Federico Bergero

PowerDEVS: a tool for hybrid system modeling and real-time simulation

In this paper we introduce a general-purpose software tool for discrete event system specification (DEVS) modeling and simulation oriented to the simulation of hybrid systems. The environment, called PowerDEVS, allows atomic DEVS models to be defined in C++ language that can then be coupled graphically in hierarchical block diagrams to create more complex systems. The environment automatically translates the graphically coupled models into a C++ code which executes the simulation. A remarkable feature of PowerDEVS is the possibility to perform simulations under a real-time operating system (RTAI) synchronizing with a real-time clock, which permits the design and automatic implementation of synchronous and asynchronous digital controllers. Combined with its continuous system simulation library, PowerDEVS is also an efficient tool for real-time simulation of physical systems. Another feature is the interconnection between PowerDEVS and the numerical package Scilab. PowerDEVS simulations can make use of Scilab workspace variables and functions, and the results can be sent back to Scilab for further processing and data analysis. In addition to describing the main features of the software tool, the article also illustrates its use with some examples which show its simplicity and efficiency.

A novel parallelization technique for DEVS simulation of continuous and hybrid systems

In this paper, we introduce a novel parallelization technique for Discrete Event System Specification (DEVS) simulation of continuous and hybrid systems. Here, like in most parallel discrete event simulation methodologies, the models are first split into several sub-models which are then concurrently simulated on different processors. In order to avoid the cost of the global synchronization of all processes, the simulation time of each sub-model is locally synchronized in a real-time fashion with a scaled version of physical time, which implicitly synchronizes all sub-models. The new methodology, coined Scaled Real-Time Synchronization (SRTS), does not ensure a perfect synchronization in its implementation. However, under certain conditions, the synchronization error introduced only provokes bounded numerical errors in the simulation results. SRTS uses the same physical time-scaling parameter throughout the entire simulation. We also developed an adaptive version of the methodology (Adaptive-SRTS) where this parameter automatically evolves during the simulation according to the workload. We implemented the SRTS and Adaptive-SRTS techniques in PowerDEVS, a DEVS simulation tool, under a real-time operating system called the Real-Time Application Interface. We tested their performance by simulating three large-scale models, obtaining in all cases a considerable speedup.

A vectorial DEVS extension for large scale system modeling and parallel simulation

In this article we introduce an extension to the Discrete Event System (DEVS) formalism called Vectorial DEVS (VECDEVS) that allows to represent large scale systems in a graphic block diagram way. A pure VECDEVS model basically consist in an array of identical classic DEVS models that may differ in their parameters. The interconnection of VECDEVS models with some special classic DEVS models that can handle VECDEVS events allows us to easily represent large systems of arbitrary structure. A noticeable feature of this extension is that VECDEVS models can be easily split for parallel simulation. For that purpose, we developed an algorithm that automatically splits VECDEVS models into an arbitrary number of sub-models for parallel simulation. The implementation of VECDEVS and the partitioning algorithm in a DEVS simulation tool is also described and its usage is illustrated through some application examples.

Quantization-based simulation of switched mode power supplies

In this article we study the performance of quantized state system algorithms in the simulation of switched mode power supplies. Under realistic modeling assumptions, these models are stiff and exhibit frequent discontinuities, making them difficult to simulate with classic solvers. However, there are linearly implicit quantized state system methods that can efficiently handle these types of systems, providing faster and more accurate results. In order to corroborate these features, we first built the models corresponding to the different topologies of switched mode power supplies, and then analyzed the resulting equation structures in order to establish whether they can be efficiently simulated by linearly implicit quantized state system algorithms. Finally, we compared the simulation performance of linearly implicit quantized state systems with the widely used DASSL solver. The results showed that the linearly implicit quantized state systems were 3–200 times faster and noticeably more accurate than the differential algebraic system solver.

Time discretization versus state quantization in the simulation of a one-dimensional advection-diffusion-reaction equation

In this article, we study the effects of replacing the time discretization by the quantization of the state variables on a one-dimensional (1D) advection–diffusion–reaction (ADR) problem. For that purpose the 1D ADR equation is first discretized in space using a regular grid, to obtain a set of time-dependent ordinary differential equations (ODEs). Then we compare the simulation performance using classic discrete time algorithms and using quantized state systems (QSS) methods. The performance analysis is done for different sets of diffusion and reaction parameters and also changing the space discretization refinement. This analysis shows that, in advection–reaction-dominated situations, the second-order linearly implicit QSS method outperforms all of the conventional algorithms (DOPRI, Radau and DASSL) by more than one order of magnitude.

Simulation of Smart-Grid Models using Quantization-Based Integration Methods

Concepts such as smart grids, distributed generation and micro‐generation of energy, market‐driven as well as demand‐side energy management, are becoming increasingly important and relevant as emerging trends in the design, management and control of energy systems. Appropriate modeling and design, efficient management and control strategies of such systems are currently being studied. In this line of research a very important enabling component is efficient and reliable simulation. However those energy models are typically large, stiff and exhibiting heavy discontinuities, and at the same time consist of interconnected multi‐domain subsystems encompassing electrical, thermal, and thermo-fluid models. Object-Oriented (O‐O) languages such as Modelica are obviously well-suited for the modeling of such systems; however, traditional state-ofthe-art hybrid differential algebraic equation solvers cannot efficiently simulate these systems especially when their size grows to the order of hundreds, thousands, or even more interconnected units. The goal of this paper is to show, through a couple of exemplary case studies, that Quantized State System (QSS) integration methods are ideally suited to solve models of such systems, as they scale up better than traditional methods with the system size, and provide time savings of several orders of magnitude, while achieving comparable numerical precision.

QSS and multi-rate simulation of object-oriented models

Object-Oriented (O--O) languages like Modelica allow the description of multi-domain dynamical models. These models represent a Differential Algebraic Equation (DAE) that is usually converted to an Ordinary Differential Equation (ODE) formulation and simulated using numerical integration methods. Most Modelica tools include Single-Rate integration methods based on time discretization. Recently developed ODE numerical integration methods like Quantized State Systems (QSS) and Multi-Rate algorithms have some features (sparsity exploitation, efficient stiffness handling, efficient integration of loosely coupled systems of equations) that makes them suitable for many applications. By their nature, efficient implementation of these methods requires a different perspective on the model than classical methods, thus it is not a trivial task to implement them in Modelica tools. The Functional Mock-up Interface (FMI) is a tool independent standard for model exchange and co-simulation. Models are exchanged as compiled binaries (Functional Mockup Unit - FMU) with an API that allows the evaluation and simulation of the model. The FMU presents the model as a hybrid ODE on which numerical integration methods (such as Euler, Runge-Kutta) are applied for simulation. In this article we propose an extension to the FMU API to allow QSS and Multi-Rate simulation of O--O oriented models by means of FMI Model-Exchange. This extension opens up the possibility of testing and fine tuning QSS and Multi-Rate algorithms on a wide range of system models. Some results obtained with a prototype implementation on two example cases are reported.

GQLink: an implementation of Quantized State Systems (QSS) methods in Geant4

Simulations in high energy physics (HEP) often require the numerical solution of ordinary differential equations (ODE) to determine the trajectories of charged particles in a magnetic field when particles move throughout detector volumes. Each crossing of a volume interrupts the underlying numerical method that solves the equations of motion, triggering iterative algorithms to estimate the intersection point within a given accuracy. The computational cost of this procedure can grow significantly depending on the application at hand. Quantized State System (QSS) is a recent family of discrete-event driven numerical methods exhibiting attractive features for this type of problems, such as native dense output (sequences of polynomial segments updated only by accuracy-driven events) and lightweight detection and handling of volume crossings. In this work we present GQLink, a proof-ofconcept integration of QSS with the Geant4 simulation toolkit which stands as an interface for co-simulation that orchestrates robustly and transparently the interaction between the QSS simulation engine and aspects such as geometry definition and physics processes controlled by Geant4. We validate the accuracy and study the performance of the method in simple geometries (subject to intense volume crossing activity) and then in a realistic HEP application using a full CMS detector configuration.

An approach to agent-based modeling with Modelica

Abstract Modelica is a free, general-purpose object-oriented equation-based modeling language. It is mainly designed to describe systems using the physical modeling approach. Our proposal to describe Agent-Based Models (ABMs) in Modelica is discussed in this manuscript. The contribution of the presented work is twofold: firstly, to analyze the conceptual requirements to describe ABMs in Modelica; and secondly, to develop a prototype implementation following the previous analysis. Agents are described using a message passing communication mechanism previously proposed by the authors. Additional extensions to this mechanism are proposed in order to describe agent interactions. The environment, where the agents live, is described as a two-dimensional cellular automaton. A new Modelica library, named ABMLib, developed to support this functionality, is presented. A prototype implementation of the message passing mechanism and ABMLib models has been performed to demonstrate the functionality of the library as a proof-of-concept for this proposal. The library is freely available at www.euclides.dia.uned.es/vsanz .

Applying root-finding techniques to extend Quantized-State-Systems-based solvers

In this work we propose the usage of root isolation algorithms to extend Quantized-State-Systems-based methods for integrating systems of Ordinary Differential Equations to higher orders. QSS methods of order n, at their inner loop, neet to compute the minimum positive root of a n-degree polynomial. The lack of analytical expressions for the roots of polynomial of degree greater than four limits the QSS methods to fourth order or less. We make an observation which, combined with the usage of root-finding techniques, allows the generalization to QSS of any order. Moreover, we show experimentally that, considering our algorithmic improvements, higher order methods do require considerably fewer iterations than lower order ones.