DOI: https://doi.org/10.20535/1810-0546.2018.2.121504

### Wind Turbine Power Curve Exponential Model with Differentiable Cut-in and Cut-out Parts

#### Abstract

**Background.** The main characteristic of a wind turbine is its power curve. Getting measurement data off powerful wind turbines is a way harder than measuring characteristics of wind turbines for individual/home use. A yet significant gap is that all wind turbines have a few similarities in their power curves but they do not have a formalized description, which could help in selecting better turbines fitting specific areas (without precise measurements in a vicinity of cut-in and cut-out speeds).

**Objective.** As there is a straight lack of mathematical description of wind turbine power curves, the goal is to obtain a model of such curves.

**Methods.** A power curve is of seven parts. Factual power curves remotely remind trapezia with curvilinear flanks. Because of inertia, the curvilinearity is severer for those wind turbines whose output power is greater. As blades of industrial wind turbines are too massive, their inertia makes those lag effects, that could be modeled by using natural smoothness of power curves. For describing that smoothness along with the curvilinearity, we use two increasing and two decreasing exponential functions for the flanks.

**Results.** A wind turbine power output function consists of two zero parts, one rated-out part, and the suggested four exponential parts. The cut-in parts are described with two increasing exponential functions whose exponential growth factors are equal. The cut-out parts are described with two decreasing exponential functions whose exponential decrease factors are equal also. Such equal factors ensure strong differentiability of the power curve within those parts.

**Conclusions.** The exponential model is for a general description of the wind turbine power curve. Having differentiable cut-in and cut-out parts, it suggests the “natural smoothing” that happens in reality due to highly-inertial wind turbine blades. The model is not necessarily to be used to fit some experimental data, but rather for patterning power curves.

#### Keywords

#### Full Text:

PDF#### References

P. Breeze, *Wind Power Generation*. Academic Press, 2015, 104 p.

*Wind Energy Engineering. A Handbook for Onshore and Offshore Wind Turbines*, T.M. Letcher, Ed. Academic Press, 2017, 622 p.

*Offshore Wind Farms: Technologies, Design and Operation*, C. Ng and L. Ran, eds. London, UK: Woodhead Publishing, 2016, 654 p.

V. Santhanagopalan *et al.*, “Performance optimization of a wind turbine column for different incoming wind turbulence”, *Renewable Energy*, vol. 116, part B, pp. 232–243, 2018. doi: 10.1016/j.renene.2017.05.046

M. Song *et al.*, “Micro-siting optimization of a wind farm built in multiple phases”, *Energy*, vol. 137, pp. 95–103, 2017. doi: 10.1016/j.energy.2017.06.127

V.V. Romanuke, “Increasing an expected power of the wind farm with diversification in non-dominated power curves of the used wind turbines”, *Bulletin of V.N. Karazin Kharkiv National University.** **Ser. Mathematical Modelling. Information Technology. Automated Control Systems*, iss. 35, pp. 74–79, 2017.

S. Miao *et al.*, “A Markovian wind farm generation model and its application to adequacy assessment”, *Renewable Energy*, vol. 113, pp. 1447–1461, 2017. doi: 10.1016/j.renene.2017.07.011

R.J.A.M. Stevens *et al.*, “Comparison of wind farm large eddy simulations using actuator disk and actuator line models with wind tunnel experiments”, *Renewable Energy*, vol. 116, part A, pp. 470–478, 2018. doi: 10.1016/j.renene.2017.08.072

D. Villanueva and A. Feijóo, “Comparison of logistic functions for modeling wind turbine power curves”, *Electric Power Systems Res.*, vol. 155, pp. 281–288, 2018. doi: 10.1016/j.epsr.2017.10.028

L.M. Bardal and L.R. Sætran, “Influence of turbulence intensity on wind turbine power curves”, *Energy Procedia*, vol. 137, pp. 553–558, 2017. doi: 10.1016/j.egypro.2017.10.384

M. Lydia *et al.*, “A comprehensive review on wind turbine power curve modeling techniques”, *Renewable and Sustainable ** **Energy Reviews*, vol. 30, pp. 452–460, 2014. doi: 10.1016/j.rser.2013.10.030

E. Taslimi-Renani *et al.*, “Development of an enhanced parametric model for wind turbine power curve”, *Applied Energy*, vol. 177, pp. 544–552, 2016. doi: 10.1016/j.apenergy.2016.05.124

T. Ouyang *et al.*, “Modeling wind-turbine power curve: A data partitioning and mining approach”, *Renewable Energy*, vol. 102, part A, pp. 1–8, 2017. doi: 10.1016/j.renene.2016.10.032

D. Villanueva and A. Feijóo, “Reformulation of parameters of the logistic function applied to power curves of wind turbines”, *Electric Power Systems Res.*, vol. 137, pp. 51–58, 2016. doi: 10.1016/j.epsr.2016.03.045

#### GOST Style Citations

Copyright (c) 2018 Igor Sikorsky Kyiv Polytechnic Institute

This work is licensed under a Creative Commons Attribution 4.0 International License.