A Wind Farm Parameterization for WRF Manda S. Adams* and David W. Keith Institute for Sustainable Energy, Environment, and Economy University of Calgary Fdrag = CT ( V ) ρ Av 2 I. Introduction 1 Wind power is the fastest growing non-fossil (1) 2 source of primary energy. Since the 1980’s the CT ( V ) amount of energy derived from the wind has grown exponentially (Figure 1), this growth is small where is a wind speed dependent thrust compared to the anticipated growth in the next 50 coefficient, ρ is the air density, and A is the wind years. One of the factors driving the growth of wind farm density. The drag term is applied to each energy is societal concerns over CO2 emissions. If component of the wind, however the magnitude of wind energy is to play a role in stabilizing CO2 the wind is used for all wind speed dependent calculations. The energy removed from the resolved emissions, wind farms would likely cover Europe, the flow of the atmosphere by the wind turbines goes into Great Plains of North America, and a large portion of 1) electricity, 2) frictional heat loss due to mechanical eastern Asia. Wind farms would be removing workings, and 3) back into the atmosphere in the gigawatts of energy from the atmospheric boundary form of turbulent kinetic energy (tke). The amount layer. As wind energy continues to grow, it is of energy that goes into electricity is given by: important to understand the influence wind turbines will have on the atmosphere, weather and climate. A Pe = C p ( V ) ρ Av3 wind farm parameterization has been developed and 1 (2) integrated into WRF. This paper will describe the 2 wind farm parameterization, discuss initial results Cp ( V ) from the parameterization, and wrap up with the future plans for development and use of this where is a wind speed dependent power parameterization. coefficient. The amount of energy that goes into mechanical losses and tke is not fully known. It is II. Parameterization assumed that the mechanical losses are negligible and Wind farms are parameterized through the the amount of energy added to the tke is given by: PTKE = CTKE ( V ) ρ Av3 modification of the MYJ pbl scheme in WRF. While 1 wind farms are a change in land use, the hub height (3) 2 of modern wind turbines is tall enough to extend beyond the lowest grid box, especially in simulations CTKE = CT − C p (4) with high vertical resolution, and thus the modifications to WRF is implemented in the pbl The thrust, power, and tke coefficients are scheme rather than the surface or land use scheme. not only wind speed dependent, but also turbine The wind farm parameterization is a conservation of dependent. Similarly the wind farm density term (A), energy based scheme. The energy removed from the depends on the turbine specifications such as hub atmosphere by the turbines can be expressed as an height and rotor diameter. For this parameterization elevated drag: specifications were used from a Bonus Energy A/S 2.0 MW turbine, which is representative of modern wind turbines. The 2.0 MW turbine specifications are found in Table 1 and Figure 2. The thrust coefficient (CT) and power curve were provided by *Corresponding author: the manufacturer. The power curve was used to Dr. Manda Adams derive the power coefficient (Cp). A polynomial fit ISEEE / University of Calgary was used in the parameterization to describe the CT 602 Earth Sciences and Cp curves. The cut-in speed and cut-out speeds 2500 University Dr. NW represent the range of wind speeds at which the wind Calgary, AB, T2N 1V7, Canada turbines operate. Below the cut-in speed and above 403-220-7794 the cut-out speed the standing thrust coefficient is firstname.lastname@example.org used, and since no electricity is generated all of the http://www.ucalgary.ca/~asadams 2 energy removed from the resolved flow is converted The winds were from the southwest at this time and into a tke source. explain the higher tke values extending to the The hub height and rotor diameter are used northeast beyond the wind farm. in determining the wind farm density (A) for each The wind farm parameterization caused grid box. Since the wind turbine may be present in increased mixing in the atmospheric boundary layer. multiple grid boxes in the vertical, the area swept by The increased mixing was due to not only the tke the turbines, and thus the drag force induced needs to source term but mechanical mixing induced by the be appropriately divided between the vertical grid wind shear that the wind turbines create when they levels. Additionally, a horizontal turbine density slow down the wind. The increased mixing caused needs to be imposed. The wind farm density term is an increase in surface temperatures (Figure 5). given m2/m3 or m-1 can be described by: z2 − l IV. Future work ⎛z⎞ One of the unknowns of this work is how A = NT ∫ z1 −l z r 2 − z 2 + r 2 arcsin ⎜ ⎟ (5) ⎝r⎠ much of the energy that is lost due to mechanical workings and heat, versus that which goes back into tke. Wind turbines have been shown to interfere with where NT is the number of turbines per km2, r is the modern WSR-88D (Burgess et al, 2007). Using turbine radius, z1 is the bottom of the grid box, z2 is WSR-88D spectrum width data we plan to try to the top of the grid box, and l=hh-r. improve our tke calculation. In order to truly understand the impacts of Hub height (hh) 60m large wind farms, we need to look beyond just one Rotor Diameter 76m case and look at the impact over several years. Area Swept Simulations for 10 years for each of the four seasons 4536m2 are currently being run to ascertain the impact under Cut-in Speed 4ms-1 a variety of different weather situations. Cut-out Speed 25ms-1 Standing Thrust Coefficient 0.158 V. References Burgess, D.W., T. Crum, and R. J. Vogt, 2007: Impacts of wind turbine farms on WSR-88D radars. Table 1: Specifications for Bonus 2.0 MW turbine. 33rd Conference on Radar Meteorology III. Initial Results Keith, David W., Joseph F. DeCarolis, David C. A 100km by 100km hypothetical wind farm was Denkenberger, Donald H. Lenschow, Sergey L. placed in Southern Alberta. This region is home to Malyshev, Stephan Pacala and Phillip J. Rasch Pincher Creek and several other wind farms. A case (2004). The influence of large-scale wind-power on study of 12z 15 June 2005 – 12z 25 June 2005 was global climate. Proceedings of the National Academy chosen when testing the new parameterization. The of Sciences, 101, p. 16115-16120. wind turbines were given a horizontal density of 1 turbine per km2. Roy, Somnath Baidya , Steve Pacala and Robert L. The amount of electricity produced as a Walko (2004) Can Large Windfarms Affect Local function of wind speed is illustrated in Figure 3. Meteorology? J. Geophys. Res.-Atmos. VOL. 109, Notice that in areas where electricity is not being D19101. generated the wind speed is below the turbine cut-in speed in magnitude. The amount of tke generated S. Pacala and R. Socolow (2004). Stabilization due to the wind farm divided by the mean tke over Wedges: Solving the cliamte problem for the next 50 the domain is given in Figure 4. The electricity years with current technologies. Science. Vol. 305, generated is also plotted with the tke, so that the tke no. 5686, pp. 968-972 values are easily related spatially to the wind farm. 3 “Wind force 12” 12% of world’s electricity by 2020 50 1000 Rest of world Half a ‘wedge’ (P acala & Socolow) 40 800 about 1/14 of what is needed to Gigawatts Gigawatts stabilize CO2 at 550 PPM. 30 600 Europe 20 400 10 200 US EWEA 2010 target: 75GW in EU 1980 1990 2000 2010 1980 2000 2020 2040 Figure 1: Growth of wind energy since 1980 (left) and various proposed wind energy growth through 2050 (right). 2.0MW Wind Turbine (Bonus Energy A/S) 2.5 1 0.9 2 0.8 0.7 1.5 0.6 Power 0.5 Cp and Ct MW 1 0.4 0.3 0.5 0.2 0.1 0 0 Wind Speed (m/s) Power (MW) Ct Cp Figure 2: Power Curve, power coefficient and thrust coefficient used in the wind farm parameterization. 4 Figure 3: Snap-shot of electricity generated in megawatts (colorfill) related to the wind speed (m/s) at hub height (contoured). Figure 4: Contours of tke divided by average tke over the whole domain to show the fractional increase in tke. Electricity generated is color filled below tke in order to relate the tke values spatially to the wind farm. Figure 5: Average potential temperature within the wind farm (black) vs. the potential temperature from a control run with no wind farm (green).