Probability Density Function Characterization for Aggregated Large-Scale Wind Power Based on Weibull Mixtures

Effects of Large Scale Wind Power on Total System Variability and Operation: Case Study of Northern Ireland

Policy analysis for grid parity of wind power generation in China

In this paper, we are interested in investigating the causal relationships among futures sugar prices in the Zhengzhou futures exchange market (ZF), the spot sugar prices in Zhengzhou (ZS) and the futures sugar prices in New York futures exchange market (NF). A useful tool called Bayesian network is introduced to analyze the problem. Since there are only three variables in our Bayesian network, the algorithm is straightforward: we display all the 25 possible network structures and adopt certain scoring metrics to evaluate them. We applied five different scoring metrics in total. Firstly, for each metric, we obtained 24 scores, each calculated from one of the 24 possible structures i.e. a Directed Acyclic Graph (DAG). Then we eliminated the network structure which represents the independence of the three variables according to our prior knowledge concerning the futures sugar market. After that, the optimal network structure which implies the causal relationships was selected according to the corresponding scoring metric. Finally, after comparing the results from different scoring metrics, we obtained the relatively affirmative conclusion that ZS causes ZF from both the Bayesian Dirichlet (BD) metric, Bayesian Dirichlet-Akaike Information Criterion (BD-AIC) metric, Bayesian Dirichlet-Bayesian Information Criterion (BD-BIC) metric and Bayesian Information Criterion (BIC) metric. The conclusions that NF causes ZF and ZF causes ZS from the Akaike Information Criterion (AIC) metric and ZF causes ZS from the BIC metric were useful and significant to our investigation.

Time series study is of paramount importance especially in developing countries such as India. The objective of this study is to forecast the number of dengue cases by applying time series models. Furthermore, this study also aims to uncover the correlation of ecological variables with dengue cases using a p value test. The ecological variables considered are the rainfall (with a 2-month lag period) and average relative humidity. An evaluation of host factors such as age and gender is done with the number of cases to determine the most affected strata. Monthly data on dengue cases from 2014 to 2017 are taken from the integrated disease surveillance programme, Government of India, and data on ecological variables, humidity and rainfall are taken from www.Indiastat.com . A 2-month lag period is considered for rainfall. These data were analysed by the autoregressive integrated moving average (ARIMA) and exponential smoothing model (ES). Predictive performance of these techniques was assessed by evaluation parameters such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute error and mean absolute scaled error. Applying time series models was useful in the prediction. There were many more males than females according to the data for 2014–2017. The Akaike information criterion (AIC), Bayesian information criterion (BIC) and mean absolute scaled error for ARIMA are 48.6526, 448.333333, 449.30008, 453.08 and 0.507826, respectively. Based on model indices such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), mean absolute error and mean absolute scaled error, the ARIMA performed better than the ES model. Rainfall at the 2-month lag was correlated with the number of cases.

This paper introduces a SAS/IML program to select among the multivariate model candidates based on a few well-known multivariate model selection criteria. Stepwise regression and all-possible-regression are considered. The program is user friendly and requires the user to paste or read the data at the beginning of the module, include the names of the dependent and independent variables (the y's and the x's), and then run the module. The program produces the multivariate candidate models based on the following criteria: Forward Selection, Forward Stepwise Regression, Backward Elimination, Mean Square Error, Coefficient of Multiple Determination, Adjusted Coefficient of Multiple Determination, Akaike's Information Criterion, the Corrected Form of Akaike's Information Criterion, Hannan and Quinn Information Criterion, the Corrected Form of Hannan and Quinn (HQc) Information Criterion, Schwarz's Criterion, and Mallow's PC. The output also constitutes detailed as well as summarized results.

Numerous problems have emerged with the rapid development of wind power in Xinjiang. The predominant problem is the inhibition of the healthy development of the wind power industry by wind power curtailment in Xinjiang. In this study, wind power heating and high energy-consuming industries were coupled to increase wind power consumption in Xinjiang on the load side. The feasibility analysis of wind power heating in Dabancheng showed that the heating load characteristics coincide with the wind characteristics and the electric heating technology can fulfill the requirements for wind power heating. A business model innovation achieved a win–win situation. Furthermore, a wind power heating system was designed in Dabancheng, the boiler capacity and the heat storage capacity were calculated, and a heating system model with heat storage technology was established. Wind power heating with heat storage can improve the consumption of wind power and increase the local electric load and system adjustability. Furthermore, heating with curtailed wind power can save 2942 tons of standard coal as well as reduce 5172 tons of CO2, 2.9 tons of SO2, 22 tons of NOX, and 2 tons of soot emissions. Non-grid-connected distributed wind power was applied to the high energy-consuming coal chemical industry to reduce wind power curtailment, expand the consumption market, and reduce pollution. A multifunctional wind-photovoltaic complementary system with hydrogen energy storage coupled with traditional high energy-consuming coal chemical industry was established. The implementation plan using wind and solar energy to produce, store, and apply hydrogen energy was proven beneficial. Wind power consumption was improved on the load side. The wind power curtailment problem was reduced by increasing local load using the curtailed wind power to provide clean heat in Dabancheng and constructing the multifunctional wind–photovoltaic complementary system. This study will contribute to the healthy and sustainable development of the wind power industry in Xinjiang.

The age and growth information of fish is important for assessment of the dynamics, planning, and management in fisheries. In this study, the mean size at age data of 10 fish species collected from literature were fitted by the five growth models and the growth parameters were estimated by the maximum likelihood method. The best model was selected using the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The growth of most species can be best described by the von Bertalanffy and allometric growth models. The results showed that both AIC and BIC have their advantages in the testing of significance of the difference between the functions of models. As for the demersal fishes (snappers and groupers), BIC is better than AIC in selecting the best growth model.

Precise wind power forecasting has several benefits, such as optimized peak regulation in power systems, enhanced safety analysis, and improved energy efficiency. Considering the substantial influence of meteorological data, such as wind speed and temperature, on wind power generation, and to minimize the impact of fluctuations and complexity of wind power data on the forecast results, this paper proposes a combined wind power forecasting method. This approach is based on the long short-term memory network (LSTM) model, using the maximal information coefficient (MIC) method to select numerical weather prediction (NWP) and combining the efficiency of complete EEMD with the adaptive noise (CEEMDAN) method for nonlinear signal decomposition. Results indicate that the accuracy of the forecast results is supported by NWP. Moreover, wind power data are decomposed by the CEEMDAN algorithm and converted into relatively regular sub-sequences with small fluctuations. The MIC algorithm effectively reduces the redundant information in NWP data, and the LSTM algorithm addresses the uncertainty of wind power data. Finally, the wind power of multiple wind farms is forecasted. Comparison of the forecast results of different methods revealed that the NWP-CEEMDAN-LSTM method proposed in this paper, which considers feature extraction using MIC, effectively tracks power fluctuations and improves forecast performance, thereby reducing the forecast error of wind power.

Latent profile analysis with nonnormal mixtures: A Monte Carlo examination of model selection using fit indices

According to the characteristics of double fed asynchronous generator rotor energy flow, research and design based on the DSP control with two-way flow of energy function of Dual PWM converter and discusses the grid side converter control method of Dual PWM converter in particular. The wind turbine simulation model is established by using the electromagnetic transient PSCAD/EMTDC software. The simulation system is used to simulate the P, Q decoupling control and maximum wind energy tracking control of the generator. Wind is a natural phenomenon generated by the solar radiation heat, the earth's surface caused by uneven heating of the atmosphere. It is estimated that only 1% of the wind on the ground will be able to meet the needs of the world's energy. With the continuous improvement of the level of wind power generation technology, the cost of wind power gradually reduced, considering environmental benefits, the cost will be close to the cost of coal-fired power generation. Therefore, great efforts to develop wind energy as the representative of the renewable energy and new energy, to achieve sustainable development, has become the consensus of the whole society, strategic choice to solve the energy crisis and environmental problems. 2.Overview of control technology of doubly fed wind power gener ation Wind power is the kinetic energy contained in the natural wind into electrical energy in the process, the wind turbine wind energy capture and convert it into mechanical energy, driven by rotary generator, and the generator for converting mechanical energy conversion into electrical energy. As countries around the world pay more attention to wind power, wind power has become the world's fastest, most widely studied and applied new energy technology. With the development of wind power technology, wind turbine, wind turbine generator, converter and its control system and the way of the wind turbine, there are different types of. Among them, the doubly fed wind power generation system due to the converter control capacity is small, the speed of operation range wide characteristics become currently the world's most widely used VSCF wind power generation system. Variable speed constant frequency generator in asynchronous generator rotor side applied three-phase low frequency current to realize AC excitation, the output power is constant frequency and constant voltage amplitude, frequency, phase of the exciting current control. At the same time, the active power and reactive power decoupling control of the generator is realized by using the vector control technology. Control active power capable of adjusting the rotation speed of the wind turbine, to capture the maximum wind power tracking control; regulation of reactive power adjustable power factor and improve the dynamic and static stability of the wind turbine and power system operation. In addition, the VSCF wind power generation technology, so to achieve good flexible connection between the generator and power grid system, compared with the traditional constant speed constant frequency generation system easier to achieve grid connected operation and operation

This study compared the performance of Poisson regression, negative binomial regression and generalized negative binomial regression models using road traffic crashes data collected from Ekiti state command of Federal Road Safety Commission (FRSC). The method of maximum likelihood estimation was employed to determine the parameter estimate for each models, the significance of each variable consider were examined. The criteria used in selecting the best model fitted are Akaike information criterion (AIC), Bayesian information criterion and Deviance. R software package was used in analysing the data. Firstly multicollinearity was tested to determine if there is high correlation between the predictor variables. Data were analysed and the result from the three model were compared using Akaike information criterion (AIC) and Bayesian information criterion (BIC) and the deviance.The result from the three models were compared using AIC, BIC and Deviance, AIC values for the models are (414.79, 476.8 and 587.312), BIC values (490.8873, 495.59 and 589.321) and Deviance value (61.93, 66.927 and 69.927) respectively. Generalized negative binomial regression (GNBR) had the least value of AIC and BIC, thus consider as the best model for analyzing road traffic crashes data in Ekiti state, Nigeria. Having shown a smaller AIC, BIC and deviance values, the generalized negative binomial was consider a better fit model when analysing road traffic crashes in Ekiti state, Nigeria.

The demand on energy supply increases continuously as economies develop and world population grows. Most of the energy in the world comes from the fossil fuels and the increase in energy demand accelerates the rate of depleting the fossil fuel resources. As fossil fuel is finite and also due to the environmental considerations, renewable energy (RE) resources have been actively developed as the alternative sources for electricity generation. Renewable sources used for large-scale electricity production can include wind, photovoltaic (PV), waves and so on. Among all the RE resources, wind power generation is witnessing rapid developments in recent years. Unfortunately, wind tends to be unsteady. The fluctuating and uncertain output powers from wind farms can be problematic, especially if there is a high penetration level of the renewable source in a grid system. The fluctuations may lead to excessive voltage variations and unacceptable degree of frequency deviations. Moreover, the unsteady and uncertain input wind power can cause firm power dispatch commitment from wind farms a difficult task. Expensive generation reserves have to be provided for grid system to ensure adequate level of system security and reliability is guaranteed. In fact, power generation from wind farms has often been excluded in the dispatch planning of the grids. Unless other viable techniques can be found, the above issues can constitute major impediment to the successful large-scale integration of wind power generation into grid systems. In this connection, the use of energy storage system (ESS) is one possible solution to mitigate the negative impacts of the unsteady wind power on electricity supply systems and to improve on the dispatchability of the wind power. In this investigation, in order to smoothen the fluctuations in the wind and to realize the dispatch planning of the wind power in a way similar to that of conventional generators, it is proposed that a three-level ESS is incorporated in a large-scale wind power generation scheme. In essence, at cluster-level of wind turbine generators (WTG), the solution involves having the high- and mid-frequency components of the aggregated wind power routed to supercapacitors (SC) and battery banks respectively of a battery-supercapacitor hybrid energy storage system (BSHESS) by a high-pass filter (HPF) and a band-pass filter (BPF). It then results in the smoothening of the wind power harnessed by the cluster. In this thesis, the BSHESS control scheme to reduce the wind power perturbations has been shown. A statistical method is also developed to determine the capacities of the minimum-cost BSHESS to meet the power smoothing objective at pre-specified probability level. Application of the proposed design approach is demonstrated using data obtained from an existing wind farm. As for dispatch planning, attention is to use a low-pass filter (LPF) to extract the low-frequency intrinsic mode and residue functions of wind power. The relatively slow-changing characteristics of the low-frequency wind power components, which contain most of the energy in the wind power, allow accurate forecasts of the power components to be obtained using artificial neural network (ANN). Dispatch planning of the wind power is then realized through buffering the low-frequency power fluctuations by a proposed power flows control strategy applied to a pumped hydroelectric storage (PHS) system. Focusing on low-frequency wind power for dispatch planning is a distinct advantage over the dispatch planning methods proposed by other researchers. Furthermore, a statistical method to determine the power and energy capacities of the PHS is included. The efficacy of the developed approach to dispatch planning is again illustrated based on data obtained from an existing wind farm. In all the above works, suitable cut-off frequencies for the HPF, BPF and LPF are derived based on the developed concept of minimum overlap energy and the outcome of empirical mode decomposition (EMD) analysis. EMD method is used to gain insights into the frequency-time characteristics of wind power. In this manner, the wind power can then be grouped into high-, mid- and low-frequency bands.

The objective of this research work is to analyze wind characteristics and to assess wind power potential by selecting the best fit probability distribution function of Jhimpir Sindh Pakistan. This type of detailed investigation helps wind power generation companies in selecting suitable wind turbine and provides information of wind characteristics of potential site. Eight probability distribution functions are tested on the wind speed data from January 2015 to July 2018. Frequency bins of Weibull and Rayleigh distribution with maximum probabilities of 0.1210 and 0.1143 are most closest representation of our data. In order to, quantitatively analysis which distribution function is best fitting the local wind regime, we have applied the coefficient-of-determination, Kolmogorov-Smirnov, Chi square, Cramer-von Mises, Anderson-Darling tests along with Akaike information and Bayesian information criterion. These statistical test are used to rank the empirical distribution functions in order to identify two distribution function better fitting the actual wind speed data. After selecting two best fitted distribution functions, we analyze wind power potential and compare the error of wind power density based on these distribution functions (Weibull and Rayleigh). The power densities reported varied from 73.67 to 648.73W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Results indicate that power densities of Weibull and Rayleigh for the candidate site are 84.67-698.65W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 83.67-1021.4W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively. The highest error for Weibull and Rayleigh are 0.1850 and 0.5745, respectively. Whereas lowest error are 0.0178 and 0.0180, respectively. Complete analysis suggested that Weibull distribution function is the most suitable for Jhimpir Sindh Pakistan and the studied site is suitable for wind power production. In addition, comprehensive analysis of wind direction at the candidate site suggested that Eastern and Southeastern wind directions are predominant with 38.52% and 33.24% of the total time.

Objectives: To investigate the Modified Inverse Weibull Distribution (MIWD) to determine its effectiveness in modelling real customer transaction data, which is often skewed and exhibits heavy-tailed characteristics. Methods: Parameters of the model were estimated using the Maximum Likelihood Estimation (MLE) technique. The model's performance was evaluated using goodness-of-fit measures, such as the log-likelihood (ℓ), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kolmogorov–Smirnov (K–S) statistic. The probability density function (PDF), cumulative distribution function (CDF), hazard function, and survival function were derived analytically and visualized with Python to assess model behavior and data alignment. Findings: The MIWD demonstrated a better fit for the customer transaction data than its sub-models and other competing distributions. The estimated probability density function (PDF), cumulative distribution function (CDF), hazard, and survival functions highlighted the model's adaptability in representing both skewness and heavy-tailed characteristics in actual transaction data. Novelty: The main contribution of this study is the empirical validation of the four-parameter MIWD using actual customer transaction data, demonstrating its superiority over established sub-models based on various quantitative criteria. The findings provide compelling evidence that the MIWD is a robust and adaptable alternative for modelling skewed, heavy-tailed transaction and lifetime data, with practical applications in customer behavior analysis, reliability engineering, and risk modelling. Keywords: Modified Inverse Weibull Distribution, Maximum Likelihood Estimation, Customer transaction data, Parameters, Rayleigh distribution

In this paper, a new continuous probability distribution is proposed for fitting real data using Biweight kernel function and the exponential distribution. The suggested distribution is named the Biweight-exponential distribution (BiEd). Some statistical properties of this distribution are derived and illustrated mathematically. The probability density function and the cumulative distribution function are derived. Some reliability analysis functions are defined. The moments and moment generating function are derived. Re’nyi entropy is derived. The maximum likelihood method of estimation is used to derive the parameter estimates. The Bonferroni and Lorenz curves and Gini index equations are derived. The distribution of the order statistic and the quantile function are derived as well. The mean and median absolute deviations of the new distribution are derived. A numerical study was conducted to the quantile equation. An application to real data set is conducted to investigate the usefulness of the suggested distribution. In the real data application, the values of Cramer-von misses (W), Anderson Darling statistic (A), Kolmogorov-Smirnov (D) statistic, the p-value, the maximum likelihood estimates (MLE), Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan Quinn information criterion (HQIC) and minimum value of the log-likelihood function are obtained. The distribution is compared with the exponential (base) distribution based on these criteria. The results showed that the BiED fits better than the exponential distribution. This means that the suggested distribution can replace the exponential distribution for analysis of some real data sets.