Using link graphs in power electronics

Link graphs were introduced in 1961 for the analysis of mechanical systems.

The "bond graph" tool, devised by Henry Paynter of MIT Boston and formalized by D. Kamopp and R. Rosenberg, then J. Thoma, acts as an intermediary between the physical system and the mathematical models associated with it (transfer matrix in the linear case, linear or non-linear equation of state, systems of second-order differential equations). It entered Europe at the end of the 1970s, via the Netherlands (University of Twente). It is taught on a regular and organized basis at the École Centrale de Lille, the Université de Lyon-I, the INSA in Lyon and Toulouse, the ESE in Rennes, the Université de Mulhouse... Many companies, including those in the automotive industry, have adopted the link graph formalism for their modeling.

The motivation at the time was twofold: to develop a graphical tool for the coherent analysis of multi-domain physical systems, accessible and shared by specialists from different backgrounds.

The models obtained are always good knowledge models, because the very principle of their construction makes them "grey boxes" as opposed to "black boxes" obtained by identification: the structure of the model is always known, even if the parameters sometimes have to be determined experimentally. It should be pointed out, however, that this tool assumes that the physical phenomena are localized within the system. The modeling of systems with distributed constants will not be discussed here.

We'll look at a systematic procedure for writing the set of (differential) equations corresponding to the model of the physical system.

What's in it for the electrical engineer?

The link graph is a representation language designed to guide the engineer in analyzing and modeling his system. The engineer can then write a set of equations and translate them into a simulator. The link graph enables the engineer to know the quality of the analysis he is carrying out, as well as the relevance of the model he arrives at. The link graph comes upstream of the use of simulators, whatever they may be. The effort the engineer puts in before the simulation phase translates into greater efficiency (fewer variables, for example) and greater relevance of simulation results (assurance of a deterministic system, for example).

Link graph simulators (20-SIM, CAMPG, PACTE) do exist, but are not widely used. More often, engineers use link graphs to analyze and model a system. They then use a general simulator (MATLAB, SIMPLORER, MathCAD...) to translate the system's differential equations.

Readers will note that VHDL-AMS is a practical language for translating the...