Tech:Commercial

The Commercial Module implements commercial building models. Version 1.0 of this module only supports single-zone office buildings. Support for additional commercial buildings types is planned, including multi-zone office, schools, stores, and refrigerated warehouses.

= Small Office Building =

Multizone ETP Linearization
=ETP Equation Solution Algorithm=



The evolution of air temperature as a function of time is the fundamental equation in ETP, as shown in Figure 2. It takes the following form $$ f \left ( t \right ) = a e^{nt} + b e^{mt} + c $$

where both $$m$$ and $$n$$ are negative and equation $$f(t) = 0$$ must be solved for the first value of $$t > 0$$. Unfortunately, this function has no closed-form solution and must be solved numerically.

When $$a b < 0$$, the function always has one extremum and one inflexion point, and the extremum time $$t_m$$is always less than inflexion time $$t_i$$. The extremum time is found at $$t_m = \log (-a n / b m) / (m-n)$$ and the value of the function at this point is defined as $$f_m = f(t_m) $$. The inflexion point is found at $$t_m = \log ( -a n^2 / b m^2) / (m-n)$$ and the value of the function at this point is defined as $$f_i = f(t_i)$$. The initial value at $$t = 0$$ if defined as $$f_0 = f(0)$$.

The simplest efficient numerical method is Newton's method, but the method will not converge under certain conditions that depend on when the extremum and the inflexion points occur. The following tests must be made before starting the numerical solution:
 * for $$t_m > 0$$, a solution exists when $$f_0$$&times;$$f_m < 0$$ or $$c$$&times;$$f_m < 0$$
 * for $$t_m = 0$$ a solution only exists when $$f_m = 0$$
 * for $$t_m < 0$$ &le; $$ti$$ a solution only exists when $$f_m < 0 < f_i$$
 * for $$t_i = 0$$ a solution only exists when $$f_i = 0$$
 * for $$t_i < 0$$ a solution only exists when $$c$$&times;$$f_i < 0$$

When a solution exists the starting point $$t_0$$ of the numerical solution must be chosen based on the values of $$t_m$$ and $$t_i$$
 * $$t_0 = 0$$ should be used when $$t_m > 0$$ and $$f_m$$ &le; $$f_0 < 0$$
 * $$t_0 = t_i$$ should be used for all other conditions for which a solution exists

=References=


 * Taylor, ZT and RG Pratt. 1988  "The effects of model simplifications on equivalent thermal parameters calculated from hourly building performance data." In proc. 1988 ACEEE Summer Study on Energy Efficiency in Buildings, pp. 10.268-10.285.

Authors: David Chassin and Ross Guttromson, Pacific Northwest National Laboratory, Richland Washington (USA), PNNL 17615, May 2008.

= See also =


 * User's manual
 * Requirements
 * Specifications
 * Implementation