Robust estimation of risks from small samples

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited, but the impact of estimation errors may be very large. This paper presents a robust nonparametric Bayesian method to infer possible underlying distributions. The method obtains rigorous error bounds even for small samples taken from ill-behaved distributions. The approach taken has a natural interpretation in terms of the intervals between ordered observations, where allocation of probability mass across intervals is well-specified, but the location of that mass within each interval is unconstrained. This formulation gives rise to a straightforward computational resampling method: Bayesian Interval Sampling. In a comparison with common alternative approaches, it is shown to satisfy strict error bounds even for ill-behaved distributions.Comment: 13 pages, 3 figures; supplementary information provided. A revised version of this manuscript has been accepted for publication in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science

Designing colloidal ground state patterns using short-range isotropic interactions

DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. First, we determine lower limits for the interaction range between particles, depending on the complexity of the desired pattern and the underlying lattice. Then, we introduce a `recipe' for determining the pairwise interactions that exactly satisfies this minimum criterion, and we show that it is sufficient to uniquely determine the ground state for a large class of crystal structures. Finally, we verify these results using Monte Carlo simulations.Comment: 19 pages, 7 figure

Microtubule length distributions in the presence of protein-induced severing

Microtubules are highly regulated dynamic elements of the cytoskeleton of eukaryotic cells. One of the regulation mechanisms observed in living cells is the severing by the proteins katanin and spastin. We introduce a model for the dynamics of microtubules in the presence of randomly occurring severing events. Under the biologically motivated assumption that the newly created plus end undergoes a catastrophe, we investigate the steady state length distribution. We show that the presence of severing does not affect the number of microtubules, regardless of the distribution of severing events. In the special case in which the microtubules cannot recover from the depolymerizing state (no rescue events) we derive an analytical expression for the length distribution. In the general case we transform the problem into a single ODE that is solved numerically.Comment: 9 pages, 4 figure

Representative Days and Hours with Piecewise Linear Transitions for Power System Planning

Electric demand and renewable power are highly variable, and the solution of a planning model relies on capturing this variability. This paper proposes a hybrid multi-area method that effectively captures both the intraday and interday chronology of real data considering extreme values, using a limited number of representative days, and time points within each day. An optimization-based representative extraction method is proposed to improve intraday chronology capturing. It ensures higher precision in preserving data chronology and extreme values than hierarchical clustering methods. The proposed method is based on a piecewise linear demand and supply representation, which reduces approximation errors compared to the traditional piecewise constant formulation. Additionally, sequentially linked day blocks with identical representatives, created through a mapping process, are employed for interday chronology capturing. To evaluate the efficiency of the proposed method, a comprehensive expansion co-planning model is developed, including transmission lines, energy storage systems, and wind farms

Assessing Energy Storage Requirements Based on Accepted Risks

This paper presents a framework for deriving the storage capacity that an electricity system requires in order to satisfy a chosen risk appetite. The framework takes as inputs user-defined event categories, parameterised by peak power-not-served, acceptable number of events per year and permitted probability of exceeding these constraints, and returns as an output the total capacity of storage that is needed. For increased model accuracy, our methodology incorporates multiple nodes with limited transfer capacities, and we provide a foresight-free dispatch policy for application to this setting. Finally, we demonstrate the chance-constrained capacity determination via application to a model of the British network

Capturing Chronology and Extreme Values of Representative Days for Planning of Transmission Lines and Long-Term Energy Storage Systems

The growing penetration of renewable energy sources (RESs) is inevitable to reach net zero emissions. In this regard, optimal planning and operation of power systems are becoming more critical due to the need for modeling the short-term variability of RES output power and load demand. Considering hourly time steps of one or more years to model the operational details in a long-term expansion planning scheme can lead to a practically unsolvable model. Therefore, a clustering-based hybrid time series aggregation algorithm is proposed in this paper to capture both extreme values and temporal dynamics of input data by some extracted representatives. The proposed method is examined in a complex co-planning model for transmission lines, wind power plants (WPPs), short-term battery and long-term pumped hydroelectric energy storage systems. The effectiveness of proposed mixed-integer linear programming (MILP) model is evaluated using a modified 6-bus Garver test system. The simulation results confirm the proposed model efficacy, especially in modeling long-term energy storage systems.Comment: IEEE PowerTech 202

Nondisruptive decentralized control of thermal loads with second order thermal models

Abstract-Dynamic load controllers for thermostatically controlled loads should allow for accurate control of power consumption and should not disrupt the quality of service. This paper proposes an intuitive definition of nondisruptiveness for systems with second-order thermal models, based on a decomposition into fast and slow temperature modes. It enables the explicit control of the slow mode temperature using an embedded first order model; control of the fast mode is implicit. Temperature bounds are derived, and the slow mode controller is implemented using an accurate decentralised stochastic control strategy. Simulation results confirm its accuracy and nondisruptiveness

Survival of the aligned: ordering of the plant cortical microtubule array

The cortical array is a structure consisting of highly aligned microtubules which plays a crucial role in the characteristic uniaxial expansion of all growing plant cells. Recent experiments have shown polymerization-driven collisions between the membrane-bound cortical microtubules, suggesting a possible mechanism for their alignment. We present both a coarse-grained theoretical model and stochastic particle-based simulations of this mechanism, and compare the results from these complementary approaches. Our results indicate that collisions that induce depolymerization are sufficient to generate the alignment of microtubules in the cortical array.Comment: 4+ pages, 3 figures v2: significantly revised the exposition of the analytical model and expanded the discussion on our choice for the collision outcome probabilities; clarified the scope of the conclusions; numerous smaller changes throughou