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LOSS MINIMIZATION IN DC MOTOR DRIVES
DE ANGELO C., BOSSIO G., GARCÍA G.
Grupo de Electrónica Aplicada (GEA)
Facultad de Ingeniería, Universidad Nacional de Río Cuarto
Ruta Nac. #36 Km. 601, 5800 Río Cuarto, Argentina
E-mail: cdeangelo@; gbossio@; [email protected]
Keywords: Electrical Machinery Control, Electrical Drives, Power electronics.
Abstract:
In this work, a method to minimize DC Motor Drive losses is presented. It is based on a model that
includes motor and converter losses. The method is theoretically presented and experimental results to
validate the proposed model are shown.
1. Introduction
According to some researches, the majority of the
installed electric machines operate at two thirds or less
of their rated load (Nailen 1989). This means that
there is margin to improve the efficiency in these
machines.
Fig. 1 shows, according to experimental results,
how the drive efficiency raises when the excitation is
adjusted for each steady state operating point,
principally for a power demand less than its rated
value.
To minimize the DC machine losses in steady state
there are, basically, two different strategies.(Margaris
1991). The first one measures the speed and armature
current and, via a loss model, determines the optimal
excitation value. The second one measures the
incoming power to the drive and searches for the
optimal excitation value.
1.8
Optimal efficiency / Nominal efficiency
It is well known that when a DC machine power
demand is less than its rated value, it is not necessary
to maintain the excitation at its maximum value.
Excessive excitation increases the machine copper and
iron losses. Therefore, the excitation can be adjusted
according to the load requirements to reduce drive
losses in steady state.
1.9
1.7
200 rpm
1.6
400 rpm
1.5
600 rpm
1.4
800 rpm
1.3
1.2
1.1
1
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Output Power [pu]
Fig. 1. Optimal efficiency obtained by controlling field
current for different operating points (experimental results).
In the present work, a loss-model-based controller,
that includes converter losses, is proposed to obtain a
good dynamic response. Moreover, to correct the
error caused by parameter variations, this controller
uses the measurement of the drive input power to “fine
tune” the optimization during steady state.
2. Drive Model Including Losses
Losses in a DC Motor Drive (DCMD) depend on
the armature current, the field current and the machine
speed. The expressions of the most relevant drive
losses will be described in the following paragraphs.
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2.1 Copper Losses, PCu
These are due to the electric current flowing
through the armature and field windings, and are given
by (1), where Ia, If, Ra and Rf are the armature and
field currents, and the armature and field resistances,
respectively.
(1)
PCu  Ra .I a 2  R f .I f 2.
1) IGBT Conduction Losses: These losses are
modeled by considering a linear approximation of the
device data sheet curves. Therefore, the conduction
losses in each IGBT are:
Pc  Vt  a.I c .I c .D,
2.2 Brush Contact Losses, Pe
As the armature current flows, an electric arc is
formed between the brushes and the collector. The arc
voltage drop, Ve , can be considered constant for every
load condition (Langsdorf 1958). Therefore, these
losses can be represented by:
Pe  Ve .I a .
(2)
2.3 Iron Losses, PFe
These are eddy currents and hysteresis losses that
can be represented by (3), where cp and ch are the
eddy currents and hysteresis losses coefficients,
respectively,  is the rotor speed, and  is the flux
produced by the excitation current (Langsdorf 1958).
PFe  c p .2 .2  ch ..2 .
(3)
These losses can be modeled as a non-linear
resistance connected in parallel with the armature.
The expression of this iron loss resistance can be
obtained by considering that the iron losses, based on
the proposed model, are:
(4)
E 2
PFe  a ,
RPFe
(6)
where Ic is the collector current, Vt and a are
constants which depend on the IGBT characteristics
and D is the duty cycle.
2) IGBT Switching Losses: These losses are
modeled knowing the IGBT turn-on and turn-off
energy, according to a linear approximation of the
device data sheet curves:
Pon  f .h.I c .k v , Poff  f .m.I c .k v ,
(7)
where Pon are the turn-on losses, Poff are the turnoff losses, f is the switching frequency, h and m are
constants, and kv is a constant that depends on the
collector – emitter voltage, VDC, and on the test
voltage of the utilized components, Vtest.
3) Diode Conduction Losses: These losses are
modeled considering a linear approximation of the
device. These losses, for each diode, are given by:


Pcd  Vtd  ad .I fd .I fd .1  D ,
(8)
where Ifd is the forward current and Vtd and ad are
constants.
where RPFe is the iron loss resistance, and Ea =
Ke.. is the back EMF.
Equaling (3) and (4), the iron loss resistance yields:
RPFe 
manual data sheets. The converter losses can be
separated into the following components:
K e 2 .
k .
 2 ,
c p .  k1    k1
(5)
2
where k1 = ch /cp and k2 = Ke /cp.
Losses in the active device due to the reverse
recovery of the diode and diode switching losses can
be neglected since they represent, approximately, only
1.5% and 0.4%, respectively, of the converter total
losses.
By considering the losses described before,
replacing Ic and Ifd currents by the motor armature
current, and the duty cycle by its expression as a
function of the motor variables,
2.4 Converter Losses, Pconv
In this work only the armature converter losses
were modeled since the field converter losses can be
neglected if compared with the armature converter
losses.
Based on an IGBT simplified model (Clemente
1996), the parameters which the losses depend on can
be defined and their values can be obtained from the
D

1  Ea
I .R

 a a  1 ,

2  VDC VDC

(9)
the total converter losses (2 IGBTs + 2 diodes)
yields:
Pconv  Vt  2. f .kv .h  m  Vtd .I a  a  ad .I a 2 .
(10)
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From (10), it can be concluded that the converter
losses can be modeled by a term that is a function of
the armature current, and other term that depends on
the second power of the armature current. Therefore,
losses can be represented as a battery, Econv (which is a
function of the switching frequency f, the DC link
voltage VDC and the component parameters) and a
resistance, Rconv, which only depends on the
component parameters:
Pconv  Econv.I a  Rconv.I a 2 .
Based on the proposed model, an algorithm to
control the DCMD torque or speed by driving
independently the armature and field currents was
implemented. A speed or torque control loop was
closed through the armature current while a field
current control loop was closed to minimize losses for
any operating point.
(11)
From these equations it can be seen that converter
losses do not depend on the machine speed, since the
model parameters do not include the back EMF.
These results were verified experimentally.
2.5 Total Power Loss, Pt
Based on the stated, the total DCMD losses can be
represented by the following equation:
Pt  Ra  Rconv .I a 2  Ve  Econv .I a 
4. Proposal to Implement the Controller
(12)
2 2

 R f  K . .I f 2 .

RPFe 

In (12), a linear relationship between flux and field
current is assumed . Saturation can be neglected
because the aim of this work is to find a model to
minimize losses reducing the excitation. Then, the
back EMF can be expressed as Ea = K.If..
Based on the considerations above, a DCMD
equivalent circuit, including losses, as shown in Fig. 2,
is proposed
4.1 Losses Minimization
To design the field current control loop, an
excitation condition, able to produce the minimum
losses for each operating point, must be found.
Assuming that the DC machine is in steady state,
speed and torque (Te) can be considering constant to
obtain the minimum losses condition.
Considering the linear relationship between flux
and field current, the lossess minimization condition
can be derived from:
Pt
I f
(13)
 0,
Te , 
from which the following equation can be
obtained:
2.Ra  Rconv .I a 2  Ve  Econv .I a 
(14)

K 2 .2  2
2. R f 
.I f .

RPFe 

Operating (14), the following loss minimization
condition can be obtained:
If 
Fig. 2. Drive model including losses.
3. Experimental Validation of the Proposed Model
From different tests, the proposed model
parameters were obtained. Fig. 3 shows a comparison
between theoretical and experimental results that
validate the proposed model.
2.Ra  Rconv .I a 2  Ve  Econv .I a
.
2. R f  k ..k2  


(15)
Equation (15) allows to calculate the optimum
field-current value that minimizes the DCMD losses
for a specific operating point. To simplify the
implementation, in this equation, the iron losses
resistance RPFe is substituted by its equivalent (5), and
the constant k  K 2 / k1 .
As the algorithm depends on the system parameters,
which can change with temperature, time, different
machines, etc., the minimum loss condition calculated
by (15) is not exact. To solve this inconvenience, a
control loop, to perform a “fine tuning” of the field
current value to minimize the DCMD losses is
proposed. This loop is closed measuring the DC link
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power (DC link voltage VDCL times DC link current
IDCL), .
Clemente S. “A Simple Tool for Interactive Design of Inverters,”
PCIM OnLine. 1996.
The proposed controller is shown in Fig. 4.
Lehonard W. Control of Electrical Drives, 2nd ed., SpringerVerlag, Germany, 1995.
5. Conclusions
In this work, a DCMD model including copper and
iron motor losses, and converter losses is proposed.
0.70
1000 r.p.m.
0.60
600 r.p.m.
0.50
Efficiency
400 r.p.m.
0.40
200 r.p.m.
0.30
0.20
Proposed model
Experimental results
0.10
0.00
0.00
5.00
10.00
15.00
20.00
25.00
Torque [Nm]
Fig. 3. Experimental and simulated DCMD efficiency
with constant field current for different speeds.
*
ia *
Regulator
-
Langsdorf A. Principles of direct-current machines, McGraw –
Hill Book Company, New York, 1958.
Current
controled
converter
ia
Field
current
control
i f~
vDCL
i f*
Current
controled
converter
rriente
if
Fine tuning  if
control
iDCL
Fig. 4. Proposed Controller.
This model was experimentally validated. Based
on this model, an algorithm to minimize the DCMD
losses, controlling independently the armature and
field currents is proposed.
References
Nailen R. “Can field tests prove motor efficiency?,” IEEE Trans.
on Industry Applications, vol. 25, 1989.
Margaris N., Goutas T., Doulgeri Z., and Paschali A. “Loss
Minimization in DC Drives,” IEEE Trans. On Industrial
Electronics, vol. 38, No. 5, pp. 328–336. 1991.