Wind speed scenario generation based on dependency structure analysis

This article defines coefficient of upper-lower tail dependence and coefficient of lower-upper tail dependence based on coefficient of upper tail dependence and coefficient of lower tail dependence and does an empirical research on tail dependence in China stock market. A mixed Copula that can well describe dependence structure between Shanghai Exchange Composite Index(SHECI) and Shenzhen Exchange Component Index(SZECI) is found by empirical analysis firstly, and is used to calculate coefficients of tail dependence. The results show that there are strong upper tail dependence and lower tail dependence, but no upper-lower tail dependence and lower-upper tail dependence between daily returns of SHECI and SZECI.

Wind power is a significant alternate energy in times of energy crisis. In virtue of its intermittency and fluctuation, it poses several operational challenges to grid interfaced wind energy systems. This paper introduced autoregressive integrated moving average (ARIMA) model and artificial neural network (ANN) to forecast the hourly wind speed one to four hours ahead. The models are applied to wind speed records for each month separately from a wind park in Hubei province of China. The experimental results demonstrate that these models are in good agreement with measurement values. The ANN model does a better job than ARIMA model in forecasting short-term hourly wind speed. Besides, different time series with different variance must construct different models. But when the variance is too high, it needs combined models or numerical weather predicting method to pursue better results.

Tail dependence is understood as the dependence between the variables assuming that these variables take the values from the tails of univariate distributions. In the paper two approaches of tail dependence determination are discussed: conditional correlation coefficient and tail dependence coefficients. It can be argued that both approaches are the generalizations of the well-known univariate approach, based on conditional excess distribution. In the paper the proposal is also given to extend tail dependence coefficients to the general multivariate case and to represent these coefficients through copula function.

This paper is concerned with a procedure for financial time series clustering, aimed at creating groups of time series characterized by similar behavior with regard to extreme events. The core of our proposal is a double clustering procedure: the former is based on the lower tail dependence of all the possible pairs of time series, the latter on the upper tail dependence. Tail dependence coefficients are estimated with copula functions. The final goal is to exploit the two clustering solutions in an algorithm designed to create a portfolio that maximizes the probability of joint positive extreme returns while minimizing the risk of joint negative extreme returns. In financial crisis scenarios, such a portfolio is expected to outperform portfolios generated by the traditional methods. We describe the results of a simulation study and, finally, we apply the procedure to a dataset composed of the 50 assets included in the EUROSTOXX index.

Evaluation of hybrid forecasting approaches for wind speed and power generation time series

This thesis presents the concept of tail dependence in a financial context as one tool to measure dependence in the extremes of a bivariate distribution. Copulae can separate the problem of estimating a multidimensional distribution into the estimation of the marginal distributions and the dependence between the onedimensional random variables. Therefore, copulae are used in order to carry out the estimation of the tail dependence coefficient (TDC). Four estimators of the TDC are presented and compared in a simulation study for various distributions and copulae. Furthermore, an introduction into bivariate Extreme Value Theory (EVT) is given, which tries precisely to analyze the behavior at the tail of a bivariate distribution. EVT allows to construct estimators of the TDC and to derive a test for tail independence, which is recognized to be indispensable but rarely utilized in a financial context. As an application to nine different financial data sets shows, the phenomenon of tail dependence is less common than often argued in the literature: the periods where indeed tail independence can be rejected are few.

Among bivariate tail dependence measures, the tail dependence coefficient has emerged as the popular choice. Akin to the correlation matrix, a multivariate dependence measure is constructed using these bivariate measures, and this is referred to in the literature as the tail dependence matrix (TDM). While the problem of determining whether a given d × d matrix is a correlation matrix is of the order O(d3) in complexity, determining if a matrix is a TDM (the realization problem) is believed to be non-polynomial in complexity. Using a linear programming (LP) formulation, we show that the combinatorial structure of the constraints is related to the intractable max-cut problem in a weighted graph. This connection provides an avenue for constructing parametric classes admitting a polynomial in d algorithm for determining membership in its constraint polytope. The complexity of the general realization problem is justifiably of much theoretical interest. Since in practice one resorts to lower dimensional parametrization of the TDMs, we posit that it is rather the complexity of the realization problem restricted to parametric classes of TDMs, and algorithms for it, that are more practically relevant. In this paper, we show how the inherent symmetry and sparsity in a parametrization can be exploited to achieve a significant reduction in the LP formulation, which can lead to polynomial complexity of such realization problems - some parametrizations even resulting in the constraint polytope being independent of d. We also explore the use of a probabilistic viewpoint on TDMs to derive the constraint polytopes.

Wind farms commonly cluster in regions rich in wind resources. Thus, correlation of wind speeds from different wind farms should not be ignored when modeling a power system with large wind energy penetration. This paper proposes a probabilistic optimal power flow (POPF) technique based on the quasi-Monte Carlo simulation (QMCS) considering the correlation of wind speeds using copula functions. In this paper, a copula function is used to model the dependent structure of random wind speeds and their forecast errors. QMCS is employed in the sampling procedure to reduce computation burden. The proposed method is applied in probabilistic power flow (PPF). Furthermore, the PPF is used in the POPF problem that aims at minimizing the expectation and downside risk of fuel cost simultaneously. Simulation studies are conducted on a modified IEEE 118-bus power system with wind farms integrated in two areas, and the results show that the accuracy and efficiency are improved by the proposed method.

The primary objective of this study is to evaluate the accuracy of different forecasting models for monthly wind farm electricity production. This study compares the effectiveness of three forecasting models: Autoregressive Integrated Moving Average (ARIMA), Seasonal ARIMA (SARIMA), and Support Vector Regression (SVR). This study utilizes data from two wind farms located in Poland—‘Gizałki’ and ‘Łęki Dukielskie’—to exclude the possibility of biased results due to specific characteristics of a single farm and to allow for a more comprehensive comparison of the effectiveness of both time series analysis methods. Model parameterization was optimized through a grid search based on the Mean Absolute Percentage Error (MAPE). The performance of the best models was evaluated using Mean Bias Error (MBE), MAPE, Mean Absolute Error (MAE), and R2Score. For the Gizałki farm, the ARIMA model outperformed SARIMA and SVR, while for the Łęki Dukielskie farm, SARIMA proved to be the most accurate, highlighting the importance of optimizing seasonal parameters. The SVR method demonstrated the lowest effectiveness for both datasets. The results indicate that the ARIMA and SARIMA models are effective for forecasting wind farm energy production. However, their performance is influenced by the specificity of the data and seasonal patterns. The study provides an in-depth analysis of the results and offers suggestions for future research, such as extending the data to include multidimensional time series. Our findings have practical implications for enhancing the accuracy of wind farm energy forecasts, which can significantly improve operational efficiency and planning.

This paper proposes a Bayesian network (BN) that can construct the nonlinear dependence among wind speed, solar irradiation, and load. The correlations of random variables (RVs) are analyzed using the Pearson correlation coefficient, Kendall rank correlation coefficient, and Spearman rank correlation coefficient. According to Bayesian theory, the Bayesian information criterion (BIC) and maximum likelihood estimation (MLE) methods are employed to determine the structure and parameters of a BN. Then the BN model of RVs is established. The constructed model is the joint probability distribution of RVs that can present the nonlinear dependence and marginal distribution (MD) of RVs without limitation. The testing samples of wind speed, solar irradiation, and load are generated using the autoregressive integrated moving average (ARMA) model. Then these samples are utilized to construct the probability model of a BN and C-vine copula, whose modeling accuracy and efficiency are compared, and the quality of their output synthetic samples are analyzed. In the modified IEEE 118-bus test system, two kinds of synthetic samples are used to calculate the probabilistic load flow (PLF), whose accuracy and efficiency based on the BN are tested. The validity of the BN model is verified.

As one of the conventional statistical methods, the autoregressive integrated moving average (ARIMA) model has been one of the most widely used linear models in time series forecasting. However, the ARIMA model cannot easily capture the nonlinear patterns. Artificial neural network (ANN) can be utilized to construct more accurate forecasting model than ARIMA for nonlinear time series, but it is difficult to explain the meaning of the hidden layers of ANN and it does not produce a mathematical equation. In this study, by combining ARIMA with genetic programming (GP), a hybrid forecasting model will be used for elevator traffic flow time series which can improve the accuracy both the GP and the ARIMA forecasting models separately. At last, simulations are adopted to demonstrate the advantages of the proposed ARIMA-GP forecasting model.

Relationship of meteorological factors and human brucellosis in Hebei province, China

Wind-sensitive structures usually suffer from violent vibrations or severe damages under the action of tropical storms. It is of great significance to forecast tropical-storm winds in advance for the sake of reducing or avoiding consequent losses. The model used for forecasting becomes a primary concern in engineering applications. This paper presents a performance evaluation of linear and nonlinear models for the short-term forecasting of tropical storms. Five extensively employed models are adopted to forecast wind speeds using measured samples from the tropical storm Rumbia, which facilitates a comparison of the predicting performances of different models. The analytical results indicate that the autoregressive integrated moving average (ARIMA) model outperforms the other models in the one-step ahead prediction and presents the least forecasting errors in both the mean and maximum wind speeds. However, the support vector regression (SVR) model has the worst performance on the selected dataset. When it comes to the multi-step ahead forecasting, the prediction error of each model increases as the number of steps expands. Although each model shows an insufficient ability to capture the variation of future wind speed, the ARIMA model still appears to have the least forecasting errors. Hence, the ARIMA model can offer effective short-term forecasting of tropical-storm winds in both one-step and multi-step scenarios.

We explore extreme return-volumes dependence among different cryptocurrencies such as Bitcoin, Ethereum, Ripple, and Litecoin by using the Copula approach. We use Student-t, Frank, Clayton, Survival Clayton, Gumbel, and SJC copulas. We filter out margins by using the EGARCH model for return series and GARCH model for volume series. Evidence of significant symmetric dependence between return-volume is not found due to insignificance of student-t and Frank copula parameters. In a return-volume relationship, coefficients of lower tail dependence are significant for Bitcoin, Ripple, and Litecoin which means that low returns are followed by low volumes. Lower tail dependence for the return-volume relationship is stronger than the upper tail dependence for Bitcoin, Ripple, and Litecoin. Moreover, for negative return-volume, left tail dependence coefficients are significant for Ripple and Litecoin, which means that high returns are followed by low volumes for Ripple and Litecoin. Our investigation shows that investors (buyer or seller) are very careful in extreme market conditions for both Ripple and Litecoin. Extreme upper tail and lower tail dependence coefficients are insignificant for Ethereum.

As a new energy source, the use of wind power is conducive to the protection of global resources and the environment, thus it plays an increasingly important role in alleviating the energy crisis. Due to the fluctuation and strong randomness of wind speed, wind power generation is difficult to integrate into the grid. To overcome these challenges and further enhance wind speed forecasting performance and stability, a forecasting method is developed based on long short-term memory network. To verify the properties of this deep learning algorithm, the 15-min wind speed data of four wind farms in Inner Mongolia of China are analyzed. The results of root mean square error, mean absolute error and mean absolute percentage error show that this new algorithm is superior to the autoregressive integrated moving average model in prediction accuracy and stability. Among them, compared with the ARIMA model, the root mean square error of the new model for Datasets 1-4 decreased by 60.40%, 52.19%, 75.12% and 85.64%, respectively. Thus, deep learning algorithm based on long short-term memory network is extremely useful for enhancing prediction precision, and is a reasonable and valid tool for intelligent grid programming. It also provides strong technical support for the formulation of wind power industry policies. In the future, we should improve the legal regulatory system and diversified financial tools, as well as strengthening scientific research incentive mechanisms to promote the development of the wind power industry.