Field Calculation Algorithm for General Beam Distributions
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Siemann, R.↗
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Results for “distributed algorithms”
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Gradient-Based Multi-Area Distribution System State Estimation
The increasing distributed and renewable energy resources and controllable devices in distribution systems make fast distribution system state estimation (DSSE) crucial in system monitoring and control. We consider a large multi-phase distribution system and formulate DSSE as a weighted least squares (WLS) problem. We divide the large distribution system into smaller areas of subtree structure, and by jointly exploring the linearized power flow model and the network topology, we propose a gradient-based multi-area algorithm to exactly and efficiently solve the WLS problem. The proposed algorithm enables distributed and parallel computation of the state estimation problem without compromising any performance. Numerical results on a 4,521-node test feeder show that the designed algorithm features fast convergence and accurate estimation results. Comparison with traditional Gauss-Newton method shows that the proposed method has much better performance in distribution systems with a limited amount of reliable measurement. The real-time implementation of the algorithm tracks time-varying system states with high accuracy.
41 EE - Solar Energy Technologies Office (EE-4S)↗
Solving a system of linear equations: From centralized to distributed methods
For a wide range of control engineering applications, the problem of solving a system of linear equations is often encountered and has been well studied. Traditionally, this problem has been mainly solved in a centralized manner. However, for applications related to large-scale complex networked systems, centralized algorithms are often subjected to some practical issues due to limited computational power and communication bandwidth. As a promising and viable alternative, distributed algorithms can effectively address the issues associated with centralized algorithms by solving the problem efficiently in a multi-agent setting that accords with the distributed nature of networked systems. Distributed algorithms decompose the entire problem into many sub-problems that are solved by individual agents in a cooperative manner. In this survey paper, we provide a detailed overview of the state of the art relevant to distributed algorithms for solving a system of linear equations. We will first review basic distributed algorithms including both discrete-time and continuous-time algorithms. Then we will discuss the extended algorithms to achieve communication efficiency. Furthermore, we will also introduce distributed algorithms to obtain the minimum-norm solution for a system of linear equations with multiple solutions, as well as the least-squares solutions when there is no solution. Finally, the relationship of distributed algorithms for solving a system of linear equations to the existing distributed optimization algorithms is discussed.
Wang, Peng↗
A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization
In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.
97 MATHEMATICS AND COMPUTING↗
Distributed Control Strategy to Achieve Synchronized Operation of an Islanded MG
To seamlessly transition a microgrid (MG) from islanded to grid-connected mode, it is necessary to synchronize the magnitude, frequency, and phase of the MG voltage to the voltage of the main grid. In this paper, we present a distributed control strategy to achieve synchronized operation of an islanded MG supported by multiple controllable distributed generators (DGs). The proposed method utilizes pinning-based consensus algorithm to ensure explicit coordination between magnitude, frequency and phase angle regulation, while ensuring proportional power sharing. System frequency is regulated by all the DGs in proportion to their capacity, while a selected DG eliminates the phase and magnitude regulation errors. Controller design criteria is based on small-signal stability analysis. Here, the proposed control strategy is implemented in hardware controllers and its effectiveness is demonstrated using a real-time hardware-in-the-loop MG testbed.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
A Monte Carlo Rectangle Packing Algorithm for Identifying Likely Spatial Distributions of Final Closure Cap Subsidence in the E-Area Low-Level Waste Facility
A Monte Carlo rectangle packing algorithm, summarized in Figure ES-1, has been developed to provide insights into the likely spatial distribution of subsided areas or holes in the final closure cap for the E-Area Low-Level Waste Facility (ELLWF) resulting from the placement of non-crushable waste containers within slit and engineered trench disposal units. Using historical records provided by Solid Waste Management as an indicator of future waste streams, a probability distribution of unique waste containers was constructed, and Monte Carlo sampling was used to sequentially select waste containers for placement in a rectangular region bounded by the disposal unit footprint. Within this Monte Carlo approach, the probability of any container type being selected is weighted by the fractional abundance relative to all other container types. For each Monte Carlo realization, the frequency of non-crushable waste containers appearing at each location on a spatially discretized mesh is updated. After many realizations, the location(s) with the highest frequencies of non-crushable waste containers are regarded as the most likely locations to experience subsidence (i.e., for a hole to form). Utilizing this approach has enabled the down-selection of a computationally intractable set of subsidence hole combinations to be explored in three-dimensional finite element groundwater flow and contaminant transport models. Such an approach can be applied to a number of different packaging problems.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Distributed Load Shedding Application Architecture and Bi-Level Predictive Estimator Algorithm
Increasing penetrations of distributed renewables are decreasing the effectiveness of traditional decentralized under-frequency load shedding (UFLS) schemes. As more distribution circuits begin to back-feed the transmission system, operation of traditional UFLS may exacerbate frequency instability. This paper presents the conceptual framework for a data-rich environment to coordinate UFLS across multiple distribution providers based on the laminar coordination framework in order to ensure optimal adaptive setting of UFLS relays. Communication and control are enabled through a distributed implementation of the IEC 61968-1 Common Information Model message bus structure. In addition to the proposed architecture, a novel adaptive UFLS scheme informed by a bi-level state estimator to create optimal relay setpoints is introduced. Initial simulation results are presented for the IEEE 14-bus test system on scenarios leading to mis-operation of traditional UFLS.
Anderson, Alexander A.↗
Effect of the embolization material in the dose calculation for stereotactic radiosurgery of arteriovenous malformations
It is reported in the literature that the material used in an embolization of an arteriovenous malformation (AVM) can attenuate the radiation beams used in stereotactic radiosurgery (SRS) up to 10% to 15%. The purpose of this work is to assess the dosimetric impact of this attenuating material in the SRS treatment of embolized AVMs, using Monte Carlo simulations assuming clinical conditions. A commercial Monte Carlo dose calculation engine was used to recalculate the dose distribution of 20 AVMs previously planned with a pencil beam dose calculation algorithm. Dose distributions were compared using the following metrics: average, minimal and maximum dose of AVM, and 2D gamma index. The effect in the obliteration rate was investigated using radiobiological models. It was found that the dosimetric impact of the embolization material is less than 1.0 Gy in the prescription dose to the AVM for the 20 cases studied. The impact in the obliteration rate is less than 4.0%. There is reported evidence in the literature that embolized AVMs treated with SRS have low obliteration rates. This work shows that there are dosimetric implications that should be considered in the final treatment decisions for embolized AVMs.
61 RADIATION PROTECTION AND DOSIMETRY↗
Equitable Transactive Market Design to Coordinate Networked Microgrids with Mixed Ownership
This paper presents an inter-microgrid peer-topeer (P2P) transactive market mechanism to support the coordination of multiple microgrids in a mixed-ownership environment, while enabling prosumers to actively participate in the market to get their own benefits. An equitable P2P transactive energy market is designed, in which the energy burden to customers within microgrids is fairly distributed by leveraging a peer-to-peer communication network among MG owners and the distribution system operator (DSO). To reach the market settlement, a consensus-based distributed optimization algorithm is introduced to enable each MG owner and the DSO to distributedly determine the cleared price which is compensated by a household-income-based discount factor to encourage the energy-burden equity among customers in networked microgrids service territory. Numerical results on the modified 123 node test feeder including 6 microgrids are used to demonstrate the operation of the introduced equitable transactive energy market.
Vu, Thanh Long↗
Cyber Graph Queries for Geographically Distributed Data Centers
We present new algorithms for a distributed model for graph computations motivated by limited information sharing we first discussed. Two or more independent entities have collected large social graphs. They wish to compute the result of running graph algorithms on the entire set of relationships. Because the information is sensitive or economically valuable, they do not wish to simply combine the information in a single location. We consider two models for computing the solution to graph algorithms in this setting: 1) limited-sharing: the two entities can share only a polylogarithmic size subgraph; 2) low-trust: the entities must not reveal any information beyond the query answer, assuming they are all honest but curious. We believe this model captures realistic constraints on cooperating autonomous data centers. We have algorithms in both setting for s - t connectivity in both models. We also give an algorithm in the low-communication model for finding a planted clique. This is an anomaly-detection problem, finding a subgraph that is larger and denser than expected. For both the low- communication algorithms, we exploit structural properties of social networks to prove performance bounds better than what is possible for general graphs. For s - t connectivity, we use known properties. For planted clique, we propose a new property: bounded number of triangles per node. This property is based upon evidence from the social science literature. We found that classic examples of social networks do not have the bounded-triangles property. This is because many social networks contain elements that are non-human, such as accounts for a business, or other automated accounts. We describe some initial attempts to distinguish human nodes from automated nodes in social networks based only on topological properties.
97 MATHEMATICS AND COMPUTING↗
Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation
Here we propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those methods. Our derivation assures convergence for convex problems whose feasible set is compact, subject to some standard regularity conditions and a mild “fairness” condition on subproblem selection. The method’s convergence guarantees are deterministic and do not require randomization, in contrast to other proposed asynchronous variations of progressive hedging. Computational experiments described in an online appendix show the method to outperform progressive hedging on large-scale problems in a highly parallel computing environment.
97 MATHEMATICS AND COMPUTING↗
Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling
In the Monte Carlo many-body perturbation (MC-MP) method, the conventional correlation-correction formula, which is a long sum of products of low-dimensional integrals, is first recast into a short sum of high-dimensional integrals over electron-pair and imaginary-time coordinates. These high-dimensional integrals are then evaluated by the Monte Carlo method with random coordinates generated by the Metropolis–Hasting algorithm according to a suitable distribution. The latter algorithm, while advantageous in its ability to sample nearly any distribution, introduces autocorrelation in sampled coordinates, which in turn increases the statistical uncertainty of the integrals and thus the computational cost. It also involves wasteful rejected moves and an initial “burn-in” step as well as displays hysteresis. Here, an algorithm is proposed that directly produces a random sequence of electron-pair coordinates for the same distribution used in the MC-MP method, which is free from autocorrelation, rejected moves, a burn-in step, or hysteresis. Furthermore, this direct-sampling algorithm is shown to accelerate second- (MC-MP2) and third-order Monte Carlo many-body perturbation (MC-MP3) calculations by up to 222% and 38%, respectively.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Security-Oriented and Load-Balancing Wireless Data Routing Game in the Integration of Advanced Metering Infrastructure Network in Smart Grid
Ensuring flexible and reliable data routing is indispensable for the integration of Advanced Metering Infrastructure (AMI) networks, we propose a secure-oriented and load-balancing wireless data routing scheme. A novel utility function is designed based on security routing scheme. Then, we model the interactive security-oriented routing strategy among meter data concentrators or smart grid meters as a mixed-strategy network formation game. Finally, such problem results in a stable probabilistic routing scheme with proposed distributed learning algorithm. One contributions is that we studied that different types of applications affect the routing selection strategy and the strategy tendency. Another contributions is that the chosen strategy of our mixed routing can adaptively to converge to a new mixed strategy Nash equilibrium (MSNE) during the learning process in the smart grid.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A probabilistic graphical model approach to stochastic multiscale partial differential equations
We develop a probabilistic graphical model based methodology to efficiently perform uncertainty quantification in the presence of both stochastic input and multiple scales. Both the stochastic input and model responses are treated as random variables in this framework. Their relationships are modeled by graphical models which give explicit factorization of a high-dimensional joint probability distribution. The hyperparameters in the probabilistic model are learned using sequential Monte Carlo (SMC) method, which is superior to standard Markov chain Monte Carlo (MCMC) methods for multi-modal distributions. Finally, we make predictions from the probabilistic graphical model using the belief propagation algorithm. Numerical examples are presented to show the accuracy and efficiency of the predictive capability of the developed graphical model.
97 MATHEMATICS AND COMPUTING↗
Real-Time Optimization and Control of Next-Generation Distribution Infrastructure
This presentation highlights the key developments of the ARAP-e NODES project, including the innovative real-time optimal power flow (RT-OPF) algorithm for distributed energy resource (DER) management, trip planning for T+D coordination, and extensive validation of the RT-OPF algorithm in NREL ESIF laboratory with 100+ physical hardware devices, controller-hardware-in-the-loop test at Southern California Edison (SCE), and two field demonstrations.
hardware-in-the-loop↗
Real-Time Distributed Control of Smart Inverters for Network-level Optimization
The limitations of centralized optimization methods in managing electric power distribution systems operations have led to the distributed paradigm of computing and decision-making. Unfortunately, the existing distributed optimization algorithms are limited in their applicability to managing fast varying phenomena such as those resulting from highly variable Distributed Energy Resource (DER) generation patterns. They require a large number of communication rounds (in the order of 10 2 to 10 3 ) among the computing agents to solve one instance of the optimization problem. Related real-time distributed control methods are equally limited in their applications to power distribution systems with fast-changing DER generation; they require hundreds of rounds of communication and thus are slow in tracking the network-level optimal solutions. In this paper, we propose a novel distributed voltage controller that provides a fast-tracking of rapidly varying DER generation profiles while simultaneously converging to network-level optimal solutions within a few communication rounds. The proposed control algorithm leverages the radial topology of the system, which reduces the required communication rounds to reach the network-level optimum solution by order of magnitude. The novelty lies in carefully reducing the electrical network model from the perspective of each distributed controller and enabling appropriate data sharing among upstream and downstream nodes to achieve fast convergence. The simulation results demonstrate the effectiveness of the proposed approach in minimizing the feeder losses while maintaining the node voltage within the pre-specified limits.
voltage control, optimization, reactive power, inv↗