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Optimization of wind farm (WF) layout has been studied in the literature with the objective of maximizing the wind energy capture. Based on the power spectrum density (PSD) theorem, this paper shows that the WF layout affects not only the total harvested energy but also the level of power fluctuation, which in turn influences required capacity of battery energy storage system (BESS) needed to mitigate the inherent power fluctuation of the wind farms. Since both harvested energy level and BESS capacity directly influence the profit of WF owner, the effect of WF layout on these quantities are taken into account simultaneously and WF layout optimization problem is redefined. Genetic algorithm (GA) is then employed in order to optimize the resulting objective function. The proposed method and optimization process are performed on the layout of an actual offshore WF using real wind data. A new index is introduced to quantify the power fluctuations, and energy curtailment is assessed. The comparative analysis between the actual layout performance and the optimal layout in different scenarios is conducted, showing the reduction of power fluctuations and improvement of energy curtailment. In addition, different BESS technologies have been analyzed to study the impact of their parameters on the optimization results.

The operation of aggregators of distributed energy resources (DER) is highly complex, since it entails the optimal coordination of a diverse portfolio of DER under multiple sources of uncertainty. The large number of possible stochastic realizations that arise, can lead to complex operational models that become problematic in real-time market environments. Previous stochastic programming approaches resort to two-stage uncertainty models and scenario reduction techniques to preserve the tractability of the problem. However, two-stage models cannot fully capture the evolution of uncertain processes and the a priori scenario selection can lead to suboptimal decisions. In this context, this paper develops a novel stochastic dual dynamic programming (SDDP) approach which does not require discretization of either the state space or the uncertain variables and can be efficiently applied to a multi-stage uncertainty model. Temporal dependencies of the uncertain variables as well as dependencies among different uncertain variables can be captured through the integration of any linear multidimensional stochastic model, and it is showcased for a p-order vector autoregressive (VAR) model. The proposed approach is compared against a traditional scenario-tree-based approach through a Monte-Carlo validation process, and is demonstrated to achieve a better trade-off between solution efficiency and computational effort.

This paper proposes a frequency support control scheme for large-scale wind farm (WF) by considering distributed layout of wind turbines (WT) and wake effects inside the WF. The frequency support of WF is formulated as optimization problems. A novel clustering-based optimization method is proposed to coordinate all the WTs so that the whole WF can work at the optimal operating states. In large-scale WF, number of WTs is numerous. With the proposed method, the WTs are first clustered into groups according to their wind profiles. By dispatching the same control commands to the WTs belonging to the same group, each group can be further seen as one single WT. As a result, the number of the WTs and control variables reduces significantly and hence the optimization problems are highly simplified. A case study is carried out to verify the effectiveness of the proposed method.

The accurate quantitative reliability evaluation of off-shore wind power plants (OWPPs) is an important part in planning and helps to obtain economic optimization. However, loop structures in collector systems and large quantities of components with correlated failures caused by shared ambient influences are significant challenges in the reliability evaluation. This paper proposes an ana-lytical approach to evaluate the reliability of OWPPs considering environmental impact on failures and solve the challenges by protection zone models, equivalent power unit models and common cause failure (CCF) analysis. Based on investigation of the characteristics of OWPP and related failures mechanisms, the components are divided into three CCF subsets. With the aid of the protection zone model and equivalent power unit model merged with CCF, the faulty collector system state eval-uation is applied to reduce the computational burden. The case studies present the necessity and improved per-formance of merging CCF analysis into modeling via the comparison with other two simplified methods. A sensi-tivity analysis is also carried out to account for inaccu-racy of failure data. The results show that the assump-tion of independent failures in the conventional method might lead to over-optimistic or over-pessimistic evalua-tion depending on the CCF style.

High penetration of wind generation causes concerns over frequency stability, as currently wind plants do not provide frequency response support. Extensive research has been conducted to investigate alternative designs of controllers to facilitate the provision of synthetic inertia and primary frequency response from wind plants. However, frequency response support from wind plants differs from that provided by conventional plants and its impact on the system's economic performance is not yet fully understood. In this context, this paper develops a novel methodology to incorporate the frequency response support from wind plants into generation scheduling, thus enabling the benefits of alternative control strategies to be quantified. Studies are carried out on the future Great Britain power system with different wind energy penetration levels and frequency response requirements. The impact of the uncertainty associated with the quantity of wind plants being online and the energy recovery effect are also analyzed. The results demonstrate that the benefits of frequency response support from wind plants may be significant, although these are system specific. The proposed model could also inform the development of grid codes, market mechanisms, and business cases associated with the frequency response support from wind plants.

This paper presents modeling and analysis of electrical oscillations in a wind farm system. The detailed modeling and modal analysis of a wind farm system are presented in this paper. The approach to modeling uses detailed representation of a wind turbine generator and collection system including high-voltage direct-current (HVDC) power converter system control, facilitating a comprehensive analysis of the wind farm system. Various modes are classified according to the frequency of oscillation. The detailed modal analysis is used to characterize the critical modes. Time-domain simulation also confirms the presence of these modes. The effect of wind farm operating conditions and voltage source converter control tuning on critical oscillatory modes are also assessed and discussed in detail.

In this paper, the electrical response of a partially shaded photovoltaic (PV) array, comprising several strings connected in parallel, is investigated. The PV array is simulated by employing an enhanced version of the widely used single-diode model, reformulated in an explicit manner employing the Lambert $\bm{W}$ function. The multiple maximum power points (MPPs) that appear on the $\bm{P}-\bm{V}$ characteristic of the array in partial shading conditions are analyzed, in terms of their number and properties. Simplified empirical expressions are then derived to calculate the voltage, current, and power for each local MPP, at any irradiance level and temperature, using only datasheet information, in a most simple and straightforward manner, without resorting to detailed modeling and simulations. The derived formulae are validated using both simulation and experimental results.

In this paper, a reformulation of the widely used one-diode model of the photovoltaic (PV) cell is introduced, employing the Lambert W function. This leads to an efficient PV string model, where the terminal voltage is expressed as an explicit function of the current, resulting in significantly reduced calculation times and improved robustness of simulation. The model is experimentally validated and then used for studying the operation of PV strings under partial shading conditions. Various shading patterns are investigated to outline the effect on the string I-V and P-V characteristics. Simplified formulae are then derived to calculate the maximum power points of a PV string operating under any number of irradiance levels, without resorting to detailed modeling and simulation. Both the explicit model and the simplified expressions are intended for application in shading loss and energy yield calculations.