# AN IMPROVED SEARCH BASED ALGORITHM FOR EFFICIENCY OPTIMIZATION IN

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```					   AN IMPROVED SEARCH BASED ALGORITHM FOR EFFICIENCY OPTIMIZATION IN
THE INDUCTION MOTOR DRIVES
Branko Blanu{a, Petar Mati}, Faculty of Electrical Engineering in Banja Luka
Slobodan N. Vukosavi}, Faculty of Electrical Engineering in Belgrade

Abstract - Fuzzy logic based on-line efficiency
Functional approximation of the power losses in the
optimization control of vector-controlled induction motor
vector controlled induction motor drive is given in the second
drive is presented in this paper. Implementation of this
Section. Problems related to the efficiency optimization and
algorithm, power and energy losses as well as heating of
search controller design are discussed in the third Section.
machine are reduced. It keeps all qualitative characteristics
Simulation and experimental results are given in the fourth
of search algorithms but also gives less torque ripple with
and fifth Section respectively.
flux changes, less sensitivity to load perturbations and better
control characteristics. Model of applied search controller is    2.   FUNCTIONAL APPROXIMATION OF THE
given in a paper. Also, both simulation and experimental               POWER LOSSES IN THE INDUCTION MOTOR
studies are performed to validate a theoretical development            DRIVE.
and these results are presented.
The process of energy conversion within motor drive
1. INTRODUCTION                                                   converter and motor leads to the power losses in the motor
windings and magnetic circuit as well as conduction and
The induction motor is without doubt the most used          commutation losses in the inverter.
electrical motor and a great energy consumer [1]. Three-                Inverter losses: Depending on the power rating, the
phase induction motors         consume 60% of industrial          inverter losses are 3-5% and their main constituents are the
electricity and it takes considerable efforts to improve their    rectifier, inverter conductive and inverter commutation
efficiency [1]. Most of the motors operate at constant speed      losses. The overall flux-dependent inverter losses are usually
although the market for variable speed is expanding.              given by:
Moreover, induction drive is often used in servo drive                                                         (    )
PINV = R INV ⋅i s2 = R INV ⋅ i d + i q ,
2     2
(1)
applications. Vector control is the most used control
technique in high performance induction motor drive               where id, iq are components of the stator current is in d,q
applications. Control algorithm is usually applied in digital     rotational system and RINV is inverter loss coefficient.
microcontroller and current regulated PWM voltage inverter
is most often used actuator.                                           Motor losses: These losses consist of hysteresis and
eddy current losses in the magnetic circuit (core losses),
The evolution of the powerful digital microcontrollers      losses in the stator and rotor conductors (copper losses) and
allows applying not only method of vector control, but also       stray losses. At nominal operating point, the core losses are
different functions which make drives more economic and           typically 2-3 times smaller then the cooper losses, but they
more robust. One of the most interesting algorithm which can      represent main loss component of a highly loaded induction
be applied in drive controller is algorithm for efficiency        motor drives. The main core losses can be modelled by:
optimization [1].
PFE = c Fe Ψd ω ep ,                    (2)
There are three strategies which are usually used in
efficiency optimization of induction motor drive; Simple           where ψd is magnetizing flux, ωe supply frequency and cFe
State Control, Model Based Control and Search Control[4].         core loss coefficient. The fractional exponent p in the core
loss representation is to be avoided in order to facilitate the
Search strategy methods have an important advantage         implementation on the controller board. Expression (2) is
compared to other strategies. It is completely insensitive to     usually used with p=2.
parameter changes while effects of the parameter variations
caused by temperature and saturation are very expressed in             Copper losses are due to flow of the electric current
two other strategy. The on-line efficiency optimization           through the stator and rotor windings and these are given by:
control on the basis of search , where the flux is decremented
p Cu = R s i s2 + R r i q ,
2
(3)
in steps until the measured input power settles down to the
lowest value is very attractive. The control does not require     where Rs is stator resistance, and Rr rotor resistance.
the knowledge of motor parameters and the algorithm is                  The stray flux losses depend on the form of stator and
applicable universally to any motor.                              rotor slots and are frequency and load dependent [5]. The
Besides all good characteristics of search strategy          total secondary losses (stray flux, skin effect and shaft stray
methods, there is an outstanding problem in its use. When the     losses) usually don't exceed 5% of the overall losses.
load is low and optimal operating point is found, flux is so      Considering also, that the stray losses are of importance at
low that the motor is very sensitive to load perturbations [2].   high load and overload conditions, while the efficiency
In the presented paper search based algorithm with torque         optimizer is effective at light load, the stray losses are not
margin control is purposed. Experimental results show             considered as a separate loss component in the loss function.
significant less motor sensitivity to load perturbation.          Formal omission of the stray loss representation in the loss
function have no impact on the accuracy algorithm for on-                         Variables Vdc and Idc are voltage and current in DC link.
line optimization.                                                            Variable ωr is mechanical speed. Current Idc can be direct
Based on previous consideration, total flux dependent                    measured in DC link and Te are known variables in a drive.
power losses in the drive are given by the following                          Speed ωr is measured or estimated. So, we can calculate
equitation:                                                                   power losses without knowledge of motor parameters and
Pγ = (R INV + R s )i d + (R INV + R s + R r )i q + c Fe ω 2 ψ 2 .
2                         2
d   (4)   power loss calculation is independent of the motor parameter
Taking into account expressions for electromagnetic torque:                 changes in the working area.
Te = kψ d i q ,                   (5)
3.         MODEL OF EFFICIENCY                OPTIMIZATION
where k is positive constant                                                             CONTROLLER
and magnetizing flux for a linear approximation and a steady
state is:                                                                          This algorithm for efficiency optimization is based on
ψ d = Mi d ,                    (6)                 search strategy. Characteristic of the search strategy is that
where M is magnetizing inductance, power losses can be                        active input power is measured in drive and that this power is
given by:                                                                     minimized by adjusting one of the drive variables, slip
T2                                               frequency, magnetizing current (magnetizing flux) or stator
Pγ = c1 e2 + c2ψ m .
2
(7)                 voltage [4]. The principle of the search control is shown in
ψm                                            Fig.1.
where                                                                              Pin
c1 = (R s + R INV + R r ) / k 2
Power loss calculation
(8)         ωr
Pγ    Efficiency    Ψ*(id )
optimization
Pγ ≅ Pin −ω r Te*            controller
and                                                                                Te*
R s + R INV            2
c2 =                 + c Fe ω e .                     (9)
M      2                                                  Fig.1. Mechanism of search control, based on adjusting
Second derivative of function (7) gives:                                                      magnetizing flux to load torque.
There is an important advantage this strategy compared
∂ 2 Pγ               c ⋅T 2                                      to others:” It is independent from the motor parameters
= 2 ⋅ c2 + 6 ⋅ 1 2e > 0                          (10)
∂Ψ 2                  Ψm                                         changes”[2].
Based on expression (10) it can be concluded that                             But, also, there are some problems in the use of search
function (7) is concave and it has an unique minimum.                         strategy methods:
Therefore, it is possible to minimize power losses by                         1. Torque ripple appears each time the flux is stepped.
variation of magnetizing flux in the machine.                                 2. When the optimal operating point is found,
Also, next can be seen from the expressions (5),(6) and                      electromagnetic torque reserve is low, so motor is very
(7): “For a given working point of the induction motor, only                       sensitive to load perturbations.
one pair of the stator currents produce flux which gives                      3. Convergence of the magnetizing current to the value for
minimum of the power losses”[4].                                                   which power losses are minimal is to slow.
But, there are several problems in calculating pair (id, iq)            4. Magnetizing current is never reached its optimal value
of the stator current which gives minimum losses. If the                           then in small steps oscillates around it.
losses in the drive were known exactly, it would be possible                  Based on expression (7) it can be concluded that function of
to calculate the optimal operating point and control of drive                 power losses is non-linear. Also, controller for efficiency
in accordance to that. For the following reasons it is not                    improvement should follow known rules. These are reasons
possible in practice [3] .                                                    why fuzzy logic technique should be applied in the
1. Even though efficiency optimization could be calculated                    realization of efficiency optimization controller [3].
exactly, it is probably that limitation in computation                         Simulink model of efficiency optimization controller is
power in industrial drives would make this impossible.                   shown in Fig.2. It consists of 3 blocks:
2. A number of fundamental losses are difficult to predict:                   1. In the first block sign and step of power loss decrement
stray load, iron losses in case of saturation changes,                        (∆Pγ) are calculated as difference between two last
copper losses because of temperature rise etc.                                samples of the power losses according expression (11).
3. Due to limitation in costs all the measurable signals can                  2. Electromagnetic torque margin is calculated in the
not be acquired. It means that certain quantities must be                      second block.
estimated which naturally leads to an error.                             3. New value of magnetizing flux is determined in the third
For above mentioned reasons it is impractically calculate                           block.
power losses on the basis of loss model. Total power losses                   Input variables in controller are electromagnetic torque
can be calculated as difference between input and output                      reference, power losses calculated according expression (11)
drive power:                                                                  and magnetizing current. Output variables are new values of
Pγ = Pin − Pout ,                  (11)              stator current components in d, q coordinate system (id, iq).
Sign and step of power loss decrement are calculated in
where                                                                         the first block as:
Pin = Vdc ⋅ I dc                              (12)                    ∆Pγ (n) = Pγ (n ) − Pγ (n − 1)            (14)
is input drive power and
and
Pout = ω r Te                                 (13)
 1 , ∆Pγ (n) ≥ 0
is output drive power.                                                                       sgn(∆Pγ (n)) =                                 (15)
− 1 , ∆Pγ (n) < 0
Pγ                                                  1
z
Power losses                  Sign and step of power loss
(input variable)              increment γ P (n)-P (n-1)                                       Sign of magnetizing
γ
current step

1
z          -1

I BLOCK

i dref
New value of
Mux                                          u
magnetizing current
id(output variable)
1                                 Fuzzy
z                                 kontroler
III BLOCK

Te
Electromagnetic torque reference                                      2Lr
(input variable)                                                                                                                            iqref
3pLm
Calculation of               New value of
1                                                                    electromagnetic torque       active current iq
id                Lm                                                                                                                   (output variable)
U                                                                    margin
1
Previous sample of                                                                         z
magnetizing current                           1
(input variable)                              z                        2Lr
3pLm            I q,max
T e,max

X

II BLOCK

Fig .2. Simulink model of controller for efficiency improvement in the vector controlled induction motor drive.

Sign of the power loss decrement determines direction of the                             further flux decreasing will not be allowed even optimal
flux changes. If the sign is positive, losses increase so                                 operating point is not reached.
direction of the magnetizing flux decrement (M∆id) should be                                   Sign and step of power losses decrement and
inverted. In the other case, if the sign is negative, losses                              electromagnetic torque margin are input variables of fuzzy
decrease so direction of the magnetizing flux decrement                                   controller. On these basis, new step of magnetizing current is
should be kept.                                                                           generated from fuzzy rules through fuzzy inference and
Step of power loss decrement determines step of                                      defuzzification.
magnetizing flux decrement. If the working point is a far
from the optimal, step of flux decrement is a maximal                                     4. SIMULATION RESULTS
allowed. This step are decreased by the approaching to the
optimal operating point of the machine.                                                        Simulation studies     are performed to validate a
Electromagnetic torque margin (∆Te) is calculated in the                             theoretical development. Simulation model was made in
second block as difference between machine torque                                         Simulink-Matlab software. Model of efficiency controller is
maximum and maximal torque which can be reached from                                      incorporated in the model of motor drive. Power losses and
the instantaneous working point by increasing of iq current                               drive performances were tested with efficiency controller and
Step of electromagnetic torque can be defined by the                                      compared with the case when efficiency controller is not
following expression:                                                                     included in a drive model. Some characteristic cases were
∆Te (n) = kid (n) I s2,max − i d (n)  ,

2
      (16)                          and sudden increase of load torque. Especially interesting
                    
case is when sudden increase of torque load is appeared.
where Is,max is maximum of the stator current.
Enough electromagnetic torque margin is essential to prevent
If ∆Te is sufficient, it has no effect in the determination next
speed drops in the speed control drives. Power losses in a
flux decrement. In the other case, if ∆Te is unsufficient                                 motor drive with and without efficiency controller and for a
sudden increase of load torque from 0.3 pu to 0.7 pu is shown                                - three-phase drive converter (DC/AC converter and DC
- PC and dSPACE1102 controller board with TMS320C31
120                                                                        floating point processor and peripherals,
- interface between controller board and drive converter.
100                                                                            dSPACE DS1102 controller board with digital signal
processor is connected to PC via ISA slot. Control and
power losses [W]

80                                                                       acquisition function as well as signal processing are executed
on this board, while PC provides comfortable interface
60 without optimization
toward user.
Algorithms observed in this paper is software realized
40
using Matlab – Simulink and dSPACE real-time interface for
dSPACE hardware. dSPACE DS1102 Development Kit
20        with optimization
contains software for development real-time applications as
Simulink models or C programs. This software provides
0
0                           10   20   30         40           50   additional Simulink Toolbox for development real-time
applications as Simulink models and their compiling,
Fig. 2. Graphic of the power losses for a sudden increase of                                      After Simulink model is finished and simulation
load torque -simulation results.                                              parameters are specified a Build procedure can be started.
During Build procedure Simulink blocks are automatic
5. EXPERIMENTAL RESULTS                                                                      translated in the machine code and downloaded into program
memory. Handling real-time applications can be done in
Experimental tests were performed on the Laboratory                                     Matlab or СontrolDesk.
Station for Vector Control of the Induction Motor Drives -                                        Power losses in the motor drive with and without appllied
Vectra. Basic parts of the Laboratory Station Vectra are:                                    algorithm and for a sudden increase of load torque is shown
- induction motor (3 MOT, ∆380V/Y220V, 3.7/2.12A,                                            in Fig. 4. Load torque changes from 0.4 pu to 1.1 pu in a
0.75kW, cosφ=0.71, 1400o/min, 50Hz)                                                        case shown in Fig. 4.
- incremental encoder connected with the motor shaft,
Power losses [W]

Without o ptimization                             With o ptimization

time [s]
Fig. 4. Induction motor drive power losses for a sudden increase of load torque -experimental results.

6. CONCLUSIONS
[2] Branko D. Blanuša: Algoritam za minimizaciju snage
Implementation of this algorithm for efficiency                                              gubitaka vektorski regulisanog asinhronog pogona
improvement next results are obtained:                                                           zasnovan na primjeni fazi, magistarski rad, Univerzitet u
1. Less torque ripple with flux changes                                                     Banjaluci 2001.
2. Less drive sensitivity to load perturbations                                         [3] G. C. D. Sousa, B. K. Bose, J. G. Cleland, “Fuzzy Logic
3. Electromagnetic torque margin is controlled so                                           Based On-Line Efficiency Optimization of an Indirect
better control characteristics are obtained.                                            Vector-Controlled Induction Motor Drive“, IEEE Trans.
4. Total power losses are reduced especially when                                           Ind. Elec., Vol.42, No.2
motor works with light loads.                                                       [4] F. Abrahamsen, J. K. Pedersen, F. Blaabjerg: “State-of-
Both simulation and experimental studies are performed to                                        Art of Optimal Efficiency Control of Low Cost
validate a proposal algorithm.                                                                   Induction Motor Drives”, Proceedings of PESC’96, pp.
920-924, 1996.
REFERENCES                                                                                   [5] Emanuele Cerruto, Alfio Consoli, Antonio Testa,
“Fuzzy Adaptive Vector Control of Induction Motor
[1] Slobodan N. Vukosavi} "Controlled Electrical Drives -                                        Drives”, IEEE Transactions on Power Electronics,
Status of Technology", Zbornik XLII Konf. ETRAN-a,                                           vol.12, No.6 November 1999.
Vrnja~ka Banja, 2-5 juna 1998, Sveska 1, str. 3-16.                                      [6] ControlDesk Experiment Guide, dSPACE Digital Signal
Processing and Control Engineering GmbH, May 1999.

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