An Integrative Framework for Design and Control Optimization of a Variable-Ratio Gearbox in a Wind Turbine With Active Blades

2016 ◽  
Author(s):  
Amrita Lall ◽  
Hamid Khakpour Nejadkhaki ◽  
John Hall
Keyword(s):  
Cost Function ◽  
Wind Turbine ◽  
Low Cost ◽  
Electrical Power ◽  
Induction Machine ◽  
Power Production ◽  
Wind Data ◽  
Variable Ratio ◽  
Machine Model ◽  
Blade Root

A variable ratio gearbox (VRG) provides discrete variable rotor speed operation, and thus increases wind capture, for small fixed-speed wind turbines. It is a low-cost, reliable alternative to conventional variable speed operation, which requires special power-conditioning equipment. The authors’ previous work has demonstrated the benefit of using a VRG in a fixed-speed system with passive blades. This work characterizes the performance of the VRG when used with active blades. The main contribution of the study is an integrative design framework that maximizes power production while mitigating stress in the blade root. As part of the procedure, three gear ratios are selected for the VRG. It establishes the control rules by defining the gear ratio and pitch angle used in relation to wind speed and mechanical torque. A 300 kW wind turbine model is used for a case study that demonstrates how the framework is implemented. The model consists of aerodynamic, mechanical, and electrical submodels, which work collaboratively to convert kinetic air to electrical power. Blade element momentum theory is used in the aerodynamic model to compute the blade loads. The resulting torque is passed through a mechanical system and subsequently to the induction machine model to generate power. The BEM method also provides the thrust and bending loads that contribute to blade-root stress. The stress in the root of the blade is also computed in response to these loads, as well as those caused by gravity and centrifugal force. Two case studies are performed using wind data that was obtained from the National Renewable Energy Laboratory (NREL). Each of these represents an installation site with a unique set of wind conditions that are used to customize the wind turbine design. The framework uses dynamic programming to simulate the performance of an exhaustive set of combinations. Each combination is evaluated over each set of recorded wind data. The combinations are evaluated in terms of the total energy and stress that is produced over the simulation period. Weights are applied to a multi-objective cost function that identifies the optimal design configurations with respect to the design objectives. As a final design step, a VRG combination is selected, and a control algorithm is established for each set of wind data. During operation, the cost function can also be used to bias the system towards higher power production or lower stress. The results suggest a VRG can improve wind energy production in Region 2 by roughly 10% in both the low and high wind regions. In both cases, stress is also increased in Region 2, as the power increases. However, the stress in Region 3 may be reduced for some wind speeds through the optimal selection of gear combinations.

Design and Control Framework for Selecting Wind Turbine Gear Ratios Based on Optimal Power Generation and Blade Stress

2016 ◽  
Author(s):  
Amrita Lall ◽  
Hamid Khakpour Nejadkhaki ◽  
John Hall
Keyword(s):  
Wind Turbine ◽  
Energy Production ◽  
Control Algorithm ◽  
Power Production ◽  
Wind Data ◽  
Data Set ◽  
Blade Root ◽  
Partial Load ◽  
And Control ◽  
Root Stress

A variable ratio gearbox (VRG) can enable small wind turbines to operate at discrete variable rotor speeds. This reliable, low-cost, alternative does not require power conversion equipment, as is the case with conventional variable speed. Previous work conducted by the author has demonstrated that a VRG can increase the power production for a fixed-speed system with passive blades. The current study characterizes the performance of a wind turbine equipped with a VRG and active blades. The contribution of this work is an integrative framework that optimizes power production with blade root stress. It works by defining a set of control rules that specify the VRG gear ratio and pitch angle that will be used in relation to wind speed. Three ratios are selected through the proposed procedure. A case study based on the simulation of a 300-kW wind turbine model is performed to demonstrate the proposed technique. The model is constructed with aerodynamic, mechanical, and electrical submodels. These drivetrain components work together to simulate the conversion of moving air to electrical power. The blade element momentum (BEM) technique is used here to compute the blade loading. The resulting torque and rotor speed are reduced and increased, respectively, through the mechanical system gearbox. The output from this is then applied to the electrical generator. The BEM technique is also used here to determine the bending and thrust and loads that are applied to the blade. The stress in the root of the blade is then determined based on these loads, and that caused by centrifugal force and gravity. The proposed method devises a VRG design and control algorithm based on the unique wind conditions at a given installation site. Two case studies are conducted using wind data sets provided by the National Renewable Energy Laboratory (NREL). Low and high-speed data set are selected as inputs to demonstrate the versatility of the proposed method. Dynamic programming is used to reduce the computational expense. This enables the simulation of an exhaustive set of potential VRG combinations over each set of recorded wind data. Each possible combination is evaluated in terms of the total energy production and blade-root stress produced over the simulation period. A set of weights is applied to a multi-objective function that computes the cost associated with each combination. A Pareto analysis is then used to identify the VRG combination and establish the control algorithm for both systems. The results suggest that the VRG can improve energy production in the partial-load region by roughly 10% in both cases. Although stress increases in Region 2, it decreases in Region 3, and overall, through the optimal selection of gear combinations.

scholarly journals A method for preliminary rotor design – Part 2: Wind turbine Optimization with Radial Independence

2021 ◽  
Vol 6 (3) ◽  
pp. 917-933 ◽  
Author(s):  
Kenneth Loenbaek ◽  
Christian Bak ◽  
Michael McWilliam
Keyword(s):  
Cost Function ◽  
Wind Turbine ◽  
Energy Production ◽  
Optimization Problems ◽  
Turbine Rotor ◽  
Global Optimum ◽  
Blade Root ◽  
Rotor Design ◽  
Global Power ◽  
Optimization Methodology

Abstract. A novel wind turbine rotor optimization methodology is presented. Using an assumption of radial independence it is possible to obtain an optimal relationship between the global power (CP) and load coefficient (CT, CFM) through the use of Karush–Kuhn–Tucker (KKT) multipliers, leaving an optimization problem that can be solved at each radial station independently. It allows solving load constraint power and annual energy production (AEP) optimization problems where the optimization variables are only the KKT multipliers (scalars), one for each of the constraints. For the paper, two constraints, namely the thrust and blade root flap moment, are used, leading to two optimization variables. Applying the optimization methodology to maximize power (P) or annual energy production (AEP) for a given thrust and blade root flap moment, but without a cost function, leads to the same overall result with the global optimum being unbounded in terms of rotor radius (R̃) with a global optimum being at R̃→∞. The increase in power and AEP is in this case ΔP=50 % and ΔAEP=70 %, with a baseline being the Betz optimum rotor. With a simple cost function and with the same setup of the problem, a power-per-cost (PpC) optimization resulted in a power-per-cost increase of ΔPpC=4.2 % with a radius increase of ΔR=7.9 % as well as a power increase of ΔP=9.1 %. This was obtained while keeping the same flap moment and reaching a lower thrust of ΔT=-3.8 %. The equivalent for AEP-per-cost (AEPpC) optimization leads to increased cost efficiency of ΔAEPpC=2.9 % with a radius increase of ΔR=17 % and an AEP increase of ΔAEP=13 %, again with the same, maximum flap moment, while the maximum thrust is −9.0 % lower than the baseline.

scholarly journals The Use of a Real-Time Simulator for Analysis of Power Grid Operation States with a Wind Turbine

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2327
Author(s):  
Zbigniew Kłosowski ◽  
Sławomir Cieślik
Keyword(s):  
Differential Equations ◽  
Power Systems ◽  
Wind Turbine ◽  
Real Time ◽  
Power Transformer ◽  
Power Grid ◽  
Induction Machine ◽  
Integration Step ◽  
Machine Model ◽  
The Real

The main issue in this paper is the real-time simulator of a part of a power grid with a wind turbine. The simulator is constructed on the basis of a classic PC running under a classic operating system. The proposed solution is expected and desired by users who intend to manage power microgrids as separate (but not autonomous) areas of common national power systems. The main reason for the decreased interest in real-time simulators solutions built on the basis of PC is the simulation instability. The instability of the simulation is due to not keeping with accurate results when using small integration steps and loss of accuracy or loss of stability when using large integration steps. The second obstacle was due to the lack of a method for integrating differential equations, which gives accurate results with a large integration step. This is the scientific problem that is solved in this paper. A new solution is the use of a new method for integrating differential equations based on average voltage in the integration step (AVIS). This paper shows that the applied AVIS method, compared to other methods proposed in the literature (in the context of real-time simulators), allows to maintain simulation stability and accurate results with the use of large integration steps. A new (in the context of the application of the AVIS method) mathematical model of a power transformer is described in detail, taking into account the nonlinearity of the magnetization characteristics. This model, together with the new doubly-fed induction machine model (described in the authors’ previous article), was implemented in PC-based hardware. In this paper, we present the results of research on the operation states of such a developed real-time simulator over a long period (one week). In this way, the effectiveness of the operation of the real-time simulator proposed in the paper was proved.

scholarly journals Predicting the Extreme Loads in Power Production of Large Wind Turbines Using an Improved PSO Algorithm

2019 ◽  
Vol 9 (3) ◽  
pp. 521 ◽  
Author(s):  
Caicai Liao ◽  
Kezhong Shi ◽  
XiaoLu Zhao
Keyword(s):  
Control System ◽  
Wind Turbine ◽  
Pitch Angle ◽  
Bending Moment ◽  
Pso Algorithm ◽  
Power Production ◽  
Bending Moments ◽  
Rotor Speed ◽  
Blade Root ◽  
Extreme Loads

Predicting the extreme loads in power production for the preliminary-design of large-scale wind turbine blade is both important and time consuming. In this paper, a simplified method, called Particle Swarm Optimization-Extreme Load Prediction Model (PSO-ELPM), is developed to quickly assess the extreme loads. This method considers the extreme loads solution as an optimal problem. The rotor speed, wind speed, pitch angle, yaw angle, and azimuth angle are selected as design variables. The constraint conditions are obtained by considering the influence of the aeroelastic property and control system of the wind turbine. An improved PSO algorithm is applied. A 1.5 MW and a 2.0 MW wind turbine are chosen to validate the method. The results show that the extreme root load errors between PSO-ELPM and FOCUS are less than 10%, while PSO-ELPM needs much less computational cost than FOCUS. The distribution of flapwise bending moments are close to the results of FOCUS. By analyzing the loads, we find that the extreme flapwise bending moment of the blade root in chord coordinate (CMF_ROOT) is largely reduced because of the control system, with the extreme edgewise bending moment of the blade root in chord coordinate (CME_ROOT) almost unchanged. Furthermore, higher rotor speed and smaller pitch angle will generate larger extreme bending moments at the blade root.

scholarly journals A Method for Preliminary Rotor Design – Part 2: Wind Turbine Rotor Optimization with Radial Independence

2020 ◽  
Author(s):  
Kenneth Loenbaek ◽  
Christian Bak ◽  
Michael McWilliam
Keyword(s):  
Cost Function ◽  
Wind Turbine ◽  
Energy Production ◽  
Optimization Problems ◽  
Turbine Rotor ◽  
Global Optimum ◽  
Blade Root ◽  
Global Power ◽  
Optimization Methodology ◽  
Wind Turbine Rotor

Abstract. A novel wind turbine rotor optimization methodology is presented. Using an assumption of radial independence it is possible to obtain an optimal relationship between the global power- (CP) and load-coefficient (CT, CFM) through the use of KKT-multipliers, leaving an optimization problem that can be solved at each radial station independently. It allows to solve load constraint power and Annual-Energy-Production (AEP) optimization problems where the optimization variables are only the KKT-multipliers (scalars), one for each of the constraint. For the paper two constraints, namely the thrust and blade-root-flap-moment is used, leading to two optimization variables. Applying the optimization methodology to maximize power (P) or Annual-Energy-Production (AEP) for a given thrust and blade-root-flap-moment, but without a cost-function, leads to the same overall result with the global optimum being unbounded in terms of rotor radius (R~) with a global optimum being at R~ → ∞. The increase in power and AEP is in this case ΔP = 50 % and ΔAEP = 70 %, with a baseline being the Betz-optimum rotor. With a simple cost function and with the same setup of the problem a Power-per-Cost (PpC) optimization resulted in a Power-per-Cost increase of ΔPpC = 4.2 % with a radius increase of ΔR = 7.9 % as well as a power increase of ΔP = 9.1 %. This was obtained while keeping the same flap-moment and reaching a lower thrust of ΔT = −3.8 %. The equivalent for AEP-per-Cost (AEPpC) optimization leads to an increased cost efficiency of ΔAEPpC = 2.9 % with a radius increase of a ΔR = 17 % and an AEP increase of ΔAEP = 13 %, again with the same, maximum flap-moment, while the maximum thrust is −9.0 % lower than the baseline.

A Methodology to Synthesize Gearbox and Control Design for Increased Power Production and Blade Root Stress Mitigation in a Small Wind Turbine1

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Hamid Khakpour Nejadkhaki ◽  
Amrita Lall ◽  
John F. Hall
Keyword(s):  
Wind Speed ◽  
Low Cost ◽  
Control Design ◽  
Power Production ◽  
Wind Speeds ◽  
Blade Root ◽  
Squirrel Cage Induction Generator ◽  
And Control ◽  
Root Stress ◽  
Selection Of

Large wind turbines typically have variable rotor speed capability that increases power production. However, the cost of this technology is more significant for small turbines, which have the highest cost-per-watt of energy produced. This work presents a low-cost system for applications where cost and reliability are of concern. The configuration utilizes the fixed-speed squirrel cage induction generator. It is combined with a variable ratio gearbox (VRG) that is based on the automated-manual automotive transmission. The design is simple, low cost and implements reliable components. The VRG increases efficiency in lower wind speeds through three discrete rotor speeds. In this study, it is implemented with active blades. The contribution of this work is a methodology that synthesizes the selection of the gearbox ratios with the control design. The design objectives increase the power production while mitigating the blade stress. Top-down dynamic programming reduces the computational expense of evaluating the performance of multiple gearbox combinations. The procedure is customizable to the wind conditions at an installation site. A case study is presented to demonstrate the ability of the strategy. It employs a 300 kW wind turbine drivetrain model that simulates power production. Two sets of wind data representing low and high wind speed installation sites were used as the input. The results suggest a VRG can improve energy production by up to 10% when the system operates below the rated wind speed. This is also accompanied by a slight increase in the blade-root stress. When operating above the rated speed, the stress decreases through the optimal selection of gear combinations.

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