Variable pitch control for vertical-axis wind turbines

Abstract

NENUPHAR aims at developing the next generation of large-scale floating offshore vertical-axis wind turbine. To challenge the horizontal-axis wind turbine, the variable blade pitch control appears to be a promising solution. This article focuses on blade pitch law optimization and resulting power and thrust gain depending on the operational conditions. The aerodynamics resulting from the implementation of a variable blade pitch control are studied through numerical simulations, either with a three-dimensional vortex code or with two-dimensional Navier-stokes simulations (two-dimensional computational fluid dynamics). Results showed that the three-dimensional vortex code used as quasi-two-dimensional succeeded to give aerodynamic loads in very good agreement with two-dimensional computational fluid dynamics simulation results. The three-dimensional-vortex code was then used in three-dimensional configuration, highlighting that the variable pitch can enhance the vertical-axis wind turbine power coefficient (C_p) by more than 15% in maximum power point tracking mode and decrease it by more than 75% in power limitation mode while keeping the thrust below its rated value.

Keywords

Vertical-axis wind turbine individual pitch control variable pitch power maximization thrust limitation torque limitation

Introduction

Improving the performance of vertical-axis wind turbines (VAWTs) is key to make them commercially successful. Scientists have investigated several interesting concepts for that purpose: increasing the swept area, especially to limit the losses due to three-dimensional (3D) effects, using counter-rotating wind turbines (Parneix et al., 2016), or using flap and pitch systems to control the flow around the blades (Ertem, 2015; Houf, 2016). NENUPHAR suggests to take advantage of optimized variable blade pitching strategies to improve the efficiency of a VAWT along the entire operating curve. Indeed, one of the main drawbacks of VAWTs is the fact that the angle of attack seen by their blades continuously varies over one rotor revolution. For example, at high wind speeds, where the torque must be limited to ensure the mechanical integrity of the power conversion chain, known solutions inherited from horizontal-axis wind turbines (HAWTs) control strategies consist either in reducing the rotational speed or in using static blade pitch control. But while the first solution allows to maintain the rated power production by dramatically increasing not only the aerodynamic torque but also the blade aerodynamic stall (and consequently the loads and the vibration levels), the second solution, while maintaining the average aerodynamic torque at its rated value, also considerably increases both the average value and the amplitude of variation of the loads exerted on the wind turbine because of the unsteady aerodynamics that is specific to VAWTs. Using variable blade pitching strategies on VAWTs allows the angle of attack to be optimized over a rotation depending on wind conditions, thus optimizing performances. For example, Houf (2016) used a load form optimization problem with actuator cylinder model to study variable pitch control strategy, with following targets: maximizing the power coefficient (C_p) without increasing the thrust coefficient, minimizing the C_p, and eventually minimizing the thrust coefficient while maintaining a given C_p. NENUPHAR objectives are to maintain a maximum power production (at rated power level) at high wind speeds even in the power limitation phase (as for the HAWTs), to maximize the power production in the maximum power point tracking (MPPT) phase, and to reduce and limit the rotor aerodynamic thrust, which is a critical objective for floating wind turbines, as showed in Houf (2016). A variable pitch system serves these three specific objectives that lower the levelized cost of energy (LCoE) of a VAWT: it guarantees the generator integrity, and it improves the rotor and the floater competitiveness by allowing the power production to be maximized without oversizing the rotor, drivetrain, and floating support structure (as summarized in Figure 1).

Figure 1.

Key aerodynamic objectives to develop a competitive product.

Simulations presented in this article were carried out with a vortex panel method and with two-dimensional computational fluid dynamics (2D CFD) to investigate the impact of blade pitching strategies on the VAWT performances. The studied configuration was a three-bladed Darrieus-H VAWT with a diameter of 60 m and a blade length greater than 100 m. This article presents the main results of this study and the positive impact of blade pitching strategies.

Materials and methods

To study the benefits of the variable pitch control strategy implemented on VAWTs, a vortex code (PHARWEN (Venet et al., 2016)) was developed by ADWEN OFFSHORE and NENUPHAR. CFD modeling was also used to get a better modeling of the viscous effects and obtain partial code validation. As the flow regime encountered by a typical VAWT is at relatively low speed (Mach number, M < 0.3) and in a range of Reynolds number of 1e5–1e7, both models consider incompressible flow. The main difference between the two types of calculation is the modeling of the viscous effects: they are inherently calculated in CFD simulations, but are calculated using a semi-empirical model in the vortex method code.

PHARWEN: a vortex method, called ARDEMA3D, with a dynamic stall module

Inviscid solver

The vortex code ARDEMA3D (Deglaire, 2008; Dixon, 2008) solves the Euler equation (equation (2)), that is, the Navier–Stokes equation under the assumption that the flow is incompressible, adiabatic, and inviscid outside the boundary layer. Therefore, the mass conservation and energy equations can be written as

\nabla \cdot ν = 0

(1)

\frac{\partial \vec{ν}}{\partial t} + \vec{ν} \cdot \nabla \cdot \vec{ν} = \vec{f} - \frac{\nabla p}{ρ}

(2)

where $ν$ is the velocity field, $p$ is the pressure, and $ρ$ is the fluid density. In these conditions, the velocity can be represented as the gradient of a scalar potential (potential flow) that satisfies the Laplace equation

ν = \nabla ϕ

(3)

\nabla^{2} ϕ = 0

(4)

Equation (4) is a linear differential equation, meaning that two solutions may be added and the result will remain a valid solution. This characteristic is especially convenient when confronted by an arbitrary geometry whose general solution can be broken down into a summation of more fundamental solutions. The potential velocity solution is found using the source doublet formulation with Dirichlet boundary conditions on the surface and Kutta conditions at each section trailing edges. Euler equation (equation (2)) provides the relationship between the local fluid pressure and the velocity and is used to determine the lift, moment, and pressure drag acting on the surface. As a time dependent term is present in equation (2), the local fluid pressure is function of the local velocity and its derivative. Eventually, the Euler equation may be transformed into the more familiar Bernoulli equation which can be used to compare any two arbitrary points in an inviscid and incompressible flow field. The unsteady Bernoulli equation (equation (5)) provides the pressure from the potential velocity solution, leading to the computation of the aerodynamic loads on the sections

\frac{p_{\infty} - p}{ρ} = \frac{\partial ϕ}{\partial t} + E + \frac{ν^{2}}{2}

(5)

Effects of friction are taken into account through the transport of the vorticity that is related to the circulation (Stokes theorem along a closed path) (Dixon, 2008). ARDEMA3D was validated against theoretical and experimental cases (Deglaire, 2008; Dixon, 2008) and is continuously improved and compared to experimental and numerical data.

Viscous correction

To correctly model the dynamic stall phenomenon inherent to the complex aerodynamics involved in VAWTs, a Beddoes–Leishman (BL)-type dynamic stall model (Beaudet, 2014; Leishman and Beddoes, 1986) was implemented, extending the code validity domain to low tip speed ratio (TSR). The BL model is coupled with ARDEMA3D, using the relative velocities and angle of attacks issued from the inviscid solver as model inputs. It implements flow separation, pressure lag and friction lag depending on empirical parameters to compute viscous corrected lift and drag variables.

Blade pitch

In uniform and steady wind conditions, the radial blade sections of a HAWT see a constant angle of attack over one rotation while the blade sections of a VAWT see a varying angle of attack over one rotation (see Figure 2). For a HAWT, the pitch consists in turning the blades more or less into the wind direction: for a given wind speed at hub height, thanks to a collective pitch system, the blades are turned simultaneously by a certain angle in order to see an optimal angle of attack.

Figure 2.

Typical angle of attack seen by a blade section along one rotation for a HAWT and a VAWT (uniform wind).

Because of the complex aerodynamics, each blade of a VAWT needs a variable pitch system to achieve a similar objective: an individual pitch system controlled with regard to the wind speed and the blade azimuthal position. Such dependence on the blade azimuthal position was fundamental in the building process of the optimal pitch laws.

The operating curve of a VAWT

Along the operating curve of a wind turbine, there are three identifiable phases that implies three different types of variable pitch control strategies.

The MPPT phase

The MPPT phase starts at the cut-in wind speed and stops when the maximum rotational speed or the rated power is reached. Usually, during this phase, no constraint limits the wind turbine performances. The efficiency can, therefore, be improved through pitch optimization processes that aim at maximizing the blade airfoil performances.

The power limitation phase

Above the rated wind speed, when the maximum electrical power is reached, the wind turbine enters the power limitation phase. The main objective in this phase is to limit the torque with respect to electrical power constraint. This must be done by keeping a constant rotational speed that allows to produce the maximum power output until the cut-out wind speed and to optimize the generator use. A well-known strategy to limit the torque for HAWTs is the fixed pitch stall control that consists in increasing the angles of attack at high wind speeds to reach a deeper stall and a consequent loss of lift, sufficient to limit the torque. But such strategy might not suit well to floating VAWTs as it increases the load variations and it could not satisfy a demanding thrust requirement. Therefore, the strategy elaborated in this phase consists, on the contrary, in minimizing the angles of attack in order to reduce both the average value and the variations of the loads while limiting the torque.

The thrust peak shaving phase

Eventually, there may be a transition phase between the MPPT and the power limitation phases where the wind turbine is limited in rotational speed but not yet in power. As the wind speed rises, the efficiency decreases and the loads exerted on the wind turbine increase. Thus, the average thrust can exceed a maximum value defined regarding the floater capabilities. In this case, this phase is called a thrust peak shaving phase, whose objective is to limit the thrust without losing too much power. The pitch strategy developed to fulfill this goal is a trade-off between the two previous strategies.

Model abilities for variable blade pitch control

Part of the code validation process consisted in comparing 2D CFD results for identical VAWT solidities with results from ARDEMA3D vortex code that implements a very long—semi-infinite blade length. Indeed, using very high rotor aspect ratio allows to assimilate the blade mid-span results with 2D results. CFD simulations are performed using the commercial solver ANSYS Fluent V15 (ANSYS, 2014), with a unsteady Reynolds-averaged Navier–Stokes (URANS) method and closed with a shear stress transport (SST) k-ω turbulence model. Simulations are carried out in a horizontal plane situated at the middle height of the rotor (Figure 3), with a rotating mesh around each blade simulating the blade pitch movement. An example of comparison of the quasi-2D vortex code with 2D CFD in power limitation phase is provided (Figure 4), highlighting that the vortex code is in very good agreement with 2D CFD for the loads calculation when running a variable pitch strategy.

Figure 3.

Blade azimuthal $(θ)$ , pitch angle $(δ)$ , normal (Cn) and tangential (Ct) coefficient conventions.

Figure 4.

Vortex code results comparisons with CFD in power limitation.

Results

PHARWEN was used to evaluate the impact of variable blade pitching on the different phases of the operating curve of the studied VAWT configuration in 3D real scale.

Pitch laws optimization in MPPT

Along the MPPT phase, the wind turbine rotates at its optimal TSR, thus the angle of attack variation over one rotation is very similar for all the wind speeds. As a result, a unique optimal variable pitch law can be used along the entire MPPT phase, which simplifies the control. Using such a law, an optimal angle of attack can be approached over the main part of the rotation, thus maximizing the average tangential coefficient (see Figure 5). The tangential coefficient increase leads to a power gain by increasing the average torque.

Figure 5.

Impact of the optimized pitch law in MPPT on the angle of attack (AoA) and the tangential coefficient (C_t).

Based on the power maximization objective, an optimization ran with PHARWEN led to an optimal variable blade pitch law, and an increase in aerodynamic performance higher than 15% (see Figure 6) was simulated with the code thanks to this law. Also, it was observed that the lower the wind speed, the higher the power increase, which shows that a VAWT could be adapted to sparsely windy area as well.

Figure 6.

Impact of the optimized pitch law in MPPT on Power coefficient (C_p).

Pitch laws optimization in rotational speed limitation phase

During the thrust peak shaving phase, the wind turbine has reached its maximum rotational speed making its TSR decrease. As a result, the MPPT pitch law is no longer optimal since the angle of attack variation over one rotation has changed. Therefore, a new set of optimal pitch laws needs to be found for this phase with the prior objective to limit the average thrust to a maximum value and the second objective to limit the consequent power losses. The best laws found through the corresponding optimization process aim at slightly lower angles of attack (in comparison with the MPPT), but this is sufficient to considerably decrease the average thrust (by more than 35%) compared to the case without pitch. Thanks to this strategy, a thrust limitation to the maximum value along the entire rotational speed limitation phase could be simulated with PHARWEN (see Figure 6), with less than 5% power losses.

Pitch laws optimization in power limitation phase

For the power limitation phase, an optimization based on a pitch stall control strategy was ran as a first step. But even if the torque limitation objective was successfully reached, the thrust could not be sufficiently reduced. As a second step, pitch laws aiming at small angles of attack were optimized to allow the average torque to be limited to its maximum value (see Figure 7), the average thrust to be reduced below its maximum value (see Figure 8) and the maximum power output to be produced until the cut-out wind speed. Compared with the case without a pitch control, a power reduction of more than 75% at the cut-out wind speed was simulated with PHARWEN.

Figure 7.

Impact of optimized pitch laws on average torque in power limitation.

Figure 8.

Impact of optimized pitch laws on average thrust in rotational speed and power limitation.

Conclusion

This article presents numerical results of variable blade pitching strategies applied on a VAWT with a 3D vortex method. It shows that the vortex method can realistically estimate the performance improvement in 2D thanks to variable blade pitch control strategies. Aiming at optimal angles of attack depending on the wind speed thanks to optimized pitch laws allows key aerodynamic objectives to be reached. A 3D C_p increase of more than 15% in MPPT phase was computed, and the ability to maintain the maximum power production and not to exceed the admissible torque and thrust in power limitation and rotational speed limitation phases was acquired thanks to the selected variable pitch control strategies. These numerical results provide valuable information about how to increase the efficiency of VAWTs, thus improving confidence that a next generation of VAWTs can be designed with higher aerodynamic efficiency. This is a crucial step in order to make VAWTs competitive on the wind energy market. The next step of this technology development will include 3D experimental validation steps based on the measurements made on NENUPHAR 1HB onshore prototype and on the VODCA prototype (VAWT Open Data for Code Assessment, Politecnico di Milano).

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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