projekt „ issnb “ niš, september-october 2007.- 1 - daad deutscher akademischer austausch...

Projekt „ISSNB“

Niš, September-October 2007. - 1 -

DAADDeutscher Akademischer Austausch DienstGerman Academic Exchange Service

Efficiency Optimization of Induction Motor Efficiency Optimization of Induction Motor Drive Based on Dynamic Programming Drive Based on Dynamic Programming

ApproachApproach

Presented by: Presented by: Branko Blanu{aBranko Blanu{a University of Banja Luka, Faculty of Electrical Engineering

E-mail: [email protected]

Research director: Prof. Slobodan N. Vukosavi}, Ph.D

Niš2007

Projekt „ISSNB“



Main goal:For a known operating conditions, define optimal control so the drive operates with minimal energy consumption

Projekt „ISSNB“



FUNCTIONAL APPROXIMATION OF THE POWER LOSSES IN THE INDUCTION MOTOR DRIVE.Inverter losses:

where id , iq are components of the stator current in d,q rotational system and RINV is inverter loss coefficient.Motor losses:Main core losses:

where D is rotor flux, esupply frequency and c1 and c2 are hystresis and eddy current loss coefficient.

222qdINVsINVINV iiRiRP

)()()()( 222

21 iiciicP DeDeFe

Projekt „ISSNB“



Copper losses:

where Rs is stator resistance, and Rr rotor resistance.

Stray losses:The stray flux losses depend on the form of stator and rotor slots and are frequency and load dependent. The total secondary losses (stray flux, skin effect and shaft stray losses) must not exceed 5% of the overall losses-requirments of the EU for 1.1-90kW motors

22qrssCu iRiRp

Projekt „ISSNB“



Important conclusions

1. It is possible to minimize power losses by variation of magnetizing flux in the machine.

2. For a given working point of the induction motor, only one pair of the stator currents produce flux which gives minimum of the power losses.

3. For a known operating conditions and for closed-cycle operation, it is possible to define optimal control so the drive operates with minimal energy consumption

Projekt „ISSNB“



Optimal Control Computation Using Dynamic Programming Aproach

1. Performance index:(1)

where N=T/Ts, T is a period of close-cycled operation and Ts is sample time. The L function is a scalar function of x-state variables and u-control variables, where x(i) , a sequence of n-vector, is determined by u(i), a sequence of m-vector

In order to do that, it is necessary to define performance index, system equations, constraints and boundary conditions for control and state variables and present them in a form suitable for computer processing

))(),(()(1

1

N

iiuixLNxJ

Projekt „ISSNB“



2. System equations

1..0,,)1( Niiuixfix

3. Constrains

Equality contraintsC[u(i)]=0 (Control variable equality constrains)C[x(i),u(i)]=0 (Equality constraints on function of control and state variables)S[x(i)]=0 (Equality constraints on function of state variables)

Inequality contraintsC[u(i)]0 (Control variable inequality constrains)C[x(i),u(i)] 0 (Inequality constraints on function of control and state variables)S[x(i)] 0 (Inequality constraints on function of state variables)

i=0,1,..N-1

4. Boundary conditionsx(0) has to be knownn

Projekt „ISSNB“



Following the above mentioned procedure, performance index, system equations, constraints and boundary conditions for a vector controlled induction motor drive in the rotor flux oriented reference frame, can be defined as follows

1. Performance index

1

0

222

21

22 )()()()()(N

iDeDeqd iiciicibiiaiJ

2. System equation (dynamic of the rotor flux)

iiLT

T

T

Tii dm

r

s

r

sDD

11

where Tr=Lr/Rr is a rotor time constant

Projekt „ISSNB“



3. Constrains

.0

,0

,

,0

,22

3,

min

2max

22

2

i

i

Iiiii

L

LpkiTiiiki

DD

DnD

rnrrn

sqd

r

memqd

For torque

Stator current

Rotor speed

Rotor flux

4. Boundary conditions

constrainsgconsiderinfreeN

NTT

N

DnDn

emem

rr

,0

,00

,00

Basically, this is a boundary-value problem between two points the boundary conditions of which are defined by starting and final value of state variables:

Projekt „ISSNB“



Following the dynamic programming theory , a system of differential equations can be defined as follows:

,1,..,2,1,0

,

012

02

21 221

Ni

i

ii

T

LiiiTiiiki

LT

Tiikiiiai

ikiiibi

iicicT

TTii

D

q

r

mreemqd

mr

Sqd

dq

Deer

Sr

where and are Lagrange multipliers.

(1)

Projekt „ISSNB“



By solving the system of equations (1) and including boundary conditions, we come to the following system:

.1,..,2,1,0

12

,,)(

)(1

2)()1()(2

221

22

34

Ni

T

TTiiicici

i

ii

T

Lii

iki

iTii

iiLTT

Ti

TT

Ti

iTk

bii

T

Tiiai

r

srDee

D

q

r

mre

d

emq

dmsr

sD

sr

rD

emdr

Sd

(2)

Projekt „ISSNB“



Every sample time values of r(i) and Tem(i) defined by operation conditions is used to compute the optimal control (id(i), iq(i), i=0,..,N-1) through the iterative procedure and applying the backpropagation rule, from stage i =N-1 down to stage i =0. Value of D and have to be known. In this case, D(N)=Dmin and

.0)(

NN

D

Projekt „ISSNB“



Simulation Results

Operation conditions (speed reference and load torque ) are given in Fig. 1. and Fig. 2.

Graph of power loss for given operation condition are presented in Fig. 3.

Graph of power loss and speed response during transient process and for different methods are presented in Fig. 4. and 5.

Projekt „ISSNB“



Fig.2 Speed reference.

Projekt „ISSNB“



Fig 3. Load torque reference.

Projekt „ISSNB“



Fig. 3. Graph of total power loss.

Projekt „ISSNB“



Fig. 4. Graph of total power loss during transient process.

Projekt „ISSNB“



Fig. 5. Speed response to step change of load torque.

Projekt „ISSNB“



Expermental results

Experimental tests have been performed in the laboratory station for digital control of induction motor drives which consists of:

- induction motor (3 MOT, D380V/Y220V, 3.7/2.12A, cos=0.71, 1400o/min, 50Hz)- incremental encoder connected with the motor shaft,- three-phase drive converter (DC/AC converter and DC

link),- PC and dSPACE1102 controller board with TMS320C31 floating point processor and peripherals,- interface between controller board and drive converter.

Projekt „ISSNB“



1 .0

0 .9

0 .8

0 .7

0 .6

0 .5

a) b)tim e (5s /d iv) tim e (5s /d iv)

mag

netiz

atio

n fl

ux p

.u.

Fig. 6 Graph of magnetization flux for LMC method a), dynamic programming approach b)

Projekt „ISSNB“



0

0.5

0.4

0.3

0.2

0.1

a)time (5s/div)

b)time (5s/div)

mec

hani

cal s

peed

p.u

.

Fig. 7 Graph of mechanical speed for LMC method a), dynamic programming approach b)

Projekt „ISSNB“



140

120

100

80

60

40

20

time (5s/div)b)a)

time (5s/div)

pow

er l

oss

(W)

Fig. 8 Graph of power loss for dynamic programming a), nominal flux b)

Projekt „ISSNB“



Conclusions

1. If load torque has a nominal value or higher in steady state, magnetization flux is also nominal regardless of whether an algorithm for efficiency optimization is applied or not.

2. At low loads in steady state, power loss for the LMC method and method based on dynamic programming is practically the same but significantly less than when the drive runs with nominal flux.

3. The method based on dynamic programming works in a way that magnetization flux starts to rise before the increase of load torque and keeps a higher value of magnetization flux during the transient processes than other methods for efficiency optimization. As a result, transient loss is lower and speed response is better.

Projekt „ISSNB“



4. The procedure of on-line parameter identification has been carried out in the background. In case the parameters change, a new optimal control value is computed for the next cycle of the drive operation. This increases the robustness of the algorithm in response to parameter variations.

5. Few simplifications in the computation of optimal control for the dynamic programming method have been made. Therefore, the computation time is significantly reduced. Some theoretical and experimental results show that some effects like nonlinearity of magnetic circuit for DDn has negligible influence in the calculation of optimal control.

6. One disadvantage of this algorithm is its off-line control computation.Yet, it is not complicated in terms of software.

7. This algorithm is applicable to different close-cycled processes of electrical drives, like transport systems, packaging systems, robots, etc.

Projekt „ISSNB“



Thank you

projekt „ issnb “ niš, september-october 2007.- 1 - daad deutscher akademischer austausch...

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