This tutorial will walk through the process of going from TMY data to AC power using the SAPM.
Table of contents:
This tutorial requires pvlib >= 0.6.0.
Authors:
These are just your standard interactive scientific python imports that you'll get very used to using.
In [1]:
# built-in python modules
import os
import inspect
# scientific python add-ons
import numpy as np
import pandas as pd
# plotting stuff
# first line makes the plots appear in the notebook
%matplotlib inline
import matplotlib.pyplot as plt
import matplotlib as mpl
# finally, we import the pvlib library
import pvlib
pvlib comes with a couple of TMY files, and we'll use one of them for simplicity. You could also load a file from disk, or specify a url. See this NREL website for a list of TMY files:
http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/tmy3/by_state_and_city.html
In [2]:
# Find the absolute file path to your pvlib installation
pvlib_abspath = os.path.dirname(os.path.abspath(inspect.getfile(pvlib)))
# absolute path to a data file
datapath = os.path.join(pvlib_abspath, 'data', '703165TY.csv')
# read tmy data with year values coerced to a single year
tmy_data, meta = pvlib.tmy.readtmy3(datapath, coerce_year=2015)
tmy_data.index.name = 'Time'
# TMY data seems to be given as hourly data with time stamp at the end
# shift the index 30 Minutes back for calculation of sun positions
tmy_data = tmy_data.shift(freq='-30Min')['2015']
The file handling above looks complicated because we're trying to account for the many different ways that people will run this notebook on their systems. You can just put a simple string path into the readtmy3 function if you know where the file is.
Let's look at the imported version of the TMY file.
In [3]:
tmy_data.head()
Out[3]:
This is a pandas DataFrame object. It has a lot of great properties that are beyond the scope of our tutorials.
Plot the GHI data from the TMY file
In [4]:
tmy_data['GHI'].plot()
plt.ylabel('Irradiance (W/m**2)')
Out[4]:
Before we can calculate power for all times in the TMY file, we will need to calculate:
First, define some PV system parameters.
In [5]:
surface_tilt = 30
surface_azimuth = 180 # pvlib uses 0=North, 90=East, 180=South, 270=West convention
albedo = 0.2
# create pvlib Location object based on meta data
sand_point = pvlib.location.Location(meta['latitude'], meta['longitude'], tz='US/Alaska',
altitude=meta['altitude'], name=meta['Name'].replace('"',''))
print(sand_point)
Calculate the solar position for all times in the TMY file.
The default solar position algorithm is based on Reda and Andreas (2004). Our implementation is pretty fast, but you can make it even faster if you install numba and use add method='nrel_numba' to the function call below.
In [6]:
solpos = pvlib.solarposition.get_solarposition(tmy_data.index, sand_point.latitude, sand_point.longitude)
solpos.plot()
Out[6]:
The funny looking jump in the azimuth is just due to the coarse time sampling in the TMY file.
In [7]:
# the extraradiation function returns a simple numpy array
# instead of a nice pandas series. We will change this
# in a future version
dni_extra = pvlib.irradiance.get_extra_radiation(tmy_data.index)
dni_extra = pd.Series(dni_extra, index=tmy_data.index)
dni_extra.plot()
plt.ylabel('Extra terrestrial radiation (W/m**2)')
Out[7]:
In [8]:
airmass = pvlib.atmosphere.get_relative_airmass(solpos['apparent_zenith'])
airmass.plot()
plt.ylabel('Airmass')
Out[8]:
The funny appearance is due to aliasing and setting invalid numbers equal to NaN. Replot just a day or two and you'll see that the numbers are right.
Use the Hay Davies model to calculate the plane of array diffuse sky radiation. See the irradiance module tutorial for comparisons of different models.
In [9]:
poa_sky_diffuse = pvlib.irradiance.haydavies(surface_tilt, surface_azimuth,
tmy_data['DHI'], tmy_data['DNI'], dni_extra,
solpos['apparent_zenith'], solpos['azimuth'])
poa_sky_diffuse.plot()
plt.ylabel('Irradiance (W/m**2)')
Out[9]:
In [10]:
poa_ground_diffuse = pvlib.irradiance.get_ground_diffuse(surface_tilt, tmy_data['GHI'], albedo=albedo)
poa_ground_diffuse.plot()
plt.ylabel('Irradiance (W/m**2)')
Out[10]:
In [11]:
aoi = pvlib.irradiance.aoi(surface_tilt, surface_azimuth, solpos['apparent_zenith'], solpos['azimuth'])
aoi.plot()
plt.ylabel('Angle of incidence (deg)')
Out[11]:
Note that AOI has values greater than 90 deg. This is ok.
In [12]:
poa_irrad = pvlib.irradiance.poa_components(aoi, tmy_data['DNI'], poa_sky_diffuse, poa_ground_diffuse)
poa_irrad.plot()
plt.ylabel('Irradiance (W/m**2)')
plt.title('POA Irradiance')
Out[12]:
In [13]:
pvtemps = pvlib.pvsystem.sapm_celltemp(poa_irrad['poa_global'], tmy_data['Wspd'], tmy_data['DryBulb'])
pvtemps.plot()
plt.ylabel('Temperature (C)')
Out[13]:
Get module data.
In [14]:
sandia_modules = pvlib.pvsystem.retrieve_sam(name='SandiaMod')
Choose a particular module
In [15]:
sandia_module = sandia_modules.Canadian_Solar_CS5P_220M___2009_
sandia_module
Out[15]:
Calculate the effective irradiance
In [16]:
effective_irradiance = pvlib.pvsystem.sapm_effective_irradiance(poa_irrad.poa_direct, poa_irrad.poa_diffuse, airmass, aoi, sandia_module)
Run the SAPM using the parameters we calculated above.
In [17]:
sapm_out = pvlib.pvsystem.sapm(effective_irradiance, pvtemps.temp_cell, sandia_module)
print(sapm_out.head())
sapm_out[['p_mp']].plot()
plt.ylabel('DC Power (W)')
Out[17]:
In [18]:
cec_modules = pvlib.pvsystem.retrieve_sam(name='CECMod')
cec_module = cec_modules.Canadian_Solar_CS5P_220M
In [19]:
d = {k: cec_module[k] for k in ['a_ref', 'I_L_ref', 'I_o_ref', 'R_sh_ref', 'R_s']}
In [20]:
photocurrent, saturation_current, resistance_series, resistance_shunt, nNsVth = (
pvlib.pvsystem.calcparams_desoto(poa_irrad.poa_global,
pvtemps['temp_cell'],
cec_module['alpha_sc'],
EgRef=1.121,
dEgdT=-0.0002677, **d))
In [21]:
single_diode_out = pvlib.pvsystem.singlediode(photocurrent, saturation_current,
resistance_series, resistance_shunt, nNsVth)
In [22]:
single_diode_out[['p_mp']].plot()
plt.ylabel('DC Power (W)')
Out[22]:
Get the inverter database from the web
In [23]:
sapm_inverters = pvlib.pvsystem.retrieve_sam('sandiainverter')
Choose a particular inverter
In [24]:
sapm_inverter = sapm_inverters['ABB__MICRO_0_25_I_OUTD_US_208_208V__CEC_2014_']
sapm_inverter
Out[24]:
In [25]:
p_acs = pd.DataFrame()
p_acs['sapm'] = pvlib.pvsystem.snlinverter(sapm_out.v_mp, sapm_out.p_mp, sapm_inverter)
p_acs['sd'] = pvlib.pvsystem.snlinverter(single_diode_out.v_mp, single_diode_out.p_mp, sapm_inverter)
p_acs.plot()
plt.ylabel('AC Power (W)')
Out[25]:
In [26]:
diff = p_acs['sapm'] - p_acs['sd']
diff.plot()
plt.ylabel('SAPM - SD Power (W)')
Out[26]:
Plot just a few days.
In [27]:
p_acs.loc['2015-07-05':'2015-07-06'].plot()
Out[27]:
Some statistics on the AC power
In [28]:
p_acs.describe()
Out[28]:
In [29]:
p_acs.sum()
Out[29]:
In [30]:
# create data for a y=x line
p_ac_max = p_acs.max().max()
yxline = np.arange(0, p_ac_max)
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(111, aspect='equal')
sc = ax.scatter(p_acs['sd'], p_acs['sapm'], c=poa_irrad.poa_global, alpha=1)
ax.plot(yxline, yxline, 'r', linewidth=3)
ax.set_xlim(0, None)
ax.set_ylim(0, None)
ax.set_xlabel('Single Diode model')
ax.set_ylabel('Sandia model')
fig.colorbar(sc, label='POA Global (W/m**2)')
Out[30]:
We can change the value of color value c to see the sensitivity of model accuracy to measured meterological conditions. It can be useful to define a simple plotting function for this kind of exploratory analysis.
In [31]:
def sapm_sd_scatter(c_data, label=None, **kwargs):
"""Display a scatter plot of SAPM p_ac vs. single diode p_ac.
You need to re-execute this cell if you re-run the p_ac calculation.
Parameters
----------
c_data : array-like
Determines the color of each point on the scatter plot.
Must be same length as p_acs.
kwargs passed to ``scatter``.
Returns
-------
tuple of fig, ax objects
"""
fig = plt.figure(figsize=(12,12))
ax = fig.add_subplot(111, aspect='equal')
sc = ax.scatter(p_acs['sd'], p_acs['sapm'], c=c_data, alpha=1, **kwargs)
ax.plot(yxline, yxline, 'r', linewidth=3)
ax.set_xlim(0, None)
ax.set_ylim(0, None)
ax.set_xlabel('Single diode model power (W)')
ax.set_ylabel('Sandia model power (W)')
fig.colorbar(sc, label='{}'.format(label), shrink=0.75)
return fig, ax
In [32]:
sapm_sd_scatter(tmy_data.DryBulb, label='Temperature (deg C)')
Out[32]:
In [33]:
sapm_sd_scatter(tmy_data.DNI, label='DNI (W/m**2)')
Out[33]:
In [34]:
sapm_sd_scatter(tmy_data.AOD, label='AOD')
Out[34]:
In [35]:
sapm_sd_scatter(tmy_data.Wspd, label='Wind speed', vmax=10)
Out[35]:
Notice the use of the vmax keyword argument in the above example. The **kwargs pattern allows us to easily pass non-specified arguments to nested functions.
In [36]:
def sapm_other_scatter(c_data, x_data, clabel=None, xlabel=None, aspect_equal=False, **kwargs):
"""Display a scatter plot of SAPM p_ac vs. something else.
You need to re-execute this cell if you re-run the p_ac calculation.
Parameters
----------
c_data : array-like
Determines the color of each point on the scatter plot.
Must be same length as p_acs.
x_data : array-like
kwargs passed to ``scatter``.
Returns
-------
tuple of fig, ax objects
"""
fig = plt.figure(figsize=(12,12))
if aspect_equal:
ax = fig.add_subplot(111, aspect='equal')
else:
ax = fig.add_subplot(111)
sc = ax.scatter(x_data, p_acs['sapm'], c=c_data, alpha=1, cmap=mpl.cm.YlGnBu_r, **kwargs)
ax.set_xlim(0, None)
ax.set_ylim(0, None)
ax.set_xlabel('{}'.format(xlabel))
ax.set_ylabel('Sandia model power (W)')
fig.colorbar(sc, label='{}'.format(clabel), shrink=0.75)
return fig, ax
In [37]:
sapm_other_scatter(tmy_data.DryBulb, tmy_data.GHI, clabel='Temperature (deg C)', xlabel='GHI (W/m**2)')
Out[37]:
Next, we will assume that the SAPM model is representative of the real world performance so that we can use scipy's optimization routine to derive simulated PVUSA coefficients. You will need to install scipy to run these functions.
Here's one PVUSA reference:
In [38]:
def pvusa(pvusa_data, a, b, c, d):
"""
Calculates system power according to the PVUSA equation
P = I * (a + b*I + c*W + d*T)
where
P is the output power,
I is the plane of array irradiance,
W is the wind speed, and
T is the temperature
Parameters
----------
pvusa_data : pd.DataFrame
Must contain the columns 'I', 'W', and 'T'
a : float
I coefficient
b : float
I*I coefficient
c : float
I*W coefficient
d : float
I*T coefficient
Returns
-------
power : pd.Series
Power calculated using the PVUSA model.
"""
return pvusa_data['I'] * (a + b*pvusa_data['I'] + c*pvusa_data['W'] + d*pvusa_data['T'])
In [39]:
from scipy import optimize
In [40]:
pvusa_data = pd.DataFrame()
pvusa_data['I'] = poa_irrad.poa_global
pvusa_data['W'] = tmy_data.Wspd
pvusa_data['T'] = tmy_data.DryBulb
In [41]:
popt, pcov = optimize.curve_fit(pvusa, pvusa_data.dropna(), p_acs.sapm.values, p0=(.0001,0.0001,.001,.001))
print('optimized coefs:\n{}'.format(popt))
print('covariances:\n{}'.format(pcov))
In [42]:
power_pvusa = pvusa(pvusa_data, *popt)
fig, ax = sapm_other_scatter(tmy_data.DryBulb, power_pvusa, clabel='Temperature (deg C)',
aspect_equal=True, xlabel='PVUSA (W)')
maxmax = max(ax.get_xlim()[1], ax.get_ylim()[1])
ax.set_ylim(None, maxmax)
ax.set_xlim(None, maxmax)
ax.plot(np.arange(maxmax), np.arange(maxmax), 'r')
Out[42]: