Search NASA⌕ Search

SEARCH · Search NASA

Results for “Distributed Power Generation”

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 613 records · Page 34

Distributed Coordination of Energy Storage with Distributed Generators

With a growing emphasis on energy efficiency and system flexibility, a great effort has been made recently in developing distributed energy resources (DER), including distributed generators and energy storage systems. This paper first formulates an optimal coordination problem considering constraints at both system and device levels, including power balance constraint, generator output limits, storage energy and power capacity and charging/discharging efficiencies. An algorithm is then proposed to dynamically and automatically coordinate DERs in a distributed manner. With the proposed algorithm, the agent at each DER only maintains a local incremental cost and updates it through information exchange with a few neighbors, without relying on any central decision maker. Simulation results are used to illustrate and validate the proposed algorithm.

Distributed control↗

ARPA-E PNDIODES "PN Junctions by Ion Implantation" Project (Final Report)

Electricity accounts for nearly 40% of the energy generated in the United States, of which 65% is lost to electrical system inefficiency before reaching end-use sectors. Power electronics will play a growing role in this distribution and end-use, with up to 80% of electricity estimated to pass through power electronics from generation to consumption by 2030. This gives technical improvements in power electronics enormous potential to drive efficiency gains throughout the U.S. economy. Current Si-based power architectures including MOSFETs and IGBTs are limited by high losses, low switching frequency, and poor high-temperature performance. Given the material properties of GaN, devices can exhibit a given turn-on resistance and breakdown voltage with a minute fraction of the area of a Si device—all with higher switching speeds. While n-type doping of III-nitrides has reached a high level of maturity and integration into commercialized products, p-type doping presents distinct challenges that requires continued research. The success of the next generation of GaN-based power devices depends in large part on the ability to form selective-area p-type regions, which can be accomplished by ion implantation of the prevailing acceptor dopant, Mg. This approach is relatively inexpensive and is a fab-ready processing step for creation of current-generation power electronic devices including BJTs, IGBTs, and diode rectifiers. However, ion implantation induces lattice damage and creates point defects within the material, which negatively impacts dopant activation annealing. These forms of damage may be removed by high-temperature annealing, however short annealing time and higher pressures are required to prevent decomposition of the material. We approach this challenge through an innovative combination of approaches toward obtaining high-conductivity p-type GaN. By the novel employment of a gyrotron, a microwave source that can be shaped into a highly localized beam to dissipate very high power in a semiconductor target, a wafer of GaN can be annealed in short (<2 s) ‘pulses’ at temperatures of 1450 °C (2640 °F) to achieve p-type activation without appreciable surface degradation. The p-type activation of Mg-implanted GaN can be further aided by co-implantation with N, believed to enhance the removal of point defects that compensate the acceptors dopant. Elevation to such high temperatures for even a short time induces degradation of GaN-to overcome, we have implemented additional measures to retain high-quality crystalline GaN while removing implant damage and activating Mg dopant. A bilayer cap of AlN is deposited by a combination of chemical and physical vapor deposition to protect the GaN surface. To prevent decomposition of GaN loss of N during annealing, a custom vessel—to contain pressurized N while allowing injection of microwave energy—is employed. By detailed study of the interaction of various measures that are implemented to protect the sample surface (GaN), activate the implanted dopants, and mitigate damage of the lattice heating damage during annealing, we are able to achieve p-type GaN and observe recovery of the crystal and removal of substantial density of defects created during the implantation process.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Large-scale optimal control of interconnected natural gas and electrical transmission systems

We present a detailed optimal control model that captures spatiotemporal interactions between gas and electric transmission networks. We use the model to study flexibility and economic opportunities provided by coordination. A large-scale case study in the Illinois system reveals that coordination can enable the delivery of significantly larger amounts of natural gas to the power grid. In particular, under a coordinated setting, gas-fired generators act as distributed demand response resources that can be controlled by the gas pipeline operator. This enables more efficient control of pressures and flows in space and time and overcomes delivery bottlenecks. We demonstrate that the additional flexibility not only can benefit the gas operator but can also lead to more efficient power grid operations and results in increased revenue for gas-fired power plants. We also use the optimal control model to analyze computational issues arising in these complex models. We demonstrate that the interconnected Illinois system with full physical resolution gives rise to a highly nonlinear optimal control problem with 4400 differential and algebraic equations and 1040 controls that can be solved with a state-of-the-art sparse optimization solver. (C) 2016 Elsevier Ltd. All rights reserved.

Chiang, Nai-Yuan↗

Risk-Based Distributionally Robust Optimal Power Flow With Dynamic Line Rating

In this paper, we propose a risk-based data-driven distributionally robust approach to investigating the optimal power flow with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the objective function. To robustify the solution, we consider a distributional uncertainty set based on the second-order moment, that captures the correlation between wind generation outputs and line ratings, and also the Wasserstein distance, that hedges against data perturbations. We show that the proposed model can be reformulated as a convex conic program. Approximations of the proposed model are suggested, which leads to a significant reduction of the number of the constraints. For practical large-scale test systems, a distributionally robust optimal power flow model with Wasserstein-distance-based distributional uncertainty set and its convex reformulation are also provided. Simulation results on the 5-bus, the IEEE 118-bus and the Polish 2736-bus test systems validate the effectiveness of the proposed models.

distributionally robust optimization↗

Integration of renewable energy generation and storage systems for emissions reduction in an islanded campus microgrid

Microgrid connected building communities are projected to play an integral part in the clean energy transition. These types of systems, when integrated with distributed energy resources (DERs) such as combined heat and power (CHP), district heating and cooling, renewable generation, and energy storage, can provide clean, reliable power to critical facilities and vulnerable communities. The intermittent nature of renewable generation is a challenge when integrating renewables into any grid system, but particularly in islanded microgrids. The University of Texas at Austin (UT) operates an islanded microgrid powered by a CHP plant, while also utilizing district heating and cooling systems and thermal energy storage (TES). High fidelity operating data was used to develop a validated reduced order model of UT’s integrated campus energy systems to serve as a testbed for use in a case study. Hypothetical renewable energy installations on land owned by UT in west Texas were modeled and integrated into the validated campus models along with battery energy storage (BES). Simulations showed that a combination of renewable energy from wind, and optimally controlled 24-hour thermal and battery storage systems could reduce carbon dioxide emissions on campus by 45.4%. The additional retrofit of burner systems to utilize hydrogen natural gas blends resulted in an overall annual emissions reduction of 54.7%. Carbon capture and storage eliminated the majority of the remaining emissions with increased plant energy expenditure. The presented simulations display the practical limitations of a CHP system complemented by renewable generation and short-term storage in eliminating emissions. Furthermore, results highlight the need for further research and development in long duration storage technologies and hydrogen fueled turbines to increase penetration of renewable energy and reduce emissions.

CHP↗

Effective Selective Area Doping for GaN Vertical Power Transistors Enabled by Innovative Materials Engineering

GaN vertical power transistors have emerged as promising candidates for future high efficiency high power electronic applications, with the potential to outperform conventional GaN lateral power devices in terms of power, breakdown, and avalanche characteristics. However, the development of current GaN vertical power transistors is seriously hindered by the poor materials performance of selective area doped p-n junctions. A mechanistic understanding of these fundamental materials issues is essential in order to achieve high performance selective area doped p-n junctions and consequently to advance the GaN vertical power transistor technology. To address this challenge, we carried out a comprehensive research program that advance fundamental knowledge in the selective area doping for GaN materials, and which will lead to the development of high performance GaN vertical power transistors. First, we developed innovative fabrication processes, including novel surface etching, surface passivation, and metalorganic chemical vapor deposition (MOCVD) growth, which provided enhanced opportunities for solving the unique challenges of selective area doping in GaN materials. Second, we performed a fundamental materials study using powerful characterization methods including transmission electron microscopy (TEM), ultraviolet (UV-), x-ray and angle-resolved photoelectron spectroscopy (UPS/XPS/ARPES), electron holography, and cathodoluminescence (CL); Third, we investigated several related issues, including Mg incorporation, polarization effects in carrier transport, and non-ideal material effects, which have rarely been explored so far. At the end of this project, we successfully demonstrated (1) fundamental understanding of selective area etching, regrowth, and doping of GaN, and associated knowledge on defects, interface, and breakdown properties. (2) Effective etch and regrowth processing recipes to achieve etch/regrowth GaN p-n diodes with very low leakage of 3.5 nA at 600 V, which meets the ARPA-E target. (2) High performance vertical GaN p-n didoes and vertical junction termination extension (JTE) devices with breakdown voltage of ~ 2 kV, and breakdown electric field of ~ 3.5 MV/cm, which are close to the performance limit of GaN. The successful outcome has resulted in new fundamental understandings in the selective area doping and regrowth process for GaN, which will lead to groundbreaking GaN vertical transistors for high performance next generation power electronics.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Ultrasonic Measurements of Temperature Profile and Heat Fluxes in Coal-Fired Power Plants (Final Report)

Many industrial processes are inaccessible or inhospitable to characterization by traditional temperature measurement methods, such as thermocouples, especially over prolonged exposure to harsh environments. Ultrasound is an established characterization technology with diverse applications ranging from medical imaging to therapies to flaw detection to nondestructive evaluation. Ultrasound may characterize solid materials and components noninvasively as a nondestructive evaluation modality and obtain internal measurements of material properties. For example, the speed of ultrasound propagation changes with Young’s modulus and Poisson’s ratio, which can be found from its measurements. Traditional ultrasonic characterization assumes all material properties remain constant with the position. When this assumption holds, a property of interest may be measured by relating it to the speed of ultrasound propagation (or a speed of sound, SOS) and measuring the SOS by timing the ultrasound propagation through a known distance. However, when a property of interest is spatially distributed, the propagation time depends on the SOS changing with the position along the ultrasound propagation path. The multiple temperature distributions may lead to an identical time of flight (TOF). Temperature is one property that impacts the speed of ultrasound and often cannot be assumed to remain constant with the position. Previously, in the context of temperature, we addressed the challenge of ultrasonic characterization of spatially distributed properties by developing a method for measuring segmental temperature distributions (MSTD). This method divides the ultrasonic propagation into segments bound by echogenic features. These features provide ultrasonic interfaces where some energy is reflected toward the receiving transducer, and the rest continues through the medium. The time-of-flight between the echoes reflected from echogenic features characterizes the spatial distribution in the properties of interest in the corresponding segment of the ultrasonic propagation path. This project demonstrated the application of the MSTD method in industrial conditions of the coal-fired power plant. We implemented the MSTD using metals and alloys waveguides, which may be the existing structure for which the temperature distribution is characterized or purposefully designed waveguides added to the structure by welding or other means specifically to quantify thermal properties using the MSTD method. Previous iterations of the MSTD method used ceramic and cementitious waveguides, which significantly attenuate ultrasound. On the other hand, low attenuation in metallic waveguides creates interactions between echogenic features which compilates the signal analysis in the segmental TOF measurements. We have established the WG design principles that minimize the interferences between trailing and primary echoes and, in some cases, eliminate them. The waveguides in which echoes do not interfere improve the timing accuracy and the robustness of ultrasonic measurements of the spatial distributions in material properties. Our emphasis remained on the estimation of the temperature distributions. We have developed general recommendations for designing ultrasonically segmented waveguides with the reduced influence of trailing echoes. Two of our waveguide designs were tested in the industry. The first waveguide was designed for insertion into a combustion zone of the utility-scale coal-fired power plant boiler. The second design allows the characterization of temperature distribution in the direction normal to the boiler’s water wall, a large heat exchanger converting the chemical energy released during combustion to the steam driving the electrical power generation turbines. These waveguides were designed to operate within a restrictive space of thermally insulated water wall and incorporate densely located echogenic features while combatting the influence of trailing echoes. The project has successfully demonstrated the feasibility of using the developed method for accurate, continuous, and robust temperature measurements in extreme environments of power generation and other industrial processes. It, therefore, has achieved its overarching goal of advancing the technology readiness level of the novel Ultrasound Measurements of Segmental Temperature Distribution (US-MSTD) method for real-time measurements of the temperature distribution and heat fluxes closer to commercial availability, developing a prototype multipoint measurement system, and validating its performance on coal-fired utility boilers. The success of this project was achieved in collaboration with the power generator, Rocky Mountain Power, and set the stage for the transfer of this technology from the laboratory to the industry.

01 COAL, LIGNITE, AND PEAT↗

Spectral Analytics of Solar Photovoltaic Power Output for Optimal Distributed Energy Resource Utilization

This paper examines the spectral analytics of solar photovoltaic (PV) power in order to understand its frequency content. This information is then used to illustrate that the different frequency components of PV generation can be consumed locally by controlling local distributed energy resources in residential/commercial buildings. The solar PV generation signal is divided into three components: high frequency (second-level), medium frequency (minute-level), and low-frequency that correlate with the solar activity. One year of solar PV power data is analyzed with 1-second resolution to find the ideal bounds for the different frequency bands. Results show that by employing intelligent control of Heating, Ventilation and Air-Conditioning (HVAC) systems, HVAC loads are able to accommodate the low and medium frequency components of the PV generation while local energy storage systems can be used to offset the high frequency components. This demonstrates the ability to spatially-local consumption of PV generation using controllable loads so as to minimize impact on the grid, reduce size of storage devices, and increase solar PV penetration levels.

Olama, Mohammed M.↗

Integrated Optimization and Control of a Hybrid Gas Turbine/sCO 2 Power System

During phase-I, the project team led by Echogen Power Systems (EPS) had two primary objectives based on investigating the application of gas turbines with supercritical carbon dioxide (sCO 2 ) power cycles. The first objective was to improve the overall efficiency and performance of a hybrid gas turbine/sCO 2 power system through a joint optimization of the two subsystems (gas turbine and sCO 2 power cycle) using non-linear optimization techniques that simultaneously evaluate thermal performance of the combined cycle. The hybrid power system included several points of interaction, including (but not limited to) gas turbine exhaust, fuel heating, inlet chilling and turbine cooling. The second objective was to establish a baseline transient response model of the hybrid power system and a notional microgrid and begin steps to integrate the control systems of the three major elements (gas turbine, sCO 2 cycle and grid controller). The project team established a baseline performance for a combined cycle power plant using a production gas turbine and scaled sCO 2 power cycle only utilizing exhaust heat recovery. Echogen’s non-linear techno-economic optimization code was extended by adding gas turbine component models derived from a in-house developed gas turbine design code. With the two cycles coupled by the gas turbine exhaust, design parameters of both cycles were allowed to vary simultaneously to determine performance opportunity versus isolated designs. Returning to the baseline gas turbine/sCO 2 power cycle transient models: Echogen had in-house developed sCO 2 cycle transient model in GT-Suite system simulation software, and had partnered with Siemens Finspång for gas turbine transient model, and Siemens PTI group to provide micro-grid load profile as well as hybrid power cycle generated load (power and frequency) analysis. The transient model for the SGT-750 Siemens gas turbine was a “black-box” functional mock-up interface (FMI) model developed by Siemens Industrial Turbomachinery in Finspång, Sweden. The SGT-750 is a twin-shaft gas turbine that produces 40 MW electricity with an efficiency of about 40% at ISO conditions. At 100% gas turbine throttle (load), the SGT-750 has average exhaust conditions of 114.6 kg/s and 469.8°C. The transient model for sCO 2 power cycle was developed by Echogen in GT-SUITE 1D system simulation software platform. The basic CO 2 flow circuit has single-shaft turbomachinery with net 11.5 MW electrical power output at design conditions. The power turbine has a double-ended shaft with one end connected to synchronous generator through a fixed-ratio gearbox. The other end of power turbine is connected to the compressor through a continuously variable transmission. The major components of the sCO 2 power cycle modeled include air cooled condenser/cooler, CO 2 compressor, recuperator, two waste heat exchanger coils, power turbine, continuous variable transmission, gearbox and generator. Integration of SGT-750 transient model and sCO 2 power cycle transient model was done in Matlab Simulink. In the integrated model, the gas turbine and sCO 2 power cycle interacted at two points, first one being the gas turbine exhaust gas flow rate and temperature, which were inputs to sCO 2 power cycle model. The second point was the distribution of micro-grid load demand signal between the SGT-750 generator and sCO 2 cycle generator. For a given combined-cycle load demand, the gas turbine load demand was equal to the total demand minus the sCO 2 cycle power generated. In the present study the integrated model was simulated for two cases of grid load demand: (i) for a step change, both positive-step and negative-step, in grid load demand (ii) for a micro-grid load demand curve provided by Siemens PTI group. Finally, the time series plots representing load demand versus integrated system response were presented including the sCO 2 power cycle control system performance plots. The actual generated power and frequency of both the generators, gas turbine and sCO 2 power cycle, was supplied to Siemens PTI group for dynamic grid assessment, results of which are provided in appendices.

03 NATURAL GAS↗

Graph-based Simulation Framework for Power Resilience Estimation and Enhancement

The increasing frequency of extreme weather events poses significant risks to power distribution systems, leading to widespread outages and severe economic and social consequences. This paper presents a novel simulation framework for assessing and enhancing the resilience of power distribution networks under such conditions. Resilience is estimated through Monte Carlo simulations, which simulate extreme weather scenarios and evaluate the impact on infrastructure fragility. Due to the proprietary nature of power network topology, a distribution network is synthesized using publicly available data. To generate the weather scenarios, an extreme weather generation method is developed. To enhance resilience, renewable resources such as solar panels and energy storage systems (batteries in this study) are incorporated. A customized Genetic Algorithm is proposed to determine the optimal locations and capacities for solar panels and battery installations, maximizing resilience while balancing cost constraints. Experiment results demonstrate that on a large-scale synthetic distribution network with more than 300,000 nodes and 300,000 edges, the proposed framework can efficiently evaluate the resilience, and enhance the resilience through the installations of distributed energy resources (DERs), providing utilities with valuable insights for community-level power system resilience estimation and enhancement.

Wang, Xuesong [Wayne State Univ., Detroit, MI (Uni↗

Tri-level hybrid interval-stochastic optimal scheduling for flexible residential loads under GAN-assisted multiple uncertainties

Various building loads, such as heating, ventilation, and air conditioners (HVACs), electric water heaters (EWHs), and electric vehicles (EVs), can introduce opportunities for improving the flexibility of electricity consumption while satisfying the needs of building owners as well as benefiting the resilience of distribution system. To utilize such flexibility, a tri-level distribution market framework is established, including residential consumers, load aggregators (LAs), and the distribution system operator (DSO). In this work, the uncertainties from all three levels are considered. The random consumption behavior at the consumer level is modeled as a Gaussian noise that is also aggregated and transmitted to the LA level. The weather temperature in the LA level is forecasted as an interval, and the photovoltaic (PV) power in the market-clearing level is modeled by a set of power scenarios generated by Generative Adversarial Networks (GANs). Then, a hybrid interval-stochastic programming is proposed to transform the uncertain problems in the first two levels into deterministic ones. For real-time implementations, a rolling horizon optimization (RHO) scheme is employed to continuously optimize the power consumption based on the latest operating information. Finally, case studies on a modified IEEE 69-bus system validate the effectiveness of the proposed uncertainty modeling strategies and the RHO scheme.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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

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

Co-simulation↗

System and method for islanding detection and prevention in distributed generation

A method for detecting and preventing islanding includes issuing a command to an inverter connected to a power source, where the inverter is coupled to a power grid and supplies power to the power grid, the command causes a frequency of a waveform output by the inverter to vary, and the frequency of the waveform output by the inverter is a command frequency, determining that a amount of change of the command frequency is a constant value for a predetermined amount of time, removing the power supplied by the inverter from the power grid, and determining whether the power grid is valid.

Bhowmik, Shibashis↗

Stability Assessment of a System Comprising a Single Machine and Inverter with Scalable Ratings

From the inception of power systems, synchronous machines have acted as the foundation of large-scale electrical infrastructures and their physical properties have formed the cornerstone of system operations. However, power electronics interfaces are playing a growing role as they are the primary interface for several types of renewable energy sources and storage technologies. As the role of power electronics in systems continues to grow, it is crucial to investigate the properties of bulk power systems in low inertia settings. In this paper, we assess the properties of coupled machine-inverter systems by studying an elementary system comprised of a synchronous generator, three-phase inverter, and a load. Furthermore, the inverter model is formulated such that its power rating can be scaled continuously across power levels while preserving its closed-loop response. Accordingly, the properties of the machine-inverter system can be assessed for varying ratios of machine-to-inverter power ratings and, hence, differing levels of inertia. After linearizing the model and assessing its eigenvalues, we show that system stability is highly dependent on the interaction between the inverter current controller and machine exciter, thus uncovering a key concern with mixed machine-inverter systems and motivating the need for next-generation grid-stabilizing inverter controls.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Surrogate Model for Distribution Networks Influenced by Weather

Here, we propose a method for generating reduced representations of time series and for constructing low dimensional surrogate models for time dependent calculations of power and voltage in distribution networks. We employ Fourier polynomials. The surrogate model strategy is aimed at reducing the computational cost of time dependent simulations, albeit, at the expense of fidelity. The reduced representation is achieved by identifying a small and most consequential subset of degrees of freedom. In power and voltage distribution networks dynamics that are heavily influenced by strong cyclic weather events, e.g., the hourly, diurnal and seasonal cycles, the weather/climate time series spectrum exposes these most energetic components. Once the degrees of freedom are identified their amplitudes are optimized using training data. The key challenge in using spectral methods in power network surrogates is addressing the computation of quotients. For this we propose a numerically-stable deconvolution strategy.

Weather events↗

Distributed Energy Management for Networked Microgrids Using Online ADMM With Regret

We propose a distributed algorithm for online energy management in networked microgrids with a high penetration of distributed energy resources (DERs). A high penetration of DERs introduces high uncertainty of power generation to the microgrids. In general, the state-of-the-art forecasting for non-dispatchable DERs such as solar energy is not sufficiently accurate, which results in inaccurate energy scheduling. To address the high uncertainty issue in the networked microgrids, we propose an online energy management based on the online alternating direction method of multipliers algorithm with the past power generation information from the DERs. The online algorithm provides less conservative schedule than the robust optimization-based approach. The effectiveness of the proposed algorithm is verified by various numerical examples.

alternating direction method of multipliers↗

Current Practices in Distribution Utility Resilience Planning for Winter Storms

This report is part of a series of hazard-focused case studies examining common practices in electric utility resilience planning. We use standard terminology defining resilience as the ability to anticipate, withstand, absorb, and recover from hazards that cause long duration outages. We distinguish between reliability and resilience using Institute of Electrical and Electronics Engineers (IEEE) 1366-2022, which defines major events as an event that exceeds reasonable design and/or operational limits of the electric power system. Resilience planning is focused on major event days and reliability planning is focused on nonmajor event days. Utility resilience plans are assessed according to common resilience components identified in existing resilience frameworks. The focus of this report is on winter storms in which the primary hazards are heavy snowfall, freezing rain, ice, extreme cold, severe wind, and flooding. These hazards can also contribute to generation shortages, resulting in bulk power system impacts that have consequences for the distribution system, such as load shedding. Stand-alone reports focusing on wildfires and nonwinter storms have been published in parallel with this report. This report can be used as a starting point for understanding potential investment prioritization processes and investment options. This report is intended to improve utility resilience planning by supporting constructive dialogue among utilities, regulators, and other stakeholders.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Impacts of Time Delays on Distributed Algorithms for Economic Dispatch

Economic dispatch problem (EDP) is an important problem in power systems. It can be formulated as an optimization problem with the objective to minimize the total generation cost subject to the power balance constraint and generator capacity limits. Recently, several consensus-based algorithms have been proposed to solve EDP in a distributed manner. However, impacts of communication time delays on these distributed algorithms are not fully understood, especially for the case where the communication network is directed, i.e., the information exchange is unidirectional. This paper investigates communication time delay effects on a distributed algorithm for directed communication networks. The algorithm has been tested by applying time delays to different types of information exchange. Several case studies are carried out to evaluate the effectiveness and performance of the algorithm in the presence of time delays in communication networks. It is found that time delay effects have negative effects on the convergence rate, and can even result in an incorrect converge value or fail the algorithm to converge.

Yang, Tao↗