Minimum Motor Losses Point Tracking for a
Stand-Alone Photovoltaic Pumping System
Tomás Corrêa∗ , Francisco A. S. Neves†, Seleme I. Seleme Jr.∗ and Selênio R. Silva∗
∗ PPGEE/UFMG
- Belo Horizonte, MG, Brazil
E-mail: tpcorrea@uol.com.br, seleme@ppgee.ufmg.br and selenios@ppgee.ufmg.br
† DEESP/UFPE - Recife, PE, Brazil
E-mail: fneves@ufpe.br
Abstract— Solar photovoltaic energy has been, for many years
now, a promising alternative in the diversification of global energetic sources. Although photovoltaic energy has many advantages,
it has not yet become commercially popular, because it is still an
expensive alternative. In fact, studies have already shown that the
investment in such systems are paid back, but it is still hard to
find people willing to wait five or six years to have their money
back. The aim of this work is to reduce the payback time of
photovoltaic stand-alone pumping systems, optimizing not only
the efficiency of the photovoltaic conversion, using a maximum
power point tracking algorithm, but also minimizing the losses in
the induction motor. Based on the design procedures described
in this paper, a prototype has been developed and experimental
results with the optimizing strategie are shown.
I. I NTRODUCTION
The process of photovoltaic energy conversion has special
intrinsic features which, for a given condition on solar irradiance and panel temperature, make possile to find an operation
point where the conversion efficiency is maximum. Fig. 1
shows typical curves of a photovoltaic array (PV) under certain
conditions on the temperature (curves a and b) and irradiance
(curves c and d), where curves a and b show the array current
(Ipv ) as function of voltage (Vpv ) and curves b and d show
the array power (Ppv ) as function of voltage.
(a)
Current [A]
4
25oC
55oC
3
(b)
1500
2
Power [W]
5
25oC
1000
55oC
500
1
0
0
200
300
400
Power [W]
3
2
1
200 Wm−2
0
100
200 300 400
Voltage [V]
Fig. 1.
0
100
500
200
300
400
500
(d)
1500
1000 Wm−2
4
0
0
500
(c)
5
Current [A]
100
1000 Wm−2
1000
500
0
200 Wm−2
0
100
200 300 400
Voltage [V]
500
Typical curves of a PV array.
Authors would like to thank Eletrobrás/LENHS and CAPES for the
financial support.
Considering that the prices of solar panels are still quite high
and the variation of their efficiency with the operating point,
as seen from Fig. 1, the use of some technique for tracking the
point of maximum power (MPPT) is imperative. This has been
a subject of interest of several studies and many approaches
have been proposed in the literature [1]. Among the existing
MPPT techniques, the most popular ones are those known as
Perturb and Observe (P&O) [2]–[4] and those based on the
Incremental Conductance (InCond) [5], [6].
The aim of this work is to study a photovoltaic standalone pumping system, optimizing not only the efficiency of
the photovoltaic conversion, using a maximum power point
tracking algorithm, but also minimizing the losses in the
induction motor that drive the centrifugal pump. Such thing
has not yet gained much attention to this specific application and it consists in operating the motor at its maximum
efficiency which, in association with the MPPT, renders the
whole system even more efficient. The principle behind this
technique is quite simple and it is based on the control of stator
voltage. It will be shown in section III that, under partial loads,
instead of keeping the same Volts-Hertz ratio, a reduction on
flux level can minimize losses and keep the machine close
to its rated efficiency. Computer simulations were made to
investigate how to work close to the minimum losses point and
propose a minimum losses point tracking (MLPT) algorithm.
Then, it was tested on the experimental system to quantify its
improvement and a gain up to 10% of machines’s rated power
was estimated. In such a system where energy price is one of
the key points, this result is quite impressive.
Both improvement techniques work with small perturbations
on the steady state, which can cause misworking. To avoid
conflict between them, which can lead to misworking, some
care need to be taken and it will be discussed in section IV.
The development and implementation of a photovoltaic
pumping system are presented in the next section. The motor
losses reduction theory is exposed and studied in section III.
Section V brings some experimental results, obtained with
a supervisory system, which measures and stores the most
important variables of the system, and real-time data from
the Digital Signal Controller (DSC), which provide means for
better analyzing and designing both algorithms.
II. PV
The pumping system (Fig. 2) is composed by 12 solar
panels of 120 Wp each, a conventional 1 hp three-phase
squirrel-cage induction motor (IM) and a centrifugal pump
(CP). A standard three-leg IGBT PWM inverter converts DC
voltage of PV panels into AC voltage to feed the motor. The
inverter control allows varying the motor speed (open loop)
and thus, modulating the load to the panels and tracking the
maximum power point of operation of the array. The inverter
is controlled by a low cost DSC manufactured by Freescale,
model MC56F8013. The measured variables available to the
DSC are Ipv , Vpv , Ia and Ib , which are the array’s current and
voltage, and two of three motor’s line current, respectively.
As this system main advantages are:
•
•
•
•
•
•
Ipv
PUMPING SYSTEM DESCRIPTION
The converter topology results in a high efficiency converter, with losses less than 10%. Also, as it uses a standard inverter topology, there are few options of modules
at an affordable cost;
It uses induction motors and standard centrifugal pumps,
which are cheaper, more rugged and with a better maintenance frequency/cost than other technological options;
It is a modular system: it can be increased gradually by
adding new panels;
It does not require energy accumulators, which imply in
lower initial investment and low maintenance cost, as well
as reduced losses, complexity and weight;
It works automatically with no need for operators;
The system design concepts are general and not specific
for utilized components, which allow great flexibility of
use.
A. MPPT method
As mentioned in the previous section, several MPPT methods have been proposed in the literature, applying several
different techniques as, for example, fuzzy logic and neural
networks. In order to evaluate the quantity of papers published
on this area, [1] lists 91 articles in its references, all of
them proposing either new approaches or improvement on the
existing ones. These approaches vary also with respect to their
complexity, used sensors, convergence rate, steady-state error
and cost, among others.
The algorithm adopted in this work was the incremental
conductance, which computes the inclination of curve Vpv
x Ppv using measurements of array’s voltage and current
(1), establishing whether the systems is at the current source
region, voltage source region or at the maximum power point.
PV
Ipv
Vpv
Icc
Ic
C
Inverter
Fig. 2.
a Ia
b
c Ib
Ic
IM
Simplified diagram of the system.
CP
MPPT
Vref +
-
C(s)
ωe
G(s)
Icc -
+
Ic
1
Cs
Vpv
Vpv
Fig. 3.
Block diagram of the MPPT control.
TABLE I
L OGIC OF THE MULTI - CRITERION ALGORITHM [9]
Measurements
∆Ppv
∆Vpv
∆Ipv
<0
<0
<0
<0
<0
≥0
<0
≥0
<0
>0
<0
≥0
>0
≥0
<0
>0
>0
<0
=0
–
–
Vref
↑
↑
↓
↓
↑
↓
↔
∂P
∂I
= I + V.
∂V
∂V
State of the PV
Irradiance ↓
Current source
Voltage source
Voltage source
Current source
Irradiance ↑
MPP
(1)
This is one of first proposed MPPT algorithms and it has
been chosen for some nice basic features as convergence
rate, simplicity, low number of sensors, low cost and low
steady-state error. These advantages, when compared to other
strategies, are described in [1], [7], [8]. The main drawback of
this approach when applied to pumping systems, as described
in [9], is its lack of stability when fast irradiance changes
occur. This was also verified in our experimental setup and
solved by adding an inner voltage control loop. The general
block diagram of MPPT control is depicted in Fig. 3, where
G(s) represents the system dynamics and ωe is the stator
voltage angular frequency. This is a more formal and natural
approach than that adopted by [9]. It allows a better design of
the controller and can avoid problems such as those noticed
in [10].
When implementing the incremental conductance approach
using a fixed point DSC, there is a limitation computing the
division Ipv /Vpv which can, eventually, imply in unacceptable
errors. This potential problem is avoided by using a multicriterion logic described in Table I.
The perturbation frequency and its amplitude were both
chosen by pratical tests. The first one was easier to chose,
as it is possible to check the control loop response time by
experimental means. The frequency should be as fast as the
controller allows, or in other words, as soon as the panels
voltage has stabilized at the next set point, another perturbation
can be done. The amplitude is more hard to determine and a
more formal approach must be chased, which is beyond of
this article scope. As known, it may not be to high, as it
will result a poor steady state response, neither to low, which
causes problems with quick changes in irradiance. The values
adopted to those variables were 2Hz and 1% of the open circuit
voltage (Voc ).
Is
B. Automation
A crucial concern in an autonomous pumping system, which
can be installed several kilometers away of a nearby assistance,
is its robustness and the automation of its operation. Nevertheless, even when the system is located in inhabited places,
as in isolated communities, the availability of technicians with
the necessary skills to operate and maintain such systems is
quite unlikely. Therefore, some strategies have been adopted,
which will be described next.
Given that the water column has to be overcome, there
is a minimum motor speed that produces a significant water
flow. Thus, the hydraulical and electrical systems determine
a minimum frequency for the motor voltage supply. On the
other hand, if the irradiance decreases below a certain level
and the available power is not sufficient to drive the motor, the
voltage in the panels will drop and the system will be turned
off due to under voltage protection. This procedure will wait
for the measured voltage to be inferior to a pre-established
value (50% of Voc ) for at least 10 cycles of the PWM and
then, it will withdraw the pulses from the inverter. After a
short interval, a new start should be commanded.
The aim of starting procedure is to ensure that the system
operates only when it is possible to pump water. For that sake,
a voltage/frequency ramp is applied to the motor up to the
minimum operating point, when the DC link voltage (Vpv )
is used as the first reference value and the MPPT algorithm
assumes control. If during the motor acceleration the DC
voltage collapses, this means that the irradiance is very low.
So, a longer period of time has to be waited before a new
start is tried. If, at any moment, Vpv stays for more than
10 PWM cycles below its inferior admissible limit, for any
possible reason as, for instance, some perturbation that the
control was not capable to reject, or the rotor blocking, etc.,
then the system stops and a new start procedure is immediately
commanded.
As the night comes, the panel voltages reduce considerably.
Then, the controller detects that there is no irradiance anymore
and starts the hibernation mode. This mode lasts for 10 hours,
after which it starts to measure the DC link voltage again.
In the case this voltage stays below 20% of Voc , new tests
are made, every 15 minutes. If the DC link voltage is over
50% of Voc , the system enters in the active mode and starting
procedures as described above are initiated.
III. I MPROVEMENT OF
MOTOR EFFICIENCY
A. Theory
The principle of flux weakening applied to induction motors
under partial loads to improve induction machines efficiency
dates back, at least, to 1983, when Rowan and Lipo have
studied its effect on a silicon-controlled rectifier (SCR) voltage
controller drive system [11]. From that time on, many authors
have been studying this matter [12]–[16]. Nevertheless, it is
not usual to be applied on a photovoltaic pumping system,
where it can be really advantageous, as in this kind of system
partial load is rule (as only at few moments the motor works
Rs
IsT
σLs
+
+
Vs
Er
-
-
Fig. 4.
Ife
Isλ
Rfe
L m’
Rr’.ωe
sωe
Induction motor’s vetorial equivalent circuit
at rated load) and, moreover, a few watts on savings represents
great amount of money.
To understand why it is possible to improve motor’s efficiency, let us analyze the induction machine’s equivalent
circuit of Fig. 4, which represents the core losses as a
equivalent shunt resistance (Rf e ) [17].
It is known that the eletromagnetic torque (Te ) is
(2)
Te = 3(P/2).(Lm /Lr )λr IsT ,
and the rotor flux (λr ) is
(3)
λr = Lm .Isλ ,
where Lm is the mutual inductance, Lr is the rotor self
inductance, P is the number of pole pairs, IsT and Isλ are
the torque and flux currents, as it is shown in Fig. 4.
For a given load condition, there is an infinite number of
pairs λr –IsT which keep the system in its equilibrium. As
Te is constant, a rotor flux reduction will lead to a increase
in IsT and vice-versa. As λr is proportional to Isλ and the
motor losses (PLoss ) can be expressed by (4), there must be a
2
flux which minimizes Ploss , i. e., a compromise between IsT
2
losses and Isλ ones.
PLoss = 3Rs .|Is |2 + 3Rf e |If e |2 + 3.Rr0 |IsT |2
(4)
Using (2) and (3), we can write the losses as a function of
the motor’s parameters, angular frequency (ωe ), load torque
(TL ) and rotor flux, (5).
PLoss
"
Rs
=3
+
L2m
#
(Rs + Rf e )
.
|λr |2 +
Rf2 e
2
(Rs + Rr0 ) 2 Lr
1
+
.
.TL
3
P Lm
|λr |2
2 R s Lr
.
ωe .TL .
+2 .
P R f e Lm
ωe L m
Lr
2
(5)
Notice that (5) is a convex function where it’s minimum
can be easily obtained as a function of the optimum flux:
p
|λro | = kλo (ωe ) TL
(6)
where kλo is equal to
v
u
2
u
(Rs +R0r )
2 Lr
u
.
3
P Lm
4
.
kλo (ωe ) = u
u
2
t
(Rs +Rf e )
ω e Lm
Rs
3 L2 +
. R2
Lr
m
fe
(7)
B. Obtaining efficiency improvements
As shown, loss reduction can be achieved by voltage control as function of machine’s load and frequency. The main
question now is: how to determine the correct voltage? Two
different strategies have been used in the literature: machine’s
parameters are estimated and some relation, as in (6), is used
to determine which voltage is to be applied; or an adaptative
scheme is adopted.
One very common strategy is the input power minimization.
This approach works quite well for constant loads, but in those
which torque decreases with speed, the minimum input power
occurs when the motor is not moving at all. A mathematical
model including core saturation and losses was used in order
to evaluate the alternatives of input variables that could, in
some way, be related with the maximum efficiency point. For
this model, a test procedure of the motor was carried out,
following IEEE-Std 114-2004. Windage and stray-load losses
were not considered in this work, because of its hardness of
measure and modeling [19].
Fig. 5 and Fig. 6 show the machine input variables and also
the power output and efficiency for two electrical frequencies,
50Hz and 40 Hz, respectively. The load was modeled as in
(8), where T60Hz is the pump nominal torque in per unity.
The circles shows maximum or minimum points. As it was
already expected, slip increases with voltage reduction, and the
input and output powers are strictly decrescent, what makes
the minimum input power approach impracticable. In both
figures, the minimum current point is located very close to
the maximum efficiency point.
TL [pu] = T60Hz .ωe [pu]2
(8)
This closeness gives us a clue that the current minimization
strategy might be a good way of tracking the maximum
efficiency point. The results presented in Fig. 5 and Fig. 6 were
made with T60Hz equal to 1 pu. This might not be the rule,
as the pump may not have been correctly chosen. To validate
the minimum current strategy, the maximum efficiency and
the efficiency at minimum current point were calculated for a
wide range of the parameter T60Hz , in (8), from 0.2 pu to 1.2
pu, at the frequency range of interest, from 0.62 pu to 1.1 pu.
The graph of Fig. 7 shows the MLPT’s relative efficiency for
the mentioned range. In this graph, a perfect quadratic load
would be represented as a straight vertical line. The result is
far beyond expected, with a maximum “tracking error” less
than 0.03%! In other words, the worst case is only 0,03%
worse then the best one.
Power [pu]; Current [pu]; Effiency; Power factor
1.6
1.4
input power
output power
efficiency
input current
power factor
1.2
1
0.8
0.6
0.4
0.2
0
0.3
0.4
0.5
0.6
Stator voltage [pu]
0.7
0.8
0.9
Fig. 5. Effect of voltage variation on efficiency, power output and input
variables (ωe = 50Hz).
Power [pu]; Current [pu]; Efficiency; Power factor
Equation (6) shows us that there is an unique flux for which
the machine’s efficiency is maximum. In fact, the efficiency is
not only at a maximum, but is constant for all loads [18] in a
given frequency. Although in this approach the core saturation
was not taken into account, for the sake of simplicity, it is
clear that, as the equivalent inductance is increased with the
decrease of flux, the effect in the current reduction is greater
than it would be without saturation and the loss reduction is
even greater.
1.6
input power
output power
efficiency
input current
power factor
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.2
0.3
0.4
0.5
Stator voltage [pu]
0.6
0.7
Fig. 6. Effect of voltage variation on efficiency, power output and input
variables (ωe = 40Hz).
The results presented are all for steady state, which is a
reasonable assumption, given that both the solar irradiance
and the hydraulic dynamics are slow if compared with the
electromagnetic one.
The tracking of the minimum current point is quite similar to
MPPT methods. Here, again, a fast track response, low steady
state error, low complexity and robustness are aimed. As a
first approach, the perturb and observe algorithm was chosen.
It isn’t the best method, its drawback are largely known, but, as
it is very simple, it can be used to test the maximum efficiency
strategy feasibility.
The results obtained in the system described in section II
are shown and discussed in section V.
IV. MPPT
AND
MLPT
DECOUPLING
Although the efficiency improvement methods use small
perturbations in the steady state, both can be used together
without compromising each other performance. This is a
matter of great concern, as unwanted interferences can cancel
the methods benefits or even have a perverse effect, causing
system’s performance to become worse. Thus, it surely needs
further discussion.
The aim here is to analyze what would be the crossed effects
of the MLPT’s perturbation on the panel’s variables and of the
MPPT ones on the motor input.
1.1
1
1.05
e
Electric angular frequency, ω [pu]
0.9995
1
(a)
0.95
0.999
0.9
0.9985
0.85
(c)
0.8
(b)
0.998
0.75
0.9975
0.7
0.65
0.2
0.997
0.4
0.6
0.8
1
Normalized torque with variable quadratic base, T
60Hz
Fig. 7.
[pu]
1.2
Minimum current point relative efficiency
Let us start with the first case. The MLPT changes the
motor voltage searching for the minimum current point. If the
stator voltage is reduced and the frequency is kept constant,
motor’s slip would increase, pump speed decreases and the
output power also would be reduced. As a consequence, the
load seen by the panels would change and their operation point
is also perturbed, but not by the MPPT algorithm. This would
be true if the DC link voltage was not controlled. But, as
it is controlled, frequency increases to maintain DC voltage
constant, the operation point of the panels does not change,
and the final result is an increase in pump speed and output
power, as expected.
The second case is harder to analyze. Throughout the whole
motor losses minimization analysis, frequency was treated as
constant, although it isn’t. It is, in fact, the main control
variable of the entire system and it is affected by three
factors: solar irradiance variation, set point changes of DC
link voltage (caused by the MPPT) or the MLPT itself. From
those three types of variations, irradiance changes have the
greatest potential of misleading the MLPT method, for at least
two reasons: there is no control on solar irradiance and it can
change abruptly.
Two alternatives were taken into account on how MLPT
actuates to modify stator voltage. It can be either acting
directly upon this variable (Fig. 8) or in an indirect way, acting
on the volts-hertz ratio (Fig. 9).
When irradiance increases, the stator current increases as
well and the sign of perturbation changes every MLPT cycle
(Fig. 8(a) and Fig. 9(a)). When it decreases, current follows
it and the sign of perturbation is kept constant throughout the
entire fall process (Fig. 8(b,c) and Fig. 9(b,c)).
The indirect method does not cause a side cross (from
dIs /dVs > 0 to dIs /dVs < 0 or the reverse) and almost
maintains the relative operation point on cases (a) and (b). In
fact, a deeper analysis shows that when the indirect method is
used, the variable that is controlled (and kept constant between
steps) is related to the flux. On the other hand, the direct
method controls voltage only, and that is why the first is better
than the second.
Stator voltage [pu]
Fig. 8. Behaviour of MLPT algorithm under irradiance change, direct MLPT
(c)
(b)
(a)
Stator voltage [pu]
Fig. 9.
MLPT
Behaviour of MLPT algorithm under irradiance change, indirect
V. E XPERIMENTAL RESULTS
Experimental results were obtained, which confirm the
improvement of the stand-alone photovoltaic pumping system
in terms of its efficiency when the extra algorithm is added
to the MPPT technique. Preliminary results are shown, which
give a quantitative idea of this improvement.
The evaluation of the MLPT algorithm was made with the
inverter supplied by the grid, in order to keep the power
constant and render the analysis of the approach easier. The
procedure was to, keeping a constant frequency (f ), run
the system without and with the MLPT on. Fig. 10 shows
the result obtained with f = 45Hz. Notice that, when the
algorithm is turned on, both the input power and the speed
(and output power) decrease. It was quite expected, since the
slip frequency increase is not compensated by a synchronous
frequency increase. It is important to have an idea on how the
output power changes with speed. In the used pump, small
perturbations on an operation point leads to almost no change
on torque, so Po = k.ωR , where Po is the power output, ωR
the rotor speed and k some proportionality constant. It can be
easily shown that for this load
dPo
dωR
=
,
Po
ωR
(9)
what means that if the rate of change in the power input
0.12
1.4
P = k.ω
Pin [pu]
1.2
o
Vs [pu]
1
100
200
300
400
500
600
700
800
900
Speed [rpm]
filtered [rpm]
1320
Power saved [pu]
0
1340
0.08
0.06
0.04
0.02
0
0.65
1300
Fig. 10.
R
s
0.6
1280
o
I [pu]
0.8
0.4
R
P = k.ω2
0.1
0
100
200
300
400
500
Time [s]
600
700
800
900
Fig. 11.
0.7
0.75
0.8
0.85
Frequency [pu]
0.9
0.95
1
Estimative of the power saved by the MLPT
Test of minimum losses point tracking algorithm for f = 45Hz
(dPi /Pi ) is greater than the speed change (dωR /ωR ), some
efficiency improvement is achieved. In order to be more conservative, the pump should be modeled as quadratic function
2
of the speed (Po = k.ωR
), and efficiency would improve if
dPi /Pi > 2.dωR /ωR . Notice that the slip frequency variation
is very small and limited. In fact, when reducing the motor
losses through the MLPT, while keeping the PV array at its
point of maximum power, the saving of losses of the motor
is converted in useful power at the pump. This is done as
follows: the DC voltage control increases the stator frequency
with the motor losses reduction due to the MLPT. A higher
frequency applied to the motor causes an increase in the rotor
speed an in the power delivered to the load.
Fig. 11 shows an estimative of the power saved for the
two models of the load. It is expected that the savings are
somewhere between the two lines.
VI. C ONCLUSION
The presented work aims the optimization of a stand-alone
solar pumping system. The improvements proposed here can
ease the path of this kind of system to popularization, reducing
the initial costs and its payback time.
The proposed motor losses minimization algorithm is quite
similar to a known MPPT, as neither of them require sensors,
search for maximum efficiency operation points and use small
perturbations to achieve their goals. It was shown that with the
proposed algorithm it is possible to reduce the motor losses
and have power savings up to 10% of input power, maximizing
the converted solar energy. The experimental results show the
feasibility of this strategy and confirm the theory.
R EFERENCES
[1] T. Esram and P. L. Chapman, “Comparison of photovoltaic array
maximum powrer point tracking techniques,” IEEE Transactions on
Energy Conversion, vol. 22, no. 2, pp. 439–449, Jun 2007.
[2] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optmizing of
perturb and observe maximum power point tracking,” IEEE Trans. on
Power Electronics, vol. 20, no. 4, pp. 963–973, Jul 2005.
[3] C. Hua and J. R. Lin, “Dsp-based controller application in battery storage
photovoltaic system,” In Proc. IEEE IECON ’96, pp. 1705–1710, 1996.
[4] N. S. Souza, L. A. C. Lopes, and X. Liu, “An intelligent maximum power
point tracker using peak current control,” In Proc. IEEE PESC’05, pp.
172–177, 2005.
[5] C. Pan, J. Chen, C. Chu, and Y. Huang, “A fast maximum power point
tracker for photovoltaic power systems,” In Proc. IECON’99, pp. 390–
393, 1999.
[6] T. Kim, H. Ahn, S. K. Park, and Y. Lee, “A novel maximum power point
tracking control for photovoltaic power system under rapdily changing
solar radiation,” IEEE int. Symp Ind Electronics, pp. 1011–1014, 2001.
[7] K. C. Oliveira, M. C. Cavalcanti, G. M. S. Azevedo, and F. A. S. Neves,
“Comparative study of maximum power point tracking techniques for
photovoltaic systems,” In Proc. VII INDUSCON, Aug 2006.
[8] D. P. Hohm and M. E. Ropp, “Comparative study of maximum power
point tracking algorithms using an experimental, programmable, maximum power point tracking bed,” IEEE, pp. 1699–1702, 2000.
[9] G. Heng, X. Zheng, L. You-Chun, and W. Hui, “A novel maximum
power point traking strategy for stand-alone solar pumping system,”
IEEE/PES Transmission and Distribution Conference and Exhibition,
pp. 1–5, 2005.
[10] S. Zhang, Z. Xu, Y. Li, and Y. Ni, “Optimization of mppt step size in
stand-alone solar pumping system,” Power Engineering Society General
Meeting, p. 6 pp, Jun 2006.
[11] T. A. Lipo, “A quantitative analisys of induction motor performance
improvement by scr voltage control,” IEEE Trans. on Industry Applications, vol. IA-19, no. 4, pp. 545–553, July/August 1983.
[12] D. S. Kirschen, D. W. Novotny, and W. Suwanwisoot, “Minimizing
induction motor losses by excitation control in variable frequency
drives,” IEEE Trans. on Industry Applications, vol. 20, pp. 1244–1251,
sep/oct 1984.
[13] K. Matsuse, S. Taniguchi, T. Yoshizumi, and K. Namiki, “A speedsensorless vector control of induction motor operating at high efficiency
taking core loss into acount,” IEEE Trans. on Industry Application,
vol. 37, no. 2, pp. 548–558, Mar/Abr 2001.
[14] M. N. Uddin and S. W. Nam, “Adaptive backstepping based online loss
minimization control of an im drive,” Canadian Journal of Electrical
and Computer Engineering, vol. 32, pp. 97 – 102, 2007.
[15] M. Tsuji, S. Chen, T. Kai, E. Yamada, S. Hamasaki, and A. D. Pizzo, “A
precise torque and high efficiency control for q-axis flux-based induction
motor sensorless vector control system,” SPEEDAM 2006, pp. 990 – 995,
May 2006.
[16] H. Sepahvand and S. Farhangi, “Enhacing performance of a fuzzy
efficiency optimizer for induction motor drives,” PESC ’06, pp. 1 –
5, June 2006.
[17] E. Levi, A. Lamine, and A. Cavagnino, “Impact of stray load losses
on vector control accuracy in current-fed induction motor drives,” IEEE
Trans. on Energy Conversion, vol. 21, pp. 442–450, Jun 2006.
[18] T. W. Jian, N. L. Schmitz, and D. W. Novotny, “Characteristic induction
motor slip values for variable voltage part load performance optimization,” IEEE Trans. on Power Apparatus and Systems, vol. PAS-102,
no. 01, pp. 38–46, Jan/Feb 1983.
[19] K. J. Bradley, W. Cao, and J. Arellano-Padilla, “Evaluation of stray
load loss in induction motors with a comparison of input-output and
calorimetric methods,” IEEE Trans. on Energy Conversion, vol. 21,
no. 3, pp. 682–689, Sep 2006.