1. Projekt „ ISSNB “ Niš, September-October 2007.- 1 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Efficiency Optimization of Induction Motor Drive Based on Dynamic Programming Approach Presented by: Branko Blanu{a University of Banja Luka, Faculty of Electrical Engineering E-mail: bbranko@etfbl.net Research director: Prof. Slobodan N. Vukosavi}, Ph.D Niš 2007

2. Projekt „ ISSNB “ Niš, September-October 2007.- 2 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Main goal: For a known operating conditions, define optimal control so the drive operates with minimal energy consumption

3. Projekt „ ISSNB “ Niš, September-October 2007.- 3 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service FUNCTIONAL APPROXIMATION OF THE POWER LOSSES IN THE INDUCTION MOTOR DRIVE. Inverter losses:  i d, i q  d,q  R INV  Motor losses: Main core losses:   D   e   c 1  c 2  

4. Projekt „ ISSNB “ Niš, September-October 2007.- 4 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Copper losses:  R s  R r  Stray losses:    

5. Projekt „ ISSNB “ Niš, September-October 2007.- 5 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 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

6. Projekt „ ISSNB “ Niš, September-October 2007.- 6 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Optimal Control Computation Using Dynamic Programming Aproach 1. Performance index: (1) where N=T/T s, T is a period of close-cycled operation and T s 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

7. Projekt „ ISSNB “ Niš, September-October 2007.- 7 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 2. System equations 3. Constrains Equality contraints C[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 contraints C[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 conditions x(0) has to be knownn

8. Projekt „ ISSNB “ Niš, September-October 2007.- 8 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 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 2. System equation (dynamic of the rotor flux) where Tr=L r /R r is a rotor time constant

9. Projekt „ ISSNB “ Niš, September-October 2007.- 9 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 3. Constrains For torque Stator current Rotor speed Rotor flux 4. Boundary conditions 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:

10. Projekt „ ISSNB “ Niš, September-October 2007.- 10 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Following the dynamic programming theory, a system of differential equations can be defined as follows: where and  are Lagrange multipliers. (1)

11. Projekt „ ISSNB “ Niš, September-October 2007.- 11 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service By solving the system of equations (1) and including boundary conditions, we come to the following system: (2)

12. Projekt „ ISSNB “ Niš, September-October 2007.- 12 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Every sample time values of  r (i) and T em (i) defined by operation conditions is used to compute the optimal control (i d (i), i q (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

13. Projekt „ ISSNB “ Niš, September-October 2007.- 13 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 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.

14. Projekt „ ISSNB “ Niš, September-October 2007.- 14 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig.2 Speed reference.

15. Projekt „ ISSNB “ Niš, September-October 2007.- 15 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig 3. Load torque reference.

16. Projekt „ ISSNB “ Niš, September-October 2007.- 16 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig. 3. Graph of total power loss.

17. Projekt „ ISSNB “ Niš, September-October 2007.- 17 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig. 4. Graph of total power loss during transient process.

18. Projekt „ ISSNB “ Niš, September-October 2007.- 18 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig. 5. Speed response to step change of load torque.

19. Projekt „ ISSNB “ Niš, September-October 2007.- 19 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 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.

20. Projekt „ ISSNB “ Niš, September-October 2007.- 20 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig. 6 Graph of magnetization flux for LMC method a), dynamic programming approach b)

21. Projekt „ ISSNB “ Niš, September-October 2007.- 21 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig. 7 Graph of mechanical speed for LMC method a), dynamic programming approach b)

22. Projekt „ ISSNB “ Niš, September-October 2007.- 22 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Fig. 8 Graph of power loss for dynamic programming a), nominal flux b)

23. Projekt „ ISSNB “ Niš, September-October 2007.- 23 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 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.

24. Projekt „ ISSNB “ Niš, September-October 2007.- 24 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service 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  D  Dn 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.

25. Projekt „ ISSNB “ Niš, September-October 2007.- 25 - DAAD Deutscher Akademischer Austausch Dienst German Academic Exchange Service Thank you