{
 "cells": [
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   "source": [
    "# Yawed rotor wakes"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example demonstrates wake modelling for yawed wind turbine rotors, following [Bastankhah & Porte-Agel](https://doi.org/10.1017/jfm.2016.595). Let's start by importing the required packages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import foxes\n",
    "import foxes.variables as FV\n",
    "import foxes.constants as FC"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our aim in this example is to model two turbines that are located along the x axis, and uniform wind from west. Three states should be computed, with identical wind conditions, in a setup where the first turbine is yawed by 30, 0, -30 degrees, respectively.\n",
    "\n",
    "We can realize these wind conditions with the `StatesTable` class, using a `pandas.DataFrame` object as data as source:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sdata = pd.DataFrame(index=range(3))\n",
    "sdata[FV.WS] = 8.0\n",
    "sdata[FV.WD] = 270.0\n",
    "sdata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "states = foxes.input.states.StatesTable(\n",
    "    data_source=sdata,\n",
    "    output_vars=[FV.WS, FV.WD, FV.TI, FV.RHO],\n",
    "    fixed_vars={FV.RHO: 1.225, FV.TI: 0.05},\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each of these 3 states, and for each of the two turbines, we wish to set the yaw misalignment variable `FV.YAWM`. The following `numpy.ndarray` defines these angles, with shape `(3, 2)` representing `(FC.STATE, FC.TURBINE)` dimensions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "yawm = np.array([\n",
    "    [30.0, 0.0], [0.0, 0.0], [-30.0, 0.0]\n",
    "])\n",
    "yawm"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For transferring these data to the variable `FV.YAWM`, we invoke the turbine model `SetFarmVars`, by adding it to the `turbine_models` section of the `ModelBook`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "mbook = foxes.ModelBook()\n",
    "mbook.turbine_models[\"set_yawm\"] = foxes.models.turbine_models.SetFarmVars()\n",
    "mbook.turbine_models[\"set_yawm\"].add_var(FV.YAWM, yawm)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that this models appears together with the model `yawm2yaw`, which exists by default in the `ModelBook`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "farm = foxes.WindFarm()\n",
    "farm.add_turbine(\n",
    "    foxes.Turbine(\n",
    "        xy=[0.0, 0.0],\n",
    "        turbine_models=[\"set_yawm\", \"yawm2yaw\", \"NREL5MW\", \"kTI_05\"],\n",
    "    )\n",
    ")\n",
    "farm.add_turbine(\n",
    "    foxes.Turbine(\n",
    "        xy=[1000.0, 0.0],\n",
    "        turbine_models=[\"set_yawm\", \"yawm2yaw\", \"NREL5MW\", \"kTI_05\"],\n",
    "    )\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `yawm2yaw` updates the `FV.YAW` variable by adding `FV.YAWM` to the wind direction, i.e., the yaw misalignment defines the absolute rotor yaw in this case (in cases where the latter is set, you may want to include the inverse model `yaw2yawm` instead).\n",
    "\n",
    "We can now create an `Algorithm` object and calculate the farm results. We combine the yaw-sensitive wake model `PorteAgel_linear` (c.f. [reference](https://doi.org/10.1017/jfm.2016.595)) with the wake frame called `yawed`, which is also based on the same publication:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "algo = foxes.algorithms.Downwind(\n",
    "    mbook,\n",
    "    farm,\n",
    "    states,\n",
    "    rotor_model=\"centre\",\n",
    "    wake_models=[\"Bastankhah2016_linear\", \"IECTI2019_max\"],\n",
    "    wake_frame=\"yawed\",\n",
    "    partial_wakes_model=\"auto\",\n",
    "    chunks=None,\n",
    "    verbosity=0,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "farm_results = algo.calc_farm()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the wind farm results are ready we can continue and plot the wind field:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "o = foxes.output.FlowPlots2D(algo, farm_results)\n",
    "g = o.gen_states_fig_xy(FV.WS, resolution=10, xmin=-100, xmax=3000, verbosity=0)\n",
    "for fig in g:\n",
    "    plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As well as some vertical cross sections some distance downstream:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "o = foxes.output.FlowPlots2D(algo, farm_results)\n",
    "g = o.gen_states_fig_yz(FV.WS, resolution=10, x=750, ymin=-200,ymax=200,zmin=0,zmax=250,verbosity=0)\n",
    "for fig in g:\n",
    "    plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, the model bends the wake and a frontal hit of the downstream rotor is avoided under yawed conditions. This also reflects in the rotor equivalent wind speed (REWS) values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "farm_df = farm_results.to_dataframe()\n",
    "print(\"\\nFarm results:\\n\")\n",
    "print(farm_df[[FV.X, FV.WD, FV.YAW, FV.YAWM, FV.REWS]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the turbine type models in `foxes` apply $\\cos(\\gamma)^p$ type yaw corection factors to the variables `FV.P` and `FV.CT`, where `\\gamma` is the yaw misalignment angle (i.e., `FV.YAWM` translated to radiants), and `p` is a constant exponent (in fact there is one for power and another for thrust). These exponents can be setup as desired, here the default values $p_P = 1.88$ and $p_{ct}=1.0$ were invoked.\n",
    "\n",
    "Note that the `yawed` wake frame can bend any kind of wake model. For example, we invoked the `CrespoHernandez` model for turbulence intensity wake effects above. This wake model follows the same bending rules as the wind deficit model, even though it is a simple top-hat type model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "o = foxes.output.FlowPlots2D(algo, farm_results)\n",
    "g = o.gen_states_fig_xy(FV.TI, resolution=10, xmin=-100, xmax=3000, verbosity=0)\n",
    "for fig in g:\n",
    "    plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly any other choice of wake models can be combined with the `yawed` wake frame. Note, however, that the intensity of most wake models only depends on the yaw angle implicitely via ct in such setups."
   ]
  }
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