A Tutorial Review of the Solar Power Curve: Regressions, Model Chains, and Their Hybridization and Probabilistic Extensions

Owing to the persisting hype in pushing toward global carbon neutrality,the study scope of atmospheric science is rapidly expanding.Among numerous trending topics,energy meteorology has been attracting the most attention hitherto.One essential skill of solar energy meteorologists is solar power curve modeling,which seeks to map irradiance and auxiliary weather variables to solar power,by statistical and/or physical means.In this regard,this tutorial review aims to deliver a complete overview of those fundamental scientific and engineering principles pertaining to the solar power curve.Solar power curves can be modeled in two primary ways,one of regression and the other of model chain.Both classes of modeling approaches,alongside their hybridization and probabilistic extensions,which allow accuracy improvement and uncertainty quantification,are scrutinized and contrasted thoroughly in this review.

General solutions of plane problem for power function curved cracks

A new exact and universal conformal mapping is proposed. Using Muskhelishvili＇s complex potential method, the plane elasticity problem of power function curved cracks is investigated with an arbitrary power of a natural number, and the general solutions of the stress intensity factors （SIFs） for mode I and mode II at the crack tip are obtained under the remotely uniform tensile loads. The present results can be reduced to the well-known solutions when the power of the function takes different natural numbers. Numerical examples are conducted to reveal the effects of the coefficient, the power, and the projected length along the x-axis of the power function curved crack on the SIFs for mode I and mode II.

A Novel Power Curve Prediction Method for Horizontal-Axis Wind Turbines Using Artificial Neural Networks

Accurate prediction of wind turbine power curve is essential for wind farm planning as it influences the expected power production.Existing methods require detailed wind turbine geometry for performance evaluation,which most of the time unattainable and impractical in early stage of wind farm planning.While significant amount of work has been done on fitting of wind turbine power curve using parametric and non-parametric models,little to no attention has been paid for power curve modelling that relates the wind turbine design information.This paper presents a novel method that employs artificial neural network to learn the underlying relationships between 6 turbine design parameters and its power curve.A total of 198 existing pitch-controlled and active stall-controlled horizontal-axis wind turbines have been used for model training and validation.The results showed that the method is reliable and reasonably accurate,with average R^(2)score of 0.9966.

Comments on “General solutions of plane problem for power function curved cracks”

An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：

A method for cleaning wind power anomaly data by combining image processing with community detection algorithms

Current methodologies for cleaning wind power anomaly data exhibit limited capabilities in identifying abnormal data within extensive datasets and struggle to accommodate the considerable variability and intricacy of wind farm data.Consequently,a method for cleaning wind power anomaly data by combining image processing with community detection algorithms(CWPAD-IPCDA)is proposed.To precisely identify and initially clean anomalous data,wind power curve(WPC)images are converted into graph structures,which employ the Louvain community recognition algorithm and graph-theoretic methods for community detection and segmentation.Furthermore,the mathematical morphology operation(MMO)determines the main part of the initially cleaned wind power curve images and maps them back to the normal wind power points to complete the final cleaning.The CWPAD-IPCDA method was applied to clean datasets from 25 wind turbines(WTs)in two wind farms in northwest China to validate its feasibility.A comparison was conducted using density-based spatial clustering of applications with noise(DBSCAN)algorithm,an improved isolation forest algorithm,and an image-based(IB)algorithm.The experimental results demonstrate that the CWPAD-IPCDA method surpasses the other three algorithms,achieving an approximately 7.23%higher average data cleaning rate.The mean value of the sum of the squared errors(SSE)of the dataset after cleaning is approximately 6.887 lower than that of the other algorithms.Moreover,the mean of overall accuracy,as measured by the F1-score,exceeds that of the other methods by approximately 10.49%;this indicates that the CWPAD-IPCDA method is more conducive to improving the accuracy and reliability of wind power curve modeling and wind farm power forecasting.

Influences of Resistor-Type Superconducting Fault Current Limiter on Power System Transient Stability with Asymmetrical Short-Circuit Faults

The transient stability of a single machine to infinite-busbar power system with resistortype superconducting fault current limiters （SFCL） is analyzed under asymmetrical short-circuit fault conditions. The SFCL is considered to introduce a resistance into the three-phase circuits when faults occur. Based on the power-angle curves for different short-circuit conditions of the single-line to ground, double-line to ground and line to line short-circuit faults, the influences of the SFCLs on transient stability are analyzed in detail. The time-domain simulation of transient stability is carried out to verify the analytical results.

An explainable AI framework for robust and transparent data-driven wind turbine power curve models

In recent years,increasingly complex machine learning methods have become state-of-the-art in modelling wind turbine power curves based on operational data.While these methods often exhibit superior performance on test sets,they face criticism due to a perceived lack of transparency and concerns about their robustness in dynamic,non-stationary environments encountered by wind turbines.In this work,we address these issues and present a framework that leverages explainable artificial intelligence methods to gain systematic insights into data-driven power curve models.At its core,we propose a metric to quantify how well a learned model strategy aligns with the underlying physical principles of the problem.This novel tool enables model validation beyond the conventional error metrics in an automated manner.We demonstrate,for instance,its capacity as an indicator for model generalization even when limited data is available.Moreover,it facilitates understanding how decisions made during the machine learning development process,such as data selection,pre-processing,or training parameters,affect learned strategies.As a result,we obtain physically more reasonable models,a prerequisite not only for robustness but also for meaningful insights into turbine operation by domain experts.The latter,we illustrate in the context of wind turbine performance monitoring.In summary,the framework aims to guide researchers and practitioners alike toward a more informed selection and utilization of data-driven wind turbine power curve models.

Dynamic Setting Method of Assessment Indicators for Power Curves of Renewable Energy Sources Considering Scarcity of Reserve Resources

With the increasing proportion of renewable energy sources(RESs)in power grid,the reserve resource(RR)scarcity for correcting power deviation of RESs has become a potential issue.Consequently,the power curve of RES needs to be more rigorously assessed.The RR scarcity varies during different time periods,so the values of assessment indicators should be dynamically adjusted.The assessment indicators in this paper include two aspects,i.e.,deviation exemption ratio and penalty price.Firstly,this paper proposes a method for dynamically calculating the supply capacity and RR cost,primarily taking into account the operating status of thermal units,forecast information of RES,and load curve.Secondly,after clarifying the logical relationship between the degree of RR scarcity and the values of assessment indicators,this paper establishes a mapping function between them.Based on this mapping function,a dynamic setting method for assessment indicators is proposed.In the future,RES will generally be equipped with battery energy storage systems(BESSs).Reasonably utilizing BESSs to reduce the power deviation of RESs can increase the expected income of RESs.Therefore,this paper proposes a power curve optimization strategy for RESs considering self-owned BESSs.The case study demonstrates that the dynamic setting method of assessment indicators can increase the revenue of RESs while ensuring that the penalty fees paid by RESs to the grid are sufficient to cover the RR costs.Additionally,the power curve optimization strategy can help RESs further increase income and fully utilize BESSs to reduce power deviation.

Volatilization behaviors of diesel oil from the soils

The volatilization of diesel oil, Shengli crude oil and 90# gasoline on glass surface of petri dishes were conducted at the ambient temperature of 25℃. Diesel oil evaporates in a power manner, where the loss of mass is approximately power with time. 90# gasoline evaporates in a logarithmic with time. Where as the volatilization of Shengli crude oil fit either the logarithmic or power equation after different time, and has similar R2. And the effects of soil type and diesel oil and water content on volatilization behavior in unsaturated soil were studied in this paper. Diesel oil and water content in the soils play a large role in volatilization from soils. Appropriate water helps the wicking action but too much water stops it. The wicking action behaves differently in four different types of soils in the same volatilization experiment of 18% diesel oil content and air-dry condition.

An Algorithm for Practical Power Curve Estimation of Wind Turbines

Practical power curve estimation is necessary for evaluating the actual power output of a wind farm;since a power curve provided by the wind turbine manufacture will be different with the actual power curve following several years of operation.It can be estimated using the collected power output data including wind power generation and wind speed.This data is commonly ill-distributed due to a noticeable number of outliers,which impose a serious bias to the estimation models obtained from this data.It introduces an interesting challenge in estimation of a power curve.In this paper,an intelligent algorithm is proposed for estimating a power curve using the measured data while modeling and bias errors,imposed to the estimation model by the outliners,are minimized.More specifically,this algorithm is designed based on the Statistical Analysis Software(SAS)programming software package in order to facilitate analyzing and managing big datasets of wind speed and wind power generation.The effectiveness and practical application of the proposed algorithm is demonstrated using a real-world dataset.

Power Curve Modeling for Wind Turbine Using Hybrid-driven Outlier Detection Method

Wind power curve modeling is essential in the analysis and control of wind turbines(WTs),and data preprocessing is a critical step in accurate curve modeling.As traditional methods do not sufficiently consider WT models,this paper proposes a new data cleaning method for wind power curve modeling.In this method,a model-data hybrid-driven(MDHD)outlier detection method is constructed,and an adaptive update rule for major parameters in the detection algorithm is designed based on the WT model.Simultaneously,because the MDHD outlier detection method considers multiple types of operating data of WTs,anomaly detection results require further analysis.Accordingly,an expert system is developed in which a knowledgebase and an inference engine are designed based on the coupling relationships of different operating data.Finally,abnormal data are eliminated and the power curve modeling is completed.The proposed and traditional methods are compared in numerical cases,and the superiority of the proposed method is demonstrated.

Wind Shear Investigation for Site-Specific Wind Turbine Performance Assessment

The wind energy assessment studies are generally performed referring to neutral stability conditions for the atmosphere; this is considered a good hypothesis because neutral conditions characterize the high wind situations. However the increasing size of modem multi megawatt wind turbines allows to produce energy even in low wind regimes and non-neutral conditions can involve significant production period. In such situations the variations of the vertical wind shear can affect the energy production in a sensible way and it could be fundamental to investigate how atmospheric stability and orography can affect the wind profile and the power conversion. In this paper meso-scale numerical data, CFD modeling and remote sensed wind data were used in order to analyze such behavior and to understand how wind shear influences the energy content and the discussion about how to adjust the power curve to the site specific conditions.

Investigating the impacts of spatial-temporal variation features of air density on assessing wind power generation and its fluctuation in China

Air density plays an important role in assessing wind resource.Air density significantly fluctuates both spatially and temporally.But literature typically used standard air density or local annual average air density to assess wind resource.The present study investigates the estimation errors of the potential and fluctuation of wind resource caused by neglecting the spatial-temporal variation features of air density in China.The air density at 100 m height is accurately calculated by using air temperature,pressure,and humidity.The spatial-temporal variation features of air density are firstly analyzed.Then the wind power generation is modeled based on a 1.5 MW wind turbine model by using the actual air density,standard air densityρst,and local annual average air densityρsite,respectively.Usingρstoverestimates the annual wind energy production(AEP)in 93.6%of the study area.Humidity significantly affects AEP in central and southern China areas.In more than 75%of the study area,the winter to summer differences in AEP are underestimated,but the intra-day peak-valley differences and fluctuation rate of wind power are overestimated.Usingρsitesignificantly reduces the estimation error in AEP.But AEP is still overestimated(0-8.6%)in summer and underestimated(0-11.2%)in winter.Except for southwest China,it is hard to reduce the estimation errors of winter to summer differences in AEP by usingρsite.Usingρsitedistinctly reduces the estimation errors of intra-day peak-valley differences and fluctuation rate of wind power,but these estimation errors cannot be ignored as well.The impacts of air density on assessing wind resource are almost independent of the wind turbine types.

Transfer Strategy for Power Output Estimation of Wind Farm at Planning Stage Based on a SVR Model

The conventional wind farm(WF)power generation modelling method highly relies on wind hindcast produced by record time-series data or numerical weather modelling.However,estimating production at future sites is challenging in the absence of local wind monitoring.To address this,a data-driven WF modelling and model transfer strategy is proposed in this work.It considers the challenge of how to transpose metered data from existing operational WFs to sites that might feature as a prospective site for a new WF.By modelling 14 WFs distributed across Scotland using a machine learning(ML)approach,this study proved it was possible to effectively model metered production at a site using modelled wind speed and direction.In addition,this study also found when the latitude difference between two WFs is less than 0.2 degrees and the distance is less than 5o km,two WFs in non-mountainous areas can share an ML model.The results of the shared ML model remain superior to the results of the given power curve from manufacturers,after adjusting the results by the ratio of the power curve in these two WFs.The WF model transfer strategy investigated in this work offered a novel approach to transposing WF production estimates to new sites and appeared to offer better value than simple power curves,which is of importance at the early planning stage for site selection,although it would likely not fully replace detailed micro-siting modelling which are well established in the industry.Index Terms-Machine learning,model transfer strategy,power curve,power output estimation,wind farm.

Comparison of modeling methods for wind power prediction:a critical study

Prediction of power generation of a wind turbine is crucial,which calls for accurate and reliable models.In this work,six different models have been developed based on wind power equation,concept of power curve,response surface methodology(RSM)and artificial neural network(ANN),and the results have been compared.To develop the models based on the concept of power curve,the manufacturer’s power curve,and to develop RSM as well as ANN models,the data collected from supervisory control and data acquisition(SCADA)of a 1.5 MW turbine have been used.In addition to wind speed,the air density,blade pitch angle,rotor speed and wind direction have been considered as input variables for RSM and ANN models.Proper selection of input variables and capability of ANN to map input-output relationships have resulted in an accurate model for wind power prediction in comparison to other methods.

Wind speed equalization-based incoming wind classification by aggregating DFIGs

With the development of wind energy,it is necessary to develop equivalent models to represent dynamic behaviors of wind farms in power systems.The equivalent wind method is investigated for the aggregation of doubly-fed induction generator wind turbines.The detailed procedures for the calculation of equivalent wind are analyzed.The necessity of classifying incoming winds is shown.To improve the performances of the method,incoming winds are classified according to mean wind speeds and positive/negative semi-variances of wind speeds,and a group of turbines with similar incoming winds are aggregated together.The effectiveness of the method is verified through simulations in MATLAB/Simulink.

Effect of Ag substitution on structural,magnetic and magnetocaloric properties of Pr_(0.6)Sr_(0.4–x)Ag_xMnO_3 manganites

A systematic investigation on the structural, magnetic and magnetocaloric properties of Pr_（0.6）Sr_（0.4-x）Ag_xMnO_3（x=0.05 and 0.1） manganites was reported. Rietveld refinements of the X-ray diffraction patterns confirmed that all samples were single phase and crystallized in the orthorhombic structure with Pnma space group. Magnetic measurements in a magnetic applied field of 0.01T revealed that the ferromagnetic-paramagnetic transition temperature T_C decreased from about 293 to 290 K with increasing silver content from x=0.05 to 0.1. The reported magnetocaloric entropy change and relative cooling power for both samples were considerably remarkable with a △S_（max） value of 1.9 J/（kg·K）and maximum RCP values of 100 J/kg, under a magnetic field change（？μ0H） equal to 1.8T. The analysis of the universal curves gave an evidence of a second order magnetic transition for the studied samples. The magnetic field influence on both the magnetic entropy change and the relative cooling power was also studied and discussed.

Experimental investigation of photovoltaic systems for performance improvement using water cooling

This research aims to analyse the comparative performance of two identical photovoltaic(PV)panels with load variations and integrating an automated water-cooling process under the climatic conditions of the United Arab Emirates.The work also presents the steps of system design,implementation and performance evaluation of the proposed PV system,and all electrical,control and mechanical components along with how they were integrated within a 100-W PV system.MATLAB/Simulink?was used only to simulate the behaviours of the PV panel under wide ranges of incident sunlight and ambient temperature.The tests were performed for a day-long operation during a clear summer day.The experimental results demonstrate an improvement in the PV system performance compared with the uncooled system by~1.6%in terms of total harvested energy using the proposed water-cooling process with a frequency of 2 minutes of cooling operation every 30 minutes during day hours.

Memory Based Scheme to Monitor Non-Random Small Shift Patterns in Manufacturing Process

Consistent high-quality and defect-free production is the demand of the day. The product recall not only increases engineering and manufacturing cost but also affects the quality and the reliability of the product in the eye of users. The monitoring and improvement of a manufacturing process are the strength of statistical process control. In this article we propose a process monitoring memory-based scheme for continuous data under the assumption of normality to detect small non-random shift patterns in any manufacturing or service process.The control limits for the proposed scheme are constructed. The in-control and out-of-control average run length(AVL) expressions have been derived for the performance evaluation of the proposed scheme. Robustness to non-normality has been tested after simulation study of the run length distribution of the proposed scheme, and the comparisons with Shewhart and exponentially weighted moving average(EWMA) schemes are presented for various gamma and t-distributions. The proposed scheme is effective and attractive as it has one design parameter which differentiates it from the traditional schemes. Finally, some suggestions and recommendations are made for the future work.