Overview of Circuit Simulation Programs

ECE 546 DIGITAL COMPUTATIONAL TECHNIQUES FOR ELECTRONIC CIRCUITSJanuary 10, 2005Oleg Wasynczuk

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 properlyInter-dependencies between subsystems are becoming more and more prominent

More-Electric Aircraft Power System

Modeling Approaches

Synchronous Machine Subsystem Models

Distributed Parameter Coupled Circuit Steady State

)( uxfx ,dtd

= IZEeV j ~~ −= δ

+−

δjEe

jXRZ +=

I~V~

+

−

Power Electronic Subsystem ModelsAverage ValueDetailed

)( uxfx ,dtd

=)()(

)()( );(iiii

f

if

iiiiii

sgst

ttsdtd

,,

,

1

110

x

Txxxfx

=

==

+

−−

Simulation Approaches

Circuit-Based Approaches (Spice, EMTP, Saber, PSIM, Simplorer)System-Based Approaches (Simulink, ACSL, Dymola)

Block-diagram and/or differential equation orientedExtensive set of tool boxes including

ASMG (Simulink, ACSL)Power System Blockset (Simulink)…

Finite-Element-Based Approaches (Ansys, Maxwell, …)

Circuit-Based Approaches

Circuit-Based Approaches

Example Subsystem

(Motor Controller)

Circuit-Based Approaches

Circuit-Based Approaches

Resistor-Companion Circuit

15

2

1

654

321321

9

8

7

+

++

−−−−+++

=

−

k

SS

S

S

v

vv

ggggggggggg

iiiii

Update Formula

O(n3) computational complexity where n = number of non-datum nodes

Circuit-Based Approaches

Simulation Approaches

Circuit-Based Approaches (Spice, Saber, PSIM, Simplorer)System-Based Approaches (Simulink, ACSL, Dymola)

Block-diagram and/or differential equation orientedExtensive set of tool boxes including

ASMG (Simlink, ACSL)Power System Blockset (Simulink)…

Finite-Element-Based Approaches (Ansys, Maxwell, …)

System-Based Approaches

Hierarchical system definition

System-Based Approaches

Common Simulink Component Models

System-Based Approaches

System-Based Approaches

( )∑∑−

−=

−−−

=

−+ +=1

1

1

01 p

i

ikiki

p

i

iki

k th ,xfxx βα

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 01 =−β

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!

System-Based Approaches

Computational Complexity

System-Based Approaches

Dilemma

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

Simulation Approaches

Circuit-Based Approaches (Spice, Saber, PSIM, Simplorer)System-Based Approaches (Simulink, ACSL, Dymola)

Block-diagram and/or differential equation orientedExtensive set of tool boxes including

ASMG (Simulink, ACSL)Power System Blockset (Simulink)…

Finite-Element-Based Approaches (Ansys, Maxwell, …)

Finite-Element Based Approaches

4000-10000 Nodes

uSaaM =+dtd

FEA

Conventional Parallel Computing Paradigm

Integration algorithm (master)

slave 1

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slave 2 slave n -1

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Σ+

+

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Σ+

+

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Conventional Parallel Computing Paradigm

Conventional Parallel Computing Paradigm

Conventional Parallel Computing Paradigm

At best m-fold reduction in computation time assuming zero communication latencyComputational gain further bounded by Amdahl’s Law

pT)α1(αTT 1

1 −+=p where serial portion [ ]1,0α∈

therefore

α1S)α1(α

1TTS 1 ≡≤

−+

== ∞

pp

p

Distributed Heterogeneous Simulation (DHS)

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)

Sample DHS Computer Setup

DHS Concept

Much better than M-fold (potentially M3) improvement in speed

DHS Links Environment

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, ScramnetTM, MyrinetTM,...)

Use “best” language for each component/subsystemProprietary information protectedSuper-linear increase in computational speed across a network of desktop computersNo need to translate models into common languageLegacy code can be used directlyConducive to team design/analysisRemote interconnectionEliminate need to develop average-value models for system stability assessmentReal-time (hardware-in-the-loop) capability for some systemsSystem Integrator(s) do not have to be familiar with the language(s) used to create subsystem simulation(s)

Key Advantages of DHS

More-Electric Aircraft Power System

Optimum Allocation

Optimum Allocation

Optimum Allocation

18.5 speedup with 4 computers