In [23]:
# Configure Jupyter so figures appear in the notebook
%matplotlib inline
# Configure Jupyter to display the assigned value after an assignment
%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'
# import functions from the modsim.py module
from modsim import *
from mpl_toolkits import mplot3d
import matplotlib.gridspec as gridspec
from scipy import integrate
In [24]:
def make_system(absorb,weight,loss_coeff,specif,area): #defines new function with parameters
init = State(temp = 25, irradiance=[0,0,0,0,0,0,0,0,0,1,33,97,157,259,328,396,496,567,
617,676,700,720,739,694,684,686,639,549,412,393,290
,226,204,223,142,58,40,19,4,0,0,0,0,0,0,0,0] )
#makes new state with starting temperature of 25C and the irradiance over the course of the day
temp_year = [274.8, 272.95, 276.6, 282.1, 287.55, 293, 296.15, 295.4, 291.4, 285.35, 280.2, 274.65]
irr_year = [
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 75, 147, 233, 318, 378, 421, 448, 444, 404,373,325,237,154,86,28,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0 , 0, 0, 0, 0, 0, 4, 27, 58, 93, 148, 201, 217, 225, 187, 177, 194, 294, 411, 372, 341, 295, 230, 150, 89, 37, 4, 0, 0, 0, 0, 0, 0 ,0 ,0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 68, 161, 251, 314, 397, 503, 571, 621, 609, 583, 668, 550, 387, 300, 260, 296, 266, 236, 181, 117, 46, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 24, 54, 97, 117, 282, 343, 461, 516, 580, 597, 568, 616, 531, 459, 427, 388, 302, 386, 459, 381, 303, 239, 126, 57, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 87, 186, 264, 317, 483, 428, 615, 621, 641, 708, 580, 389, 220, 446, 829, 880, 837, 782, 677, 554, 543, 433, 277, 176, 98, 48, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 42, 88, 126, 208, 137, 268, 392, 384, 450, 409, 465, 429, 347, 294, 294, 287, 366, 352, 326, 379, 320, 253, 264, 189, 109, 64, 47, 22, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[0,0,0,0,0,0,0,0,0,1,33,97,157,259,328,396,496,567, 617,676,700,720,739,694,684,686,639,549,412,393,290,226,204,223,142,58,40,19,4,0,0,0,0,0,0,0,0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 28, 54, 110, 173, 264, 297, 374, 274, 505, 259, 228, 252, 232, 233, 187, 241, 383, 283, 450, 387, 375, 331, 313, 227, 200, 117, 47, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 101, 170, 266, 349, 388, 468, 565, 699,743, 793, 837, 837, 822, 792, 552, 426, 555, 446, 390, 212, 135, 100, 50, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 11, 20, 32, 45, 58, 71, 140, 320, 421, 550, 450, 159, 95, 63, 87, 83, 81, 56, 22, 21, 10, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 18, 37, 54, 40, 49, 126, 200, 349, 450, 500, 450, 340, 215, 142, 100, 103, 51, 15, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 66, 137, 210, 279, 339, 388, 425, 448, 456, 451, 428, 399, 353, 260, 174, 114, 58, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
#includes the temperature and irradiance over the course of the year in the state
t_0 = 0
t_end = 1440
dt = 30
#defines the values for "t_0", "t_end", and "dt"
return System(init=init, absorb=absorb, weight=weight, loss_coeff=loss_coeff, specif=specif, area=area, t_0=t_0, t_end=t_end, dt=dt, panel_num= 19,maxPower=320, irr_year = irr_year, temp_year = temp_year)
#returns the new system variables
In [25]:
system = make_system(.833,26.847,.005,710.08,30.547) #places all of the system variables in a system
Out[25]:
In [26]:
def simulation_day(system): #defines a new function with parameter "system"
temp,irradiance = system.init #takes global system variables into "temp" and "irradiance"
p_loss_percent = [] #creates an empty list
ducalc = [] #creates an empty list
ucalc = [] #creates an empty list
delta_u = [] #creates an empty list
delta_T = [] #creates an empty list
T_celcius = [] #creates an empty list
T_current = [295.15] #creates a list for the starting temperature
kwh_final = [0] #creates a list with stored value of 0
delta_irradiance = [0] #creates a list with stored value of 0
ideal_produced = [] #creates an empty list
real_produced = [] #creates an empty list
real_kwh = [] #creates an empty list
ideal_psum = [0] #creates a list with stored value of 0
ideal_kwh = [] #creates an empty list
real_psum = [0] #creates a list with stored value of 0
kwh_sum_real = [0] #creates a list with stored value of 0
kwh_sum_ideal = [0] #creates a list with stored value of 0
irradiance1=[0,0,0,0,0,0,0,0,0,1,33,97,157,259,328,396,496,567,
617,676,700,720,739,694,684,686,639,549,412,393,290
,226,204,223,142,58,40,19,4,0,0,0,0,0,0,0,0]
#creates a list with the values of irradiance over the course of 24 hours (30 min intervals)
stamp = linrange(system.t_0, system.t_end, system.dt) #creates a timeseries with starting time at 0 minutes, an interval of 30 minutes, and an ending time of 1440 minutes)
for i in range(47): #creates a forloop with 47 iterations
diffU = system.area * irradiance[i] * system.absorb #calculates how much energy is absorbed by the PV Panels from irradiance
ducalc.append(diffU) #adds diffU to the list "ducalc"
UU = ducalc[i] * system.dt #multiplies the "ducalc" of the current list by dt
ucalc.append(UU) #places "UU" in the list "ucalc"
delta_u.append(ucalc[i]- ucalc[i-1]) #subtracts "ucalc" from the previous value of "ucalc", then places the answer in a list named "delta_u"
delta_T.append(delta_u[i] / (system.specif * system.weight) ) #divides "delta_u" by the product of "system.specif" and "system.weight", then places it in a list named "delta_T"
T_current.append(delta_T[i] + T_current[i]) #adds "delta_T" or change in temperature from the current iteration to the current temperature ("T_current"), then adds it to a list
T_celcius.append(T_current[i] - 273.15) #converts the current temperature from Kelvin to Celcius, then adds it to a list
p_loss_percent.append(T_celcius[i] * system.loss_coeff) #multiplies the current temperature by the loss coefficient of the PV panels, then adds it to a list
ideal_produced.append(system.maxPower * system.panel_num * irradiance1[i] / 1000) #calculates the ideal amount of power produced by the PV panels without inefficiencies due to heat, then adds it to a list
real_produced.append(ideal_produced[i]*( 1 - p_loss_percent[i])) #calculated the actual power produced by the PV panels, then adds it to a list
return(stamp, real_produced, ideal_produced,p_loss_percent,real_kwh,ideal_kwh) #returns the outputs
In [27]:
stamp_day, real_produced_day, ideal_produced_day, p_loss, real_kwh_day, ideal_kwh_day= simulation_day(system) #places the outputs of the system into each of 6 variables
In [28]:
def integrator(produced): #defines new function with parameter "produced"
kwh_conv = [0] #creates a list with stored value of 0
stamp_h = [0] #creates a list with stored value of 0
stamp = linrange(system.t_0, system.t_end-30, system.dt) #creates a timeseries
for i in range(47): #runs a forloop for 47 iterations
kwh_conv.append(produced[i] / 1000) #converts the output of Wh to KWh and places it in a list
stamp_h.append(stamp[i]/60) #converts minutes to hours and places it in a list
stamp_int = (integrate.cumtrapz(kwh_conv, stamp_h)) #takes the integral of the KWh's produced with respect to time to produce "stamp_int"
return stamp_int #returns "stamp_int"
In [29]:
kwh_real = integrator(real_produced_day) #takes the integral of "real_produced_day"
kwh_ideal = integrator(ideal_produced_day) #takes the integral of "ideal_produced_day"
Out[29]:
In [30]:
def plot_2D(ideal, real): #defines a new function with parameters "real" and "ideal"
stamp_h = [] #creates a new empty list
stamp = linrange(system.t_0, system.t_end-30, system.dt) #creates a timeseries named "stamp"
for i in range(47): #creates a forloop with 47 iterations
stamp_h.append(stamp[i]/60) #converts minutes to hours
plot(stamp_h,real) #plots the actual power generated over time
plot(stamp_h,ideal) #plots the ideal power generated over time
decorate(title = 'Kwh total Generated over a day ideal vs heat inefficiency',
xlabel='Time (hours)',
ylabel='Total Kwh Generated over a day') #adds the title and labels to the plots
In [43]:
plot(real_produced_day) #plots "real_produced_day"
plot(ideal_produced_day) #plots "ideal_produced_day"
decorate(title = 'Watts Generated over a day ideal vs heat inefficiency',
xlabel='Time (half hours)',
ylabel='Total Wats Generated') #adds title and axis labels to graph
Out[43]:
In [32]:
plot_2D(kwh_real, kwh_ideal) #plots the cumilative ideal and actual energy produced over the course of a day
Out[32]:
In [33]:
def simulation_year(system): #defines new function with parameter "system"
temp,irradiance = system.temp_year, system.irr_year #takes temperature and irradiance values over a year into "temp" and "irradiance"
p_loss_percent = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
ducalc = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
ucalc = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
delta_u = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
delta_T = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
T_celcius = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
ideal_produced_month = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
real_produced_month = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
T_current = [[0],[0],[0],[0],[0],[0],[0],[0],[0],[0],[0],[0]] #creates an empty list with starting values of 0
ideal_produced_month_total= [] #creates an empty list
real_produced_month_total = [] #creates an empty list
for j in range(12):
for i in range(46): #runs same "simulation_day" but includes new variables of the real and ideal energy produced over the course of a month
diffU = system.area * irradiance[j][i] * system.absorb
ducalc[j].append(diffU)
UU = ducalc[j][i] * system.dt
ucalc[j].append(UU)
delta_u[j].append(ucalc[j][i]- ucalc[j][i-1])
delta_T[j].append(delta_u[j][i] / (system.specif * system.weight) )
T_current[j][i] = temp[j]
T_current[j].append(delta_T[j][i] + T_current[j][i])
T_celcius[j].append(T_current[j][i] - 273.15)
p_loss_percent[j].append(T_celcius[j][i] * system.loss_coeff)
ideal_produced_month[j].append(system.maxPower * system.panel_num * irradiance[j][i] / 1000) #calculates the ideal power produced over the course of a day
real_produced_month[j].append(ideal_produced_month[j][i]*( 1 - p_loss_percent[j][i])) #calculates the real power produced over the course of a day
ideal_produced_month_total.append((sum(ideal_produced_month[j])*30)) #calculates the ideal power produced over the course of a month
real_produced_month_total.append((sum(real_produced_month[j])*30)) #calculated the real power produced over the course of a month
return(real_produced_month, ideal_produced_month,ideal_produced_month_total,real_produced_month_total ) #returns the outputs
In [34]:
RPM, IPM, IPMT, RPMT = simulation_year(system) #places the system variables from the output of "simulation_year" into 4 variables
In [35]:
plot(IPMT) #plots "IPMT"
plot(RPMT) #plots "RPMT"
decorate(title = 'W total Generated over a year ideal vs heat inefficiency',
xlabel='Month, 0 = January',
ylabel='Total W Generate during that month') #labels the plots with title and axis labels
Out[35]:
In [36]:
def integrator_year(produced,system): #defines a new function with parameters
monthly_sum = [] #creates an empty list
kwh_conv = [[],[],[],[],[],[],[],[],[],[],[],[]] #creates an empty list
stamp_h = [] #creates an empty list
tot_int = [] #creates an empty list
stamp = linrange(system.t_0, system.t_end-60, system.dt) #defines a timeseries
for j in range(11): #creates a forloop with 11 iterations
for i in range(46): #creates a forloop with 46 iterations
kwh_conv[j].append(produced[j][i] / 1000) #converts Wh to KWh
for i in range(46): #creates a forloop with 46 iterations
stamp_h.append(stamp[i]/60) #converts minutes to hours and places it in a list
for j in range(11): #creates a forloop with 11 iterations
stamp_int = (integrate.trapz(kwh_conv[j], stamp_h)) #integreates the energy generated with respect to time
tot_int.append(stamp_int) #places the previous line into a list
return tot_int #returns the outputs
In [37]:
RPM_integral = integrator_year(RPM, system) #runs the function "integrator_year" for parameters "RPM" and "system"
IPM_integral = integrator_year(IPM, system) #runs the function "integrator_year" for parameters "IPM" and "system"
Out[37]:
In [38]:
plot(IPM_integral) #plots IPM_integral
plot(RPM_integral) #plots RPM_integral
decorate(title = 'Kwh total Generated over a day ideal vs heat inefficiency',
xlabel='Months, 0 = January',
ylabel='Total Kwh Generated over a year')
#labels the graph with a title and axis labels
Out[38]:
In [39]:
def difference(ideal, real): #defines a new function with parameters
error = [] #creates an empty list
for i in range(11): #creats a forloop with 11 iterations
error.append(ideal[i] - real[i]) #takes the difference between the real and idean energy produced and places it into a list
plot(error) #plots the difference fromt he previous line
decorate(title = 'Average Kwh Difference per month, ideal vs Heat Inefficiency',
xlabel='Months, January = 0',
ylabel='Difference in Kwh')
#labels the graph with a title and axis labels
In [40]:
difference(IPM_integral, RPM_integral) #runs the function "difference"
Out[40]:
