Uncertainty Of Wind Speed Research Articles

Optimization and Uncertainty Analysis of Hybrid Energy Systems Using Monte Carlo Simulation Integrated with Genetic Algorithm

This study investigates the optimization of hybrid energy systems (HES) composed of wind turbines, battery banks, and diesel generators, focusing on addressing the challenges posed by wind speed uncertainty. This research contributes significantly to the field by developing a novel methodology that combines uncertainty analysis with hybrid optimization techniques to improve the reliability and cost-effectiveness of HES. The findings revealed that initial simulations without renewable energy sources result in high diesel consumption, with fuel usage reaching 534,810 liters per year and associated carbon emissions totaling 797,070 kg/year. Through optimization, an economically viable configuration is identified, consisting of 37 battery banks, two 250 kW wind turbines, and a 340-kW diesel generator, achieving an Annualized System Cost (ASC) of $166,500 and a Cost of Energy (COE) of $0.1480/kWh. The Monte Carlo simulations indicate a most probable COE of $0.1450/kWh for the wind turbine/battery/diesel system, occurring with an 8.3% probability, while approximately 90% of COE values fall below $0.1669/kWh. The average COE is $0.14834/kWh, with a minimum of $0.12163/kWh. The Renewable Energy Fraction (REF) spans from 28% to 97%, with an average of 64% and a standard deviation error of 9.6% at a 95% confidence level. The results underscore the potential implications for informing policymakers and industry leaders about the design and evaluation of HES under uncertain environmental conditions. By addressing the limitations of current approaches, this work contributes valuable insights into the economic, environmental, and social dimensions of hybrid renewable energy systems.

Impact of Surface Turbulent Fluxes on the Formation of Roll Vortices in a Mediterranean Windstorm

AbstractRoll vortices can have a significant influence on the exchanges of momentum, sensible heat and moisture throughout the boundary layer. They have been shown to reinforce air‐sea interactions under strong wind conditions. This raises the question of how air‐sea exchanges can, in turn, affect the roll vortices. However, representing surface turbulent fluxes during extreme wind conditions is a major challenge in numerical weather prediction and can lead to large uncertainties in surface wind speed. The sensitivity of rolls to different representations of surface fluxes is investigated using large eddy simulations. The study focuses on Mediterranean windstorm Adrian, where rolls are responsible for the transport of strong winds to the surface. Considering the effects of sea spray increases surface heat fluxes and significantly influences the roll morphology. The rolls become narrower and extend over a greater height, while the downward transport of momentum is intensified and results in higher wind speed near the surface. Roll vortices vanish within a few minutes in the absence of momentum fluxes, which maintain the wind shear necessary for their organization. They also quickly weaken without sensible heat fluxes, which sustain the near‐neutral stratification required for their development. In contrast, latent heat fluxes play a minor role. These findings emphasize the necessity of precisely representing the processes occurring at the air‐sea interface, which do not only affect the thermodynamic surface conditions but also the vertical transport of momentum within the windstorm.

A tri-level hybrid stochastic-IGDT dynamic planning model for resilience enhancement of community-integrated energy systems

In this paper, a resilience-oriented dynamic planning framework is developed for optimal sizing of the community-integrated energy system components, including photovoltaic system, wind turbine, boiler, power to gas technology, combined heat and power, and storage devices. The proposed framework is formulated as a tri-level linear programming that performs Community-Integrated Energy Systems design under normal conditions at the first level while evaluating system operation during disastrous conditions at the second level. In the third level, re-planning is done based on information-gap decision theory to enhance community-integrated energy systems’ resilience against various natural disasters. Stochastic programming is also employed at all levels to address the uncertainty of electricity market price, energy demand, solar radiation, and wind speed. A detailed P2G system including, a methanation device, electrolysis, and hydrogen storage is designed to improve the resilience of the system. In addition, the power to gas proposed in this model is coupled with a carbon capture unit to mitigate carbon emission by reusing emitted carbon from the flue gas of the boiler and combined heat and power. Various economic metrics and technical constraints are also considered to achieve a realistic design. Numerical simulation results demonstrate that the positive interplay of renewable energy resources and energy storage technologies, specifically P2G, assisted the CIES in maintaining a stable and uninterrupted energy supply during extreme events. The results exhibit that increasing only 10 % of the resilience budget can decrease >93 % of unserved demand and helps reduction of >37 % of carbon emissions.

A machine learning-based probabilistic wind speed prediction model with multi-resolution data, quantile regression and bound estimation

Wind speed prediction can be important for management of long-span cross-sea bridges, and probabilistic prediction models are needed to take uncertainty of future wind speed into consideration. However, there are two shortcomings of existing models. One is the lack of supplementary input of detailed fluctuations of wind speed, and the other is that fixed quantiles are usually selected when the predicted probability distribution is converted into a confidence interval. To this end, we propose a novel machine learning-based probabilistic model with multi-resolution data, quantile regression and bound estimation. The proposed model is composed of the distribution prediction part and the interval prediction part. In the distribution prediction part, we employ multi-resolution data as input, which can complement details of fluctuations of wind speed to reduce uncertainty. The interval prediction part employs the lower upper bound estimation method to postprocess predicted quantiles and output a superior interval than selecting fixed quantiles. The proposed model is validated on the monitoring wind speed data of two long-span cross-sea bridges, where the superiority of the distribution part and the effectiveness of the interval part are demonstrated.

Scenario-based stochastic optimization on the variability of solar and wind for component sizing of integrated energy systems

The inherent intermittency and variability of renewable energy sources present significant challenges to the optimal design and implementation of integrated energy systems (IES). This paper introduces a novel stochastic optimization model that integrates advanced scenario generation and clustering algorithm for renewable energy sources within a multi-objective, bi-level optimization framework. Specifically, the clearness index is employed to represent the stochastic distribution of solar radiation intensity by beta distribution, while wind speed uncertainty is modeled seasonally using the Weibull distribution. Monte Carlo sampling with synchronous back substitution is applied for scenario generation and reduction of solar radiation and wind speed. To address the multi-objective evaluation, the analytic hierarchy process is utilized, and the joint optimization is achieved by combining a region contraction algorithm with stochastic programming. The proposed methodology is validated on an IES featuring various heating devices, incorporating uncertainties in both wind and solar energy. The results indicate that the absorption heat pump-based scheme achieves superior energy-saving performance, achieving an energy rate of 0.4724. Additionally, the compression heat pump-based scheme exhibits excellent economic efficiency and environmental sustainability, with a cost of energy of 0.3639 and a renewable fraction of 0.5536.

Multi-objective Mathematical Model for Optimal Wind Turbine Placement in Wind Farm under Uncertainty

The main objective of this research is to introduce three energy risk management models grounded in optimization techniques for the strategic placement of wind turbines, considering wake effects and uncertainties in wind speed and direction. For this purpose, wind speed and direction data are gathered, and Monte Carlo simulation is employed to model the uncertainties. Subsequently, the risk management models undergo optimization using Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Pareto envelope-based selection algorithm II (PESA-II), and Multi-Objective Particle Swarm Optimization (MOPSO) algorithms. Findings reveal that the wind farm's maximum power output reaches approximately 5.8 megawatts across all three algorithms and optimal turbine placements. A risk assessment was conducted using a tenth percentile criterion, revealing a significant production risk within the study area, with production falling below 1.8 megawatts in 90% of cases. Regarding the performance evaluation of the algorithms across all three models, superior performance in terms of solution proximity to the ideal solution is exhibited by PESA-II, while enhanced diversity and solution spread compared to the other algorithms are demonstrated by NSGA-II.

Peer‐to‐peer electricity trading via a bi‐level optimization approach for renewable energy‐driven microgrids connected to the distribution grid

AbstractThis study employs a sophisticated bi‐level optimization methodology to model the most efficient operation of microgrids (MGs) within the operational framework of distribution companies (DCs). In this bi‐level optimization problem, the upper level strives to maximize the profits of both MGs owners and DCs, while the lower level is dedicated to ensuring load balance, managing distributed generation, and implementing load curtailment strategies. The coordination of power transmission is facilitated by the DCs. At the upper level of decision‐making, the optimal pricing strategies for power transactions are determined, accounting for various factors such as market prices, demand response programs, and uncertainties in wind speed. Through the utilization of a bi‐level optimization framework, this study comprehensively captures the complex interactions between MGs and DCs, taking into consideration the objectives and constraints of both entities. This approach offers a more precise representation of the decision‐making process in retail electricity markets, thereby providing valuable insights into the optimal operation of MGs within the DCs setting.

Maximization of Total Profit for Hybrid Hydro-Thermal-Wind-Solar Power Systems Considering Pumped Storage, Cascaded Systems, and Renewable Energy Uncertainty in a Real Zone, Vietnam

The study maximizes the total profit of a hybrid power system with cascaded hydropower plants, thermal power plants, pumped storage hydropower plants, and wind and solar power plants over one operation day, considering the uncertainty of wind speed and solar radiation. Wind speed and solar radiation in a specific zone in Vietnam are collected using the wind and solar global atlases, and the maximum data are then supposed to be 120% of the collection for uncertainty consideration. The metaheuristic algorithms, including the original Slime mould algorithm (SMA), Equilibrium optimizer, and improved Slime mould algorithm (ISMA), are implemented for the system. ISMA is a developed version of SMA that cancels old methods and proposes new methods of updating new solutions. In the first stage, the cascaded system with four hydropower plants is optimally operated by simulating two cases: simultaneous optimization and individual optimization. ISMA is better than EO and SMA for the two cases, and the results of ISMA from the simultaneous optimization reach greater energy than individual optimization by 154.8 MW, equivalent to 4.11% of the individual optimization. For the whole system, ISMA can reach a greater total profit than EO and SMA over one operating day by USD 6007.5 and USD 650.5, equivalent to 0.12% and 0.013%. The results indicate that the optimization operation of cascaded hydropower plants and hybrid power systems can reach a huge benefit in electricity sales

Stochastic Model Predictive Control Based on Polynomial Chaos Expansion With Application to Wind Energy Conversion Systems

The wind energy conversion system (WECS) has a complex structure, and its state space model is highly nonlinear. Due to the random uncertainty of wind speed, it poses a huge challenge to achieve optimal control tasks and ensure the safe and stable operation of the system. Therefore, this article proposes a stochastic model predictive control strategy based on Polynomial Chaotic Expansion (PCE), which achieves the control tasks of MPPT and constant power regions in wind energy conversion systems. Firstly, a simple algorithm is proposed to obtain a set of basis functions that are suitable for the stochastic variable wind speed. Then, the obtained basis functions are used to propagate the uncertainty of the original uncertain differential equation of the wind energy conversion system through polynomial chaotic expansion. Combining the operating region and constraint conditions of the wind energy conversion system, the original stochastic uncertainty problem is transformed into a deterministic convex optimization problem. Using NREL 5MW wind turbine as the research object for simulation, the task of capturing maximum wind energy in MPPT area and tracking rated power points in constant power area was achieved. The experimental results show that the proposed control method can effectively improve the wind energy capture capability and achieve accurate tracking of output power to rated power.

Probabilistic assessment of short‐term voltage stability under load and wind uncertainty

AbstractContemporary electricity networks are exposed to operational uncertainties, which may jeopardise the stability of the power grid. More specifically, the increasing penetration level of variable renewable energy generation and uncertainty in load demand are key catalysts for these emerging stability issues. A mathematical relationship is established to track the system voltage trajectory with respect to variations in uncertain inputs (associated with wind speed, system load, and wind power penetration levels). Additionally, it demonstrates the consequences of varying uncertain inputs on the short‐term voltage response across different potential operating conditions. The theoretical proposition has further been verified by the simulation studies with two test power networks in DIgSILENT PowerFactory software. The simulation results revealed that uncertain injection sources significantly impacted the system voltage at the receiving end. High uncertainty in wind speed and system loads increased voltage recovery variation, causing delays in voltage response during low wind speeds and high system loads. Additionally, increased wind power penetration levels expanded voltage recovery uncertainties, resulting in decreased system voltage and potentially leading to voltage violations and instability at 30% wind power levels. Moreover, the results showed that the system's response time increased, and in some cases, it collapsed due to increased system capacity (>80%) and dynamic load (>75%), as well as encountering a large disturbance under uncertain circumstances.

Wind speed multi-step prediction based on the comparison of wind characteristics and error correction: Focusing on periodic thermally-developed winds

To leverage the abundant wind energy resources available in mountainous regions, an increasing number of wind power facilities and associated transportation infrastructure are being constructed in these areas. There are different types of intense winds in mountainous areas and the non-linear characteristics of the different intense winds vary significantly. The periodic thermally-developed winds are the commonly occurring type of intense wind. Based on the comparison of wind characteristics, this research proposes a prediction model for the periodic thermally-developed winds. The research utilizes the Bi-directional Long Short-Term Memory model(Bi-LSTM), which has been optimized by the Bayesian optimization(BO), to predict wind speed. Based on the relationship between wind field characteristics in periodic thermally-developed winds, a regression correction module is proposed using a joint probability model. Additionally, to address the volatility and uncertainty of wind speed, a Gaussian mixture model is employed for probability prediction. The experimental results demonstrate several findings: 1. The BO-Bi-LSTM model accurately and reliably predicts multi-step results for periodic thermally-developed winds in mountainous areas. 2. The proposed correction module, when combined with other models, yields improved wind speed accuracy compared to the uncorrected values. 3. The Gaussian mixture model produces probabilistic prediction results that consider both interval coverage and interval bandwidth simultaneously. 4. The proposed model can successfully predict periodic thermally-developed winds in mountainous areas for practical engineering purposes, resulting in reliable probabilistic prediction outcomes. It is of great significance for the utilization of wind energy resources and the driving safety of vehicles on ancillary structures.

Buffeting reliability of high-rise bridge tower in mountain area based on CNN-BiLSTM

In recent years, the wind-induced vibration of structures has received a great deal of scholarly attention due to the increasing scale of large structures. In this study, an algorithm that combines a stochastic pseudo excitation method (SPEM), a convolutional neural network (CNN) and a bidirectional long short-term memory network (BiLSTM), named as SPEM-CNN-BiLSTM (SCBL), is proposed. The SCBL is a surrogate model consisting of three different computational modules, in which the SPEM can provide training samples for CNN-BiLSTM (CBL) network architecture, a convolutional layer extracts features of stochastic parameters and a BiLSTM handles time histories of bridge response. The accuracy of the SCBL prediction results is ensured by the set error threshold. The model also accounts for structural uncertainty in the inputs and is adapted during the training step to be more suitable for reliability analysis. According to the output qualified prediction data, the dynamic reliability based on the 99 % threshold is calculated by obtaining its probability density function, and the wind-induced vibration responses of uncertain bridge towers are studied. Firstly, the wind environment of the bridge tower was analyzed, and the average wind speed of 20 m/s among the bridge area was obtained by field measurements, and Computational Fluid Dynamics (CFD). Secondly, the proposed artificial neural network algorithm is applied to bridge jitter reliability analysis and compared with the traditionally recognized methods: the Monte Carlo method (MCM) and the stochastic pseudo excitation method (SPEM). The results of SCBL calculations are closer to the results of MCM than those of other methods. Additionally, the computational efficiency of the method is improved by 40 times over MCM and 2 times over SPEM. Finally, the data generated by the SCBL method will be used for reliability analysis. Uncertainties in structure, wind speed, and yaw angle all contribute to the uncertainty and dispersion of the stochastic response prediction. Among them, the uncertainty in wind speed has the greatest impact on the reliability.

Deep Learning Wind Power Prediction Model Based on Attention Mechanism-Based Convolutional Neural Network and Gated Recurrent Unit Neural Network

Accurate prediction of wind power is crucial for the efficient operation and risk management of wind farms. This paper introduces a deep learning model for wind power prediction that integrates an Attention mechanism with a convolutional neural network (CNN) and a gated recurrent unit (GRU) neural network. Addressing the randomness, intermittency, volatility and uncertainty of wind speed, we first apply swarm decomposition (SWD) to preprocess the original wind power data into subsequences. Subsequently, the CNN extracts spatial features, and the GRU identifies temporal correlations. The Attention mechanism enhances feature significance, further optimizing prediction accuracy. Complex error sequences generated by the CNN–GRU–Attention (CGA) model are corrected using the autoregressive integrated moving average (ARIMA). We evaluated the model’s performance using three wind power datasets against 16 other models, employing six evaluation indices (MSE, RMSE, MAPE, Theil’s [Formula: see text], TIC and SPL) and the Diebold–Mariano (DM) test and model confidence set (MCS) for model testing. Our results demonstrate the proposed model’s superior accuracy and efficiency in predicting wind power.

Frequency Regulation Adaptive Control Strategy of Wind Energy Storage System for Wind Speed Uncertainty

In order to reduce the negative influence of wind speed randomness and prediction error on frequency modulation, the reliability of the wind storage system was assessed effectively. In the wind storage frequency modulation system, a state of charge (SOC) adaptive adjustment method for wind speed randomness is proposed. Firstly, through the correlation analysis between the standby capacity of frequency modulation and the output power of wind turbine, the uncertainty of its frequency modulation capacity is revealed. Secondly, in view of the uncertainty of wind turbine frequency modulation, the output power of energy storage frequency modulation is optimized with the goal of minimizing the frequency modulation power deviation of the wind storage front under the framework of model predictive control, and the improved whale optimization algorithm (WOA) is used to solve the problem. Finally, the simulation results show that, under the given 5 min continuous disturbance, the root mean square of frequency regulation of the proposed restoration method is reduced by 56.65% compared to the SOC recovery base point set to 0.5. Under continuous large perturbations, the maximum frequency deviation is reduced by 0.0455 Hz. This effectively shows that this method can not only improve the frequency modulation reliability of wind power system but also improve the continuous frequency modulation capability of energy storage system.

Integration of optimal power flow with combined heat and power dispatch of renewable wind energy based power system using chaotic driving training based optimization

Combined heat and power economic dispatch (CHPED) based optimal power flow (OPF) problem has been studied in this article using a new, practical approach based on chaotic driving training optimization (DTBO) (CDTBO). In the proposed technique (CDTBO), the chaotic based learning is integrated with DTBO to overcome the local optimal problem and inferior convergence speed of the existing algorithms. OPF is an important concern to retain the power system running effectively. In order to meet the demand for reasonably priced power generation with optimal power flow in transmission lines, the authors combined CHPED and OPF. Since fuel is changing daily in the current environment, using renewable energy sources to generate electricity economically is crucial. The renewable energy source like wind energy is integrated with thermal units for economic power generation with reducing the thermal fuel consumption of CHPED-based OPF system. The proposed technique implemented on CHPED based IEEE-30 bus system for renewable and without renewable energy sources with considering different cases. The suggested problem considering with valve point loading of thermal units, transmission losses and uncertainties of wind speed to address the non-linearity of the renewable-based CHPED-OPF system. Cost minimization, voltage deviation control, transmission losses minimization and stability index are the single objectives of the prospective system. Furthermore tested on multi-objective functions for simultaneously minimization of cost with emission and simultaneously minimization of active power loss with voltage profile. It is observed that the proposed CDTBO technique helps to reduce the cost by 2% and 12.8% for renewable based system as compared to non-renewable system for multi-objective function. The robustness of the proposed solution has been verified by implementing the statistical analysis on two systems with least variation of mean and optimal values of cost with the tolerance of less than 0.0035%. A comparison has been made with recent well known optimization techniques to address the superiority of the suggested CDTBO algorithm.

Multi-objective RIME algorithm-based techno economic analysis for security constraints load dispatch and power flow including uncertainties model of hybrid power systems

In recent times, the landscape of power systems has undergone significant evolution, particularly with the integration of diverse renewable energy sources (RESs). This advancement presents an invaluable opportunity to enhance energy efficiency in the modern power grid, primarily by bolstering the role of stochastic RESs. The challenge lies in the optimal power flow (OPF), a multifaceted and non-linear optimization challenge that grows more complex with the inclusion of stochastic RESs that aims to optimize the allocation of power system resources to minimize the operational cost while maintaining the stability and security of the system. Addressing this, the current study introduces an innovative optimization approach, the Multi-Objective RIME (MORIME) algorithm. Drawing inspiration from the physical phenomenon of rime-ice, called the RIME, the MORIME seeks to effectively tackle OPF issues. This algorithm enhances solution accuracy by smartly dividing with non-dominated sorting and crowding distance mechanism. The proposed OPF model incorporates three types of RESs: solar photovoltaic, wind and small-scale hydropower units. While uncertainties in wind speed and solar irradiation are managed through Monte Carlo simulations, the small hydro unit is considered a constant power source. The efficacy of the MORIME algorithm is tested on IEEE 30 bus systems and results indicate that the MORIME method identifies the optimal solution for the multi-objective OPF problem while satisfying the power system constraints, thereby proving its effectiveness and superiority over MOWOA, MOGWO, MOALO, MOMRFO and MOAGDE in terms of Hyper Volume (HV) and reciprocal of Pareto Sets Proximity (1/PSP) metrices. The MORIME source code is available at: https://github.com/kanak02/MORIME

Artificial neural network-based direct power control to enhance the performance of a PMSG-wind energy conversion system under real wind speed and parameter uncertainties: An experimental validation

With the increasing emphasis on embedding advanced technology into system controls, the Direct Power Control (DPC) approach has garnered considerable attention due to its simple and highly adaptable algorithm. This approach has been increasingly recognized in numerous applications. However, the variable frequency, harmonic distortion of the currents, and power ripples caused by Hysteresis controllers and switching tables decrease its effectiveness and robustness, affecting the system’s performance. For this reason, this paper proposed a new DPC based on Artificial Neural Network (ANN) approaches. In this approach, the hysteresis comparator and the switching table are substituted with ANN controllers and then applied on both sides: machine-side converter (MSC) and grid-side converter (GSC) of a Permanent Magnet Synchronous Generator based Wind Energy Conversion System (PMSG-WECS). Moreover, to make the system more efficient in varying wind conditions, this study expands the utilization of the artificial neural networks (ANN) to encompass the maximum power point tracking (MPPT) control strategy. To demonstrate the effectiveness of the proposed approach on the system behaviors, a simulation test was carried out in the Matlab/Simulink environment, using a real wind profile of a Moroccan city (Essaouira). In comparison to the classical DPC control, the simulation results showed the superior performance of the proposed ANN-DPC control in terms of reference tracking, response time, overshoot, precision, and its capacity to reduce the rate of power ripples and total harmonic distortion (THD) in the injected currents. Furthermore, a robustness test was also included in this work to check the robustness of the proposed control against parameters variation. In conclusion, the feasibility and effectiveness of the ANN-DPC control approach were confirmed through experimental validation using the dSPACE DS1104 board.

Enhancing standard CFD based practices for site assessment through polynomial surrogates for estimating uncertainty in wind speed

One of the challenges in digitizing the wind energy sector is to have reliable, accurate and efficient data assessment and prediction tools. We believe that accurate surrogates are key towards improving efficiency and reliability for informed decision making. For a quantitative understanding of wind and energy in complex terrains, a detailed site assessment is done, most often using mesoscale and/or microscale computational fluid dynamics (CFD) based approach. Typically, one would require multiple scenarios/case for a CFD simulator to incorporate the influence of a parameter on variability of wind speed and energy production. These simulations are computationally expensive, and the industry is constantly on a look out for more efficient methods. Towards this end, we propose using a polynomial surrogate based on Polynomial Chaos Expansion (PCE) for uncertainty quantification that requires only a few CFD simulations to assess the variability of wind speed with respect to variability in an input parameter. The variability estimates from PCE were first validated against the standard Monte Carlo method on simple benchmarks and then tested for complex terrains. In this work, we present results that help us understand how canopy foliage, particularly its height, impacts the variability in wind speed in complex terrains. Since the polynomial surrogate relies only on a limited set of input variations (forest height) to estimate the variability distributions for wind speed locally (for specified points of interests), it has proven to be a low-cost and accurate method for estimating uncertainty. In this paper, we discuss the results for wind speed variability for five sites with varying complexity using the polynomial surrogate model. Furthermore, the singular value decomposition (SVD) entropy value is used to quantify terrain complexity for the sites considered. We show how the variability in wind speed can potentially be correlated to terrain complexity. This is our first attempt in providing an empirically (including multiple sites) derived relationship that can be used as a basis for fast and reliable variability estimator for wind resource planners.

Optimal Operation and Market Integration of a Hybrid Farm with Green Hydrogen and Energy Storage: A Stochastic Approach Considering Wind and Electricity Price Uncertainties

In recent years, growing interest has emerged in investigating the integration of energy storage and green hydrogen production systems with renewable energy generators. These integrated systems address uncertainties related to renewable resource availability and electricity prices, mitigating profit loss caused by forecasting errors. This paper focuses on the operation of a hybrid farm (HF), combining an alkaline electrolyzer (AEL) and a battery energy storage system (BESS) with a wind turbine to form a comprehensive HF. The HF operates in both hydrogen and day-ahead electricity markets. A linear mathematical model is proposed to optimize energy management, considering electrolyzer operation at partial loads and accounting for degradation costs while maintaining a straightforward formulation for power system optimization. Day-ahead market scheduling and real-time operation are formulated as a progressive mixed-integer linear program (MILP), extended to address uncertainties in wind speed and electricity prices through a two-stage stochastic optimization model. A bootstrap sampling strategy is introduced to enhance the stochastic model’s performance using the same sampled data. Results demonstrate how the strategies outperform traditional Monte Carlo and deterministic approaches in handling uncertainties, increasing profits up to 4% per year. Additionally, a simulation framework has been developed for validating this approach and conducting different case studies.

Photovoltaic-penetrated power distribution networks’ resiliency-oriented day-ahead scheduling equipped with power-to-hydrogen systems: A risk-driven decision framework

Hydrogen energy and the pioneering power-to-hydrogen (P-2-H) systems have garnered significant interest due to their potential to revolutionize power systems, offering exceptional long-term energy storage capabilities and augmenting the resilience and flexibility of the grid. This paper presents a novel approach for optimizing the day-ahead proactive scheduling of power distribution networks with high solar penetration. The approach utilizes power-to-hydrogen (P-2-H) technology to enhance resiliency and mitigate risks. Uncertainties in solar irradiation, wind speed, electricity demands, and day-ahead market prices are modeled using a scenario-based probabilistic procedure. The optimization problem is formulated as a mixed-integer linear program that minimizes the network's expected normal and resiliency costs while incorporating downside risk constraints. The approach is applied to an IEEE 33-bus power distribution network, demonstrating the effectiveness of P-2-H facilities and risk assessment in improving resiliency during normal and power outage scenarios. Implementing P-2-H facilities in circumstances with and without risk results in a reduction of total operation costs by 40.89% and 40.32%, respectively, according to the simulation findings. Furthermore, the numerical analysis results show that the network's overall operation cost increase for achieving zero risk is only 3.93%, which reduces to 2.32% with the use of P-2-H facilities.