Weiyang Tong

Impact of Different Wake Models On the Estimation of Wind Farm Power Generation

The power generation of a wind farm is significantly less than the summation of the power generated by each turbine when operating as a standalone entity. This power reduction can be attributed to the energy loss due to the wake effects the resulting velocity deficit in the wind downstream of a turbine. In the case of wind farm design, the wake losses are generally quantified using wake models. The effectiveness of wind farm design (seeking to maximize the farm output) therefore depends on the accuracy and the reliability of the wake models. This paper compares the impact of the following four analytical wake models on the wind farm power generation: (i) the Jensen model, (ii) the Larsen model, (iii) the Frandsen model, and (iv) the Ishihara model. The sensitivity of this impact to the Land Area per Turbine (LAT) and the incoming wind speed is also investigated. The wind farm power generation model used in this paper is adopted from the Unrestricted Wind Farm Layout Optimization (UWFLO) methodology. Single wake case studies show that the velocity deficit and the wake diameter estimated by the different analytical wake models can be significantly different. A maximum difference of 70% was also observed for the wind farm capacity factor values estimated using different wake models

Quantifying regional error in surrogates by modeling its relationship with sample density

Approximation models (or surrogate models) provide an efficient substitute to expensive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such approximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) information regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Regional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as intermediate training points, is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors within the region of interest for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The estimated statistical mode of the median and the maximum error, and the absolute maximum error are then represented as functions of the density of intermediate training points, using regression models. The regression models are then used to predict the expected median and maximum regional errors when all the sample points are used as training points. Standard test functions and a wind farm power generation problem are used to illustrate the effectiveness and the utility of such a regional error quantification method.

Modeling the Influence of Land-Shape on the Energy Production Potential of a Wind Farm Site

During wind farm planning, the farm layout or turbine arrangement is generally opti-mized to minimize the wake losses, and thereby maximize the energy production. How-ever, the scope of layout design itself depends on the specified farm land-shape, wherethe latter is conventionally not considered a part of the wind farm decision-making pro-cess. Instead, a presumed land-shape is generally used during the layout design process,likely leading to sub-optimal wind farm planning. In this paper, we develop a novelframework to explore how the farm land-shape influences the output potential of a site,under a given wind resource variation. Farm land-shapes are defined in terms of their as-pect ratio and directional orientation, assuming a rectangular configuration. Simultane-ous optimizations of the turbine selection and placement are performed to maximize theenergy production capacity, for a set of sample land-shapes with fixed land area. Themaximum farm capacity factor or farm output potential is then represented as a functionof the land aspect ratio and land orientation, using quadratic and Kriging response surfa-ces. This framework is applied to design a 25MW wind farm at a North Dakota site thatexperiences multiple dominant wind directions. An appreciable 5% difference in capacityfactor is observed between the best and the worst sample farm land-shapes at this windsite. It is observed that among the 50 sample land-shapes, higher energy production isaccomplished by the farm lands that have aspect ratios significantly greater than one,and are oriented lengthwise roughly along the dominant wind direction axis. Subsequentoptimization of the land-shape using the Kriging response surface further corroboratesthis observation. [DOI: 10.1115/1.4026201]Keywords: capacity factor, farm land-shape, response surface, wind distribution, windfarm layout optimization

Adaptive Switching of Variable-Fidelity Models in Population-Based Optimization

This article presents a novel model management technique to be implemented in population-based heuristic optimization. This technique adaptively selects different computational models (both physics-based models and surrogate models) to be used during optimization, with the overall objective to result in optimal designs with high fidelity function estimates at a reasonable computational expense. For example, in optimizing an aircraft wing to obtain maximum lift-to-drag ratio, one can use low fidelity models such as given by the vortex lattice method, or a high fidelity finite volume model, or a surrogate model that substitutes the high-fidelity model. The information from these models with different levels of fidelity is integrated into the heuristic optimization process using the new adaptive model switching (AMS) technique. The model switching technique replaces the current model with the next higher fidelity model, when a stochastic switching criterion is met at a given iteration during the optimization process. The switching criterion is based on whether the uncertainty associated with the current model output dominates the latest improvement of the relative fitness function, where both the model output uncertainty and the function improvement (across the population) are expressed as probability distributions. For practical implementation, a measure of critical probability is used to regulate the degree of error that will be allowed, i.e., the fraction of instances where the improvement will be allowed to be lower than the model error, without having to change the model. In the absence of this critical probability, model management might become too conservative, leading to premature model-switching and thus higher computing expense. The proposed AMS-based optimization is applied to two design problems through Particle Swarm Optimization, which are: (i) Airfoil design, and (ii) Cantilever composite beam design. The application case studies of AMS illustrated: (i) the computational advantage of this method over purely high fidelity model-based optimization, and (ii) the accuracy advantage of this method over purely low fidelity model-based optimization.

New Modular Product-Platform-Planning Approach to Design Macroscale Reconfigurable Unmanned Aerial Vehicles

The benefits of a family of macroscale reconfigurable unmanned aerial vehicles to meet distinct flight requirements are readily evident. The reconfiguration capability of an unmanned-aerial-vehicle family for different aerial tasks offers a clear cost advantage to end users over acquiring separate unmanned aerial vehicles dedicated to specific types of missions. At the same time, it allows the manufacturer the opportunity to capture distinct market segments, while saving on overhead costs, transportation costs, and after-market services. Such macroscale reconfigurability can be introduced through effective application of modular product-platform-planning concepts. This paper advances and implements the Comprehensive Product Platform Planning framework to design a family of three reconfigurable twin-boom unmanned aerial vehicles with different mission requirements. The original Comprehensive Product Platform Planning method was suitable for scale-based product-family design. In this paper, important modifi...

Sensitivity of Wind Farm Output to Wind Conditions, Land Configuration, and Installed Capacity, Under Different Wake Models

In conventional wind farm design and optimization, analytical wake models are generally used to estimate the wake-induced power losses. Different wake models often yield significantly dissimilar estimates of wake velocity deficit and wake width. In this context, the wake behavior, as well as the subsequent wind farm power generation, can be expressed as functions of a series of key factors. A quantitative understanding of the relative impact of each of these key factors, particularly under the application of different wake models, is paramount to reliable quantification of wind farm power generation. Such an understanding is however not readily evident in the current state of the art in wind farm design. To fill this important gap, this paper develops a comprehensive sensitivity analysis (SA) of wind farm performance with respect to the key natural and design factors. Specifically, the sensitivities of the estimated wind farm power generation and maximum farm output potential are investigated with respect to the following key factors: (i) incoming wind speed, (ii) ambient turbulence, (iii) land area per MW installed, (iv) land aspect ratio, and (v) nameplate capacity. The extended Fourier amplitude sensitivity test (e-FAST), which helpfully provides a measure of both first-order and total-order sensitivity indices, is used for this purpose. The impact of using four different analytical wake models (i.e., Jensen, Frandsen, Larsen, and Ishihara models) on the wind farm SA is also explored. By applying this new SA framework, it was observed that, when the incoming wind speed is below the turbine rated speed, the impact of incoming wind speed on the wind farm power generation is dominant, irrespective of the choice of wake models. Interestingly, for array-like wind farms, the relative importance of each input parameter was found to vary significantly with the choice of wake models, i.e., appreciable differences in the sensitivity indices (of up to 70%) were observed across the different wake models. In contrast, for optimized wind farm layouts, the choice of wake models was observed to have marginal impact on the sensitivity indices. [DOI: 10.1115/1.4029892]

A consolidated visualization of wind farm energy production potential and optimal land shapes under different land area and nameplate capacity decisions

Effective and time-efficient decision-making in the early stages of wind farm planning can lay the foundation of a successful wind energy project. Undesirable concept-to-installation delays in wind farm development is often caused by conflicting decisions from the major parties involved (e.g., developer, investors, landowners, and local communities), which in turn can be (in a major part) attributed to the lack of an upfront understanding of the trade-offs between the technical, socio-economic, and environmental-impact aspects of the wind farm for the given site. This paper proposes a consolidated visualization platform for wind farm planning, which could facilitate informed and co-operative decision-making by the parties involved. This visualization platform offers a GUI-based land shape chart, which provides the following information: the variation of the energy production capacity and of the corresponding required optimal land shape with different land area and nameplate capacity decisions. In order to develop this chart, a bi-objective optimization problem is formulated (using the Unrestricted Wind Farm Layout Optimization framework) to maximize the capacity factor and minimize the land usage, subject to different nameplate capacity decisions. The application of an Optimal Layout-based land usage estimate allows the wind farm layout optimization to run without pre-specifying any farm boundaries; the optimal land shape is instead determined as a post process, using convex hull and minimum bounding rectangle concept, based on the optimal arrangement of turbines. Three land shape charts are generated under three characteristic wind patterns - (i) single dominant wind direction, (ii) two opposite dominant wind directions, and (ii) two orthogonal dominant wind directions, all three patterns comprising the same wind speed distribution. The results indicate that the optimal land shape is highly sensitive to the variation in LAMI for small-capacity wind farms (few turbines) and to the variation in nameplate capacity for small allowed land area. For the same decided nameplate capacity and LAMI values, we observe reasonable similarity in the optimal land shapes and the maximum energy production potentials given the “single dominant direction” and the “two opposite dominant directions” wind patterns; the optimal land shapes and the maximum energy production potentials yielded by the “two orthogonal dominant directions” wind pattern is however observed to be relatively different from the other two cases.

SENSITIVITY OF ARRAY-LIKE AND OPTIMIZED WIND FARM OUTPUT TO KEY FACTORS AND CHOICE OF WAKE MODELS

The creation of wakes, with unique turbulence characteristics, downstream of turbines significantly increases the complexity of the boundary layer flow within a wind farm. In conventional wind farm design, analytical wake models are generally used to compute the wake-induced power losses, wi th different wake models yielding significantly different estimates. In this context, the wake behavior, and subsequently the far m power generation, can be expressed as functions of a series o key factors. A quantitative understanding of the relative i mpact of each of these factors is paramount to the development of more reliable power generation models; such an understandi ng is however missing in the current state of the art in wind farm design. In this paper, we quantitatively explore how the far m

A New Multi-Objective Mixed-Discrete Particle Swarm Optimization Algorithm

Complex system design problems tend to be high dimensional and nonlinear, and also often involve multiple objectives and mixed-integer variables. Heuristic optimization algorithms have the potential to address the typical (if not most) characteristics of such complex problems. Among them, the Particle Swarm Optimization (PSO) algorithm has gained significant popularity due to its maturity and fast convergence abilities. This paper seeks to translate the unique benefits of PSO from solving typical continuous single-objective optimization problems to solving multi-objective mixed-discrete problems, which is a relatively new ground for PSO application. The previously developed Mixed-Discrete Particle Swarm Optimization (MDPSO) algorithm, which includes an exclusive diversity preservation technique to prevent premature particle clustering, has been shown to be a powerful single-objective solver for highly constrained MINLP problems. In this paper, we make fundamental advancements to the MDPSO algorithm, enabling it to solve challenging multi-objective problems with mixed-discrete design variables. In the velocity update equation, the explorative term is modified to point towards the non-dominated solution that is the closest to the corresponding particle (at any iteration). The fractional domain in the diversity preservation technique, which was previously defined in terms of a single global leader, is now applied to multiple global leaders in the intermediate Pareto front. The multi-objective MDPSO (MO-MDPSO) algorithm is tested using a suite of diverse benchmark problems and a disc-brake design problem. To illustrate the advantages of the new MO-MDPSO algorithm, the results are compared with those given by the popular Elitist Non-dominated Sorting Genetic Algorithm-II (NSGA-II).© 2014 ASME

Adaptive Model Refinement in Surrogate-based Multiobjective Optimization

Surrogate-Based Optimization (SBO), while providing a computationally-efficient alternative to expensive high-fidelity optimization of complex systems, is often plagued by the low reliability of the optimum values obtained thereof. Model refinement techniques are one of the most recognized means to increasing the reliability of the optimum solutions while preserving the computational efficiency of SBO. One such method is the recently developed Adaptive Model Refinement (AMR) technique, which decides when to refine and the desired extent of the refinement, for single-objective optimization using any type of surrogate models (i.e., a model independent approach). In this paper, we make fundamental modifications to the AMR technique to extend its applicability to multiobjective problems, both in the case of problems involving multiple and single high-fidelity source codes or simulations. The AMR technique is designed to work particularly with population-based optimization algorithms. In AMR, the reconstruction of the model is performed by sequentially adding a batch of new samples at any given iteration (of SBO), when a refinement metric is met. This metric is formulated by comparing (1) the uncertainty associated with the outputs of the current model, and (2) the distribution of the latest fitness function improvement over the population of candidate designs. Conservative, non-conservative, and balanced approaches are explored for multiobjective implementation, in terms of the fraction of objectives for which the model refinement metric has been satisfied. In the case of an affirmative decision for model refinement, the history of the fitness function improvement is used to determine the desired fidelity for the upcoming iterations of SBO. The location of the new samples in the input space is determined based on the smallest hypercube enclosing the entire population of candidate designs, the smallest hypercube enclosing the current set of non-dominated designs, and a distance-based criterion that minimizes the correlation between the current sample points and the new points. A multiobjective implementation of GA algorithm is used in conjunction with Kriging surrogate model to apply the new AMR method. The performance of the new multiobjective AMR method is investigated by applying it to a structural wind blade design problem.