Mathematical definitions

Activity Index mathematical definitions

• The activity of an element i in a submodel is defined as a temporal integration of the power absolute value. Equation 1:

where P is the power in the element. The unit of activity is J. The activity represents a quantity of energy that crosses the element being studied. This is a different definition from energy because it takes into account the absolute value of power.

• The activity index of an element i in a submodel is the ratio between the activity of the considered element and the total activity of the system. Equation 2:

Note

The definition of activity suggests that it should be a state variable. However, the values of activity vary over a huge range and great accuracy is completely unnecessary. For this reason a simple trapezoidal integrator is employed for activity variables. This updates activities only at print points. This enables activity calculations to be done with very small overheads. Naturally with this approach, activities do not appear in linear analysis.

Note

For practical information on how to implement Activity Index variables in your submodels, please refer to the Submodel Editor manual, where comprehensive information is provided.