Overview of Circuit Simulation
Programs
ECE 546 DIGITAL COMPUTATIONAL TECHNIQUES
FOR ELECTRONIC CIRCUITS
January 8, 2008
Oleg 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
properly
Inter-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
Z  R  jX


Ee
j
~
I

~
V

dx
 f (x, u)
dt
~
~
V  Ee j  ZI
Power Electronic Subsystem Models
Detailed
dxi
 f ( xi , si ); xi (t0i )  Tx i 1 (t fi 1 )
dt
(t fi , si 1 )  g ( xi , si )
Average Value
dx
 f (x, u)
dt
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,
…)
Circuit-Based Approaches
Circuit-Based Approaches
Example Subsystem
(Motor Controller)
Circuit-Based Approaches
Circuit-Based Approaches
Resistor-Companion Circuit
Circuit-Based Approaches
Update Formula
 iS   g1  g 2  g 3  g S
 i  

 S 
 i7   

 
i
 8  
 i9  
 gS
 g1
 g2
g 4  g5  g6


 g 3  v1 
  v2 
  
 
 
 v5 
k 1
O(n3) computational complexity where n = number of nondatum nodes
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,
…)
System-Based Approaches
Hierarchical system definition
System-Based Approaches
Common Simulink Component Models
System-Based Approaches
System-Based Approaches
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
x
k 1
p 1
  i x
i 0
Explicit if
k i
p 1

 h  i f x k i , t k i
i  1

1  0
Implicit algorithms require solution of nonlinear equation
(dimension = number of states) at each time step. NewtonRaphson iteration generally used.
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
System-Based Approaches
Simulink Algorithms
Shampine and Reichelt, The MATLAB ODE Suite, SIAM J. Sci. Comput.,
Vol. 18, No. 1, pp. 1-22, January 1997.
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,
…)
Finite-Element Based Approaches
FEA
M
4000-10000 Nodes
da
 Sa  u
dt
Conventional Parallel Computing Paradigm
Conventional Parallel Computing Paradigm
Conventional Parallel Computing Paradigm
Conventional Parallel Computing Paradigm


At best m-fold reduction in computation time
assuming zero communication latency
Computational gain further bounded by Amdahl’s
Law
T1
Tp  αT1  (1  α)
p
therefore
where serial portion α 0,1
T1
1
1
Sp 

 S 
Tp α  (1  α)
α
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, multirate, state model based, resistor-companion, finite
difference/element,...)
Heterogeneous networks (Ethernet, SCI, ScramnetTM,
MyrinetTM,...)
Key Advantages of DHS










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)
Optimum Allocation
More-Electric Aircraft Power System
Optimum Allocation
Optimum Allocation
18.5 speedup with 4 computers