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Battery participation in the service of power system frequency regulation is universally recognized as a viable means for counteracting the dramatic impact of the increasing utilization of renewable energy sources. One of the most complex aspects, in both the planning and operation stage, is the adequate characterization of the dynamic variation of the state of charge of the battery in view of lifetime preservation as well as the adequate participation in the regulation task. Since the power system frequency, which is the input of the battery regulation service, is inherently of a stochastic nature, it is easy to argue that the most proper methodology for addressing this complex issue is that of the theory of stochastic processes. In the first part of the paper, a preliminary characterization of the power system frequency is presented by showing that with an optimal degree of approximation it can be regarded as an Ornstein–Uhlenbeck process. Some considerations for guaranteeing desirable performances of the control strategy are performed by assuming that the battery-regulating power depending on the frequency can be described by means of a Wiener process. In the second part of the paper, more realistically, the regulating power due to power system changes is described as an Ornstein–Uhlenbeck or an exponential shot noise process driven by a homogeneous Poisson process depending on the frequency response features requested of the battery. Because of that, the battery state of charge is modeled as the output of a dynamic filter having this exponential shot noise process as input and its characterization constitutes the central role for the correct characterization of the battery life. Numerical simulations are carried out for demonstrating the goodness and the applicability of the proposed probabilistic approach.

Battery participation in the service of power system frequency regulation is universally recognized as a viable means for counteracting the dramatic impact of the increasing utilization of renewable energy sources. One of the most complex aspects, in both the planning and operation stage, is the adequate characterization of the dynamic variation of the state of charge of the battery in view of lifetime preservation as well as the adequate participation in the regulation task. Since the power system frequency, which is the input of the battery regulation service, is inherently of a stochastic nature, it is easy to argue that the most proper methodology for addressing this complex issue is that of the theory of stochastic processes. In the first part of the paper, a preliminary characterization of the power system frequency is presented by showing that with an optimal degree of approximation it can be regarded as an Ornstein–Uhlenbeck process. Some considerations for guaranteeing desirable performances of the control strategy are performed by assuming that the battery-regulating power depending on the frequency can be described by means of a Wiener process. In the second part of the paper, more realistically, the regulating power due to power system changes is described as an Ornstein–Uhlenbeck or an exponential shot noise process driven by a homogeneous Poisson process depending on the frequency response features requested of the battery. Because of that, the battery state of charge is modeled as the output of a dynamic filter having this exponential shot noise process as input and its characterization constitutes the central role for the correct characterization of the battery life. Numerical simulations are carried out for demonstrating the goodness and the applicability of the proposed probabilistic approach.

Nature-based solutions may actively reduce hydro-meteorological risks in urban areas as a part of climate change adaptation. However, the main reason for the increasing uptake of this type of solution is their many benefits for the local inhabitants, including recreational value. Previous studies on recreational value focus on studies of existing nature sites that are often much larger than what is considered as new NBS for flood adaptation studies in urban areas. We thus prioritized studies with smaller areas and nature types suitable for urban flood adaptation and divided them into four common nature types for urban flood adaptation: sustainable urban drainage systems, city parks, nature areas and rivers. We identified 23 primary valuation studies, including both stated and revealed preference studies, and derived two value transfer functions based on meta-regression analysis on existing areas. We investigated trends between values and variables and found that for the purpose of planning of new NBS the size of NBS and population density were determining factors of recreational value. For existing NBS the maximum travelling distance may be included as well. We find that existing state-of-the-art studies overestimate the recreational with more than a factor of 4 for NBS sizes below 5 ha. Our results are valid in a European context for nature-based solutions below 250 ha and can be applied across different NBS types and sizes.

Nature-based solutions may actively reduce hydro-meteorological risks in urban areas as a part of climate change adaptation. However, the main reason for the increasing uptake of this type of solution is their many benefits for the local inhabitants, including recreational value. Previous studies on recreational value focus on studies of existing nature sites that are often much larger than what is considered as new NBS for flood adaptation studies in urban areas. We thus prioritized studies with smaller areas and nature types suitable for urban flood adaptation and divided them into four common nature types for urban flood adaptation: sustainable urban drainage systems, city parks, nature areas and rivers. We identified 23 primary valuation studies, including both stated and revealed preference studies, and derived two value transfer functions based on meta-regression analysis on existing areas. We investigated trends between values and variables and found that for the purpose of planning of new NBS the size of NBS and population density were determining factors of recreational value. For existing NBS the maximum travelling distance may be included as well. We find that existing state-of-the-art studies overestimate the recreational with more than a factor of 4 for NBS sizes below 5 ha. Our results are valid in a European context for nature-based solutions below 250 ha and can be applied across different NBS types and sizes.

Phase change materials (PCM) are used in many industrial and residential applications for their advantageous characteristic of high capacity of latent thermal storage by means of an isothermal process. In this context, it is very useful to have predictive mathematical models for the analysis of the thermal performance and for the thermal design of these layers. In this work, an experimental validation of an analytical model that resolves the steady periodic heat transfer problem in a finite layer of PCM is presented. The experimental investigation was conducted employing a PCM with thermophysical and thermochemical behavior very close to those hypothesized in the formulation of the analytical model. For the evaluation of the thermophysical properties of the PCM sample used, an experimental procedure created by the authors was employed. In all tests realized in a sinusoidal and non-sinusoidal periodic regime, the comparison between the measured and calculated trends of the temperature at different sample heights and of the surface heat fluxes show an excellent agreement. Moreover, also having verified the analytical total stored energy, the analytical model constitutes a valid instrument for the evaluation of the latent and sensible contribution and the trend in time of the position of the bi-phase interface. Peer Reviewed

Phase change materials (PCM) are used in many industrial and residential applications for their advantageous characteristic of high capacity of latent thermal storage by means of an isothermal process. In this context, it is very useful to have predictive mathematical models for the analysis of the thermal performance and for the thermal design of these layers. In this work, an experimental validation of an analytical model that resolves the steady periodic heat transfer problem in a finite layer of PCM is presented. The experimental investigation was conducted employing a PCM with thermophysical and thermochemical behavior very close to those hypothesized in the formulation of the analytical model. For the evaluation of the thermophysical properties of the PCM sample used, an experimental procedure created by the authors was employed. In all tests realized in a sinusoidal and non-sinusoidal periodic regime, the comparison between the measured and calculated trends of the temperature at different sample heights and of the surface heat fluxes show an excellent agreement. Moreover, also having verified the analytical total stored energy, the analytical model constitutes a valid instrument for the evaluation of the latent and sensible contribution and the trend in time of the position of the bi-phase interface. Peer Reviewed