Fan and pump model that has a unique solution for any pressure boundary condition and control signal

Some building performance simulation programs compute the volume flow rate in ducts and pipe net-works for a given fan speed, which may be computed by a feedback controller, based on the intersection of the flow resistance and fan curve. We show ana-lytically and based on numerical simulations that fan models that use affinity laws and polynomials for the fan curve can lead to equations that become singular, have no, one, multiple or an infinite number of solu-tions. In experiments in which we used such a model, the simulations failed due to non-convergence or the time integration algorithm stalled due to oscillatory behavior. We therefore developed a new fan model, presented in this paper, that is a composition of a fan model that is used for low speeds and normal speeds. In each region, the model has a unique solution and eliminates the previously discussed numerical prob-lems. The composite model is differentiable in all in-puts. The approach for developing this model was to enforce constraints in each region that are mathemati-cally sufficient to ensure the existence and uniqueness of a solution. The fan model is implemented in the free open-source Modelica Buildings library version 1.3.