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DOE OSTI2023

Modeling and Rapid Prototyping of Integrated Transmission-Distribution OPF Formulations with PowerModelsITD.jl

Conventional electric power systems are composed of different unidirectional power flow stages of generation, transmission, and distribution, managed independently by transmission system and distribution system operators. However, as distribution systems increase in complexity due to the integration of distributed energy resources, coordination between transmission and distribution networks will be imperative for the optimal operation of the power grid. However, coupling models and formulations between transmission and distribution is non-trivial, in particular due to the common practice of modeling transmission systems as single-phase, and distribution systems as multi-conductor phase-unbalanced. To enable the rapid prototyping of power flow formulations, in particular in the modeling of the boundary conditions between these two seemingly incompatible data models, we introduce PowerModelsITD.jl, a free, open-source toolkit written in Julia for integrated transmission-distribution (ITD) optimization that leverages mature optimization libraries from the InfrastructureModels.jl-ecosystem. The primary objective of the proposed framework is to provide baseline implementations of steady-state ITD optimization problems, while providing a common platform for the evaluation of emerging formulations and optimization problems. In this work, we introduce the nonlinear formulations currently supported in PowerModelsITD.jl, which include AC-polar, AC-rectangular, current-voltage, and a linear network transportation model. Results are validated using combinations of IEEE transmission and distribution networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Generalized Analytical Estimation of Sensitivity Matrices in Unbalanced Distribution Networks

Fast and accurate estimation of sensitivity matrices is significant for the enhancement of distribution system modeling and automation. Analytical estimations have mainly focused on voltage magnitude sensitivity to active/reactive power injections for unbalanced networks with Wye-connected loads and neglecting DERs' smart inverter functionality. Hence, this paper enhances the scope of analytical estimation of sensitivity matrices for unbalanced networks with 1- Φ, 2- Φ, and 3- Φ Delta/Wye-connected loads, DERs with smart inverter functionality, and substation/line step-voltage regulators (SVR). A composite bus model comprising of DER, Delta- and Wye-connected load is proposed to represent a generic distribution bus, which can be simplified to load, PV, or voltage-controlled bus as required. Furthermore, the proposed matrix-based analytical method consolidates voltage magnitude and angle sensitivity to active/reactive power injection and tap-position of all SVRs into a single algorithm. Extensive case studies on IEEE and EPRI networks show the accuracy and wide scope of the proposed algorithm compared to the existing benchmark method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Black Start of Unbalanced Microgrids Harmonizing Single- and Three-Phase Grid-Forming Inverters

As power systems are transforming with increasing penetrations of inverter-based resources (IBRs), system restoration using IBRs has drawn attention. Using distributed grid-forming (GFM) assets located near critical loads, either three-phase or single-phase, to establish microgrid voltages in the absence of a bulk grid, a distribution system could obtain high system survivability. For swift and secure recovery of a critical load in a single-phase lateral, local single-phase GFM inverters can form a microgrid, and then it can be combined with a neighbouring grid with the inverters remaining in GFM mode for voltage and frequency regulation until the bulk grid comes online. It leads to dynamic interoperation of single-phase GFM inverters with three-phase ones in the black start process. This paper studies the novel approach with electromagnetic transient (EMT) simulations. To evaluate the potential and the technical challenges of the heterogeneous IBR-driven black start, three-phase and single-phase GFM inverter models are developed, including negative-sequence control for voltage balance and a phase-by-phase current limiter (three-phase) and current magnitude limiter (single-phase). To examine dynamic aspects of the black-start process, the EMT simulation also models transformer and motor dynamics emulating their inrush and startup behavior as well as network dynamics. Involvement of grid-following assets to facilitate the black-start process is also modeled. By allowing multiple GFM inverters to collectively black start without leader-follower coordination, regardless of phases, a system can achieve extreme resilience. An inverter-driven black start of a heavily unbalanced 2-MVA distribution feeder using 1 three-phase and 3 single-phase GFM inverters is demonstrated. The simulation shows the heterogeneous system can maintain stability with the single-phase GFM dynamics coupled with the three-phase one.

grid-forming inverter↗

DOE OSTI2023

Black Start of Unbalanced Microgrids Harmonizing Single- and Three-Phase Grid-Forming Inverters: Preprint

grid-forming inverter↗

DOE OSTI2024

Equivalent-Circuit Models for Grid-Forming Inverters under Unbalanced Steady-State Operating Conditions: Preprint

Positive- and negative-sequence equivalent-circuit models are put forth to capture the operation of grid-forming (GFM) inverters in unbalanced steady-state operating conditions acknowledging the impact of current limiting. The particular control architecture examined adopts droop control (for primary control), nested inner-current and outer-voltage control (in the stationary reference frame), and it is adaptable to two different types of current limiting (current-reference saturation and virtual-impedance limiting). We anticipate the proposed models to be of interest in modeling, analysis, and simulation of GFM inverters in unbalanced settings that may arise, e.g., in the face of faults. Validation of the equivalent-circuit models is pursued via comparison with full-order electromagnetic-transient (EMT) simulations for representative balanced and unbalanced faults.

equivalent-circuit models↗

DOE OSTI2023

Inverter Controls for Smooth Transition Operation and Voltage Balancing of Networked Microgrids

With increasing penetrations of distributed energy resources (DERs), researchers have extensively studied the formation and networking of microgrids to improve reliability during distribution system outages. However, these operations might require DERs in the microgrids to switch between grid-following (GFL) and grid-forming (GFM) modes of operation. A smooth transition between the operation modes should be ensured to have a stable system operation and to avoid nuisance tripping. Additionally, as we network microgrids, inverter control schemes with voltage-balancing controls are needed for unbalanced distribution networks. This paper presents the design of a GFM and GFL capable inverter control scheme for reliable operation in networked microgrids with mechanisms for 1) smooth transition between the GFL and GFM modes, and 2) negative sequence voltage control for voltage balancing. Using electromagnetic transient (EMT) simulations, the control scheme is first tested on a simple two-source power system using a digital real-time simulator. Next, a real-world distribution feeder with unbalanced loading and multiple DERs is used to demonstrate stable operation during the networking of microgrids with voltage balance support.

distributed energy resources↗

DOE OSTI2025

Combined Effects of Electric Vehicle Charging and Rooftop Solar Integration on Voltage Imbalance in Residential Distribution Networks

Residential electric vehicle (EV) chargers, as single phase loads, contribute to unbalanced voltage drops across phases, while rooftop solar systems, as single phase generators, can exacerbate voltage imbalance by causing unbalanced voltage increases. This paper investigates combined effects of residential EV charging and rooftop solar generation on voltage imbalance in residential distribution grids. The study examines these simultaneous impacts using the IEEE 8500-node test system, enhanced with a secondary network to realistically model the EV chargers and rooftop solar integration. To account for the variability and uncertainty in the EV charging loads and solar generation, a Monte Carlo approach is employed to capture and quantify the simultaneous impact of the EV charging and rooftop solar integration. In this approach, multiple influencing factors are considered, including state-of-charge (SOC), maximum charging power levels, and geographic distribution of chargers. The results provide practical insights for utilities and stakeholders, offering expectations for planning and operating strategies that effectively manage the increasing adoption of EVs and solar power while maintaining grid reliability.

Choi, Jongchan [ORNL] (ORCID:000000025952455X)↗

DOE OSTI2021

A Data-Driven Global Sensitivity Analysis Framework for Three-Phase Distribution System with PVs

Global sensitivity analysis (GSA) of distribution systems with respect to stochastic PV and load variations plays an important role in designing optimal voltage control schemes. This paper proposes a data-driven framework for GSA of distribution systems. In particular, two representative surrogate modeling-based approaches are developed, including the traditional Gaussian process-based and the analysis of variance (ANOVA) kernel ones. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol indices can be conveniently calculated through either the sampling-based method or the analytical method to assess the global sensitivity of voltage to variations of PV and load power injections. The sampling-based method approximates the Sobol indices using Monte Carlo simulations while the analytical method calculates them by resorting to the ANOVA expansion framework. Comparison results with other model-based GSA methods on the unbalanced three-phase IEEE 37-bus and 123-bus distribution systems show that the proposed framework can achieve much higher computational efficiency with negligible loss of accuracy. The results on a real 240-node distribution system using actual smart meter data further validate the feasibility and scalability of the proposed framework.

14 SOLAR ENERGY↗

DOE OSTI2025

Distribution System Resilience Assessment Considering PV Vulnerabilities for Hurricane Events

Distribution networks are increasingly vulnerable to damage and outages from extreme weather events. The integration of solar photovoltaics (PVs) further complicates resilience analysis due to its weather-dependent nature. However, limited research has examined the impacts of weather on PVs under severe events like hurricanes. This paper proposes a probabilistic framework to assess distribution system resilience considering PV vulnerabilities during hurricanes. The framework incorporates (i) a spatiotemporal fragility model to evaluate failure probabilities for distribution lines and PVs, and (ii) resilience indices at both system and component levels. The approach offers valuable insights into the resilience of modern distribution grids under extreme weather conditions. Numerical results on the unbalanced IEEE 123-bus test system validate the effectiveness of the framework.

Vahedi, Soroush [University of Connecticut, Storrs↗

DOE OSTI2021

Microwave–photonic low-coherence interferometry for dark zone free distributed optical fiber sensing

A microwave–photonic low-coherence interferometry (MPLCI) system is proposed for fully distributed optical fiber sensing. Assisted by an unbalanced Michelson interferometer, a low-coherence laser source is used to interrogate cascaded Fabry–Perot interferometers along with an optical fiber for a dark zone free (or spatially continuous) distributed measurement. Here, by combining the advantages of microwaves and photonics, the MPLCI system can synergistically achieve high sensitivity and high spatial resolution. Our tests have confirmed a strain resolution of 95 nε at the spatial resolution of 10 cm.

42 ENGINEERING↗

DOE OSTI2024

Specifying angular reference for robust three-phase state estimation

While the phase angle of any of the bus voltages can be chosen as the angular reference in the state estimation formulation of positive sequence networks, the same approach does not readily extend to three-phase network state estimation problem. It is commonly assumed that there is at least one bus where the bus voltages are perfectly balanced with phase angles displaced ±120° and these balanced three phase voltages are used as the three-phase reference in solving the three-phase state estimation problem. This assumption may be quite realistic in transmission networks, and for distribution networks with a strong transmission system connection. However, it might not be realistic to assume existence of a perfectly balanced reference bus in today’s distribution systems with ever increasing penetration of renewable sources or for isolated operation of microgrids. In this paper, a novel state estimation formulation will be presented which facilitates correct solution irrespective of the existence of buses with perfectly balanced voltages. The new formulation is general, and lends itself to bad data processing. It yields accurate results in any three-phase power system irrespective of its operating conditions (balanced or highly unbalanced), configuration (isolated microgrid, connected to transmission system, etc.) and whether or not it contains any synchronous generators. The performance of the method is validated using the IEEE 123 bus three-phase system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Joint Matrix Completion and Compressed Sensing for State Estimation in Low-observable Distribution System

Limited measurement availability at the distribution grid presents challenges for state estimation and situational awareness. This paper combines the advantages of two sparsity-based state estimation approaches (matrix completion and compressive sensing) that have been proposed recently to address the challenge of unobservability. The proposed approach exploits both the low rank structure and a suitable transform domain representation to leverage the correlation structure of the spatio-temporal data matrix while incorporating the powerflow constraints of the distribution grid. Simulations are carried out on three phase unbalanced IEEE 37 test system to verify the effectiveness of the proposed approach. The performance results reveal - (1) the superiority over traditional matrix completion and (2) very low state estimation errors for high compression ratios representing very low observability.

Dahale, Shweta↗

DOE OSTI2025

A Novel Protection Scheme for Unbalanced Faults in Inverter Dominated Networks: A Computationally Efficient Algorithm for Entry-Level Relays

Microgrids are now a common practice in distribution systems to increase resilience and reliability. However, microgrid protection remains a critical challenge, considering its requirement to operate in both grid connected and islanded, and the variability in fault characteristics under each mode of operation. This paper presents unbalanced power (S unb ) based fault detection algorithm, which considers local voltage and current unbalances to determine faults in the system. S unb is a computationally efficient fault detection algorithm that is suitable for implementation in the programmable logic of entry level protective relays. In addition, the difference in current and voltage unbalance (D n ) is used to determine the fault type. The proposed method demonstrates high sensitivity and selectivity for line-to-ground (LG), line-to-line (LL), and double line-to-ground (LLG) faults, representing the most common faults in distribution systems. It also allows relay coordination with upstream and downstream protection devices in both island and grid connected operation, while preserving grading margins. The same pickup and time multiplier settings of a particular relay for both modes of operation eliminates the need for adaptive settings, which rely on communication networks. Validation was performed with a hardware-in-the-loop (HIL) setup using Typhoon HIL real time simulator interfaced with three entry-level, SEL 751 relays. Results confirmed the algorithm’s ability to discriminate fault conditions, and determine the fault type under both operating modes, maintain fast detection times, and ensure proper protection coordination.

fault classification↗

DOE OSTI2020

BEEAM (Building Electrical Efficiency Analysis Model) [SWR-20-107]

Modern high-performance buildings exhibit an increasing number of building loads that use direct current (DC) electricity internally, rather than alternating current (AC), due to the advent of low-cost computing and advanced power electronics. Powering DC devices from the AC grid requires AC/DC power conversion, which introduces energy losses and reduces efficiency. As DC loads proliferate, the cumulative wasted energy associated with hundreds of millions of AC/DC converters has become one of the broadest energy savings opportunities in buildings. DC power distribution systems have been proposed as an elegant and transformative solution to the problem of DC devices. In a DC distribution system, the building's wires carry DC electricity, rather than AC; and a few centralized, highly efficient AC/DC converters replace the many smaller, less efficient converters that serve individual DC loads. Unfortunately, the trade-offs associated with DC distribution systems are not well understood. Reported energy savings associated with DC power distribution differ widely and have not been well validated. The Building Electrical Efficiency Analysis Model (BEEAM) is a Modelica library that simulates the efficiency of building electrical distribution systems using harmonic power flow. BEEAM can model a wide variety of building distribution topologies, including three-phase AC, single-phase AC, unipolar DC, bipolar DC, and hybrid networks under both balanced and unbalanced load conditions. BEEAM accurately models power electronic converter losses, provides granular estimates of losses throughout the distribution system, and properly models efficiency at part load conditions. Users can package BEEAM within a functional mockup unit (FMU), enabling co-simulation with other modeling platform, such as EnergyPlus. In summary, BEEAM provides a tool suite for fair and accurate comparison of the efficiency of building electrical distribution systems, including AC, DC, and hybrid systems.

Frank, Stephen↗

DOE OSTI2024

A Neural Network-Based Power Mismatch Elimination Strategy for Integrated Solar and ESS AC/DC Systems (MARS)

The multiport autonomous reconfigurable solar power plant (MARS) is a promising concept for the integration of photovoltaic (PV) and energy storage system (ESS) to the transmission ac grid and a high-voltage direct current (HVdc) link. The presence of PV and ESS in each arm of the MARS results in uneven distribution of active power among different submodules (SMs), thereby leading to unbalanced SM capacitor voltages and potentially compromising the system stability. Moreover, in the case of partial shadings, shaded PV SMs will suffer from decreased power injections causing power mismatch in the MARS system. To address this issue, a neural-network-based power mismatch elimination (NNPME) strategy is proposed in this article. The proposed NNPME strategy optimizes ESS usage and leverages both dc and ac circulating currents to facilitate power transfer among the SMs, arms, and phases of the MARS system. Simulation and control hardware-in-the-loop (cHIL) experiments demonstrate the effectiveness of the proposed NNPME strategy. Compared with the traditional approaches, the proposed NNPME strategy can significantly enhance system efficiency and ensure stable and continuous operation, even in the presence of uneven power distribution within the MARS system.

14 SOLAR ENERGY↗

DOE OSTI2025

Geographically Distributed Co-Simulation for the Interplay of Integrated Energy Systems and Power Grid

The increased penetration of renewable generation induces unbalanced demand-supply on a power grid, while integrated energy systems (IES) can provide high part-load efficiency and high flexibility to support grid resilience. To study the transients and improve dynamic operability, it’s important to investigate the interplay between IES and power grid concurrently using real-time co-simulation approaches. In this presentation, we showed the previous co-simulation test between NETL and INL and discussed how this co-simulation can be beneficial for both IES and power grid research. In addition, we gave an overview about the SuperLab2.0 project, which was a federated national platform to address future power grid challenges. (Virtual presentation to the MILLENNIUM CLEAN and SUSTAINABLE POWER workshop 2025).

Co-simulation↗

DOE OSTI2020

Robust and resilient coordination of feeders with uncertain distributed energy resources: from real-time control to long-term planning

To enable flexible demand and ensure reliable and economical operation of distribution systems, we present a novel hierarchical scheme that actively coordinates responsive behind-the-meter grid resources, including distributed energy resources (DERs), to reliably manage each unbalanced distribution feeder and exploits the available flexibility to economically optimize the entire network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.

14 SOLAR ENERGY↗

DOE OSTI2020

Hierarchical, Grid-Aware, and Economically Optimal Coordination of Distributed Energy Resources in Realistic Distribution Systems

Renewable portfolio standards are targeting high levels of variable solar photovoltaics (PV) in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliably manage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimizes the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.

distribution network↗