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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+
+
���������
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