Approximating model predictive control with existing building simulation tools and offline optimization

Abstract

Model predictive control (MPC) is an established control technique in other fields and holds promise for improved controls in high-performance buildings. It has been receiving increasing attention in buildings research but has yet to find its way into common practice. This is due, at least in part, to a mismatch between the tools and techniques used in most MPC development and those commonly found in building design and operation. This article investigates the use of offline optimization with common building simulation tools to approximate MPC with lookup tables. Particular attention is paid to methods for limiting problem dimensionality. The approach is presented through three illustrative case studies, and its benefits and range of applicability are discussed.

Keywords:

• model predictive control
• offline optimization
• control visualization

Acknowledgements

The research described herein was made possible by fellowships from the National Science and Engineering Research Council of Canada and the American Society of Heating, Refrigeration and Air conditioning Engineers, and through research projects at the Lawrence Berkeley National Laboratory. The author would like to thank Phil Haves, Gail Brager, Ed Arens, Francesco Borrelli, Michael Wetter, Gregor Henze, Peter May-Ostendorp, Meli Stylianou, Edward Kutrowski, Edward Morofsky and Eleanor Lee for their assistance and feedback.

Notes

The penalty function P _{multSolPenalty} in Equation (11) was added to the model after learning from initial test iterations. It is used to avoid noise caused by the existence of multiple optimal control solutions in some parts of the conditions space. When computing the lookup table and within the online MPC model, M is set to an arbitrarily large number. When the model is being used as the simulation test model in annual simulations, M is set to zero.

The spacing of these variables has more significant impacts than does that of T _amb – interested readers are directed to the analysis and discussion on pages 47–51 of Coffey (2011).

In the case of T _amb, one could use a pre-defined standard curve (e.g. ASHRAE 2005, Thevenard 2009). Other disturbance predictions can be similarly parametrized, for example direct and diffuse solar can be parametrized by length of day and cloudiness, making use of solar position equations.

Readers interested in the details are referred to pages 61–62 of Coffey (2011).

Basecase1 rules: l _charge = if Apr ⇒ 1, if May ⇒ 3, if Jun ⇒ 5, if Jul ⇒ 7, if Aug ⇒ 5, if Sep ⇒ 3, if Oct ⇒ 1.

Basecase2 rules: l _charge=if (T _amb < 16°C) ⇒  0.25, elseif (T _amb > 26°C) ⇒ 10, else ⇒ (T _amb – 16).

To consider imperfect month-ahead predictions, the predictions fed to the main problem optimization were set uniformly randomly within ±20% of the ‘actual’ loads and hourly prices used in the annual simulation. Note that the results are nearly identical to the results when one assumes perfect prediction.

Java code for collecting weather predictions from the National Digital Forecast Database (NDFD) is available on the ftp site (Coffey 2012). An example user interface is also available here.