SEARCH · Engineering Papers

Results for “control algorithm”

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 649 records · Page 36

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Intelligent Process Visualization through Nuclear Operation Process Modeling, Reasoning, and Object Detection from Field Videos (Final Report)

This report is a deliverable for the “Final Report” task of DOE NEET Project 19-16790, "Context-Aware Safety Information Display for Nuclear Field Workers." This project's overall goal is to test the hypothesis that integrating computer vision and process reasoning methods will enable proactive visualization of the safe operation and maintenance processes of Nuclear Power Plants (NPP) for field workers. Augmented Reality (AR) glasses adopting such proactive safety information visualization techniques can significantly increase personnel safety and reduce the NPP’s operating costs. The current practice of monitoring NPPs requires workers to switch between digital models, data, and physical workspaces in identifying relevant but potentially occluded objects and in assessing the risks of operation and maintenance processes. On the other hand, frequently changed field conditions require field workers to report to supervisors for real-time guidance. Such guidance is essential to ensure that changing conditions will not invalidate or endanger the work order and other ongoing processes that may jeopardize NPP operations. Additionally, incorrect recognition of equipment objects can result in communication errors and safety problems. AR techniques can assist engineers in viewing the physical workspaces with objects labeled with detailed operation procedures and safety reminders during field operations. The project team developed an “Intelligent Context-Aware Safety Information Display” (ICAD) for supporting Nuclear Power Plant (NPP) field workers in achieving safe and efficient execution of a series of operational tasks in uncertain and changing workspaces of an NPP. Before designing the ICAD-AR prototype, the project team synthesized NPP operational knowledge models through literature review studies, surveys, interviews with domain experts, and knowledge modeling. The project team conducted an extensive study of the operational procedures of various NPPs, and digital technologies that can support the safe and efficient execution of those procedures in different NPP operational contexts. This literature review helped the project team conduct surveys and interviews with nuclear engineers and field workers to identify three categories of information. The NPP knowledge modeling efforts reveal that the three categories of information identified have different levels of importance in a typical procedure of carrying out a series of tasks to achieve a specific NPP operation goal (e.g., shutdown, mode changes). These three categories of information include 1) Workspace dynamics – the changing spatial arrangements of workspaces, tools, protection equipment, and supporting materials, 2) Workflow prognostics – the dynamic dependencies between different parts of an NPP that functionally support and influence each other in terms of safety and efficiency, and 3) Hazards – objects and spaces that contain hazardous materials or physical conditions that can pose risks to workers or mechanical systems. The project team has profiled the importance levels of these categories of information into a knowledge model. This knowledge model specifies what types of information are more critical for a given task in a given workspace so that computers can automatically identify critical objects and sensors in a scene for delivering context-ware safety information to field workers through AR devices. Significant research development of this project results in technical research outcomes and a prototyping system that illustrates the technical feasibility of establishing an ICAD-AR system supporting the proactive safety information display for nuclear field workers. This final report summarizes the project team’s technological achievements in the past three years. Overall, the project team completed the development and integration of five techniques into a prototype ICAD Augmented Reality (ICAD-AR) system and demonstrated the developed system’s real-time execution in a mechanical room. The project team completed the analysis of using this prototype in other types of workspaces based on 3D image data and digital design models collected from two additional workspaces (a water treatment plant and a flow loop training facility). The integrated techniques include 1) Natural Language Processing (NLP) algorithms supporting the generation and updates of nuclear fieldwork process models based on text analysis of work packages and operation manuals; 2) sensor log analysis for predicting control actions in given sensor reading contexts; 3) computer vision algorithms for automatic localization and navigation of workers; 4) object detection algorithms for identifying task-related objects and correlated sensors for safety checking; 5) AR technique as a platform for supporting the integration. The testing results of these five techniques have shown that 1) the sensor log analysis model can predict the next control action with an accuracy of 0.883; 2) the trained natural language processing model can extract more than 80% of the critical information from paper-based procedures (PBPs); 3) the navigation algorithm with the integration of Visual Inertial Odometry (VIO) and Non-Recursive Bayesian Filter methods make operator’s trajectory estimation resilient to drift error; 4) the computer vision algorithm can detect task-specific and safety-critical objects with an average accuracy of 95.3%. The project team used work procedures collected from a flow loop training facility and two datasets collected from two mechanical rooms simulating the workspaces of NPPs to demonstrate the technical capabilities of the developed ICAD-AR prototype. The demonstration validated the technical feasibility of establishing the ICAD-AR system for nuclear field workers and identified the challenges in 1) automatic text analysis of work packages; 2) use of limited samples of sensor logs for predicting the proper timings of control actions; 3) reliably tracking workers and their task progress in mechanical rooms with many similar objects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Nonlinear, real-time optimization for actuator management in tokamaks

Experiments in DIII-D have been carried out to test a novel actuator management approach in tokamaks. Here, the actuator management scheme is posed as a nonlinear-optimization problem in which the actuator commands are calculated in real time according to the changing control priorities, plasma state, and actuator availability. Such optimization problem is solved using the augmented Lagrangian method, combined with a gradient projection method and a conjugate-gradient iteration algorithm. The algorithmic approach followed in this work does not depend on the particular control objectives or actuators considered, which facilitates its integration with other independently-designed control components within a plasma-control system. In addition, the actuator-management algorithm is able to handle the optimization problem in a computationally efficient manner, making it suitable for real-time implementations. Initial DIII-D results in the steady-state high-q min scenario have demonstrated the capabilities of the actuator manager to perform both simultaneous multiple mission and repurposing sharing, which will be required in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Resilient Autonomous Wind Farms: Preprint

With the advent of an increasing number of control strategies that seek to optimize wind turbine performance on a farm-level, taking account of individual wind turbine information to achieve wind farm-level objectives has become an increasingly important goal. Methods for controlling wind turbines on an individual and farm level have seen significant development, and an abundance of new implementations for gathering and using data from turbines have created potential for novel control mechanisms which can further optimize the performance and delivery characteristics of a wind farm. A key element of making these wind farms more efficient is to develop reliable algorithms that use local sensor information that is already being collected, such as supervisory control and data acquisition (SCADA) data, local meteorological stations, and nearby radars/sodars/lidars. Making use of information from all wind turbines in a wind farm can enable such approaches as determining the atmospheric conditions across the farm, improving fault-finding, and enabling more efficient overall control of farm-wide optimizations through mechanisms such as wake-steering. However, these approaches typically involve a centralized communications and control center. In order to ensure the resilient operation of the farm, it is necessary to develop an approach which distributes the calculation and communication amongst multiple nodes throughout the farm. In this fashion, a redundant, robust, and secure network can be created, which can tolerate faults in calculation, communication, and even external attacks which seek to disrupt the operation of the wind farm. This paper introduces the use of the Raft Byzantine Fault Tolerance algorithm in the implementation of autonomous control of a wind farm. This implementation will allow for fault tolerance for malfunctioning nodes, sensors, transmitters, and connectors. This approach is equally extensible to account for malicious actors. It will be shown to achieve overall consensus, provided the number of faults/malicious nodes is less than 3$n$+1, where $n$ is the number of turbine cluster faults which may occur, and to be robust in the face of multiple arbitrary faults.

autonomous↗

DOE OSTI2021

Validation and Demonstration of Control System Functional Capabilities within the IES Plug-and-Play Simulation Environment

The concept of an integrated energy system (IES) is meant to combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The RAVEN-based HYBRID framework is used to find the optimal installed capacity and the optimal economical dispatch of each component of the IES. The new RAVEN plugin for grid and capacity optimization (HERON) only addresses the limits that affect the production variables and the corresponding rates of variation (explicit constraints). However, other variables are subject to constraints, and the associated limits should be accounted for (implicit constraints). In particular, for the power dispatch problem, the optimization algorithm takes into account the limits on the electrical power output and the corresponding hourly power variations but does not consider other constraints on process variables whose response affects the service life of the IES. This report describes a scheme that allows accounting for implicit constraints without increasing the size of the optimization problem. To obtain a more accurate approximation of the nonlinear dynamic behavior, a parametric version of the dynamic mode decomposition with control (DMDc) algorithm was developed to derive the state-space representation matrices of the IES components at different scheduling parameter. Thanks to this approach, a more accurate approximation of the system response can be obtained, the limits imposed by thermal mechanical implicit constraints can be translated into power dispatch limits, and the feedbacks to HERON power dispatcher can be provided. To assess the developed methodology, a power dispatching test case composed of three power generating and storage units (Balance of Plant, Secondary Energy Source, Thermal Energy Storage) was developed. The power output of each one of the three units was optimized to meet the imposed time-dependent load demand trajectory and to maximize the IES profitability by meeting both the explicit and implicit constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Drgona, Jan↗

DOE OSTI2020

Distributed Outage Detection in Power Distribution Networks

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

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

Development of an Encoding Method on an Co-simulation Platform for Mitigating the Impact of Unreliable Communication

This report presents a hardware-in-the-loop (HIL) based modeling approach for simulating impacts of unreliable communication on the performance of centralized volt-var control and for developing an encoding method to mitigate the impacts. First, an asynchronous real-time HIL simulation platform is introduced to enable multi-rate co-simulation of a distribution system with many inverter-based distributed energy resources (DERs). The distribution system is modeled by milliseconds phasor-based models and the DERs are modeled by micro-seconds power electronic models. Communication connections between a centralized volt-var controller (modeled externally to the HIL testbed) and smart inverters are built by implementing Modbus links and the Long Term Evolution network. On this co-simulation platform, an enhanced, augmented Lagrangian multiplier based encoded data recovery (EALM-EDR) algorithm for mitigating the impact of unreliable communication is developed and validated. Simulation results demonstrate the efficacy of using the HIL-based co-simulation platform as a power grid digital twin for developing algorithms that coordinate a large number of heterogeneous control systems through wired and wireless communication links.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Beyond PID Controllers: PPO with Neuralized PID Policy for Proton Beam Intensity Control in Mu2e

We introduce a novel Proximal Policy Optimization (PPO) algorithm aimed at addressing the challenge of maintaining a uniform proton beam intensity delivery in the Muon to Electron Conversion Experiment (Mu2e) at Fermi National Accelerator Laboratory (Fermilab). Our primary objective is to regulate the spill process to ensure a consistent intensity profile, with the ultimate goal of creating an automated controller capable of providing real-time feedback and calibration of the Spill Regulation System (SRS) parameters on a millisecond timescale. We treat the Mu2e accelerator system as a Markov Decision Process suitable for Reinforcement Learning (RL), utilizing PPO to reduce bias and enhance training stability. A key innovation in our approach is the integration of a neuralized Proportional-Integral-Derivative (PID) controller into the policy function, resulting in a significant improvement in the Spill Duty Factor (SDF) by 13.6%, surpassing the performance of the current PID controller baseline by an additional 1.6%. This paper presents the preliminary offline results based on a differentiable simulator of the Mu2e accelerator. It paves the groundwork for real-time implementations and applications, representing a crucial step towards automated proton beam intensity control for the Mu2e experiment.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Distributed Optimization in Distribution Systems: Use Cases, Limitations, and Research Needs

We report electric distribution grid operations typically rely on both centralized optimization and local non-optimal control techniques. As an alternative, distribution system operational practices can consider distributed optimization techniques that leverage communications among various neighboring agents to achieve optimal operation. With the rapidly increasing integration of distributed energy resources (DERs), distributed optimization algorithms are growing in importance due to their potential advantages in scalability, flexibility, privacy, and robustness relative to centralized optimization. Implementation of distributed optimization offers multiple challenges and also opportunities. This paper provides a comprehensive review of the recent advancements in distributed optimization for electric distribution systems and classifications using key attributes. Problem formulations and distributed optimization algorithms are provided for example use cases, including volt/var control, market clearing process, loss minimization, and conservation voltage reduction. Finally, this paper also presents future research needs for the applicability of distributed optimization algorithms in the distribution system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Development of Control System Functional Capabilities within the IES Plug-and-Play Simulation Environment

The concept of an Integrated Energy System (IES) is meant to combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The RAVEN-based HYBRID framework is used to find the optimal installed capacity and the optimal economical dispatch of each component of the IES. A new RAVEN (Risk Analysis Virtual ENvironment) plugin for grid and capacity optimization (HERON) has been developed for optimizing the production variables of the IES given the demand profile. Currently, only the limits that affect the production variables and their corresponding time rates of change are considered (explicit constraints). However, other variables are additionally subject to constraints, but the associated limits are not accounted for (implicit constraints). In particular, for the power dispatch problem, the optimization algorithm takes into account the limits on the electrical power output and the corresponding hourly power variations but does not consider other constraints on process variables whose response effects the service life of the IES. This report describes a scheme that allows accounting for implicit constraints without increasing the size of the optimization problem. The Reference Governor (RG) algorithm is traditionally used for enforcing state and control constraints by modifying the set-point trajectories supplied to the feedback regulators. In our application, the RG is coupled within an iterative loop with the HERON-power dispatcher to generate optimal trajectories that ensure the operational constraints are met. A data-driven procedure to derive a representation of the dynamics of the controlled system was developed. First, the variables that represented the state of the system are selected (PCA-based approach), and then state-space representation matrices are derived from the collected measurements (DMDc algorithm). A preliminary version of the developed workflow based on Linear Time Invariant matrices was assessed by adopting a two-unit test case. More sophisticated versions of this workflow foreseeing the on-line derivation of system matrices will be deployed in FY 2021. Finally, a “plug-and-play” library of controllers and state observers was developed in Dymola. Some aspects of the current configuration of the IES unit components, e.g., the encapsulation of the control schemes into dedicated blocks, are consistent with the “plug-and-play” philosophy. Other features, e.g., the system buses collecting the input and the output variables, are not. For this reason, once listed and described the limits of the current configuration, necessary modifications to the plant model interface are presented. As a test-case, the interfaces of the SES model in the RAVEN-based HYBRID framework were reworked accordingly, and two different control schemes were applied to the same plant model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Analysis of a Runtime Data Sharing Architecture over LTE for a Heterogeneous CAV Fleet

This paper describes a lightweight runtime architecture for telemetry, communication, and control of cars deployed with advanced driver assistance systems where a human is in the loop with the car, via an LTE connection. The system architecture supports both local control decisions based on car sensors and safety algorithms as well as high-level input from external systems that may provide insight into traffic state ahead of sensor data. Implementation of the architecture is done in ROS and depends on open-source software packages for runtime decoding of information from the vehicle’s controller area network (CAN) and integration of GPS data from accompanying sensors. The contribution of the paper is to describe the overall architecture, the data it can communicate to other systems, performance of the system at runtime, and challenges faced when deploying the architecture across a heterogeneous fleet. Preliminary results from analysis of test data will provide insights into whether the use of high-latency communication can be effective for societal-scale intelligent transportation systems when applied in future scenarios

Richardson, Alex↗

DOE OSTI2021

Deep reinforcement learning control of hydraulic fracturing

Hydraulic fracturing is a technique to extract oil and gas from shale formations, and obtaining a uniform proppant concentration along the fracture is key to its productivity. Recently, various model predictive control schemes have been proposed to achieve this objective. But such controllers require an accurate and computationally efficient model which is difficult to obtain given the complexity of the process and uncertainties in the rock formation properties. In this article, we design a model-free data-based reinforcement learning controller which learns an optimal control policy through interactions with the process. Deep reinforcement learning (DRL) controller is based on the Deep Deterministic Policy Gradient algorithm that combines Deep-Q-network with actor-critic framework. In addition, we utilize dimensionality reduction and transfer learning to quicken the learning process. We show that the controller learns an optimal policy to obtain uniform proppant concentration despite the complex nature of the process while satisfying various input constraints.

42 ENGINEERING↗

DOE OSTI2024

Demonstrating the Potential of Adaptive LMS Filtering on FPGA-Based Qubit Control Platforms for Improved Qubit Readout in 2D and 3D Quantum Processing Units

Advancements in quantum computing underscore the critical need for sophisticated qubit readout techniques to accurately discern quantum states. This abstract presents our research intended for optimizing readout pulse fidelity for 2D and 3D Quantum Processing Units (QPUs), the latter coupled with Superconducting Radio Frequency (SRF) cavities. Focusing specifically on the application of the Least Mean Squares (LMS) adaptive filtering algorithm, we explore its integration into the FPGA-based control systems to enhance the accuracy and efficiency of qubit state detection by improving Signal-to-Noise Ratio (SNR). Implementing the LMS algorithm on the Zynq UltraScale+ RFSoC Gen 3 devices (RFSoC 4x2 FPGA and ZCU216 FPGA) using the Quantum Instrumentation Control Kit (QICK) open-source platform, we aim to dynamically test and adjust the filtering parameters in real-time to characterize and adapt to the noise profile presented in quantum computing readout signals. Our preliminary results demonstrate the LMS filter's capability to maintain high readout accuracy while efficiently managing FPGA resources. These findings are expected to contribute to developing more reliable and scalable quantum computing architectures, highlighting the pivotal role of adaptive signal processing in quantum technology advancements.

Johnson, Hans↗

DOE OSTI2024

Demonstrating the Potential of Adaptive LMS Filtering on FPGA-Based Qubit Control Platforms for Improved Qubit Readout in 2D and 3D Quantum Processing Units

Johnson, Hans↗

DOE OSTI2023

Citadels Final Report (GMLC 2.2.1: Citadels)

This is the final project report for the Grid Modernization Laboratory Consortium (GMLC) Resilient Distribution System (RDS) Citadels project. The primary goal of this GMLC project was to increase the operational flexibly of power systems by engaging microgrids distributedly, coordinated using consensus algorithms. The primary goal was successfully achieved. The primary goal was divided into three areas: Implement peer-to-peer control between microgrid controllers using the Open Field Message Bus (OpenFMB) approach; Develop and implement consensus algorithms on commercially available hardware that allows a group of microgrids to distributedly implement operational controls; Develop the architectures and controls to enable groups of microgrids to coordinate their operations to support the bulk power system during abnormal events, and end-use loads in the event the bulk power systems fail.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Seismic Spatial Gradients and Machine Learning-Based Classifiers for Explosion Monitoring (LDRD 218327)

This final report summarizes the work completed under the Laboratory Directed Research and Development (LDRD) project “Seismic Spatial Gradients as a Machine Learning-Based Classifier for Explosion Monitoring.” The overarching goal of the project was to explore the efficacy of using machine learning-based classification algorithms where the input data are the spatial gradient of the seismic wavefield collected at a single point on the Earth’s surface. The methods that I describe here are in direct contrast to conventional methods of seismic discrimination which typically rely on a spatially extended network of instruments and physics-based wavefield attributes such as, for example, the ratio between $\textit{P}$ and $\textit{S}$ waves. Rather, we use the spatial gradient of the seismic wavefield observed at a single point on the Earth’s surface and data processing approaches inspired by the machine learning community. We tested two algorithms, a neural network and a modified version of principal component analysis termed Spectrally Filtered Principal Component Analysis (SFPCA). To test these algorithms, we first conducted a series of numerical tests using synthetic data and then conducted a small-scale controlled field experiment. The tests using synthetic data showed that both algorithms had high success rates on gradiometric data, even when simulated noise was added to the signal. Furthermore, we found that using seismic spatial gradients increased the performance of our discrimination algorithms when compared to using just the traditional translational motion seismic data. The tests with field data also showed a high degree of discriminative success.

58 GEOSCIENCES↗

DOE OSTI2025

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.↗

DOE OSTI2022

Quantum microgrid state estimation

This paper investigates the feasibility and efficiency of quantum-circuit-based algorithms for microgrid state estimation. Here, our new contributions include: (1) a general quantum state estimation (GQSE) formulation is devised for swing-bus-contained microgrids through the quantized Gaussian–Newton iteration, (2) a preconditioned quantum linear solver (PQLS) is developed for tackling the ill-conditioned GQSE with limited quantum resources, and (3) an enhanced quantum state estimation (EQSE) algorithm is further established for hierarchical-control-based microgrids with exogenous disturbances. Extensive case studies demonstrate the correctness of GQSE, PQLS and EQSE in two typical microgrids. The robustness and convergence performance of EQSE are also verified.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗