This paper focuses on the control of microgrids where both gas and electricity are provided to the final customer, i.e., multi-carrier microgrids. Hence, these microgrids include thermal and electrical loads, renewable energy sources, energy storage systems, heat pumps, and combined heat and power units. The parameters characterizing the multi-carrier microgrid are subject to several disturbances, such as fluctuations in the provision of renewable energy, variability in the electrical and thermal demand, and uncertainties in the electricity and gas pricing. With the aim of accounting for the data uncertainties in the microgrid, we propose a Robust Model Predictive Control (RMPC) approach whose goal is to minimize the total economical cost, while satisfying comfort and energy requests of the final users. In the related literature various RMPC approaches have been proposed, focusing either on electrical or on thermal microgrids. Only a few contributions have addressed the robust control of multi-carrier microgrids. Consequently, we propose an innovative RMPC algorithm that employs on an uncertainty set-based method and that can provide better performance compared with deterministic model predictive controllers applied to multi-carrier microgrids. With the aim of mitigating the conservativeness of the approach, we define suitable robustness factors and we investigate the effects of such factors on the robustness of the solution against variations of the uncertain parameters. We show the effectiveness of the proposed RMPC approach by applying it to a realistic residential multi-carrier microgrid and comparing the obtained results with the ones of a baseline robust method.

Electrification of the heat network in buildings together with a rise in popularity of Electric Vehicles (EVs) will result in a need to make investments in the electrical energy infrastructure in order to prevent congestion. This paper discusses the influence of hydrogen in future smart microgrids on these investments. Moreover, smart control strategies, i.e., EV management and demand response programs are used in this paper to lower the peak of electrical energy demand resulting in the reduction of these investments. Performances of microgrid with different levels of hydrogen penetration are discussed. It is shown that an increase in the level of hydrogen in the microgrid will reduce the electric grid investments costs but is not economically more beneficial than using ‘green’ gas due to the higher total economic costs.

State-of-the-art Model Predictive Control (MPC) applications for building heating adopt either a deterministic controller together with a nonlinear model or a linearized model with a stochastic MPC controller. However, deterministic MPC only considers one single realization of the disturbances and its performance strongly depends on the quality of the forecast of the disturbances, which can lead to low performance. In fact, inadequate building energy management can lead to high energy costs and CO₂ emissions. On the other hand, a linearized model can fail to capture some dynamics and behavior of the building under control. In this article, we combine a stochastic scenario-based MPC (SBMPC) controller together with a nonlinear Modelica model that is able to provide a richer building description and to capture the dynamics of the building more accurately than linear models. The adopted SBMPC controller considers multiple realizations of the external disturbances obtained through a statistically accurate model, so as to consider different possible disturbance evolutions and to robustify the control action. To this purpose, we present a scenario generation method for building temperature control that can be applied to several exogenous perturbartions, e.g. solar irradiance, outside temperature, and that satisfies several important stastistical properties, in contrast with simpler and less accurate methods adopted in the literature. We show the benefits of our proposed approach through several simulations in which we compare our method against the standard ones from the literature, for several combinations of a trade-off parameter between comfort and energy cost. We show how our SBMPC controller approach outperforms the standard controllers available in the literature.

We present a Robust Model Predictive Control (RMPC) approach for multi-carrier microgrids, i.e., microgrids based on gas and electricity. The microgrid that we consider includes thermal loads, electrical loads, renewable energy sources, energy storage systems, heat pumps, and combined heat and power plants. Moreover, the system under control is affected by several external disturbances, e.g., uncertainty in renewable energy generation, electrical and thermal demand. The goal of the controller is to minimize the overall economical cost and the energy exchange with the main grid, while guaranteeing comfort. Whereas several RMPC methods have been developed for electrical or thermal microgrids, little or no attention has been devoted to robust control of multi-carrier microgrids. Therefore, we consider a novel RMPC algorithm that can improve the performance with respect to classical deterministic Model Predictive Control (Det-MPC) controllers in the context of multi-carrier microgrids. The RMPC method relies on the box-uncertainty-set robust optimization, where uncertain parameters are assumed to take their values from different intervals independently. The RMPC approach is able to successfully satisfy the constraints even in the presence of the mentioned disturbances. Simulations of a realistic residential case study show the benefits of the proposed approach with respect to Det-MPC controllers.

Energy systems influence many aspects of society, from the residential sector to the commercial one. Improving the performance and efficiency of energy systems and guaranteeing their stability is a fundamental task of control engineers. In this regard, this thesis presents modeling and control solutions for energy systems, with a focus on both electric and thermal ones. The thesis is divided in three parts. Firstly, we consider an online partitioning and stability problem of a network applied to frequency regulation. Secondly, we present algorithms for energy management system of an electrical microgrid. In particular, we focus on providing a trade-off between computational complexity and performance of the obtained solution. Lastly, we focus on thermal energy systems by designing an algorithm for room temperature control in commercial buildings. In the first part of the thesis, we consider a linear switching large-scale system and we focus on the problem of partitioning the system into smaller subsystems. We assume that the different modes of the switching system are not known a priori, but they can be detected. We propose an online scheme that can partition the system when the mode switches, adapting therefore the partition to the mode of the switching system. The goal of the partitioning algorithmis on the one hand to minimize the coupling between subsystems, in order to facilitate the task of a distributed/decentralized controller, and on the other hand to obtain subsystems with similar sizes, in order to distribute the control effort equally. Moreover, after the system has been partitioned, we apply a decentralized state-feedback control scheme to stabilize the overall system. In order to prove stability, we apply a dwell time stability scheme such that the closed-loop system remains stable even after both the mode and partition changes. The online partitioning method, together with the control algorithm, is applied to an automatic generation control problem of frequency regulation in a large-scale power network. In the second part of the thesis,we consider the energy management system problem in a microgrid. We present several Model Predictive Control (MPC) approaches for optimally managing the power flows in the microgrid, from an economical point of view. The microgrid is modeled using the Mixed Logical Dynamical (MLD) framework. We provide three different strategies that yield a trade-off between computational complexity and performance by parameterizing the inputs to the system. First, we propose a parametric MPC approach, in which the continuous inputs are expressed as parametric functions and the binary variables are heuristically parameterized. Next, we propose an if-then-else parametrization of the binary variables in the MLD model, so that they are assigned a value before the optimization takes place, yielding therefore a real-valued optimization instead of a mixed-integer one. Finally, we use past optimization results obtained from simulations to develop two machine learning methods, i.e. decision trees and random forests, that can provide a binary variable configuration so as to, once again, remove the binary variables from the optimization problem. The results obtained show that the methods can provide a very large decrease in computation time while having almost no loss in performance. Simulation results show how the developed methods are able to provide a large reduction in computation time while having a very little performance loss. Lastly, in the third part we focus on thermal networks. We propose a scenario-based MPC approach to control the temperature room in office buildings. The building is modeled using the tool Modelica that yields a better model description compared to linearized models. The adopted scenario generation method improves upon the current literature by considering that the marginal distributions depend both the prediction time steps and on time itself and that the distributions of the disturbances are not stationary. By combining scenario-based MPC together with Modelica, we can improve the performance of the controller of the building and we show this by comparing our method against a deterministic method using a Modelica model description, but also against the same controllers with a linearized model.

In the context of building heating systems control in office buildings, the current state-of-the-art applies either a deterministic Model Predictive Control (MPC) controller together with a nonlinear model, or a linearized model with a stochastic MPC controller. Deterministic MPC considers only one realization of the external disturbances, which can lead to a low performance solution if the forecasts of the disturbances are not accurate. Similarly, linear models are simplified representations of the building dynamics and might fail to capture some relevant behavior. In this paper, we improve upon the current literature by combining these two approaches, i.e. we adopt a nonlinear model together with a stochastic MPC controller. We consider a scenario-based MPC (SBMPC), where many realizations of the disturbances are considered, so as to include more possible future trajectories for the external disturbances. The adopted scenario generation method provides statistically significant scenarios, whereas so far in the current literature only approximate methods have been applied. Moreover, we use Modelica to obtain the model description, which allows to have a more accurate and nonlinear model. Lastly, we perform simulations comparing standard MPC vs SBMPC vs an optimal control approach with measurements of the external disturbances, and we show how our proposed scenario-based MPC controller can achieve a better performance compared to standard deterministic MPC.

A novel partitioning approach for linear switching large-scale systems is presented. We assume that the modes of the switching system are unknown a priori but can be detected. We propose an online partitioning scheme that can partition the system when the mode switches, thus adapting the partition to the mode. Moreover, after the system has been partitioned, we apply a decentralized state-feedback control scheme to stabilize the system. We also apply a dwell time stability scheme to prove that the closed-loop system remains stable even after both the mode and partition changes. The proposed approach is illustrated by means of an automatic generation control problem related to frequency deviation regulation in a large-scale power network.

A single-level rule-based model predictive control (RBMPC) scheme is presented for optimizing the energy management of a grid-connected microgrid composed of local production units, renewable energy sources, local loads, and several types of energy storage systems (ESSs). The single-level controller uses two different models that yield different descriptions of the microgrid and use different sampling times. The model with a smaller sampling time provides a more detailed description of the microgrid, in order to keep track of the fast dynamics, while the model with a higher sampling time provides a less detailed description and is used for making long-term predictions when it is not needed anymore to track the fast dynamics. Moreover, we propose a novel RBMPC method that assigns the value to the binary decision variables in the hybrid microgrid model, e.g., ON or OFF status of the generators and charging or discharging mode of ESSs, through if-then-else rules, which rely on the price of electricity and the local net imbalance. The standard method of applying model predictive control (MPC) to a hybrid model results in a mixed-integer linear programming (MILP) problem. Our proposed rule-based method is able to convert the standard MILP problem into a linear one. We compare our approach through simulations to the MILP approach and show that our method yields almost no loss in performance while providing a significant reduction in the computation time.

We propose a parametrized Model Predictive Control (MPC) approach for optimal operation of microgrids. The parametrization expresses the control input as a function of the states, variables, and parameters. In this way, it is possible to apply an MPC approach by optimizing only the parameters and not the inputs. Moreover, the value of the binary control variables in the model is assigned according to parametrized heuristic rules, thus obtaining a formulation for the optimization problem that is more scalable compared to standard approaches in the literature. Furthermore, we propose a control scheme based on one single controller that uses two different sampling times and prediction models. By doing so, we can include both fast and slow dynamics of the system at the same level. This control approach is applied to an operational control problem of a microgrid, which includes local loads, local production units, and local energy storage systems and results show the effectiveness of the proposed appro.