Turbulent Power Curves


I’ve evaluated a “pseudo-steady” power curve for a turbine using a Taylor’s series approach with turbulence intensity for different wind speeds. I was provided with power/thrust curves for a range of different wind speeds and quoted turbulence intensities. My back-calculated steady-power coefficient looks very cubic all the way up to rated, which I found somewhat reassuring.

The problem that I have is now, given I’ve come up what I believe to be a sensible aerodynamic model and control system for the steady-state and zero turbulence performance, I barely see any variation in the binned power curve when I introduce turbulence into my simulations.

The true turbulent thrust and power curves I have available to me have a marked increase in smoothing as a function of turbulence intensity around rated speed, however my simulations are not capturing this at all.

In a helpful reply to another post I made, it was previously suggested I use peak-shaving and set-point smoothing to capture that effect. However, with regards to peak shaving, I no longer I believe I require it in steady-state and zero-turbulence because I think my power curve is fairly cubic in nature up to rated wind-speed. I’m am using set-point smoothing.

The turbulent simulations I’m running I believe are fairly realistic of a normal test situation. I modelling the problem aero-structurally, although I have disabled yaw and drive-train flexibility. All other DOFS are active and I’m using a ROSCO controller. I’m running ElastoDyn, AeroDynv15, SubDyn ServoDyn and InflowWind.

The difference between the power and thrust curves I’m evaluating for different turbulence intensities is essentially negligible which doesn’t make sense to me.

I’m evaluating turbulent thrust and power coefficients by taking the average generator power (W) / rotor thrust (N) and normalising by the standard terms using 10-minute average wind speed at hub height. I’ve included a power-law exponent of 0.1. Wind-speed at hub height, rather than equivalent wind speed is the method which was used by the provider of the turbulent power curves to me.

Are there possible aspects of a given simulation setup up (such disabling drive-train flexibility) which could explain this behaviour (no effect of turbulence of power/thrust curves) ? Should one expect the ROSCO controller inputs, such as target frequency and damping of VS and PC regions to effect the response under turbulence? Responding too quickly or slowly?

Additionally, because I’d specified the turbulence intensity in TurbSim, I’m not using any scaling in InflowWind (=0). I’m also using TSR tracking in the controller. Could this be the cause?

I’d appreciate any possible guidance.

Best wishes,

Hi Sam,

I gather that you are running simulations with turbulent wind (from TurbSim) and are comparing the time-series mean of power and thrust against similar simulations run with steady, uniform wind. Is my understanding correct?

I would guess that the variability of the time-series mean will depend on the variability of the turbulent conditions you are using, as well as length of the simulation (1 minute means versus 10 minute means versus other lengths). When varying the turbulent conditions, what are you varying? Are you considering variations in TI, or also variations in shear, veer, turbulent length scales, spatial coherence, Reynolds stresses, etc.? Some of these parameters will likely have more influence on mean effects than others. Also, the length of the simulation will impact the variation in time-series mean (the shorter the simulation, the more variation would be expected).

Best regards,

Hi Jason,

Thanks so much for your assistance.

I believe your understanding is correct. I’ve running wind-only aero-elastic simulations with a TSR-tracking controller in the region 2 in order generate power and thrust curves for different turbulent intensities and plotting as a function of wind-speed.

I’ve been told that the mean shear in the curves I’ve been provided with is 0.1 (varies between -0.1 and 0.3) and the horizontal/lateral shear has a mean of zero.

My turbulence intensity range is large, 5-15%, in 2% increments at a reference wind-speed of 15 m/s. I’ve been provided with a formula to convert any given reference intensity at 15% to a corresponding value at a different wind speed.

I’m running 10 minute simulations. The only variable between runs is the TurbSim .bts file. The TurbSim .bts file is changed by varying mean wind speed at reference height and the turbulence intensity at that speed which corresponds an associated turbulence intensity at 15 m/s (of which I have 11, 5-15% in steps of 2, reference values). Therefore, I’m varying velocity and TI_15 m/s, and TI_v (TI at a particular wind-speed), is a dependent variable depending on v and TI_15 (TI at 15 m/s).

My current thinking is that the TSR tracking is too good. If for a given reference velocity, regardless of TI, the TSR tracking is sufficiently good to hold the specified TSR on average, then for me that may explain why there is so little variability with changes in TI at any given wind-speed for 10 minute averaged thrust coefficients and power coefficients from unsteady, aeroelastic simulations.

When I say there is no variation with TI, there is literally almost none. It is not believable to me and suggests that I’m lacking some fundamental understanding about the behaviour of my system.

I’m wondering if it may be better for me to use a traditional T = komega^2 controller. Am I right in thinking, that apart from region 2.5, this isn’t a PI controller? Does it just work by demanding T = komega^2?

How important is drive-train flexibility in all of this?

My turbulence seed never changes, perhaps this is the problem?
How many simulations should be performed in each wind speed bin for a given turbulence intensity?

Thanks again.

Best wishes,

Dear Sam,

I would expect the traditional T = k*omega^2 approach to result in larger variations in rotor speed than a PI-based torque controller would do. That said, these variations may average themselves out when only looking at the mean response over 10 minutes.

I would not expect the drivetrain torsion flexibility to play a large role in the mean response.

You could certainly try changing the turbulence seed and running additional seeds, but from my experience, mean values tend to converge quickly. The convergence of standard deviations takes a bit longer (more seeds), and the convergences of extreme values takes much longer (many more seeds).

Best regards,