def f_optim(c):
'''
Objective function. Returns the profitability of the system.
Note that some global variables are used.
Global variables: Demand,eta_inv,eta_bat,CapacityFactorPV,coef,CountryData,
Inv, country
'''
[r_PV, r_bat] = c
# if the ratios are negative, set them to zero and add a penalty to the objective function
penalty_PV = -1E10 * np.minimum(0, r_PV)
penalty_bat = -1E10 * np.minimum(0, r_bat)
r_PV = np.maximum(0, r_PV)
r_bat = np.maximum(0, r_bat)
E = EnergyFlows(r_PV, r_bat, Demand, eta_inv, eta_bat,
CapacityFactorPV, coef)
F = FinancialAnalysis(E, CountryData, Inv)
#print 'PV = ' + str(r_PV) + ', BAT = ' + str(r_bat) + ', PR = ' + str(PR) + ', LCOE = ' + str(LCOE)
return F['LCOE'] + penalty_PV + penalty_bat
def SCoptim(CapacityFactorPV, CountryData, Inv, coef, max_RPV=10):
'''
Main optimization function
:param CapacityFactorPV: Yearly capacity factor, kWh/kWp
:param CountryData: Dictionary with the financial variables of the considered country
:param Inv: Investment data. Defined as a dictionary with the fields 'FixedPVCost','PVCost_kW','FixedBatteryCost','BatteryCost_kWh','PVLifetime','BatteryLifetime','OM'
:param coef: Coefficient of the empirical SSR function the number of coefficients depends on the version of the function
:return: list with the optimal values [r_pv, r_bat, LCOE]
'''
# Checking that country data is a dictionary:
if not isinstance(CountryData, dict):
sys.exit('CountryData must be a dictionnary in the SCoptim function')
# Definition of the objective functionS of the optimization
def f_optim(c):
'''
Objective function. Returns the profitability of the system.
Note that some global variables are used.
Global variables: Demand,eta_inv,eta_bat,CapacityFactorPV,coef,CountryData,
Inv, country
'''
[r_PV, r_bat] = c
# if the ratios are negative, set them to zero and add a penalty to the objective function
penalty_PV = -1E10 * np.minimum(0, r_PV)
penalty_bat = -1E10 * np.minimum(0, r_bat)
r_PV = np.maximum(0, r_PV)
r_bat = np.maximum(0, r_bat)
E = EnergyFlows(r_PV, r_bat, Demand, eta_inv, eta_bat,
CapacityFactorPV, coef)
F = FinancialAnalysis(E, CountryData, Inv)
#print 'PV = ' + str(r_PV) + ', BAT = ' + str(r_bat) + ', PR = ' + str(PR) + ', LCOE = ' + str(LCOE)
return F['LCOE'] + penalty_PV + penalty_bat
def f_optim_0(c):
'''
Objective function. Returns the profitability of the system with r_bat = 0.
Note that some global variables are used.
Global variables: Demand,eta_inv,eta_bat,CapacityFactorPV,coef,CountryData,
Inv, country
'''
[r_PV] = c
r_bat = 0
# if the ratios are negative, set them to zero and add a penalty to the objective function
penalty_PV = -1E10 * np.minimum(0, r_PV)
penalty_bat = -1E10 * np.minimum(0, r_bat)
r_PV = np.maximum(0, r_PV)
r_bat = np.maximum(0, r_bat)
E = EnergyFlows(r_PV, r_bat, Demand, eta_inv, eta_bat,
CapacityFactorPV, coef)
F = FinancialAnalysis(E, CountryData, Inv)
#print 'PV = ' + str(r_PV) + ', BAT = ' + str(r_bat) + ', PR = ' + str(PR) + ', LCOE = ' + str(LCOE)
return F['LCOE'] + penalty_PV + penalty_bat
def f_optim_fixedPV(c):
'''
Objective function. Returns the profitability of the system with r_PV fixed.
Note that some global variables are used.
Global variables: Demand,eta_inv,eta_bat,CapacityFactorPV,coef,CountryData,
Inv, country
'''
r_PV = max_RPV
[r_bat] = c
# if the ratios are negative, set them to zero and add a penalty to the objective function
penalty_PV = -1E10 * np.minimum(0, r_PV)
penalty_bat = -1E10 * np.minimum(0, r_bat)
r_PV = np.maximum(0, r_PV)
r_bat = np.maximum(0, r_bat)
E = EnergyFlows(r_PV, r_bat, Demand, eta_inv, eta_bat,
CapacityFactorPV, coef)
F = FinancialAnalysis(E, CountryData, Inv)
#print 'PV = ' + str(r_PV) + ', BAT = ' + str(r_bat) + ', PR = ' + str(PR) + ', LCOE = ' + str(LCOE)
return F['LCOE'] + penalty_PV + penalty_bat
# Constraints:
cons = ({
'type': 'ineq',
'fun': lambda x: x[0]
}, {
'type': 'ineq',
'fun': lambda x: x[1]
})
bnds = ((0, max_RPV), (0, 10))
# Hard coded system efficiencies:
eta_inv = 0.96
eta_bat = 0.92
Demand = 3500
# Since there are 3 discrete variants of the problem, the optimization is performed 3 times and the best one is selected
# With PV and Battery:
result = optimize.minimize(f_optim, [1.1, 1.1],
method='Nelder-Mead',
tol=1e-5,
constraints=cons,
bounds=bnds).values()
# With PV, without Battery
result2 = optimize.minimize(f_optim_0, [1.1],
method='Nelder-Mead',
tol=1e-5,
constraints=cons,
bounds=bnds).values()
# Without PV, without battery:
E_0 = EnergyFlows(0, 0, Demand, eta_inv, eta_bat, CapacityFactorPV, coef)
F_0 = FinancialAnalysis(E_0, CountryData, Inv)
# Selecting the best solution:
if F_0 <= result2[4] and F_0 <= result[4]:
r_PV = 0
r_bat = 0
LCOE = F_0
elif result2[4] <= F_0 and result2[4] <= result[4]:
r_PV = result2[5][0]
r_bat = 0
LCOE = result2[4]
elif result[4] <= F_0 and result[4] <= result2[4]:
r_PV = result[5][0]
r_bat = result[5][1]
LCOE = result[4]
# if r_PV is unbounded, do the univariate optimization with its max value
if r_PV > max_RPV:
result_fixedPV = optimize.minimize(f_optim_fixedPV, [1.1],
method='Nelder-Mead',
tol=1e-5,
constraints=cons,
bounds=bnds).values()
E_fixedPV = EnergyFlows(max_RPV, 0, Demand, eta_inv, eta_bat,
CapacityFactorPV, coef)
F_fixedPV = FinancialAnalysis(E_fixedPV, CountryData, Inv)
if F_fixedPV <= result_fixedPV[3]:
r_PV = max_RPV
r_bat = 0
LCOE = F_fixedPV
else:
r_PV = max_RPV
r_bat = result_fixedPV[5][0]
LCOE = result_fixedPV[4]
return [r_PV, r_bat, LCOE]
costs = np.arange(100,250,2)
LCOEs = []
BAT = []
PV=[]
LCOE_stor = []
for c in costs:
# Optimisation
Inv['BatteryCost_kWh'] = c
[r_PV, r_bat, LCOE] = SCoptim(CapacityFactorPV,CountryData.loc[country,:].to_dict(),Inv,coef)
BAT.append(r_bat)
LCOEs.append(LCOE)
PV.append(r_PV)
# Recalculating the whole set of values with the optimum inputs:
E = EnergyFlows(r_PV,r_bat,Demand,eta_inv,eta_bat,CapacityFactorPV,coef)
F = FinancialAnalysis(E,CountryData.loc[country,:].to_dict(),Inv)
LCOE_stor.append(F['LCOE_stor'])
# Plotting:
fig4 = plt.figure(2,figsize=[7,5])
plt.subplot(211)
plt.plot(costs,BAT,linestyle='--',linewidth=2, marker='o',label='Battery')
plt.plot(costs,PV,label='PV', marker='o',linewidth=2)
plt.ylabel('Relative PV/Battery sizes [-]')
plt.ylim(0,2.5)
plt.legend(fontsize=16)
plt.grid()
#remove xaxis:
ax = plt.gca()