Structure of an ‘urbs’ Model¶
urbs is an abstract generator for linear optimization problems. Such problems can in general be written in the following standard form:
where \(x\) is the variable vector, \(c\) the coefficient vector for the objective function and \(A\) and \(B\) the matrices for the equality and inequality constraints, respectively. The equality constraints could also be represented by inequality constraints, which is not done here for simplicity reasons. There are two options for the objective function: either the total system costs or environmental emissions can be used. The structure of the following parts will be first a description of \(x\) and \(c\) and subsequently a general formulation of the constraint functions that make up the matrices \(A\) and \(B\) as well as the vectors \(b\) and \(d\). All variables and equations will be first presented for a minimally complex problem and the optional additional variables and equations are presented in extra parts.
Energy System Entities¶
For all models that can be generated with urbs, the energy system is built up out of the following entities:
- Commodities, which represent the various forms of material and energy flows in the system.
- Processes, which convert commodities from one type to another. These entities are always multiple-input/multiple-output (mimo) that is, a certain fixed set of input commodities is converted into another fixed set of output commodities.
- Transmission lines, that allow for the transport of commodities between the modeled spatial vertices.
- Storages, which allow the storage of a single type of commodity.
- DSM potentials, which make the time shifting of demands possible.
In the documentation the greek letters are used exclusively for the variables. For the parameters latin letters are used.