diff --git a/docs/examples/financial/lcoe_sam_validation.py b/docs/examples/financial/lcoe_sam_validation.py new file mode 100644 index 0000000000..fd4a3a0d6e --- /dev/null +++ b/docs/examples/financial/lcoe_sam_validation.py @@ -0,0 +1,193 @@ +""" +LCOE Calculation +================ + +Example of an LCOE calculation for a utility-scale site in Albuquerque, NM +using the approach implemented by NREL's SAM software +""" + +# This example shows usage of pvlib's lcoe calculation with +# :py:meth:`pvlib.financial.lcoe`, :py:meth:`pvlib.financial.wacc`, +# :py:meth:`pvlib.financial.nominal_to_real`, and +# :py:meth:`pvlib.financial.crf` to generate a Series of annual cost and +# production data, and a real LCOE. TMY GHI, DNI, and DHI irradiance data +# for Albuquerque is loaded from the NSRDB and +# :py:meth:`pvlib.location.get_solarposition` is used with +# :py:meth:`pvlib.irradiance.get_total_irradiance`to calculate POA +# irradiance. DC energy production is calculated with +# :py:meth:`pvlib.pvsystem.pvwatts_dc` to get annual AC power output. +# Capital cost is calculated using the FCR method described here: +# http://samrepo.nrelcloud.org/help/index.html?fin_lcoefcr.htm with real +# discount rates. Construction interest is assumed to be zero. Input values +# with an asterisk were sourced from NREL's ATB projections for a residential +# system in 2022 with moderate +# technological advancement or the set of financial assumptions under which +# NREL produces the ATB. Monthly POA output [kWh/m^2], annual AC output [kWh], +# and LCOE should match values calculated by SAM. + +import numpy as np +import pandas as pd +import datetime +from pvlib import location +from pvlib import irradiance +from pvlib import temperature +from pvlib import pvsystem +from pvlib import inverter +from pvlib import financial +# from .conftest import DATA_DIR + +from pvlib.tests.conftest import DATA_DIR + +# Get annual AC output + +# Installed DC capacity [W] (total is 1 MW) +installed_dc = 1000000 + +# Surface tilt and azimuth +tilt, surface_azimuth = 30, 180 + +# Set Albuquerque as location +lat, lon, elev = 35.054942, -106.540485, 1657.8 +loc = location.Location(lat, lon, altitude=elev) + +# Albuquerque TMY data from NSRDB +data_file = DATA_DIR / 'albuquerque_tmy.csv' +data = pd.read_csv(data_file, skiprows=[0, 1]) + +# Set DatetimeIndex for data +data.set_index(pd.DatetimeIndex(data[['Month', 'Day', 'Hour', 'Minute']] + .apply(lambda x: + datetime.datetime(2022, x['Month'], + x['Day'], + x['Hour'], + x['Minute']), + axis=1)), inplace=True) + +# loc.get_solarposition() assumes UTC unless times is localized +# but Albuquerque is in Etc/GMT-7 +temp = loc.get_solarposition(times=pd.date_range(start=data.index[0] + + pd.Timedelta(7, 'h'), + end=data.index[-1] + + pd.Timedelta(7, 'h'), + freq='1H')) +# Shift index back to align with Etc/GMT-7 +solar_position = temp.set_index(temp.index.shift(periods=-7, freq='1H')) + +# Get POA and apply AOI modifier to direct and diffuse components +poa_irrad = irradiance.get_total_irradiance( + surface_tilt=tilt, surface_azimuth=surface_azimuth, + dni=data['DNI'], ghi=data['GHI'], dhi=data['DHI'], + solar_zenith=solar_position['zenith'], + solar_azimuth=solar_position['azimuth'], + albedo=data['Surface Albedo'])['poa_global'] + +# Calulate and display daily/monthly stats +daily_ghi = data['GHI'].groupby(data.index.map(lambda x: x.date())).sum().\ + mean()/1000 +daily_dhi = data['DHI'].groupby(data.index.map(lambda x: x.date())).sum().\ + mean()/1000 +daily_dni = data['DNI'].groupby(data.index.map(lambda x: x.date())).sum().\ + mean()/1000 +monthly_poa = poa_irrad.groupby(poa_irrad.index.map(lambda x: + x.date().month)).\ + sum()/1000 + +print('Daily average GHI is ' + str(np.round(daily_ghi, 3)) + ' kWh/m^2') +print('Daily average DHI is ' + str(np.round(daily_dhi, 3)) + ' kWh/m^2') +print('Daily average DNI is ' + str(np.round(daily_dni, 2)) + ' kWh/m^2') +print('Monthly POA averages [kWh/m^2]:') +print(monthly_poa) + +# Get system losses +losses = pvsystem.pvwatts_losses()/100 + +# Get cell temperature +cell_temp = temperature.pvsyst_cell(poa_irrad, data['Temperature'], + data['Wind Speed']) + +# Get hourly DC output using PVWatts [W DC] +dc_power = pvsystem.pvwatts_dc(poa_irrad, cell_temp, installed_dc, + -0.0037) * (1 - losses) + +# Get hourly AC output using PVWatts [W AC] +ac_power = inverter.pvwatts(dc_power, installed_dc/1.1) + +# Check that AC power data is evenly spaced over hour increments +if ~np.all(np.unique(np.diff(ac_power.index)/np.timedelta64(1, 'h')) == 1): + raise ValueError + +# Riemann-sum to get annual AC output [kWh] +annual_ac_output = ac_power.sum()/1000 +print('Annual AC output is ' + str(np.round(annual_ac_output, 2)) + ' kWh') + +# Period of financial analysis +n = 20 + +# Assume system degradation rate is 1% +sdr = 0.01 + +# Apply degradation rate to AC production over analysis period +production = np.array([annual_ac_output*(1 - sdr)**i for i in range(n)]) + +# Total installed capital costs [$] * +capex = 1119.82*installed_dc/1000 + +# Fixed O&M costs [$] * +fixed_op_cost = np.full(n, 19.95*installed_dc/1000) + +# Inflation rate * +inflation_r = 0.025 + +# Nominal interest rate * +interest_r = 0.04 + +# Real interest rate +rint = financial.nominal_to_real(interest_r, inflation_r) + +# Nominal internal rate of return * +irr = 0.0775 + +# Real internal rate of return +rroe = financial.nominal_to_real(irr, inflation_r) + +# Fraction of capital cost covered by a loan * +loan_frac = 0.518577595078774 + +# Effective tax rate * +tax_r = 0.2574 + +# Real weighted average cost of capital +my_wacc = financial.wacc(loan_frac, rroe, rint, inflation_r, tax_r) +print('Real weighted average cost of capital is ' + str(np.round(my_wacc, 5))) + +# Depreciation schedule +dep_sch = pd.Series([20, 32, 19.2, 11.52, 11.52, 5.76])/100 + +# Present value of depreciation +pvdep = np.sum([dep_sch.at[j]/((1 + my_wacc)*(1 + inflation_r))**(j+1) + for j in range(len(dep_sch))]) + +# Project financing factor +pff = (1 - (tax_r*pvdep))/(1 - tax_r) + +# Construction financing factor +cff = 1 + +# Capital recovery factor +my_crf = financial.crf(my_wacc, n) + +# Fixed charge rate +fcr = my_crf*pff*cff +print('Fixed charge rate is ' + str(np.round(fcr, 5))) + +debt_tenor = n + +# Annuity (annual payment) on total capital cost [$] +cap_cost = np.full(n, capex*fcr) +print('Annual payment on capital cost is $' + str(np.round(cap_cost[0], 2))) + +# Call lcoe() +my_lcoe = financial.lcoe(production=production, cap_cost=cap_cost, + fixed_om=fixed_op_cost) + +print('Real LCOE = ' + str(my_lcoe) + str(' cents/kWh')) diff --git a/docs/examples/financial/simple_lcoe_calculator.py b/docs/examples/financial/simple_lcoe_calculator.py new file mode 100644 index 0000000000..1aae51a481 --- /dev/null +++ b/docs/examples/financial/simple_lcoe_calculator.py @@ -0,0 +1,65 @@ +""" +LCOE Calculation +================ + +Example of an LCOE calculation using an approach implemented in NREL's "Simple +LCOE Calculator", accessible at http://www.nrel.gov/analysis/tech-lcoe.html +""" +# %% +# This example shows basic usage of pvlib's lcoe calculation with +# :py:meth:`pvlib.financial.lcoe` and :py:meth:`pvlib.financial.crf`. +# The example shown here will generate a Series of annual cost and production +# data, and a numerical LCOE. To be comparable with NREL's implemenation, +# this example adheres to the following assumptions: that energy production +# and O&M costs are constant and that the entire project is financed with a +# loan. Input values for CAPEX, capacity factor, and O&M were sourced from +# NREL's ATB for a residential system in 2022 located in Resource Class 5 +# with moderate technological advancement. The discount rate is set to the +# value recommended in NREL's implementation. + +import numpy as np +import pandas as pd +from pvlib import financial + +# Analysis period +n = 20 + +# Capacity factor +cf = 0.15357857 + +# Constant annual energy production +energy = np.full(n, cf*8760) + +# Real discount rate +discount_rate = 0.03 + +# Capital recovery factor +my_crf = financial.crf(discount_rate, n) + +# CAPEX +capex = 2443.45 + +# Fraction of capital cost +loan_frac = 1 + +# Annual capital costs +cap_cost = np.array([capex*loan_frac*my_crf for i in range(n)]) + +# Constant annual O&M +fixed_om = pd.Series(data=[26.98 for j in range(n)]) + +# Put data in table and display +table = pd.DataFrame(columns=['Production [kWh/kW]', 'Capital cost [$/kW]', + 'O&M [$/kW]']) +table['Production [kWh/kW]'] = energy +table['Capital cost [$/kW]'] = cap_cost +table['O&M [$/kW]'] = fixed_om +table.index.name = 'Year' +table + +# %% +# Get LCOE + +my_lcoe = financial.lcoe(production=energy, cap_cost=cap_cost, + fixed_om=fixed_om) +print('LCOE = ' + str(my_lcoe) + str(' cents/kWh')) diff --git a/docs/sphinx/source/reference/financial.rst b/docs/sphinx/source/reference/financial.rst new file mode 100644 index 0000000000..1d2b9d73ff --- /dev/null +++ b/docs/sphinx/source/reference/financial.rst @@ -0,0 +1,13 @@ +.. currentmodule:: pvlib + +Financial +========= + +.. autosummary:: + :toctree: generated/ + + financial.lcoe + financial.crf + financial.nominal_to_real + financial.real_to_nominal + financial.wacc \ No newline at end of file diff --git a/docs/sphinx/source/reference/index.rst b/docs/sphinx/source/reference/index.rst index 9083f85bdd..8894e73986 100644 --- a/docs/sphinx/source/reference/index.rst +++ b/docs/sphinx/source/reference/index.rst @@ -20,3 +20,4 @@ API reference bifacial scaling location + financial diff --git a/docs/sphinx/source/whatsnew/v0.10.2.rst b/docs/sphinx/source/whatsnew/v0.10.2.rst index 3b82d98613..a5dd8f825c 100644 --- a/docs/sphinx/source/whatsnew/v0.10.2.rst +++ b/docs/sphinx/source/whatsnew/v0.10.2.rst @@ -24,6 +24,11 @@ Enhancements * :py:class:`~pvlib.pvsystem.PVSystem` objects with a single :py:class:`~pvlib.pvsystem.Array` can now be created without wrapping the ``Array`` in a list first. (:issue:`1831`, :pull:`1854`) +* Added :py:mod:`pvlib.financial` module with functions + :py:func:`~pvlib.financial.lcoe`, :py:func:`~pvlib.financial.crf`, + :py:func:`~pvlib.financial.nominal_to_real`, + :py:func:`~pvlib.financial.real_to_nominal`, and + :py:func:`~pvlib.financial.wacc` (:pull:`1687`) Bug fixes @@ -84,3 +89,4 @@ Contributors * Will Holmgren (:ghuser:`wholmgren`) * Mark Mikofski (:ghuser:`mikofski`) * Kevin Anderson (:ghuser:`kandersolar`) +* Emma Cooper (:ghuser:`eccoope`) diff --git a/docs/sphinx/source/whatsnew/v0.9.5.rst b/docs/sphinx/source/whatsnew/v0.9.5.rst index 23766d566e..3fb3bb3353 100644 --- a/docs/sphinx/source/whatsnew/v0.9.5.rst +++ b/docs/sphinx/source/whatsnew/v0.9.5.rst @@ -37,6 +37,7 @@ Enhancements * Use `Horner's Method `_ to evaluate polynomials in :py:func:`~pvlib.irradiance.disc`, may decrease runtime by 20%. (:issue:`1180`, :pull:`1183`) + Bug fixes ~~~~~~~~~ @@ -65,6 +66,8 @@ Testing Documentation ~~~~~~~~~~~~~ * Remove LGTM.com integration. (:issue:`1550`, :pull:`1651`) +* Added two examples demonstrating how :py:mod:`pvlib.financial` can + be used (:pull:`1687`) Benchmarking ~~~~~~~~~~~~~ diff --git a/pvlib/data/albuquerque_tmy.csv b/pvlib/data/albuquerque_tmy.csv new file mode 100644 index 0000000000..979db68cba --- /dev/null +++ b/pvlib/data/albuquerque_tmy.csv @@ -0,0 +1,8763 @@ +Source,Location ID,City,State,Country,Latitude,Longitude,Time Zone,Elevation,Local Time Zone,Dew Point Units,DHI Units,DNI Units,GHI Units,Temperature Units,Pressure Units,Wind Direction Units,Wind Speed Units,Surface Albedo Units,Version +NSRDB,93740,-,-,-,35.05,-106.54,-7,1636,-7,c,w/m2,w/m2,w/m2,c,mbar,Degrees,m/s,N/A,3.2.0 +Year,Month,Day,Hour,Minute,DNI,DHI,GHI,Dew Point,Temperature,Pressure,Wind Direction,Wind Speed,Surface Albedo +2020,1,1,0,30,0,0,0,-9.1,-3.1,834,298,1.6,0.21 +2020,1,1,1,30,0,0,0,-9.5,-3.6,833,298,1.5,0.21 +2020,1,1,2,30,0,0,0,-9.9,-4.1000000000000005,833,298,1.5,0.21 +2020,1,1,3,30,0,0,0,-10.3,-4.5,832,298,1.5,0.21 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lcoe(production=None, cap_cost=None, fixed_om=None): + """ + Real levelized cost of electricity (LCOE). + + Includes cost of capital and fixed operations and maintenance (O&M). + Described in [1]_, pp. 43 and 47-48, and defined here as + .. math:: + \frac{\text{total capital cost} + \text{total fixed O&M costs}} + {\text{lifetime energy production}} + + Parameters + ---------- + production : np.array, or pd.Series, default None + Annual production [kWh/kW installed] + cap_cost : np.array, or pd.Series, default None + Initial and annual payments on capital costs using real discount rates + [$/kW installed] + fixed_om : np.array, or pd.Series, default None + Annual payments on operations and maintenance costs [$/kW installed] + + Returns + ---------- + LCOE [cents/kWh] + + References + ---------- + .. [1] W. Short, D. J. Packey, and T. Holt, "A Manual for the Economic + Evaluation of Energy Efficiency and Renewable Energy Technologies", + NREL/TP-462-5173, 1995. + """ + + cost = cap_cost + fixed_om + return np.nansum(cost)*100/np.nansum(production) + + +def crf(rate, n_years): + """ + Capital recovery factor. + + Described in [1]_, pp. 23. + + Parameters + ---------- + rate : float + Real (as opposed to nominal) rate at which CRF is calculated + n_years: int + Number of years over which CRF is calculated + + Returns + ---------- + crf : float + Real capital recovery factor + + References + ---------- + .. [1] W. Short, D. J. Packey, and T. Holt, "A Manual for the Economic + Evaluation of Energy Efficiency and Renewable Energy Technologies", + NREL/TP-462-5173, 1995. + """ + + return (rate*(1+rate)**n_years)/((1+rate)**n_years-1) + + +def nominal_to_real(nominal, rate): + + """ + Convert nominal to real (inflation-adjusted) rate. + + Described in [1]_, pp. 6. + Parameters + ---------- + nominal : float + Nominal rate (does not include adjustments for inflation) + rate : float + Inflation rate + + Returns + ---------- + Real rate (includes adjustments for inflation) + + References + ---------- + .. [1] W. Short, D. J. Packey, and T. Holt, "A Manual for the Economic + Evaluation of Energy Efficiency and Renewable Energy Technologies", + NREL/TP-462-5173, 1995. + """ + + return (1+nominal)/(1+rate)-1 + + +def real_to_nominal(real, rate): + + """ + Convert real (inflation-adjusted) rate to nominal rate. + + Described by [1]_, pp. 6. + + Parameters + ---------- + real : float + Real rate (includes adjustments for inflation) + rate : float + Inflation rate + + Returns + ---------- + Nominal rate (does not include adjustments for inflation) + + References + ---------- + .. [1] W. Short, D. J. Packey, and T. Holt, "A Manual for the Economic + Evaluation of Energy Efficiency and Renewable Energy Technologies", + NREL/TP-462-5173, 1995. + """ + + return (real+1)*(1+rate)-1 + + +def wacc(loan_frac, rroi, rint, inflation_rate, tax_rate): + + """ + Weighted average cost of capital (WACC). + + The average expected rate that is paid to finance assets [1]_. + + Parameters + ---------- + loan_frac : float + Fraction of capital cost paid for with a loan + rroi : float + Real internal rate of return on investment + rint : float + Real interest rate + inflation_rate : float + Effective inflation rate + tax_rate : float + Tax rate + + Returns + ---------- + wacc : float + Weighted average cost of capital + + References + ---------- + .. [1] NREL, "Equations and Variables in the ATB", Available: + https://atb.nrel.gov/electricity/2022/index + """ + + numerator = (1 + ((1 - loan_frac)*((1 + rroi)*(1 + inflation_rate)-1)) + + loan_frac*((1 + rint)*(1 + inflation_rate) + - 1)*(1 - tax_rate)) + denominator = 1 + inflation_rate + return numerator/denominator - 1 diff --git a/pvlib/tests/test_financial.py b/pvlib/tests/test_financial.py new file mode 100644 index 0000000000..f25a8ee6dc --- /dev/null +++ b/pvlib/tests/test_financial.py @@ -0,0 +1,84 @@ +import pandas as pd +import numpy as np +from pvlib import financial +from numpy.testing import assert_allclose + + +def test_lcoe_series(): + n, cf = 20, 0.5 + production = pd.Series(data=[cf*8670 for j in range(n)]) + capex, loan_frac, my_crf, debt_tenor = 1000, 0.5, 0.05, n + cap_cost = pd.Series(data=[capex*loan_frac*my_crf for i in + range(debt_tenor)] + + [0 for j in range(debt_tenor, n)]) + base_om = 25 + fixed_om = pd.Series(data=[base_om for j in range(n)]) + + expected = 1.1534025374855825 + out = financial.lcoe(production=production, cap_cost=cap_cost, + fixed_om=fixed_om) + + assert_allclose(expected, out) + + +def test_lcoe_arrays(): + n, cf = 20, 0.5 + production = np.full(n, cf*8670) + capex, loan_frac, my_crf, debt_tenor = 1000, 0.5, 0.05, n + cap_cost = np.array([capex*loan_frac*my_crf for i in range(debt_tenor)] + + [0 for j in range(debt_tenor, n)]) + base_om = 25 + fixed_om = np.full(n, base_om) + expected = 1.1534025374855825 + out = financial.lcoe(production=production, cap_cost=cap_cost, + fixed_om=fixed_om) + assert_allclose(expected, out) + + +def test_lcoe_nans(): + n, cf = 20, 0.5 + production = np.full(n, cf*8670) + capex, loan_frac, my_crf, debt_tenor = 1000, 0.5, 0.05, n + cap_cost = np.array([capex*loan_frac*my_crf for i in range(debt_tenor)] + + [0 for j in range(debt_tenor, n)]) + base_om = 25. + fixed_om = np.full(n, base_om) + cap_cost[1] = np.nan + fixed_om[2] = np.nan + production[3] = np.nan + expected = 1.092697140775815 + out = financial.lcoe(production=production, cap_cost=cap_cost, + fixed_om=fixed_om) + assert_allclose(expected, out) + + +def test_crf(): + rate, n = 0.05, 20 + expected = 0.08024258719069129 + out = financial.crf(rate, n) + assert_allclose(expected, out) + + +def test_nominal_to_real(): + nominal, rate = 0.04, 0.025 + expected = 0.014634146341463428 + out = financial.nominal_to_real(nominal, rate) + assert_allclose(expected, out) + + +def test_real_to_nominal(): + real, rate = 0.04, 0.025 + expected = 0.066 + out = financial.real_to_nominal(real, rate) + assert_allclose(expected, out) + + +def test_wacc(): + loan_frac = 0.5 + rroi = 0.12 + rint = 0.04 + inflation_rate = 0.025 + tax_rate = 0.28 + expected = 0.07098536585365856 + out = financial.wacc(loan_frac, rroi, rint, inflation_rate, tax_rate) + assert_allclose(expected, out)