Bayesian Semiparametic estimation of densities with unknown support

We address the nonregular semiparametric problem of estimating a boundary point of the support of an unknown density, under local asymptotic exponentiality. The aim is to find the limiting marginal posterior distribution of the nonregular parameter and the rate of concentration for the density. Here we investigate two approaches. The first consists in extending the results found for parametric models to the case where the dimension of the regular nuisance parameter grows to infinity along with the number of observations. We used a Log-Spline prior to obtain the local concentration result for the marginal posterior of the lower support point; a Bernstein - von Mises type theorem with exponential limiting distribution. We also obtained contraction for the density at minimax rate up to a log factor. In the second approach, we constructed an adaptive mixture prior for a decreasing density with the following properties: a) posterior distribution of the density with known lower support point concentrates at minimax rate, up to log factor, b) the density is estimated consistently, uniformly in a neighbourhood of the lower support point, c) marginal posterior distribution of the lower support point of the density has shifted exponential distribution in the limit. In particular, to ensure that the density is asymptotically consistent pointwise in a neighbourhood of the lower support point, instead of a usual Dirichlet mixture weights, we consider a non-homogeneous Completely Random Measure mixture. This is important since the rate parameter of the limiting Exponential distribution is equal to the value of the density at the lower support point. The general conditions for the BvM type result we have are different from those by Knapik and Kleijn (2013); the latter don’t hold for a hierarchical mixture prior we consider. We implement this model using two different representations of the prior process; illustrate performance of this approach on simulated data, and apply it to model distribution of bids in procurement auctions

Potential micro-plastics dispersal and accumulation in the North Sea, with application to the MSC Zoe incident

The fate and effects of microplastics in the marine environment are an increasingly important area of research, policy and legislation. To manage and reduce microplastics in the seas and oceans, and to help understand causes and effects, we need improved understanding of transport patterns, transit times and accumulation areas. In this paper, we use a particle tracking model to investigate the differences in dispersal and accumulation of microplastics with different properties (floating and sinking) in the North Sea. In these simulations, particles were released with a uniform horizontal distribution, and also from rivers at rates proportional to the river runoff. The results showed that floating particles can accumulate temporarily on salinity fronts and in gyres, and are deposited predominantly on west-facing beaches. Sinking particles moved more slowly and less far, accumulated in deeper areas associated with fine sediments, and were deposited more on west- and north-facing beaches. The model was also applied to the MSC Zoe incident of 1 January 2019, in which 342 containers were lost north of the Dutch Wadden islands in the southern North Sea, tracking two types of microplastics with similar properties (∼5mm floating HDPE pellets and ∼0.6mm sinking PS grains) to identify release locations and potential accumulation areas. We used field observations collected by a citizen science initiative (waddenplastic.nl) to constrain the model results. For these simulations, particles were released along the ship’s trajectory and at locations on the trajectory where debris was found. The simulations of the MSC Zoe incident showed that over 90% of floating (∼5mm) HDPE pellets beached within 3–7 weeks, and predominantly on the more eastern Dutch Wadden Islands in agreement with the field observations, and that most of the sinking (∼0.6mm) PS grains were still at sea after 6 weeks, and a large proportion may have been deposited on German shores. The work is relevant to Descriptor 10 (Marine Litter) of the EU Marine Strategy Framework Directive

Observing and modelling phytoplankton community structure in the North Sea

© Author(s) 2017. CC Attribution 3.0 License. Phytoplankton form the base of the marine food chain, and knowledge of phytoplankton community structure is fundamental when assessing marine biodiversity. Policy makers and other users require information on marine biodiversity and other aspects of the marine environment for the North Sea, a highly productive European shelf sea. This information must come from a combination of observations and models, but currently the coastal ocean is greatly under-sampled for phytoplankton data, and outputs of phytoplankton community structure from models are therefore not yet frequently validated. This study presents a novel set of in situ observations of phytoplankton community structure for the North Sea using accessory pigment analysis. The observations allow a good understanding of the patterns of surface phytoplankton biomass and community structure in the North Sea for the observed months of August 2010 and 2011. Two physical-biogeochemical ocean models, the biogeochemical components of which are different variants of the widely used European Regional Seas Ecosystem Model (ERSEM), were then validated against these and other observations. Both models were a good match for sea surface temperature observations, and a reasonable match for remotely sensed ocean colour observations. However, the two models displayed very different phytoplankton community structures, with one better matching the in situ observations than the other. Nonetheless, both models shared some similarities with the observations in terms of spatial features and inter-annual variability. An initial comparison of the formulations and parameterizations of the two models suggests that diversity between the parameter settings of model phytoplankton functional types, along with formulations which promote a greater sensitivity to changes in light and nutrients, is key to capturing the observed phytoplankton community structure. These findings will help inform future model development, which should be coupled with detailed validation studies, in order to help facilitate the wider application of marine biogeochemical modelling to user and policy needs

Towards Congestion Management in Distribution Networks:a Dutch Case Study on Increasing Heat Pump Hosting Capacity

The current high gas prices motivate end-users to replace their gas heating with electric heat pumps. This will likely cause frequent congestion issues in low-voltage (LV) distribution grids and slow down the heat pump adoption rate. To avoid or defer the expensive and complicated grid expansion, this study shares a solution approach of a Dutch Distribution System Operator (DSO) to enable the increasing adoption of heat pumps in existing dense housing areas. Data of the DSO and a local housing company have been combined to investigate the heat pump hosting capacity on a dense urban LV feeder, including realistic data of grid topology, load and heat dynamics, and practical operating characteristics of heat pumps. Our simulation compares two control strategies: (1) individual peak shaving and (2) central optimal power flow control. We show the central optimal power flow control with end-users' thermal comfort constraints and an objective function of minimizing losses can smoothen total grid loading and lead to flat voltage profiles. This allows the approach to be robust against baseload forecast errors, while the individual peak shaving is more prone to such errors. Moreover, by simulating the strategies on the worst-case scenarios where heat pumps are allocated to end-users at the end of the feeder, we determine the individual peak shaving strategy can slightly increase the heat pump hosting capacity from 49% where no control is imposed to 51%, while the central optimal power flow control allows 100% heat pump connections without causing grid congestion. Finally, recommendations to increase the heat pump hosting capacity are given based on simulation results

Developing Computational Thinking Teaching Strategies to Model Pandemics and Containment Measures.

COVID-19 has been extremely difficult to control. The lack of understanding of key aspects of pandemics has affected virus transmission. On the other hand, there is a demand to incorporate computational thinking (CT) in the curricula with applications in STEM. However, there are still no exemplars in the curriculum that apply CT to real-world problems such as controlling a pandemic or other similar global crises. In this paper, we fill this gap by proposing exemplars of CT for modeling the pandemic. We designed exemplars following the three pillars of the framework for CT from the Inclusive Mathematics for Sustainability in a Digital Economy (InMside) project by Asia-Pacific Economic Cooperation (APEC): algorithmic thinking, computational modeling, and machine learning. For each pillar, we designed a progressive sequence of activities that covers from elementary to high school. In an experimental study with elementary and middle school students from 2 schools of high vulnerability, we found that the computational modeling exemplar can be implemented by teachers and correctly understood by students. We conclude that it is feasible to introduce the exemplars at all grade levels and that this is a powerful example of Science Technology, Engineering, and Mathematics (STEM) integration that helps reflect and tackle real-world and challenging public health problems of great impact for students and their families

Fairness-incorporated Online Feedback Optimization for Real-time Distribution Grid Management

With the increasing penetration of distributed energy resources such as photovoltaics (PVs), frequent voltage and congestion problems are expected to occur in distribution grids. Existing solution approaches based on centralized or distributed offline optimization cannot handle the dynamics of distribution grids in real time, i.e., by the time the computations are finished, the used data are already outdated as the grid loadings evolve so fast. Moreover, the unfair distribution of costs or burdens among end-users to relieve network issues, for example with PV curtailment, has not been sufficiently considered either. To address these issues, a fairness-incorporated online feedback optimization (OFO) approach is proposed. This approach produces implementable intermediate iterates for inverter-based assets using online optimization and suitably integrated measurements, and thus can work with the distribution grid dynamics. Moreover, it addresses the unfairness issue by modifying the voltage sensitivity matrices and leverages the feedback-based nature of OFO to compensate for the resulting modeling inaccuracies. Case studies based on a 96-bus low-voltage grid demonstrate the effectiveness of the fairness-incorporated OFO to handle the distribution grid dynamics and improve fairness, in both static and dynamic cases, with balanced and unbalanced grid models

Multi-timescale Coordinated Distributed Energy Resource Control Combining Local and Online Feedback Optimization

Recently, online feedback optimization (OFO) emerges as a promising approach for real-time distribution grid management. OFO offers several advantages, including not requiring precise grid models or real-time load metering and demonstrating robustness against inaccurate problem data. However, one important limitation is that OFO does not consider the intertemporal relationships and short-term planning capabilities of assets, thus not harnessing the full potential of a variety of distributed energy resources (DER) such as batteries and electric vehicles. To address this limitation, this paper proposes a multi-timescale coordinated control framework. In the slower timescale, local optimization problems are solved to provide real-time OFO controllers with reference setpoints. The overall approach thereby maintains minimal model, computation, and communication requirements while enforcing grid limits. Case studies based on a 96-bus unbalanced low-voltage grid with a high DER penetration level and second-scale data demonstrate its effectiveness and solution quality benchmarked with a centralized optimal power flow approach

Stable Distributed Online Feedback Optimization for Distribution System Voltage Regulation

We investigate the distributed voltage regulation problem in distribution systems employing online feedback optimization and short-range communication between physical neighbours. We show that a two-metric approach can be unstable. As a remedy, we propose a nested feedback optimization strategy. Simulation results reveal that while the two-metric approach fails to regulate voltages, the proposed approach achieves even less voltage limit violations than its centralized counterpart

Review of Recent Developments in Technical Control Approaches for Voltage and Congestion Management in Distribution Networks

The increasing installation of distributed energy resources in residential households is causing frequent voltage and congestion issues in low- and medium-voltage electrical networks. To defer or avoid the costly and complicated grid expansion, technical, pricing-based, and market-based approaches have been proposed in the literature. These approaches can help distribution system operators (DSOs) exploit flexible resources to manage their grids. This study focuses on technical control approaches, which are easier to implement, and provides an up-to-date review of their developments in modeling, solution approaches, and innovative applications facilitating indirect control from DSOs. Challenges and future research directions are also discussed