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In this paper, several clustering algorithms are investigated in order to group together wind parks with close statistical behavior. Here, the proposed approach is practically founded on a fast incremental algorithm validated by a normal- ized principal component analysis combined with a k-means process. Both methods are practically based on the de...
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... the general case, when p random variables (the wind speed of site in our case) are characterized by n observations (wind speed of site j during the ith hour: ), it is possible to associate a point to each variable in (Fig. 1). However, such a representation can hardly be displayed when n becomes greater than 3 and the correlation between those variables is consequently impossible to estimate ...
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... as the one obtained with the fast incremental process. It can thus be concluded that the former solution is a good one for a number of clusters set to 14. Moreover, the so- lution of the direct k-means algorithm (with a number of clus- ters set to 14 and the solution of the fast incremental algorithm as initial iteration) is also proposed in Fig. 12 and shows that the application of this algorithm converges towards a totally dif- ferent clustering solution due to its sensitivity towards the het- erogeneity of the collected wind speed ...
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... order to be able to apply the proposed wind speed sam- pling methodology to the present application, the next step is to associate 14 distributions to the differences between the calcu- lated mean global wind speed evolution and the 14 mean ones associated to each cluster. Fig. 10 shows that those distributions can again be approximated by normal ...
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... be compared to the one based on the mean wind speed measurements. Indeed, by calculating the relative error made on the obtained correlation coefficients with the proposed "mean distribution normal noise" sampling process and by comparing it to the corresponding relative errors made with the totally independent (all the correlation coefficients Fig. 11. Relative errors on mean inter-cluster correlation coefficients using (a) "mean distribution + normal noise" (continuous) and "entirely correlated" (dashed) wind speed sampling and (b)"mean distribution + normal noise" (con- tinuous) and "totally independent" (dotted) wind speed sampling. equal to 0 and equal to 1) or with the totally ...
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... distribution + normal noise" (continuous) and "entirely correlated" (dashed) wind speed sampling and (b)"mean distribution + normal noise" (con- tinuous) and "totally independent" (dotted) wind speed sampling. equal to 0 and equal to 1) or with the totally correlated (all coefficients equal to 1) sampling process, it can again be con- cluded (Fig. 11) that the proposed "mean distribution + normal noise" sampling process with the imposed clustering threshold generally allows to better approach the real correlation existing between mean wind speed distributions associated to different clusters than it was permitted with the totally independent or correlated sampling methods. ...
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... threshold generally allows to better approach the real correlation existing between mean wind speed distributions associated to different clusters than it was permitted with the totally independent or correlated sampling methods. Nevertheless, note that, in the case of highly uncorrelated clusters (clusters 10 and 2 or clusters 5 and 7), Fig. 11(b) shows that the totally uncorrelated wind speed sampling can logically give better results than the ones obtained with the proposed new ...
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... Fig. 12, we compare the relative errors between the real ex- isting correlation coefficients (based on the real wind speed data [20]) for the seven considered wind areas and the ones calcu- lated, respectively, with the "global mean distribution + normal noise" algorithm, with the "entirely correlated" process and with "the totally ...
Citations
... A non-sequential Monte Carlo simulation was developed in [126] to determine the optimal dispatch of conventional (oil, coal, etc.) thermal generation to reduce harmful gases (CO 2 , NO x , etc.) emissions considering wind power and constraints. The author in [127], proposed several clustering algorithms for suitability assessment in system generation studies based on non-sequential MCS. In [128], an approach was proposed for incorporating actual wind generation into a non-sequential Monte Carlo adequacy evaluation with economic dispatch in a transmission power system. ...
The continuously growing population and urban growth rates are responsible for the sharp rise in energy consumption , which leads to increased CO 2 emissions and demand-supply imbalances. The power sector is switching to alternative energy sources, including renewable energy resources (RES) such as Photovoltaic (PV) and wind power (WP) and battery energy storage systems (BESS), among others, due to an increase in the use of fossil fuels and their shortage. Since the power generation of these resources is uncertain due to climatic fluctuations and the direct integration of these resources into the power grid is very complex due to the issues such as; voltage and frequency regulation, overloading of active transmission lines, and supply-demand disparity, the research on system uncertainties is receiving increasing attention. This study provides a comprehensive analysis of the several parameters of uncertainty, approaches for dealing with the uncertainty in battery energy storage (BES)-based RES integrated grid, and the advantages and disadvantages of each method. Moreover, various analytical and numerical approaches were developed for integrating RES and BESS into the power grid, including proba-bilistic methods, possibilistic methods, robust optimization-based techniques, and machine learning algorithms. The comparative analysis of these approaches highlights their relative strengths and weaknesses, providing a valuable resource for researchers and utility planners. Additionally, this review paper identifies several issues and challenges associated with the integration of RES and BESS into the power grid, such as power quality, economical effect, battery aging effect, and environmental effect. Furthermore, the paper suggests a few future research directions, including the development of novel models for analyzing uncertainty in power systems, coordination of uncertainty parameters, integration of BESS into RES and grid, power electronics integration, and environmental factor. Overall, this article's novel contributions include a comprehensive analysis of uncertainty parameters, a comparative analysis of uncertainty modeling approaches, an identification of critical issues and challenges, and the suggestion of future research directions to promote a sustainable and reliable power system. This article will aid in defining the requirements and specifications for novel models for analyzing uncertainty in power systems. The discussion and analysis will assist researchers and utility planners in selecting a suitable uncertainty modeling approach with significant penetrations of distributed RESs, which can lead to achieving a reliable and sustainable power system.
... For the reliability analysis of the active distribution network with the load and the renewable energy, the SMC method is adopted in order to simulate the working state sampling of the DGs and the load [20,30]. Meanwhile, the states of the devices are related in the active distribution network and the state transition of the devices has a certain sequence. ...
... Further, the reliability indexes are calculated by using other common algorithms, including the minimum path (MP) algorithm [34] and the nonsequential Monte Carlo (NMC) algorithm [30] under scenario 1. The results and the calculation time obtained by three algorithms are compared in Table 4. Comparing with the reliability indexes obtained by the MP algorithm and NMC algorithm, the indexes calculated by the proposed method in the paper are obviously smaller. ...
An active distribution network is an important development trend of the power grid with widespread use of the distributed generation. The reliability of the active distribution network is not negligible due to the uninterruptible power supply. In the paper, the reliability evaluation method of the active distribution network is proposed in detail, based on combining the roulette wheel selection and the sequential Monte Carlo algorithm. The uncertainty of both the distribution generation and the load is taken into consideration based on the power probability distribution and the working state in the presented model. Furthermore, the IEEE-RBTS Bus 6 is used to verify the validity of the proposed method. The result shows that the new energy access improves the availability and the reliability of the active distribution network.
... While the former category considers the peak load demand and available generation to evaluate the capacity (or deficit) margin, the latter generally takes advantage of Monte Carlo simulations that permit to capture the uncertain nature of load and generation. Sequential and non-sequential Monte Carlo methods for adequacy assessments have been studied in [1]- [3]. ...
... The final decision of the RF classifier is made by aggregating the decisions of individual trees that helps it to exhibit a good generalization capability. Within its training phase, the RF algorithm aims at defining the right features in each tree to grow and the optimal split of the selected features so that the loss function L can be minimized according to (3). The parameters that need to be selected to optimize the performance of the RF classifier are the number of trees to grow and number of input features (variables) considered in each split. ...
To represent the cross-border exchange capacities defined by the flow-based approach in the European resource adequacy assessments, transmission system operators currently employ a data-driven methodology that consists of sequential clustering and correlation steps. This methodology entails assumptions and simplifications within both clustering and correlation analyses that may lead to an erroneous representation of import-export capacities in the subsequent adequacy assessments. While the first stage of this methodology can be improved by leveraging a clustering technique tailored to adequacy assessments, the correlation step presents a poor performance in terms of accuracy and scalability. To address the latter challenges, this paper proposes a supervised learning-based model that can enhance the mapping between several relevant explanatory variables and the pre-clustered flow-based domains, leading to a more accurate representation of the flow-based domains in adequacy assessments. Furthermore, the current paper leverages supervised learning to develop a single-step approach that directly maps the selected explanatory variables to the flow-based domains using the K-Nearest Neighbors algorithm, eliminating the clustering step. This circumvents inaccuracies introduced by the significant intra-cluster discrepancies due to numerous shapes and forms of the flow-based domains and enables an enhanced modeling of the flow-based domains in adequacy assessments. In an extensive case study, we demonstrate that the proposed single-step model can significantly improve the accuracy of adequacy assessments, compared to the best-in-class result obtained by the two-step setup. Moreover, the proposed single-step model involves no hyper-parameters, eliminates the computational complexity of the two-step setup , and efficiently upscales to integrate the new zones joining to the flow-based market coupling.
... While the former category considers the peak load demand and available generation to evaluate the capacity (or deficit) margin, the latter generally takes advantage of Monte Carlo simulations that permit to capture the uncertain nature of load and generation. Sequential and non-sequential Monte Carlo methods for adequacy assessments have been studied in [1]- [3]. ...
... The final decision is made by aggregating the decisions of individual trees that helps the RF classifier to exhibit a good generalization capability. Within its training phase, the RF algorithm aims at defining the right features in each tree to grow and the optimal split of the selected features so that the loss function L can be minimized according to (3). ...
To represent the cross-border exchange capacities defined by the flow-based approach in the European resource adequacy assessments, transmission system operators currently employ a data-driven methodology that consists of sequential clustering and correlation steps. This methodology entails assumptions and simplifications within both clustering and correlation analyses that may lead to an erroneous representation of import-export capacities in the subsequent adequacy assessments. While the first stage of this methodology can be improved by leveraging a clustering technique tailored to adequacy assessments, the correlation step presents a poor performance in terms of accuracy and scalability. To address the latter challenges, this paper proposes a supervised learning-based model that can enhance the mapping between several relevant explanatory variables and the pre-clustered flow-based domains, leading to a more accurate representation of the flow-based domains in adequacy assessments. Furthermore, the current paper leverages the supervised learning to develop a single-step approach that directly maps the selected explanatory variables to the flow-based domains using the K-Nearest Neighbors algorithm, eliminating the clustering step. This circumvents inaccuracies introduced by the significant intra-cluster discrepancies due to numerous shapes and forms of the flow-based domains and enables an enhanced modeling of the flow-based domains in adequacy assessments. In an extensive case study, we demonstrate that the proposed single-step model can significantly improve the accuracy of adequacy assessments, compared to the best-in-class result obtained by the two-step set-up. Moreover, the proposed single-step model involves no hyper-parameters, eliminates the computational complexity of the two-step set-up, and efficiently upscales to integrate the new zones joining to the flow-based market coupling. Index Terms: Adequacy assessments, flow-based market coupling, cross-border power exchanges, machine learning.
... Sequential and non-sequential Monte Carlo methods for generation adequacy assessment in single-and multi-area electric power systems have been studied in [6]. Also, Monte Carlo simulations have been utilized in [7], [8] to integrate wind generation into adequacy assessments. An importance-based Monte Carlo sampling approach has been developed in [9] that improves the computational performance of the considered adequacy problem. ...
The resource adequacy of the interconnected Central Western Europe (CWE) electricity system is assessed considering the cross-border exchange capacities defined through the Flow-Based (FB) domains. Integration of FB domains into adequacy assessments poses several challenges since the FB domains depend on factors which are not known over the horizon of adequacy study. Computing hourly FB domains for each generated scenario of adequacy study, firstly, requires adopting assumptions on those unknown parameters (that may not fully match with the reality). Secondly, it noticeably increases the computational complexity of the study. The above challenges can, however, be circumvented by the data-driven alternatives. This paper presents a novel clustering technique for FB domains, which is specifically tailored for adequacy assessments. In contrast to the classical approach employed by the CWE Transmission System Operators (TSOs), which clusters the FB domains based on their overall geometrical resemblance, the proposed technique relies on the maximum and minimum zonal balances allowed by the FB domains, which are decisive factors in the CWE resource adequacy assessments. Indeed, during scarcity moments, the zonal net positions (balances) tend to reach their extreme values to reduce the costs of energy not served. The proposed goal-oriented clustering technique is examined against the classical clustering methodology employed by the CWE TSOs. The conducted simulations demonstrate that the proposed technique considerably (by a factor of over 5.5) improves the accuracy of the CWE adequacy assessments while being scalable with the future evolution of the Flow-based Market Coupling (FBMC). As such, it has direct implications for the adequacy assessment considering the FB domains.
... Taking the data of a district in China in August 2019 as an example, the correlation between wind power consumption capacity and fluctuation characteristics is qualitatively analyzed by Pearson correlation coefficient (PCC). PCC is the most commonly used method to measure the correlation of series, and has many application examples in wind power output prediction (Vallée et al., 2011;Zhou et al., 2019;Wang and Zou, 2020). The correlation between any two variable sequences x and y can be calculated by Eq. 7. ...
An analysis model of wind power consumption capacity is established with the multi-fractal theory. Firstly, the fluctuation characteristics of wind power are described through multi-fractal parameters, and the correlation between wind power fluctuation characteristics and consumption capacity are analyzed. Afterwards, the swinging door algorithm (SDA) is applied to divide the wind power curve in the evaluation period, and the fluctuation process with similar characteristics is clustered. Further, a functional analysis model to evaluate wind power consumption capacity is mentioned based on the fluctuation clustering results. Finally, the effectiveness of the method is verified by an example of a regional power grid in China, and the influence of adjustable parameters in the model on the consumption capacity is quantitatively analyzed.
... Therefore, (1, ) j is selected as the feature vector for DFIGs clustering in area 2. Therefore, the DFIGs in area 2 are reasonably divided into several groups, and the DFIGs in the same group have similar wind speeds. In this paper, the machine learning method k-means implements clustering [28]. ...
The injection of a significant amount of wind power tends to increase the difficulty of the grid frequency control. Therefore, wind farm (WF) has to have the ability to participate in system frequency support. However, during the frequency control process in a large WF, individual wind generators may prone to instability due to possible over-deceleration. In addition, the deeply-intertwined cyber physical power system (CPPS) has gradually replaced the traditional grid due to the development of information and communication technology. However, CPPS also introduces cyber uncertainties that have a significant negative impact on the real-time control of power system. To address above issues, this paper considering possible cyber uncertainty, and proposes a grouping-based hierarchical frequency support scheme for WF. In the proposed scheme, the variable speed wind turbines (VSWTs) are clustered into several groups, according to their wind profiles at first, by dispatching the same control commands to the VSWTs belonging to the same group. As a result, the number of the VSWTs and control variables reduces significantly. Then, a hierarchical control scheme based on virtual inertial control is proposed with consideration of possible cyber uncertainty. The top-layer controller determines whether cyber uncertainty exists, and calculates power increment based on frequency deviation and cyber uncertainty. The bottom-layer controller coordinates the power increment distribution on the basis of ensuring the safe operation of all VSWTs. By do this, it is expected to achieve not only optimal frequency response but also wind generator stability. The effectiveness of proposed scheme is verified on a simulation platform built using MATLAB.
... Recently, data mining techniques have been applied to power system studies to process large volumes of data in a diverse set of literature studies. 36,37 Typical applications include cable layout design, evaluation of transfer capabilities, reliability of networks, and also wind power forecasting. 38 In the study by Vallee et al., 37 a clustering method is developed to group 94 wind areas into 14 clusters, which are then used to generate samples of wind speed to evaluate system reliability through a non-sequential Monte Carlo simulation. ...
A critical step in stochastic optimization models of power system analysis is to select a set of appropriate scenarios and significant numbers of scenario generation methods exist in the literature. This paper develops a clustering based scenario generation method, which aims to improve the performance of existing scenario generation techniques by grouping a set of correlated wind sites into clusters according to their cross-correlations. Copula based models are utilized to model spatiotemporal correlations and the Gibbs sampling is then used to generate scenarios for day-ahead markets. Our results show that the generated scenarios based on clustered wind sites outperform existing approaches in terms of reliability and sharpness and can reduce the total computational time for scenario generation and reduction significantly. The clustering-based framework can therefore provide a better support for real-world market simulations with high wind penetration.
... Calculation burden reduction will be more necessary in probabilistic studies. Recently, clustering methods have been considered in power system probabilistic studies [28][29][30][31][32]. The task of organizing a collection of objects in such a way that objects within the same group are more similar to one another than to those in other groups is called clustering. ...
... Also, it is assumed that the loads on nodes 13,14,15,16,19,20,22,27,32, and 37 are random variables that follow normal distribution [34]. It is supposed that the expected values of these variables in various time intervals are equal to their values obtained from (28) and (29). The value of the standard deviation of each load in each time interval is equal to its related expected value divided to 5. Table 2 shows the probabilistic information related to the wind generators connected to different nodes. ...
... A wind clustering method was presented in [14] based on the Kmeans method, in order to group wind parks with a close statistical behaviour. Probabilistic assessment of available transfer capability was also presented in [15] based on a vector quantification clustering algorithm. ...
... Using Cholesky decomposition technique, R X is represented according to (14) ...
The growing popularity of renewable‐based generations along with loads fluctuation and network topology variation has exposed distribution systems to high uncertainties, causing difficulties in operating and planning decisions. In addition, the correlation among various uncertain variables has introduced more complexity to this problem. The probabilistic assessment of power systems with various uncertain variables and with any correlation between them can be efficiently handled by Monte–Carlo simulation (MCS) method, but the calculation burden in this method is heavy and thus it is not appropriate in online applications. Keeping the accuracy of the results, data clustering techniques can be efficiently substituted for this method with much less calculation time and burden. In this study, two methods based on data clustering which can consider the correlation between different variables in a straightforward manner are presented for the probabilistic power flow of distribution systems. In order to demonstrate the efficiency of the proposed methods, IEEE 37 node test feeder and IEEE 123 node test feeder were selected as the case study. The results obtained by the proposed methods were compared with those of the MCS method in terms of accuracy and calculation time.
