A scalable graph generation algorithm to sample over a given shell distribution.
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Here, the rapid evolution of modern electric power distribution systems into complex networks of interconnected active devices, distributed generation (DG), and storage poses increasing difficulties for system operators. The large-scale integration of distributed energy resources (DERs) and the rapid exchange of measurement data via communication networks present major opportunities for advancing grid operations but also introduce greater uncertainty, higher data dimensionality, more complex network and device models, and challenging control and optimization problems. Deep reinforcement learning (DRL) algorithms are promising in addressing these challenges. However, they have not been effectively adapted for power systems applications, requiring extensive customization for implementation and evaluation. This has resulted in reproducibility challenges and a steep learning curve for researchers new to applying DRL algorithms to the power systems domain. To bridge these gaps, this tutorial aims to serve as a valuable resource for researchers interested in exploring learning-based algorithms to operate active power distribution networks. Specifically, this work presents a generalized process for translating sequential decision-making problems in power distribution systems into Markov decision process (MDP) formulations, illustrated through concrete grid service examples. Additionally, we introduce a simple environment design strategy to develop and evaluate example DRL algorithms for distribution system applications, complete with an included code repository to guide users through environment construction.
In this paper, we describe a system for real-time automated Dynamic and Sustainable Demand Response with sparse data consumption prediction implemented on the University of Southern California campus microgrid. Supply side approaches to resolving energy supply-load imbalance do not work at high levels of renewable energy penetration. Dynamic Demand Response (D 2 R) is a widely used demand-side technique to dynamically adjust electricity consumption during peak load periods. Our D 2 R system consists of accurate machine learning based energy consumption forecasting models that work with sparse data coupled with fast and sustainable load curtailment optimization algorithms that provide the ability to dynamically adapt to changing supply-load imbalances in near real-time. Our Sustainable DR (SDR) algorithms attempt to distribute customer curtailment evenly across sub-intervals during a DR event and avoid expensive demand peaks during a few sub-intervals. It also ensures that each customer is penalized fairly in order to achieve the targeted curtailment. We develop near linear-time constant-factor approximation algorithms along with Polynomial Time Approximation Schemes (PTAS) for SDR curtailment that minimizes the curtailment error defined as the difference between the target and achieved curtailment values. Our SDR curtailment problem is formulated as an Integer Linear Program that optimally matches customers to curtailment strategies during a DR event while also explicitly accounting for customer strategy switching overhead as a constraint. We demonstrate the results of our D 2 R system using real data from experiments performed on the USC smartgrid and show that 1) our prediction algorithms can very accurately predict energy consumption even with noisy or missing data and 2) our curtailment algorithms deliver DR with extremely low curtailment errors in the 0.01-0.05 kWh range.
Atmospheric aerosol microphysical processes are a significant source of uncertainty in predicting climate change. Specifically, aerosol nucleation, emissions, and growth rates, which are simulated in chemical transport models to predict the particle size distribution, are not understood well. However, long-term size distribution measurements made at several ground-based sites across Europe implicitly contain information about the processes that created those size distributions. This work aims to extract that information by developing and applying an inverse technique to constrain aerosol emissions as well as nucleation and growth rates based on hourly size distribution measurements. We developed an inverse method based upon process control theory into an online estimation technique to scale aerosol nucleation, emissions, and growth so that the model–measurement bias in three measured aerosol properties exponentially decays. The properties, which are calculated from the measured and predicted size distributions, used to constrain aerosol nucleation, emission, and growth rates are the number of particles with a diameter between 3 and 6 nm, the number with a diameter greater than 10 nm, and the total dry volume of aerosol ( N 3–6 , N 10 , V dry ), respectively. In this paper, we focus on developing and applying the estimation methodology in a zero-dimensional “box” model as a proof of concept before applying it to a three-dimensional simulation in subsequent work. The methodology is first tested on a dataset of synthetic and perfect measurements that span diverse environments in which the true particle emissions, growth, and nucleation rates are known. The inverse technique accurately estimates the aerosol microphysical process rates with an average and maximum error of 2 % and 13 %, respectively. Next, we investigate the effect that measurement noise has on the estimated rates. The method is robust to typical instrument noise in the aerosol properties as there is a negligible increase in the bias of the estimated process rates. Finally, the methodology is applied to long-term datasets of in situ size distribution measurements in western Europe from May 2006 through June 2007. At Melpitz, Germany, and Hyytiälä, Finland, the average diurnal profiles of estimated 3 nm particle formation rates are reasonable, having peaks near noon local time with average peak values of 1 and 0.15 cm –3 s –1 , respectively. The normalized absolute error in estimated N 3–6 , N 10 , and V dry at three European measurement sites is less than 15 %, showing that the estimation framework developed here has potential to decrease model–measurement bias while constraining uncertain aerosol microphysical processes.
This study presents the designs and implementations of a distribution level open-universal grid analyser (Open-UGA) platform. The proposed Open-UGA platform consists of distribution-level phasor measurement units (PMUs), a standard signal generator, a router, and a server. Firstly, an overall introduction for the software, hardware, and server architectures of the Open-UGA platform is given. To give a detailed design, the software, hardware, server block diagrams, flowcharts, and printed circuit board photo of the Open-UGA platform are presented in detail. Then, four different types of distribution level PMU algorithms are introduced and implemented in the Open-UGA platform to verify the flexibility and reconfigurability. The flowcharts and functionalities of these four UGAs with different PMU algorithms are given as example implementations. Lastly, a performance comparison is conducted with both quantitative and illustrative results.
Computing a Voronoi or Delaunay tessellation from a set of points is a core part of the analysis of many simulated and measured datasets. As the scale of simulations and observations surpasses billions of particles, a distributed-memory scalable parallel algorithm is the only feasible approach. The primary contribution of this software is a distributed-memory parallel Delaunay and Voronoi tessellation algorithm based on existing serial computational geometry libraries that automatically determines which neighbor points need to be exchanged among the subdomains of a spatial decomposition. Other contributions include the addition of periodic and wall boundary conditions.
Computing a Voronoi or Delaunay tessellation from a set of points is a core part of the analysis of many simulated and measured datasets. As the scale of simulations and observations surpasses billions of particles, a distributed-memory scalable parallel algorithm is the only feasible approach. The primary contribution of this software is a distributed-memory parallel Delaunay and Voronoi tessellation algorithm based on existing serial computational geometry libraries that automatically determines which neighbor points need to be exchanged among the subdomains of a spatial decomposition. Other contributions include the addition of periodic and wall boundary conditions.
The increasing frequency of extreme events and the integration of distributed energy resources (DERs) into modern grids have elevated the need for resilient and efficient critical load restoration strategies in distribution systems. However, the stochastic nature of renewable DERs, limited energy resource availability and the intricate nonlinearities inherent in complex grid control problem make the problem challenging. Although reinforcement learning (RL) and warm-start RL methods have shown promising results, their performance often falls short in rapidly adapting to new, unseen situations and typically requires exhaustive problem-specific tuning. To address these gaps, we propose a First-Order Meta-based RL (FOM-RL) algorithm within an online framework for adaptive and robust critical load restoration. By harnessing local DERs as the enabling technology, FOM-RL allows the RL agent to swiftly adapt to new unseen scenarios by leveraging previously acquired knowledge of different tasks. Experimental results provide evidence that proposed algorithm learns more efficiently and showcases generalization capabilities across diverse set of operational scenarios. Moreover, a rigorous theoretical analysis yields a tight sublinear regret bound, sensitive to temporal variability, with a task-averaged optimality gap bounded by O(VM+D*/(Tsquare root(M))). These results suggest that optimality improves with task similarity and an increased number of tasks M, reaffirming the efficacy and scalability of the proposed approach in addressing the complexities of critical load restoration in distribution systems.
We propose a novel algorithm to solve optimal power flow (OPF) that aims at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large distribution networks by utilizing an information structure based on networked autonomous grids (AGs). Specifically, each AG is a subtree of a large distribution network that has a tree topology. The topology and line parameters of each AG are known only to a regional coordinator (RC) that is responsible for communicating with and dispatching the DERs within this AG. The reduced network, where each AG is treated as a node, is managed by a central coordinator (CC), which knows the topology and line parameters of the reduced network only and communicates with all the RCs. We jointly explore this information structure and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation burden compared to the centrally coordinated implementation of the primal-dual algorithm. Numerical results on a 4,521-node test feeder show that the proposed hierarchical distributed algorithm can achieve more than 10-fold improvement in the speed of convergence compared to the centrally coordinated primal-dual algorithm.
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov chain Monte Carlo (MCMC) is often used for the numerical solution of such problems. An alternative to MCMC is importance sampling, which can exhibit near perfect scaling with the number of cores on high performance computing systems because samples are drawn independently. However, finding a suitable proposal distribution is a challenging task. Several sampling algorithms have been proposed over the past years that take an iterative approach to constructing a proposal distribution. We investigate the applicability of such algorithms by applying them to two realistic and challenging test problems, one in subsurface flow, and one in combustion modeling. More specifically, we implement importance sampling algorithms that iterate over the mean and covariance matrix of Gaussian or multivariate t-proposal distributions. Our implementation leverages massively parallel computers, and we present strategies to initialize the iterations using “coarse” MCMC runs or Gaussian mixture models.
Despite technological advances making computing devices faster, smaller, and more prevalent in today's age, data generation and collection has outpaced data processing capabilities. Simply having more compute platforms does not provide a means of addressing challenging problems in the big data era. Rather, alternative processing approaches are needed and the application of machine learning to big data is hugely important. The MapReduce programming paradigm is an alternative to conventional supercomputing approaches, and requires less stringent data passing constrained problem decompositions. Rather, MapReduce relies upon defining a means of partitioning the desired problem so that subsets may be computed independently and recom- bined to yield the net desired result. However, not all machine learning algorithms are amenable to such an approach. Game-theoretic algorithms are often innately distributed, consisting of local interactions between players without requiring a central authority and are iterative by nature rather than requiring extensive retraining. Effectively, a game-theoretic approach to machine learning is well suited for the MapReduce paradigm and provides a novel, alternative new perspective to addressing the big data problem. In this paper we present a variant of our Support Vector Machine (SVM) Game classifier which may be used in a distributed manner, and show an illustrative example of applying this algorithm.
The transition to active distribution grids with real-time monitoring and control depends on the proliferation of advanced communication networks and devices. This paradigm shift towards a cyber-physical architecture also introduces new vulnerabilities for adversaries to exploit and launch sophisticated cyber-physical attacks targeting grid observability. Current research highlights the challenges in distinguishing attacks on voltage phasor or nodal injection measurements and isolating multi-source attack locations in a multiphase distribution grid. The attack detection and localization methods in literature face accuracy issues, applications across diverse attack scenarios, or scalability limits. Here, to bridge these gaps, this paper proposes a distributed Voltage Inference framework for real-time detection and localization of cyber-physical attacks, addressing scalability, adaptability, and accuracy challenges in state-of-the-art methods. The proposed methodology leverages the distributed nature of the Voltage Inference framework through a two-step process of prediction and correction, together with a tractable graph partitioning approach, providing a reliable solution to identify compromised measurement sources and facilitate isolation. Extensive testing on IEEE 13 and 123-node distribution feeders underscores the algorithm’s efficacy, enhancing the security and resilience of active distribution grids against evolving cyber threats. Additionally, Hardware-in-the-Loop (HIL) implementation validates the proposed strategy’s practical applicability in real-world scenarios.
Cascaded H-bridge topology has been used in grid-tied converters for battery energy storage system due to its modular structure. To fully utilize the converter’s modularity, this paper proposes a hierarchical distributed control architecture that consists of primary control, secondary control and battery state of charge (SOC) balancing control. Primary control ensures accurate current tracking while a distributed secondary control based on consensus algorithm is presented to regulate power sharing among modules and is proved to be stable theoretically. Here, a distributed SOC balancing control is further introduced to improve energy efficiency of battery energy storage system. Finally, the hierarchical distributed control strategy is implemented using hardware controllers and a software platform. Besides, a carrier phase shift control is also implemented to achieve multilevel output voltage and harmonic reduction. The experimental results demonstrate the performance of the proposed control scheme effectively.
The so-called “asymptotic projection technique” developed in previous papers of the authors is applied to the calculation of electronic transition-dipole moments (TDMs) in the one-determinant approximation between states of the same spin and spatial symmetry. The basic equations of the method and specific features of their application to a TDM calculation are briefly discussed. The attention focusses on the choice of a finite one-particle basis set. For this purpose, two possible algorithms for constructing distributed basis sets are proposed. In the first of them, the construction is based on minimization of the Hartree–Fock energy (E{sub HF}) with respect to nonlinear basis set parameters. In the second case, the parameters are determined by minimizing the functional E = E{sub HF} + E{sub MP2}, which includes the electron correlation through the second order of Møller–Plesset perturbation theory (Е{sub МР2}). On the whole, the results of calculations in both basis sets are in agreement with high-accuracy calculations performed by configuration interaction methods. The basis set adapted for E = E{sub HF} + E{sub MP2} significantly improves the accuracy as compared to the basis set of the first type.
As today's power grid is evolving into a densely interconnected cyber-physical system (CPS), a high fidelity and multifaceted testbed environment is needed to perform cybersecurity experiments in a realistic grid environment. Traditional standalone CPS testbeds lack the ability to emulate complex cyber-physical interdependencies between multiple smart grid domains in a real-time environment. Therefore, there are ongoing research and development (R&D) efforts to develop an interconnected CPS testbed by sharing geographically dispersed testbed resources to perform distributed simulation while analysing simulation fidelity. This paper presents a networked federation testbed for cybersecurity evaluation of today's and emerging smart grid environments. Specifically, it presents two novel testbed architectures, including cyber federation and cyber-physical federation, identifies R&D applications, and also describes testbed building blocks with experimental case studies. It also presents a novel co-simulation interface algorithm to facilitate distributed simulation within cyber-physical federation. The resources available at the PowerCyber CPS security testbed at Iowa State University (ISU) and the US Army Research Laboratory are utilised to develop this platform for performing multiple experimental case studies pertaining to wide-area protection and control applications in power system. Finally, experimental results are presented to analyse the simulation fidelity and real-time performance of the testbed federation.
Purpose: A rapid cycling proton beam has several distinct characteristics superior to a slow extraction synchrotron: The beam energy and energy spread, beam intensity and spot size can be varied spot by spot. The feasibility of using a spot scanning beam from a rapidc-ycling-medical-synchrotron (RCMS) at 10 Hz repetition frequency is investigated in this study for its application in proton therapy. Methods: The versatility of the beam is illustrated by two examples in water phantoms: (1) a cylindrical PTV irradiated by a single field and (2) a spherical PTV irradiated by two parallel opposed fields. A uniform dose distribution is to be delivered to the volumes. Geant4 Monte Carlo code is used to validate the dose distributions in each example. Results: Transverse algorithms are developed to produce uniform distributions in each transverseplane in the two examples with a cylindrical and a spherical PTV respectively. Longitudinally, different proton energies are used in successive transverse planes toproduce the SOBP required to cover the PTVs. In general, uniformity of dosedistribution within 3% is obtained for the cylinder and 3.5% for the sphere. The transversealgorithms requires only few hundred beam spots for each plane The algorithms may beapplied to larger volumes by increasing the intensity spot by spot for the same deliverytime of the same dose. The treatment time can be shorter than 1 minute for any fieldconfiguration and tumor shape. Conclusion: The unique beam characteristics of a spot scanning beam from a RCMS at 10 Hz repetitionfrequency are used to design transverse and longitudinal algorithms to produce uniformdistribution for any arbitrary shape and size of targets. The proposed spot scanning beam ismore versatile than existing spot scanning beams in proton therapy with better beamcontrol and lower neutron dose. This work is supported in part by grants from the US Department of Energy under contract; DE-FG02-12ER41800 and the National Science Foundation NSF PHY-1205431.
We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.