1. Overview of Circuit Simulation Programs ECE 546 DIGITAL COMPUTATIONAL TECHNIQUES FOR ELECTRONIC CIRCUITS January 8, 2008 Oleg Wasynczuk

2. Need for System-of-Subsystems Approach  Complex engineered systems such as aircraft, modern automobiles, or the terrestrial electric power grid involve a broad spectrum of technologies and interactive subsystems that must work synergistically in order to operate properly  Inter-dependencies between subsystems are becoming more and more prominent

3. More-Electric Aircraft Power System

4. Modeling Approaches

5. Synchronous Machine Subsystem Models Distributed ParameterCoupled CircuitSteady State  

6. Power Electronic Subsystem Models Average ValueDetailed

7. Simulation Approaches  Circuit-Based Approaches (Spice, EMTP, Saber, PSIM, Simplorer)  System-Based Approaches (Simulink, ACSL, Dymola) Block-diagram and/or differential equation oriented Extensive set of tool boxes including  ASMG (Simulink, ACSL)  Power System Blockset (Simulink)  …  Finite-Element-Based Approaches (Ansys, Maxwell, …)

8. Circuit-Based Approaches

9. Example Subsystem (Motor Controller)

10. Circuit-Based Approaches

11. Resistor-Companion Circuit

12. Update Formula O(n 3 ) computational complexity where n = number of non- datum nodes Circuit-Based Approaches

13. Simulation Approaches  Circuit-Based Approaches (Spice, Saber, PSIM, Simplorer)  System-Based Approaches (Simulink, ACSL, Dymola) Block-diagram and/or differential equation oriented Extensive set of tool boxes including  ASMG (Simlink, ACSL)  Power System Blockset (Simulink)  …  Finite-Element-Based Approaches (Ansys, Maxwell, …)

14. System-Based Approaches Hierarchical system definition

15. System-Based Approaches Common Simulink Component Models

16. System-Based Approaches

17. When user starts model, Simulink applies selected integration algorithm to approximate solution at discrete but not necessarily uniform instants of time General Multi-step Formula Implicit algorithms require solution of nonlinear equation (dimension = number of states) at each time step. Newton- Raphson iteration generally used. Explicit if

18. System-Based Approaches Stiff System: A system with both fast and slow dynamics Stiffly Stable Integration Algorithm: the ability to increase the time step after fast transients subside Stiffly Stable Algorithms are implicit!

19. System-Based Approaches Computational Complexity

20. System-Based Approaches Dilemma

21. Simulink Algorithms Shampine and Reichelt, The MATLAB ODE Suite, SIAM J. Sci. Comput., Vol. 18, No. 1, pp. 1-22, January 1997. System-Based Approaches

22. Simulation Approaches  Circuit-Based Approaches (Spice, Saber, PSIM, Simplorer)  System-Based Approaches (Simulink, ACSL, Dymola) Block-diagram and/or differential equation oriented Extensive set of tool boxes including  ASMG (Simulink, ACSL)  Power System Blockset (Simulink)  …  Finite-Element-Based Approaches (Ansys, Maxwell, …)

23. Finite-Element Based Approaches 4000-10000 Nodes FEA

24. Conventional Parallel Computing Paradigm

27.  At best m -fold reduction in computation time assuming zero communication latency  Computational gain further bounded by Amdahl’s Law where serial portion therefore

28. Distributed Heterogeneous Simulation (DHS)

29. DHS Definition  Synchronized interconnection of any number of dynamic subsystem simulations  Developed using any combination of programs/languages  Implemented on: Single computer/workstation/supercomputer Local area network (Intranet) Wide area network (Internet)

30. Sample DHS Computer Setup

31. DHS Concept Much better than M-fold (potentially M 3 ) improvement in speed

32. DHS Links Environment

33. Flexibility of DHS  Heterogeneous platforms (Windows, Unix, Linux,...)  Heterogeneous languages (ACSL, MATLAB/Simulink, Saber, EASY5, C, C++, FORTRAN, Java,…)  Heterogeneous simulation approaches (single-rate, multi- rate, state model based, resistor-companion, finite difference/element,...)  Heterogeneous networks (Ethernet, SCI, Scramnet TM, Myrinet TM,...)

34. Use “best” language for each component/subsystem Proprietary information protected Super-linear increase in computational speed across a network of desktop computers No need to translate models into common language Legacy code can be used directly Conducive to team design/analysis Remote interconnection Eliminate need to develop average-value models for system stability assessment Real-time (hardware-in-the-loop) capability for some systems System Integrator(s) do not have to be familiar with the language(s) used to create subsystem simulation(s) Key Advantages of DHS

35. More-Electric Aircraft Power System Optimum Allocation

37. 18.5 speedup with 4 computers