+
+ 
- 
+ 
+
+
-
+
ver: 221212t18
+Corrections and additions for comments by : +Cliff Hansen, Kevin Anderson, Anton Driesse and Mark Campanelli
+see details for each function in mlfm.py
+I) The Loss Factors Model (LFM) 2011 ref [1] quantifies normalised losses
+from module parameters (e.g. pr_dc, i_sc, r_sc, i_mp, v_mp, r_oc and v_oc)
+by analysing module measurements or the shape of the IV curve and comparing
+it with STC reference values from the datasheet.
II) The Mechanistic performance model (MPM) 2017 ref [2] has "meaningful,
+independent, robust and normalised" coefficients which fit how the LFM values
+depend on irradiance, module temperature (and windspeed) and time.
III) This tutorial shows how to take module measured and weather data,
+(either outdoor or IEC 61853-like matrix data), normalise it, generate MLFM
+coefficients, fit them with the MPM then analyse module performance looking for
+loss values, degradation and allowing performance predictions as shown in fig 2.
Fig 1 illustrates the loss factors model (LFM).
+Depending on the number of measurements available the LFM is defined
+with a suffix number x = 1..12 LFM_n as in ref [4] -
It uses the shape and values from dc measurements to quantify the values of each
+of the loss factors (coloured arrors on the y=current or x=voltage axes
+going from (1) ref_p_mp to (6) meas_p_mp.
Fig 1: Loss Factors Model
+
Fig 2: MLFM overview flow chart of this tutorial.
+ +1) ref_p_mp = Initial datasheet value at STC.
+Multiply by 1/FF to get to (ref_i_sc * ref_v_oc) to start to analyse current and voltage losses
+2->3) Three 'current' losses get from ref_i_sc to norm_i_mp
+4->5) Three 'voltage' losses (plus a temperature coefficient) get from from ref_v_oc to norm_v_mp
+6) These losses cause the performance to fall to pr_dc (= meas_p_mp / ref_p_mp)
+pr_dc = 1/ff *
+ (norm_i_sc * norm_r_sc * norm_i_ff ) *
+ (norm_v_ff * norm_r_oc * norm_v_oc_t * norm_temp_corr )
Note:
+The gamma temperature correction is just subtracted from voc for simplicity.
+In reality there will be temperature dependencies for i_sc and ff but they are smaller.
import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+# import mlfm
+
+from pvlib.mlfm import meas_to_norm, mpm_a_fit, mpm_b_fit, meas_to_stack_lin
+from pvlib.mlfm import mpm_a_calc, mpm_b_calc
+
+from pvlib.mlfm import plot_scatter, plot_stack # , mpm_calc
+
+# FIND AND SHOW INSTALLATION CURRENT WORKING DIRECTORY
+import os
+root_dir = os.getcwd()
+
+# uncomment to see root dir
+# print(root_dir)
+
+# STANDARD DEFINITIONS (also in mlfm.py)
+G_STC = 1000.0 # STC irradiance [W/m^2]
+T_STC = 25.0 # STC temperature [C] temperature_ref
+
+# https://matplotlib.org/stable/tutorials/introductory/customizing.html
+plt.rcParams['figure.figsize'] = [7, 5] # setup fig size inches ~[7, 5]
+plt.rcParams.update({'font.size': 12}) # setup fontsize ~12
+plt.linewidth = 1.5 # line width in points ~1.5
+plt.linestyle = '--' # solid line ~'--'
+plt.marker = 's' # the default marker square ~'s'
+plt.markersize = 9 # marker size, in points ~9
+plt.bbox = 1.4 # offset --> to not overwrite ~1.4
+# save graphs as png files to the output directory?
+save_figs = True
+# select which mpm to model : must be 'a original 2017' or 'b advanced 2022'
+mpm_sel = 'b' # 'a' or 'b'
+Three default files are included (* = version number )
+(0) g78_T16_Xall_F10m_R900*.csv (6 LFM params)
+(1) n05667_Y13_R1k6_fClear*.csv (4 LFM params)
+(2) x19074001_iec61853*.csv (4 LFM params)
(Some variants are added to the IEC 61853 with fewer data points
+or added scatter to test the fit algorithms)
Essential default column names in meas( ) are :-
+meas {
+'date_time', 'module_id',
+'poa_global', 'temp_module',
+'v_oc', 'i_sc', 'i_mp', 'v_mp',
+'r_sc', 'r_oc', <-- optional for LFM_6
+'wind_speed', 'temp_air', <-- optional
+}
File naming conventions can be used to help identify files, for example
+x81_T1906_D3_Fh.csv
where
+# Uncomment just one line to select a file from
+# directory ''\pvlib-python\docs\tutorials\mlfm_data\meas_gtw'
+
+# PTS COMMENTS
+
+# 0) LFM 6 outdoor Gantner Instruments
+# mlfm_meas_file = 'g78_T16_Xall_F10m_R900_041.csv' # 900 <<< raw data with rsc and roc
+# mlfm_meas_file = 'g78_T16_Xall_F10m_R900_041_4param.csv' # 900 deleted rsc,roc
+# mlfm_meas_file = 'g78_T16_Xall_F10m_R1_041.csv' # 1 test record only
+
+# 1) LFM 4 outdoor NREL
+# mlfm_meas_file = 'n05667_Y13_R1k6_fClear_041.csv' # 1600 <<< raw data no rsc,roc measured
+
+# 2) IEC 61853 CFV : either raw data or fewer points and/or added scatter error
+mlfm_meas_file = 'x19074001_iec61853_041.csv' # 27 <<< raw data no rsc,roc measured
+# mlfm_meas_file = 'x19074001_iec61853_041_6pts.csv' # 6 raw but fewer points
+# mlfm_meas_file = 'x19074001_iec61853_041_rand5pc.csv' # 27 rand 5% rmse
+# mlfm_meas_file = 'x19074001_iec61853_041_rand1pc.csv' # 27 rand 1% rmse
+# mlfm_meas_file = 'x19074001_iec61853_041_rand5pc_6pts.csv' # 6 rand 5% rmse fewer points
+
+
+# extract module id from filename e.g. 'g78'
+mlfm_mod = mlfm_meas_file.split('_')
+
+mlfm_mod_sel = mlfm_mod[0]
+meas = pd.read_csv(
+ # root_dir + '/mlfm_data/meas_gtw/' + mlfm_meas_file,
+ os.path.join(root_dir, 'mlfm_data', 'meas_gtw', mlfm_meas_file),
+ index_col='date_time'
+)
+# user must keep updated with their modules from their measurements
+
+
+ref_file_name = os.path.join(root_dir, 'mlfm_data', 'ref', 'mlfm_reference_modules.csv')
+
+ref_data = pd.read_csv(
+ ref_file_name, index_col='module_id')
+try:
+ ref_data = ref_data[
+ ref_data.index == mlfm_mod_sel]
+
+except IndexError:
+ print("You must define module ref data to use this module ...")
+
+# Put relevant data into a dict for easy use
+# ignore any other columns that may be database specific
+# as they aren't needed
+
+ref = dict(
+ # module_id=ref_data['module_id'].values[0],
+ i_sc=ref_data['i_sc'].values[0],
+ i_mp=ref_data['i_mp'].values[0],
+ v_mp=ref_data['v_mp'].values[0],
+ v_oc=ref_data['v_oc'].values[0],
+
+ alpha_i_sc=ref_data['alpha_i_sc'].values[0],
+ beta_v_oc=ref_data['beta_v_oc'].values[0],
+ alpha_i_mp=ref_data['alpha_i_mp'].values[0],
+ beta_v_mp=ref_data['beta_v_mp'].values[0],
+ gamma_pdc=ref_data['gamma_pdc'].values[0],
+
+ p_mp= ref_data['p_mp'].values[0],
+
+
+ ff=ref_data['ff'].values[0],
+)
+
+# uncomment to show ref data
+# ref
+# calculate p_mp and pr_dc as they might be missing
+meas['p_mp'] = meas['i_mp'] * meas['v_mp']
+
+meas['pr_dc'] = (meas['p_mp'] / ref['p_mp']
+ / (meas['poa_global'] / G_STC))
+
+# temperature corrected v_c and pr_dc
+meas['v_oc_temp_corr'] = \
+ (meas['v_oc'] * (1 - ref['beta_v_oc']*(meas['temp_module'] - T_STC)))
+
+meas['pr_dc_temp_corr'] = \
+ (meas['pr_dc'] * (1 - ref['gamma_pdc']*(meas['temp_module'] - T_STC)))
+
+# show some meas data
+meas.describe()
+| + | module_id | +temp_module | +poa_global | +i_sc | +v_oc | +i_mp | +v_mp | +p_mp | +wind_speed | +pr_dc | +v_oc_temp_corr | +pr_dc_temp_corr | +
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | +27.0 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.0 | +27.000000 | +27.000000 | +27.000000 | +
| mean | +19074001.0 | +42.222222 | +581.481481 | +3.450926 | +65.054815 | +3.194407 | +54.227778 | +175.637260 | +0.0 | +0.922290 | +67.566148 | +0.964306 | +
| std | +0.0 | +23.588350 | +358.455058 | +2.123715 | +4.683176 | +1.974740 | +4.486576 | +110.698594 | +0.0 | +0.078215 | +2.555701 | +0.038515 | +
| min | +19074001.0 | +15.000000 | +100.000000 | +0.595000 | +54.600000 | +0.541000 | +44.320000 | +24.065760 | +0.0 | +0.746677 | +61.265287 | +0.856461 | +
| 25% | +19074001.0 | +25.000000 | +200.000000 | +1.203000 | +61.595000 | +1.094500 | +49.875000 | +62.091200 | +0.0 | +0.849048 | +66.072455 | +0.948074 | +
| 50% | +19074001.0 | +50.000000 | +600.000000 | +3.542000 | +65.780000 | +3.298000 | +54.250000 | +177.944780 | +0.0 | +0.926241 | +68.502670 | +0.974878 | +
| 75% | +19074001.0 | +62.500000 | +900.000000 | +5.337500 | +69.305000 | +4.946500 | +58.400000 | +269.232420 | +0.0 | +0.996683 | +69.543433 | +0.994383 | +
| max | +19074001.0 | +75.000000 | +1100.000000 | +6.578000 | +71.850000 | +6.061000 | +60.210000 | +354.156950 | +0.0 | +1.026992 | +70.440000 | +1.000051 | +
usually LFM_4 = matrix (i_sc, i_mp, v_mp, v_oc)
+and LFM_6 = iv (i_sc, i_mp, v_mp, v_oc + r_sc, r_oc)
def get_qty_lfm_vars(dmeas):
+ """Find the quantity of LFM variables in the measured data.
+
+ (e.g. I_MP+V_MP=2, MATRIX=4, IV_CURVE=6).
+
+ Parameters
+ ----------
+ dmeas: DataFrame
+ Measured weather and module electrical values per time or measurement
+
+ Returns
+ -------
+ qty_lfm_vars : int
+ number of lfm_values present in data usually
+
+ 2 = ( i_mp, v_mp ) from mpp tracker
+ 4 = (i_sc, i_mp, v_mp, v_oc) from matrix
+ 6 = (i_sc, r_sc, i_mp, v_mp, r_oc, v_oc) from iv curve.
+
+ """
+ # find how many lfm variables were measured
+ qty_lfm_vars = 0
+ for lfm_sel in ('i_sc', 'r_sc', 'i_mp', 'v_mp', 'r_oc', 'v_oc'):
+ if lfm_sel in dmeas.columns:
+ qty_lfm_vars += 1
+ # print(qty_lfm_vars, lfm_sel)
+
+ return qty_lfm_vars
+qty_lfm_vars = get_qty_lfm_vars(meas)
+norm = meas_to_norm(meas, ref)
+
+# show some normalised data
+norm.head(3)
+| + | poa_global | +temp_module | +wind_speed | +pr_dc | +pr_dc_temp_corr | +i_sc | +i_mp | +v_oc | +v_oc_temp_corr | +v_mp | +
|---|---|---|---|---|---|---|---|---|---|---|
| date_time | ++ | + | + | + | + | + | + | + | + | + |
| 0 | +100 | +15 | +0 | +0.936042 | +0.908517 | +1.007988 | +0.912605 | +0.936845 | +0.913971 | +0.844634 | +
| 1 | +200 | +15 | +0 | +0.978361 | +0.949591 | +1.002058 | +0.923922 | +0.965471 | +0.941899 | +0.851158 | +
| 2 | +400 | +15 | +0 | +1.007065 | +0.977451 | +0.996976 | +0.928207 | +0.991961 | +0.967743 | +0.853123 | +
# poa_global bin e.g. 100, 200 .. 1100W/m2
+norm['poa_global_bin'] = \
+ norm['poa_global'].round(-2)
+
+# temp_module bin e.g. 5, 10 .. 75C
+norm['temp_module_bin'] = \
+ (5 * round(norm['temp_module'] / 5, 0))
+It's easier to sanity check and study normalised data than raw values.
+1) Remove bad, missing, unwanted or outlier data
+2) User defined limits may depend on data scatter and degradation
+3) Can either select on values e.g. '0.5 <pr_dc < 1.5' or on '>x stdev from mean'
+4) Possible to select on dates if desired.
# select by irradiance poa_global range e.g. 100-1100 W/m2
+norm = norm[(norm['poa_global'] >= 100) &
+ (norm['poa_global'] <= 1100)]
+
+# remove specific lfm values outside limits e.g. <0.5 or >1.5
+norm = norm[((norm['pr_dc'] > 0.5) &
+ (norm['pr_dc'] < 1.5))]
+# remove all mlfm values outside x~3 stdevs
+if qty_lfm_vars == 6:
+ # only needed for outdoor data as indoor ought to be less scattered
+ # remove all mlfm data > x stdev usually 3
+ stdevs = 3
+
+ for lfm in ('i_sc', 'r_sc', 'i_ff', 'v_ff', 'r_oc', 'v_oc'):
+ norm = norm[
+ ((norm[lfm] - norm[lfm].mean()) /
+ norm[lfm].std()).abs() < stdevs
+ ]
+like an inner join but leave data in separate norm and meas frames
+ +# drop meas rows that aren't in norm
+meas_not_in_norm = ~meas.index.isin(norm.index)
+meas = meas.drop(meas[meas_not_in_norm].index)
+
+# drop norm rows that aren't in meas
+norm_not_in_meas = ~norm.index.isin(meas.index)
+norm = norm.drop(norm[norm_not_in_meas].index)
+For outdoor data -
+LFM values norm() should be narrow, smooth lines (around 70-120% on the yaxis).
For matrix data -
+LFM values norm() should be close, almost parallel lines (around 70-120% on the yaxis).
All traces should be thin, smoot lines usually around 0.9 ± 0.1
+i_sc may be more scattered if there is uncorrected soiling, spectral and angle of incidence ###
# scatter plot normalised values vs. irradiance
+fig_scatter = plot_scatter(
+ norm, mlfm_meas_file, qty_lfm_vars, save_figs)
+
+Fig [E] : LFM multiplicative factors (y) vs. poa irradiance (x)
+Multiplicative losses are easier to understand but to represent them on a graph
+it's easier to show them as a stacked plot where the values are 'translated'
+so the sum of the stacked losses is shown to equate to the product of the
+multiplicative losses.
LFM losses can be analysed as either
+multiplicative pr_dc = 1/ff PRODUCT(norm(i_sc), ... \ stack(v_oc_t), stack(temp_corr) ).
+subtractive pr_dc = 1/ff - SUM(stack(i_sc), ... stack(v_oc_t), stack(temp_corr) ).
+# translate multiplicative to stack losses and add to
+# dataframe stack add a gap between i and v losses
+
+stack = meas_to_stack_lin(meas, ref, qty_lfm_vars, gap=0.0) # gap = 0.01
+Fig 3 Shows how to quantify losses by loss parameters stack(i_sc, .. v_oc).
+
Fig 3 Stacked losses by measurement
+It plots them in a stacked format from the lossless limit 1/ff (top)
+subtracting each loss value in turn until it reaches pr_dc (bottom).
This figure shows a typical c-Si module for four clear days for
+different months July to Oct in AZ.
In the middle of the days the high irradiance results in the biggest
+losses being due to r_oc (red, ~rseries, pink) and temp_module
+(as the module heats to 60C).
Early mornings/late afternoons there is a slight Isc gain (purple,
+top, due to spectral mismatch) but an Isc loss mid day due to soiling.
Stack losses are indicated by their colours
+(from top to bottom for lfm_4=matrix and lfm_6=ivcurve)
Graph options :
+is_i_sc_self_ref : boolean
+ = self corrects i_sc to remove angle of incidence, spectrum,
+ snow or soiling.
is_v_oc_temp_module_corr : boolean
+ = calc temperature loss due to gamma, subtract from voc loss
# plot stack loss vs. time (or measurement) chart
+fig_stack = plot_stack(
+ dstack=stack, # dataframe measurements
+ fill_factor=ref['ff'], # dataframe reference STC
+ title=mlfm_meas_file, #
+ xaxis_labels=12, # show num x_labels or 0 to show all
+ is_i_sc_self_ref=False, # is isc self referenced?
+ save_figs=save_figs # save the figure?
+)
+
+Fig [G] Stacked loss values (y) s. date and time (outdoor) or matrix measurement (x)
+Perform a Mechanistic Performance Model (MPM) fit to the lfm parameters
+poa_global (W/m$^2$), temp_module (C), wind_speed (ms$^-$$^1$).
mpm_a = c_1 +c_2*(t_mod-25) +c_3*log10(g) +c_4*g +c_5*ws +c_6\/g (deprecated)
+mpm_b = c_1 +c_2*(t_mod–25) +c_3*log10(g)*(t_k\/t_stc_k) +c_4*g +c_5*ws
+Report the fit (coeffs) and error (errs) coefficients.
+ +lfm_sel = 'pr_dc'
+# add selected variable to measured data frame to ensure data indexes match.
+meas_temp = meas.copy()
+meas_temp[lfm_sel] = norm[lfm_sel]
+
+# try to fit measurement data and print outputs
+
+"""
+# full_outputboolean, optional
+If True, this function returns additioal information:
+ infodict, mesg, and ier.
+
+https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html
+
+mesgstr (returned only if full_output is True)
+A string message giving information about the solution.
+
+ierint (returnned only if full_output is True)
+An integer flag. If it is equal to 1, 2, 3 or 4, the solution was found.
+Otherwise, the solution was not found. In either case,
+the optional output variable mesg gives more information.
+"""
+
+try:
+
+ if mpm_sel == 'a':
+ cc, coeffs, ee, errs, infodict, mesg, ier = mpm_a_fit(meas_temp, lfm_sel)
+
+ if mpm_sel == 'b':
+ cc, coeffs, ee, errs, infodict, mesg, ier = mpm_b_fit(meas_temp, lfm_sel)
+
+
+ # store calculated value of LFM variable
+ norm['calc_' + lfm_sel] = cc
+
+ # store residual difference of LFM variable
+ norm['diff_' + lfm_sel] = norm[lfm_sel] - norm['calc_' + lfm_sel]
+
+ # show infodict data, uncomment fvec to show per row
+ print('nfev =', infodict['nfev'], '\n \n',
+ # 'fvec =', infodict['fvec'],'\n \n',
+ 'mesg = ', mesg, '\n \n',
+ 'ier = ', ier, "NOTE : if ier in (1,2,3,4) then fit found")
+
+except:
+ print("CAN'T FIT DATA")
+nfev = 22 + + mesg = `ftol` termination condition is satisfied. + + ier = 2 NOTE : if ier in (1,2,3,4) then fit found ++
Show a heatmap of the average residual (meas - fit) error
+for each irradiance (100W/m^2) and tmod bin (5C).
def plot_heatmap(dnorm, fit, y_axis, x_axis, z_axis,
+ title, save_figs, clip=0.02,):
+ """Plot a heatmap of Z vs. binned X and Y axes.
+
+ Parameters
+ ----------
+ dnorm : dataframe
+ Normalised multiplicative loss values (values approx 1).
+
+ fit : string
+ fitted parameter e.g. 'pr_dc'.
+
+ x_axis : string
+ binned x axis e.g. 'poa_global_bin'.
+
+ y_axis : string
+ binned y axis e.g. 'temp_module_bin'.
+
+ z_axis : string
+ value as a colour surface plot e.f. 'diff_pr_dc'.
+
+ clip : value
+ clipping of z axis usually 0.02
+
+ title : string
+ title for graph e.g. mlfm_meas_file.
+
+ """
+ df_piv = pd.pivot_table(
+ dnorm,
+ index=y_axis, # e.g. 'temp_module_bin'
+ columns=x_axis, # e.g. 'poa_global_bin'
+ values=z_axis, # value to aggregate
+ fill_value=0, # fill empty cells with this ?
+ aggfunc=[np.mean], # e.g. min, np.sum, len->count
+ margins=False, # grand totals hide
+ dropna=True # hide missing rows or columns
+ )
+
+ fig, ax1 = plt.subplots()
+
+ # force z limits to be -2% to +2% if desired
+ df_piv = df_piv.clip(lower=-clip, upper=+clip)
+
+ im = ax1.imshow(
+ df_piv,
+ cmap='RdYlBu',
+ origin='lower'
+ )
+
+ cbar = ax1.figure.colorbar(im, ax=ax1, shrink=0.75, label=z_axis)
+
+ # Y AXIS : show only 1 of each y_skip labels
+ y_ticks = df_piv.shape[0]
+ plt.yticks(np.arange(0, y_ticks), rotation=0)
+ yax2 = [''] * y_ticks
+ y_skip = 2
+ y_count = 0
+ while y_count < y_ticks:
+ if y_count % y_skip == 0:
+ yax2[y_count] = df_piv.index[y_count]
+ y_count += 1
+
+ ax1.set_yticklabels(yax2)
+ ax1.set_ylabel(y_axis)
+
+ # X AXIS : show only 1 of each x_skip labels
+ x_ticks = df_piv.shape[1]
+ plt.xticks(np.arange(0, x_ticks), rotation=90)
+
+ xax2 = [''] * x_ticks
+ x_skip = 2
+ x_count = 0
+ while x_count < x_ticks:
+ if x_count % x_skip == 0:
+ xax2[x_count] = df_piv.columns.levels[1][x_count]
+ x_count += 1
+
+ ax1.set_title(title)
+
+ ax1.set_xticklabels(xax2)
+ ax1.set_xlabel(x_axis)
+
+ ax1.grid(color='k', linestyle=':', linewidth=1)
+
+ if save_figs:
+ # remove '.csv', high resolution= 300 dots per inch
+ plt.savefig(
+ os.path.join('mlfm_data', 'output', 'heatmap_' + title[:len(title)-4]),
+ dpi=300
+ )
+
+ plt.show()
+# plot heatmap
+heatmap_plot = plot_heatmap(
+ dnorm=norm,
+ fit=lfm_sel,
+ y_axis='temp_module_bin',
+ x_axis='poa_global_bin',
+ z_axis='diff_' + lfm_sel,
+ clip=0.025,
+ title='residual_m' + mpm_sel + '_' + mlfm_meas_file,
+ save_figs=save_figs
+)
+
+Fig [I] Residual LFM fit heatmap vs. poa_global bin (x) and temp_module bin (y)
+ +def plot_fit(dmeas, dnorm, fit, title, save_figs, coeffs):
+ """Scatter plot fit to normalised measured.
+
+ Parameters
+ ----------
+ dmeas : dataframe
+ measurements, must include 'poa_global_kwm2'
+
+ dnorm : dataframe
+ normalised multiplicative lfm loss values 'i_sc' .. 'v_oc'
+ where pr_dc = 1/ff * product('i_sc', ... 'v_oc').
+
+ fit : string
+ name of fitted variable e.g. 'pr_dc'.
+
+ title : string
+ title for graph e.g. mlfm_meas_file.
+
+ """
+ fig, ax1 = plt.subplots()
+
+ plt.title(title)
+
+ plt.ylabel('fit ' + fit + ' * poa_global kW/m^2')
+ ax1.set_ylim(0, 1.2)
+
+ plt.xlabel('meas ' + fit + '* poa_global_kW/m^2')
+ ax1.set_xlim(0, 1.2)
+
+ plt.plot(
+ dnorm[fit] * dmeas['poa_global'] / G_STC,
+ dnorm['calc_' + fit] * dmeas['poa_global'] / G_STC,
+ 'c^',
+ label=fit
+ )
+
+ # plot 1:1 line to show optimum fit
+ plt.plot((0, 1.2), (0, 1.2), 'yo-')
+
+ # plot LIC, NOCT and STC irradiances
+ for x in (0.2, 0.8,1):
+ plt.plot((0, x), (x, x), 'k--')
+ plt.plot((x, x), (x, 0), 'k--')
+
+ plt.legend(loc='upper left')
+
+ if save_figs:
+ # remove '.csv', high resolution= 300 dots per inch
+ plt.savefig(
+ os.path.join('mlfm_data', 'output', 'fit_meas_' + title[:len(title)-4]),
+ dpi=300
+ )
+
+
+
+ plt.show()
+# plot fit vs. measured, include a 1:1 line for comparison
+fit_plot = plot_fit(dmeas=meas,
+ dnorm=norm,
+ fit=lfm_sel,
+ title='fit_m' + mpm_sel + '_' + mlfm_meas_file,
+ save_figs=save_figs,
+ coeffs=coeffs
+ )
+
+Fig [J] scatter plot of 'fit_lfm_sel poa_global# (y) vs. 'measured_lfm_sel poa_global' (x)
+ +Read in a matrix with complete values of
+Irradiance (G=100,200 .. 1100,1200) and module temperature (T=0,5 .. 65,70)
+to predict all MPM values
# read in the complete matrix data
+matr = pd.read_csv(os.path.join(root_dir, 'mlfm_data', 'ref', 'mlfm_matrix.csv'),
+ index_col='id')
+# show model coefficients
+mpm_sel, coeffs
+('b', array([ 1.06780656, -0.0028452 , 0.14860936, -0.07080871, 0.01 ]))
+# populate pivot table from predicted mpm data
+if mpm_sel == 'a':
+ matr[lfm_sel] = mpm_a_calc(matr, *coeffs) # not mpm_sel
+
+if mpm_sel == 'b':
+ matr[lfm_sel] = mpm_b_calc(matr, *coeffs) # not mpm_sel
+
+
+matr.head(10)
+| + | mid | +poa_global | +temp_module | +wind_speed | +pr_dc | +
|---|---|---|---|---|---|
| id | ++ | + | + | + | + |
| 1 | +matrix | +100 | +0 | +0 | +0.995707 | +
| 2 | +matrix | +100 | +5 | +0 | +0.978989 | +
| 3 | +matrix | +100 | +10 | +0 | +0.962271 | +
| 4 | +matrix | +100 | +15 | +0 | +0.945553 | +
| 5 | +matrix | +100 | +20 | +0 | +0.928834 | +
| 6 | +matrix | +100 | +25 | +0 | +0.912116 | +
| 7 | +matrix | +100 | +30 | +0 | +0.895398 | +
| 8 | +matrix | +100 | +35 | +0 | +0.878680 | +
| 9 | +matrix | +100 | +40 | +0 | +0.861962 | +
| 10 | +matrix | +100 | +45 | +0 | +0.845244 | +
def plot_contourf(df, x_axis, y_axis, z_axis, title,
+ vmin=0, vmax=1.2, levels=5,
+ save_figs=False):
+ """Plot filled contour plot Z vs. X and Y bins.
+
+ Parameters
+ ----------
+ df : dataframe
+ measured or normalised data containing weather columns
+ (poa_global, temp_module and wind_speed).
+
+ x_axis : string
+ binned x axis e.g. 'poa_global'.
+
+ y_axis : string
+ binned y axis e.g. 'temp_module'.
+
+ z_axis : string
+ measured value as a colour surface plot.
+
+ title : string
+ title for graph e.g. mlfm_meas_file.
+
+ vmin, vmax : float
+ minimum and maximum values for contour chart ###
+
+ """
+ piv = pd.pivot_table(
+ df,
+ index=y_axis,
+ columns=x_axis,
+ values=z_axis,
+ fill_value=0, # fill empty cells?
+ aggfunc=[np.mean], # min, np.sum, len->count
+ margins=False, # grand totals
+ dropna=True # hide missing rows or columns
+ )
+
+ piv = piv.clip(vmin, vmax)
+
+ fig, ax1 = plt.subplots()
+
+ cs = plt.contourf(
+ piv,
+ cmap='RdYlBu', # or 'nipy_spectral',
+ # origin='lower'
+ # nchunkint=1,
+ levels=levels,
+ vmin=vmin,
+ vmax=vmax
+ )
+
+ cbar = fig.colorbar(cs, ax=ax1)
+ cbar.ax.set_ylabel(z_axis,
+ rotation=90,
+ va='bottom',
+ labelpad=+30)
+
+ plt.title(title)
+ # # get_yaxis().set_major_formatter(FormatStrFormatter('%.2f'))
+
+ y_ticks = piv.shape[0]
+
+ plt.yticks(np.arange(0, y_ticks), rotation=0)
+
+ # show only 1 of each y_skip labels
+ yax2 = [''] * y_ticks
+ y_skip = 2
+ y_count = 0
+ while y_count < y_ticks:
+ if y_count % y_skip == 0:
+ yax2[y_count] = piv.index[y_count]
+ y_count += 1
+
+ ax1.set_yticklabels(yax2)
+ ax1.set_ylabel(y_axis)
+
+ x_ticks = piv.shape[1]
+ plt.xticks(np.arange(0, x_ticks), rotation=90)
+
+ # show only 1 of each x_skip labels
+ xax2 = [''] * x_ticks
+ x_skip = 2
+ x_count = 0
+ while x_count < x_ticks:
+ if x_count % x_skip == 0:
+ xax2[x_count] = piv.columns.levels[1][x_count]
+ x_count += 1
+
+ ax1.set_xticklabels(xax2)
+ ax1.set_xlabel(x_axis)
+
+ ax1.grid(color='k', linestyle=':', linewidth=1)
+
+ if save_figs:
+ # remove '.csv', high resolution= 300 dots per inch
+ plt.savefig(os.path.join('mlfm_data', 'output', 'contourf_'+ title[:len(title)-4])
+ , dpi=300
+ )
+# REMOVE LOW TEMPERATURE DATA WHICH MAY CONTAIN SNOW
+
+matr2 = matr[matr['temp_module'] >= 10]
+contour_plot = plot_contourf(
+ df=matr2,
+ y_axis='temp_module',
+ x_axis='poa_global',
+ z_axis=lfm_sel,
+ title='matrix predicted_m' + mpm_sel + '_' + mlfm_meas_file,
+ vmin=0.7,
+ vmax=1.05,
+ levels=9,
+ save_figs=save_figs
+)
+
+Fig [L1] Contour plot (colours) of predicted lfm_sel vs. poa_global (x) and temp_mod (y)
+ +contour_plot = plot_contourf(
+ df=norm,
+ y_axis='temp_module_bin',
+ x_axis='poa_global_bin',
+ z_axis=lfm_sel,
+ title='avg normalised_m' + mpm_sel + '_' + mlfm_meas_file,
+ vmin=0.7,
+ vmax=1.05,
+ levels=9,
+ save_figs=save_figs
+)
+
+Fig [L2] Contour plot (colours) of measured lfm_sel vs. poa_global (x) and temp_mod (y)
+ +
+The Loss Factors Model (LFM) and Mechanistic Performance Model (MPM)
+together known as "MLFM" have been developed by SRCL and Gantner Instruments
+(previously Oerlikon Solar and Tel Solar) since 2011 MLFM and 2017 MPM
.. [1] J. Sutterlueti(now Gantner Instruments) and S. Ransome
+ '4AV.2.41 Characterising PV Modules under Outdoor Conditions:
+What's Most Important for Energy Yield'
+26th EU PVSEC 8 September 2011; Hamburg, Germany
+http://www.steveransome.com/pubs/2011Hamburg_4AV2_41.pdf
.. [2] Steve Ransome and Juergen Sutterlueti(Gantner Instruments)
+ 'Choosing the best Empirical Model for predicting energy yield'
+ 7th PV Energy Rating and Module Performance Modeling Workshop,
+ Canobbio, Switzerland 30-31 March, 2017
.. [3] S. Ransome and J. Sutterlueti (Gantner Instruments)
+'Checking the new IEC 61853.1-4 with high quality 3rd party data to
+benchmark its practical relevance in energy yield prediction'
+PVSC June 2019 Chicago, USA
+http://www.steveransome.com/PUBS/1906_PVSC46_Chicago_Ransome.pdf
.. [4] Steve Ransome (SRCL) and Juergen Sutterlueti (Gantner Instruments)
+'5CV.4.35 Quantifying Long Term PV Performance and Degradation
+under Real Outdoor and IEC 61853 Test Conditions
+Using High Quality Module IV Measurements'
+36th EU PVSEC Sep 2019
+http://www.steveransome.com/PUBS/1909_5CV4_35_PVSEC36_Marseille_Ransome_PPT.pdf
.. [5] Steve Ransome (SRCL)
+'How to use the Loss Factors and Mechanistic Performance Models
+effectively with PVPMC/PVLIB'
+PVPMC Webinar on PV Performance Modeling Methods, Aug 2020
+https://pvpmc.sandia.gov/download/7879/
.. [6] W.Marion et al (NREL)
+'New Data Set for Validating PV Module Performance Models'
+https://www.researchgate.net/publication/286746041_New_data_set_for_validating_PV_module_performance_models
+https://www.nrel.gov/docs/fy14osti/61610.pdf
.. [7] Steve Ransome (SRCL) +'Benchmarking PV performance models with high quality IEC 61853 Matrix +measurements (Bilinear interpolation, SAPM, PVGIS, MLFM and 1-diode)' +http://www.steveransome.com/pubs/2206_PVSC49_philadelphia_4_presented.pdf
+.. [8] Juergen Sutterlueti (Gantner Instruments) +'Advanced system monitoring and artificial intelligent data-driven analytics +to serve GW-scale photovoltaic power plant and energy storage requirements' +https://pvpmc.sandia.gov/download/8574/
+Many more papers are available at www.steveransome.com
+ +# =============================================================================================
+## TEST CODE CAN DELETE AFTER HERE IF NOT NEEDED
+
+test = False
+
+if test:
+ # save meas data to csv
+ meas.to_csv(
+ os.path.join('mlfm_data', 'output', 'meas.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+ # save norm data to csv
+ norm.to_csv(
+ os.path.join('mlfm_data', 'output', 'norm.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+ # save matr data to csv
+ matr.to_csv(
+ os.path.join('mlfm_data', 'output', 'matr.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+ # save ref data to csv
+ ref_data.to_csv(
+ os.path.join('mlfm_data', 'output', 'ref_data.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+
+if test:
+ # print mlfm fit coeffs
+ print(coeffs[0],coeffs[1],coeffs[2],coeffs[3],coeffs[4],) # coeffs[5], )#coeffs[6],)
+
+
+if test:
+ # only works with mlfm_meas_file = 'g78_T16_Xall_F10m_R900_041.
+ #
+ # check data for test
+
+ n= norm.loc['2016-03-23 09:00:00-07:00']
+
+ print('\n n= \n', n)
+
+
+ n= norm.loc['2016-03-23 09:00:00-07:00']
+
+ print('\n n= \n', n)
+
+ s = stack.loc['2016-03-23 09:00:00-07:00']
+
+ print('\n s= \n', s)
+
+
+if test:
+ # show all versions
+ import sys
+
+ for name, module in sorted(sys.modules.items()):
+ if hasattr(module, '__version__'):
+ print (name, module.__version__ )
+# whos
+| \n", + " | module_id | \n", + "temp_module | \n", + "poa_global | \n", + "i_sc | \n", + "v_oc | \n", + "i_mp | \n", + "v_mp | \n", + "p_mp | \n", + "wind_speed | \n", + "pr_dc | \n", + "v_oc_temp_corr | \n", + "pr_dc_temp_corr | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | \n", + "27.0 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.0 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "
| mean | \n", + "19074001.0 | \n", + "42.222222 | \n", + "581.481481 | \n", + "3.451762 | \n", + "65.341513 | \n", + "3.191874 | \n", + "54.327655 | \n", + "175.784279 | \n", + "0.0 | \n", + "0.923192 | \n", + "67.867073 | \n", + "0.965356 | \n", + "
| std | \n", + "0.0 | \n", + "23.588350 | \n", + "358.455058 | \n", + "2.126455 | \n", + "4.838053 | \n", + "1.976012 | \n", + "4.450850 | \n", + "110.950879 | \n", + "0.0 | \n", + "0.077022 | \n", + "2.916070 | \n", + "0.038490 | \n", + "
| min | \n", + "19074001.0 | \n", + "15.000000 | \n", + "100.000000 | \n", + "0.586188 | \n", + "54.257739 | \n", + "0.538878 | \n", + "44.791292 | \n", + "24.156797 | \n", + "0.0 | \n", + "0.749502 | \n", + "60.881244 | \n", + "0.859701 | \n", + "
| 25% | \n", + "19074001.0 | \n", + "25.000000 | \n", + "200.000000 | \n", + "1.216783 | \n", + "61.819074 | \n", + "1.100956 | \n", + "50.166468 | \n", + "61.966794 | \n", + "0.0 | \n", + "0.849704 | \n", + "66.158148 | \n", + "0.951905 | \n", + "
| 50% | \n", + "19074001.0 | \n", + "50.000000 | \n", + "600.000000 | \n", + "3.577538 | \n", + "65.709173 | \n", + "3.258584 | \n", + "54.298885 | \n", + "178.676199 | \n", + "0.0 | \n", + "0.930519 | \n", + "68.745275 | \n", + "0.976175 | \n", + "
| 75% | \n", + "19074001.0 | \n", + "62.500000 | \n", + "900.000000 | \n", + "5.325936 | \n", + "69.072708 | \n", + "4.935815 | \n", + "58.162051 | \n", + "270.721147 | \n", + "0.0 | \n", + "0.979747 | \n", + "69.800996 | \n", + "0.992304 | \n", + "
| max | \n", + "19074001.0 | \n", + "75.000000 | \n", + "1100.000000 | \n", + "6.616982 | \n", + "72.945871 | \n", + "6.098910 | \n", + "61.126873 | \n", + "357.769360 | \n", + "0.0 | \n", + "1.039431 | \n", + "71.534675 | \n", + "1.023443 | \n", + "
| \n", + " | poa_global | \n", + "temp_module | \n", + "wind_speed | \n", + "pr_dc | \n", + "pr_dc_temp_corr | \n", + "i_sc | \n", + "i_mp | \n", + "v_oc | \n", + "v_oc_temp_corr | \n", + "v_mp | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|
| date_time | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 0 | \n", + "100 | \n", + "15 | \n", + "0 | \n", + "0.940226 | \n", + "0.912578 | \n", + "1.020792 | \n", + "0.902408 | \n", + "0.940634 | \n", + "0.917668 | \n", + "0.843822 | \n", + "
| 1 | \n", + "200 | \n", + "15 | \n", + "0 | \n", + "0.962432 | \n", + "0.934130 | \n", + "0.991252 | \n", + "0.934837 | \n", + "0.970955 | \n", + "0.947249 | \n", + "0.831821 | \n", + "
| 2 | \n", + "400 | \n", + "15 | \n", + "0 | \n", + "1.000800 | \n", + "0.971371 | \n", + "1.002495 | \n", + "0.912154 | \n", + "0.988403 | \n", + "0.964271 | \n", + "0.861077 | \n", + "
| \n", + " | mid | \n", + "poa_global | \n", + "temp_module | \n", + "wind_speed | \n", + "pr_dc | \n", + "
|---|---|---|---|---|---|
| id | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 1 | \n", + "matrix | \n", + "100 | \n", + "0 | \n", + "0 | \n", + "0.996087 | \n", + "
| 2 | \n", + "matrix | \n", + "100 | \n", + "5 | \n", + "0 | \n", + "0.979860 | \n", + "
| 3 | \n", + "matrix | \n", + "100 | \n", + "10 | \n", + "0 | \n", + "0.963633 | \n", + "
| 4 | \n", + "matrix | \n", + "100 | \n", + "15 | \n", + "0 | \n", + "0.947405 | \n", + "
| 5 | \n", + "matrix | \n", + "100 | \n", + "20 | \n", + "0 | \n", + "0.931178 | \n", + "
| 6 | \n", + "matrix | \n", + "100 | \n", + "25 | \n", + "0 | \n", + "0.914951 | \n", + "
| 7 | \n", + "matrix | \n", + "100 | \n", + "30 | \n", + "0 | \n", + "0.898723 | \n", + "
| 8 | \n", + "matrix | \n", + "100 | \n", + "35 | \n", + "0 | \n", + "0.882496 | \n", + "
| 9 | \n", + "matrix | \n", + "100 | \n", + "40 | \n", + "0 | \n", + "0.866269 | \n", + "
| 10 | \n", + "matrix | \n", + "100 | \n", + "45 | \n", + "0 | \n", + "0.850041 | \n", + "
ver: 221212t18
+Corrections and additions for comments by : +Cliff Hansen, Kevin Anderson, Anton Driesse and Mark Campanelli
+see details for each function in mlfm.py
+I) The Loss Factors Model (LFM) 2011 ref [1] quantifies normalised losses
+from module parameters (e.g. pr_dc, i_sc, r_sc, i_mp, v_mp, r_oc and v_oc)
+by analysing module measurements or the shape of the IV curve and comparing
+it with STC reference values from the datasheet.
II) The Mechanistic performance model (MPM) 2017 ref [2] has "meaningful,
+independent, robust and normalised" coefficients which fit how the LFM values
+depend on irradiance, module temperature (and windspeed) and time.
III) This tutorial shows how to take module measured and weather data,
+(either outdoor or IEC 61853-like matrix data), normalise it, generate MLFM
+coefficients, fit them with the MPM then analyse module performance looking for
+loss values, degradation and allowing performance predictions as shown in fig 2.
Fig 1 illustrates the loss factors model (LFM).
+Depending on the number of measurements available the LFM is defined
+with a suffix number x = 1..12 LFM_n as in ref [4] -
It uses the shape and values from dc measurements to quantify the values of each
+of the loss factors (coloured arrors on the y=current or x=voltage axes
+going from (1) ref_p_mp to (6) meas_p_mp.
Fig 1: Loss Factors Model
+
Fig 2: MLFM overview flow chart of this tutorial.
+ +1) ref_p_mp = Initial datasheet value at STC.
+Multiply by 1/FF to get to (ref_i_sc * ref_v_oc) to start to analyse current and voltage losses
+2->3) Three 'current' losses get from ref_i_sc to norm_i_mp
+4->5) Three 'voltage' losses (plus a temperature coefficient) get from from ref_v_oc to norm_v_mp
+6) These losses cause the performance to fall to pr_dc (= meas_p_mp / ref_p_mp)
+pr_dc = 1/ff *
+ (norm_i_sc * norm_r_sc * norm_i_ff ) *
+ (norm_v_ff * norm_r_oc * norm_v_oc_t * norm_temp_corr )
Note:
+The gamma temperature correction is just subtracted from voc for simplicity.
+In reality there will be temperature dependencies for i_sc and ff but they are smaller.
import numpy as np
+import pandas as pd
+import matplotlib.pyplot as plt
+
+# import mlfm
+
+from pvlib.mlfm import meas_to_norm, mpm_a_fit, mpm_b_fit, meas_to_stack_lin
+from pvlib.mlfm import mpm_a_calc, mpm_b_calc
+
+from pvlib.mlfm import plot_scatter, plot_stack # , mpm_calc
+
+# FIND AND SHOW INSTALLATION CURRENT WORKING DIRECTORY
+import os
+root_dir = os.getcwd()
+
+# uncomment to see root dir
+# print(root_dir)
+
+# STANDARD DEFINITIONS (also in mlfm.py)
+G_STC = 1000.0 # STC irradiance [W/m^2]
+T_STC = 25.0 # STC temperature [C] temperature_ref
+
+# https://matplotlib.org/stable/tutorials/introductory/customizing.html
+plt.rcParams['figure.figsize'] = [7, 5] # setup fig size inches ~[7, 5]
+plt.rcParams.update({'font.size': 12}) # setup fontsize ~12
+plt.linewidth = 1.5 # line width in points ~1.5
+plt.linestyle = '--' # solid line ~'--'
+plt.marker = 's' # the default marker square ~'s'
+plt.markersize = 9 # marker size, in points ~9
+plt.bbox = 1.4 # offset --> to not overwrite ~1.4
+# save graphs as png files to the output directory?
+save_figs = True
+# select which mpm to model : must be 'a original 2017' or 'b advanced 2022'
+mpm_sel = 'b' # 'a' or 'b'
+Three default files are included (* = version number )
+(0) g78_T16_Xall_F10m_R900*.csv (6 LFM params)
+(1) n05667_Y13_R1k6_fClear*.csv (4 LFM params)
+(2) x19074001_iec61853*.csv (4 LFM params)
(Some variants are added to the IEC 61853 with fewer data points
+or added scatter to test the fit algorithms)
Essential default column names in meas( ) are :-
+meas {
+'date_time', 'module_id',
+'poa_global', 'temp_module',
+'v_oc', 'i_sc', 'i_mp', 'v_mp',
+'r_sc', 'r_oc', <-- optional for LFM_6
+'wind_speed', 'temp_air', <-- optional
+}
File naming conventions can be used to help identify files, for example
+x81_T1906_D3_Fh.csv
where
+# Uncomment just one line to select a file from
+# directory ''\pvlib-python\docs\tutorials\mlfm_data\meas_gtw'
+
+# PTS COMMENTS
+
+# 0) LFM 6 outdoor Gantner Instruments
+# mlfm_meas_file = 'g78_T16_Xall_F10m_R900_041.csv' # 900 <<< raw data with rsc and roc
+# mlfm_meas_file = 'g78_T16_Xall_F10m_R900_041_4param.csv' # 900 deleted rsc,roc
+# mlfm_meas_file = 'g78_T16_Xall_F10m_R1_041.csv' # 1 test record only
+
+# 1) LFM 4 outdoor NREL
+# mlfm_meas_file = 'n05667_Y13_R1k6_fClear_041.csv' # 1600 <<< raw data no rsc,roc measured
+
+# 2) IEC 61853 CFV : either raw data or fewer points and/or added scatter error
+mlfm_meas_file = 'x19074001_iec61853_041.csv' # 27 <<< raw data no rsc,roc measured
+# mlfm_meas_file = 'x19074001_iec61853_041_6pts.csv' # 6 raw but fewer points
+# mlfm_meas_file = 'x19074001_iec61853_041_rand5pc.csv' # 27 rand 5% rmse
+# mlfm_meas_file = 'x19074001_iec61853_041_rand1pc.csv' # 27 rand 1% rmse
+# mlfm_meas_file = 'x19074001_iec61853_041_rand5pc_6pts.csv' # 6 rand 5% rmse fewer points
+
+
+# extract module id from filename e.g. 'g78'
+mlfm_mod = mlfm_meas_file.split('_')
+
+mlfm_mod_sel = mlfm_mod[0]
+meas = pd.read_csv(
+ # root_dir + '/mlfm_data/meas_gtw/' + mlfm_meas_file,
+ os.path.join(root_dir, 'mlfm_data', 'meas_gtw', mlfm_meas_file),
+ index_col='date_time'
+)
+# user must keep updated with their modules from their measurements
+
+
+ref_file_name = os.path.join(root_dir, 'mlfm_data', 'ref', 'mlfm_reference_modules.csv')
+
+ref_data = pd.read_csv(
+ ref_file_name, index_col='module_id')
+try:
+ ref_data = ref_data[
+ ref_data.index == mlfm_mod_sel]
+
+except IndexError:
+ print("You must define module ref data to use this module ...")
+
+# Put relevant data into a dict for easy use
+# ignore any other columns that may be database specific
+# as they aren't needed
+
+ref = dict(
+ # module_id=ref_data['module_id'].values[0],
+ i_sc=ref_data['i_sc'].values[0],
+ i_mp=ref_data['i_mp'].values[0],
+ v_mp=ref_data['v_mp'].values[0],
+ v_oc=ref_data['v_oc'].values[0],
+
+ alpha_i_sc=ref_data['alpha_i_sc'].values[0],
+ beta_v_oc=ref_data['beta_v_oc'].values[0],
+ alpha_i_mp=ref_data['alpha_i_mp'].values[0],
+ beta_v_mp=ref_data['beta_v_mp'].values[0],
+ gamma_pdc=ref_data['gamma_pdc'].values[0],
+
+ p_mp= ref_data['p_mp'].values[0],
+
+
+ ff=ref_data['ff'].values[0],
+)
+
+# uncomment to show ref data
+# ref
+# calculate p_mp and pr_dc as they might be missing
+meas['p_mp'] = meas['i_mp'] * meas['v_mp']
+
+meas['pr_dc'] = (meas['p_mp'] / ref['p_mp']
+ / (meas['poa_global'] / G_STC))
+
+# temperature corrected v_c and pr_dc
+meas['v_oc_temp_corr'] = \
+ (meas['v_oc'] * (1 - ref['beta_v_oc']*(meas['temp_module'] - T_STC)))
+
+meas['pr_dc_temp_corr'] = \
+ (meas['pr_dc'] * (1 - ref['gamma_pdc']*(meas['temp_module'] - T_STC)))
+
+# show some meas data
+meas.describe()
+| + | module_id | +temp_module | +poa_global | +i_sc | +v_oc | +i_mp | +v_mp | +p_mp | +wind_speed | +pr_dc | +v_oc_temp_corr | +pr_dc_temp_corr | +
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | +27.0 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.000000 | +27.0 | +27.000000 | +27.000000 | +27.000000 | +
| mean | +19074001.0 | +42.222222 | +581.481481 | +3.450926 | +65.054815 | +3.194407 | +54.227778 | +175.637260 | +0.0 | +0.922290 | +67.566148 | +0.964306 | +
| std | +0.0 | +23.588350 | +358.455058 | +2.123715 | +4.683176 | +1.974740 | +4.486576 | +110.698594 | +0.0 | +0.078215 | +2.555701 | +0.038515 | +
| min | +19074001.0 | +15.000000 | +100.000000 | +0.595000 | +54.600000 | +0.541000 | +44.320000 | +24.065760 | +0.0 | +0.746677 | +61.265287 | +0.856461 | +
| 25% | +19074001.0 | +25.000000 | +200.000000 | +1.203000 | +61.595000 | +1.094500 | +49.875000 | +62.091200 | +0.0 | +0.849048 | +66.072455 | +0.948074 | +
| 50% | +19074001.0 | +50.000000 | +600.000000 | +3.542000 | +65.780000 | +3.298000 | +54.250000 | +177.944780 | +0.0 | +0.926241 | +68.502670 | +0.974878 | +
| 75% | +19074001.0 | +62.500000 | +900.000000 | +5.337500 | +69.305000 | +4.946500 | +58.400000 | +269.232420 | +0.0 | +0.996683 | +69.543433 | +0.994383 | +
| max | +19074001.0 | +75.000000 | +1100.000000 | +6.578000 | +71.850000 | +6.061000 | +60.210000 | +354.156950 | +0.0 | +1.026992 | +70.440000 | +1.000051 | +
usually LFM_4 = matrix (i_sc, i_mp, v_mp, v_oc)
+and LFM_6 = iv (i_sc, i_mp, v_mp, v_oc + r_sc, r_oc)
def get_qty_lfm_vars(dmeas):
+ """Find the quantity of LFM variables in the measured data.
+
+ (e.g. I_MP+V_MP=2, MATRIX=4, IV_CURVE=6).
+
+ Parameters
+ ----------
+ dmeas: DataFrame
+ Measured weather and module electrical values per time or measurement
+
+ Returns
+ -------
+ qty_lfm_vars : int
+ number of lfm_values present in data usually
+
+ 2 = ( i_mp, v_mp ) from mpp tracker
+ 4 = (i_sc, i_mp, v_mp, v_oc) from matrix
+ 6 = (i_sc, r_sc, i_mp, v_mp, r_oc, v_oc) from iv curve.
+
+ """
+ # find how many lfm variables were measured
+ qty_lfm_vars = 0
+ for lfm_sel in ('i_sc', 'r_sc', 'i_mp', 'v_mp', 'r_oc', 'v_oc'):
+ if lfm_sel in dmeas.columns:
+ qty_lfm_vars += 1
+ # print(qty_lfm_vars, lfm_sel)
+
+ return qty_lfm_vars
+qty_lfm_vars = get_qty_lfm_vars(meas)
+norm = meas_to_norm(meas, ref)
+
+# show some normalised data
+norm.head(3)
+| + | poa_global | +temp_module | +wind_speed | +pr_dc | +pr_dc_temp_corr | +i_sc | +i_mp | +v_oc | +v_oc_temp_corr | +v_mp | +
|---|---|---|---|---|---|---|---|---|---|---|
| date_time | ++ | + | + | + | + | + | + | + | + | + |
| 0 | +100 | +15 | +0 | +0.936042 | +0.908517 | +1.007988 | +0.912605 | +0.936845 | +0.913971 | +0.844634 | +
| 1 | +200 | +15 | +0 | +0.978361 | +0.949591 | +1.002058 | +0.923922 | +0.965471 | +0.941899 | +0.851158 | +
| 2 | +400 | +15 | +0 | +1.007065 | +0.977451 | +0.996976 | +0.928207 | +0.991961 | +0.967743 | +0.853123 | +
# poa_global bin e.g. 100, 200 .. 1100W/m2
+norm['poa_global_bin'] = \
+ norm['poa_global'].round(-2)
+
+# temp_module bin e.g. 5, 10 .. 75C
+norm['temp_module_bin'] = \
+ (5 * round(norm['temp_module'] / 5, 0))
+It's easier to sanity check and study normalised data than raw values.
+1) Remove bad, missing, unwanted or outlier data
+2) User defined limits may depend on data scatter and degradation
+3) Can either select on values e.g. '0.5 <pr_dc < 1.5' or on '>x stdev from mean'
+4) Possible to select on dates if desired.
# select by irradiance poa_global range e.g. 100-1100 W/m2
+norm = norm[(norm['poa_global'] >= 100) &
+ (norm['poa_global'] <= 1100)]
+
+# remove specific lfm values outside limits e.g. <0.5 or >1.5
+norm = norm[((norm['pr_dc'] > 0.5) &
+ (norm['pr_dc'] < 1.5))]
+# remove all mlfm values outside x~3 stdevs
+if qty_lfm_vars == 6:
+ # only needed for outdoor data as indoor ought to be less scattered
+ # remove all mlfm data > x stdev usually 3
+ stdevs = 3
+
+ for lfm in ('i_sc', 'r_sc', 'i_ff', 'v_ff', 'r_oc', 'v_oc'):
+ norm = norm[
+ ((norm[lfm] - norm[lfm].mean()) /
+ norm[lfm].std()).abs() < stdevs
+ ]
+like an inner join but leave data in separate norm and meas frames
+ +# drop meas rows that aren't in norm
+meas_not_in_norm = ~meas.index.isin(norm.index)
+meas = meas.drop(meas[meas_not_in_norm].index)
+
+# drop norm rows that aren't in meas
+norm_not_in_meas = ~norm.index.isin(meas.index)
+norm = norm.drop(norm[norm_not_in_meas].index)
+For outdoor data -
+LFM values norm() should be narrow, smooth lines (around 70-120% on the yaxis).
For matrix data -
+LFM values norm() should be close, almost parallel lines (around 70-120% on the yaxis).
All traces should be thin, smoot lines usually around 0.9 ± 0.1
+i_sc may be more scattered if there is uncorrected soiling, spectral and angle of incidence ###
# scatter plot normalised values vs. irradiance
+fig_scatter = plot_scatter(
+ norm, mlfm_meas_file, qty_lfm_vars, save_figs)
+
+Fig [E] : LFM multiplicative factors (y) vs. poa irradiance (x)
+Multiplicative losses are easier to understand but to represent them on a graph
+it's easier to show them as a stacked plot where the values are 'translated'
+so the sum of the stacked losses is shown to equate to the product of the
+multiplicative losses.
LFM losses can be analysed as either
+multiplicative pr_dc = 1/ff PRODUCT(norm(i_sc), ... \ stack(v_oc_t), stack(temp_corr) ).
+subtractive pr_dc = 1/ff - SUM(stack(i_sc), ... stack(v_oc_t), stack(temp_corr) ).
+# translate multiplicative to stack losses and add to
+# dataframe stack add a gap between i and v losses
+
+stack = meas_to_stack_lin(meas, ref, qty_lfm_vars, gap=0.0) # gap = 0.01
+Fig 3 Shows how to quantify losses by loss parameters stack(i_sc, .. v_oc).
+
Fig 3 Stacked losses by measurement
+It plots them in a stacked format from the lossless limit 1/ff (top)
+subtracting each loss value in turn until it reaches pr_dc (bottom).
This figure shows a typical c-Si module for four clear days for
+different months July to Oct in AZ.
In the middle of the days the high irradiance results in the biggest
+losses being due to r_oc (red, ~rseries, pink) and temp_module
+(as the module heats to 60C).
Early mornings/late afternoons there is a slight Isc gain (purple,
+top, due to spectral mismatch) but an Isc loss mid day due to soiling.
Stack losses are indicated by their colours
+(from top to bottom for lfm_4=matrix and lfm_6=ivcurve)
Graph options :
+is_i_sc_self_ref : boolean
+ = self corrects i_sc to remove angle of incidence, spectrum,
+ snow or soiling.
is_v_oc_temp_module_corr : boolean
+ = calc temperature loss due to gamma, subtract from voc loss
# plot stack loss vs. time (or measurement) chart
+fig_stack = plot_stack(
+ dstack=stack, # dataframe measurements
+ fill_factor=ref['ff'], # dataframe reference STC
+ title=mlfm_meas_file, #
+ xaxis_labels=12, # show num x_labels or 0 to show all
+ is_i_sc_self_ref=False, # is isc self referenced?
+ save_figs=save_figs # save the figure?
+)
+
+Fig [G] Stacked loss values (y) s. date and time (outdoor) or matrix measurement (x)
+Perform a Mechanistic Performance Model (MPM) fit to the lfm parameters
+poa_global (W/m$^2$), temp_module (C), wind_speed (ms$^-$$^1$).
mpm_a = c_1 +c_2*(t_mod-25) +c_3*log10(g) +c_4*g +c_5*ws +c_6\/g (deprecated)
+mpm_b = c_1 +c_2*(t_mod–25) +c_3*log10(g)*(t_k\/t_stc_k) +c_4*g +c_5*ws
+Report the fit (coeffs) and error (errs) coefficients.
+ +lfm_sel = 'pr_dc'
+# add selected variable to measured data frame to ensure data indexes match.
+meas_temp = meas.copy()
+meas_temp[lfm_sel] = norm[lfm_sel]
+
+# try to fit measurement data and print outputs
+
+"""
+# full_outputboolean, optional
+If True, this function returns additioal information:
+ infodict, mesg, and ier.
+
+https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html
+
+mesgstr (returned only if full_output is True)
+A string message giving information about the solution.
+
+ierint (returnned only if full_output is True)
+An integer flag. If it is equal to 1, 2, 3 or 4, the solution was found.
+Otherwise, the solution was not found. In either case,
+the optional output variable mesg gives more information.
+"""
+
+try:
+
+ if mpm_sel == 'a':
+ cc, coeffs, ee, errs, infodict, mesg, ier = mpm_a_fit(meas_temp, lfm_sel)
+
+ if mpm_sel == 'b':
+ cc, coeffs, ee, errs, infodict, mesg, ier = mpm_b_fit(meas_temp, lfm_sel)
+
+
+ # store calculated value of LFM variable
+ norm['calc_' + lfm_sel] = cc
+
+ # store residual difference of LFM variable
+ norm['diff_' + lfm_sel] = norm[lfm_sel] - norm['calc_' + lfm_sel]
+
+ # show infodict data, uncomment fvec to show per row
+ print('nfev =', infodict['nfev'], '\n \n',
+ # 'fvec =', infodict['fvec'],'\n \n',
+ 'mesg = ', mesg, '\n \n',
+ 'ier = ', ier, "NOTE : if ier in (1,2,3,4) then fit found")
+
+except:
+ print("CAN'T FIT DATA")
+nfev = 22 + + mesg = `ftol` termination condition is satisfied. + + ier = 2 NOTE : if ier in (1,2,3,4) then fit found ++
Show a heatmap of the average residual (meas - fit) error
+for each irradiance (100W/m^2) and tmod bin (5C).
def plot_heatmap(dnorm, fit, y_axis, x_axis, z_axis,
+ title, save_figs, clip=0.02,):
+ """Plot a heatmap of Z vs. binned X and Y axes.
+
+ Parameters
+ ----------
+ dnorm : dataframe
+ Normalised multiplicative loss values (values approx 1).
+
+ fit : string
+ fitted parameter e.g. 'pr_dc'.
+
+ x_axis : string
+ binned x axis e.g. 'poa_global_bin'.
+
+ y_axis : string
+ binned y axis e.g. 'temp_module_bin'.
+
+ z_axis : string
+ value as a colour surface plot e.f. 'diff_pr_dc'.
+
+ clip : value
+ clipping of z axis usually 0.02
+
+ title : string
+ title for graph e.g. mlfm_meas_file.
+
+ """
+ df_piv = pd.pivot_table(
+ dnorm,
+ index=y_axis, # e.g. 'temp_module_bin'
+ columns=x_axis, # e.g. 'poa_global_bin'
+ values=z_axis, # value to aggregate
+ fill_value=0, # fill empty cells with this ?
+ aggfunc=[np.mean], # e.g. min, np.sum, len->count
+ margins=False, # grand totals hide
+ dropna=True # hide missing rows or columns
+ )
+
+ fig, ax1 = plt.subplots()
+
+ # force z limits to be -2% to +2% if desired
+ df_piv = df_piv.clip(lower=-clip, upper=+clip)
+
+ im = ax1.imshow(
+ df_piv,
+ cmap='RdYlBu',
+ origin='lower'
+ )
+
+ cbar = ax1.figure.colorbar(im, ax=ax1, shrink=0.75, label=z_axis)
+
+ # Y AXIS : show only 1 of each y_skip labels
+ y_ticks = df_piv.shape[0]
+ plt.yticks(np.arange(0, y_ticks), rotation=0)
+ yax2 = [''] * y_ticks
+ y_skip = 2
+ y_count = 0
+ while y_count < y_ticks:
+ if y_count % y_skip == 0:
+ yax2[y_count] = df_piv.index[y_count]
+ y_count += 1
+
+ ax1.set_yticklabels(yax2)
+ ax1.set_ylabel(y_axis)
+
+ # X AXIS : show only 1 of each x_skip labels
+ x_ticks = df_piv.shape[1]
+ plt.xticks(np.arange(0, x_ticks), rotation=90)
+
+ xax2 = [''] * x_ticks
+ x_skip = 2
+ x_count = 0
+ while x_count < x_ticks:
+ if x_count % x_skip == 0:
+ xax2[x_count] = df_piv.columns.levels[1][x_count]
+ x_count += 1
+
+ ax1.set_title(title)
+
+ ax1.set_xticklabels(xax2)
+ ax1.set_xlabel(x_axis)
+
+ ax1.grid(color='k', linestyle=':', linewidth=1)
+
+ if save_figs:
+ # remove '.csv', high resolution= 300 dots per inch
+ plt.savefig(
+ os.path.join('mlfm_data', 'output', 'heatmap_' + title[:len(title)-4]),
+ dpi=300
+ )
+
+ plt.show()
+# plot heatmap
+heatmap_plot = plot_heatmap(
+ dnorm=norm,
+ fit=lfm_sel,
+ y_axis='temp_module_bin',
+ x_axis='poa_global_bin',
+ z_axis='diff_' + lfm_sel,
+ clip=0.025,
+ title='residual_m' + mpm_sel + '_' + mlfm_meas_file,
+ save_figs=save_figs
+)
+
+Fig [I] Residual LFM fit heatmap vs. poa_global bin (x) and temp_module bin (y)
+ +def plot_fit(dmeas, dnorm, fit, title, save_figs, coeffs):
+ """Scatter plot fit to normalised measured.
+
+ Parameters
+ ----------
+ dmeas : dataframe
+ measurements, must include 'poa_global_kwm2'
+
+ dnorm : dataframe
+ normalised multiplicative lfm loss values 'i_sc' .. 'v_oc'
+ where pr_dc = 1/ff * product('i_sc', ... 'v_oc').
+
+ fit : string
+ name of fitted variable e.g. 'pr_dc'.
+
+ title : string
+ title for graph e.g. mlfm_meas_file.
+
+ """
+ fig, ax1 = plt.subplots()
+
+ plt.title(title)
+
+ plt.ylabel('fit ' + fit + ' * poa_global kW/m^2')
+ ax1.set_ylim(0, 1.2)
+
+ plt.xlabel('meas ' + fit + '* poa_global_kW/m^2')
+ ax1.set_xlim(0, 1.2)
+
+ plt.plot(
+ dnorm[fit] * dmeas['poa_global'] / G_STC,
+ dnorm['calc_' + fit] * dmeas['poa_global'] / G_STC,
+ 'c^',
+ label=fit
+ )
+
+ # plot 1:1 line to show optimum fit
+ plt.plot((0, 1.2), (0, 1.2), 'yo-')
+
+ # plot LIC, NOCT and STC irradiances
+ for x in (0.2, 0.8,1):
+ plt.plot((0, x), (x, x), 'k--')
+ plt.plot((x, x), (x, 0), 'k--')
+
+ plt.legend(loc='upper left')
+
+ if save_figs:
+ # remove '.csv', high resolution= 300 dots per inch
+ plt.savefig(
+ os.path.join('mlfm_data', 'output', 'fit_meas_' + title[:len(title)-4]),
+ dpi=300
+ )
+
+
+
+ plt.show()
+# plot fit vs. measured, include a 1:1 line for comparison
+fit_plot = plot_fit(dmeas=meas,
+ dnorm=norm,
+ fit=lfm_sel,
+ title='fit_m' + mpm_sel + '_' + mlfm_meas_file,
+ save_figs=save_figs,
+ coeffs=coeffs
+ )
+
+Fig [J] scatter plot of 'fit_lfm_sel poa_global# (y) vs. 'measured_lfm_sel poa_global' (x)
+ +Read in a matrix with complete values of
+Irradiance (G=100,200 .. 1100,1200) and module temperature (T=0,5 .. 65,70)
+to predict all MPM values
# read in the complete matrix data
+matr = pd.read_csv(os.path.join(root_dir, 'mlfm_data', 'ref', 'mlfm_matrix.csv'),
+ index_col='id')
+# show model coefficients
+mpm_sel, coeffs
+('b', array([ 1.06780656, -0.0028452 , 0.14860936, -0.07080871, 0.01 ]))
+# populate pivot table from predicted mpm data
+if mpm_sel == 'a':
+ matr[lfm_sel] = mpm_a_calc(matr, *coeffs) # not mpm_sel
+
+if mpm_sel == 'b':
+ matr[lfm_sel] = mpm_b_calc(matr, *coeffs) # not mpm_sel
+
+
+matr.head(10)
+| + | mid | +poa_global | +temp_module | +wind_speed | +pr_dc | +
|---|---|---|---|---|---|
| id | ++ | + | + | + | + |
| 1 | +matrix | +100 | +0 | +0 | +0.995707 | +
| 2 | +matrix | +100 | +5 | +0 | +0.978989 | +
| 3 | +matrix | +100 | +10 | +0 | +0.962271 | +
| 4 | +matrix | +100 | +15 | +0 | +0.945553 | +
| 5 | +matrix | +100 | +20 | +0 | +0.928834 | +
| 6 | +matrix | +100 | +25 | +0 | +0.912116 | +
| 7 | +matrix | +100 | +30 | +0 | +0.895398 | +
| 8 | +matrix | +100 | +35 | +0 | +0.878680 | +
| 9 | +matrix | +100 | +40 | +0 | +0.861962 | +
| 10 | +matrix | +100 | +45 | +0 | +0.845244 | +
def plot_contourf(df, x_axis, y_axis, z_axis, title,
+ vmin=0, vmax=1.2, levels=5,
+ save_figs=False):
+ """Plot filled contour plot Z vs. X and Y bins.
+
+ Parameters
+ ----------
+ df : dataframe
+ measured or normalised data containing weather columns
+ (poa_global, temp_module and wind_speed).
+
+ x_axis : string
+ binned x axis e.g. 'poa_global'.
+
+ y_axis : string
+ binned y axis e.g. 'temp_module'.
+
+ z_axis : string
+ measured value as a colour surface plot.
+
+ title : string
+ title for graph e.g. mlfm_meas_file.
+
+ vmin, vmax : float
+ minimum and maximum values for contour chart ###
+
+ """
+ piv = pd.pivot_table(
+ df,
+ index=y_axis,
+ columns=x_axis,
+ values=z_axis,
+ fill_value=0, # fill empty cells?
+ aggfunc=[np.mean], # min, np.sum, len->count
+ margins=False, # grand totals
+ dropna=True # hide missing rows or columns
+ )
+
+ piv = piv.clip(vmin, vmax)
+
+ fig, ax1 = plt.subplots()
+
+ cs = plt.contourf(
+ piv,
+ cmap='RdYlBu', # or 'nipy_spectral',
+ # origin='lower'
+ # nchunkint=1,
+ levels=levels,
+ vmin=vmin,
+ vmax=vmax
+ )
+
+ cbar = fig.colorbar(cs, ax=ax1)
+ cbar.ax.set_ylabel(z_axis,
+ rotation=90,
+ va='bottom',
+ labelpad=+30)
+
+ plt.title(title)
+ # # get_yaxis().set_major_formatter(FormatStrFormatter('%.2f'))
+
+ y_ticks = piv.shape[0]
+
+ plt.yticks(np.arange(0, y_ticks), rotation=0)
+
+ # show only 1 of each y_skip labels
+ yax2 = [''] * y_ticks
+ y_skip = 2
+ y_count = 0
+ while y_count < y_ticks:
+ if y_count % y_skip == 0:
+ yax2[y_count] = piv.index[y_count]
+ y_count += 1
+
+ ax1.set_yticklabels(yax2)
+ ax1.set_ylabel(y_axis)
+
+ x_ticks = piv.shape[1]
+ plt.xticks(np.arange(0, x_ticks), rotation=90)
+
+ # show only 1 of each x_skip labels
+ xax2 = [''] * x_ticks
+ x_skip = 2
+ x_count = 0
+ while x_count < x_ticks:
+ if x_count % x_skip == 0:
+ xax2[x_count] = piv.columns.levels[1][x_count]
+ x_count += 1
+
+ ax1.set_xticklabels(xax2)
+ ax1.set_xlabel(x_axis)
+
+ ax1.grid(color='k', linestyle=':', linewidth=1)
+
+ if save_figs:
+ # remove '.csv', high resolution= 300 dots per inch
+ plt.savefig(os.path.join('mlfm_data', 'output', 'contourf_'+ title[:len(title)-4])
+ , dpi=300
+ )
+# REMOVE LOW TEMPERATURE DATA WHICH MAY CONTAIN SNOW
+
+matr2 = matr[matr['temp_module'] >= 10]
+contour_plot = plot_contourf(
+ df=matr2,
+ y_axis='temp_module',
+ x_axis='poa_global',
+ z_axis=lfm_sel,
+ title='matrix predicted_m' + mpm_sel + '_' + mlfm_meas_file,
+ vmin=0.7,
+ vmax=1.05,
+ levels=9,
+ save_figs=save_figs
+)
+
+Fig [L1] Contour plot (colours) of predicted lfm_sel vs. poa_global (x) and temp_mod (y)
+ +contour_plot = plot_contourf(
+ df=norm,
+ y_axis='temp_module_bin',
+ x_axis='poa_global_bin',
+ z_axis=lfm_sel,
+ title='avg normalised_m' + mpm_sel + '_' + mlfm_meas_file,
+ vmin=0.7,
+ vmax=1.05,
+ levels=9,
+ save_figs=save_figs
+)
+
+Fig [L2] Contour plot (colours) of measured lfm_sel vs. poa_global (x) and temp_mod (y)
+ +
+The Loss Factors Model (LFM) and Mechanistic Performance Model (MPM)
+together known as "MLFM" have been developed by SRCL and Gantner Instruments
+(previously Oerlikon Solar and Tel Solar) since 2011 MLFM and 2017 MPM
.. [1] J. Sutterlueti(now Gantner Instruments) and S. Ransome
+ '4AV.2.41 Characterising PV Modules under Outdoor Conditions:
+What's Most Important for Energy Yield'
+26th EU PVSEC 8 September 2011; Hamburg, Germany
+http://www.steveransome.com/pubs/2011Hamburg_4AV2_41.pdf
.. [2] Steve Ransome and Juergen Sutterlueti(Gantner Instruments)
+ 'Choosing the best Empirical Model for predicting energy yield'
+ 7th PV Energy Rating and Module Performance Modeling Workshop,
+ Canobbio, Switzerland 30-31 March, 2017
.. [3] S. Ransome and J. Sutterlueti (Gantner Instruments)
+'Checking the new IEC 61853.1-4 with high quality 3rd party data to
+benchmark its practical relevance in energy yield prediction'
+PVSC June 2019 Chicago, USA
+http://www.steveransome.com/PUBS/1906_PVSC46_Chicago_Ransome.pdf
.. [4] Steve Ransome (SRCL) and Juergen Sutterlueti (Gantner Instruments)
+'5CV.4.35 Quantifying Long Term PV Performance and Degradation
+under Real Outdoor and IEC 61853 Test Conditions
+Using High Quality Module IV Measurements'
+36th EU PVSEC Sep 2019
+http://www.steveransome.com/PUBS/1909_5CV4_35_PVSEC36_Marseille_Ransome_PPT.pdf
.. [5] Steve Ransome (SRCL)
+'How to use the Loss Factors and Mechanistic Performance Models
+effectively with PVPMC/PVLIB'
+PVPMC Webinar on PV Performance Modeling Methods, Aug 2020
+https://pvpmc.sandia.gov/download/7879/
.. [6] W.Marion et al (NREL)
+'New Data Set for Validating PV Module Performance Models'
+https://www.researchgate.net/publication/286746041_New_data_set_for_validating_PV_module_performance_models
+https://www.nrel.gov/docs/fy14osti/61610.pdf
.. [7] Steve Ransome (SRCL) +'Benchmarking PV performance models with high quality IEC 61853 Matrix +measurements (Bilinear interpolation, SAPM, PVGIS, MLFM and 1-diode)' +http://www.steveransome.com/pubs/2206_PVSC49_philadelphia_4_presented.pdf
+.. [8] Juergen Sutterlueti (Gantner Instruments) +'Advanced system monitoring and artificial intelligent data-driven analytics +to serve GW-scale photovoltaic power plant and energy storage requirements' +https://pvpmc.sandia.gov/download/8574/
+Many more papers are available at www.steveransome.com
+ +# =============================================================================================
+## TEST CODE CAN DELETE AFTER HERE IF NOT NEEDED
+
+test = False
+
+if test:
+ # save meas data to csv
+ meas.to_csv(
+ os.path.join('mlfm_data', 'output', 'meas.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+ # save norm data to csv
+ norm.to_csv(
+ os.path.join('mlfm_data', 'output', 'norm.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+ # save matr data to csv
+ matr.to_csv(
+ os.path.join('mlfm_data', 'output', 'matr.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+ # save ref data to csv
+ ref_data.to_csv(
+ os.path.join('mlfm_data', 'output', 'ref_data.csv'),
+ sep=';',
+ quotechar='"',
+ encoding='utf-8',
+ decimal='.'
+ )
+
+
+if test:
+ # print mlfm fit coeffs
+ print(coeffs[0],coeffs[1],coeffs[2],coeffs[3],coeffs[4],) # coeffs[5], )#coeffs[6],)
+
+
+if test:
+ # only works with mlfm_meas_file = 'g78_T16_Xall_F10m_R900_041.
+ #
+ # check data for test
+
+ n= norm.loc['2016-03-23 09:00:00-07:00']
+
+ print('\n n= \n', n)
+
+
+ n= norm.loc['2016-03-23 09:00:00-07:00']
+
+ print('\n n= \n', n)
+
+ s = stack.loc['2016-03-23 09:00:00-07:00']
+
+ print('\n s= \n', s)
+
+
+if test:
+ # show all versions
+ import sys
+
+ for name, module in sorted(sys.modules.items()):
+ if hasattr(module, '__version__'):
+ print (name, module.__version__ )
+# whos
+| \n", + " | module_id | \n", + "temp_module | \n", + "poa_global | \n", + "i_sc | \n", + "v_oc | \n", + "i_mp | \n", + "v_mp | \n", + "p_mp | \n", + "wind_speed | \n", + "pr_dc | \n", + "v_oc_temp_corr | \n", + "pr_dc_temp_corr | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | \n", + "27.0 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.0 | \n", + "27.000000 | \n", + "27.000000 | \n", + "27.000000 | \n", + "
| mean | \n", + "19074001.0 | \n", + "42.222222 | \n", + "581.481481 | \n", + "3.450926 | \n", + "65.054815 | \n", + "3.194407 | \n", + "54.227778 | \n", + "175.637260 | \n", + "0.0 | \n", + "0.922290 | \n", + "67.566148 | \n", + "0.964306 | \n", + "
| std | \n", + "0.0 | \n", + "23.588350 | \n", + "358.455058 | \n", + "2.123715 | \n", + "4.683176 | \n", + "1.974740 | \n", + "4.486576 | \n", + "110.698594 | \n", + "0.0 | \n", + "0.078215 | \n", + "2.555701 | \n", + "0.038515 | \n", + "
| min | \n", + "19074001.0 | \n", + "15.000000 | \n", + "100.000000 | \n", + "0.595000 | \n", + "54.600000 | \n", + "0.541000 | \n", + "44.320000 | \n", + "24.065760 | \n", + "0.0 | \n", + "0.746677 | \n", + "61.265287 | \n", + "0.856461 | \n", + "
| 25% | \n", + "19074001.0 | \n", + "25.000000 | \n", + "200.000000 | \n", + "1.203000 | \n", + "61.595000 | \n", + "1.094500 | \n", + "49.875000 | \n", + "62.091200 | \n", + "0.0 | \n", + "0.849048 | \n", + "66.072455 | \n", + "0.948074 | \n", + "
| 50% | \n", + "19074001.0 | \n", + "50.000000 | \n", + "600.000000 | \n", + "3.542000 | \n", + "65.780000 | \n", + "3.298000 | \n", + "54.250000 | \n", + "177.944780 | \n", + "0.0 | \n", + "0.926241 | \n", + "68.502670 | \n", + "0.974878 | \n", + "
| 75% | \n", + "19074001.0 | \n", + "62.500000 | \n", + "900.000000 | \n", + "5.337500 | \n", + "69.305000 | \n", + "4.946500 | \n", + "58.400000 | \n", + "269.232420 | \n", + "0.0 | \n", + "0.996683 | \n", + "69.543433 | \n", + "0.994383 | \n", + "
| max | \n", + "19074001.0 | \n", + "75.000000 | \n", + "1100.000000 | \n", + "6.578000 | \n", + "71.850000 | \n", + "6.061000 | \n", + "60.210000 | \n", + "354.156950 | \n", + "0.0 | \n", + "1.026992 | \n", + "70.440000 | \n", + "1.000051 | \n", + "
| \n", + " | poa_global | \n", + "temp_module | \n", + "wind_speed | \n", + "pr_dc | \n", + "pr_dc_temp_corr | \n", + "i_sc | \n", + "i_mp | \n", + "v_oc | \n", + "v_oc_temp_corr | \n", + "v_mp | \n", + "
|---|---|---|---|---|---|---|---|---|---|---|
| date_time | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 0 | \n", + "100 | \n", + "15 | \n", + "0 | \n", + "0.936042 | \n", + "0.908517 | \n", + "1.007988 | \n", + "0.912605 | \n", + "0.936845 | \n", + "0.913971 | \n", + "0.844634 | \n", + "
| 1 | \n", + "200 | \n", + "15 | \n", + "0 | \n", + "0.978361 | \n", + "0.949591 | \n", + "1.002058 | \n", + "0.923922 | \n", + "0.965471 | \n", + "0.941899 | \n", + "0.851158 | \n", + "
| 2 | \n", + "400 | \n", + "15 | \n", + "0 | \n", + "1.007065 | \n", + "0.977451 | \n", + "0.996976 | \n", + "0.928207 | \n", + "0.991961 | \n", + "0.967743 | \n", + "0.853123 | \n", + "
| \n", + " | mid | \n", + "poa_global | \n", + "temp_module | \n", + "wind_speed | \n", + "pr_dc | \n", + "
|---|---|---|---|---|---|
| id | \n", + "\n", + " | \n", + " | \n", + " | \n", + " | \n", + " |
| 1 | \n", + "matrix | \n", + "100 | \n", + "0 | \n", + "0 | \n", + "0.995707 | \n", + "
| 2 | \n", + "matrix | \n", + "100 | \n", + "5 | \n", + "0 | \n", + "0.978989 | \n", + "
| 3 | \n", + "matrix | \n", + "100 | \n", + "10 | \n", + "0 | \n", + "0.962271 | \n", + "
| 4 | \n", + "matrix | \n", + "100 | \n", + "15 | \n", + "0 | \n", + "0.945553 | \n", + "
| 5 | \n", + "matrix | \n", + "100 | \n", + "20 | \n", + "0 | \n", + "0.928834 | \n", + "
| 6 | \n", + "matrix | \n", + "100 | \n", + "25 | \n", + "0 | \n", + "0.912116 | \n", + "
| 7 | \n", + "matrix | \n", + "100 | \n", + "30 | \n", + "0 | \n", + "0.895398 | \n", + "
| 8 | \n", + "matrix | \n", + "100 | \n", + "35 | \n", + "0 | \n", + "0.878680 | \n", + "
| 9 | \n", + "matrix | \n", + "100 | \n", + "40 | \n", + "0 | \n", + "0.861962 | \n", + "
| 10 | \n", + "matrix | \n", + "100 | \n", + "45 | \n", + "0 | \n", + "0.845244 | \n", + "