Unrestricted Wind Farm Layout Optimization Research Articles

A low-order wake interaction modeling framework for the performance of ocean current turbines under turbulent conditions

Understanding the effects of ambient turbulence (expressed often in terms of the turbulence intensity It) is critical to the development of predictive models for the performance of Ocean Current Turbine (OCTs). This paper describes a new, wake interaction modeling framework capable of capturing the detailed effects of turbulence on various performance parameters associated with OCTs that may be arranged in any arbitrary configuration. The model accounts for the effects of turbulence on the structure of the turbine wakes, specifically the extents of near- and far-wake regions, and the dependence of the transition point between the two regions on It. The analytical description for turbine wake is combined with an existing wake interaction model, the Unrestricted Wind Farm Layout Optimization (UWFLO) model to predict the global power output from an array of OCTs. The resulting modelling framework accurately captures the effect of inlet turbulence on the OCT farm power and efficiency, and can be applied to any array configuration. Results from the model are validated against Large Eddy Simulations (LES) in which the OCTs are modeled using the Blade Element Momentum (BEM) model, while the inlet flow is superposed with a synthetic turbulence field designed to approximate turbulence properties obtained from observational measurements of the Gulf Stream. The simulations show that OCT wakes recover faster at higher levels of inlet turbulence due to the enhanced entrainment and mixing between ambient flow and the wake, an effect that is captured by the modified UWFLO model.

A Mixed Integer Linear Programing Formulation for Unrestricted Wind Farm Layout Optimization

This paper presents a novel mixed integer linear programing (MILP) formulation for finding the optimal layout of a fixed number of identical turbines that maximizes wind farm power generation. Previous MILP formulations with power maximizing objectives discretize the feasible space by using a grid of possible turbine locations. The proposed MILP formulation takes a different approach by allowing unrestricted placement of turbines, but treats wake cone overlap as a binary outcome. The rationale behind the proposed formulation is that the expansion of the feasible space for turbine placement in the proposed formulation would offset the disadvantage of using a lower fidelity binary wake cone overlap model. For small wind farms, the proposed formulation was able to produce superior layouts compared to a grid-based MILP formulation.

A comprehensive measure of the energy resource: Wind power potential (WPP)

Currently, the quality of available wind energy at a site is assessed using wind power density (WPD). This paper proposes to use a more comprehensive metric: the wind power potential (WPP). While the former accounts for only wind speed information, the latter exploits the joint distribution of wind speed and wind direction and yields more credible estimates. The WPP investigates the effect of wind velocity distribution on the optimal net power generation of a farm. A joint distribution of wind speed and direction is used to characterize the stochastic variation of wind conditions. Two joint distribution methods are adopted in this paper: bivariate normal distribution and anisotropic lognormal method. The net power generation for a particular farmland size and installed capacity is maximized for different distributions of wind speed and wind direction, using the Unrestricted Wind Farm Layout Optimization (UWFLO) framework. A response surface is constructed to represent the computed maximum wind farm capacity factor as a function of the parameters of the wind distribution. Two different response surface methods are adopted in this paper: (i) the adaptive hybrid functions (AHF), and (ii) the quadratic response surface method (QRSM). Toward this end, for any farm site, we can (i) estimate the parameters of the joint distribution using recorded wind data (for bivariate normal or anisotropic lognormal distributions) and (ii) predict the maximum capacity factor for a specified farm size and capacity using this response surface. The WPP metric is illustrated using recorded wind data at four differing stations in the state of North Dakota. The results illustrate the variation of wind conditions and, subsequently, its influence on the quality of wind resources. A comparison of four sites in North Dakota shows that WPD and WPP follow different trends, and the ranking of candidate sites in terms of a realistic resource potential measure is not captured by WPD.

Optimizing the arrangement and the selection of turbines for wind farms subject to varying wind conditions

The development of large scale wind farms that can compete with conventional energy resources presents significant challenges to today's wind energy industry. A powerful solution to these daunting challenges can be offered by a synergistic consideration of the key design elements (turbine selection and placement) and the variations in the natural resource. This paper significantly advances the Unrestricted Wind Farm Layout Optimization (UWFLO) method, enabling it to simultaneously optimize the placement and the selection of turbines for commercial-scale wind farms that are subject to varying wind conditions. The advanced UWFLO method avoids the following limiting traditional assumptions: (i) array/grid-wise layout pattern, (ii) fixed wind condition, or unimodal and univariate distribution of wind conditions, and (iii) the specification of a fixed and uniform type of turbine to be installed in the farm. Novel modifications are made to the formulation of the inter-turbine wake interactions, which allow turbines with differing features and power characteristics to be considered in the UWFLO method. The annual energy production is estimated using the joint distribution of wind speed and direction. A recently developed Kernel Density Estimation-based model that can adequately represent multimodal wind data is employed to characterize the wind distribution. A response surface-based wind farm cost model is also developed and implemented to evaluate and favorably constrain the Cost of Energy of the designed farm. The selection of commercially available turbines introduces discrete variables into the optimization problem; this challenging problem is solved using an advanced mixed-discrete Particle Swarm Optimization algorithm. The effectiveness of this wind farm optimization methodology is illustrated by applying it to design a 25-turbine wind farm in N. Dakota. A remarkable improvement of 6.4% in the farm capacity factor is accomplished when the farm layout and the turbine selection are simultaneously optimized.

Characterizing and mitigating the wind resource-based uncertainty in farm performance

A farm planning strategy that simultaneously accounts for the key engineering design factors and addresses the uncertainties in a wind project can offer a powerful impetus to the development of wind energy. In this context, the resource itself is highly uncertain – wind conditions, including wind speed, wind direction, and air density, show strong temporal variations; in addition, the distribution of wind conditions varies significantly from year to year. The resulting ill-predictability of the annual distribution of wind conditions introduces significant uncertainties in the estimated resource potential or the predicted performance of the wind farm. In this paper, a new methodology is developed (i) to characterize the uncertainties in the annual distribution of wind conditions, and (ii) to model the propagation of uncertainties into the local wind power density (WPD) and into farm performance evaluation. Key measures of farm performance include annual energy production (AEP), cost of energy (COE), and payback period. Both parametric and nonparametric uncertainty models are formulated, which can be leveraged in conjunction with a wide variety of stochastic wind distribution models. The AEP and the COE are evaluated using advanced analytical models, adopted from the recently developed Unrestricted Wind Farm Layout Optimization (UWFLO) framework. The year-to-year variations in the wind distribution and the quantified uncertainties are illustrated using two case studies: an onshore and an offshore wind site. Appreciable uncertainties are observed in the estimated yearly WPDs over the 10-year period – approximately 11% for the onshore site and 30% for the offshore site. The uncertainty in COE is mitigated for the onshore site using the nonparametric uncertainty model within the UWFLO framework. The ensuing robust optimization process illustrated how important it is to reduce the sensitivity of the farm performance to unreliable wind conditions, even though they may be frequent in certain years and/or contain higher energy density.

Unrestricted wind farm layout optimization (UWFLO): Investigating key factors influencing the maximum power generation

A new methodology, the Unrestricted Wind Farm Layout Optimization (UWFLO), that addresses critical aspects of optimal wind farm planning is presented in this paper. This methodology simultaneously determines the optimum farm layout and the appropriate selection of turbines (in terms of their rotor diameters) that maximizes the net power generation. The farm layout model obviates traditional restrictions imposed on the location of turbines. A standard analytical wake model has been used to account for the velocity deficits in the wakes created by individual turbines. The wind farm power generation model is validated against data from a wind tunnel experiment on a scaled down wind farm. Reasonable agreement between the model and experimental results is obtained. The complex nonlinear optimization problem presented by the wind farm model is effectively solved using constrained Particle Swarm Optimization (PSO). It is found that an optimal combination of wind turbines with differing rotor diameters can appreciably improve the farm efficiency. A preliminary wind farm cost analysis is performed to express the cost in terms of the turbine rotor diameters and the number of turbines in the farm. Subsequent exploration of the influences of (i) the number of turbines, and (ii) the farm land size, on the cost per Kilowatt of power produced, yields important observations.