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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Risk-Informed Condition Evaluation of Solar-centered Energy Generation and Distribution Networks through Bayesian Learning and Inference

We develop a methodology based on Bayesian inference over Probabilistic Graphical Models (PGMs) to understand and quantify risk in solar-centered grids using targeted measurements and learned system behavior. Being non-prescriptive but, rather, able to infer system behavior and, ultimately, address risk queries from data, our machine learning-type paradigm is tailored for diverse topologies and threat scenarios often associated with distributed energy generation and photovoltaic distributed energy resources (PV-DERs) in particular. We describe algorithmic processes for: (i) learning the structure of PGMs that result from attack-prone PV-DER-proliferated distribution systems, (ii) quantifying cause-effect relationships, and (iii) evaluating risk queries based on diverse evidence. The contributions are illustrated on a residential grid subject to output impairment attacks on its PV-DER infrastructure.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Optimizing Fast Charging and Wetting in Lithium-Ion Batteries with Optimal Microstructure Patterns Identified by Genetic Algorithm

To sustain the high-rate current required for fast charging electric vehicle batteries, electrodes must exhibit sufficiently high effective ionic diffusion. Additionally, to reduce battery manufacturing costs, wetting time must decrease. Both of these issues can be addressed by structuring the electrodes with mesoscale pore channels. However, their optimal spatial distribution, or patterns, is unknown. Herein, a genetic algorithm has been developed to identify these optimal patterns using a CPU-cheap proxy distance-based model to evaluate the impact of the added pore networks. Both coin-cell and pouch cell form factors have been considered for the wetting analysis, with their respective electrolyte infiltration mode. Regular hexagonal and mud-crack-like patterns, respectively, for fast charging and fast wetting were found to be optimal and have been compared with pre-determined, easier to manufacture, patterns. The model predicts that using cylindrical channels arranged in a regular hexagonal pattern is ∼6.25 times more efficient for fast charging as compared to grooved lines with both structuring strategies being restricted to a 5% electrode total volume loss. The model also shows that only a very limited electrode volume loss (1%–2%) is required to dramatically improve the wetting (5–20 times) compared to an unstructured electrode.

25 ENERGY STORAGE↗
DOE OSTI2024

Trust-Based Detection and Mitigation of Cyber Attacks in Distributed Cooperative Control of Islanded AC Microgrids

In this study, we address the challenge of detecting and mitigating cyber attacks in the distributed cooperative control of islanded AC microgrids, with a particular focus on detecting False Data Injection Attacks (FDIAs), a significant threat to the Smart Grid (SG). The SG integrates traditional power systems with communication networks, creating a complex system with numerous vulnerable links, making it a prime target for cyber attacks. These attacks can lead to the disclosure of private data, control network failures, and even blackouts. Unlike machine learning-based approaches that require extensive datasets and mathematical models dependent on accurate system modeling, our method is free from such dependencies. To enhance the microgrid’s resilience against these threats, we propose a resilient control algorithm by introducing a novel trustworthiness parameter into the traditional cooperative control algorithm. Our method evaluates the trustworthiness of distributed energy resources (DERs) based on their voltage measurements and exchanged information, using Kullback-Leibler (KL) divergence to dynamically adjust control actions. We validated our approach through simulations on both the IEEE-34 bus feeder system with eight DERs and a larger microgrid with twenty-two DERs. The results demonstrated a detection accuracy of around 100%, with millisecond range mitigation time, ensuring rapid system recovery. Additionally, our method improved system stability by up to almost 100% under attack scenarios, showcasing its effectiveness in promptly detecting attacks and maintaining system resilience. These findings highlight the potential of our approach to enhance the security and stability of microgrid systems in the face of cyber threats.

Computer Science↗
DOE OSTI2024

Microgrid Service Restoration Incorporating Unmonitored Automatic Voltage Controllers and Net Metered Loads

Islanded microgrids may experience voltage and frequency instability due to uncontrolled state changes of voltage regulation devices and inaccurate demand forecasts. Uncontrolled state changes can occur if optimal microgrid restoration and dispatch algorithms, used for generating control commands for distributed energy resources, do not incorporate the behavior of automatic controllers of voltage regulation devices. Inaccurate demand forecasts may be encountered since post-outage demand of behind-the-meter net metered (NM) loads can vary significantly from their historical NM profiles. Here, this paper proposes an optimization formulation which allows optimal control of voltage regulators and capacitor banks without remote control and communication capabilities. A generalized demand model for NM loads is proposed which incorporates the cold load pickup phenomenon and their time varying post-outage demand in accordance with the IEEE 1547 standard. The time dependent optimal control formulation and the NM demand model are integrated in a sequential microgrid restoration algorithm by linearization of the involved logic propositions. A detailed case study on the unbalanced IEEE 123-node test system in OpenDSS validates the effectiveness of the proposed approach.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2020

Agent-Based Coordination Scheme for PV Integration (ABC4PV)

Renewables and especially photovoltaics (PV) have benefitted significantly from a host of incentives and policies targeted toward enhanced integration and adoption of specific energy technologies. However, with the push to move forward into a subsidy-free market framework, behind-the-meter residential PV applications have generally struggled to retain their value (unlike utility scale and commercial projects) [1]. This project focused on developing control-theoretic solutions aimed at improving the integration and interaction of behind-the-meter residential PV with other distribution system assets (controllable and non-controllable) to enhance the integrated value of residential PV. To this end, a suite of decentralized control methodologies have been developed to enable effective coordination and control of behind-the-meter residential load customers’ PV, battery storage systems (BSS), controllable loads and other similar assets within a distribution feeder. This interaction aims at procuring energy savings and, thus, energy bill savings. The main source of savings is drawn from reducing the effect of demand charge pricing and is realized at the feeder level, assuming community level interaction and management among the aforementioned assets. Optimal control of the assets is implemented with a distributed optimization methodology, leveraging consensus-based algorithms. The results gathered from the optimal control simulations demonstrates that the savings can be duly achieved and the algorithm decision times (to dynamically control asset set points, for example) are fast. As for the overall efficiency of PV+BSS systems, to procure energy savings from curtailment of the demand charge pricing effects, the optimal control is set up so as to minimize the variance of the load for all customers, throughout a feeder and throughout time in a rolling horizon scheduling with model predictive control. The control takes into account inter-temporal electrochemical storage (battery) degradation costs: specifically, we have developed a long-term lifetime model for the BSS that weighs in the effect of the degradation factor in the dispatch formulations, thus, a considerable operating cost that affects energy decision making. The levelized cost of energy (LCOE – redefined for the purpose of quantifying asset integration effectiveness through the customers’ energy cost) is shown to be below the threshold set for the combined PV+BSS topology of $ 0.14/kWh for multiple cases of PV penetration all the way up to 50%, provided that a policy of shared ownership of and savings is in place. Further, the LCOE calculated for the case before the deployment PV+BSS systems is also achievable, i.e. the deployment of PV+BSS, if planned and scheduled optimally. will have no effect on customers’ energy costs. From the control methodology viewpoint, the developed consensus-based algorithms are shown to converge for a wide range of problem cases (spanning normal operating scenarios and contingencies), guaranteeing dispatch solutions under forecasting errors, communication break-downs and cyber-security attacks. The proposed control solutions are scalable and real-time implementable, with dispatch computations and device set-point updates converging in less than 2s in most practical instances of the above events.

14 SOLAR ENERGY↗
DOE OSTI2014

Identifying high-redshift gamma-ray bursts with RATIR

We present a template-fitting algorithm for determining photometric redshifts, z {sub phot}, of candidate high-redshift gamma-ray bursts (GRBs). Using afterglow photometry, obtained by the Reionization and Transients InfraRed (RATIR) camera, this algorithm accounts for the intrinsic GRB afterglow spectral energy distribution, host dust extinction, and the effect of neutral hydrogen (local and cosmological) along the line of sight. We present the results obtained by this algorithm and the RATIR photometry of GRB 130606A, finding a range of best-fit solutions, 5.6 < z {sub phot} < 6.0, for models of several host dust extinction laws (none, the Milky Way, Large Magellanic Clouds, and Small Magellanic Clouds), consistent with spectroscopic measurements of the redshift of this GRB. Using simulated RATIR photometry, we find that our algorithm provides precise measures of z {sub phot} in the ranges of 4 < z {sub phot} ≲ 8 and 9 < z {sub phot} < 10 and can robustly determine when z {sub phot} > 4. Further testing highlights the required caution in cases of highly dust-extincted host galaxies. These tests also show that our algorithm does not erroneously find z {sub phot} < 4 when z {sub sim} > 4, thereby minimizing false negatives and allowing us to rapidly identify all potential high-redshift events.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Distributed Solution Approach for a Stackelberg Pricing Game of Aggregated Demand Response

Demand-side management is a fundamental up-to-date strategy that transforms the traditional power grid to a modern smart grid where the flexible pricing mechanisms play a critical role in its successful implementation. In this paper, the pricing-demand response between a distribution system operator (DSO) and load aggregators (LAs) is modeled as a Stackelberg game, where the DSO is the price maker that adjusts its strategy based on observed responses from LAs. With the concerns of computational cost and privacy protection, two distributed solution approaches, particle swarm optimization and pattern search algorithm, are conducted and compared with the classical centralized backward induction approach. Numerical results on a small case study demonstrate the effectiveness of the proposed distributed solution approaches in leveraging flexible demand response potential.

Chen, Yang↗
DOE OSTI2016

Estimating the Propagation of Interdependent Cascading Outages with Multi-Type Branching Processes

In this paper, the multi-type branching process is applied to describe the statistics and interdependencies of line outages, the load shed, and isolated buses. The offspring mean matrix of the multi-type branching process is estimated by the Expectation Maximization (EM) algorithm and can quantify the extent of outage propagation. The joint distribution of two types of outages is estimated by the multi-type branching process via the Lagrange-Good inversion. The proposed model is tested with data generated by the AC OPA cascading simulations on the IEEE 118-bus system. The largest eigenvalues of the offspring mean matrix indicate that the system is closer to criticality when considering the interdependence of different types of outages. Compared with empirically estimating the joint distribution of the total outages, good estimate is obtained by using the multitype branching process with a much smaller number of cascades, thus greatly improving the efficiency. It is shown that the multitype branching process can effectively predict the distribution of the load shed and isolated buses and their conditional largest possible total outages even when there are no data of them.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Parallel peak pruning for scalable SMP contour tree computation

As data sets grow to exascale, automated data analysis and visualisation are increasingly important, to intermediate human understanding and to reduce demands on disk storage via in situ analysis. Trends in architecture of high performance computing systems necessitate analysis algorithms to make effective use of combinations of massively multicore and distributed systems. One of the principal analytic tools is the contour tree, which analyses relationships between contours to identify features of more than local importance. Unfortunately, the predominant algorithms for computing the contour tree are explicitly serial, and founded on serial metaphors, which has limited the scalability of this form of analysis. While there is some work on distributed contour tree computation, and separately on hybrid GPU-CPU computation, there is no efficient algorithm with strong formal guarantees on performance allied with fast practical performance. Here in this paper, we report the first shared SMP algorithm for fully parallel contour tree computation, withfor-mal guarantees of O(lgnlgt) parallel steps and O(n lgn) work, and implementations with up to 10x parallel speed up in OpenMP and up to 50x speed up in NVIDIA Thrust.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Scalable Contour Tree Computation by Data Parallel Peak Pruning

As data sets grow to exascale, automated data analysis and visualization are increasingly important, to intermediate human understanding and to reduce demands on disk storage via in situ analysis. Trends in architecture of high performance computing systems necessitate analysis algorithms to make effective use of combinations of massively multicore and distributed systems. One of the principal analytic tools is the contour tree, which analyses relationships between contours to identify features of more than local importance. Unfortunately, the predominant algorithms for computing the contour tree are explicitly serial, and founded on serial metaphors, which has limited the scalability of this form of analysis. While there is some work on distributed contour tree computation, and separately on hybrid GPU-CPU computation, there is no efficient algorithm with strong formal guarantees on performance allied with fast practical performance. Furthermore, we report the first shared SMP algorithm for fully parallel contour tree computation, with formal guarantees of O(lg V lg t) parallel steps and O(V lg V) work for data with V samples and t contour tree supernodes, and implementations with more than 30× parallel speed up on both CPU using TBB and GPU using Thrust and up 70× speed up compared to the serial sweep and merge algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A computer vision algorithm for interpreting lacustrine carbonate textures at Searles Valley, USA

Investigations of the paleohydrologies of pluvial lake systems have often employed lake carbonate deposits called “tufa” that grow subaqueously and can be preserved long after the drying of the lake. For this reason, tufa have been used as a proxy for minimum lake level. However, they exhibit a variety of textures that hold the potential to reveal richer paleoclimatological information. With the goal of determining if tufa texture can be used as a proxy for lake environment, this study investigates the textures of tufa at Mono Lake, California in comparison to the fossil tufa in Searles Valley, California. While observations in the last century suggest that the tufa in the Mono basin grew in waters similar to the modern, the tufa at Searles formed during the last glacial period, when the Great Basin contained a system of pluvial lakes on the scale of the modern Great Lakes. The tufa at both basins have been observed to have a range of classifiable textures, and new methods of inspecting visual data could be informative about what factors control these textures. To this end, a t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm is used to project images of the tufa at Searles and Mono into a coordinate space, allowing for simple, quantitative comparisons of the visual similarity of textures. In this work, the textures of tufa at Searles are compared to each other, as well as to the tufa at Mono. This study performs a robust assessment of the feasibility of Mono Lake as a modern analogue for Searles Valley. It finds that there is a justifiable basis for the comparison of certain fossil facies at Searles to the tufa at Mono, significant progress towards the goal of using texture as a metric for the environment in which tufa formed.

58 GEOSCIENCES↗
DOE OSTI2013

Investigation of realistic PET simulations incorporating tumor patient's specificity using anthropomorphic models: Creation of an oncology database

Purpose: The GATE Monte Carlo simulation toolkit is used for the implementation of realistic PET simulations incorporating tumor heterogeneous activity distributions. The reconstructed patient images include noise from the acquisition process, imaging system's performance restrictions and have limited spatial resolution. For those reasons, the measured intensity cannot be simply introduced in GATE simulations, to reproduce clinical data. Investigation of the heterogeneity distribution within tumors applying partial volume correction (PVC) algorithms was assessed. The purpose of the present study was to create a simulated oncology database based on clinical data with realistic intratumor uptake heterogeneity properties.Methods: PET/CT data of seven oncology patients were used in order to create a realistic tumor database investigating the heterogeneity activity distribution of the simulated tumors. The anthropomorphic models (NURBS based cardiac torso and Zubal phantoms) were adapted to the CT data of each patient, and the activity distribution was extracted from the respective PET data. The patient-specific models were simulated with the Monte Carlo Geant4 application for tomography emission (GATE) in three different levels for each case: (a) using homogeneous activity within the tumor, (b) using heterogeneous activity distribution in every voxel within the tumor as it was extracted from the PET image, and (c) using heterogeneous activity distribution corresponding to the clinical image following PVC. The three different types of simulated data in each case were reconstructed with two iterations and filtered with a 3D Gaussian postfilter, in order to simulate the intratumor heterogeneous uptake. Heterogeneity in all generated images was quantified using textural feature derived parameters in 3D according to the ground truth of the simulation, and compared to clinical measurements. Finally, profiles were plotted in central slices of the tumors, across lines with heterogeneous activity distribution for visual assessment.Results: The accuracy of the simulated database was assessed against the original clinical images. The PVC simulated images matched the clinical ones best. Local, regional, and global features extracted from the PVC simulated images were closest to the clinical measurements, with the exception of the size zone variability and the mean intensity values, where heterogeneous tumors showed better reproducibility. The profiles on PVC simulated tumors after postfiltering seemed to represent the more realistic heterogeneous regions with respect to the clinical reference.Conclusions: In this study, the authors investigated the input activity map heterogeneity in the GATE simulations of tumors with heterogeneous activity distribution. The most realistic heterogeneous tumors were obtained by inserting PVC activity distributions from the clinical image into the activity map of the simulation. Partial volume effect (PVE) can play a crucial role in the quantification of heterogeneity within tumors and have an important impact on applications such as patient follow-up during treatment and assessment of tumor response to therapy. The development of such a database incorporating patient anatomical and functional variability can be used to evaluate new image processing or analysis algorithms, while providing control of the ground truth, which is not available when dealing with clinical datasets. The database includes all images used and generated in this study, as well as the sinograms and the attenuation phantoms for further investigation. It is freely available to the interested reader of the journal at http://www.med.upatras.gr/oncobase/.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Effect of Network Structure on Characterization and Flow Modeling Using X-ray Micro-Tomography Images of Granular and Fibrous Porous Media

Image-based network modeling has become a powerful tool for modeling transport in real materials that have been imaged using X-ray computed micro-tomography (XCT) or other three-dimensional imaging techniques. Network generation is an essential part of image-based network modeling, but little quantitative work has been done to understand the influence of different network structures on modeling. We use XCT images of three different porous materials (disordered packings of spheres, sand, and cylinders) to create a series of four networks for each material. Despite originating from the same data, the networks can be made to vary over two orders of magnitude in pore density, which in turn affects network properties such as pore-size distribution and pore connectivity. Despite the orders-of-magnitude difference in pore density, single-phase permeability predictions remain remarkably consistent for a given material, even for the simplest throat conductance formulas. Detailed explanations for this beneficial attribute are given in the article; in general, it is a consequence of using physically representative network models. The capillary pressure curve generated from quasi-static drainage is more sensitive to network structure than permeability. However, using the capillary pressure curve to extract pore-size distributions gives reasonably consistent results even though the networks vary significantly. These results provide encouraging evidence that robust network modeling algorithms are not overly sensitive to the specific structure of the underlying physically representative network, which is important given the variety image-based network-generation strategies that have been developed in recent years.

42 ENGINEERING↗
DOE OSTI2016

Geometrical characterization of perlite-metal syntactic foam

This paper introduces an improved method for the detailed geometrical characterization of perlite-metal syntactic foam. This novel metallic foam is created by infiltrating a packed bed of expanded perlite particles with liquid aluminium alloy. The geometry of the solidified metal is thus defined by the perlite particle shape, size and morphology. The method is based on a segmented micro-computed tomography data and allows for automated determination of the distributions of pore size, sphericity, orientation and location. The pore (i.e. particle) size distribution and pore orientation is determined by a multi-criteria k-nearest neighbour algorithm for pore identification. The results indicate a weak density gradient parallel to the casting direction and a slight preference of particle orientation perpendicular to the casting direction. - Highlights: •A new method for identification of pores in porous materials was developed. •It was applied on perlite-metal syntactic foam samples. •A porosity decrease in the axial direction of the samples was determined. •Pore shape analysis showed a high percentage of spherical pores. •Orientation analysis showed that more pores are oriented in the radial direction.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Towards Integrating Data Quality Assessments and Radiometer Uncertainty for Determining the Expanded Uncertainty of Three-Component Solar Radiation Measurements

Accurate solar irradiance data are fundamental for determining the design and performance characteristics of photovoltaic systems. The uncertainty of solar irradiance measurements depends on many factors including radiometer design, calibration, installation, maintenance, and operational environment. The key contributors to this uncertainty can be classified as the measurement uncertainty of a particular radiometer and the operational uncertainty determined for the time of measurement. Radiometer measurement uncertainty estimates (U R ) can be based on well-established methods used as part of the radiometer calibration process. Estimates of operational uncertainties (U o ) require consideration of additional site-specific factors that affect data quality. A method is needed for establishing the accuracy of solar irradiance data by integrating an existing data quality process and measurement uncertainty estimates for specific radiometers. An algorithm has been developed to integrate data quality analyses and measurement uncertainty estimates for three-component solar irradiance data: global horizontal (total hemispheric) irradiance, direct normal (beam) irradiance, and diffuse horizontal (sky) irradiance collected at one- to 60-minute intervals. The algorithm has been tested using one-minute irradiance measurements. The goal of the project is to distribute a user-friendly software package based on the new algorithm.

data integrity↗
DOE OSTI2016

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A multi-objective optimization approach to optimal sensor location problem in $\mathrm{IGCC}$ power plants

Integrated Gasification Combined Cycle (IGCC) power plants provide a cleaner and more efficient way to obtain energy from coal. In order to operate an IGCC power plant in a safe and stable manner, several input and output process parameters need to be monitored. However, due to economic and operational constraints, it is infeasible to place sensors at every input and output process parameter location. Hence, it becomes important to select the most effective sensor locations which lead to maximum information gain about the plant conditions. Practical issues present in an IGCC power plant, such as harsh physical conditions and variability in process parameters, make the optimal sensor location problem an especially complicated one. Further, sensors can have multiple objectives and they can produce uncertainties due to measurement errors. Here this work considers hybrid hardware and virtual sensing for advanced power systems with multiple objectives. In order to solve this real world large scale problem, we use a novel algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS). BONUS works in probability distribution space and avoids sampling for each optimization and derivative calculations iterations. A new algorithm for multi-objective optimization is also developed specifically for problem. The result of this nonlinear stochastic multi-objective problem is the non-dominated, or Pareto set, which provides trade-offs between various objectives like observability, cost, and thermal efficiency. This is the first attempt at solving the problem of optimal sensor deployment in advanced power plants, with consideration of hybrid hardware and virtual sensing and incorporation of uncertainty with multiple objectives.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2024

H ∞ Control for Energy Dispatch in Autonomous Nanogrid With Communication Delays

This paper proposes an optimal controller and estimator for energy dispatch to balance the power supply and demand considering communication delays. The proposed algorithm involves modeling an autonomous nanogrid (ANG) consisting of distributed energy resources, energy storage systems, loads, an $H$ ∞ controller with a reference power modulation technique, and a state estimator. The ANG was developed to express the dynamic supply-demand energy balance of a nanogird system. Reference power modulation was designed to generate the desired ESS power based on the imbalanced energy. Random communication delays were modeled using a stochastic variable satisfying the Bernoulli random binary distribution. The optimal $H$ ∞ controller and estimator were developed using a linear matrix inequality approach to exponentially stabilize the closed-loop system. Simulations were performed using real daily demand forecasts obtained from the Korea Meteorological Administration to demonstrate the effectiveness of the proposed real-time optimization algorithm.

24 POWER TRANSMISSION AND DISTRIBUTION↗