Final Report Summary - SMPCBCSG (Stochastic Model Predictive Control, Energy Efficient Building Control, Smart Grid) This research project focuses on stochastic model predictive control applied to buildings and electricity grids. Energy management both on the building level as well on the grid level is challenging due to various uncertainties originating from weather and occupancy in buildings on the one hand and renewables and trading in electricity grids on the other. This provides the motivation for the development of new control methods for addressing these challenges.BackgroundEnergy efficient management of buildings systems will play a major role in minimizing overall energy consumption and costs, since, worldwide, the residential and commercial sectors use 2589 Mtoe (mega tones of oil equivalent) in energy, which accounts for almost 40% of final energy use in the world; and in European countries, 76% of this energy goes towards comfort control in buildings – heating, ventilation and air conditioning (HVAC). Because of the long lifespan of buildings and due to the fact that the main building stock is already in place in industrialized countries and refurbishments are expensive, it is urgent to improve the control to increase the energy efficiency of the existing HVAC systems, i.e. to reduce the energy use and utility costs while guaranteeing comfort for the building’s occupants.A natural idea is to make use of the thermal storage capacity of the building and to take into account upcoming boundary conditions, i.e. weather and occupancy predictions. This can be done by applying suitable model predictive control methods.A stochastic formulation is motivated by the definitions in building standards that thermal comfort constraints should be fulfilled with a predefined probability which gives rise to so-called chance constraints. Furthermore, a stochastic formulation provides the possibility to formulate a tradeoff between performance and constraint satisfaction.A second field concerned with energy arises in the area of power grids. The control and optimization of power grids is of major concern due to the increasing complexity of the network with an increasing number of energy producers and consumers of diverse kinds, due to the increase in renewable energy sources, which are inherently variable, and due to the advent of competition and deregulation. Traditionally, energy consumption and power generation had to be very closely matched, which is formulated as the classical optimal power flow problem and leads to a static optimization problem. The integration of renewable energy sources leads to additional variability, which can be mitigated against by using (additional) storage in the grid. Due to the storage management, the optimization problems in each period are now coupled, which gives rise to a dynamic optimal power flow problem. A very prominent idea when looking at including additional storage in power grids is to leverage the thermal energy storage of buildings. This clearly links the two described fields.Stochastic Model Predictive ControlIn order to handle the above mentioned problems, new stochastic formulations of Model Predictive Control (MPC) can be of great help. Hence a novel control paradigm was developed and tested in this project. The developed method starts with an initialization phase based on the so-called scenario approach (random convex programming) and then online adapts the constraint tightening based on its empirical violation probability. This ensures that the empirical violation probability in closed-loop converges to the desired violation probability. The method is based on martingale theory, which was also studied and used for the developed method. The new method was described and published in a conference paper (Adaptively constrained stochastic model predictive control for closed-loop constraint satisfaction, Deliverable D1.1). A journal paper about different analytical chance constraint reformulations was written (Security Constrained Optimal Power Flow with Distributionally Robust Chance Constraints, Deliverable D1.2). This journal paper also focuses on the question how to achieve an appropriate constraint tightening in presence of uncertainty, however, the focus is on analytical reformulations. These reformulations are applied to an optimal power flow problem. For the developments in this part, the fellow had to intensively study the relevant theory and got exposed to the latest research results in this field. Based on this, the fellow developed and proposed a novel technique, which is useful in particular for practical applications. Application to Building ControlA stochastic control strategy for buildings, which can be used for provision of frequency regulation for the power grid was developed and published in a conference paper (Contract design for provision of frequency regulation capacity via aggregation of commercial buildings, Deliverable D2.1). This formulation includes chance constraints due to the weather uncertainty as well as robust constraints to ensure frequency reserve provision for all possible (pre-defined) frequency deviations. Finally, the MPC problem is included in a bi-level optimization problem and posed as a contract design problem for an aggregator, who is offering frequency reserves of several buildings in the frequency reserve market. The problem is reformulated in order to be tractable by standard optimization software. The proposed method is tested on an example model identified from experiments on the test-bed at UC Berkeley. Afterwards, the fellow focused on a real building at UC Berkeley. A building model for this was developed and the implementation on the building at UC Berkeley was carried out. Experimental results were published in a conference paper. For the developments in this part, the fellow had to establish a group of PhD and Master students and also the cooperation with the building manager and technical personnel working on the building. The fellow also collaborated with researchers from ETH Zurich and used the so-called BRCM toolbox developed there. Furthermore, she collaborated with researchers from Lawrence Berkeley National Lab and used their EnergyPlus model of the building under investigation. The fellow also gained further experience as a team-leader and disseminated the research results in terms of several presentations. Application to Power GridsThis new stochastic MPC method was then tested for application to power grids and results were published in a conference paper (Adaptively constrained stochastic model predictive control applied to security constrained optimal power flow, Deliverable 3.1). The results show that the violation probability converges to the desired level and hence cost savings can be expected. A second formulation limiting the risk of cascading events was investigated in a journal paper (Risk-based optimal power flow with probabilistic guarantees, Deliverable 3.2). Finally, different analytical chance constraint reformulations were compared in a security constrained optimal power flow formulation (Security Constrained Optimal Power Flow with Distributionally Robust Chance Constraints, Deliverable D1.2). For the developments in this part, the fellow had to study and familiarize herself with a new field to develop problem formulations, which are relevant and important in practice.
