• Energy Research

Flexible and responsive demand is key to the decarbonising of energy systems. In this paper, an economic dispatch model of a district heating system, modelled as a linear program, is soft-linked to a so-called flexibility function of end-consumer responses to time-varying heat prices, modelled generically as a set of ordinary differential equations. This linkage allows us to determine the cost savings potential of demand response in order to quantify its role in smart energy systems. Our key contribution is an optimal soft-linking framework for energy system and demand response models, named Frigg. Frigg finds the aforementioned economic potential under consideration of end-consumer behaviour. The dynamics of this behaviour lead to a significant problem complexity and pose computational challenges. Hence, the proposed method decomposes the problem based on backward dynamic programming and solves it efficiently. The framework is to be understood as a generic blue-print for soft-linking demand response and energy system models: It can be applied to a variety of energy systems and sources of demand response as well as other objectives than production cost minimisation. We compute the cost savings in a case study of the district heating system of Ejby, Denmark, under different degrees of demand flexibility. The results are compared with the alternative of investing in heat storage systems. Our results suggest substantial cost savings through demand response. Nevertheless, cost savings from heat storage that is cost-optimal in size exceed those achieved through demand response in the system configurations analysed.

Abstract This paper introduces a non-linear grey-box (GB) model based on stochastic differential equations that describes the heat dynamics of a school building in Denmark, equipped with a water-based heating system. The building is connected to a local district heating network through a heat exchanger. The heat is delivered to the rooms mainly through radiators and partially through a ventilation system. A monitoring system based on IoT sensors provides data on indoor climate in the rooms and on the heat load of the building. Using this data, we estimate unknown states and parameters of a model of the building’s heating system using the maximum likelihood method. Important novelties of this paper include models of the water flow in the circuit and the state of the valves in the radiator thermostats. The non-linear model accurately predicts the indoor air temperature, return water temperature and heat load. The ideas behind the model lay a foundation for GB models of buildings that use different kinds of water-based heating systems such as air-to-water/water-to-water heat pumps. Such GB models enable model predictive control to control e.g. the indoor air climate or provide flexibility services.

Abstract The large penetration rate of renewable energy sources leads to challenges in planning and controlling the energy production, transmission, and distribution in power systems. A potential solution is found in a paradigm shift from traditional supply control to demand control. To address such changes, a first step lays in a formal and robust characterization of the energy flexibility on the demand side. The most common way to characterize the energy flexibility is by considering it as a static function at every time instant. The validity of this approach is questionable because energy-based systems are never at steady-state. Therefore, in this paper, a novel methodology to characterize the energy flexibility as a dynamic function is proposed, which is titled as the Flexibility Function. The Flexibility Function brings new possibilities for enabling the grid operators or other operators to control the demand through the use of penalty signals (e.g., price, CO2, etc.). For instance, CO2-based controllers can be used to accelerate the transition to a fossil-free society. Contrary to previous static approaches to quantify Energy Flexibility, the dynamic nature of the Flexibility Function enables a Flexibility Index, which describes to which extent a building is able to respond to the grid’s need for flexibility. In order to validate the proposed methodologies, a case study is presented, demonstrating how different Flexibility Functions enable the utilization of the flexibility in different types of buildings, which are integrated with renewable energies.

Abstract Renewable energy integration in power systems and increasing electrification of energy demand create new challenges to which energy flexibility can provide effective solutions. Trough an innovative use of cumulative energy consumption curves, which represent the maximum and minimum energy limits, as well as the associated flexible energy consumption, this paper presents a methodology to characterise and use the energy flexibility provided by water pumping and storage systems (WPSS) in order to achieve specific objectives at different levels of power systems. The methodology is applied to a case study considering a real WPSS where energy flexibility is used to reduce electricity costs and support the operation of the power system during a wind generation curtailment event. Collected results show that savings around 16% can be achieved while reducing pumping cycles by 57%. Furthermore, the WPSS operation can be modified according to the needs of the power system using the available energy flexibility.

Abstract The operation of electric and heat grids alike is complicated due to the dynamic demand, with the increasing penetration of renewable energy sources adding to the problem. In order to improve the integration of variable renewable energy sources, the flexibility of the system needs to be improved. This paper proposed a novel characterization of the short-term energy flexibility, which was further utilized for the district heating capacity extension. The soft-linking of the models includes feedback, but the added computational complexity is kept at a minimum. Compared to the other literature in the field, due to the accurate characterization of the dynamics of the energy flexibility, flexibility is utilized much more frequently. The method was demonstrated for the case of the district heating of Zagreb. Results showed that both capital and operational savings can be achieved by adopting the proposed method. In the best performing scenario, which included the capacity extension planning, the savings of the district heating system were 5.4%. The extensive power exchange in the best performing scenario meant that the flexibility was used to help balancing the power grid as well.

Rapid increase of the renewable energy share in electricity production requires optimization and flexibility of the power consumption side. Thermostatically controlled loads (TCLs) have a large potential for regulation service provision. Economic model predictive control (MPC) is an advanced control method which can be used to syncronize the power consumption with undispatchable renewable electricity production. Thermal behavior of TCLs can be described by linear models based on energy balance of the system. In some cases, parameters of the model may be time-varying. In this work, we present a modified economic MPC based on linear parameter-varying model. In particular, we provide an exact transformation from a standard economic MPC formulation to a linear program. We assume that the variables influencing the model parameters are known (predictable) for the prediction horizon of the controller. As a case study, we present control system that minimizes operational cost of swimming pool heating system, where parameters of the model depend on the weather forecast. Simulation results demonstrate that the proposed method is able to deal with this kind of systems.

If CO2-emissions are to be reduced, the shares of renewable energy sources will have to be significantly increased. However, energy flexibility is required to cope with the increased share of renewable energy. Utilising it necessitates mathematical models of the operational response of energy flexible consumers. In this paper we present an accurate and general dynamic model of energy flexibility based on stochastic differential equations. The intuitive interpretation of the parameters is explained, to show the generality of the proposed model. To validate the approach, the parameters are estimated for three water towers and three buildings controlled by economic model predictive controllers. The model is then used to offer the energy flexibility on the current electricity market of Scandinavia, Nord Pool, using the so called “flexi orders”. Finally, the energy flexibility is used by controlling the demand of the water towers indirectly, through price signals designed based on the proposed model. Compared to having perfect foresight of electricity prices and future demand, between 63% and 98% of the potential savings were obtained in for these case studies. This shows that even without direct control of energy flexible systems, most of the potential can be reached under the current market conditions.