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At least 181 records · Page 10

Scalable/Secure Cooperative Algorithms and Framework for Extremely-high Penetration Solar Integration (SolarExPert) (Final Technical Report)

This SolarExPert project has developed a Sustainable Grid Platform (SGP) with scalable architecture of distributed control and optimization. The SGP consists of the following major functions: 1) an advanced grid architecture with hierarchical and distributed communication and control, combined with the OpenFMB standard and implemented on the Multi-Agent OpenDSS (MA-OpenDSS) platform; 2) an online distributed stochastic optimal power flow; 3) an online distributed system state estimation algorithm; 4) the distributed Volt/VAR optimization and frequency control algorithms; 5) the distributed distribution system restoration strategy. The developed SGP together with advanced functions are tested in 1 million (1M)-node distribution system on the MA-OpenDSS platform. Furthermore, the models and algorithms are tested in 100,000-node system HiL simulation, and also in P-HiL implementation with 100 physical devices. The developed functions haven been validated and tested on the selected actual distribution feeder with the data collected from the field of Maui Meadows in Hawaii. The distributed PV hosting capacities with cooperative Volt/VAR and Volt/VAR/Watt control are estimated and compared to provide recommendations for customers and the utility company.

14 SOLAR ENERGY↗

Distributed Outage Detection in Power Distribution Networks

Real time topology knowledge is essential for situational awareness of power distribution networks. Line outages change the topology of a distribution network. Hence, outage detection is an important task. Most of the existing outage detection algorithms are centralized, in which sensors communicate their data to a control center which performs outage detection using the received data. However, with the increasing size of the distribution network and with different areas of the network being monitored by different operators, communication is a bottleneck and scalability is a major concern. To address these issues, we propose a novel outage detection algorithm using a divide and conquer approach. First, we divide a distribution network into sub-networks, such that outage detection can be run in parallel in each sub-network independently ensuring scalability to large networks. Further, to reduce the latency, bandwidth and attenuation challenges associated with communications in a large network, we divide each sub-network into multiple control areas which communicate only with their neighbors. We employ a distributed iterative load estimation across the control areas of each sub-network and then use the load estimate for local outage detection in each control area. Here, the performance of our algorithm is evaluated for multiple feeder models and compared against traditional centralized outage detection algorithms.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Ordovician-Cambrian Units: Hierarchical Evaluation of Geologic Carbon Storage Resource Estimates

The Indiana Geological and Water Survey (IGWS) led subtask 1.1 to assess the regional distribution and estimate the storage capacity of Ordovician-Cambrian stratigraphic units located within the partnership region. This report includes the geologic interpretations and storage resource estimates (SREs) for three potential storage reservoirs calculated using six methodologies.

geologic characterization↗

Ordovician-Cambrian Units: Hierarchical Evaluation of Geologic Carbon Storage Resource Estimates

The Indiana Geological and Water Survey (IGWS) led subtask 1.1 to assess the regional distribution and estimate the storage capacity of Ordovician-Cambrian stratigraphic units located within the partnership region. A comprehensive data set of wireline logs and petrophysical information was used to generate these interpretations. These data include core analysis for porosity and permeability, mercury injection capillary pressure (MICP), and existing well data including location and stratigraphic information. This report includes storage resource estimates (SREs) for three potential storage reservoirs(limestone and dolostone from the Upper Ordovician Trenton Limestone/Black River Group and equivalent units, the Middle Ordovician St. Peter Sandstone, and primary target reservoir rocks of the Lower Ordovician and Upper Cambrian Knox Supergroup and equivalent units) calculated using six methodologies: (1) a fixed value of porosity of 10 percent in all units evaluated; (2) a unique average porosity (per well) from wireline-derived porosity (neutron, sonic, and/or density porosity for each unit); (3) porosity values from core analysis; (4) a depth-dependent porosity model (Knox Supergroup only); (5) porosity based on a model based on petrophysical facies; and (6) SREs using National Energy Technology Laboratory’s CO2 Storage prospeCtive Resource Estimation Excel aNalysis (CO2-SCREEN beta V2). All methods used the same values for thickness for each unit. However, the areal extent of each assessment was limited by the data available for each method. Estimated volumes were calculated in 1-by-1 kilometer grid cells and summarized as county and total stratigraphic unit volumes. The resultant SREs mass are displayed using boxplots, which allow for comparing data statistics (mean values and variability) between methods. Differences observed in SRE results from the six methods are mainly attributable to differences in the data and conceptual models used to interpret or estimate porosity in each method. Based on this systematic variability between methods, it is inferred that methods 1, 4, and 6 are best used for regional-scale reconnaissance estimates of storage capacity while methods 2, 3, and 5 are more appropriate for local scales where more data is required. All estimates are data-density dependent and different methods require different amounts of data for reasonable assessments. ArcMap 10.5.1 software was used to portray SREs to help visualize spatial variance of estimates for each methodology, and more importantly, to highlight those areas having the greatest total storage potential estimates.

01 COAL, LIGNITE, AND PEAT↗

Project 57 Air Monitoring Report: January 1 through December 31, 2017

On April 24, 1957, the Atomic Energy Commission (AEC) (now the Department of Energy [DOE]) conducted the Project 57 safety experiment in western Emigrant Valley northeast of the Nevada National Security Site (NNSS, formerly the Nevada Test Site) on lands withdrawn by the Department of Defense (DOD) for the Nevada Test and Training Range (NTTR). The test was undertaken to develop (1) a means of estimating plutonium distribution resulting from a non-nuclear detonation; (2) biomedical evaluation techniques for use in plutonium-laden environments; (3) methods of surface decontamination; and (4) instruments and field procedures for prompt estimation of alpha contamination (Shreve, 1958). Although the test did not result in the fission of nuclear materials, it did disseminate plutonium across the land surface. Following the experiment, the AEC fenced the contaminated area and returned control of the surrounding land to the DOD. Various radiological surveys were performed in the area and in 2007, the DOE expanded the demarked Contamination Area (CA) by posting signs 200 to 400 ft (60 to 120 m) outside of the original fence. Plutonium in soil attaches preferentially to smaller particles (Tamura, 1985; Friesen, 1992; Murarik et al., 1992; and Misra et al., 1993). Therefore, redistribution of soil particles by wind (dust) and water are the mechanisms most likely to transport plutonium beyond the boundary of the Project 57 CA. Monitoring was implemented in 2011 by Desert Research Institute (DRI) to determine if radionuclide contamination was detectable in samples of airborne dust and to characterize meteorological and environmental parameters that influence dust transport. Initially, two monitoring stations consisting of radiological, meteorological, and dust sampling equipment were installed near the southeast and northeast corners of the CA. In January 2015, the original monitoring stations were dismantled and moved farther to the west along the CA boundary. This move was made to place the monitoring stations downwind of ground zero and the High Contamination Area (HCA) during the dominant northerly and southerly winds. Samples of particles suspended in the air are collected every two weeks and submitted for laboratory assessments of gross alpha and gross beta radioactivity, and for determinations of gamma-emitting radionuclides. In calendar year (CY) 2017, the mean gross alpha concentration at monitoring station P57-4 was approximately 4.25 times the value at monitoring station P57-3. In CY2015 and CY2016, the difference in mean gross alpha concentration at the two stations was approximately 1.5. The mean gross alpha concentrations at P57-3 and P57-4 were approximately 1.9 and 7.9 times, respectively, the mean gross alpha concentrations at the surrounding Community Environmental Monitoring Program (CEMP) stations. The minimum gross alpha concentrations reported for the Project 57 stations are in the range of the minimum values observed at the CEMP stations. However, maximum gross alpha concentrations are greater than the maximum concentrations observed at the surrounding CEMP stations. Gamma spectroscopy analyses resulted in the detection of seven radionuclides. Except for americium-241 (Am-241), all reported radionuclides occur naturally in the environment. The Am-241 detection by gamma spectroscopy was confirmed by alpha spectroscopy. During each quarter of CY2017, four suspended particulate matter samples were selected for alpha spectroscopy analysis. Two were selected each quarter from the regular biweekly samples collected at each of the two monitoring stations. Of the eight samples from P57-3, one was reported to have plutonium-238 (Pu-238) above the minimum detectable activity (MDA) and five were reported to have plutonium 239/240 (Pu-239/240) above the MDA. Of the eight samples from P57-4, three were reported to have Pu-238 above the MDA and six were reported to have Pu-239/240 above the MDA. Soil material is also transported by saltation, which is a wind driven phenomena that bounces sand-sized soil particles across the land surface because they are too heavy to be suspended in the air. Samples of particles transported by saltation were collected downwind and upwind of the CA at both monitoring stations in May 2017 after a 190-day deployment and again in September 2017 after a 114-day deployment. Mass of the saltation samples was determined after oven drying. The September sample had greater mass than the May sample. The same relationship was observed for the suspended particulate matter samples during periods of saltation sample collection. The difference in the collected mass appears to be because of the amount of soil moisture. Higher soil moisture exerts additional isotopic bonds between soil particles and water molecules, and between water molecules that envelop soil particles, making it more difficult for wind to raise the particles as dust. In general, samples collected from saltation traps facing south contained more material than samples collected from traps facing north. This suggests that although saltation material may have been moving back and forth in conjunction with the two dominant wind directions, there was a net trend for saltation material to be transported toward the north. Radiological analyses of the saltation samples show that the smaller particle size faction (<63 μm) generally produced the highest activity levels of Am-241, Pu-238, and Pu-239/240. In general, the isotope activity levels decreased as the particle size increased. These results are consistent with the expectation that the greatest potential for transport of radiological contamination is with the smaller particles. Thermoluminescent dosimeters (TLDs) indicated that the average annual external radioactivity dose at the monitoring stations is slightly higher than the dose determined at the surrounding CEMP stations, but approximately half of the estimated national average dose received by the general public from exposure to natural sources. The TLDs at the Project 57 monitoring stations are exposed to both natural sources (terrestrial and cosmic) and radioactive releases from the Project 57 CA. Winds in excess of approximately 15 mph (24 km/hr) begin to generate dust movement by saltation or suspension, as determined by the monitoring instruments. Saltated particles, PM10 (i.e., inhalable dust), and PM2.5 (i.e., fine particulate dust) exhibit an approximately exponential increase with increasing wind speed. The greatest concentrations of dust occurred for winds exceeding 20 mph (32 km/hr). When the wind/dust analysis was performed for winds separated into the dominant northerly and southerly wind directions, it was evident that the northerly winds generated the higher PM10 concentrations and had the dominate influence on the PM10 concentration determined for all wind speeds when all wind directions were evaluated together. During the year, winds in excess of 20 mph (32 km/hr) occurred approximately one percent of the time. Although winds sufficient to generate dust occur at the Project 57 site, they are infrequent and of short duration. A preliminary assessment of individual wind events suggests that dust generation in response to specific wind conditions is highly variable. Wind speeds that would be expected to generate noticeable dust may not do so in every instance. Additionally, saltation transport in response to wind conditions was less common than expected. These variations were likely because of the influence of meteorological and environmental parameters other than wind.

54 ENVIRONMENTAL SCIENCES↗

The PAU Survey: Photometric redshifts using transfer learning from simulations

In this paper, we introduce the DEEPZ deep learning photometric redshift (photo-z) code. As a test case, we apply the code to the PAU survey (PAUS) data in the COSMOS field. DEEPZ reduces the σ68 scatter statistic by 50 percent at iAB = 22.5 compared to existing algorithms. This improvement is achieved through various methods, including transfer learning from simulations where the training set consists of simulations as well as observations, which reduces the need for training data. The redshift probability distribution is estimated with a mixture density network (MDN), which produces accurate redshift distributions. Our code includes an autoencoder to reduce noise and extract features from the galaxy SEDs. It also benefits from combining multiple networks, which lowers the photo-z scatter by 10 percent. Furthermore, training with randomly constructed coadded fluxes adds information about individual exposures, reducing the impact of photometric outliers. In addition to opening up the route for higher redshift precision with narrow bands, these machine learning techniques can also be valuable for broad-band surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Simulating PV System Performance with Component Reliability Distributions

A feature developed by Sandia National Laboratories (SNL) for simulating PV system component reliability has been integrated into the National Renewable Energy Laboratory's System Advisor Model (SAM). The PV Reliability Performance Model (PV-RPM) uses fault/failure and repair distributions to estimate impacts to power, energy production and operational costs. Realization results include the number of failures per component, failure rate, O&M costs incurred based on maintenance strategies, and energy lost based on the failure estimates. As the inputs are inherently uncertain and based on probability distributions, the model realizations include statistical confidence intervals to help bracket the probability that the sample interval contains the true mean value of the variable in question. This paper presents the current validation efforts and provides detail on how this feature is utilized in a PV performance model.

14 SOLAR ENERGY↗

Agent-Based Model of Combined Community- and Jail-Based Take-Home Naloxone Distribution

Importance Opioid-related overdose accounts for almost 80 000 deaths annually across the US. People who use drugs leaving jails are at particularly high risk for opioid-related overdose and may benefit from take-home naloxone (THN) distribution. Objective To estimate the population impact of THN distribution at jail release to reverse opioid-related overdose among people with opioid use disorders. Design, Setting, and Participants This study developed the agent-based Justice-Community Circulation Model (JCCM) to model a synthetic population of individuals with and without a history of opioid use. Epidemiological data from 2014 to 2020 for Cook County, Illinois, were used to identify parameters pertinent to the synthetic population. Twenty-seven experimental scenarios were examined to capture diverse strategies of THN distribution and use. Sensitivity analysis was performed to identify critical mediating and moderating variables associated with population impact and a proxy metric for cost-effectiveness (ie, the direct costs of THN kits distributed per death averted). Data were analyzed between February 2022 and March 2024. Intervention Modeled interventions included 3 THN distribution channels: community facilities and practitioners; jail, at release; and social network or peers of persons released from jail. Main Outcomes and Measures The primary outcome was the percentage of opioid-related overdose deaths averted with THN in the modeled population relative to a baseline scenario with no intervention. Results Take-home naloxone distribution at jail release had the highest median (IQR) percentage of averted deaths at 11.70% (6.57%-15.75%). The probability of bystander presence at an opioid overdose showed the greatest proportional contribution (27.15%) to the variance in deaths averted in persons released from jail. The estimated costs of distributed THN kits were less than $\$$15 000 per averted death in all 27 scenarios. Conclusions and Relevance This study found that THN distribution at jail release is an economical and feasible approach to substantially reducing opioid-related overdose mortality. Training and preparation of proficient and willing bystanders are central factors in reaching the full potential of this intervention.

Tatara, Eric [Argonne National Laboratory (ANL), A↗

Improving Performance of Multi-Area State Estimation Using Spectral Clustering

This paper investigates the problem of dividing a large power system into several areas to be solved by a state estimator which coordinates locally obtained decentralized estimates. By applying automatic partitioning to the utility system, the performance of the distributed state estimator can be improved as compared to the pre-defined utility control areas. The presented approach utilizes the spectral properties of the un-directed graph formed by assigning a vertex to every bus and an edge to every pair of buses connected by a line. The graph Laplacian matrix and associated eigenvectors and eigenvalues are used to cluster the graph vertices in such a way that each area has a large number of internal connections, but a small number of external connections. This approach is demonstrated using the IEEE 118 bus system.

Kelle, David↗

Distributional Deep Reinforcement Learning-Based Emergency Frequency Control

Emergency frequency control is one of the most critical approaches to maintain power system stability after major disturbances. With the increasing number of grid-connected renewable energy sources, existing model-based methods of frequency control are facing up with challenges of computational speed and scalability for large-scale systems. In this paper, the emergency frequency control problem is formulated as a Markov Decision Process (MDP) and solved through a novel Distributional Deep Reinforcement Learning (DDRL) method, namely the distributional soft actor critic (DSAC) method. Compared with other RL methods that only estimate the mean value, the proposed DSAC model estimates the distribution of value function over returns. This advancement can lead to more insights and knowledge for the agent, with the benefit of a much faster and more stable learning process, and the improved frequency control performance. Here, the simulation results on IEEE 39-bus and IEEE 118-bus systems demonstrate the effectiveness and robustness of proposed models, as well as the advantage compared to other state-of-the-art DRL algorithms.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Equity-driven Planning of Distributed Solar PV using Optimal Transport

Typically, distribution system planning processes do not explicitly incorporate energy equity considerations, such as identifying consumers most affected by energy costs and determining how investments in the distribution system can address existing energy burden imbalances. This paper proposes a novel optimal transport (OT)-based method to improve the energy burden distribution of consumers. The approach involves the strategic siting and sizing of solar PV in order to assist customers with high energy burden and improve the overall energy burden distribution of the community. The desired energy burden distribution is defined using the equal distribution equivalent (EDE) concept. The OT-based method is then used to estimate the distributed solar PV capacity to be installed at various locations and the tariffs to be adjusted, all while improving the energy burden distribution and providing valuable insights into distributed generation (DG) planning. The results on IEEE 37 bus test system demonstrate how DG planning, considering EDE and OT, can help reduce the energy burden of low-income consumers. Additionally, the approach also reveals optimal tariff adjustments needed to ensure revenue neutrality for distribution utilities.

Optimal transport, equal distribution equivalent, ↗

An Adaptive-Importance-Sampling-Enhanced Bayesian Approach for Topology Estimation in an Unbalanced Power Distribution System

The reliable operation of a power distribution system relies on a good prior knowledge of its topology and its system state. Although crucial, due to the lack of direct monitoring devices on the switch statuses, the topology information is often unavailable or outdated for the distribution system operators for real-time applications. Apart from the limited observability of the power distribution system, other challenges are the nonlinearity of the model, the complicated, unbalanced structure of the distribution system, and the scale of the system. To overcome the above challenges, we, in this paper, propose a Bayesian-inference framework that allows us to simultaneously estimate the topology and the state of a three-phase, unbalanced power distribution system. Specifically, by using the very limited number of measurements available that are associated with the forecast load data, we efficiently recover the full Bayesian posterior distributions of the system topology under both normal and outage operation conditions. This is performed through an adaptive importance sampling procedure that greatly alleviates the computational burden of the traditional Monte-Carlo (MC)-sampling-based approach while maintaining a good estimation accuracy. The simulations conducted on the IEEE 123-bus test system and an unbalanced 1282-bus system reveal the excellent performances of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Joint Estimation of Topology and Injection Statistics in Distribution Grids with Missing Nodes

Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This article discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular, we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance is validated using both linearized and nonlinear ac power flow samples in test distribution grids.

97 MATHEMATICS AND COMPUTING↗

Sequential Mitigation Solutions to Enable Distributed PV Grid Integration

This paper presents a method to assess the technical impacts of a series of distribution system mitigations for integrating increasing penetrations of distributed generation from solar photovoltaics (DGPV). Solutions considered include distribution grid upgrades and advanced control technologies. This study helps pave the way to estimate the distribution integration costs needed to reach various PV penetration levels. The approach uses three stream-lined, bounding scenarios for increased PV penetration patterns. It begins by studying the distribution impact of PV power and quantifying the PV hosting capacity. Then, it studies multiple mitigation solutions to increase PV penetration on distribution feeders. These mitigation solutions are implemented in a sequential manner according to their typical costs. The proposed technique is demonstrated on two representative distribution feeders.

14 SOLAR ENERGY↗

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗

Data-Driven Mean-Corrected Recursive Estimation-Based Optimal DER Dispatch for Distribution System Voltage Control

Recent advances in smart inverters offer opportunities to mitigate adverse grid impacts caused by high penetrations of distributed photovoltaics (PV) in distribution grids, such as voltage violations. Here, this paper proposes a novel measurement-driven optimal power flow (OPF)-based distributed energy resource management system (DERMS) voltage regulation via recursive sensitivity estimation informed coordinated control of distributed PV inverters. The proposed approach leverages available grid and controllable DER measurements, eliminating reliance on system model information while being adaptive and robust to volatile operating conditions. A mean-corrected recursive ridge regression (MCRRR) algorithm is proposed for sensitivity estimation, continuously refining the sensitivity model through a closed-form solution. It effectively manages varying grid operating conditions, such as changes in power injections and topology reconfiguration, to facilitate a time-varying update of the Load Sensitivity Factors (LSF). The proposed approach is formulated as a linear programming (LP) problem and is thus scalable to larger-scale distribution systems. Its effectiveness and efficiency are demonstrated on a realistic distribution feeder with high PV penetrations in Southern California, USA.

14 SOLAR ENERGY↗

Formulation of Three-Phase State Estimation Problem Using a Virtual Reference

State Estimation (SE) is the backbone of modern Energy Management System (EMS) due its capability of processing real time measurements and provide reliable information to system operators. Since its introduction to power systems in the 70’s, SE has been widely used in transmission networks. Distribution grids on the other hand lack sufficient number of real time measurements, and for that reason SE has not been widely implemented on these systems. The recent increase in the number of renewable energy sources connected to the grid at lower voltage levels, the advent of Distribution Automation (DA) and Smart Grids necessitate closer monitoring of distribution networks and thus forcing utilities to upgrade their operations and deploy Advanced Distribution Management Sytems (ADMS). Therefore, Distribution System State Estimation (DSE) is paramount to provide real time monitoring of active distribution grids. This papers investigates the formulation of the three-phase distribution state estimation where in the most general case, none of the system buses may have balanced three phase voltages. In such a case, the choice and definition of the slack bus need to be revisited. Most of the existing work arbitrarily assign the root bus of the distribution feeder as the balanced three-phase reference which may not be realistic for today’s active distribution systems. This paper addresses this shortcoming of the existing SE formulations by introducing a virtual reference bus. Here, the proposed approach is effectively validated by simulations carried out on distribution test systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Uncertainty Error Modeling for Non-Linear State Estimation With Unsynchronized SCADA and µPMU Measurements

Distribution systems of the future smart grid require enhancements to the reliability of distribution system state estimation (DSSE) in the face of low measurement redundancy, unsynchronized measurements, and dynamic load profiles. Micro phasor measurement units (µPMUs) facilitate co-synchronized measurements with high granularity, albeit at an often prohibitively expensive installation cost. Supervisory control and data acquisition (SCADA) measurements can supplement µPMU data, although they are received at a slower sampling rate. Further complicating matters is the uncertainty associated with load dynamics and unsynchronized measurements–not only are the SCADA and µPMU measurements not synchronized with each other, but the SCADA measurements themselves are received at different time intervals with respect to one another. This paper proposes a non-linear state estimation framework which models dynamic load uncertainty error by updating the variances of the unsynchronized measurements, leading to a time-varying system of weights in the weighted least squares state estimator. Case studies are performed on the 33-Bus Distribution System in MATPOWER, using Ornstein–Uhlenbeck stochastic processes to simulate dynamic load conditions.

Cooper, Austin↗