SEARCH · Search NASA

Results for “three-phase unbalanced distribution network”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Retracted Article: Distributed energy management for networked microgrids in a three-phase unbalanced distribution network

Owing to increased penetration of three-phase and single-phase microgrids, distributed energy resources (DERs), and responsive loads, the maintenance of a three-phase balance by distribution networks is a significant challenge. Existing literature on distributed energy management for networked microgrids generally neglects the distribution network or employs a simplified phase balanced distribution network; thus, these evaluations are not applicable. Further, the underlying mutual coupling between the different phases of distribution feeders results in a more challenging situation. Here, to solve this issue, this study sought to propose distributed energy management based on a three-phase unbalanced distribution network. Various three-phase or single-phase microgrids, utility-owned DERs, and responsive loads were coordinated through iteratively adjusted price signals. Based on the price signals received, the microgrid controllers (MCs) and distribution management system (DMS) updated the schedules of the DERs and responsive loads under their jurisdiction separately. The price signals were then updated according to the generation-load mismatch at each node and distributed to the corresponding MCs and DMS for the next iteration. The iteration continued until a sufficiently small generation-load mismatch was achieved at all nodes, that is, a balanced generation and load at all nodes under the agreed price signals. Considering a three-phase unbalanced distribution network, the price signals were determined per phase per node. Overall, the proposed distributed energy management coordinates microgrids, utility-owned DERs, responsive loads with guaranteed network constraints, and preserves the privacy of microgrid customers. This distributed energy management method was further demonstrated through various case studies on a three-phase networked microgrid test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Neumann Series Based Voltage Sensitivity Analysis for Three Phase Distribution System

In this letter, a simplified voltage sensitivity analysis technique that can provide accurate estimates of voltage change across the network for a given change in bus power injections in a three-phase unbalanced distribution network is proposed. This technique is derived from the first-order approximation of the Neumann series, which allows maintaining the accuracy of the solution while the computational effort is reduced. Here, the proposed technique is tested on a 559-bus unbalanced distribution system with multiple distributed generation resources. The results show that the average error in the voltage estimates with the proposed method is not more than 0.3% with the execution time of similar order relative to the state-of-the-art sensitivity analysis methods.

42 ENGINEERING↗

DOE OSTI2024

Spatial-Temporal PV Hosting Capacity Estimation and Evaluation

Evaluating Photovoltaic Hosting Capacity (PVHC) is an essential step in the process of integrating solar energy into power grids, particularly when focusing on the distribution network (DN) as the primary integration target. PVHC needs to be investigated, especially in cases where the grids are unbalanced, and their operational conditions vary spatially and temporally. This motivation prompted us to propose a scalable model tailored to this application. In this paper, we applied linearization to the alternating current optimal power flow (AC-OPF) and solar inverters, transforming the original problem into a mixed-integer linear programming (MILP) problem. Additionally, we accounted for the battery energy storage system (BESS) as a time-coupling factor for calculating PVHC. We then compared the PVHC results between the IEEE-13 bus and SMART-DS San Francisco (SFO) cases and discussed the extent to which BESS can enhance the PVHC of a DN. Furthermore, we designed a web-based graphical visualization for the SFO case, enabling user interaction with raw data and simulation results on a map through a graphical user interface (GUI). In summary, our results and findings provide valuable insights for future three-phase unbalanced AC-OPF PVHC practices and their visualization.

AC-optimal power flow↗

DOE OSTI2026

Enabling Grid-Forming Control with Fault Ride-Through in Unbalanced Distribution Networks

Distribution networks are often unbalanced, causing oscillatory responses in inverter control designed for balanced conditions. Here, to address this problem, this paper proposes a novel time-domain transformation appropriate for inverter control and enables the decomposition of three-phase unbalanced signals into constant positive and negative components. Relations useful for calculating unbalanced active and reactive power are derived from first principle, providing insight into vector products of unbalanced three-phase signals. Furthermore, a grid-forming control effective under unbalanced conditions is developed, which delivers superior performance while meeting UNIFI1 specifications for grid-forming control under unbalanced conditions. specifications applicable to category 4 inverter-based resource, like setting and regulating frequency/voltage, providing voltage support, sharing active power, injecting negative sequence current, and riding through faults. A current limiter is proposed for safe fault ride-through and integrates with the grid-forming control featuring frequency/voltage droop controllers and current and voltage control loops. The transformation of interconnected inverters is formulated and stability of the proposed control analyzed to support robust parameter selections. The effectiveness of the proposed transformation and grid-forming control is demonstrated through analytical results and real-time simulation of a IEEE 123 distribution network on the Real-Time Digital Simulator. Comparison with existing methods shows that the proposed strategy satisfies the UNIFI specifications with a much better performance.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Iteration-based Linearized Distribution-level Locational Marginal Price for Three-phase Unbalanced Distribution Systems

Distributed energy resources (DERs) are rocking the utilities’ business landscape. It calls for competitive market environments that incentivize DERs to form maximum operating efficiency. Among proposed pricing schemes, distribution-level locational marginal price (DLMP) is effective in signaling the marginal generation cost differences driven by energy losses and network constraints. It can be derived from a distribution-level optimal power flow (OPF) framework, as it essentially presents the sensitivity of optimized generation cost towards incremental loads. However, due to the high resistance-to-inductance ratio and unbalanced characteristics of distribution networks, computational affordable DLMPs are highly challenged. This article provides a linear-approximated DLMP that can be solved efficiently and generalized to account for reactive power flow, three-phase unbalanced loads and meshed network structure. The successive linear programming technique is introduced to enhance the model accuracy. Case studies on an IEEE 123-Bus system validate its accuracy against a nonlinear benchmark and capability in offering proper incentives.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Further, negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Detecting False Data Injection Attacks in Smart Grids: A Semi-Supervised Deep Learning Approach

The dependence on advanced information and communication technology increases the vulnerability in smart grids under cyber-attacks. Recent research on unobservable false data injection attacks (FDIAs) reveals the high risk of secure system operation, since these attacks can bypass current bad data detection mechanisms. To mitigate this risk, this paper proposes a data-driven learning-based algorithm for detecting unobservable FDIAs in distribution systems. We use autoencoders for efficient dimension reduction and feature extraction of measurement datasets. Further, we integrate the autoencoders into an advanced generative adversarial network (GAN) framework, which successfully detects anomalies under FDIAs by capturing the unconformity between abnormal and secure measurements. Also, considering that the datasets collected from practical power systems are partially labeled due to expensive labeling costs and missing labels, the proposed method only requires a few labeled measurement data in addition to unlabeled data for training. Numerical simulations in three-phase unbalanced IEEE 13-bus and 123-bus distribution systems validate the detection accuracy and efficiency of this method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Detection of Stealthy False Data Injection Attacks in Unobservable Distribution Networks

In this paper, a composite scheme is proposed for detecting stealthy data manipulation attacks on distribution system which is unobservable with standard least squares based state estimators. This technique has three stages where the process of data imputation, voltage phasor estimation and the bad data detection are carried out in a systematic manner. The proposed approach is then integrated with moving target defense strategies which perturbs the network parameters to reveal stealthy false data injection attacks. The proposed approach is tested is validated on a three-phase, unbalanced 37-node distribution system and its results are presented. It is shown that the proposed approach has the ability to accurately detect the presence of FDI attacks using limited measurements (i.e., the test system is unobservable).

Rajasekaran, James K.↗

DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗

DOE OSTI2021

Integrating Transactive Energy into Reliability Evaluation for a Self-healing Distribution System with Microgrid

Non-utility owned distributed energy resources (DERs) are mostly untapped currently, but they can provide many grid services such as voltage regulation and service restoration, if properly controlled, and can improve the distribution systems reliability when coordinated with utility-owned assets such as self-healing control and microgrids. This paper integrates transactive energy control into the distribution system reliability evaluation to quantitatively assess the impact of non-utility owned DERs on reliability improvement. Here, a transactive reactive power control strategy is designed to incentivize the DERs to provide reactive power support for improving voltage profiles thus enabling additional customer load restoration during an outage. Also, an operational sequence to coordinate the non-utility owned DERs with the utility owned self-healing control and utility owned microgrids is designed and integrated into the service restoration process with the operational constraints guaranteed by checking the three-phase unbalanced power flow for post-fault network reconfiguration. The reliability indices are then calculated through a Monte Carlo simulation. The transactive reactive power control strategy is tested on a four-feeder distribution system operated by Duke Energy in the U.S. Results demonstrate that the non-utility owned DERs with the transactive control improve the reliability of both the system and critical loads by more than 30%.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Physics-Informed Graph Neural Networks for Collaborative Dynamic Reconfiguration and Voltage Regulation in Unbalanced Distribution Systems

Network reconfiguration has long been employed as a strategic approach to minimize power distribution system losses and effectively regulate voltage levels. Tap-changing voltage regulators are also critical for controlling bus voltages, especially in accommodating the increasing integration of distributed energy resources (DERs) with intermittent outputs. This paper introduces novel methodologies to address the challenges of dynamic reconfiguration and optimal tap setting in unbalanced three-phase distribution systems. We propose an approximated mixed-integer quadratically constrained program (MIQCP) to model dynamic reconfiguration, along with a pioneering formulation for voltage regulator (VR) tap-setting based on Special Ordered Set type 1 (SOS1). To mitigate computational complexity, we propose a physics-informed spatial-temporal graph convolutional network (STGCN) with an integrated link classifier. The proposed approach enables efficient solution generation by fixing specific variables in the MIQCP instance and solving the simplified sub-MIP using an MIP solver. Numerical studies demonstrate the superior prediction accuracy of our STGCN model compared to baseline neural network models, resulting in reduced DER curtailment and voltage deviation with shorter computation time.

dynamic reconfiguration↗

DOE OSTI2024

Ensuring Solution Uniqueness in Three-Phase Power System State Estimation

This paper is concerned with the issue of potential non-unique solutions in three-phase state estimation. Theory of observability analysis for positive sequence power system state estimation is based on certain assumptions that avoid possibility of multiple solutions. Also, it is shown that observability of a positive sequence network remains independent of the network parameters or the operating state. When extending single-phase observability analysis directly to the three-phase case, this paper considers the possibility of converging to multiple solutions, i.e. solution non-uniqueness, even for cases where state estimator successfully converges. The study illustrates via numerical examples the likelihood of converging to entirely different solutions for certain network parameters. It also examines how the operating state, particularly under unbalanced loading, leads to solution non-uniqueness. The paper then describes an alternative approach to ensure a unique solution in three-phase state estimation. This method aims to accurately and uniquely estimate the state of any unbalanced three-phase system, irrespective of load imbalance, network configuration, existence of synchronous generators or transformers.

Power System State Estimation, Three-Phase, Distri↗

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

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 OSTI2026

Safe Deep Reinforcement Learning for Active Distribution System Model Predictive Control with EVs and DERs

The temporal and spatial mismatch between PV generation and electric vehicle (EV) charging and discharging may cause voltage violations in active distribution networks. Despite the widespread use of deep reinforcement learning (DRL) in power system optimization and control, it lacks guarantees on constraint satisfaction during both training and deployment. This paper proposes a Lagrangian-based safe DRL approach for model predictive control (MPC) of active distribution systems with large-scale integration of PVs, EVs, and energy storage systems (ESSs). A Transformer-LSTM time-series model is proposed to forecast EV charging demand, which is then formulated as a constraint to ensure charging requirements are met. Using this prediction, a Lagrangian-based safe soft actor-critic (SAC) framework is developed for real-time control in a three-phase unbalanced distribution system, enforcing voltage safety constraints while optimizing the cumulative net reward. By integrating the forecasting model with multi-period constraints, the proposed framework jointly coordinates PV systems, EV charging and discharging, and ESS scheduling within the MPC horizon. Numerical experiments on a modified IEEE 123-bus system with real-world data show that, under a high PV penetration scenario, the proposed method increases the net reward by 30.74% and reduces average voltage violations from 0.0011 p.u. to 0.0002 p.u. compared with standard SAC. Compared with the optimal power flow (OPF) approach, it achieves similar voltage security while yielding lower line losses. It also maintains real-time control capability, reducing operation latency to 53.21 ms per 15-minute control interval. The proposed method remains effective under varying PV/EV penetrations and load conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Resilient Inverter-Driven Black Start with Collective Parallel Grid-Forming Operation

As modern power systems are experiencing exceptional changes with increasing penetrations of inverter-based resources (IBRs), system restoration using IBRs has received attention. Using local grid-forming (GFM) assets near consumers, engineered to establish grid voltages in the absence of a stiff grid, i.e., bottom-up restoration, a distribution system could obtain high system resilience by not relying on the bulk power system restoration, which requires significant human intervention and procedure. This paper studies the technical feasibility of the novel approach with detailed electromagnetic transient (EMT) simulations. To thoroughly evaluate the potential of GFM inverters and the technical challenges in IBR-driven black start, a detailed three-phase inverter model is developed, including negative-sequence control for voltage balance and a phase-by- phase current limiter to sustain momentary overloading during the black start. To examine dynamic aspects of the black-start process, the EMT simulation also models transformer and motor dynamics to emulate their inrush and startup behaviors as well as network dynamics. In addition, active involvement of grid- following distributed energy resources is also studied to facilitate the black-start process. By allowing multiple GFM inverters to collectively black start without leader-follower coordination, we demonstrate that a system can achieve high resilience even with a fraction of assets lost. Two test cases of inverter-driven black start, using two and one GFM inverters, respectively, for a heavily unbalanced 2-MVA distribution feeder are demonstrated. Takeaways for further study and field deployment are provided.

grid-forming inverter↗

DOE OSTI2022

Resilient Inverter-Driven Black Start with Collective Parallel Grid-Forming Operation: Preprint

As the modern power systems are experiencing exceptional changes with increasing penetration of inverter-based resources (IBRs), system restoration using IBRs has received attention. Using local grid-forming (GFM) assets near consumers, engineered to establish grid voltages in the absence of a stiff grid, i.e., bottom-up restoration, a distribution system would obtain high system resilience, by not relying on the bulk power system restoration requiring significant human intervention and procedure to restore. This paper studies the technical feasibility of the novel approach with detailed electromagnetic transient (EMT) simulations. To thoroughly evaluate the potential of GFM inverters and technical challenges in IBR-driven black start, a detailed three-phase inverter model is developed, including negative-sequence control for voltage balance and a phase-by-phase current limiter to sustain momentary overloading during the black start. To examine dynamic aspects of the black start process, the EMT simulation also models transformer and motor dynamics to emulate their inrush and start-up behaviors as well as network dynamics. In addition, active involvement of grid-following distributed energy resources (DER) is also studied to facilitate the black start process. It is shown that, by allowing multiple GFM inverters to collectively black start without master-slave coordination, a system can achieve high resilience even with a fraction of assets lost. Two test cases of inverter-driven black start using two and one GFM inverters, respectively, for a heavily unbalanced 2-MVA distribution feeder are demonstrated. Takeaways for further study and field deployment are provided.

grid-forming inverter↗