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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Enhancing Active Distribution Systems Resilience by Fully Distributed Self-Healing Strategy

Distributed restoration can exploit smart grid technologies to enhance the resilience of active distribution networks toward a self-healing smart grid. However, the large number of decision variables, especially the binary ones for reconfiguration, bring challenges to developing scalable distributed distribution service restoration (DDSR) strategies. This paper proposes a fully distributed solution procedure based on the alternating direction method of multipliers (ADMM) for mixed-integer programming problems and applies to develop the DDSR framework. The method consists of relax-drive-polish phases, 1) relaxing binary variables, and applying the convex ADMM as a warm start; 2) driving the solutions toward Boolean values through a proximal operator; 3) fixing the obtained binding binary variables and solving the rest of the problem to polish results and achieve a high-quality suboptimal solution. Then, an autonomous clustering strategy and consensus ADMM are integrated with the proposed method to realize the fully distributed cluster-based framework of DDSR. This framework can first determine DER scheduling and switch status for reconfiguration to energize the out-of-service areas from local faults, and then provide the load restoration solution in a distributed manner for total blackouts in large-scale distribution networks. Furthermore, the effectiveness and scalability of the proposed DDSR framework are demonstrated through testing on the IEEE 123-node, IEEE 8500-node, and synthetic 100k-node test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Hierarchical Distribution System Adaptive Restoration with Diverse Distributed Energy Resources

Distributed energy resources (DERs) can be utilized as alternative power sources for fast service recovery in cases of distribution system outages. However, the diverse characteristics and stochastic nature of DERs impose challenges on the optimal operation of di-verse resources during the restoration phase. Here, we introduce a hierarchical structure to coordinate distribution system entities and propose an adaptive restoration strategy to sustain a reliable power supply to outage loads in an unbalanced distribution system utilizing DERs. An efficient system reconfiguration model is developed to guarantee the radiality of restoration islands. The flexibility of DERs is evaluated by a novel method that focuses on the cumulative energy consumption, the superiority of which is also proven. Model predictive control (MPC) is adopted to enable the adjustment of system topology and DER operation strategies based on up-to-date data. The performance of the proposed restoration model is validated on a modified IEEE 123-bus test system. Moreover, the effectiveness of the proposed novel flexibility assessment and the MPC-based adaptive restoration strategy are verified through comparative studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Hemispherically symmetric strategies for stratospheric aerosol injection

Stratospheric aerosol injection (SAI) comes with a wide range of possible design choices, such as the location and timing of the injection. Different stratospheric aerosol injection strategies can yield different climate responses; therefore, understanding the range of possible climate outcomes is crucial to making informed future decisions on SAI, along with the consideration of other factors. Yet, to date, there has been no systematic exploration of a broad range of SAI strategies. This limits the ability to determine which effects are robust across different strategies and which depend on specific injection choices. This study systematically explores how the choice of SAI strategy affects climate responses in one climate model. Here, we introduce four hemispherically symmetric injection strategies, all of which are designed to maintain the same global mean surface temperature: an annual injection at the Equator (EQ), an annual injection of equal amounts of SO 2 at 15° N and 15° S (15N+15S), an annual injection of equal amounts of SO 2 at 30° N and 30° S (30N+30S), and a polar injection strategy that injects equal amounts of SO 2 at 60° N and 60° S only during spring in each hemisphere (60N+60S). We compare these four hemispherically symmetric SAI strategies with a more complex injection strategy that injects different quantities of SO 2 at 30° N, 15° N, 15° S, and 30° S in order to maintain not only the global mean surface temperature but also its large-scale horizontal gradients. All five strategies are simulated using version 2 of the Community Earth System Model with the middle atmosphere version of the Whole Atmosphere Community Climate model, version 6, as the atmospheric component, CESM2(WACCM6-MA), with the global warming scenario, Shared Socioeconomic Pathway (SSP)2-4.5. We find that the choice of SAI strategy affects the spatial distribution of aerosol optical depths, injection efficiency, and various surface climate responses. In addition, injecting in the subtropics produces more global cooling per unit injection, with the EQ and the 60N+60S cases requiring, respectively, 59 % and 50 % more injection than the 30N+30S case to meet the same global mean temperature target. Injecting at higher latitudes results in larger Equator-to-pole temperature gradients. While all five strategies restore Arctic September sea ice, the high-latitude injection strategy is more effective due to the SAI-induced cooling occurring preferentially at higher latitudes. These results suggest trade-offs wherein different strategies appear better or worse, depending on which metrics are deemed important.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Scenario Planning Management Actions to Restore Cold Water Stream Habitat: Comparing Mechanistic and Statistical Modeling Approaches

ABSTRACT Under the United States Clean Water Act, states are required to periodically assess state waters to determine compliance with water quality criteria (including temperature) and then to develop total maximum daily loads (TMDLs) for impaired waters as necessary to bring them into compliance. We compared the performance of mechanistic stream temperature models (HeatSource, QUAL2K, and QUAL2Kw) applied to the mainstem of three TMDL watersheds (Middle Fork John Day, OR; Wind River, WA; South Fork Nooksack, WA) with that of spatial stream network (SSN) models applied to the full watersheds and used these to evaluate the potential effectiveness of restoration strategies. SSN models performed well with slightly lesser accuracy (RMSE = 0.47–0.87) for mainstem predictions than mechanistic models (RMSE = 0.4) but provided additional benefits to inform management, including information on spatial and temporal heterogeneity of restoration effectiveness throughout the watershed. Of the four scenarios considered (restoration of riparian zones to potential natural vegetation, channel narrowing, increasing flow by restricting irrigation withdrawals, and combined applications), riparian zone restoration was consistently the most effective in reducing temperatures at the outlet, mainstem, and throughout the watersheds. Predicted restoration effectiveness for thermal regimes varied significantly both within and among watersheds. A focus on water quality criteria exceedance only at the watershed outlet or along the mainstem reach can obscure knowledge of restoration potential for fish habitat in tributaries and headwaters, potential for creation of thermal refuge areas along the mainstem critical for maintaining migration corridors, and thermal regime heterogeneity across space and time.

Fuller, M. R.↗
DOE OSTI2025

Decoding Resilience by Modeling Outage and Restoration Processes in Distribution Grids: A Pittsburgh Case Study

Climate-induced extreme weather events, such as floods and heatwaves, pose significant challenges to the resilience of urban power distribution grids. This paper examines the outage and restoration dynamics of Pittsburgh's power grid during the flood event in April 2024 and three heatwaves in June, July, and August 2024. We introduce a comprehensive modeling framework that integrates outage and restoration processes, enabling the quantification of resilience metrics, including total customer-hours of power outage, maximum residual values, and restoration durations across various ZIP codes. Our analysis highlights spatial disparities in outage impacts and restoration efficiencies, with ZIP Code 15222 experiencing the highest cumulative disruptions, while ZIP Code 15217 shows lower susceptibility. By linking statistical trends with weather events, this study underscores the critical need for targeted infrastructure upgrades and advanced restoration strategies. Furthermore, the proposed framework offers valuable insights for planning and managing resilient power systems in the face of increasing climate stress.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Enhancing Distribution System Resilience: A First-Order Meta-RL Algorithm for Critical Load Restoration

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.

complexity theory↗
DOE OSTI2021

Supporting cost-effective watershed management strategies for Chesapeake Bay using a modeling and optimization framework

Extensive efforts to adaptively manage nutrient pollution rely on Chesapeake Bay Program’s (Phase 6) Watershed Model, called Chesapeake Assessment Scenario Tool (CAST), which helps decision-makers plan and track implementation of Best Management Practices (BMPs). We describe mathematical characteristics of CAST and develop a constrained nonlinear BMP-subset model, software, and visualization framework. This represents the first publicly available optimization framework for exploring least-cost strategies of pollutant load control for the United States’ largest estuary. The optimization identifies implementation options for a BMP subset modeled with load reduction effectiveness factors, and the web interface facilitates interactive exploration of >30,000 solutions organized by objective, nutrient control level, and for ~200 counties. We assess framework performance and demonstrate modeled cost improvements when comparing optimization-suggested proposals with proposals inspired by jurisdiction plans. Stakeholder feedback highlights the framework’s current utility for investigating cost-effective tradeoffs and its usefulness as a foundation for future analysis of restoration strategies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Achieving Productivity to Recover and Restore Columbia River Stream-Type Chinook Salmon Relies on Increasing Smolt-To-Adult Survival

Abstract We analyzed and compared productivity and survival rates of populations of stream-type Chinook Salmon Oncorhynchus tshawytscha from the upper and middle ranges of their distribution in the Columbia River basin. These two groups of populations undergo vastly different exposures during migration through the Federal Columbia River Power System (FCRPS). Declines of the Snake River populations, listed as threatened under the U.S. Endangered Species Act, have been associated with the development and operation of the FCRPS. In contrast, John Day River stream-type Chinook Salmon populations, which were less affected by the FCRPS, have declined to a lesser extent and are not listed. Smolt-to-adult survival rates (SARs) accounted for a majority of the variation in life cycle survival rates of Snake River Chinook Salmon. Productivity declined to 13% and 44% of historical productivity levels for Snake River and John Day River populations, respectively. A synthesis of previous studies contrasting anthropogenic impacts between the two regions supports the conclusion that FCRPS impacts explain the large difference in population productivity. Our results suggest that SARs of 4% would result in an expected productivity of up to 70% of historical levels (a SAR level consistent with regional restoration objectives). The SARs have been shown to be highly influenced by conditions within the FCRPS (e.g., water velocity and passage through dam powerhouses). Marine conditions also influence SARs; however, meaningful management actions are only available to affect conditions within the FCRPS. Given the importance of SARs to overall life cycle productivity, recovery and restoration strategies need to prioritize actions that have potential to substantially increase SARs by addressing the significant impacts of main-stem dams. This study highlights the importance of considering river management options in the face of increasingly variable and warming ocean conditions.

Petrosky, Charles E.↗
DOE OSTI2025

A unified funnel restoration SQP algorithm

We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of basic algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.

Kiessling, David [Katholieke Univ. Leuven, Heverle↗
DOE OSTI2023

Guest Editorial: Special issue on flexible and resilient urban energy systems

This guest editorial summarizes the topics and the papers selected for the Special Issue on Flexible and Resilient Urban Energy Systems. After rigorous reviewing process, 21 papers are accepted for publication. These 21 accepted papers cover various aspects of urban energy systems and are distributed as following: situational awareness of urban energy systems (2 papers), quantification metrics of flexibility and resilience of urban energy systems (3 papers), vulnerability modeling of urban energy systems under various extreme events (3 papers), planning of flexible and resilient urban energy systems (4 papers), robust and resilient operation and control of urban energy systems (4 papers), recovery and restoration strategy of urban energy systems (2 papers), and coordination and interoperability of interconnected energy systems (3 papers). The Guest Editorial Board hopes this Special Issue can provide a valuable information for future research and advancements in the field of flexible and resilient urban energy systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Sinuosity‐Driven Hyporheic Exchange: Hydrodynamics and Biogeochemical Potentials

Abstract Hydrologic exchange processes are critical for ecosystem services along river corridors. Meandering contributes to this exchange by driving channel water, solutes, and energy through the surrounding alluvium, a process called sinuosity‐driven hyporheic exchange. This exchange is embedded within and modulated by the regional groundwater flow (RGF), which compresses the hyporheic zone and potentially diminishes its overall impact. Quantifying the role of sinuosity‐driven hyporheic exchange at the reach‐to‐watershed scale requires a mechanistic understanding of the interplay between drivers (meander planform) and modulators (RGF) and its implications for biogeochemical transformations. Here, we use a 2D, vertically integrated numerical model for flow, transport, and reaction to analyze sinuosity‐driven hyporheic exchange systematically. Using this model, we propose a dimensionless framework to explore the role of meander planform and RGF in hydrodynamics and how they constrain nitrogen cycling. Our results highlight the importance of meander topology for water flow and age. We demonstrate how the meander neck induces a shielding effect that protects the hyporheic zone against RGF, imposing a physical constraint on biogeochemical transformations. Furthermore, we explore the conditions when a meander acts as a net nitrogen source or sink. This transition in the net biogeochemical potential is described by a handful of dimensionless physical and biogeochemical parameters that can be measured or constrained from literature and remote sensing. This work provides a new physically based model that quantifies sinuosity‐driven hyporheic exchange and biogeochemical reactions, a critical step toward their representation in water quality models and the design and assessment of river restoration strategies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Soil resistance and recovery during neotropical forest succession

The recovery of soil conditions is crucial for successful ecosystem restoration and, hence, for achieving the goals of the UN Decade on Ecosystem Restoration. Here, we assess how soils resist forest conversion and agricultural land use, and how soils recover during subsequent tropical forest succession on abandoned agricultural fields. Our overarching question is how soil resistance and recovery depend on local conditions such as climate, soil type and land-use history. For 300 plots in 21 sites across the Neotropics, we used a chronosequence approach in which we sampled soils from two depths in old-growth forests, agricultural fields (i.e. crop fields and pastures), and secondary forests that differ in age (1–95 years) since abandonment. We measured six soil properties using a standardized sampling design and laboratory analyses. Soil resistance strongly depended on local conditions. Croplands and sites on high-activity clay (i.e. high fertility) show strong increases in bulk density and decreases in pH, carbon (C) and nitrogen (N) during deforestation and subsequent agricultural use. Resistance is lower in such sites probably because of a sharp decline in fine root biomass in croplands in the upper soil layers, and a decline in litter input from formerly productive old-growth forest (on high-activity clays). Soil recovery also strongly depended on local conditions. During forest succession, high-activity clays and croplands decreased most strongly in bulk density and increased in C and N, possibly because of strongly compacted soils with low C and N after cropland abandonment, and because of rapid vegetation recovery in high-activity clays leading to greater fine root growth and litter input. Furthermore, sites at low precipitation decreased in pH, whereas sites at high precipitation increased in N and decreased in C : N ratio. Extractable phosphorus (P) did not recover during succession, suggesting increased P limitation as forests age. These results indicate that no single solution exists for effective soil restoration and that local site conditions should determine the restoration strategies.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Deep Reinforcement Learning From Demonstrations to Assist Service Restoration in Islanded Microgrids

Microgrids can be operated in island mode during utility grid outages to support service restoration and improve system resilience. To schedule and dispatch distributed energy resources (DERs) in an islanded microgrid, conventional model-based methods rely on accurate distribution network models and lack generalization and adaptability. Data-driven methods are promising for DER coordination but face practical challenges such as potential hazards to microgrids during online training and insufficient online training opportunities due to low outage rates. This paper presents a novel two-stage learning framework that builds on the deep deterministic policy gradient from demonstrations to identify an optimal restoration strategy. At the pre-training stage, imitation learning is applied to equip the control agent with expert experiences to guarantee acceptable initial performance. At the online training stage, action clipping, reward shaping, and expert demonstrations are leveraged to ensure safe exploration while accelerating the training process. In conclusion, the proposed method is illustrated using the IEEE 123-node system and compared with a representative model-based method and the standard deep deterministic policy gradient method to prove solution accuracy and demonstrate increased computational efficiency.

Du, Yan↗
DOE OSTI2021

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↗
DOE OSTI2025

Validating Greater Sage-Grouse Individual-based Model (IBM) Tool (Final Report)

The project focused on validating the previously developed Greater Sage-Grouse Individual-based Model (GrSG IBM; LaGory et al. 2012, 2021). The objective was to transform this predictive, spatially and temporally explicit model into a portable resource to assist siting/resource managers in proactively assessing the cumulative impacts of wind energy development on the greater sage-grouse. Utilizing a bottom-up, individual-based approach, the GrSG IBM accounts for landscape context and species behavior, aiming to reduce uncertainty in estimating development impacts and support ecologically mindful land-based wind energy development. The validation effort covered approximately 6,540 km 2 near the Seven Mile Hill Wind Project in Wyoming. The GrSG IBM tool, built on the NetLogo platform (Tisue and Wilensky 2004), was executed over a 50-year period, with the analysis focusing on years following a 10-year initialization phase. Key results demonstrated the tool’s biological soundness across five key biological metrics: non-chick age class distribution (older than 10 weeks), adult sex ratio, life expectancy, population size, and overall population growth. For instance, the tool estimated that 58.6% of the non-chick population was reproductively immature, while the reference ranges from 51.4% to 57.8% (Patterson 1952, Rogers 1964). Experts confirmed the tool’s estimate was within a reasonable range for the species. The tool estimated average life expectancy of 1.43 years, while the reference ranges from 0.9 years to 1.1 years (Ammann 1957, Hamerstrom 1949). Experts also supported the model’s life-expectancy estimate as ecologically sound for the species in the study area. In terms of population change, the model estimated an annual shift between a 0.6% decline and a 1.0% increase over 50 years. While the reference suggests 2.9% annual decline in range-wide populations (Cortes et al. 2023), that includes many at-risk populations in South Dakota and Washington, for example. Our study area—in the northeastern part of Carbon County and western-edge of Albany County, Wyoming—is one of the remaining greater sage-grouse habitats supporting some of the most stable populations. Experts confirmed that the range of the annual population change spanning from a 0.6% decline to a 1.0% increase estimated by the tool was reasonable for our study area for this reason and confirmed that aligned with population estimates from existing studies on the greater sage-grouse and wind energy development in the study area (LeBeau et al. 2017a, Smith et al. 2024). Furthermore, the project showed that temporally explicit biological metrics generated by the GrSG IBM tool can complement the USGS’ Prioritizing Restoration of Sagebrush Ecosystems Tool (PReSET; Duchardt et al. 2021) by incorporating habitat restoration strategies into seasonal habitat suitability models to visualize population responses over time.

17 WIND ENERGY↗
DOE OSTI2022

Decentralized Distribution System Restoration with Grid-Forming/Following Inverter-Based Resources

The high penetration of distributed energy resources (DERs) in active distribution systems has posed challenges to the centralized distribution system restoration (DSR) strategies in current practice. On the other hand, the advancement in smart inverter technologies enables the bottom-up restoration capability. This paper is motivated to develop a 3-layered hierarchical framework for decentralized DSR, based on the grid-forming (GFM) and grid-following (GFL) grid-edge inverters. The first layer presents the tertiary control, which determines the load pickup schedule and generation dispatch of DERs, using the alternating direction method of the multipliers algorithm. The second layer consists of two control functions: GFM control, which regulates voltage and frequency, establishing a stable grid for GFL inverters to follow; and GFL control, which regulates the real and reactive power. In the third layer, the primary control is proposed to regulate the inverter voltage and current, which is developed based on the virtual oscillator control (VOC). Furthermore, the developed framework is tested in the modified IEEE 13-node test feeder. Two scenarios of grid-connected and islanded operating modes are designed, and simulation results demonstrate the effectiveness of decentralized DSR strategies for controlling grid-edge inverters to enhance the distribution system resilience.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Aqueous-based recycling of perovskite photovoltaics

Abstract Cumulative silicon photovoltaic (PV) waste highlights the importance of considering waste recycling before the commercialization of emerging PV technologies 1,2 . Perovskite PVs are a promising next-generation technology 3 , in which recycling their end-of-life waste can reduce the toxic waste and retain resources 4,5 . Here we report a low-cost, green-solvent-based holistic recycling strategy to restore all valuable components from perovskite PV waste. We develop an efficient aqueous-based perovskite recycling approach that can also rejuvenate degraded perovskites. We further extend the scope of recycling to charge-transport layers, substrates, cover glasses and metal electrodes. After repeated degradation–recycling processes, the recycled devices show similar efficiency and stability compared with the fresh devices. Our holistic recycling strategy reduces by 96.6% resource depletion and by 68.8% human toxicity (cancer effects) impacts associated with perovskite PVs compared with the landfill treatment. With recycling, the levelized cost of electricity also decreases for both utility-scale and residential systems. This study highlights unique opportunities of perovskite PVs for holistic recycling and paves the way for a sustainable perovskite solar economy.

Science & Technology - Other Topics↗
DOE OSTI2022

Co-optimization of repairs and dynamic network reconfiguration for improved distribution system resilience

In this work, a post-disaster distribution system repair and restoration (DSRR) strategy is proposed to improve distribution system resilience. The DSRR strategy is formulated as a two-stage optimization. The first stage is a comprehensive co-optimization of repair crew scheduling, dynamic network reconfiguration, and distributed energy resource (DER) dispatch based on the forecast load profile. The goal is to minimize the accumulative operating cost caused by the load reduction payment as well as DER operating cost. In particular, since the number of available repair crews is usually smaller than the number of faulted lines after a disaster event, the DSRR strategy determines the optimal scheduling for repairing faulted lines. The second stage is a re-dispatch of the DER power output and load shedding based on the real-time load demand of each bus. The proposed algorithm is validated by case studies of the IEEE 33-bus and 123-bus test systems. We consider those scenarios in which faults occur in multiple heavy-loaded feeders. The simulation results demonstrate that the DSRR strategy effectively coordinate the repair scheduling, network reconfiguration and load shedding to minimize the operating cost.

24 POWER TRANSMISSION AND DISTRIBUTION↗