The probability density function (PDF) of wind speed is important in numerous wind energy applications. A large number of studies have been published in scientific literature related to renewable energies that propose the use of a variety of PDFs to describe wind speed frequency distributions. In this paper a review of these PDFs is carried out. The flexibility and usefulness of the PDFs in the description of different wind regimes (high frequencies of null winds, unimodal, bimodal, bitangential regimes, etc.) is analysed for a wide collection of models. Likewise, the methods that have been used to estimate the parameters on which these models depend are reviewed and the degree of complexity of the estimation is analysed in function of the model selected: these are the method of moments (MM), the maximum likelihood method (MLM) and the least squares method (LSM). In addition, a review is conducted of the statistical tests employed to see whether a sample of wind data comes from a population with a particular probability distribution. With the purpose of cataloguing the various PDFs, a comparison is made between them and the two parameter Weibull distribution (W.pdf), which has been the most widely used and accepted distribution in the specialised literature on wind energy and other renewable energy sources. This comparison is based on: (a) an analysis of the degree of fit of the continuous cumulative distribution functions (CDFs) for wind speed to the cumulative relative frequency histograms of hourly mean wind speeds recorded at weather stations located in the Canarian Archipelago; (b) an analysis of the degree of fit of the CDFs for wind power density to the cumulative relative frequency histograms of the cube of hourly mean wind speeds recorded at the aforementioned weather stations. The suitability of the distributions is judged from the coefficient of determination R2. Amongst the various conclusions obtained, it can be stated that the W.pdf presents a series of advantages with respect to the other PDFs analysed. However, the W.pdf cannot represent all the wind regimes encountered in nature such as, for example, those with high percentages of null wind speeds, bimodal distributions, etc. Therefore, its generalised use is not justified and it will be necessary to select the appropriate PDF for each wind regime in order to minimise errors in the estimation of the energy produced by a WECS (wind energy conversion system). In this sense, the extensive collection of PDFs proposed in this paper comprises a valuable catalogue.

A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands

A review of wind speed probability distributions used in wind energy analysis: case studies in the canary islands: case studies in the canary islands

Development in the field of electronics and communication set up new paradigm. The need of making the grid smart is increasing due to environmental constrain and effective use of the available electricity. The use of digital information and controls technology to improve reliability, security, and efficiency of the electric grid.

Smart grid

Influence of the data sampling interval in the estimation of the parameters of the Weibull wind speed probability density distribution: a case study

Estimating wind speed probability distribution using kernel density method

A review of induction motor fault modeling

Voltage instability within the power system has severe consequences including a wide-spread low voltage profile and system blackout. The development and use of accurate methods to predict incipient voltage instability is crucial in preventing such voltage collapse situations. A comparison of the common steady-state methods for voltage stability analysis was undertaken, along with a brief examination into the dynamic approach. Special attention is given to the modal analysis technique presented in [2], which provides both a relative proximity of the system to instability, as well identifies the key contributing factors to instability. A PC-based MATLAB prototype application was developed to assist power system operators in the assessment and analysis of the voltage stability of a power network, at any given operating point, using the modal analysis technique, in addition to useful features such as power flow analysis and traditional V-P/V-Q analysis. Using multiple practical test cases on the IEEE 30 bus system the modal analysis technique was shown to provide an accurate estimate of the system proximity to the voltage stability limit, and to consistently and correctly predict the critical buses and the weakest branches in the transmission system. These results clearly demonstrate the suitability of modal analysis technique as applied to voltage stability analysis, and the need for closer analysis, possible refinement to the method and incorporation into more commercial analysis packages.

Determination of Power System Voltage Stability Using Modal Analysis

Significant efforts has been dedicated to a statistical bivariate or univariate probability density function (pdf) as the model for compact representation of the enormous volume of raw wind data of a regime. This is essential for wind energy conversion system (W ECS) studies or for power system planning and reliability studies. However, the literature review of this paper found that acceptance of only the industry-standard two-parameter Weibull model (WE2) is questionable. Complex wind speed phenomena demand a model that is good for both interpolation and extrapolation. The main objective of this study is to revitalise interest in wind speed frequency modelling by defining a catalogue of flexible theoretical/ empirical models belonging to the Johnson, Gamma and Extreme Value families for new applicability. Definition is focussed on the three or more parameter models that are physically adaptable to wind speed. The robust Maximum Likelihood Method (MLM) and Probability Weighted Moments (PWM) method accompl...

Wind speed distributions: a new catalogue of defined models

The development and use of accurate methods to predict incipient voltage instability is crucial in preventing such voltage collapse situations. A comparison of the common steady-state methods for voltage stability analysis was undertaken, along with a brief examination into the dynamic approach. Special attention is given to modal analysis technique which provides both a relative proximity of the system to instability, as well identifies the key contributing factors to instability. A PC-based MATLAB prototype application was developed to assist power system operators in the assessment and analysis of the voltage stability of a power network, at any given operating point. Using modal analysis technique, useful features such as power flow analysis and traditional V-P/V-Q analysis have been incorporated. Using the IEEE 30 bus system, the modal analysis technique was shown to provide an accurate estimate of the system's proximity to the voltage stability limit, and to consistently and correctly predict the critical buses and the weakest branches in the transmission system.

Determination of the applicability of using modal analysis for the prediction of voltage stability

The electric utility depends on accurate load predictions for scheduling spinning reserve, unit commitment, fuel allocation and maintenance. Artificial neural networks (ANNs) have been the popular method for load forecasting but support vector machines (SVM) have recently been successfully applied to the challenge of load forecasting. In this study, the ANN and SVM techniques were applied to short term (one hour) load forecasting on a small island power system of Trinidad and Tobago for three load types. These load types are batch, continuous and batch-continuous load types which represent three unique industrial customers. A performance comparison between the ANN and SVM showed that the SVM produced repeatability, always yielding the global minimum. Both ANN and SVM were unable to accurately perform load forecasts where there may be erratic load patterns or missing data, yielding deviations greater than 3%. For the continuously varying load, the ANN and SVM load forecasts yielded a maximum deviation of 1.20%.

Chandrabhan Sharma

Papers

A review of induction motor fault modeling

Determination of Power System Voltage Stability Using Modal Analysis

Wind speed distributions: a new catalogue of defined models

Determination of the applicability of using modal analysis for the prediction of voltage stability

A comparison of artificial neural networks and support vector machines for short-term load forecasting using various load types