Wind farm density and harvested power in very large wind farms: a low-order model

This project aims to develop a simplistic numerical model to determine the number of wind turbines that should be placed given a land extension, in order to maximize the power output as a function of different atmospheric stabilities

Wind Farm Density and Harvested Power in Very Large Wind Farms: A Low-order Model Gerard Cortina & Marc Calaf Mean Kinetic Energy Budget Equation Wind farm configurations Overall Project Objective Develop a simplistic numerical model to determine the number of wind turbines that should be placed given a land extension, in order to maximize the power output as a function of different atmospheric stabilities. Low order model: Power vs. WF density Increase in wind farm density Advection Work due to pressure gradient Dissipation Flux of MKE Unstable Motivation & Background • Within this project we seek to better understand the physical phenomena that contribute to the recovery of the wind turbine's wake. This velocity recovery directly drives the amount of total power that can be extracted from the atmospheric flow. Gravitational acceleration Effect of the Coriolis force Wind turbine power extraction • With a better understanding of the wake recovery we are seeking the answer of the following questions that motivated the present study: 1) How many wind turbines can we place in a certain location? 2) What happens as the number of wind turbines increases? Vertical profiles of the MKE budget terms Unstable Low dense wind farm Medium dense wind farm Neutral Stable Largely dense wind farm s1 Diurnal cycle: CASES-99 field experiment (3) We can estimate the power output per wind turbine unit Increase in wind farm density Night - time 3) How is this affected by changing the flow stratification? Study period 1 Day - time Study period 2 4) And the most important… how much power can we obtain? Unstable Wind Farm efficiency Stable (2) Given a wind farm density (CASES-99) Goal: Relationship between the wind farm density and the Mean Kinetic Energy (MKE) of the ABL flow. Large eddy simulation of the ABL Unstable Stable Neutral Ideal case How much power can we obtain? (1) Neutral simulation: No time dependent surface temperature (2) (3) Buoyancy forces Geostrophic forcing (CASES-99) Wind turbine force (1) Given an atmospheric stability Constant vertical temperature profile Mean Kinetic Energy Incoming wind Integration of the MKE budget terms over the CV WT model: Actuator disc with rotation & yaw alignment 10 minutes yaw readjustment time Unstable Neutral Stable Summary & Conclusions • A first order approximation solution has been found to be very approximate when quantifying the total wind turbine power as a function of the stability and wind farm density. s1 Unstable •As the packing of the wind farm is increased there exists a decrease of MKE available for power extraction. s3 Neutral • In largely spaced wind farms the power extracted by the turbines is mainly recovered by advection. In largely populated wind farms the power extracted by the turbines is mainly recovered by the flux of MKE. • When advection dominates, the wind farm is more efficient than if the MKE flux dominates. s5 Stable vs. GCSC Environment and Sustainability Research Symposium February 8, 2017