Solar module I-V

The parameters of a solar panel are given in the table below.
Parameter Value
$P_{max}$ (W) 320
Voltage at $P_{max}$ (V) 33.4
Current at $P_{max}$ (A) 9.59
$V_{OC}$ at STC (V) 40.9
$I_{SC}$ at STC (A) 10.15
Temperature coefficient for $I_{SC}$ ($\%/^oC$) 0.058
Temperature coefficient for $V_{OC}$ ($\%/^oC$) -0.32
Number of cells in series ($N_C$) 60

Two such panels, along with bypass diodes (assumed to be ideal), are connected in series as shown in the figure. The irradiation for PV1 is $1000\,$W/m$^2$ and that for PV2 is $500\,$W/m$^2$. The load is a current source with $I_S = I_{MPP}$ (the panel current at the maximum power point). Determine the following.

  1. currents through the panels PV1 and PV2.
  2. currents through the bypass diodes $D_1$ and $D_2$.
  3. power delivered to the current source load.
In [1]:
from IPython.display import Image
Image(filename =r'solar_5_fig_1.png', width=180)
Out[1]:
No description has been provided for this image
In [2]:
# run this cell to view the circuit file.
%pycat solar_5_orig.in

We now replace the strings such as \$Voc_ref with the values of our choice by running the python script given below. It takes an existing circuit file solar_5_orig.in and produces a new circuit file solar_5.in, after replacing \$Voc_ref, etc. with values of our choice.

In [3]:
import gseim_calc as calc

s_g_rad_1 = '1000'
s_g_rad_2 = '500'
s_t_C = '25'
s_Nc = '60'
s_Voc_ref = '40.9'
s_Isc_ref = '10.15'
s_Vm_ref = '33.4'
s_Im_ref = '9.59'
s_coef_Isc = '0.058'
s_coef_Voc = '-0.32'

l = [
  ('$g_rad_1', s_g_rad_1),
  ('$g_rad_2', s_g_rad_2),
  ('$t_C', s_t_C),
  ('$Nc', s_Nc),
  ('$Voc_ref', s_Voc_ref),
  ('$Isc_ref', s_Isc_ref),
  ('$Vm_ref', s_Vm_ref),
  ('$Im_ref', s_Im_ref),
  ('$coef_Isc', s_coef_Isc),
  ('$coef_Voc', s_coef_Voc),
]
calc.replace_strings_1("solar_5_orig.in", "solar_5.in", l)
print('solar_5.in is ready for execution')

solar_5.in is ready for execution
Execute the following cell to run GSEIM on solar_5.in.
In [4]:
import os
import dos_unix
# uncomment for windows:
#dos_unix.d2u("solar_5.in")
os.system('run_gseim solar_5.in')

Circuit: filename = solar_5.in
main: i_solve = 0
GSEIM: Program completed.
Out[4]:
0

The circuit file (solar_5.in) is created in the same directory as that used for launching Jupyter notebook. The last step (i.e., running GSEIM on solar_5.in) creates a data file called solar_5.dat in the same directory. We can now use the python code below to compute/plot the various quantities of interest.

In [5]:
import numpy as np
import matplotlib.pyplot as plt 
import gseim_calc as calc
from setsize import set_size

slv = calc.slv("solar_5.in")

i_slv = 0
i_out = 0
filename = slv.l_filename_all[i_slv][i_out]
print('filename:', filename)
u = np.loadtxt(filename)

col_i1   = slv.get_index(i_slv,i_out,"i1")
col_i2   = slv.get_index(i_slv,i_out,"i2")
col_ID1  = slv.get_index(i_slv,i_out,"ID1")
col_ID2  = slv.get_index(i_slv,i_out,"ID2")
col_p1   = slv.get_index(i_slv,i_out,"p1")
col_p2   = slv.get_index(i_slv,i_out,"p2")
col_v_p  = slv.get_index(i_slv,i_out,"v_p")
col_P_Is = slv.get_index(i_slv,i_out,"P_Is")

i1_0   = u[col_i1  ]
i2_0   = u[col_i2  ]
ID1_0  = u[col_ID1 ]
ID2_0  = u[col_ID2 ]
p1_0   = u[col_p1  ]
p2_0   = u[col_p2  ]

P_Is_0 = abs(u[col_P_Is])

print('IPV1:', "%7.3f"%i1_0, "A")
print('IPV2:', "%7.3f"%i2_0, "A")
print('ID1:', "%7.3f"%ID1_0, "A")
print('ID2:', "%7.3f"%ID2_0, "A")
print('P (PV1):', "%7.3f"%p1_0, "W")
print('P (PV2):', "%7.3f"%p2_0, "W")
print('P (Is):', "%7.3f"%P_Is_0, "W")

filename: solar_5.dat
IPV1:   9.590 A
IPV2:   5.075 A
ID1:  -0.000 A
ID2:   4.515 A
P (PV1): 320.307 W
P (PV2):  -0.000 W
P (Is): 320.307 W

This notebook was contributed by Prof. Nakul Narayanan K, Govt. Engineering College, Thrissur. He may be contacted at nakul@gectcr.ac.in.