Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “System Reliability”

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.

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

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Tehachapi Wind Energy Storage Project - Technology Performance Report #3

The TSP is located at SCE’s Monolith Substation in Tehachapi, California. The 8 MW, 4 hours (32 MWh) BESS is housed in a 6,300 square foot facility and 2 x 4 MW/4.5 MVA smart inverters are on a concrete pad adjacent to the BESS facility. The project will evaluate the capabilities of the BESS to improve grid performance and assist in the integration of large-scale intermittent generation, e.g., wind. Project performance was measured by 13 specific operational uses: providing voltage support and grid stabilization, decreasing transmission losses, diminishing congestion, increasing system reliability, deferring transmission investment, optimizing renewable-related transmission, providing system capacity and resources adequacy, integrating renewable energy (smoothing), shifting wind generation output, frequency regulation, spin/non-spin replacement reserves, ramp management, and energy price arbitrage. Most of the operations either shift other generation resources to meet peak load and other electricity system needs with stored electricity, or resolve grid stability and capacity concerns that result from the interconnection of intermittent generation. SCE also demonstrated the ability of lithium ion battery storage to provide nearly instantaneous maximum capacity for supply-side ramp rate control to minimize the need for fossil fuel-powered back-up generation. The project began in October, 2010 and will continue through December, 2016.

25 ENERGY STORAGE↗
DOE OSTI2020

Solving Optimal Power Flow for Distribution Networks with State Estimation Feedback

Conventional optimal power flow (OPF) solvers assume full observability of the involved system states. However in practice, there is a lack of reliable system monitoring devices in the distribution networks. To close the gap between the theoretic algorithm design and practical implementation, this work proposes to solve the OPF problems based on the state estimation (SE) feedback for the distribution networks where only a part of the involved system states are physically measured. The SE feedback increases the observability of the under-measured system and provides more accurate system states monitoring when the measurements are noisy. We analytically investigate the convergence of the proposed algorithm. The numerical results demonstrate that the proposed approach is more robust to large pseudo measurement variability and inherent sensor noise in comparison to the other frameworks without SE feedback.

distirbution systems↗
DOE OSTI2016

Human Factors Principles in Information Dashboard Design

When planning for control room upgrades, nuclear power plants have to deal with a multitude of engineering and operational impacts. This will inevitably include several human factors considerations, including physical ergonomics of workstations, viewing angles, lighting, seating, new communication requirements, and new concepts of operation. In helping nuclear power utilities to deal with these challenges, the Idaho National Laboratory (INL) has developed effective methods to manage the various phases of the upgrade life cycle. These methods focus on integrating human factors engineering processes with the plant’s systems engineering process, a large part of which is the development of end-state concepts for control room modernization. Such an end-state concept is a description of a set of required conditions that define the achievement of the plant’s objectives for the upgrade. Typically, the end-state concept describes the transition of a conventional control room, over time, to a facility that employs advanced digital automation technologies in a way that significantly improves system reliability, reduces human and control room-related hazards, reduces system and component obsolescence, and significantly improves operator performance. To make the various upgrade phases as concrete and as visible as possible, an end-state concept would include a set of visual representations of the control room before and after various upgrade phases to provide the context and a framework within which to consider the various options in the upgrade. This includes the various control systems, human-system interfaces to be replaced, and possible changes to operator workstations. This paper describes how this framework helps to ensure an integrated and cohesive outcome that is consistent with human factors engineering principles and also provide substantial improvement in operator performance. The paper further describes the application of this integrated approach in the strategic modernization program at a nuclear power plant where legacy systems are upgraded to advanced digital technologies through a systematic process that links human factors principles to the systems engineering process. This approach will help to create an integrated control room architecture beyond what is possible for individual subsystem upgrades alone. In addition, several human factors design and evaluation methods were used to develop the end-state concept, including interactive sessions with operators in INL’s Human System Simulation Laboratory, three-dimensional modeling to visualize control board changes.

3D Modeling↗
DOE OSTI2026

A call to standardize metrics for monitoring baleen whales near marine construction activities

Effective monitoring is necessary to protect marine mammal species during the construction of offshore infrastructure. The tools for detecting or monitoring marine mammals span traditional (e.g., visual observers, optical cameras), to newer (e.g., passive acoustic monitoring, infrared cameras, tags), and emerging (e.g., satellite imagery, environmental DNA, dimethyl sulfide concentration) technologies. Some are better suited for use during offshore development; however, peer-reviewed literature does not typically evaluate and report on the performance of these various technologies. We define a minimum set of metrics related to efficacy (i.e., confusion matrix, precision and recall, probability of missed mitigation), detection range (i.e., maximum and reliable detection range, spatial resolution), and data delivery (i.e., detection latency, system reliability, temporal resolution) that we recommend are needed to assess the utility of monitoring technologies for this purpose. Following a literature review of relevant studies, we highlight which publications reported these metrics and used multiple technologies to compare relative performance. We also emphasize the benefits of multi-modal approaches and recommend performance assessments through modeling or large-scale collaborative field testing. These metrics will standardize data collection, reporting, and analysis; promote consistent and comparable results; and foster collaboration among developers, regulatory agencies, and scientists. This may lead to the co-development of technology that achieves multiple goals, has greater application, and can answer research questions while collecting data to fulfill permitting requirements. These metrics may also inform decisions on what systems regulatory agencies might consider using and reduce monitoring costs, which is critical to support the marine sector's rapid growth alongside marine mammal conservation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Development of High Temperature (>700°C) molten Salt Pump Technology for Gen3 Solar Power Tower Systems

Generation 3 Concentrating Solar Power (CSP) Systems require thermal energy storage that can efficiently receive solar heat and deliver it to a working fluid at temperatures greater than 700°C. For liquid systems, the thermal transfer fluid must be phase stable over large temperature ranges. High temperature molten salts meet this criteria, but are difficult liquids to handle. The high heat and salt content can be very corrosive to several different materials that are wetted by the liquid salt. For power tower collectors, the molten salt must be pumped under high pressure to the top of the collector tower. These pumps have impellers and shafts as part of their rotating elements, and under load, require bearings to control shaft movement while rotating. These high temperature pumps require submerged bearings, and thus bearing materials that can withstand the temperature and molten salt contact over long periods of time. This is essential for keeping pump maintenance costs low, and downtime to a minimum. Long running bearing materials is an enabling technology for integrated liquid systems in Generation 3 CSP Systems. Keeping costs low and systems reliable are critical for the broad adoption of Gen 3 CSP Systems. Hayward Tyler, Inc (HTI) proposed development of journal bearing materials for use in vertical pumps designed for pumping high temperature molten salt on both the hot and cold sides of the solar power tower. To complete this objective, HTI utilized the testing capabilities of Oak Ridge National Laboratory (ORNL) and High Temperature System Design (HTSD). Materials would first be selected for static corrosion testing, then downselected for tribological testing. Successful tribologically tested materials would then be downselected for use in additional test regimes. Ten samples were selected for static corrosion testing. Three passed the static testing regime. Two of these materials were downselected for ball material in tribological testing against three metallic alloys: Sintered Y2O3 Partially Stabilized Zirconia YTZP and Silicon Nitride, Grade 147-31N. HTI also proposed collecting data from a thorough bearing test regime using a test rig designed and built as part of this project, and also a conceptual design for a high temperature molten salt vertical pump. HTI withdrew from the project prior to completion of this work and this report reflects only the work completed prior to withdrawal. The completed work produced two papers, one manuscript submitted for publication, and one paper published in the journal Solar Energy Materials and Solar Cells. The papers are: “Tribological behavior of ceramic-alloy bearing contacts in molten salt lubrication for concentrating solar power” and “Material Selection and Corrosion Studies Of Candidate Bearing Materials For Use In Molten Chloride Salt."

14 SOLAR ENERGY↗
DOE OSTI2020

Electrical Energy Storage Data Submission Guidelines

Energy storage technologies are positioned to play a substantial role in power delivery systems. They are being touted as an effective new resource to maintain reliability and allow for increased penetration of renewable energy. However, due to their relative infancy, there is a lack of knowledge on how these resources truly operate over time. Data analysis can help ascertain the operational and performance characteristics of these emerging technologies. Rigorous testing and data analysis are important for all stakeholders to ensure a safe, reliable system that performs predictably on a macro level. Standardizing testing and analysis approaches to verifying the performance of energy storage devices, equipment, and systems when integrating them into the grid will improve the understanding and benefit of energy storage over time from technical and economic vantage points. Demonstrating the life-cycle value and capabilities of energy storage systems begins with the data the provider supplies for analysis. After review of energy storage data received from several providers, it has become clear that some of these data are inconsistent and incomplete, raising the question of their efficacy for robust analysis. This report reviews and proposes general guidelines such as sampling rates and data points that providers must supply for robust data analysis to take place. Consistent guidelines are the basis of the proper protocol and ensuing standards to (a) reduce the time it takes data to reach those who are providing analysis; (b) allow them to better understand the energy storage installations; and (c) enable them to provide high-quality analysis of the installations. This report is intended to serve as a starting point for what data points should be provided when monitoring. As battery technologies continue to advance and the industry expands, this report will be updated to remain current.

25 ENERGY STORAGE↗
DOE OSTI2020

Front End Engineering Design Report

Energy storage is becoming an increasingly important component on modern power grids to ensure sufficient balancing capability for intermittent renewable power generations is available to maintain system reliability. Although energy storage has traditionally been provided by pumped storage hydroelectric systems, it is not possible to install these at every location and they can be expensive to construct. Lithium Ion batteries are increasingly being used to carry out energy storage grid services, however these can be expensive when specified over a few hours of capacity. An alternative way to store substantial energy is to use thermal energy storage (TES). This has been deployed on concentrated solar units using molten nitrate salts as a storage media. Again, the cost of the material can be prohibitive, thus lower cost alternative materials are being actively sought, such as sand, rocks and concrete. This project investigates the potential for Concrete Thermal Energy Storage (CTES) when used to directly store thermal energy from a thermal plant source. This report represents the initial Front-End Engineering Design (FEED) deliverables that are submitted for the Hazard and Operability (HAZOP) safety review for process validation.

25 ENERGY STORAGE↗
DOE OSTI2020

CTES Pilot Plant Detailed Design Report

Energy storage is becoming an increasingly important component on modern power grids to ensure sufficient balancing capability for intermittent renewable power generations is available to maintain system reliability. Although energy storage has traditionally been provided by pumped storage hydroelectric systems, it is not possible to install these at every location and they can be expensive to construct. Lithium Ion batteries are increasingly being used to carry out energy storage grid services, however these can be expensive when specified over a few hours of capacity. An alternative way to store substantial energy is to use thermal energy storage (TES). This has been deployed on concentrated solar units using molten nitrate salts as a storage media. Again, the cost of the material can be prohibitive, thus lower cost alternative materials are being actively sought, such as sand, rocks and concrete. This project investigates the potential for Concrete Thermal Energy Storage (CTES) when used to directly store thermal energy from a thermal plant source. This report represents the Detailed Design phase deliverables comprising of the process, mechanical, electrical, piping along with control and instrumentation documents. Civil and structural deliverables are included on a preliminary basis due to outstanding site investigation activities. CTES block transportation testing results and the pilot plant testing plan is also included in this report.

25 ENERGY STORAGE↗
DOE OSTI2019

Prediction of Safety Level of Low-Head and Ownerless Hydraulic Structures

Methods of systems reliability theory are applied to the results of an expert inspection of more than 1000 low-head hydraulic power systems in the Moscow region. The rates of failure of homogeneous earth dams are estimated. A state graph of a hydraulic structure, represented as a system that passes through discrete states from a normal to a dangerous level without maintenance or repair, is proposed. The constant failure rates for these states are calculated. The probabilistic characteristics of the safety level of low-head earth dams are predicted.

42 ENGINEERING↗
DOE OSTI2024

Solar and Storage Integration in the Southeastern United States: Economics, Reliability, and Operations

Solar energy has the potential to be a core energy resource for the southeastern United States. To better understand the implications of higher levels of solar PV (27%-43% of total generation capacity) and electricity storage (13%-49% of peak load) would affect electricity system reliability, costs, and operations in the U.S. Southeast, this study sought to address two main questions. First, how would higher levels of solar PV and electricity storage impact the costs, reliability, and operations of electricity systems in the Southeast in 2035? Second, at different levels of solar PV and electricity storage, what are the benefits of operational coordination among utilities in the Southeast, through more efficient regional dispatch and sharing operating reserves? To answer these questions, the study used detailed capacity expansion and dispatch modeling to develop and examine 15 scenarios with different levels of solar PV, electricity storage, and operational coordination, focusing on the year 2035. The study also evaluates the benefits of operational coordination among utilities through more efficient regional dispatch and reserve sharing, at different levels of solar and storage. The study focuses on five balancing regions that cover Alabama, Georgia, Kentucky, North Carolina, South Carolina, Tennessee, and parts of Mississippi and Missouri.

14 SOLAR ENERGY↗
DOE OSTI2024

Solar and Storage Integration in the Southeastern United States: Economics, Reliability, and Operations

Solar energy has the potential to be a core energy resource for the southeastern United States. To better understand the implications of higher levels of solar PV (27%-43% of total generation capacity) and electricity storage (13%-49% of peak load) would affect electricity system reliability, costs, and operations in the U.S. Southeast, this study sought to address two main questions. First, how would higher levels of solar PV and electricity storage impact the costs, reliability, and operations of electricity systems in the Southeast in 2035? Second, at different levels of solar PV and electricity storage, what are the benefits of operational coordination among utilities in the Southeast, through more efficient regional dispatch and sharing operating reserves? To answer these questions, the study used detailed capacity expansion and dispatch modeling to develop and examine 15 scenarios with different levels of solar PV, electricity storage, and operational coordination, focusing on the year 2035. The study also evaluates the benefits of operational coordination among utilities through more efficient regional dispatch and reserve sharing, at different levels of solar and storage. The study focuses on five balancing regions that cover Alabama, Georgia, Kentucky, North Carolina, South Carolina, Tennessee, and parts of Mississippi and Missouri.

14 SOLAR ENERGY↗
DOE OSTI2025

Artificial Intelligence and Machine Learning Applications in Modern Power Systems

Machine learning (ML) and artificial intelligence (AI) algorithms offer valuable tools for the analysis and interpretation of large datasets. These tools have the capability to uncover insights that may not be readily apparent within these datasets. In recent years, the integration of ML and AI has become increasingly prevalent in various applications within the power system domain. One of the earliest instances of machine learning in power systems can be traced back to demand forecasting, where artificial neural networks were employed for short-term load forecasting. In contemporary power systems, an abundance of high-resolution geospatial and temporal data is generated at various time intervals, ranging from sub-seconds (Phasor Measurement Units or PMUs) to seconds (Supervisory Control and Data Acquisition or SCADA), minutes (Process Information or PI), and extending to days, months, and years. These datasets contain valuable information concerning system reliability and performance. This information holds the potential to offer critical insights into system operations, as well as solutions for predicting and mitigating contingencies to prevent cascading outages. Despite the immense power of machine learning tools, system operators, planners, and utilities often exhibit hesitancy in fully embracing AI-enabled system operations and planning. This cautious approach persists, even as numerous diverse applications of machine learning continue to emerge in the realm of power systems. In this chapter, our focus will delve deep into ML and AI applications tailored for power systems. These applications aim to furnish system operators with enhanced situational awareness and augment their decision-making capabilities, especially during challenging operating conditions. Specific areas of interest encompass root cause analyses of electricity market datasets and the strategic selection of representative samples from vast power system databases for training ML/AI models. Finally, the chapter will conclude with a short discussion on the future of ML/AI in power systems and possible directions that the industry is moving towards.

power system applications, machine learning (ML), ↗
DOE OSTI2025

A Review on Building Resilient Power Networks: Emphasizing Adjacent Span Dynamics

This research article presents a comprehensive review of resilience in power transmission and distribution systems, focusing on key studies that examine structural integrity, mechanical stress distribution, and system reliability under various conditions. The article synthesizes findings across multiple studies, covering assumptions, system topologies, methodologies, and challenges that affect resilience in these networks. Particular attention is given to identifying studies that address the influence of adjacent spans and tower--line interactions, as these factors play a crucial role in the stress distribution and structural dynamics within poles, towers, and transmission lines. In addition to identifying critical factors contributing to system vulnerability, this review emphasizes the importance of continued research to better understand and mitigate risks from extreme events, such as high winds combined with ice storms. By consolidating knowledge on current challenges and future needs, this work outlines future directions to advance resilience studies and contributes to ongoing efforts to strengthen power transmission and distribution networks, reducing disruptions in electricity supply and improving overall system resilience in an evolving climate landscape.

Ahmad, Tawsif [Pacific Northwest National Laborato↗
DOE OSTI2018

Transactive System Program Communication System Cost Model

Transactive energy is an economics and controls technique that aims to dynamically manage the generation and consumption of electricity within the power system. Much research has been done in the area of demonstrating the capability and performance of transactive systems, as well as valuing the benefits a transactive system can provide. Significantly less research has been done in the area of estimating the costs of a transactive system. This work aimed to build a model that would estimate the costs of the communications system that would be necessary to support a transactive system and be realized by a local utility. Dynamic pricing, and a customer’s response to this pricing, is a key aspect of a transactive system; this would require a two-way communication system between utilities and customers. Since the system will vary based on many factors, the cost model was consequently designed for use in a wide variety of applications. The cost model requires some basic user inputs regarding the system being analyzed, such as location and size. The user also identifies one or more generic circuit models that best represent the system. Additionally, a user can, but is not required to, change assumed equipment and installation costs and equipment lifetime within the model. These inputs will result in 20 year cost estimates for three different communication technologies that are capable of supporting the bandwidth needs of a transactive energy system. The three communication systems included in the model are cellular, fiber optic and wireless mesh. Each vary significantly from one another and offer unique advantages and barriers. A cellular network avoids high upfront costs, but is limited to areas where there is coverage by the service provider and subject to the ongoing rate established with the service provider. A fiber optic system requires a large up-front cost, but it will provide a reliable system to areas where cellular and mesh may be unable to do so. Additionally, fiber provides more bandwidth than necessary for transactive systems and can offer additional business opportunities. A mesh system can be installed for less upfront costs than fiber and offers enough bandwidth to support a transactive system, but the ability to model this technology is done with less certainty than the other two options. The estimated costs include the communication system that connects the customers to their nearest substation, in addition to the smart meter and radio that would be required for each customer. The communications from the substation to the utility are not included in estimates, as the need for upgrading that system would be assessed on a case-by-case basis. Although the cost of the smart meter and radio is included, no other appliance specific cost is included in the estimate provided by the model. The communication system is a key aspect of the development of a transactive system. This work resulted in easily being able to estimate the costs of a communication system specific to the system being studied. This cost model will aid ongoing valuation and simulation work in the field of transactive energy.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models, require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their suitability for control.

Shaw Cortez, Wenceslao E.↗
DOE OSTI2023

Multi-level optimization with the koopman operator for data-driven, domain-aware, and dynamic system security

Cyber-Physical Systems (CPSs) like the power grid are critically important but also increasingly vulnerable; ensuring reliable system operation in the face of disruptions is becoming more and more challenging. Multi-Level Optimization (MLO) is a powerful way to model adversarial interactions, which naturally makes it applicable to studying CPS security. However, MLO typically does not address underlying system dynamics, and incorporating nonlinear dynamics is generally infeasible. In this paper, we show how to combine MLO with the Koopman Operator (KO) to remedy this. The KO maps nonlinear dynamics to a lifted space in which those dynamics are linear, thus making it ideal for use with MLO. Moreover, the structure of the KO also provides convenient ways to incorporate domain knowledge into the data-driven process of learning the KO representation of a given system. Here we then demonstrate the use of MLO-KO on a small example problem taken from the power grid domain, discuss the scalability and computational cost of MLO-KO, and identify future research directions for this work.

42 ENGINEERING↗
DOE OSTI2014

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy composite cantilever plate subjected to in-plane harmonic and stochastic excitation

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗