Tutorial 2 - POA Irradiance.ipynb

{
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   "source": [
    "![tutorial banner](images/PVLib_PVPMCLogo.PNG)\n",
    "\n",
    "\n",
    "# Tutorial 2 - Modeling POA from GHI, DHI, and DNI\n",
    "\n",
    "This notebook shows how to use pvlib to transform the three irradiance components (GHI, DHI, and DNI) into POA irradiance, the main driver of a PV system.\n",
    "\n",
    "![Overview](images/tutorial_2_overview.PNG)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steps:\n",
    "\n",
    "<ol>\n",
    "    <li><a id='step1'>Calculating Solar Position</a></li>\n",
    "    <li><a id='step2'>Fixed Tilt POA </a></li>\n",
    "    <li><a id='step3'>Modeling POA for a tracking system</a></li>\n",
    "</ol>\n",
    "\n",
    "### PV Concepts\n",
    "- Plane of Array Irradiance\n",
    "- Angle of Incidence\n",
    "- Time delta for solar position\n",
    "- GHI vs POA for fixed tilt system and tracked systems\n",
    "\n",
    "### Python Concepts\n",
    "- pandas Timedelta\n",
    "- making a new dataframe from existing columns\n",
    "- resampling\n",
    "- bar ploting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What is transposition?\n",
    "\n",
    "The amount of sunlight collected by a PV panel depends on how well the panel orientation matches incoming sunlight.  For example, a rooftop array facing West will produce hardly any energy in the morning when the sun is in the East because the panel can only \"see\" the dim part of the sky away from the sun.  \n",
    "\n",
    "![Overview](images/t2_solarpanel_directions.PNG)\n",
    "\n",
    "\n",
    "As the sun comes into view and moves towards the center of the panel's field of view, the panel will collect more and more irradiance.  This concept is what defines plane-of-array irradiance -- the amount of sunlight available to be collected at a given panel orientation.  Like the three \"basic\" irradiance components, POA irradiance is measured in watts per square meter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Each irradiance component is considered separately when modeling POA irradiance.  For example, calculating the component of direct irradiance (DNI) that is incident on a panel is solved with straightforward geometry based on the angle of incidence.  Finding the POA component of diffuse irradiance (DHI) is more complex and can vary based on atmospheric conditions.  Many models, ranging from simple models with lots of assumptions to strongly empirical models, have been published to transpose DHI into the diffuse POA component.  A third component of POA irradiance is light that reflects off the ground before being collected by the PV panel.  Functions to calculate each of these components are provided by pvlib.\n",
    "\n",
    "\n",
    "![Overview](images/t2_POA.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How is array orientation defined?\n",
    "\n",
    "Two parameters define the panel orientation, one that measures the cardinal direction (North, East, South, West), and one that measures how high in the sky the panel faces:\n",
    "\n",
    "- tilt; measured in degrees from horizontal.  A flat panel is at tilt=0 and a panel standing on its edge has tilt=90.\n",
    "- azimuth; measured in degrees from North.  The direction along the horizon the panel is facing.  N=0, E=90, S=180, W=270.\n",
    "\n",
    "A fixed array has fixed tilt and azimuth, but a tracker array constantly changes its orientation to best match the sun's position.  So depending on the system configuration, tilt and azimuth may or may not be time series values.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# if running on google colab, uncomment the next line and execute this cell to install the dependencies and prevent \"ModuleNotFoundError\" in later cells:\n",
    "# !pip install -r https://raw.githubusercontent.com/PVSC-Python-Tutorials/PVPMC_2022/main/requirements.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href='#step1'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Calculating Solar Position\n",
    "\n",
    "As mentioned earlier, pvlib makes it easy to calculate POA irradiance.  First, let's load in the example TMY dataset from the previous tutorial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9.1\n"
     ]
    }
   ],
   "source": [
    "import pvlib\n",
    "import pandas as pd  # for data wrangling\n",
    "import matplotlib.pyplot as plt  # for visualization\n",
    "import pathlib  # for finding the example dataset\n",
    "\n",
    "print(pvlib.__version__)\n",
    "\n",
    "DATA_DIR = pathlib.Path(pvlib.__file__).parent / 'data'\n",
    "df_tmy, metadata = pvlib.iotools.read_tmy3(DATA_DIR / '723170TYA.CSV', coerce_year=1990)\n",
    "\n",
    "# make a Location object corresponding to this TMY\n",
    "location = pvlib.location.Location(latitude=metadata['latitude'],\n",
    "                                   longitude=metadata['longitude'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We are looking at data from  \"GREENSBORO PIEDMONT TRIAD INT\" , NC\n"
     ]
    }
   ],
   "source": [
    "print(\"We are looking at data from \", metadata['Name'], \",\", metadata['State'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because part of the transposition process requires knowing where the sun is in the sky, let's use pvlib to calculate solar position.  There is a gotcha here!  TMY data represents the average weather conditions across each hour, meaning we need to calculate solar position in the middle of each hour.  pvlib calculates solar position for the exact timestamps you specify, so we need to adjust the times by half an interval (30 minutes):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>apparent_zenith</th>\n",
       "      <th>zenith</th>\n",
       "      <th>apparent_elevation</th>\n",
       "      <th>elevation</th>\n",
       "      <th>azimuth</th>\n",
       "      <th>equation_of_time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-01 01:00:00-05:00</th>\n",
       "      <td>166.841893</td>\n",
       "      <td>166.841893</td>\n",
       "      <td>-76.841893</td>\n",
       "      <td>-76.841893</td>\n",
       "      <td>6.889661</td>\n",
       "      <td>-3.395097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-01 02:00:00-05:00</th>\n",
       "      <td>160.512529</td>\n",
       "      <td>160.512529</td>\n",
       "      <td>-70.512529</td>\n",
       "      <td>-70.512529</td>\n",
       "      <td>52.424214</td>\n",
       "      <td>-3.414863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-01 03:00:00-05:00</th>\n",
       "      <td>149.674856</td>\n",
       "      <td>149.674856</td>\n",
       "      <td>-59.674856</td>\n",
       "      <td>-59.674856</td>\n",
       "      <td>73.251821</td>\n",
       "      <td>-3.434619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-01 04:00:00-05:00</th>\n",
       "      <td>137.777090</td>\n",
       "      <td>137.777090</td>\n",
       "      <td>-47.777090</td>\n",
       "      <td>-47.777090</td>\n",
       "      <td>85.208599</td>\n",
       "      <td>-3.454365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-01 05:00:00-05:00</th>\n",
       "      <td>125.672180</td>\n",
       "      <td>125.672180</td>\n",
       "      <td>-35.672180</td>\n",
       "      <td>-35.672180</td>\n",
       "      <td>94.134730</td>\n",
       "      <td>-3.474102</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "                           apparent_zenith      zenith  apparent_elevation  \\\n",
       "1990-01-01 01:00:00-05:00       166.841893  166.841893          -76.841893   \n",
       "1990-01-01 02:00:00-05:00       160.512529  160.512529          -70.512529   \n",
       "1990-01-01 03:00:00-05:00       149.674856  149.674856          -59.674856   \n",
       "1990-01-01 04:00:00-05:00       137.777090  137.777090          -47.777090   \n",
       "1990-01-01 05:00:00-05:00       125.672180  125.672180          -35.672180   \n",
       "\n",
       "                           elevation    azimuth  equation_of_time  \n",
       "1990-01-01 01:00:00-05:00 -76.841893   6.889661         -3.395097  \n",
       "1990-01-01 02:00:00-05:00 -70.512529  52.424214         -3.414863  \n",
       "1990-01-01 03:00:00-05:00 -59.674856  73.251821         -3.434619  \n",
       "1990-01-01 04:00:00-05:00 -47.777090  85.208599         -3.454365  \n",
       "1990-01-01 05:00:00-05:00 -35.672180  94.134730         -3.474102  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Note: TMY datasets are right-labeled hourly intervals, e.g. the\n",
    "# 10AM to 11AM interval is labeled 11.  We should calculate solar position in\n",
    "# the middle of the interval (10:30), so we subtract 30 minutes:\n",
    "times = df_tmy.index - pd.Timedelta('30min')\n",
    "solar_position = location.get_solarposition(times)\n",
    "# but remember to shift the index back to line up with the TMY data:\n",
    "solar_position.index += pd.Timedelta('30min')\n",
    "\n",
    "solar_position.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two values needed here are the solar zenith (how close the sun is to overhead) and azimuth (what direction along the horizon the sun is, like panel azimuth).  The difference between `apparent_zenith` and `zenith` is that `apparent_zenith` includes the effect of atmospheric refraction.\n",
    "\n",
    "Now that we have a time series of solar position that matches our irradiance data, let's run a transposition model using the convenient wrapper function [`pvlib.irradiance.get_total_irradiance`](https://pvlib-python.readthedocs.io/en/stable/reference/generated/pvlib.irradiance.get_total_irradiance.html). The more complex transposition models like Perez and Hay Davies require additional weather inputs, so for simplicity we'll just use the basic `isotropic` model here, which is the default if nothing is passed for `model` keyword argument.  As an example, we'll model a fixed array tilted south at 20 degrees."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href='#step2'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Fixed Tilt POA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_poa = pvlib.irradiance.get_total_irradiance(\n",
    "    surface_tilt=20,  # tilted 20 degrees from horizontal\n",
    "    surface_azimuth=180,  # facing South\n",
    "    dni=df_tmy['DNI'],\n",
    "    ghi=df_tmy['GHI'],\n",
    "    dhi=df_tmy['DHI'],\n",
    "    solar_zenith=solar_position['apparent_zenith'],\n",
    "    solar_azimuth=solar_position['azimuth'],\n",
    "    model='isotropic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`get_total_irradiance` returns a DataFrame containing each of the POA components mentioned earlier (direct, diffuse, and ground), along with the total in-plane irradiance.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['poa_global', 'poa_direct', 'poa_diffuse', 'poa_sky_diffuse',\n",
       "       'poa_ground_diffuse'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_poa.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What angle should you tilt your modules at?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[PVEducation Solar Radiation on a Tilted Surface](https://www.pveducation.org/pvcdrom/properties-of-sunlight/solar-radiation-on-a-tilted-surface)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total POA irradiance is called `poa_global` and is the one we'll focus on. Like the previous tutorial, let's visualize monthly irradiance to summarize the difference between the insolation received by a flat panel (GHI) and that of a tilted panel (POA):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.DataFrame({\n",
    "    'ghi': df_tmy['GHI'],\n",
    "    'poa': df_poa['poa_global'],\n",
    "})\n",
    "df_monthly = df.resample('M').sum()\n",
    "df_monthly.plot.bar()\n",
    "plt.ylabel('Monthly Insolation [W h/m$^2$]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows that, compared with a flat array, a tilted array receives significantly more insolation in the winter.  However, it comes at the cost of slightly less insolation in the summer.  The difference is all about solar position -- tilting up from horizontal gives a better match to solar position in winter, when the sun is low in the sky.  However it gives a slightly worse match in summer when the sun is very high in the sky.\n",
    "\n",
    "As an example, here's a sunny day in winter vs a sunny day in summer.  Note that the daily profile doesn't just change its height, it also changes its width (summer POA is \"skinnier\" than GHI)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.loc['1990-01-15'].plot()\n",
    "plt.ylabel('Irradiance [W/m$^2$]');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.loc['1990-07-08'].plot()\n",
    "plt.ylabel('Irradiance [W/m$^2$]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The difference between GHI and POA is of course dependent on the tilt defining POA, but because it also depends on solar position, it varies from location to location.  Luckily, tools like pvlib make it easy to model!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href='#step3'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Modeling POA for a tracking system\n",
    "\n",
    "The previous section calculated the transposition assuming a fixed array tilt and azimuth.  Now we'll do the same for a tracking array that follows the sun across the sky.  The most common type of tracking array is what's called a single-axis tracker (SAT) that rotates from East to West to follow the sun.  We can calculate the time-dependent orientation of a SAT array with pvlib:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tracker_data = pvlib.tracking.singleaxis(\n",
    "    solar_position['apparent_zenith'],\n",
    "    solar_position['azimuth'],\n",
    "    axis_azimuth=180,  # axis is aligned N-S\n",
    "    )  # leave the rest of the singleaxis parameters like backtrack and gcr at their defaults\n",
    "tilt = tracker_data['surface_tilt'].fillna(0)\n",
    "azimuth = tracker_data['surface_azimuth'].fillna(0)\n",
    "\n",
    "# plot a day to illustrate:\n",
    "tracker_data['tracker_theta'].fillna(0).head(24).plot()\n",
    "plt.ylabel('Tracker Rotation [degrees]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows a single day of tracker operation.  The y-axis shows the tracker rotation from horizontal, so 0 degrees means the panels are flat.  In the morning, the trackers rotate to negative angles to face East towards the morning sun; in the afternoon they rotate to positive angles to face West towards the evening sun.  In the middle of the day, the trackers are flat because the sun is more or less overhead.\n",
    "\n",
    "Now we can model the irradiance collected by a tracking array -- we follow the same procedure as before, but using the timeseries tilt and azimuth this time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_poa_tracker = pvlib.irradiance.get_total_irradiance(\n",
    "    surface_tilt=tilt,  # time series for tracking array\n",
    "    surface_azimuth=azimuth,  # time series for tracking array\n",
    "    dni=df_tmy['DNI'],\n",
    "    ghi=df_tmy['GHI'],\n",
    "    dhi=df_tmy['DHI'],\n",
    "    solar_zenith=solar_position['apparent_zenith'],\n",
    "    solar_azimuth=solar_position['azimuth'])\n",
    "tracker_poa = df_poa_tracker['poa_global']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like before, let's compare GHI and POA:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.loc['1990-01-15', 'ghi'].plot()\n",
    "tracker_poa.loc['1990-01-15'].plot()\n",
    "plt.legend()\n",
    "plt.ylabel('Irradiance [W/m$^2$]');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how different the daily profile is for the tracker array!  This is because the array can tilt steeply East and West to face towards the sun in early morning and late afternoon, meaning the edges of day get much higher irradiance than for a south-facing array.\n",
    "\n",
    "Note also that in the middle of the day, GHI and POA just touch each other -- this is because at solar noon, the array lies flat, and so POA is momentarily identical to GHI."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the POA calculations discussed above do not address the partial blocking of diffuse light in arrays with multiple tilted rows of PV modules, so the results will be slightly (typically 1-3%) optimistic relative to real conditions or to commercial modeling software. Such corrections are likely to be added to pvlib in the future for specific generic geometries like fixed racks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Creative Commons License](https://i.creativecommons.org/l/by/4.0/88x31.png)](http://creativecommons.org/licenses/by/4.0/)\n",
    "\n",
    "This work is licensed under a [Creative Commons Attribution 4.0 International License](http://creativecommons.org/licenses/by/4.0/)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12"
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