This work presents a whole-year simulation study on nonlinear mixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, …
This work presents a whole-year simulation study on nonlinear mixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, free cooling facilities, and a large underground thermal storage. For solution of the arising Mixed-Integer Non-Linear Programs (MINLPs) we apply an existing general and optimal-control-suitable decomposition approach. To compensate deviation of forecast inputs from measured disturbances, we introduce a moving horizon estimation step within the MPC strategy. The MPC performance for this study, which consists of more than 50,000 real time suitable MINLP solutions, is compared to an elaborate conventional control strategy for the system. It is shown that MPC can significantly reduce the yearly energy consumption while providing a similar degree of constraint satisfaction, and autonomously identify previously unknown, beneficial operation modes.
This work presents a whole-year simulation study on nonlinear mixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, …
This work presents a whole-year simulation study on nonlinear mixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, free cooling facilities, and a large underground thermal storage. For solution of the arising Mixed-Integer Non-Linear Programs (MINLPs) we apply an existing general and optimal-control-suitable decomposition approach. To compensate deviation of forecast inputs from measured disturbances, we introduce a moving horizon estimation step within the MPC strategy. The MPC performance for this study, which consists of more than 50,000 real time suitable MINLP solutions, is compared to an elaborate conventional control strategy for the system. It is shown that MPC can significantly reduce the yearly energy consumption while providing a similar degree of constraint satisfaction, and autonomously identify previously unknown, beneficial operation modes.
Model predictive control has gained popularity for its ability to satisfy constraints and guarantee robustness for certain classes of systems. However, for systems whose dynamics are characterized by a high …
Model predictive control has gained popularity for its ability to satisfy constraints and guarantee robustness for certain classes of systems. However, for systems whose dynamics are characterized by a high state dimension, substantial nonlinearities, and stiffness, suitable methods for online nonlinear MPC are lacking. One example of such a system is a vehicle thermal management system (TMS) with integrated thermal energy storage (TES), also referred to as a hybrid TMS. Here, hybrid refers to the ability to achieve cooling through a conventional heat exchanger or via melting of a phase change material, or both. Given increased electrification in vehicle platforms, more stringent performance specifications are being placed on TMS, in turn requiring more advanced control methods. In this paper, we present the design and real-time implementation of a nonlinear model predictive controller with 77 states on an experimental hybrid TMS testbed. We show how, in spite of high-dimension and stiff dynamics, an explicit integration method can be obtained by linearizing the dynamics at each time step within the MPC horizon. This integration method further allows the first-order gradients to be calculated with minimal additional computational cost. Through simulated and experimental results, we demonstrate the utility of the proposed solution method and the benefits of TES for mitigating highly transient heat loads achieved by actively controlling its charging and discharging behavior.
24.1 ▪ IntroductionIn this chapter, we present some of the applications of mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (GDP) in process systems engineering (PSE). For a comprehensive review …
24.1 ▪ IntroductionIn this chapter, we present some of the applications of mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (GDP) in process systems engineering (PSE). For a comprehensive review of mixed-integer nonlinear optimization (MINLO), we refer the reader to the work by Belotti et al. [192]. Bonami et al. [305] review convex MINLP algorithms, and software in more detail. Tawarmalani and Sahinidis [1754] describe global optimization theory, algorithms, and applications. Grossmann [860] reviews nonlinear mixed-integer and disjunctive programming techniques. A systematic method for deriving MINLP models through GDP is provided by Grossmann and Trespalacios [866]. For a detailed review of MINLP solvers, we refer the reader to the work by Bussieck and Vigerske [372] and D'Ambrosio and Lodi [545]. Burer and Letchford [356] present a survey on applications, algorithms, and software specifically focused on nonconvex MINLP.
Demand-side management is very critical in China's energy systems because of its high fossil energy consumption and low system energy efficiency. A building shape factor is introduced in describing the …
Demand-side management is very critical in China's energy systems because of its high fossil energy consumption and low system energy efficiency. A building shape factor is introduced in describing the architectural characteristics of different functional areas, which are combined with the characteristics of the energy consumed by users to investigate the features of heating load in different functional areas. A Stackelberg game-based optimal scheduling model is proposed for electro-thermal integrated energy systems, which seeks to maximize the revenue of integrated energy operator (IEO) and minimize the cost of users. Here, IEO and users are the Stackelberg game leader and followers, respectively. The leader uses real-time energy prices to guide loads to participate in demand response, while the followers make energy plans based on price feedback. Using the Karush–Kuhn–Tucker (KKT) condition and the big-M method, the model is transformed into a mixed-integer quadratic programming (MIQP) problem, which is solved by using MATLAB and CPLEX software. The results demonstrate that the proposal manages to balance the interests of IEO and users. Furthermore, the heating loads of public and residential areas can be managed separately based on the differences in energy consumption and building shape characteristics, thereby improving the system operational flexibility and promoting renewable energy consumption.
Demand-side management is very critical in China's energy systems because of its high fossil energy consumption and low system energy efficiency. A building shape factor is introduced in describing the …
Demand-side management is very critical in China's energy systems because of its high fossil energy consumption and low system energy efficiency. A building shape factor is introduced in describing the architectural characteristics of different functional areas, which are combined with the characteristics of the energy consumed by users to investigate the features of heating load in different functional areas. A Stackelberg game-based optimal scheduling model is proposed for electro-thermal integrated energy systems, which seeks to maximize the revenue of integrated energy operator (IEO) and minimize the cost of users. Here, IEO and users are the Stackelberg game leader and followers, respectively. The leader uses real-time energy prices to guide loads to participate in demand response, while the followers make energy plans based on price feedback. Using the Karush-Kuhn-Tucker (KKT) condition and the big-M method, the model is transformed into a mixed-integer quadratic programming (MIQP) problem, which is solved by using MATLAB and CPLEX software. The results demonstrate that the proposal manages to balance the interests of IEO and users. Furthermore, the heating loads of public and residential areas can be managed separately based on the differences in energy consumption and building shape characteristics, thereby improving the system operational flexibility and promoting renewable energy consumption.
In the context of high fossil fuel consumption and inefficiency within China's energy systems, effective demand-side management is essential. This study examines the thermal characteristics of various building types across …
In the context of high fossil fuel consumption and inefficiency within China's energy systems, effective demand-side management is essential. This study examines the thermal characteristics of various building types across different functional areas, utilizing the concept of body coefficient to integrate their unique structural and energy use traits into a demand response framework supported by real-time pricing. We developed a Stackelberg game-based bi-level optimization model that captures the dynamic interplay of costs and benefits between integrated energy providers and users. This model is formulated into a Mixed Integer Linear Programming (MILP) problem using Karush-Kuhn-Tucker (KKT) conditions and linearized with the Big M method, subsequently solved using MATLAB and CPLEX. This approach enables distinctive management of heating loads in public and residential areas, optimizing energy efficiency while balancing the interests of both providers and users. Furthermore, the study explores how the proportion of different area types affects the potential for reducing heat loads, providing insights into the scalability and effectiveness of demand response strategies in integrated energy systems. This analysis not only highlights the economic benefits of such strategies but also their potential in reducing dependency on traditional energy sources, thus contributing to more sustainable energy system practices.
Aquifer thermal energy storages (ATES) are used to temporally store thermal energy in groundwater saturated aquifers. Typically, two storages are combined, one for heat and one for cold, to support …
Aquifer thermal energy storages (ATES) are used to temporally store thermal energy in groundwater saturated aquifers. Typically, two storages are combined, one for heat and one for cold, to support heating and cooling of buildings. This way, the use of classical fossil fuel-based heating, ventilation, and air conditioning can be significantly reduced. Exploiting the benefits of ATES beyond ``seasonal'' heating in winter and cooling in summer as well as meeting legislative restrictions requires sophisticated control. We propose a tailored model predictive control (MPC) scheme for the sustainable operation of ATES systems, which mainly builds on a novel model and objective function. The new approach leads to a mixed-integer quadratic program. Its performance is evaluated on real data from an ATES system in Belgium.
Although energy system optimisation based on linear optimisation is often used for influential energy outlooks and studies for political decision-makers, the underlying background still needs to be described in the …
Although energy system optimisation based on linear optimisation is often used for influential energy outlooks and studies for political decision-makers, the underlying background still needs to be described in the scientific literature in a concise and general form. This study presents the main equations and advanced ideas and explains further possibilities mixed integer linear programming offers in energy system optimisation. Furthermore, the equations are shown using an example system to present a more practical point of view. Therefore, this study is aimed at researchers trying to understand the background of studies using energy system optimisation and researchers building their implementation into a new framework. This study describes how to build a standard model, how to implement advanced equations using linear programming, and how to implement advanced equations using mixed integer linear programming, as well as shows a small exemplary system. - Presentation of the OpTUMus energy system optimisation framework - Set of equations for a fully functional energy system model - Example of a simple energy system model
Hybrid Energy Systems (HES), amalgamating renewable sources, energy storage, and conventional generation, have emerged as a responsive resource for providing valuable grid services. Subsequently, modeling and analysis of HES has …
Hybrid Energy Systems (HES), amalgamating renewable sources, energy storage, and conventional generation, have emerged as a responsive resource for providing valuable grid services. Subsequently, modeling and analysis of HES has become critical, and the quality of grid services hedges on it. Currently, most HES models are temperature-agnostic. However, the temperature-dependent factors can significantly impact HES performance, necessitating advanced modeling and optimization techniques. With the inclusion of temperature-dependent models, the challenges and complexity of solving optimization problem increases. In this paper, the electro-thermal modeling of HES is discussed. Based on this model, a nonlinear predictive optimization framework is formulated. A simplified model is developed to address the challenges associated with solving nonlinear problems. Further, projection and homotopy approaches are proposed. In the homotopy method, the NLP is solved by incrementally changing the C-rating of the battery. Simulation-based analysis of the algorithms highlights the effects of different battery ratings, ambient temperatures, and energy price variations. Finally, comparative assessments with a temperature-agnostic approach illustrates the effectiveness of electro-thermal methods in optimizing HES.
The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. …
The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a joint optimization is known as a challenging problem with complex network constraints and couplings of electric, hydraulic, and thermal models that are nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF) problem and develop a computationally efficient heuristic to solve it. The proposed heuristic decomposes OPWHF into subproblems, which are iteratively solved via convex relaxation and convex-concave procedure. Simulation results validate that the proposed framework can improve operational flexibility and social welfare of the integrated system, wherein the water and heating networks respond as virtual energy storage to time-varying energy prices and solar photovoltaic generation. Moreover, we perform sensitivity analysis to compare two modes of heating network control: by flow rate and by temperature. Our results reveal that the latter is more effective for heating networks with a wider space of pipeline parameters.
In this paper, we propose an economic nonlinear model predictive control (MPC) algorithm for district heating networks (DHNs). The proposed method features prosumers, multiple producers, and storage systems, which are …
In this paper, we propose an economic nonlinear model predictive control (MPC) algorithm for district heating networks (DHNs). The proposed method features prosumers, multiple producers, and storage systems, which are essential components of 4th generation DHNs. These networks are characterized by their ability to optimize their operations, aiming to reduce supply temperatures, accommodate distributed heat sources, and leverage the flexibility provided by thermal inertia and storage, all crucial for achieving a fossil-fuel-free energy supply. Developing a smart energy management system to accomplish these goals requires detailed models of highly complex nonlinear systems and computational algorithms able to handle large-scale optimization problems. To address this, we introduce a graph-based optimization-oriented model that efficiently integrates distributed producers, prosumers, storage buffers, and bidirectional pipe flows, such that it can be implemented in a real-time MPC setting. Furthermore, we conduct several numerical experiments to evaluate the performance of the proposed algorithms in closed-loop. Our findings demonstrate that the MPC methods achieved up to 9% cost improvement over traditional rule-based controllers while better maintaining system constraints.
Almost climate neutral buildings are one of the core goals in terms of sustainability. Beside the support of the necessary design decisions for an integrated, interoperable, ecological and economical operation …
Almost climate neutral buildings are one of the core goals in terms of sustainability. Beside the support of the necessary design decisions for an integrated, interoperable, ecological and economical operation of building energy systems, innovative management solutions for scheduling the operation of decentralized energy systems are of great importance. The challenge is optimal interaction between energy system components in terms of own consumption, energy efficiency and resource consumption as well as greenhouse gas emissions. To achieve these goals a modular optimization approach based on Mixed Integer Programming is proposed. In detail, and to our knowledge the first time, a MIP model for the dynamic behavior of fuel cell Combined Heat and Power plants is presented. Our approach is evaluated for the operation of heat pumps showing that their energy efficiency can be increased significantly.
Managing supply and demand in the electricity grid is becoming more challenging due to the increasing penetration of variable renewable energy sources. As significant end-use consumers, and through better grid …
Managing supply and demand in the electricity grid is becoming more challenging due to the increasing penetration of variable renewable energy sources. As significant end-use consumers, and through better grid integration, buildings are expected to play an expanding role in the future smart grid. Predictive control allows buildings to better harness available energy flexibility from the building passive thermal mass. However, due to the heterogeneous nature of the building stock, developing computationally tractable control-oriented models, which adequately represent the complex and nonlinear thermal-dynamics of individual buildings, is proving to be a major hurdle. Data-driven predictive control, coupled with the "Internet of Things", holds the promise for a scalable and transferrable approach,with data-driven models replacing traditional physics-based models. This review examines recent work utilising data-driven predictive control for demand side management application with a special focus on the nexus of model development and control integration, which to date, previous reviews have not addressed. Further topics examined include the practical requirements for harnessing passive thermal mass and the issue of feature selection. Current research gaps are outlined and future research pathways are suggested to identify the most promising data-driven predictive control techniques for grid integration of buildings.
The continuous introduction of renewable electricity and increased consumption through electrification of the transport and heating sector challenges grid stability. This study investigates load shifting through demand side management as …
The continuous introduction of renewable electricity and increased consumption through electrification of the transport and heating sector challenges grid stability. This study investigates load shifting through demand side management as a solution. We present a four-month experimental study of a low-complexity, hierarchical Model Predictive Control approach for demand side management in a near-zero emission occupied single-family house in Denmark. The control algorithm uses a price signal, weather forecast, a single-zone building model, and a non-linear heat pump efficiency model to generate a space-heating schedule. The weather-compensated, commercial heat pump is made to act smart grid-ready through outdoor temperature input override to enable heat boosting and forced stops to accommodate the heating schedule. The cost reduction from the controller ranged from 2-33% depending on the chosen comfort level. The experiment demonstrates that load shifting is feasible and cost-effective, even without energy storage, and that the current price scheme provides an incentive for Danish end-consumers to shift heating loads. However, issues related to controlling the heat pump through input-manipulation were identified, and the authors propose a more promising path forward involving coordination with manufacturers and regulators to make commercial heat pumps truly smart grid-ready.
Abstract The collocation method meshed with non-linear programming techniques provides an efficient strategy for the numerical solution of optimal control problems. Good accuracy can be obtained for the state and …
Abstract The collocation method meshed with non-linear programming techniques provides an efficient strategy for the numerical solution of optimal control problems. Good accuracy can be obtained for the state and the control trajectories as well as for the value of the objective function. In addition, the control strategy can be quite flexible in form. However, it is necessary to select the appropriate number of collocation points and number of parameters in the approximating functions with care.
My final lines go to my girlfriend Simone Evke.Thank you for your love, for your patience and support whenever my mind was entangled in upper
My final lines go to my girlfriend Simone Evke.Thank you for your love, for your patience and support whenever my mind was entangled in upper