BuildSysPro.IBPSA.Utilities.Math.Functions.powerLinearized

# .BuildSysPro.IBPSA.Utilities.Math.Functions.powerLinearized

Power function that is linearized below a user-defined threshold

## Information

Function that approximates y=xn where 0 < n so that

- the function is defined and monotonically increasing for all x.
- dy/dx is bounded and continuous everywhere (for n < 1).

For x < x0, this function replaces y=xn by a linear function that is continuously differentiable everywhere.

A typical use of this function is to replace T = T4(1/4) in a radiation balance to ensure that the function is defined everywhere. This can help solving the initialization problem when a solver may be far from a solution and hence T4 < 0.

See the package `Examples` for the graph.

#### Interface

>     function powerLinearized
>       extends Modelica.Icons.Function;
>       input Real x "Abscissa value";
>       input Real n "Exponent";
>       input Real x0 "Abscissa value below which linearization occurs";
>       output Real y "Function value";
>     end powerLinearized;

## Revisions

- February 3, 2011, by Michael Wetter:
  First implementation.

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