World3 in Modelica: System Dynamics Models

World3 in Modelica: Creating System Dynamics Models in the Modelica Framework

This paper and presentation by F. E. Cellier introduces a new release of the System-Dynamics library of Modelica and shows how it is being used by discussing a fairly large application code: Meadows’ World3 model.

Meadows’ only talked in Limits to Growth about the results obtained with the model. The model itself, originally coded in Dynamo, was described in a separate book.

Meadows’ World3 model has seen two major upgrades since its original inception, one in 1992, i.e. after 20 years, and the second in 2002, i.e., after 30 years. The World3 application code contained in SystemDynamics 2.0 implements the 2002 version of the World3 model. In the code, we offer not only the basic model, but also all 10 scenarios that Meadows and co-workers are talking about in Limits to Growth: The 30-Year Update.

Future Research

What future additions are in the works? In today’s world of dwindling fossil fuel reserves, it becomes important to track how much energy we are actually using. Whereas classical System Dynamics is designed to track material flows, it does not track energy flows. This is a major drawback of the methodology.

For this reason, a second version of the System Dynamics library has also been released as a sublibrary of BondLib, our bond graph library. In that version, all material flows are represented internally by bond graphs. A bond graph naturally tracks energy flows. Each energy flow, in that version of the library, is represented as the product of a specific enthalpy and a mass flow. Hence we can track material flows and energy flows simultaneously.

When I drive my car from home to work, I am not only spending energy in the form of the gas that my car consumes. Some energy was also spent in producing the car, and more energy will be spent in discarding it at the end of its lifecycle and in recovering those materials from it that can be recycled.

The accumulated energy that accounts for all of those indirect uses of energy is called emergy. The specific enthalpy can be used to encode in the model the specific emergy, i.e., the emergy per unit of mass.

I plan on porting examples of emergy modeling, as described in the publications by Howard Odum, over to the bond graph implementation of the System Dynamics library, but this work has not yet been completed.


Check out the full paper and presentation by Prof. Dr. François E. Cellier here.