Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all (Formula presented.) extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive.

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A class of data-driven control methods has recently emerged based on Willems' fundamental lemma. Such methods can ease the modeling burden in control design but can be sensitive to disturbances acting on the system under control. In this article, we propose a restructuring of the problem to incorporate segmented prediction trajectories. The proposed segmentation leads to reduced tracking error for longer prediction horizons in the presence of unmeasured disturbance and noise when compared with an unsegmented formulation. The performance characteristics are illustrated in a set-point tracking case study in which the segmented formulation enables more consistent performance over a wide range of prediction horizons. The method is then applied to a building energy management problem using a detailed simulation environment. The case studies show that good tracking performance is achieved for a range of horizon choices, whereas performance degrades with longer horizons without segmentation.

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Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 2 ¹⁴⁺³× ¹⁹² boundary scenarios are considered. A validation with randomly drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used.

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Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve times, while achieving the same accuracy as a fixed mesh.

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Buildings are responsible for about a quarter of global energy-related CO ₂ emissions. Consequently, the decarbonisation of the housing stock is essential in achieving net-zero carbon emissions. Global decarbonisation targets can be achieved through increased efficiency in using energy generated by intermittent resources. The paper presents a co-design framework for simultaneous optimal design and operation of residential buildings using Model Predictive Control (MPC). The framework is capable of explicitly taking into account operational constraints and pushing the system to its efficiency and performance limits in an integrated fashion. The optimality criterion minimises system cost considering time-varying electricity prices and battery degradation. A case study illustrates the potential of co-design in enhancing flexibility and self-sufficiency of a system operating under different conditions. Specifically, numerical results from a low-fidelity model show substantial carbon emission reduction and bill savings compared to an a-priori sizing approach.

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Distribution networks are undergoing fundamental changes at medium voltage level. To support growing planning and control decision-making, the need for large numbers of short-term load forecasts has emerged. Data-driven modelling of medium voltage feeders can be affected by (1) data quality issues, namely, large gross errors and missing observations (2) the presence of structural breaks in the data due to occasional network reconfiguration and load transfers. The present work investigates and reports on the effects of advanced data cleansing techniques on forecast accuracy. A hybrid framework to detect and remove outliers in large datasets is proposed; this automatic procedure combines the Tukey labelling rule and the binary segmentation algorithm to cleanse data more efficiently, it is fast and easy to implement. Various approaches for missing value imputation are investigated, including unconditional mean, Hot Deck via k-nearest neighbour and Kalman smoothing. A combination of the automatic detection/removal of outliers and the imputation methods mentioned above are implemented to cleanse time series of 342 medium-voltage feeders. A nested rolling-origin-validation technique is used to evaluate the feed-forward deep neural network models. The proposed data cleansing framework efficiently removes outliers from the data, and the accuracy of forecasts is improved. It is found that Hot Deck (k-NN) imputation performs best in balancing the bias-variance trade-off for short-term forecasting.@en

Despite a large body of research, the widespread application of Model Predictive Control (MPC) to residential buildings has yet to be realised. The modelling challenge is often cited as a significant obstacle. This chapter establishes a systematic workflow, from detailed simulation model development to control-oriented model generation to act as a guide for practitioners in the residential sector. The workflow begins with physics-based modelling methods for analysis and evaluation. Following this, model-based and data-driven techniques for developing low-complexity, control-oriented models are outlined. Through sections detailing these different stages, a case study is constructed, concluding with a final section in which MPC strategies based on the proposed methods are evaluated, with a price-aware formulation producing a reduction in operational space-heating cost of 11%. The combination of simulation model development, control design and analysis in a single workflow can encourage a more rapid uptake of MPC in the sector.

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Nowadays, in Uruguay, a considerable amount of energy produced by renewable resources is curtailed inducing frequent substantial reductions in the spot market prices. This paper analyses the incorporation of energy storage into the Uruguayan network, taking the different perspectives of a private investor and a central planner. From the investor point of view, we investigate the option of doing energy arbitrage in the wholesale market, taking advantage of the spot price fluctuations. From the national perspective, we develop an optimal power flow planning model to perform a cost-benefit analysis of batteries’ integration in reducing thermal generation. We conclude that, from a private investor perspective, fluctuations in the spot prices are not enough to make investments in batteries profitable with current prices. On the other hand, from a national perspective, results are more promising, obtaining very high revenues in some case studies.@en