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.
Highlights
Wind power is the most promising source of renewable energy
The main characteristic of a wind turbine is its power curve. This is a wind turbine power output function w(s) that shows an amount of kilowatts/megawatts produced at a range of wind speeds s
Factual power curves remotely remind trapezia with curvilinear flanks, whereon the nominal power appears at a speed greater than a cut-in speed, and the real drop to zero appears at a speed greater than a cut-out speed
Summary
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. 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. 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 . Such equal factors ensure strong differentiability of the power curve within those parts. The exponential model is for a general description of the wind turbine power curve.
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More From: Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"
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