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DOE OSTI2026

A Systematic Review on Coordinated Restoration Strategies for Power Distribution Grids

Power distribution grids are increasingly exposed to High-Impact Low-Probability (HILP) events, which cause widespread disruptions with severe societal and economic impacts. The growing complexity of modern grids, driven by the integration of distributed energy resources and smart grid technologies, has introduced new challenges to effective service restoration. While significant research has explored individual restoration strategies, such as network reconfiguration and microgrid formation, limited attention has been given to methods in which they can be effectively coordinated. Furthermore, the absence of systematic review papers addressing this issue hampers the development of cohesive restoration frameworks capable of addressing the operational complexities of modern grids. This paper presents a systematic review synthesizing existing knowledge on power grid restoration, identifying key limitations, and highlighting opportunities for coordinated strategies. By addressing research gaps and emphasizing the integration of diverse approaches, this study provides critical insights for advancing grid resiliency and recovery, offering a foundation for future research and practical applications in the face of HILP events.

Systematic review↗

DOE OSTI2021

Stability Quantification for Consensus-Based Power Flow Control between Transmission and Distribution Power Systems

With increasing integration of distributed energy resources (DERs), distribution systems (DS) with DERs are expected to provide proactive grid services. The result is that power references, or known as dispatch signals, required for DS can become faster changing than in legacy power system. Consensus-based integral controls have been proposed for the purpose of coordinating power generations of DERs in DS to match the power references. These existing controls assume the integral control signal to be sufficiently slow or constant, and ignore the potential dynamics of the integral controller when tracking more varying power references. Therefore, in this paper we present an improvement for such controls by deriving the stability condition utilizing generalized Nyquist criterion. The stability condition is quantified by a set of integral gains that guarantee stability in closed-loop system without assuming a constant integral signal. A rule-of-thumb criterion is also derived to instruct the design of the consensus topology that can provide faster convergence rate for the closed-loop system. Here, the stability and convergence improvements developed in this paper are demonstrated and verified through numerical examples.

42 ENGINEERING↗

DOE OSTI2023

Assessing the Optimality of LinDist3Flow for Optimal Tap Selection of Step Voltage Regulators in Unbalanced Distribution Networks

The adoption of distributed energy resources such as photovoltaics (PVs) has increased dramatically during the previous decade. The increased penetration of PVs into distribution networks (DNs) can cause voltage fluctuations that have to be mitigated. One of the key utility assets employed to this end are step-voltage regulators (SVRs). It is desirable to include tap selection of SVRs in optimal power flow (OPF) routines, a task that turns out to be challenging because the resultant OPF problem is nonconvex with added complexities stemming from accurate SVR modeling. While several convex relaxations based on semi-definite programming (SDP) have been presented in the literature for optimal tap selection, SDP based schemes do not scale well and are challenging to implement in large-scale planning or operational frameworks. This paper deals with the optimal tap selection (OPTS) problem for wye-connected SVRs using linear approximations of power flow equations. Specifically, the LinDist3Flow model is adopted and the effective SVR ratio is assumed to be continuous- enabling the formulation of a problem called LinDist3Flow-OPTS, which amounts to a linear program. The scalability and optimality gap of LinDist3Flow-OPTS are evaluated with respect to existing SDP-based and nonlinear programming techniques for optimal tap selection in three standard feeders, namely, the IEEE 13-bus, 123-bus, and 8500-node DNs. For all DNs considered, LinDist3Flow-OPTS achieves an optimality gap of approximately 1% or less while significantly lowering the computational burden.

linear approximations↗

DOE OSTI2025

Quantitative Trade-Off in Distributed Secondary Control for Autonomous AC Microgrids

In this paper, we propose to quantify the trade-off between voltage regulation and reactive power sharing in autonomous AC microgrids with distributed secondary control. It is known that voltage regulation and reactive power sharing in droop-controlled autonomous AC microgrids are two conflicting control objectives that present a natural trade-off between voltage regulation towards the voltage magnitude reference and reactive power sharing accuracy. This trade-off is commonly shown qualitatively without sufficient quantification. In this work, to quantify the trade-off between the two objectives, we focus on distributed secondary control and utilize regression and polynomial surface fitting to identify the requisite parameter area to satisfy the predefined error bands for voltage magnitude regulation and reactive power sharing. Extensive case studies are presented to validate the proposed method.

autonomous AC microgrids↗

DOE OSTI2023

Study of Communication Boundaries of Primal-Dual Based Distributed Energy Resource Management Systems (DERMS)

As the coordination of distributed energy re-sources becomes more necessary to provide grid services through a distributed energy resource management system (DERMS), studying the communication requirements for suc-cessful real-world, low-cost implementation becomes increasingly important. Specifically, this paper studies the necessary communication time resolutions between the different system components for a primal-dual-based DERMS, a highly de-veloped DERMS framework. We design a metric to evaluate the functionality of a DERMS with respect to providing grid services. Using numerical simulations based on a real-world feeder in Colorado, we show that the upper bound on the time resolutions is on the order of minutes instead of the previously assumed order of seconds.

communication time resolution↗

DOE OSTI2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗

DOE OSTI2022

Unleash Values From Grid-Edge Flexibility: An Overview, Experience, and Vision for Leveraging Grid-Edge Distributed Energy Resources to Improve Grid Operations

The power system landscape is presently undergoing a dramatic change with the rapid integration of numerous distributed energy resources (DERs) at the grid edge. Broadly, we consider grid-edge DERs as any electricity source, storage, and demand response program connected to the medium-to-low-voltage distribution system.

distributed energy resource↗

DOE OSTI2021

Modeling the Strategic Behavior of an Active Distribution Network in the ISO Markets

With increasing integration of distributed energy resources (DERs), active distribution networks (ADNs) can actively participate in the electricity markets by dispatching their DERs, which can change the existing electricity market paradigm. It is essential to investigate the strategic behaviors of ADNs and their DER dispatch when they participate in the wholesale market as price-makers. This paper proposes a bi-level optimization model to study the strategic behavior of an ADN in both energy and reserve markets. The optimal scheduling of DERs in the ADN is modeled as the upper level problem and the joint energy and reserve market-clearing of the ISO is modeled as the lower-level problem. The two-level optimization models exchange bidding information and energy/reserve prices with each other. The proposed bi-Ievel optimization problem is converted to a mathematical programming with equilibrium constraints (MPEC) by using Karush-Kuhn Tucker (KKT) conditions and strong duality theory. Further, the MPEC problem is reformulated as a computationally-solvable mixed integer second order cone programming (MISOCP) model. The simulation results on an illustrative case demonstrate the impact of the strategic bidding of the ADN on the day-ahead energy and reserve market prices.

active distribution network↗

DOE OSTI2021

Decentralized Voltage Control of Large-Scale Distribution System with PVs Based on MADRL

This paper proposes a model-free decentralized control framework for the voltage regulation of large-scale distribution systems through the coordinated control of PV inverters. This is achieved by developing a novel interaction mechanism between the surrogate model and the centralized training and decentralized execution multiagent deep reinforcement learning framework. Specifically, the sparse Gaussian processes regression method is first utilized to develop the surrogate model of the original distribution system for reward calculation during the training stage, where each agent represents a sub-region in the centralized fashion for coordination strategy learning. After that, the learned control rules are used to inform controllers within each sub-region for real-time decisions with only local measurements. Comparative tests among various methods on the EPRI Ckt5 test system demonstrate the effectiveness of the proposed method.

distribution system↗

DOE OSTI2021

EV Hosting Capacity Analysis on Distribution Grids

The increasing trend in electric vehicle (EV) adoption can cause challenges to traditional electric grid operations if utilities are not equipped with tools and methods to effectively manage these fleets. Growing EV charging loads will alter the magnitude and duration of conventional peaks in demand profiles and even significantly shift them, potentially causing operational violations in the distribution grid. This paper presents the development and results of an EV hosting capacity tool to quantify the impacts of injecting large numbers of EV charging loads and to determine the available capacity of existing distribution feeders to continue providing reliable and affordable grid operations. Tools like the hosting capacity analysis would enable utilities to better prepare for grid operations in the near future while exploring the impact and effectiveness of strategies to manage these loads, such as peak pricing and smart charging. This paper evaluates the hosting capacity of some real-world feeders to accommodate EV charging loads, including extreme fast-charging options.

distribution grid↗

DOE OSTI2022

Multi-Agent Deep Reinforcement Learning for Realistic Distribution System Voltage Control Using PV Inverters

Over the last few decades, the deployment of distributed solar photovoltaic (PV) systems has increased consistently. High PV penetration could cause adverse effects on the grid, such as voltage violations. This paper proposes a new distributed soft actor-critic based multi-agent deep reinforcement learning (SAC-MADRL) control solution to minimize the PV real power curtailment while keeping the grid voltage in an acceptable range. New reward functions have been designed to coordinate different agents during the learning process, yielding improved convergence. Comparison results with other control methods on a real feeder in western Colorado U.S. with 80% penetration of PVs demonstrate that the proposed method has better capability of effectively regulating voltage while minimizing the PV real power curtailment.

distribution system↗

DOE OSTI2023

Two-Stage Deep Reinforcement Learning for Distribution System Voltage Regulation and Peak Load Management

The growing integration of distributed solar photovoltaic (PV) in distribution systems could result in adverse effects during grid operation. This paper develops a two-agent soft actor critic-based deep reinforcement learning (SAC-DRL) solution to simultaneously control PV inverters and battery energy storage systems for voltage regulation and peak demand reduction. The novel two-stage framework, featured with two different control agents, is applied for daytime and nighttime operations to enhance control performance. Comparison results with other control methods on a real feeder in Western Colorado demonstrate that the proposed method can provide advanced voltage regulation with modest active power curtailment and reduce peak load demand from feeder's head.

deep reinforcement learning↗

DOE OSTI2021

Enhancement of Distribution System State Estimation Using Pruned Physics-Aware Neural Networks

Realizing complete observability in the three-phase distribution system remains a challenge that hinders the implementation of classic state estimation algorithms. In this paper, a new method, called the pruned physics-aware neural network (P2N2), is developed to improve the voltage estimation accuracy in the distribution system. The method relies on the physical grid topology, which is used to design the connections between different hidden layers of a neural network model. To verify the proposed method, a numerical simulation based on one- year smart meter data of load consumptions for three-phase power flow is developed to generate the measurement and voltage state data. The IEEE 123-node system is selected as the test network to benchmark the proposed algorithm against the classic weighted least squares (WLS). Numerical results show that P2N2 outperforms WLS in terms of data redundancy and estimation accuracy.

distribution system state estimation↗

DOE OSTI2020

Quantifying the Relationship Between Higher Photovoltaic Module Efficiency and the Adoption of Distributed Solar

The purpose of this study is understanding the relationship between module efficiency, system costs, and the economic and adoption potential of distributed rooftop solar. We use the dGen model to project the economic potential and adoption of high-efficiency photovoltaic (PV) modules across a range of efficiencies and cost scenarios in the continental United States. Our results reveal that high-efficiency modules can modestly increase the projected adoption of distributed solar, but system capital costs may play a larger role in changing the amount of projected adoption.

14 SOLAR ENERGY↗

DOE OSTI2020

Distributed Cooperative Control of Hybrid AC/DC Microgrid

This paper presents a distributed cooperative control-based power management algorithm for a hybrid AC/DC microgrid. The proposed algorithm for a hybrid microgrid system controls the power flow through the interface converter between the AC and DC microgrids. This algorithm allows power sharing between the distributed generators in the microgrid according to their power ratings. Moreover, it enables the fixed scheduled power delivery through the interface converters in both directions at different operating conditions while maintaining voltage regulation and improving the frequency profile. The effectiveness of the controller is confirmed by simulation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Recommended Functionalities for Improving Cybersecurity of Distributed Energy Resources

The current electric grid is transitioning through increasing penetration of distributed energy resources (DERs), which include intermittent renewable generation resources on the distribution side. Both the monitoring and control of DERs require extensive data-exchange and communication networks. These networks lead to cyber vulnerabilities and risks of new kinds of cyberattacks that may be extremely destructive for power system operations. Although current standards, such as IEEE Std. 1547-2018, do not discuss cybersecurity measures for DERs, cybersecurity controls should be developed for securing DER systems at the device level, communications level, and applications level. This paper discusses the current industry's best practices related to DER cybersecurity and proposes recommended functionalities for improving the cybersecurity posture of DERs, specifically at the device/distribution level. These practical recommendations have been discussed and verified with the industry through a DER cybersecurity working group.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Feedback Power Cost Optimization in Power Distribution Networks with Prosumers

Here, we propose a feedback control approach for solving optimal power flow (OPF) problems in power distribution networks (DNs) based on a projected gradient scheme, where the cost is given by the sum of functions of local power injections. This approach does not require detailed knowledge of the grid model and enables real-time tracking of the optimal generation configuration. Moreover, the communication burden is minimal: only a broadcast from a central entity, called the Network Supervisor (NS), to the agents in the network is needed. Hence, agents do not have to share local information that can be sensitive, e.g., their power injections or the value of the local costs. Our approach is then used to solve a particular OPF problem targeting DNs with high penetration of distributed energy resources (DERs) in which the energy cost is given by the remuneration that the DERs owners receive for the service they provide.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

An Online Joint Optimization–Estimation Architecture for Distribution Networks

Here in this article, we propose an optimal joint optimization-estimation architecture for distribution networks, which jointly solves the optimal power flow (OPF) problem and static state estimation (SE) problem through an online gradient-based feedback algorithm. The main objective is to enable a fast and timely interaction between the OPF decisions and state estimators with limited sensor measurements. First, convergence and optimality of the proposed algorithm are analytically established. Then, the proposed gradient-based algorithm is modified by introducing statistical information of the inherent estimation and linearization errors for an improved and robust performance of the online OPF decisions. Overall, the proposed method eliminates the traditional separation of operation and monitoring, where optimization and estimation usually operate at distinct layers and different time scales. Hence, it enables a computationally affordable, efficient, and robust online operational framework for distribution networks under time-varying settings.

24 POWER TRANSMISSION AND DISTRIBUTION↗