{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# irradiance.py" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial explores some of the functions available in the ``pvlib`` module ``irradiance.py``.\n", "\n", "Authors:\n", "* Will Holmgren (@wholmgren), University of Arizona. July 2014, April 2015." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "try:\n", " import seaborn as sns\n", "except ImportError:\n", " pass\n", " \n", "# built in python modules\n", "import datetime\n", "\n", "# python add-ons\n", "import numpy as np\n", "import pandas as pd\n", "\n", "import pvlib" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Table of contents\n", "\n", "1. [Extraterrestrial radiation](#Extraterrestrial-radiation)\n", "2. [Clear sky models](#Clear-sky-models)\n", "2. [Diffuse ground](#Diffuse-ground)\n", "2. [Diffuse sky](#Diffuse-sky)\n", " 1. [Isotropic](#Isotropic-model)\n", " 2. [Klucher](#Klucher-model)\n", " 2. [Reindl](#Reindl-model)\n", " 2. [Hay-Davies](#Hay-Davies-model)\n", " 2. [Perez](#Perez-model)\n", "2. [Angle of incidence](#Angle-of-incidence-functions)\n", "2. [total_irrad](#total_irrad)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Extraterrestrial radiation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Many solar power algorithms start with the irradiance incident on the top of the Earth's atmosphere, often known as the extraterrestrial radiation. ``pvlib`` has three different algorithms to calculate the yearly cycle of the extraterrestrial radiation given the solar constant." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "times = pd.date_range('2014-01-01', '2015-01-01', freq='1D')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "spencer = pd.Series(pvlib.irradiance.extraradiation(times, method='spencer'), times)\n", "asce = pd.Series(pvlib.irradiance.extraradiation(times, method='asce'), times)\n", "ephem = pvlib.irradiance.extraradiation(times, method='pyephem') # approx 100x slower than the above" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAgIAAAFgCAYAAADJkREAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4m+XZ9/Gvpvfedjzj5MpwhrPJ3otsAoTRAC1QoJRC\n", "obR9nrZPx9tBoS0UKKWUnQCFkL1D9iZ7504c7733kDXeP+ykCZDEgG3J9vk5Dh227iH9JAd06rqv\n", "oXM4HAghhBCia9I7O4AQQgghnEcKASGEEKILk0JACCGE6MKkEBBCCCG6MCkEhBBCiC5MCgEhhBCi\n", "CzO25YMrpYYDf9I0bcJV2+4GHtc0bWTz/aeAO5t3r9c07bdKKQ9gCRACVAH3aZpW3JZZhRBCiK6o\n", "zVoElFLPAm8AbldtSwa+e9X9BOBu4BZN00YAU5VS/YBHgROapo0F3gN+0VY5hRBCiK6sLS8NpAAL\n", "AB2AUioI+D3w5OVtQCYwTdO0y7MamYB6YBSwsXnbRmByG+YUQgghuqw2KwQ0TVsOWAGUUnrgTeDH\n", "QPVVx1g1TStVSumUUi8ARzVNuwj4AhXNh1UBfm2VUwghhOjK2rSPwFUGA4nAa4A70Ecp9VdN036s\n", "lHIH3qLpg/+x5uMraSoGAHyA8ps9gdVqc5SV1bZ68G8rIMATV8jlKjm+yBVzuWImcL1crpbnMsnV\n", 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However, as shown in the plot below, the difference is only +/-2 W/m^2 over the entire year." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFgCAYAAADNZME9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VPed7/H3jLpQQRKjLoEQ0g8hEEX0DjYYB/cax3aa\n", "Y8fJ7mY32bv7ZLPtJrk3u2lO2c3dJLYTJ3HcYxuMMTa26b1JFIkfIBAqqEuotyn3D4lEISANYmbO\n", "0cz39Tx6opmjOefDxNL5zq9aXC4XQgghhAgsVqMDCCGEEML3pAAQQgghApAUAEIIIUQAkgJACCGE\n", "CEBSAAghhBABSAoAIYQQIgAF+/qCSqkQ4FfARCAM+D9a63eGHL8T+FfADvxKa/2crzMKIYQQ/s6I\n", "FoBHgQat9XJgHfDfVw4MFgfPAGuAFcBTSqlEAzIKIYQQfs2IAuB14N+GXN8+5FgecE5r3aq17gd2\n", "A8t9nE8IIYTwez7vAtBadwIopaIZKAb+ecjhGKB1yON2INZ36YQQQojA4PMCAEAplQG8CfxMa/3K\n", "kEOtQPSQx9FAy3DncrlcLovF4vmQQgghhDl55KZnxCDAJOAD4Mta621XHT4N5Cil4oBOBpr/vz/c\n", 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"et_diff.plot()\n", "plt.ylabel('spencer-ephem (W/m**2)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also control the solar constant." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAgIAAAFoCAYAAAAlwpNtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VGXax/HvTHovpAAhCSXwkNCbIChYUJoF6SoKirpr\n", "b7v7rq5bfHdd3X13XXftHRGUJk0UBFFEEZEaICRPEnpL773MvH/MRCMLIZJMzszk/lxXrmTOnHPm\n", "NzPo3POcp5isVitCCCGEaJ/MRgcQQgghhHGkEBBCCCHaMSkEhBBCiHZMCgEhhBCiHZNCQAghhGjH\n", "pBAQQggh2jEpBIRoJUqpo0qpwQY+/iSl1NM/8xizUmq1Ukorpe5rhQwWpVR4S8/jaEqpN1vyXiml\n", "uimllrdmJiGM4ml0ACHciNGTcgwDfu6HcBfgWsBfa210/rY0FnitBcfHA6qVsghhKJNMKCRE61BK\n", "HQGmaq13K6WqgOeB64Bg4NfAdKAfcBq4XmtdoZSyAH/H9sEUADyptV6plAoAXgV6YvtwLwVu0Vqn\n", 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"/3waxnXBl6W17tVyjgQ4i9GCVAghhHBa13vswzit8LT9Z/UH8q/2fE591QBGX+5w4BdKqZbzJf8G\n", "/E0p5QccxmhVezGz2rAKIYQQbeF6j33PAW8ppW7GWH/jwas9mTQUEkIIITyYU58aEEIIIYRjSSEg\n", "hBBCeDApBIQQQggPJoWAEEII4cGkEBBCCCE8mBQCQgghhAeTQkAIIYTwYP8f8s3BJ1MvX8QAAAAA\n", "SUVORK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spencer_1400 = pd.Series(pvlib.irradiance.extraradiation(times, method='spencer', solar_constant=1400), times)\n", "\n", "spencer.plot(label='default')\n", "spencer_1400.plot(label='1400')\n", "plt.legend()\n", "plt.title('Impact of solar constant')\n", "plt.ylabel('ET Irradiance (W/m^2)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Clear sky models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "``pvlib`` has two different clear sky models: Ineichen and Haurwitz. We'll explore some of the features of each of them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we need to make a ``Location`` object so that ``pvlib`` can calculate the solar position when needed." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tucson: latitude=32.2, longitude=-111, tz=US/Arizona, altitude=700\n" ] } ], "source": [ "from pvlib.location import Location\n", "\n", "tus = Location(32.2, -111, 'US/Arizona', 700, 'Tucson')\n", "print(tus)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "times = pd.date_range(start=datetime.datetime(2014,1,1), end=datetime.datetime(2014,1,2), freq='1Min').tz_localize(tus.tz)\n", "solpos = pvlib.solarposition.get_solarposition(times, tus, method='pyephem')\n", "ephem_data = solpos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Haurwitz\n", "\n", "The Haurwitz model is a very simple model that only needs the solar zenith." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl4nGd19/HvjFZL1mrLliWv8nJ7d+LEgSRkIQQCDRB2\n", "KIVC2oSkDYECLZS8FAolhC3ARWnZUhr2LbRAICEJSRoHE8hqx+uxJXmVZFubtVn7zPvHM2MLI8kj\n", "WaNnnpnf57p82ZoZjc7xaJ4z9x6KRqOIiIhIMIX9DkBEREQmT4VcREQkwFTIRUREAkyFXEREJMBU\n", "yEVERAJMhVxERCTAspP55M65DwOvAnKArwBbgLuBCLADuMXMos65G4F3AUPAJ83s18mMS0REJF0k\n", "rUXunLsSuNjMLgGuBGqAO4HbzOxyIARc55yrBG4FLgGuAe5wzuUmKy4REZF0ksyu9ZcB251zPwfu\n", "BX4JXGBmm2P33w9cDWwCtpjZoJl1ArXA+iTGJSIikjaS2bVeASwAXonXGr8XrxUe1wWUAMVAxyi3\n", "i4iIyFkks5C3ALvNbAjY65zrA6pH3F8MnAA6gaIRtxcB7UmMS0REJG0ks5D/Dngv8AXnXBVQADzs\n", 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It automatically calculates the solar position and looks up the Linke turbidity (related to the optical depth of the atmosphere)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XmcHOV97/tP9b53zz4azWgXhRa0oF0CSexgg7GxIfax\n", "E+9gBxOfLCc+5ubkXuc48U1yfZLYOfFxTGwnThxjY4wxmwEhJKFdQgKhpbShdaTR7L3vdf/omZEE\n", "0miW7q5efu/Xi5ek7uqqX9Ez/e3nqaeeR9F1HSGEEEKUJ5PRBQghhBBi7CTIhRBCiDImQS6EEEKU\n", "MQlyIYQQooxJkAshhBBlTIJcCCGEKGOWfO1IVdVlwP+radotqqrOAH4MZIF3gEc1TdNVVf0i8DCQ\n", "Br6padrzqqo6gX8HGoAQ8GlN07ryVZcQQghRyfLSIldV9U+BHwD2gYf+F/C4pmmrAQW4X1XVZuAx\n", "YCVwF/AtVVVtwJeBtwa2/Tfgz/JRkxBCCFEN8tW1fhR4gFxoA9yoadrGgb+/CNwOLAE2a5qW0jQt\n", 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You can also specify the value yourself. You can also supply the zenith angle to avoid recalculating the solar position each time the function is called." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAA7UAAAE5CAYAAABPtAe/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xec1NW9//HXzGzvfReW3g5NpIgF7BFjbzGWRNPtaOq9\n", "ucktv2tu2k1umiYxMcYUY0yxRqyICjYUBAQEDiywLLC99zbz/f0xswRxgWXZme/M7vv5eOxDdtp5\n", "z3fXs/P5nvM9x+M4DiIiIiIiIiKxyOt2ABEREREREZHBUlErIiIiIiIiMUtFrYiIiIiIiMQsFbUi\n", "IiIiIiISs1TUioiIiIiISMxSUSsiIiIiIiIxK87tABJ7jDETgE3W2vRDbn8DSAESgOnAxtBdm621\n", "Nx7t+cfQ/tnAvdbaEwbz/KO89kTgh9baq4/yuP8GCq21t/VzXylwlbV23VDnE5Hhob9+cKB96GFe\n", "7wbga4ADtAN3WWvf7edxFwPfBRJDr/95a23Lcb8hEZF+hKGvWwrcSrCv2wncZK2t6edxPwKuBupD\n", 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"cVIbBEEQBEEQBEEQNC1xUhsEQRAEQRAEQRA0LXFSGwRBEARBEARBEDQtcVIbBEEQBEEQBEEQNC1x\n", "UhsEQRAEQRAEQRA0Lf8PzBme/cSuJRgAAAAASUVORK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solpos = pvlib.solarposition.get_solarposition(times, tus, method='pyephem')\n", "\n", "fig, axes = plt.subplots(1,3, figsize=(16,5), sharey=True)\n", "\n", "irrad_data = pvlib.clearsky.ineichen(times, tus, linke_turbidity=None, zenith_data=solpos['apparent_zenith'])\n", "ax = axes[0]\n", "irrad_data.plot(ax=ax)\n", "ax.set_title('LT lookup table')\n", "ax.set_ylabel('Irradiance W/m^2')\n", "\n", "irrad_data = pvlib.clearsky.ineichen(times, tus, linke_turbidity=2.0, zenith_data=solpos['apparent_zenith'])\n", "ax = axes[1]\n", "irrad_data.plot(ax=ax)\n", "ax.set_title('LT=2.0')\n", "\n", "irrad_data35 = pvlib.clearsky.ineichen(times, tus, linke_turbidity=3.5, zenith_data=solpos['apparent_zenith'])\n", "ax = axes[2]\n", "irrad_data35.plot(ax=ax)\n", "ax.set_title('LT=3.5')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a comparison between the clear sky algorithms. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4nNWZ8P/vMzOSRmXUR8UqtmRJx7bcKzZgGzALJCSk\n", "bXrdDaQSNmWTX7y7SdiFsHmz4d1l2TfshpRNSNkFUgEnDsXY2NjGXfXYsmT1rlFv035/jGRkkOSx\n", "rdFoZu7Pdemy9Mwzz9yHQbrnOeU+htfrRQghhBChyRTsAIQQQghx9SSRCyGEECFMErkQQggRwiSR\n", "CyGEECFMErkQQggRwiSRCyGEECHMEsiLK6U+Bnx84sdYYA1wA/BvgAcoBz6ntfYqpe4G7gFcwANa\n", "62cDGZsQQggRDoz5WkeulHoUOAW8Dfie1nq/Uur7wJ+Aw8BeYAO+hP8KsFFrPT4vwQkhhBAhal66\n", "1pVSG4EVWuvHgQ1a6/0TD+0BdgGbgINaa6fWuh+oAVbPR2xCCCFEKJuvMfLdwP0T3xtTjg8ASUAi\n", "0DfNcSGEEELMIuCJXCmVDJRorV+eOOSZ8nAi0Av0A7Ypx22AI9CxCSGEEKEuoJPdJmwHXpjy80ml\n", "1I6JxH7HxGNHgQeVUjGAFViObyLctLxer9cwjJkeFkIIIcLRtIlvPhJ5CXB+ys9fBn6glIoGKoGn\n", 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zenith_data=solpos['apparent_zenith'])\n", "haurwitz_data = pvlib.clearsky.haurwitz(solpos['apparent_zenith'])\n", "\n", "ineichen_data['GHI'].plot(label='Ineichen')\n", "haurwitz_data['GHI'].plot(label='Haurwitz')\n", "plt.ylabel('Irradiance W/m^2')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Diffuse ground" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ``grounddiffuse`` function has a few different ways to obtain the diffuse light reflected from the ground given an surface tilt and the GHI." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, you can specify the albedo of ground." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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``'snow'``. All of the available ``surface_type`` options are show in the plot below." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFSCAYAAAAJjV0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4FFXbwOHfbHY3yaaRRmjpkEPovXfsr4oFRfQVFSmC\n", "gIiAgIIIAiKIIqgUQVHxExvKa8WCdJBew1ACJJSE9LYpW+b7YwMSIKSQQsK5r4vLZGfOzHM2ic+e\n", "MzPnUTRNQ5IkSZKkqklX2QFIkiRJklR6MpFLkiRJUhUmE7kkSZIkVWEykUuSJElSFSYTuSRJkiRV\n", "YTKRS5IkSVIVpq/sACRJKpwQogMwE/DF8cE7FhirqurhEh7HA/gV8ASmqKq6uqxjzT+PF7BaVdVe\n", "5XF8SZKuJhO5JN2khBDOwI/Abaqq7s1/7QngFyFEiKqqJVkEoiVQU1XVBuUQ6uW8gbblfA5Jki4j\n", "E7kk3bxMgBfgcfEFVVVXCiHSAL0QojOwQFXVpgBCiB4XvxdCTAU6ArWAQziSa10hxG6gEzAG6AO4\n", "AG44RvnfCyH0wFvAfwArsAUYrqqqRQjxCvAQjpmBU/mvn78i5o8B1/zzzAWeV1W1c358QcBWIATI\n", 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"plt.title('Surface types')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, vary the tilt angle. We expect to see maximum ground diffuse irradiance at a 90 deg tilt, and no ground diffuse irradiance at 0 tilt." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFSCAYAAAAJjV0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd8m9W5wPGfhvfee2X4ZE8IISQhSaFsKKul0PZSKDMF\n", "LqOUMAoBChQuoyWU1ZZVRguFAg2UTQKBTLKccRI7drwd772l+4dk4wzHlixZlvx8Px9/Yknve97n\n", "WLEfvWcarFYrQgghhPBORk8HIIQQQgjnSSIXQgghvJgkciGEEMKLSSIXQgghvJgkciGEEMKLSSIX\n", "QgghvJjZ0wEI4WpKqcuBK4BwwB/YB9yptV7voXiagEla68LBHAfEA7/VWl+olEoDPgQ6gRuAB4EI\n", "4C6t9Tvujdz9lFJPA6cAr2qt73JhuVnAI1rrC5RSycCbWusTXFX+Ua57xPr0F49S6h4gRmt9nVLq\n", "V4Cf1vppd8cpfIskcuFTlFIPAPOBC7XWRfbnFgP/UUrN0loXeyCswS7WYAXQWm8ELrQ/txgo01qf\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for surf_tilt in np.linspace(0, 90, 5):\n", " ground_irrad = pvlib.irradiance.grounddiffuse(surf_tilt, irrad_data['GHI'])\n", " ground_irrad.plot(label=surf_tilt)\n", "\n", "plt.legend()\n", "plt.ylabel('Diffuse ground irradiance (W/m^2)')\n", "plt.title('Ground diffuse as a function of tilt')" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "try:\n", " sns.set_palette('deep')\n", "except:\n", " pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Diffuse sky" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "``pvlib`` has many different ways to calculate the diffuse sky component of GHI. \n", "\n", "The API for some of these functions needs some work.\n", "\n", "1. [Isotropic](#Isotropic-model)\n", "2. [Klucher](#Klucher-model)\n", "2. [Reindl](#Reindl-model)\n", "2. [Hay-Davies](#Hay-Davies-model)\n", "2. [Perez](#Perez-model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Isotropic model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ``isotropic`` model is the simplest model." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl83VWd//HX9+73JjdJm6YbXehCTzcopZRVSgUUURR/\n", "jM6Mow6IAi7j6IyjI4yizqj83EdwRBQZdMZhfoqKyKLIIjuUpS1dT3egG03TNMvdl+/vj3tTQknT\n", "tM3NN/fm/Xw88kjyvdv75Lb55HzP+Z7juK6LiIiIVCef1wFERETk6KmQi4iIVDEVchERkSqmQi4i\n", "IlLFVMhFRESqmAq5iIhIFQtU8smNMZcBl5e/jQILgDcB3weKwGrgE9Za1xhzJXAVkAe+aq29p5LZ\n", "REREaoEzVNeRG2N+AKwA3gl8x1r7qDHmJuCPwNPA/cAiSgX/ceBUa212SMKJiIhUqSE5tW6MORWY\n", 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"markdown", "metadata": {}, "source": [ "Compare just the POA diffuse to the input DHI." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl8VPW5+PHPmclk38jCGkIWyJclbIoIooK4IIqAuFWt\n", "1ap1rfXaXv312l67t7d1aaut1qXUtS64IKIoCgiKgLLK+oVA2AOEJGRfZ87vj5kJaFlmJjOZyZnn\n", "/XrZkgln5vmSyXnm+a6GaZoIIYQQomuyhTsAIYQQQgROErkQQgjRhUkiF0IIIbowSeRCCCFEFyaJ\n", "XAghhOjCJJELIYQQXVhMOF5UKbUaqPZ8uQP4A/A84AI2AHdrrWVdnBBCCHEKnZ7IlVLxAFrr8455\n", "bA7woNZ6iVLqKWAaMLuzYxNCCCG6mnBU5MOBRKXUR57X/xlwmtZ6ief784CLkEQuhBBCnFI4xsjr\n", "gYe11pOAO4BXvvX9OiCt06MSQgghuqBwJPKteJK31nobUAH0OOb7KcCRMMQlhBBCdDnh6Fr/PjAM\n", "uFsp1Rt34p6vlBqvtV4MTAYWnOwJTNM0DcMIfaRCCCFEZDhh0jM6+9AUpVQM8C+gn+ehB3BX5c8C\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sky_diffuse = pvlib.irradiance.isotropic(40, irrad_data['DHI'])\n", "sky_diffuse.plot(label='isotropic diffuse')\n", "irrad_data['DHI'].plot()\n", "plt.legend()\n", "plt.ylabel('Irradiance (W/m^2)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Klucher model" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl8VOW9+PHPmZnsZCckgRBCIDwQ9l1AFndxQ60L7tDa\n", "Wlu1i72L/npvb/u7/fX2Vu2i1bpWrbtosVpRqyjIIrJDWB72LWTf92Rmzu+PSQJahWSYzJk5832/\n", "XtFkknnO9yGT851nN0zTRAghhBDhyWF1AEIIIYTwnyRyIYQQIoxJIhdCCCHCmCRyIYQQIoxJIhdC\n", 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"4Ym2sZ74AAAAAElFTkSuQmCC\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "surf_tilt = 40\n", "surf_az = 180\n", "\n", "sky_diffuse = pvlib.irradiance.klucher(surf_tilt, surf_az, irrad_data['DHI'], irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "sky_diffuse.plot(label='klucher diffuse')\n", "irrad_data['DHI'].plot()\n", "#irrad_data['GHI'].plot()\n", "plt.legend()\n", "plt.ylabel('Irradiance (W/m^2)')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VFX6wPHvncyk956QBgEuvYUqSrNgAURAZW0oCqIi\n", "/qyrrquru6u7FiwgCgpid60oiIpIlU5IgFAuJZDee09m5v7+CLDogkkmk0wS3s/z5NHMzDnnvQmT\n", 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"output_type": "display_data" } ], "source": [ "surf_tilt = 40\n", "surf_az = 180 # south facing\n", "\n", "iso_diffuse = pvlib.irradiance.isotropic(surf_tilt, irrad_data['DHI'])\n", "iso_diffuse.plot(label='isotropic diffuse')\n", "\n", "klucher_diffuse = pvlib.irradiance.klucher(surf_tilt, surf_az, irrad_data['DHI'], irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "klucher_diffuse.plot(label='klucher diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()\n", "plt.ylabel('Irradiance (W/m^2)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Klucher as a function of surface azimuth." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", " klucher_diffuse.plot(label='klucher: {}'.format(surf_az))\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Surface azimuth should not matter if tilt is 0." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd8VFXe+PHPnZpJISEQAkmAUC+9aajSFFyxgH3dYm9g\n", "WZ993MfHuuquur/VVdeyKrqg7j6rrl1xbfQOUkKHSwuBQBJCCaRPu78/UiRSEiAzd3Lm+369fElm\n", "7tz5fjM39zvn3HPP0UzTRAghhBDNk83qAIQQQghx5qSQCyGEEM2YFHIhhBCiGZNCLoQQQjRjUsiF\n", "EEKIZkwKuRBCCNGMOax4U13XHwIuA5zAq8Bi4B0gCGwA7jYMQ+6LE0IIIRoQ9ha5rutjgGGGYQwH\n", 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"iso_diffuse.plot(label='isotropic')\n", "\n", "for surf_az in np.linspace(0, 270, 4):\n", " klucher_diffuse = pvlib.irradiance.klucher(surf_tilt, surf_az, irrad_data['DHI'], irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", " klucher_diffuse.plot(label='klucher: {}'.format(surf_az))\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reindl model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "South facing at latitude." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VFX6wPHvnZ4y6b0nlEvvvfeiqNjdta4oiiu4dsWu\n", 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irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "klucher_diffuse.plot(label='klucher diffuse')\n", "\n", "dni_et = pvlib.irradiance.extraradiation(times.dayofyear)\n", "reindl_diffuse = pvlib.irradiance.reindl(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], irrad_data['GHI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "reindl_diffuse.plot(label='reindl diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "East facing" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4HOXV9/HvbFVb9d4lWx53YxvjhjuY0AkhhDQgdBIg\n", 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ephem_data['apparent_azimuth'])\n", "reindl_diffuse.plot(label='reindl diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hay-Davies model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hay-Davies facing south." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VFX++PH3ncnMZJJMeu8JgaFX6QIBRERRsa5rQ0VR\n", "VtTv2lZx17qrv11dXWXFRQXb2huCSpEugnQILQOkV9InySSTaff3RyALmIQEkmk5r+fxMZm55XNm\n", "wv3cc+4pkizLCIIgCILgmRSuDkAQBEEQhPMnErkgCIIgeDCRyAVBEATBg4lELgiCIAgeTCRyQRAE\n", "QfBgIpELgiAIggfzcfYJ9Xq9GngXSAOswIOACXgfcAAHgfsNBoMYFycIgiAI5+CKGvk9QIPBYBh3\n", 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pvlib.irradiance.haydavies(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "haydavies_diffuse.plot(label='haydavies diffuse')\n", "\n", "reindl_diffuse = pvlib.irradiance.reindl(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], irrad_data['GHI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "reindl_diffuse.plot(label='reindl diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Facing east." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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"display_data" } ], "source": [ "surf_tilt = 32\n", "surf_az = 90 \n", "\n", "iso_diffuse = pvlib.irradiance.isotropic(surf_tilt, irrad_data['DHI'])\n", "iso_diffuse.plot(label='isotropic diffuse')\n", "\n", "klucher_diffuse = pvlib.irradiance.klucher(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "klucher_diffuse.plot(label='klucher diffuse')\n", "\n", "dni_et = pvlib.irradiance.extraradiation(times.dayofyear)\n", "\n", "haydavies_diffuse = pvlib.irradiance.haydavies(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "haydavies_diffuse.plot(label='haydavies diffuse')\n", "\n", "reindl_diffuse = pvlib.irradiance.reindl(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], irrad_data['GHI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "reindl_diffuse.plot(label='reindl diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hay-Davies appears to be very similar to Reindl. Too similar?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### King model" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl8VNXZwPHfncxkJstkn+w7gcuO7JuAiIJYVLRq3arW\n", "tb5V+1atFaxa91qtVrEqblXbWl5XRK0gm2wiskNYLkt2SMi+zySZmfv+kRBB2clkyM3z/Xz4MHPn\n", "Ls+ZSfLMWe45iq7rCCGEEKJrMvk7ACGEEEKcOknkQgghRBcmiVwIIYTowiSRCyGEEF2YJHIhhBCi\n", "C5NELoQQQnRhZl9fQFXVkcCfNU2bqKpqLPAGEAEowPWapuWpqnorcBvgBp7QNO1LX8clhBBCGIFP\n", "a+Sqqt5Pa+K2tm36C/BPTdMmAA8D/VVVjQfuAsYAU4CnVVUN9GVcQgghhFH4uml9D3AZrbVvaE3W\n", "KaqqLgSuBZYAI4BVmqa1aJpW23bMQB/HJYQQQhiCTxO5pmmf0NpcflA6UKlp2vlAAfAHwA7UHLJP\n", "HRDuy7iEEEIIo+jswW4VwLy2x58Dw4BaWpP5QXagqpPjEkIIIboknw92+5GVwM+AfwETgGzge+BJ\n", 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"haydavies_diffuse = pvlib.irradiance.haydavies(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "haydavies_diffuse.plot(label='haydavies diffuse')\n", "\n", "king_diffuse = pvlib.irradiance.king(surf_tilt,irrad_data['DHI'], irrad_data['GHI'], ephem_data['apparent_zenith'])\n", "king_diffuse.plot(label='king diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Perez model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This section walks through the Perez algorithm." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sun_zen = ephem_data['apparent_zenith']\n", "sun_az = ephem_data['apparent_azimuth']\n", "DNI = irrad_data['DNI']\n", "DHI = irrad_data['DHI']\n", "DNI_ET = pvlib.irradiance.extraradiation(times.dayofyear)\n", "AM = pvlib.atmosphere.relativeairmass(sun_zen)\n", "\n", "surf_tilt = 32\n", "surf_az = 180\n", "\n", "kappa = 1.041 #for sun_zen in radians\n", "z = np.radians(sun_zen) # convert to radians\n", "\n", "#Dhfilter = DHI > 0\n", "\n", "# epsilon is the sky's clearness\n", "eps = ( (DHI + DNI)/DHI + kappa*(z**3) ) / ( 1 + kappa*(z**3) )" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xm83FV9//HXbHfufueu2ReycAIhEMCwCSgUEBewWARK\n", "XVusu9al2Pqr1tpqrUu1VOtaBVdUtIIIyA7KLlsgJCckZL1Jbu6+5a4z8/vjO3NzSW5u7jIz32Xe\n", "z8fDh+Emwc/Hmfm+55zvOecbSqfTiIiIiD+F3S5AREREZk5BLiIi4mMKchERER9TkIuIiPiYglxE\n", "RMTHFOQiIiI+FnXjf9QYczrwBWvtecaYtcB1QBIYAt5mrd3vRl0iIiJ+U/ARuTHmWuC7QDzzo68B\n", 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"\n", "ebin.plot()\n", "plt.ylim(0,9)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAeEAAAFKCAYAAAAqkecjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmYZHV18PFv9QyLQA+iDCIqrnDcFYlxQ1RcI6DxfQnG\n", "vI9bXDCJaCQuBJfX1yQmETWSaNQoKEFFk2hcIBGiISIao0EU1wNoYpQgDMw4DDMMMHS9f/xudTed\n", "6a7q6dtV91Z9P8/Dw3Tdmq4zd2r61Pmd39LpdrtIkqThmxp1AJIkTSqTsCRJI2ISliRpREzCkiSN\n", "iElYkqQRMQlLkjQia/s9ISKeD7yg+vJ2wEOAO2Xm9dX1Y4E3AjuAMzLzg6sTqiRJ46WznHXCEfFu\n", "4Fu9RBsRuwHfB34J2AZ8BTgmM69ZhVglSRorAw9HR8QvAQ9YUOneD7giMzdn5i3ARcCRNccoSdJY\n", "Wk5P+BTgzQseWwdsnvf1FmDfFcYkSdJEGCgJR8TtgUMz80sLLm0Gpud9PQ1sqik2SZLGWt+JWZUj\n", "gS/u5PEfAodExH7A1up5py71jXbsuLW7du2aZQVZp5f+8RfYdP12nv7oe44sBknS6vr5xq189dKr\n", 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"ebin.plot()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAeAAAAFKCAYAAADFU4wdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmcZHV97/9XLb139Tbds6/MwBcYGEBQhi0KiIqAYiIq\n", "yY1KJDHkukQTlauJv9wsJvHKvXEJRnFHgoYoroggKiibCMKwfmdjhtmnp6eX6r2W8/vje6qnpqe7\n", "qnumu845Pe/n48Gju+qcqvrMobs/5/v5bjHP8xAREZHKigcdgIiIyPFICVhERCQASsAiIiIBUAIW\n", "EREJgBKwiIhIAJSARUREApAsddAYEwduBtYBI8D11totRcdfDtwExIBdwNuttaOzF66IiMjcUK4F\n", "fDVQba09H7gRl2wBMMbEgC8C77TWXgTcB6yarUBFRETmknIJ+ALgbgBr7aPAOUXHTgK6gA8aY34J\n", "tFhr7WwEKSIiMteUS8BNQF/R45xflgZoB84HPgu8GrjUGHPxzIcoIiIy95RLwH1Aqvh8a23e/74L\n", "2GydLK6lfM74NxAREZEjlRyEBTwIXAXcYYxZD2woOrYVaDTGrPYHZl0EfKnUm2WzOS+ZTBxLvCIi\n", "IlETm/DJUpsx+AOtCqOgAa4DzgYarbW3+CXnf/Hf/EFr7QdKRdDZmZ71nR86OlJ0dqZn+2NmTNTi\n", 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z[ebin.index]" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAeYAAAFKCAYAAADITfxaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4W/eZ4PvvQSNBAARBEuwUKVLikUSJspqL3FsUt1i2\n", "05zu2MmMUyYzd+/uZLJ3Zp7Znd29k7meksykedJjj2MnseMSd9mxLTf1rsMi9l4AEABJ1HP/AEhR\n", "skRSIkgC0vt5zIcCDs45L2EJL99fVXRdRwghhBDpwbDUAQghhBDiJEnMQgghRBqRxCyEEEKkEUnM\n", "QgghRBqRxCyEEEKkEUnMQgghRBoxzXRQVVUD8D2gAQgBD2ia1nKG1/0IGNY07a+Sj/cCvuThE5qm\n", "3Z/SqIUQQogL1IyJGdgOWDRN26qq6mXAQ8nnpqiq+ifAWuD15ONsAE3Trk95tEIIIcQFbram7CuB\n", "FwA0TXsP2Dz9oKqqW4FLgR8CSvLp9UCOqqovqqr6ajKhCyGEEGIOZkvMucDotMexZPM2qqqWAn8D\n", "fI2TSRkgCPyjpmnbgD8FHpk8RwghhBAzm60pexRwTHts0DQtnvzzR4FC4A9ACYkq+RjwGNAMoGla\n", "k6qqw0Ap0J3KwIUQQogL0WyJeSdwB/CEqqqXAwcnD2ia9l3guwCqqn4eUDVN+4Wqqn8KrAO+qqpq\n", 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"plt.legend()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pvlib import tools" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XV0nFea7/tvoZhZssiCEpkZYsfMcRLHFCdxsNPp6Z6G\n", "MzO3z7lnZs6cuffMzO3pHmhMBx3HEGMcQ+yYY4gZZFGJwWJmqVRw/5CTcaeTWFAoPZ+1vFas0t77\n", "eSNLP9X7blBYLBaEEEII4ZqUji5ACCGEEEMnQS6EEEK4MAlyIYQQwoVJkAshhBAuTIJcCCGEcGES\n", "5EIIIYQLs2uQ63S6GTqd7uw3fHyNTqe7ptPpLut0ulftWZMQQgjhyuwW5Dqd7m+AtwC3r31cA/wK\n", "WALMB76n0+lC7VWXEEII4crs+Y68EHgaUHzt46lAoV6vb9Xr9X3ARWCeHesSQgghXJbdglyv1x8A\n", "jN/wki/Q+tDf2wE/uxQlhBBCuDhnmOzWCvg89HcfoNlBtQghhBAuRe3oAoA8IEmn0wUAnfTfVv/F\n", 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B[ebin.index] + F2*tools.sind(surf_tilt))\n", "sky_diffuse[sky_diffuse < 0] = 0\n", "\n", "sky_diffuse.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the Perez model to others." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VFX6wPHvnZbeeyUJgaF3kCYgCoiCFMu6a0FFwQK6\n", "KhbsZdeKDRRFBdtaforSq3QVpLcQGEp6I71NMpMp9/fHhEBIBZJMMjmf5/GRmdveOzOZd865575H\n", "kmUZQRAEQRDaJoW9AxAEQRAE4fKJRC4IgiAIbZhI5IIgCILQholELgiCIAhtmEjkgiAIgtCGiUQu\n", "CIIgCG2YqqUPqNVqNcCXQCxgAh4F9MDXgBWIAx7R6XTivjhBEARBaIA9WuQPAGU6nW5o5b+/At4D\n", "ntPpdCMACZhkh7gEQRAEoc2xRyLvBqwH0Ol0J4EwYLROp9tRuXwdcJ0d4hIEQRCENsceifwQMAFA\n", 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"surf_tilt = 32\n", "surf_az = 180\n", "\n", "iso_diffuse = pvlib.irradiance.isotropic(surf_tilt, irrad_data['DHI'])\n", "iso_diffuse.plot(label='isotropic diffuse')\n", "\n", "klucher_diffuse = pvlib.irradiance.klucher(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "klucher_diffuse.plot(label='klucher diffuse')\n", "\n", "dni_et = pvlib.irradiance.extraradiation(times.dayofyear)\n", "\n", "haydavies_diffuse = pvlib.irradiance.haydavies(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "haydavies_diffuse.plot(label='haydavies diffuse')\n", "\n", "perez_diffuse = pvlib.irradiance.perez(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'],\n", " AM)\n", "perez_diffuse.plot(label='perez diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4VFX+x/H3nZo26T0kkFAuvTdBBCtiRdZ1dXXVteCq\n", "qOuKDVddu64dXBFF1vLTZa0sNlQEQSxI71xKQhIgIb1NMpMp9/dHCgRDzyTk5vt6Hh+Tafd7ZkI+\n", "Oeeee46i6zpCCCGEaJ9MbV2AEEIIIY6fBLkQQgjRjkmQCyGEEO2YBLkQQgjRjkmQCyGEEO2YBLkQ\n", "QgjRjlkCfQBVVUcAT2uadrqqqvHAG0AkoABXa5q2S1XVG4HJgBd4XNO0LwJdlxBCCGEEAe2Rq6p6\n", "D3XBba+/6Z/Au5qmjQUeAvqqqpoI3AaMAsYDT6mqagtkXUIIIYRRBHpofQcwibreN9SFdaqqqt8C\n", "VwKLgOHAj5qmeTRNq6h/Tv8A1yWEEEIYQkCDXNO0T6gbLm/QBSjRNO1sIAe4F3AA5Qc8phKICGRd\n", "QgghhFG09mS3YmB+/defAUOBCurCvIEDKG3luoQQQoh2KeCT3Q6yDDgf+D9gLLAR+BV4QlVVOxAE\n", 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irrad_data['DHI']\n", "DNI_ET = pvlib.irradiance.extraradiation(times.dayofyear)\n", "AM = pvlib.atmosphere.relativeairmass(sun_zen)\n", "\n", "surf_tilt = 32\n", "surf_az = 90\n", "\n", "iso_diffuse = pvlib.irradiance.isotropic(surf_tilt, irrad_data['DHI'])\n", "iso_diffuse.plot(label='isotropic diffuse')\n", "\n", "klucher_diffuse = pvlib.irradiance.klucher(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['GHI'], \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "klucher_diffuse.plot(label='klucher diffuse')\n", "\n", "dni_et = pvlib.irradiance.extraradiation(times.dayofyear)\n", "\n", "haydavies_diffuse = pvlib.irradiance.haydavies(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "haydavies_diffuse.plot(label='haydavies diffuse')\n", "\n", "perez_diffuse = pvlib.irradiance.perez(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'],\n", " AM)\n", "perez_diffuse.plot(label='perez diffuse')\n", "\n", "irrad_data['DHI'].plot()\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Examine the impact of the coeffecient selection." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAd4AAAFKCAYAAACzaT6WAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd81PX9wPHX9/a+7JBFEgIceyMoCiJI9Vd3rbaOWrFq\n", "W7XWah21rrpq66i11lbrXq211Vqt1lEXogyZYRwQRiAJ2eMul8ut7++PuwsJCSSBrIP38/HgkXHf\n", "u3tfILzv/fm8P5+PoqoqQgghhBgYmsEOQAghhDiaSOIVQgghBpAkXiGEEGIASeIVQgghBpAkXiGE\n", "EGIASeIVQgghBpDuYDe6XC4N8BdgNBABLgfCwHOxr4uBq9xut6xJEkIIIXqgu4p3EWB1u93HA78C\n", 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"\n", "perez_diffuse = pvlib.irradiance.perez(surf_tilt, surf_az, \n", " irrad_data['DHI'], irrad_data['DNI'], dni_et,\n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'],\n", " AM, modelt='phoenix1988')\n", "perez_diffuse.plot(label='phoenix1988')\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Angle of incidence functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ``irradiance`` module has some convenience functions to help calculate the angle of incidence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, the angle of incidence." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFKCAYAAADmCN3IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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"/WwQjNLfG4GP4hxzDNTO13iMc5nObwO/wDlG9zXgOndqM9Dc3r4LfB/4Gc4x5GFr7YOeFjZF3P5u\n", "wenxNzirm1usc/GQQHNHp2/FWYX/eWCjdW7LGXhByr2JBnkz8E6caaI64OvW2u9Mc20zJsz9hbk3\n", "CH9/RzPGXAO8B7jGHTWEhntWxXtxFiQGfgfzWGHtzxjzbpxj/ncC37XWftfjkqZMkF5bJnVBGGPM\n", "epzzqkPzQDxamPsLc28Q/v5KTAAunnGywtwbhLM/Y8zbcS7A9PmwPveC8NoypXc/ExGR8mGcy8Uq\n", "RDymIBcREQmwwK0GFRERkSMU5CIiIgGmIBcREQkwBbmIiEiAKchFREQCTEEuIiISYApyERGRAPv/\n", "2yWTQtJE0dkAAAAASUVORK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ratio = pvlib.irradiance.poa_horizontal_ratio(32, 180, ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "ratio.plot()\n", "plt.ylim(-4,4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot shows that an explicit dot product calculation gives the same result as ``aoi_projection``." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, 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"taVbH24f6cR2B0ra3p3P1hXU0HcdPm/tp8r1gY1ARAzDAX3D0vZfwxARQ/GqtbkR+mVHGlVfWp3e\n", "iNPpWnE0/n3d+1RdQ05+b2+3rFrZFXo/BaeGUG9i9oGqvsfwmTi5O/HEnmzXKINJR31LJP3RaE4c\n", "QNI87AgayokDSHoDT1AapV/uRgPruwAYj2u/tzWKE09k4/f+VR55RJwNfNmAnRFobH2NrA0aX1+h\n", "UI+kFLRjcZxGQ757OYwtXXr7WaFQKBT+P4Trvhcn0s0UR14oFAqFQsZkl9ZRKBQKhUJhF8WRFwqF\n", "QqGQMcWRFwqFQqGQMcWRFwqFQqGQMcWRFwqFQqGQMcWRFwqFQqGQMX8BA/1qynG3tToAAAAASUVO\n", "RK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "surf_tilt = 90\n", "surf_az = 90\n", "\n", "sen_alt_rad = np.radians(90 - surf_tilt)\n", "sen_azi_rad = np.radians(surf_az)\n", "\n", "alts = np.radians(90 - ephem_data['apparent_zenith'])\n", "azis = np.radians(ephem_data['apparent_azimuth'])\n", "\n", "dotprod = np.cos(sen_alt_rad)*np.cos(alts)*np.cos(sen_azi_rad-azis) + np.sin(sen_alt_rad)*np.sin(alts)\n", "dotprod.plot(label='dotprod')\n", "\n", "proj = pvlib.irradiance.aoi_projection(surf_tilt, surf_az, ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'])\n", "proj.plot()\n", "\n", "plt.ylim(-1.1,1.1)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### total_irrad" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is an experimental convenience function ``total_irrad`` that aims to make it easier to play with different models. For now, we use it to make summary plots of the models explored above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "South facing with latitude tilt." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfcAAAFSCAYAAADvpJZ6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xd4XGeV+PHvFGnUe++yZL+SZcu9xE5xnOIkpJMQfixL\n", "3YQFwobOElggEAgsZbMsJZBsNrDsAksICUlIL3biuMRdtuzXktV773Vm7u+PO3Jkx2q2RqMZnc/z\n", "6LF0587MuZY9577tvBbDMBBCCCFE4LD6OgAhhBBCzC5J7kIIIUSAkeQuhBBCBBhJ7kIIIUSAkeQu\n", "hBBCBBhJ7kIIIUSAkeQuxAKhlFqjlPrTeT73G0qpG2cxlhuUUv8+W68nhDiTRda5CyGmopR6HfgP\n", "rfWffR2LEGJqktyFWCCUUluA/wD+EfgJYAMM4AGt9RNKqWjg58AKz/HngHs9538faAG+ANwMxAGL\n", "gKeBB4BfnP08rbVLKeUG/hW4Egj3HP+LUuojwHu11jcopVKAhwAFuIGHtNb/4d2/DSECm3TLC7Fw\n", 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plt.title(model)\n", " plt.ylabel('Irradiance (W/m^2)')\n", " \n", " \n", "plt.figure()\n", "for model, total in totals.items():\n", " total['total'].plot(lw=.5, label=model)\n", " \n", "plt.legend()\n", "plt.ylabel('Irradiance (W/m^2)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "tilt = 0" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFSCAYAAAAJjV0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl83HWd+PHXTCb3Obnvq20+Se+WFkqBUqCAKFCWFdzV\n", "VUEXdBXFXdffrrgqiIgnq3gLiy6rq66AIpcgZ0s5SundJp8mzX1fk/ua4/v74ztJ0zbHtM1kMpP3\n", "8/Hoo833O/Od97eT5D2f6/2xGIaBEEIIIYKTNdABCCGEEOLsSSIXQgghgpgkciGEECKISSIXQggh\n", "gpgkciGEECKISSIXQgghgpgkciFClFLqPKXUH87yuV9RSl0/h7Fcp5T6wVxdTwhxgkXWkQshTqWU\n", 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"cell_type": "markdown", "metadata": {}, "source": [ "East facing with latitude tilt." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAfIAAAFSCAYAAAAJjV0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzs3XeYnNV1+PHvO237zvZeteWqiyLRjKkyGAeQQ7CJ44bj\n", "QFywcVySn0lcA8YlJraDO8ElcezYQIwxYGPTRBcg1KUraSVt771Pe39/vDOrlbRV2pnZmTmf59GD\n", "dup5We2eufeee65hmiZCCCGEiE22aAcghBBCiNMniVwIIYSIYZLIhRBCiBgmiVwIIYSIYZLIhRBC\n", "iBgmiVwIIYSIYZLIhYhTSqlzlVK/Oc3nfl4pdf0SxnKdUurbS/V6QojjDNlHLoQ4mVLqGeA/tNYP\n", "RjsWIcTcJJELEaeUUpcB/wF8CLgHsAMmcLfW+iGllBv4LrAhePvjwB3Bx38V6AI+BbwdyAFWAI8A\n", "dwPfO/l5Wmu/UioAfB3YDKQFb/8/pdTNwF9pra9TShUBPwAUEAB+oLX+j/D+3xAifsnUuhDxK/Qp\n", "/UvAPVrrjcDfApcHb/8O0K21XgdsxErMn9Zafxd4DfiM1vq3wccma63Xaq0/i/Xh4JTnTXvfkeB7\n", 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['isotropic', 'klutcher', 'haydavies', 'reindl', 'king', 'perez']\n", "totals = {}\n", "\n", "for model in models:\n", " total = pvlib.irradiance.total_irrad(32, 90, \n", " ephem_data['apparent_zenith'], ephem_data['apparent_azimuth'],\n", " DNI=irrad_data['DNI'], GHI=irrad_data['GHI'], DHI=irrad_data['DHI'],\n", " DNI_ET=dni_et, AM=AM,\n", " model=model,\n", " surface_type='urban')\n", " totals[model] = total\n", " total.plot()\n", " plt.title(model)\n", " plt.ylabel('Irradiance (W/m^2)')\n", " \n", " \n", "plt.figure()\n", "for model, total in totals.items():\n", " total['total'].plot(lw=.5, label=model)\n", " \n", "plt.legend()\n", "plt.ylabel('Irradiance (W/m^2)')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }