Search NASASearch

SEARCH · Search NASA

Results for “dispatch modeling”

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.

140 records · Page 8

Artificial Intelligence-Driven Management of Sustainable Energy Resources: Visibility, Operation, and Control

The rapid global transition toward sustainable energy resources (SERs) is reshaping how modern power systems are observed, optimized, and controlled. While SERs have significantly advanced decarbonization, their weather dependence, variability, and inverter-dominated characteristics challenge traditional, centralized, and deterministic grid operation. At the same time, the proliferation of high-resolution data from inverters, smart meters, and sensors offers unprecedented visibility into system dynamics. Yet, it also exceeds the analytical capability of conventional model-based approaches. Artificial intelligence (AI) provides a new foundation for addressing these challenges by bridging physical laws with data-driven learning, enabling accurate state awareness, adaptive operation, and coordinated control across distributed assets. This article examines how AI transforms the management of SER-rich power systems along three critical dimensions: 1) enhancing visibility by inferring behind-the-meter (BTM) activities, assessing SER flexibility, and reconstructing system states from sparse or noisy measurements; 2) improving operation through AI-enhanced SER service provision, volt/var control (VVC), and dynamic operating envelopes (DOE) for efficiency and security; and 3) advancing control by embedding learning-based intelligence into inverter coordination, voltage and frequency regulation, and long-term dispatch. Together, these developments reveal how AI can convert the variability of SERs from an operational challenge into a source of flexibility, resilience, and intelligence, paving the way toward sustainable, adaptive, and self-optimizing power systems.

24 POWER TRANSMISSION AND DISTRIBUTION

Use of Digital Real-Time Simulation and Optimization to Identify Maximum Real Power Injection on the Banshee Distribution Network: Preprint

This study investigates the hosting capacity of the Banshee Distribution Network by optimizing the real power injection at carefully selected Distributed Energy Resource (DER) locations. The analysis is conducted within the framework of power system operational constraints, including bus voltage ranges, thermal line ratings, and transformer loading limits. A Python-based Genetic Algorithm (GA), implemented using the PyGAD library, is employed to iteratively identify the optimal power injection configuration that maximizes network utilization while preserving system reliability. The methodology integrates a real-time simulation environment using the Real-Time Digital Simulator (RTDS), allowing high-fidelity evaluation of power flow and voltage behavior under each proposed injection scenario. By coupling the optimization algorithm with real-time simulation feedback, this approach ensures that both static and dynamic constraints are enforced during the evaluation process. The GA leverages evolutionary operators such as selection, crossover, and mutation to navigate the nonlinear search space efficiently. The results of the study delineate the feasible hosting capacity at three targeted buses, reflecting maximum real power levels that can be injected without causing voltage violations, transformer overloading, or line congestion. These findings provide a decision- support tool for distribution planners and utilities aiming to integrate higher penetrations of DERs in existing infrastructure. Additionally, the work lays the foundation for extending such optimization techniques to multi-objective formulations, including economic dispatch and reactive power coordination, in future studies.

24 POWER TRANSMISSION AND DISTRIBUTION

Reinforcement Learning‐Based Adaptation of Grid Following Inverter's Internal Controller to Networked Microgrids' Strengths

The varying topological configurations, generator commitments and dispatches, and dynamic load demand lead to changing system's strengths during the operations of networked microgrids. When the system's strengths significantly change, the fixed control gains at large devices may result in unsatisfactory system performance; this necessitates the tuning of the control gains at large devices to adapt to the changing system's strengths. In this paper, observer-based reinforcement learning (RL) is utilised to automatically tune the proportional-integral (PI) gains of phase lock loop (PLL) controller of grid-following (GFL) inverters to adapt to the changing strengths of microgrids and networked microgrids. The RL agent in this framework augments an observer predicting system's strengths, from which the RL control policy will adjust accordingly to tune the PLL controller's gains towards the system's strengths. Also, to enhance the control performance, the recently introduced Barrier function-based RL framework is leveraged for the design of reward function to prevent the high frequency nadir. An operational 26 kV electric distribution system, which is modelled as networked microgrids, is used to illustrate the need and effectiveness of the proposed RL-tuned control.

frequency response

Low-Cost Sulfur Thermal Storage for Solar Industrial Process Heat Applications

Industrial process heat (IPH) is one of the largest energy demands in U.S., representing about 10% of all domestic energy consumption. Fuel costs to generate this industrial process heat are generally a top three cost for industry, a major component in American manufacturing competitiveness. Roughly 60% of US IPH demand (about 6,500 TBtu annually) falls in the medium-temperature range of 100–250 °C. While concentrated solar thermal (CST) technologies can provide a cost-effective source of heat in this temperature range, solar intermittency limits their adoption in industries that operate 24/7. Element 16 Technologies, Inc. developed a low-cost sulfur thermal energy storage (TES) technology to bridge this gap by capturing excess solar heat during the day and dispatching it reliably during non-solar hours. The core innovation is the use of sulfur, an abundant, industrial waste byproduct that costs ten times less than molten salt used in commercial TES systems. The overall goal of the project was to advance the design and development of molten sulfur TES to a manufacturing-relevant prototype stage for solar industrial process heat applications, while establishing and validating a realistic pathway to commercial success. Key tasks included corrosion and mechanical durability testing to identify cost-effective materials, design investigations using physics-based simulation tools, techno-economic evaluations of system lifetime costs, and pilot-scale testing for performance verification. Corrosion testing of steel alloys under cyclic molten sulfur conditions showed that austenitic stainless steels in the 300 series performed particularly well, with no structural degradation of welds or joints. Thermal cyclic testing of pilot sulfur TES units up to 1.5 MWh quantified charge/discharge rates, heat losses, round-trip efficiency and validated the system's capability to operate effectively under intermittent charging conditions. A techno-economic model, informed by sulfur TES performance model validated using pilot test data, showed that hybrid solar+sulfur TES+NG boiler systems are economically competitive with incumbent natural gas boilers for multiple locations in the southwest US. In summary, this project established molten sulfur TES as a technically viable pathway to improve economic competitiveness of American manufacturing by lowering the cost of solar industrial process heat.

14 SOLAR ENERGY

Use of Digital Real-Time Simulation and Optimization to Identify Maximum Real Power Injection on Banshee Distribution Network

This study investigates the hosting capacity of the Banshee Distribution Network by optimizing the real power injection at carefully selected Distributed Energy Resource (DER) locations. The analysis is conducted within the framework of power system operational constraints, including bus voltage ranges, thermal line ratings, and transformer loading limits. A Python-based Genetic Algorithm (GA), implemented using the PyGAD library, is employed to iteratively identify the optimal power injection configuration that maximizes network utilization while preserving system reliability. The methodology integrates a real-time simulation environment using the Real-Time Digital Simulator (RTDS), allowing high-fidelity evaluation of power flow and voltage behavior under each proposed injection scenario. By coupling the optimization algorithm with real-time simulation feedback, this approach ensures that both static and dynamic constraints are enforced during the evaluation process. The GA leverages evolutionary operators such as selection, crossover, and mutation to navigate the nonlinear search space efficiently. The results of the study delineate the feasible hosting capacity at three targeted buses, reflecting maximum real power levels that can be injected without causing voltage violations, transformer overloading, or line congestion. These findings provide a decision- support tool for distribution planners and utilities aiming to integrate higher penetrations of DERs in existing infrastructure. Additionally, the work lays the foundation for extending such optimization techniques to multi-objective formulations, including economic dispatch and reactive power coordination, in future studies.

24 POWER TRANSMISSION AND DISTRIBUTION

Interregional Transmission Operational Coordination (IRTOC)

This report presents a modeling and evaluation framework developed through the Inter-Regional Transmission Operational Coordination (IRTOC) project to study market-to-market (M2M) congestion management across day-ahead and real-time markets. The framework extends the Sienna platform through Sienna Decomposition, a multi-stage evaluation architecture that enables flexible representation of multiple regions and systematic assessment of alternative market coordination designs. Additional modeling capabilities include reserve deliverability constraints, High-Voltage Direct Current (HVDC) optimization for Alternating Current (AC) congestion management, and several real-time distributed coordination algorithms. Case studies using the RTS-GMLC test system and a large-scale Eastern Interconnection model demonstrate that the framework can evaluate alternative coordination structures and quantify their economic and operational impacts. The proposed framework provides a scalable platform for analyzing inter-regional coordination strategies in large-scale electricity markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY

Characterizing and improving the performance of molten-salt-steam heat exchangers in concentrating solar power plants

Shell-and-tube heat exchangers (HXs) for steam generation from molten salts in concentrating solar power (CSP) plants experience thermal fatigue due to significant temperature gradients and inherent transient operation. Molten salt-steam HX design lifespans exceed actual lifespans, and, as a consequence, designers overpredict plant profitability and operators neglect appropriate prescriptions to optimize these lifetimes. Here, this study refines HX lifespan estimates with data benchmarked against thermal-fluid mechanical modeling of stress and accumulated fatigue. Reduced-order thermal models of the molten salt-steam, shell-and-tube evaporator and superheater predict transient temperature profiles along the two HXs salt-steam flow paths. The modeled evaporator and superheater temperature profiles enable assessment of cyclic stresses within the HX tubesheets, where molten-salt HX failures are most common. Evaporator and superheater performance data from a current 110 MW elec commercial CSP plant provide a basis for validating the reduced-order HX models. HX life predictions derived from stochastic failure distributions serve as inputs for simulating and optimizing existing plant operations. The impact of the updated lifespans on overall plant revenue depends on operating scenarios. This study suggests that typical ramping rates for a CSP plant with a high-temperature Rankine cycle result in an evaporator and superheater life of approximately 10 and 25 years, respectively, compared to the design target of 30 years. Reduced HX lifespans decrease operational plant revenue on average by 4.6-5.1%. Furthermore, there may be as many as four HX replacements over the 30-year lifetime of the plant; and, purchase agreement loss due to failure to meet contractual production requirements can have ramifications that include the risk of bankruptcy.

14 SOLAR ENERGY

Average and Marginal Capacity Credit Values of Renewable Energy and Battery Storage in the United States Power System

As deployment of renewable resources and storage continue to significantly grow in the coming decades, these technologies will play increasingly important roles in maintaining power systems' resource adequacy. Few analyses so far offer comprehensive comparisons of forward-looking average and marginal capacity credits of variable renewable energy and storage in the U.S. interconnections across a wide range of possible futures. To fill this research gap, we quantify the average and marginal capacity credits of solar PV, onshore and offshore wind, and batteries between 2026 and 2050 across the U.S power systems to examine the temporal trends, spatial patterns, and trade-offs between these two capacity accreditation approaches. Across technologies, capacity credits of solar PV most clearly follow downward trends over time, reflecting the significant rise in solar PV generation share as the grid decarbonizes. While battery storages' generation shares also rise significantly over time, their capacity credits always remain stably high due to their capabilities to be dispatched strategically during critical periods to maintain reliability. On the other hand, capacity credits of wind technologies in general follow slight upward trends as their generation shares level off. There are strong spatial variabilities of both average and marginal capacity credits across technologies, but capacity credits of solar PV displaying the most obvious spatial patterns with high capacity credits concentrating in wind-rich, solar-poor regions in SPP, PJM, and MISO, suggesting potential reliability benefits of interconnection-wide planning for renewable energy deployments. Additionally, except for offshore wind, average capacity credits of all other renewable technologies tend to be higher than their marginal capacity credits, indicating that existing renewable resources tend to be accredited higher than new resources at almost any time.

25 ENERGY STORAGE

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION

The value of hydropower flexibility for electricity system decarbonization

Hydropower is an abundant, dispatchable, clean energy resource that will play an important role in supporting the clean energy transition. In particular, dispatchable hydropower can provide the operational flexibility that will be required in future systems with high variable renewable energy penetrations. However, the theoretical operational flexibility of hydropower can be restricted in practice by various non-power constraints. In this paper, we quantify how increasing the operational flexibility of dispatchable hydropower resources with reservoirs impacts least-cost generation portfolios and supports power system decarbonization. Specifically, we conduct a capacity expansion analysis of a two-zone system: a hydro-dominated region and a neighboring region with aggressive decarbonization targets that are represented by the United States Pacific Northwest and California respectively. We then introduce a quantifiable index for characterizing the operational flexibility of reservoir hydropower and assess how changes in this metric impact the system-optimal generation portfolio. We find that increasing hydropower flexibility leads to more investment in wind generation, less investment in natural gas generation, lower system costs, and lower system emissions. We further demonstrate a substitution effect between the grid services provided by flexible hydropower operation, increased transmission capacity on a congested line, and energy storage resources. Finally, we show that increasing the operational flexibility of hydropower increases the effective load carrying capability of both hydropower and wind resources. This research supports a more nuanced understanding of how hydropower can support electricity system decarbonization and may motivate reassessing the cost-benefit tradeoffs of non-power constraints that restrict operational flexibility.

Capacity expansion modeling

Hazard and risk analysis framework for nuclear power plant–based integrated energy systems

Employing integrated energy systems (IESs) with nuclear power plants (NPPs) can improve NPP utilization by leveraging dedicated thermal and electric power delivery, but it may also increase operational safety risks. This paper presents a framework to identify and quantify hazards and risks for such IESs. The framework combines accidentology to review past industrial accidents with failure modes and effects analysis (FMEA) to identify potential future incidents. Hydrogen explosion and toxic chemical release hazards are of particular concern. Explosion consequences are quantified using the Bauwens-Dorofeev (Bauwens) and trinitrotoluene equivalent mass (TNT-EM) methods, while chemical release consequences are computed using the Gaussian atmospheric dispersion method. Operational disturbances from direct electrical and thermal integration that may affect NPP safety are modeled using probabilistic risk analysis (PRA). Hazards and risks are then evaluated for regulatory compliance. The framework is applied to IESs comprising pressurized or boiling water reactors supplying three levels of thermal and electrical power to industrial customers. Case studies include high-temperature steam electrolysis hydrogen plants of varying capacities and a synthetic fuel production plant. Sensitivity analysis examines piping component failures in the PRA model as a precursor to cost estimation for thermal extraction line design. Additionally, Fussel-Vessely (FV) and risk increase importance (RII) measures identify risk-informed design improvements for the thermal extraction system. FMEA highlights hazards such as loss of offsite power, prompt loss of electrical load, loss of thermal output, and immediate steam diversion, in addition to hydrogen explosions and toxic chemical releases. Both Bauwens and TNT-EM methods suggest maintaining several hundred meters of separation between the NPP and hydrogen facility to mitigate explosion risks. PRA results show a maximum initiating event frequency increase of 1.15% and an overall risk increase of 0.28%. Importance measure analysis identifies upstream pipe leak isolation components as critical. Evaluating the results against safety regulations, it is concluded that hazards and risks can be managed to comply with regulations through risk-informed thermal and electrical connection designs, component selection, maintenance programs, and safe separation distances between NPPs and integrated industrial facilities.

08 - HYDROGEN

How Improved Forecasting Can Increase the Bulk Power System Value of Price-Responsive Electric Vehicle Managed Charging

Personal light-duty vehicle (LDV) electric vehicle managed charging (EVMC) can reduce power system costs by better aligning electric vehicle (EV) charging with locations and times of low energy cost or infrastructure use. The need to coordinate charging demand across thousands to millions of vehicles while preserving mobility service is a barrier to realizing the value of EVMC. Price-responsive dispatch mechanisms like time-of-use rates (TOU) and hourly real-time prices (RTP) are attractive compared to direct load control (DLC) because they only require one-way communications and local controls. However, increasing participation in price responsive mechanisms can induce costly-to-serve spikes in load and otherwise increase, rather than decrease, production costs. We quantify the ability of improved EVMC forecasting to sustain savings from price responsive mechanisms beyond the limit of 14% of LDVs actively participating observed in previous work. Perfect forecasting of price-responsive EV load makes TOU and RTP value-competitive with a low-error DLC formulation with up to 27% (within-week flexibility) to 45% or more (within-session flexibility) of LDVs participating in EVMC in an envisioned New England power system with 84% clean energy. Additional costs of implementing DLC should be no more than tens of dollars per vehicle-year if DLC is to be value-competitive with accurately forecast price-responsive EVMC for double-digit percentage shares of LDVs participating.

29 ENERGY PLANNING, POLICY, AND ECONOMY

Systems Analysis of Biomass and Coal Co-firing Power Plants with Deep Carbon Capture Toward Net-zero Emissions

Achieving a net-zero emission economy in the United States requires integrating diverse low-carbon and negative-emission technologies into the existing fossil fuel-dominant power fleet. Potential technologies from the low-carbon portfolio include renewable power, fossil power with carbon capture and storage (CCS), bioenergy with CCS (BECCS), and direct air capture (DAC). Renewable power is a clean energy source but has to pair with costly battery storage to provide dispatchable electricity. Fossil power with CCS offers dispatchable electricity yet still relies on DAC to offset residual emissions, even when deploying deep CCS with more than 90% CO2 capture. Coal-biomass co-firing with CCS, a subset of BECCS, is a reliable energy production technology that can be retrofitted from existing electricity generation units (EGUs). Power plant retrofit maximizes the use of the current U.S. coal power fleet without the need for large-scale deployment of new renewable power, battery storage, or DAC. Retrofitting coal-biomass co-firing with deep CCS in EGUs is a promising option, but not a universal solution. Biomass co-firing at a power plant introduces economic challenges and indirectly poses pressure on land and water resources. Meanwhile, retrofitting deep CCS affects plant efficiency and raises electricity generation costs. Overall, the technical feasibility and economic viability of plant retrofits vary across EGUs, as they are contingent upon the regional availability of biomass, unit-specific characteristics, site-specific fuel supply costs, and adjacent CO2 storage potential. Government incentives like 45Q can improve the retrofit viability, though the impact requires further quantification. A comprehensive analysis at the unit level is essential to address the question regarding the fate of the U.S. coal-fired electricity generation fleet toward the net-zero emission goal. This study conducts a systematic techno-economic-environmental assessment of EGUs to identify the viability of biomass co-firing and deep CCS retrofits in the U.S. coal-fired power fleet. Specifically, it characterizes the techno-economic performance of deep carbon capture, estimates life cycle greenhouse gas (GHG) emissions, and conducts a fleet-level assessment on retrofit viability. The key objectives are (1) to estimate the unit-specific performance and retrofitted cost under various biomass co-firing levels and CO2 capture rates; (2) to determine the possibility of reaching net-zero emission at the fleet level; (3) to quantify the cumulative capacities that are suitable for plant retrofits under current and future biomass supply scenarios; and (4) to improve the understanding of policy impacts on such retrofits to help the power sector’s transition to a net-zero economy. Techno-economic Model of Deep Carbon Capture. This study develops the performance and economic models for Monoethanolamine-based post-combustion CO2 capture at 95–99% capture rates. The process is simulated in Aspen Plus, analyzing the performance of carbon capture technology by varying the plant sizes, solvent lean loading, CO2 concentrations, and flue gas inlet temperature. Based on the key inputs and output parameters of CO2 capture, a reduced-order performance model of deep carbon capture is formulated. In addition, an engineering-economic model integrating the performance metrics is developed to estimate the capital as well as operation and maintenance (O&M) costs. Capital cost estimations follow the framework of the Integrated Environmental Control Model (IECM) and incorporate data regressions from three technical reports by IECM, the National Energy Technology Laboratory (NETL), and the National Renewable Energy Laboratory. The O&M cost estimation utilizes the actual inventory consumption rate and labor requirements. Both performance and cost models are embedded into IECM v13.0-beta, a fossil-fuel power plant modeling tool. Life Cycle Assessment of Power Plants. This study estimates the GHG emissions of power plants through life cycle assessment (LCA). The LCA scope includes fuel supply, combustion-based power generation, and CO2 transport and storage. The fuel-based life cycle module is designed following the framework of the NETL Unit Process Library and CO2U LCA Guidance Toolkit. The module is then incorporated into IECM v13.0-beta. The process-based LCA is applied to estimate the GHG emissions of coal and biomass supply, coal- and coal-biomass co-firing power plant operation, as well as CO2 pipeline transport and geographical sequestration. An uncertainty analysis is conducted to quantify the variability and uncertainty associated with the LCA using the Latin Hypercube Sampling (LHS) method. Fleet-level Assessment. This study evaluates the technical and economic feasibility of selected coal-fired EGUs, examines the role of tax credits in retrofit viability, and assesses the competitiveness of retrofitted units against other low-carbon options. Unit screening identifies EGUs for the study, focusing on new, efficient baseload units with air pollution controls. The power plant databases are then established to organize unit-specific information on performance and operating conditions from the relevant public databases. Biomass for co-firing retrofits is selected based on home and neighboring county availability, ensuring sustained operation with at least a 5% co-firing level. The CO2 storage site is determined by state-level storage potential, with ArcGIS Pro and NETL CO2 Saline Storage Cost Model used to identify the optimal balance between the nearest transport distances and affordable storage costs. The latest IECM v13.0-beta is then employed to configure and evaluate the eligible EGUs with or without the deployment of deep CCS and biomass co-firing. A supply curve is established to illustrate the cumulative installed capacity suitable for retrofits at different cost levels. A sensitivity analysis on tax credits for carbon sequestration is performed. Finally, a unit-level cost comparison is conducted among retrofitted plants, renewable power with battery storage, and abated fossil fuels with DAC. Expected Results. This study evaluates the technical, economic, and environmental metrics of each EGU across an array of CO2 capture rates and biomass co-firing level scenarios. Unit-level comparisons will identify critical factors influencing technical performance. The supply curves with and without tax incentives will provide insights into the impact of tax credits on biomass co-firing and CCS deployment. The cost comparisons with renewables and DAC-retrofit will assess the competitiveness of the retrofitted units. Life cycle emissions from each unit will be assessed to identify the scenarios under which net-zero emissions can be achieved. These analyses are expected to determine the total coal-fired capacity suitable for serving as a low-carbon energy source with or without tax incentives. The study results are novel in identifying optimal unit-specific strategies for producing carbon-neutral power, whether through retrofitting EGUs with deep CCS, biomass co-firing, DAC, or installing renewable power with battery. The findings will provide insight into nationwide efforts to ensure reliable, affordable, and low-carbon electricity. It also will inform investment decisions and policies in the deployment of deep carbon capture and negative emission technologies for a net-zero energy future.

Biomass Co-firing

Parallel derivative-free optimization for simulation-based design of behind-the-meter energy systems

In this work, the integrated design and dispatch of behind-the-meter or distributed resources (e.g. stationary battery storage and solar PV generation) is considered. A simulation-based framework is employed, generating high-fidelity results with closed-loop predictive control at a fine resolution, at the expense of high computational cost (several minutes to a few hours per design point). To address this challenge, parallel derivative-free design methods are considered. Four methods are compared, including state-of-the-art surrogate-based methods (Radial-Basis Functions and Gaussian processes) and sampling strategies, an evolutionary-based method, and a simple sequential grid refinement method. As a case study, two types of design problem with increasing complexity are considered, namely, the design of behind-the-meter resources (three design variables) and the inclusion of grid capacity (four design variables). The second yields a constrained design problem for which violations can only be determined after solving the computationally expensive simulation. For the three-dimensional case, all methods present a good performance, achieving a solution within 1% of the optimum after the first iteration, with the sequential grid refinement exhibiting the fastest convergence and achieving the best final objective value. This indicates that the parallel evaluation of multiple sampling points may be more important than the choice of method for small decision spaces. For the four-dimensional constrained case, the Genetic Algorithm presents the best tradeoff between performance and computational effort, while the rough objective function terrain generated by constraint violation penalties reduces the performance of surrogate-based methods. Contour plots with flat regions indicate flexibility in the optimal design and highlight the importance of characterizing the solution space.

24 POWER TRANSMISSION AND DISTRIBUTION