Reliability Assessment Of Power Systems With Wind Farms And Photovoltaic Power Stations Considering Correlations

With the rapid development of the world’s economy and the worry aboutenvironmental pollutions, the exploitation and utilization of climate resources,especially for wind, solar and other renewable energies becomes one of the mostimportant strategies. The huge potential in utilization of wind and solar energies hasresulted in installations of many wind farms and photovoltaic power stations. Due torandomness and intermittence of wind and solar energies, the impacts of large-scalewind farms and photovoltaic power stations on power system reliability are differentfrom those of conventional energy sources. Therefore, the investigation into the impactsof wind and solar power stations on power system reliability has both theoretical andpractical values for power system planning.As the increase in the number and capacity of wind farms and photovoltaic powerstations, it is crucial to build more accurate reliability models of wind speeds and solarinsolations. By first studying the probability distributions of wind speeds, the author ofthe thesis presents a nonparametric kernel density estimation model for wind speed andtwo correlation models of multiple variables, and applies the models to systemreliability evaluations for generation and composite generation and transmissionsystems with wind farms, and composite generation and transmission system reliabilityevaluation with wind farms and photovoltaic power stations respectively.Wind speed probability distribution is used to characterize the statistical feature ofwind energy sources and thus is the basic model in wind farm planning and reliabilityassessment. The thesis proposes a wind speed probability distribution model using thenonparametric kernel density estimation. This model does not need any assumption ofwind speed probability distribution and, thus, does not need the estimation ofcharacteristic parameters of distribution function. Based on the principle of minimizingthe integrated mean square error between two nonparametric kernel density estimationfunctions with different kernel functions, an optimization-based method for calculatingthe band width in this model is also presented. By using the actual wind speed data atten wind farms, the thesis examines the appropriateness of this model and tenparametric distribution functions that have been popularly used in the existingliteratures in modeling wind speed probability distribution. The comparisons areperformed using the two statistical tests for goodness-of-fit, mean-square-root errors between historical data based discrete distribution and theoretical probability densitydistribution, and visualized match degrees of the distribution models to the histogramsof actual wind speed data. The comparisons from the statistical tests and posteriori testsindicate that the proposed nonparametric kernel estimation has better adaptability thanany conventional parametric distribution model for wind speed.With the rapid development of wind farms, many wind farms are installed in onegeographical region. There exist the correlations between wind speeds at different sites,and, therefore, the correlations should be considered in power system reliabilityevaluation with multiple wind farms. The linear correlation matrix is often used toexpress the correlation between wind speeds. The thesis presents a modified correlationmodel between multiple wind speeds that can follow any type of probability distribution.Firstly, the correlation matrix between wind speeds from non-normal distributions istransformed into the correlation matrix between normal distribution varaibles. Secondly,normal distribution variables follwoing the correlation matrix for normal distributionare produced by random sampling. Finally, wind speed varable samples that follow theoriginal non-normal distributions are obtained through the inverse transformationmethod. The assumption of normal distribution that is required by the traditionalcorrelation matrix method is eliminated in the presented model. The presentedcorrelation model has been incorpoated into a Monte Carlo simulation process ofgeneration system reliability evaluation with multiple wind farms. The results of thecase studies show that compared to the traditional correlation matrix method, theproposed model and method can better represent the correlation between wind speedsand, thus enhances the accuracy in generation system reliability calculation withmultiple wind farms.In a power system with multiple wind farms, a linear correlation assumption isgenerally acceptable in most cases. However, in some cases, wind speeds may containsort of non-linear correlation. It is a necessary to develop a correlation model bewteenmultiple wind speeds that can model nonlinear correlation. The thesis establishes acorrelation model between multiple wind speeds based on Copula functions. The modelincludes the two parts of the marginal distributions of each wind speed variable anddependence structure between wind speeds. In this correlation model, the parameters ofmarginal distributions and selected copula functions are estimated using a two-stepestimation method and then the optimal copula function is determined by the minimumeuclidean distance between empirical copula and theoretical copula. The optimal copula function is used to generate the correlated samples of wind speed by a conditionalsampling technique. This correlation model can handle the possible non-linearcorrelation between some wind speeds. This model has been incorpoated into a MonteCarlo simulation process of generation and transmission system reliability evaluationwith multiple wind farms.The results of the case studies indicate that compared to theconventional correlation matrix method, the proposed Copula function method canbetter keep probability distribution characteristics, basic statistics, and correlationstructures of historical wind speed data. The two methods were used to evaluate thereliability of composite system with multiple wind farms. The results show that theconventional correlation matrix method will lead to under-estimation of systemreliability index.Similar to the situation of wind farms, many photovoltaic power stations have beenbuilt and connected to actual electric power systems with the rapid development of solarenergy sources in China. It is necessary to look into methods that are appropriate to apower system containing both wind farms and photovoltaic power stations. Therelaibility of a composite system with both wind farms and photovoltaic powerstatations is dependent on various factors, including the distributions of wind speeds andsolar insolations, the penetration level of renewable energy sources, and the correlationsamong wind speeds, solar insolations and bus (or region) load curves in the powersystem. The thesis extends the correlation matrix method to establish a unified model tosimulate the multiple correlations among wind speeds, solar insolations and thebus/regional loads. The results of the case studies indicate that considering thecorrelations among wind speeds, solar insolations and bus/regional load curves isimportant and necessary in composite generation and transmission system reliabilityevaluation with multiple wind farms and solar power stations. Ignoring thesecorrelations will lead to under-or over-estimation of system reliability indices.