An assessment of the load modifying potential of model predictive controlled dynamic facades within the California context

California is making major strides towards meeting its greenhouse gas emission reduction goals with the transformation of its electrical grid to accommodate renewable generation, aggressive promotion of building energy efficiency, and increased emphasis on moving toward electrification of end uses (e.g., residential heating, etc.). As a result of this activity, the State is faced with significant challenges of systemwide resource adequacy, power quality and grid reliability that could be addressed in part with demand responsive (DR) load modifying strategies using controllable building technologies. Dynamic facades have the ability to potentially shift and shed loads at critical times of the day in combination with daylighting and HVAC controls. This study explores the technical potential of dynamic facades to support net load shape objectives. A model predictive controller (MPC) was designed based on reduced order thermal (Modelica) and window (Radiance) models. Using an automated workflow (involving JModelica.org and MPCPy), these models were converted and differentiated to formulate a non-linear optimization problem. A gradient-based, non-linear programming problem solver (IPOPT) was used to derive an optimal control strategy, then a post-optimization step was used to convert the solution to a discrete state for facade actuation. Continuous state modulation of the façade was also modeled. The performance of the MPC controller with and without activation of thermal mass was evaluated in a south-facing perimeter office zone with a three-zone electrochromic window for a clear sunny week during summer and winter periods in Oakland and Burbank, California. MPC strategies reduced total energy cost by 9–28% and critical coincident peak demand was reduced by up to 0.58 W/ft2-floor or 19–43% in the 4.6 m (15 ft) deep south zone on sunny summer days in Oakland compared to state-of-the-art heuristic control. Similar savings were achieved for the hotter, Burbank climate in Southern California. This outcome supports the argument that MPC control of dynamic facades can provide significant electricity cost reductions and net load management capabilities of benefit to both the building owner and evolving electrical grid

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Actuator design for parabolic distributed parameter systems with the moment method

First Published in SIAM Journal on Control and Optimization in Volume 55, Issue 2, 2017, Pages 1128-1152, published by the Society for Industrial and Applied Mathematics (SIAM)In this paper, we model and solve the problem of designing in an optimal way actuators for parabolic partial differential equations settled on a bounded open connected subset of Rn. We optimize not only the location but also the shape of actuators, by finding what is the optimal distribution of actuators in , over all possible such distributions of a given measure. Using the moment method, we formulate a spectral optimal design problem, which consists of maximizing a criterion corresponding to an average over random initial data of the largest L2-energy of controllers. Since we choose the moment method to control the PDE, our study mainly covers one-dimensional parabolic operators, but we also provide several examples in higher dimensions. We consider two types of controllers: Either internal controls, modeled by characteristic functions, or lumped controls, that are tensorized functions in time and space. Under appropriate spectral assumptions, we prove existence and uniqueness of an optimal actuator distribution, and we provide a simple computation procedure. Numerical simulations illustrate our resultsThe first author was partially supported by ANR project OPTIFORM. This work was partially supported by Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, GA 694126, ICON of the French ANR-2016-ACHN-0014-01, FA9550-15-1-0027 of AFOSR, A9550-14-1-0214 of EOARD-AFOSR, and grant MTM2014-52347 of MINECO (Spain