Turbine Power Generation Research Articles

Catch the wind: Optimizing wind turbine power generation by addressing wind veer effects.

Wind direction variability with height, known as "wind veer," results in power losses for wind turbines (WTs) that rely on single-point wind measurements at the turbine nacelles. To address this challenge, we introduce a yaw control strategy designed to optimize turbine alignment by adjusting the yaw angle based on specific wind veer conditions, thereby boosting power generation efficiency. This strategy integrates modest yaw offset angles into the existing turbine control systems via a yaw-bias-look-up table, which correlates the adjustments with wind speed, and wind veer data. We evaluated the effectiveness of this control strategy through extensive month-long field campaigns for an individual utility-scale WT and at a commercial wind farm. This included controlling one turbine using our strategy against nine others in the vicinity using standard controls with LiDAR-derived wind veer data and a separate 2.5 MW instrumented research turbine continuously managed using our method with wind profiles provided by meteorological towers. Results from these campaigns demonstrated notable energy gains, with potential net gains exceeding 10% during extreme veering conditions. Our economic analysis, factoring in various elements, suggests an annual net gain of up to approximately $700 K for a 100-MW wind farm, requiring minimal additional investment, with potential for even larger gains in offshore settings with the power of individual turbines exceeding 10 MW nowadays. Overall, our findings underscore the considerable opportunities to improve individual turbine performance under realistic atmospheric conditions through advanced, cost-effective control strategies.

EFFECT OF CERAMIC MATRIX COMPOSITES ON THE THERMAL EFFICIENCY OF A POWER GENERATION TURBINE

Abstract Ceramic Matrix Composites (CMCs) offer higher allowable temperatures and reduced weight, making them an attractive prospect for parts in the hot section of a gas turbine engine. As CMCs are increasingly adapted into aero and land-based engines, there is a need to quantify the performance increase based on potential for reduced cooling and increased firing temperatures. In this work, two hot section components – the first stage turbine vane and tip shroud (outer casing above the blade) - of a mid-sized power generation engine were modeled. Informed approximations about part geometry and cooling architectures were made to determine cooling requirements of each part. Thermal boundary conditions for the turbine tip shroud and turbine vane were generated as a function of coolant mass flow rate using data from literature and applied to a 2D finite element analysis model to determine maximum temperatures for both metallic and ceramic materials. A gas turbine cycle model was developed to simulate the performance of a mid-sized power generation turbine, and used to determine increase in efficiency due to reduction in cooling requirement for the CMC part. Potential reduction in chargeable cooling seen for the tip shroud was between 0.09% and 0.4% of the compressor mass flow rate, which corresponds to an increase in thermal efficiency between 0.11% and 0.45%. A similar analysis of the turbine vane resulted in a cooling reduction of 10.71% at the maximum thermal load considered which corresponds to a 3.4% increase in thermal efficiency.

A Novel Day-Ahead Optimization-Oriented Low-Carbon Economic Scheduling Scheme for Integrated Energy Systems

As the global energy structure undergoes transformation and the low-carbon development process continues to advance, integrated energy systems have progressively emerged as crucial technical support for achieving sustainable development. In this paper, a joint-day optimal scheduling model is put forward considering the existence of dispatchable resources in community integrated energy systems (CIES). The aim is to cut down the system operation cost and enhance energy utilization efficiency. This model is founded on the concept of energy hubs and combines the shiftable, transferable, and reducible characteristics of demand-side flexible loads. It includes gas turbine power generation systems, energy storage, as well as wind and solar renewable resources. System operation cost and carbon trading cost are comprehensively taken into account, and ultimately, the CIES low-carbon economic dispatch model with the lowest total cost as the optimization objective is established. The Yalmip toolbox and Cplex solver are employed to solve the model. The optimization results of flexible electric and thermal loads participating in dispatching under different scenarios are analyzed through simulation. The economic benefits of electric and thermal independent dispatching are compared and analyzed, and the economic benefits of electric and thermal coupled dispatching are verified. The study reveals that the rational scheduling of user-side flexible loads can notably reduce operating costs, lower the load peak-to-valley difference and carbon emissions, and boost the comprehensive economic and environmental benefits of the system.

Prediction of the Flame Characteristics of an Industrial Gas Turbine Operated With CO2-Diluted Air Through a High-Fidelity Numerical Analysis: A Comparison Between Flamelet Generated Manifolds and Artificially Thickened Flame

Abstract In light of the global commitment to decarbonize industrial processes, carbon capture and storage (CCS) plays a pivotal role in mitigating greenhouse gas emissions from gas turbine (GT) power generation processes. Achieving an efficient GT–CCS coupling requires the employment of high percentages of exhaust gas recirculation (EGR) to maximize the CO2 content at the CCS inlet. Nevertheless, such operating conditions pose critical challenges for conventional combustion systems due to reduced oxygen levels associated with higher EGR, limiting engine operability. To address this challenge, the development of innovative technical solutions is essential to extend the combustor operational capabilities at high EGR rates. For this goal, a significant number of computational fluid dynamics (CFD) simulations are required to identify the flame stability limits across various EGR levels and burner designs. It is imperative, in this context, to minimize computational costs while maintaining high accuracy. In this work, a comprehensive comparative study of an extended version of the flamelet generated manifolds (FGM) and the artificially thickened flame (ATF) model is performed through a large eddy simulation (LES)-based CFD analysis. The investigation is performed within the context of an industrial lean-premixed burner manufactured by Baker Hughes, operating with natural gas and CO2-diluted air at atmospheric pressure. While the extended-FGM has been previously presented by the authors in a study on the same test rig under standard air conditions, the current work aims to extend its application to critical oxygen-depleted conditions, where near-blowout phenomena such as flame liftoff and length elongation may become significantly pronounced. Numerical validation is carried out through a direct comparison of the computed averaged heat release, representing the flame topology, with detailed OH* chemiluminescence images from a test campaign conducted by the technology for high temperature (THT) Lab of the University of Florence. The experimental data will serve as the primary benchmark for assessing the models’ effectiveness in capturing the main dynamics of such critical operating conditions. Furthermore, potential disparities in both thermal and flow fields at the burner exit region between the two models will be discussed.

Numerical Investigation of Archimedes Screw Turbines under Low-Head Conditions

The development of screw turbines for micro-hydro power generation has garnered heightened interest lately, attributed to their capability to perform efficiently despite low head and low discharge. The present numerical work aims to evaluate the prospect of low-head water energy widely available in the Aceh region. In this region, the Archimedes Screw turbine is the most commonly used. In the present numerical study, the characteristics of the Archimedes screw turbine were studied under the constant of the head of 1 meter and the inclination angle of 30o, with the flow rate served as the varying parameter. In the simulation, a three-dimensional numerical investigation of pressure characteristics, flow velocity, and kinetic energy turbulence due to the change in the flow rates was carried out using the Navier-Stokes equations. Next, the turbulence model of K-Epsilon was also implemented. The comparisons between the experimental and the simulation results were carried out to ensure the accuracy of the simulation model, and the results indicated that the changes in flow rates have a marked influence on pressure distribution, the flow velocity field, and turbulent kinetic energy. It was found that the performance of the Archimedes double screw turbine was improved by increasing the flow rate due to the uniform distribution of pressure, flow velocity, and turbulent kinetic energy. Moreover, the optimum condition was achieved in a turbine with 8 screws. Therefore, maintaining the inflow rate is crucial as it significantly impacts the efficiency of the Archimedes Screw Turbine.

Measuring thermal diffusivity and gap conductance in uranium nitride and Zircaloy relevant for microreactor applications

Heat transfer across nuclear fuels and structural interfaces is an important factor for evaluating the performance of nuclear power systems. Specifically, heat generated as nuclear fuel fissions must be transported through the cladding material and through the reactor to reach the steam turbine for power generation. As new microreactor designs emerge, maximizing the efficiency of this heat transfer process becomes crucial to make them commercially viable. This article examines thermal diffusivity and gap conductance in uranium nitride (UN) fuel and Zircaloy-4 (Zry4) cladding using light flash analysis (LFA). Thermal diffusivity measurements were made on monolithic UN pellets and Zry4 exposed to carbon at peak operating temperatures of microreactors and show that carbon ingress has a minimal effect on thermal diffusivity when compared with identical materials not exposed to carbon. Evaluation of gap conductance at the UN-Zry4 interface was done using one-dimensional two-layer thermal transport models as a function of applied pressure. The results show that increasing pressure on the UN-Zry4 interface leads to gains in gap conductance per unit area in fuel-cladding assemblies at microreactor operating temperatures. While many other variables are expected to influence UN-Zry4 interfacial gap conductance (e.g. contact surface roughness, porosity, localized heating, environmental gas pressure), the work offers a demonstration of using a conventional LFA apparatus to determine this parameter at elevated temperatures.

Thermodynamic analysis and optimization of the semi-closed oxy-combustion supercritical CO2 power cycle with blending hydrogen into the natural gas/syngas

The semi-closed oxy-combustion supercritical CO2 (sCO2) cycle is regarded as a promising power cycle featuring the combined advantages of high efficiency and nearly 100 % CO2 capture. Blending hydrogen into fuels has attracted significant attention in the research of gas turbine and internal combustion engine power generation as it contributes to economy-wide decarbonization and bolsters the broader energy sources, especially green hydrogen. The present work carried out the thermodynamic analysis of a semi-closed sCO2 cycle to investigate how the hydrogen content in natural gas or syngas affects the operating parameters and performance. The results show that the energy efficiency decreases with increasing hydrogen content in natural gas whereas the maximum efficiency exists for the syngas with 60 % H2. The key factor is the increasing H2O content in the flue gas caused by adding hydrogen in fuels enhances both the heat-work conversion in the turbine and the heat transfer in the regenerator. The optimal turbine inlet temperature is around 1150 °C, which is the same as the basic cycle. The optimal turbine inlet pressure for natural gas and natural gas with 40 % H2 is both 28 MPa, while the optimal turbine inlet pressure decreases with hydrogen content in syngas. For all the fuels, the optimal turbine outlet pressure becomes lower for the higher hydrogen content. The maximum efficiencies obtained for natural gas, natural gas with 40 % H2, and syngas with 60 % H2 are 56.08 %, 55.52 % and 56.15 %. Finally, it is found that the recompression cycle and the multiple combustor arrangement (reheat cycle) cannot be the effective configuration for the semi-closed oxy-combustion sCO2 power cycle. The heat from the sCO2 recompression conflicts with the compression heat of the ASU, reducing the energy efficiency by 0.27 %, 0.34 %, and 1.23 % for the three fuels, respectively. The limitation of the regenerator allowable temperature requires the reheat cycle to either reduce the turbine inlet temperature or reduce the turbine outlet pressure, decreasing the energy efficiency for natural gas by 1.83 % and 6.38 % due to the reduced turbine output power or significantly increasing compression power.

Development of Detailed and Reduced Chemical Kinetic Models for Ammonia Gas Turbines

Abstract The power generation sector has been recently moving towards decarbonization and there is an increased interest in replacing conventional fossil fuels with fuels that produce reduced/zero carbon emissions. One such fuel is ammonia (NH3). However, ammonia is hard to ignite, has a low flame speed, and produces a significantly large amount of nitrogen oxide (NOx) emissions. Hence, using 100% ammonia as fuel in gas turbines requires significant modifications and the development of novel combustors. Blending hydrogen with ammonia, however, helps in having better control over the combustion properties. Before utilizing hydrogen-blended ammonia in an actual gas turbine combustor, thorough simulation studies are required to evaluate its performance, possible hazards, and emissions. The literature lacks well-validated chemical kinetic models for the combustion of hydrogen-blended ammonia for undiluted mixtures at gas turbine-relevant conditions (~20 bar). Hence, in this work, we develop a detailed chemical kinetic model for hydrogen blended ammonia combustion and validate it with a wide range of experimental data for both dilute and undiluted mixtures relevant to gas turbine operating conditions. The detailed chemical kinetic mechanism was reduced to a smaller version (32 species mechanism) without significant loss in accuracy using the direct relation graph with error propagation (DRGEP) and full species sensitivity analysis. The resultant mechanism can predict a wide range of experimental results with the least cumulative error and will be a valuable tool in CFD simulations that will enable the development of gas turbines for zero-carbon power generation.

Experimental Study of Natural Gas and Hydrogen Co-Firing Characteristics Using Different Types of Single Nozzles of F-Class Practical Gas Turbine Combustors

Abstract Recent research on co-firing natural gas and hydrogen, a carbon-free clean fuel, aims to reduce greenhouse gas emissions from aging gas turbine power generation, a key energy issue. This approach can enhance old gas turbines and increase the proportion of combined cycle power plant utilization as coal-fired power plants in Korea gradually shut down. This study seeks optimal operating conditions for mixed fuels without modifying the F-class gas turbine combustor. Experiments were conducted using four different types of fuel nozzles (F-Class DLN combustors) under varying loads and co-firing rates. The test used actual machine operating conditions from 30% to 100% thermal load, with hydrogen co-fired with natural gas up to 70% at each load. OH high-speed imaging and an OH-PLIF technique analyzed flame structure and characteristics. Dynamic pressure was measured to check combustion instability, and exhaust gas emissions were evaluated for combustion characteristics. Key findings include critical co-firing rates for each nozzle based on NOx emission levels and combustion dynamics. As the hydrogen co-firing rate increased, flame length decreased, and NOx levels rose rapidly beyond 30%vol. Dynamic pressure oscillations showed no significant variations compared to natural gas combustion. This study successfully derived a characteristic operation map for a single nozzle based on the hydrogen co-firing rate.

Global optimization of capacity ratios between electrolyser and renewable electricity source to minimize levelized cost of green hydrogen

This paper presents a novel and effective approach for calculating Levelized Cost of Hydrogen production across the globe, without requiring timely resolved modelling or data. We select characteristic production patterns of photovoltaic and wind turbine power generation based on location qualities indicated by full load hours. These representative patterns are applied worldwide on similar locations to evaluate the proportion of electricity that electrolyzers can use if they have a smaller capacity than the renewable electricity source. Hence, the ratio of capacities is optimized to minimize hydrogen cost. The findings from various worldwide locations reveal that decreasing electrolyzer capacity is economically beneficial across all locations for boosting full load hours and curbing investments, particularly in locations with lower electricity generation. Validation using precise electricity production timeseries in specific locations revealed minimal errors in the methodology, though the quality of the results is impacted by the seasonality index differences between representative and exact location.

Control of wind energy conversion systems with permanent magnet synchronous generator for isolated green hydrogen production

This paper addresses the design and analysis of the control system for a Wind Energy Conversion System (WECS) with a Permanent Magnet Synchronous Generator (PMSG) and its application for isolated green hydrogen production. The designed control maximizes the wind turbine (WT) power generation by regulating the electrolyzer current consumption, where the electrolyzer operates as a controlled load, ensuring power balance in the system and enabling the generation of maximum power from the WECS without the use of any energy storage system. The system involves directly integrating a WECS with an alkaline electrolyzer (AEL), and its configuration includes a WT with a PMSG, an AC/DC voltage source converter (VSC) acting as the generator side converter (GSC), and a DC/DC converter acting as the electrolyzer side converter (ESC) with Maximum Power Point Tracking (MPPT) control for the WT. The proposed control system has been fully modeled and tested through simulations in Matlab/Simulink, demonstrating its reliable performance under variable wind speeds. Simulation results illustrate how, over rated wind speeds, the pitch control limits the rotational speed and power to their maximum values, and at under rated wind speeds, the ESC control regulates the AEL current following the MPPT of the WT, while the GSC control maintains the DC bus voltage at its designated nominal value. Overall, the proposed control system shows robust and effective performance across the entire range of possible operational points, ensuring no wind generation power losses by following the maximum power point.

Multi-device wind turbine power generation forecasting based on hidden feature embedding

In recent years, the global installed capacity of wind power has grown rapidly. Wind power forecasting, as a key technology in wind turbine systems, has received widespread attention and extensive research. However, existing studies typically focus on the power prediction of individual devices. In the context of multi-turbine scenarios, employing individual models for each device may introduce challenges, encompassing data dilution and a substantial number of model parameters in power generation forecasting tasks. In this paper, a single-model method suitable for multi-device wind power forecasting is proposed. Firstly, this method allocates multi-dimensional random vectors to each device. Then, it utilizes space embedding techniques to iteratively evolve the random vectors into representative vectors corresponding to each device. Finally, the temporal features are concatenated with the corresponding representative vectors and inputted into the model, enabling the single model to accomplish multi-device wind power forecasting task based on device discrimination. Experimental results demonstrate that our method not only solves the data dilution issue and significantly reduces the number of model parameters but also maintains better predictive performance. Future research could focus on using more interpretable space embedding techniques to observe representation vectors of wind turbine equipment and further explore their semantic features.

Investigation and optimization into flow dynamics for an axial flow pump as turbine (PAT) with ultra-low water head

When the water downstream is abundant, axial flow pumps are often used as turbines (PAT) for reverse power generation to obtain additional benefits. However, due to the actual water level difference, PAT usually operates at off-design conditions. The CFD technology and entropy production theory were used to study the working performance, flow characteristics, and energy loss mechanism of the blade adjustable axial-flow PAT under a low water head. The results indicate that the strength of the tubular vortex at the pressure surface and the separation position of the tip-leakage-vortex at the suction surface depend on the inlet angle of the blade. The energy loss in the draft tube is influenced by the velocity circulation at the runner’s outlet, which depends on the blade’s outlet angle. Subsequently, the blade inlet and outlet angles in the runner were optimized. In turbine mode, the overall efficiency of the optimized runner increased by an average of 0.99 %. The blade pressure load distribution of the optimized runner has improved, and the pressure fluctuation in the draft tube is also under control. In pump mode, due to the increasing of the inlet angle within the same demand pump head range, the optimized runner’s pumping flow increases by an average of 2 m3/s.

An Approach to Improve Power System Resiliency in Grid-Connected Wind Turbine Generator Power System

An Approach to Improve Power System Resiliency in Grid-Connected Wind Turbine Generator Power System

Data-driven fault detection framework for offshore wind-hydrogen systems

Offshore wind-hydrogen systems operate in harsh marine environments for extended periods, posing risks of low accessibility and high failure rates. This paper proposes a data-driven fault detection framework for offshore wind-hydrogen systems, aiming to promptly detect potential faults based on the system's physical parameters. The research establishes a comprehensive model based on the operating principles of offshore wind-hydrogen systems. The study uses fault injection techniques to simulate common partial faults in offshore wind-hydrogen systems and collects relevant physical parameters (such as wind turbine power generation, energy storage battery charging/discharging current, and electrolyzer hydrogen production rate). A fault detection model was constructed using a combination of Convolutional Neural Networks (CNN) and Bidirectional Long Short-Term Memory (BiLSTM) to enable precise detection of potential faults in the system. The established model provides theoretical support for designing, optimizing, and operating offshore wind-hydrogen systems, reducing reliance on actual experiments and lowering project risks and costs. Introducing artificial faults can evaluate the system's performance in different fault scenarios. This paper proposes a CNN-BiLSTM fault detection method that achieves automatic feature extraction and high-precision classification of time-series fault data, confirming the practicality and feasibility of offshore wind-hydrogen systems. This investigation realizes the integration of the offshore wind-hydrogen system model and deep learning, as well as a fully automated learning process from data to fault detection. By calculating and comparing results, it is verified that the framework has a high accuracy of 96.9%. This innovative research offers new methods and perspectives for enhancing the reliability and efficiency of fault detection in offshore wind-hydrogen systems.

Emissions reduction in LNG production facilities through emerging post-combustion carbon capture and storage technologies

The liquefied natural gas (LNG) sector relies extensively on gas turbines for on-site power generation and to drive refrigeration compressors. They provide an efficient and reliable energy source for LNG operations in remote locations. With upcoming changes to the Safeguard Mechanism in Australia, there is an increased focus on Scope 1 emissions, so management and targeted reduction are a priority to reduce liabilities. Despite technology advancements, gas turbines remain one of the largest sources of carbon dioxide (CO2) emissions in LNG production facilities. Also, in Australia, many facilities are not grid-connected, meaning that displacement of Scope 1 emissions through renewable electricity sourcing is a challenge. To develop deeper cuts in Scope 1 emissions, one solution is to deploy post-combustion carbon capture and storage (CCS) on existing gas turbines, with the potential to reduce associated emissions by over 90%. Globally, a number of LNG facilities are already deploying CCS to permanently store reservoir CO2 from the LNG processing trains. Several Australian LNG facilities are located in close proximity to potential CO2 storage reservoirs, meaning that a coordinated approach to both reservoir and post-combustion CO2 should be considered when sizing pipelines, shipping systems and storage wells to optimise and leverage the required investment. This paper outlines the technological, economic and policy aspects of integrating both reservoir post-combustion CCS on LNG facilities, including barriers and opportunities for deployment. It will discuss new developments and enablers for CCS to be more widely deployed at LNG production sites.

Optimal sizing of standalone hybrid renewable energy system based on reliability indicator: A case study

The economical electrification of rural settlements extensively utilizes renewable energy sources. In recent years, the deployment of solar photovoltaic, wind turbine, and biomass gasifier-based power generation technologies for electricity accessibility in remote regions has received greater prominence. This paper presents an optimal component design of a hybrid solar PV-wind and battery system along with a biomass gasifier to provide continuous electricity for rural communities of Uttarakhand, India. In this study, a recently developed population-based giza pyramids construction (GPC) methodology is applied to determine the optimal component sizing. The findings of the GPC method are contrasted with the particle swarm optimization (PSO) methodology to assess the effectiveness of the proposed method. The annualized system cost and levelized cost of energy of the hybrid renewable energy system have been minimized subject to technical reliability indicators such as loss of power supply probability and renewable fraction.Moreover, a systematic exploration of the system has been conducted to assess its optimal feasibility across different values of power loss probability ranging from (0% to 4%). The simulation indicates that the proposed method adeptly identifies globally optimal values, leading to a $177 decrease in annual cost and 8% reduction in average simulation time compared to PSO. The research reveals that the balanced point (relative attainment), where system reliability and cost-effectiveness intersect optimally, is achieved at a 3% power loss level, resulting in the most significant cost reduction of $199 compared to other probability levels.

Research on Low Concentration Gas Catalytic Oxidation Power Generation System

In response to the difficulties in direct utilization of low concentration gas in coal mines and the slow development of industrial application of catalytic oxidation technology, a new mode of direct utilization of low concentration gas with a methane concentration of 1.0% in coal mines in catalytic oxidation gas turbine power generation is explored. And based on the development of a 30kW low concentration gas catalytic oxidation gas turbine power generation system, this paper introduces the design process of key equipment such as catalytic oxidation burners, low-temperature and low-pressure turbines, and countercurrent regenerators, providing a technical reference for the utilization of low concentration gas catalytic oxidation.

Hydrokinetic resource assessment in Colombia’s Non-Interconnected Zones: Case study

Energy accessibility in Non-Interconnected Zones (NIZ), together with the energy transition context, converges on exploring non-conventional renewable energy sources and the technology to harness them. Hydrokinetics is an interesting and abundant resource in Colombia, present in many cases near NIZ communities but with unavailable information about (flow velocity) its actual power generation potential. This work presents a method to assess the hydrokinetic resource in NIZ based on the estimation of river flow velocity from river discharge, river level, and cross-sectional profile data available from the Colombian Institute of Hydrology, Meteorology and Environmental Studies (IDEAM). It is applied in a case study where a year of data was studied to characterise the hydrokinetic resource and match a local household load demand with the potential power generation of a hydrokinetic turbine. An average river flow velocity of 1.14 m/s was obtained, showing a consistent behaviour that means reliability in potential energy production. This approach could be helpful for researchers or power suppliers who aim to harness hydrokinetic resources near NIZ users with hydrokinetic technology in the project planning stages.

Multidisciplinary Design Methodology for Micro-Gas-Turbines—Part I: Reduced Order Component Design and Modeling

Abstract Ultramicrogas turbines (UMGTs) for electric power generation up to 1 kW are a viable replacement technology for lithium batteries in drones due to their high energy density. Previous research has shown that small-scale effects disqualify conceptual design practices applied to larger gas turbines owing to highly coupled, nonlinear component interactions. To fill this gap, we propose an interdisciplinary conceptual design and analysis framework based on reduced order models. To this end, the current work is divided into two parts covering component design and system integration, analysis, and optimization. In Part I, automated conceptual design of all engine subcomponents is elaborated facilitating interdependent reduced order models for compressor, turbine, combustor and high-speed generator while also considering additive manufacturing constraints. In a second step, the reduced order performance models are compared to computational fluid dynamics (CFD) Reynolds-averaged-Navier–Stokes (RANS) simulations of various turbomachinery geometries as well as experimental data of combustor and high-speed generator prototypes, showing good agreement and thus validating the component modules. In conclusion, the first part of this work elaborates an automated and efficient method to conceptual design of all components required for a functional UMGT. Since the strategy is applicable independent of component arrangement and engine layout, the proposed methods offer a universal framework for small gas turbine generators.