
REFERENCES
[1] KIOSKERIDIS I., MARGARIS N.: Loss Minimization in Induction Motor Adjustable- Speed Drives,
IEEE Transactions on Industrial Electronics, Vol. 43, No. 1, February 1996, p. 226–231.
[2] KRYGIER J.: Zagadnienia energooszczędnej pracy trójfazowych silników asynchronicznych klatkowych (Energy efficient operation of three-phase induction squirrel-cage motors). Prace Naukowe
Politechniki Szczecińskiej nr 494, Szczecin 1992.
[3] GRUSZCZYŃSKI P.: Wybrane zagadnienia optymalizacji statycznej sterowania
napędów
przekształtnikowych (Selected problems of state optimization of power electronic drive control).
Zeszyty Naukowe PG nr 499, Elektryka, Gdańsk 1993.
[4] FERNANDEZ F., GARCIA A., FAURE R.: Model-Based Loss Minimization for DC and AC VectorControlled Motors Including Core Saturation. IEEE Transactions on Industry Applictions,Vol. 36,
No. 3, May/June 2000, p.755–763.
[5] KAŹMIERKOWSKI M., KRISHNAN R., BLLABJERG F.: Control in power electronics Selected
problems. Akademic Press, 2002.
METODA DOBORU NAPIĘCIA ZASILAJĄCEGO DLA MINIMALIZACJI STRAT MOCY
W INDUKCYJNYM SILNIKU PIERŚCIENIOWYM
Minimalizacja całkowitych strat mocy w indukcyjnym silniku pierścieniowym realizowana jest przez
odpowiednie sterowanie napięcia zasilającego. Dla każdej wartości obciążenia istnieje optymalna
wartość napięcia, która powoduje maksymalną redukcję strat. Tę optymalną wartość napięcia można
wyznaczyć posługując się metodą analityczną opracowaną przez autora. Zastosowanie tej metody
wymaga znajomości strat mechanicznych i strat w żelazie, charakterystyki magnesowania, spadku
napięcia na zestyku ślizgowym, wartości rezystancji uzwojeń oraz reaktancji rozproszenia uzwojenia
stojana. Weryfikacji opracowanej metody dokonano na silniku pierścieniowym małej mocy o danych:
P = 0,9 kW, nN = 905 obr/min. Dla badanego silnika wyznaczono po dwie charakterystyki sterowania
Uopt = f(Ts); jedną na podstawie pomiarów laboratoryjnych i drugą stosując opracowaną metodę.
Charakterystyki te sporządzono dla pięciu wartości częstotliwości; 10, 20, 30, 40, 50 Hz., i
przedstawiono je na rys. 1. Porównanie obu charakterystyk potwierdza ich dużą zgodność. Przedstawione
wyniki badań wskazują na dużą dokładność i tym samym przydatność opracowanej metody do
wyznaczania optymalnych wartości napięcia.