Quickstart

Evaluating the performance of a hybrid power plant using HyDesign

In this notebook we will evaluate a simplified hybrid power plant design in a specific location.

A simplified hybrid power plant design consists on selecting the following parameters:

Wind Plant design:

1. Number of wind turbines in the wind plant [-] (Nwt)

2. Wind power installation density [MW/km2] (wind_MW_per_km2): This parameter controls how closely spaced are the turbines, which in turns affect how much wake losses are present.

PV Plant design:

3. Solar plant power capacity [MW] (solar_MW)

Battery Storage design:

4. Battery power [MW] (b_P)

5. Battery energy capacity in hours [MWh] (b_E_h): Battery storage capacity in hours of full battery power (b_E = b_E_h * b_P).

6. Cost of battery power fluctuations in peak price ratio [-] (cost_of_batt_degr): This parameter controls how much penalty is given to do ramps in battery power in the HPP operation.

Imports

Install hydesign if needed. Import basic libraries. Import HPP model assembly class. Import the examples file path.

# Install hydesign if needed
import importlib
if not importlib.util.find_spec("hydesign"):
    !pip install git+https://gitlab.windenergy.dtu.dk/TOPFARM/hydesign.git

import os
import time
import yaml
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

from hydesign.assembly.hpp_assembly import hpp_model
from hydesign.examples import examples_filepath

Specifying the site

Hydesign, provides example data from several sites in India and Europe.

The site coordinates (longitude, latitude, and altitude) are given in examples_sites.csv.

examples_sites = pd.read_csv(f'{examples_filepath}examples_sites.csv', index_col=0, sep=';')
examples_sites

	case	name	longitude	latitude	altitude	input_ts_fn	sim_pars_fn	price_fn	price_col	H2_demand_col	Unnamed: 11	input_HA_ts_fn	price_up_ts	price_dwn_ts
0	India	Indian_site_good_wind	77.500226	8.334294	679.803454	India/GWA2/input_ts_Indian_site_good_wind.csv	India/hpp_pars.yml	India/Indian_elec_price_t.csv	Price	India/H2_demand.csv	NaN	NaN	NaN	NaN
1	India	Indian_site_good_solar	68.542204	23.542099	29.883557	India/GWA2/input_ts_Indian_site_good_solar.csv	India/hpp_pars.yml	India/Indian_elec_price_t.csv	Price	India/H2_demand.csv	NaN	NaN	NaN	NaN
2	India	Indian_site_bad_solar_bad_wind	77.916878	17.292316	627.424643	India/GWA2/input_ts_Indian_site_bad_solar_bad_...	India/hpp_pars.yml	India/Indian_elec_price_t.csv	Price	India/H2_demand.csv	NaN	NaN	NaN	NaN
3	Europe	France_good_solar	4.229736	44.422011	204.000000	Europe/GWA2/input_ts_France_good_solar.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	FR_R	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
4	Europe	France_good_wind	-0.864258	48.744116	302.000000	Europe/GWA2/input_ts_France_good_wind.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	FR_R	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
5	Europe	France_bad_solar_n_wind	2.167969	47.428087	140.000000	Europe/GWA2/input_ts_France_bad_solar_n_wind.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	FR_R	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
6	Europe	Germany_bad_solar_n_wind	10.766602	49.310798	442.000000	Europe/GWA2/input_ts_Germany_bad_solar_n_wind.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	DE_ME	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
7	Europe	Germany_good_wind	7.873535	53.287111	5.000000	Europe/GWA2/input_ts_Germany_good_wind.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	DE_NW	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
8	Europe	Denmark_good_solar	11.813965	55.397760	42.000000	Europe/GWA2/input_ts_Denmark_good_solar.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	DK_E	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
9	Europe	Denmark_good_wind	8.594398	56.227322	85.000000	Europe/GWA2/input_ts_Denmark_good_wind.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	DK_W	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
10	Europe	Denmark_offshore	7.906111	55.529722	85.000000	Europe/GWA2/input_ts_Denmark_offshore.csv	Europe/hpp_pars_offshore.yml	Europe/2030-EL_PRICE.csv	DK_W	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
11	Europe	Denmark_good_wind_BM	8.594398	56.227322	85.000000	Europe/GWA2_BM/input_ts_Denmark_good_wind_DA.csv	Europe/hpp_pars.yml	Europe/2030-EL_PRICE.csv	DK_W	Europe/H2_demand.csv	NaN	Europe/GWA2_BM/input_ts_Denmark_good_wind_HA.csv	Europe/BM_Prices/Up_reg_price.csv	Europe/BM_Prices/Down_reg_price.csv
12	Europe	Denmark_hybridization_wind_Norhede_Hjortmose	8.366400	56.095400	16.662000	Europe/GWA2/input_ts_Denmark_hybridization_win...	Europe/hpp_pars_Hjortmose.yml	Europe/2030-EL_PRICE.csv	DK_W	Europe/H2_demand.csv	NaN	NaN	NaN	NaN
13	Europe	Denmark_hybridization_solar_Langelinie	11.290641	54.717469	0.042000	Europe/GWA2/input_ts_Denmark_hybridization_sol...	Europe/hpp_pars_Langelinie.yml	Europe/2030-EL_PRICE.csv	DK_E	Europe/H2_demand.csv	NaN	NaN	NaN	NaN

select a site to run

name = 'France_good_wind'
ex_site = examples_sites.loc[examples_sites.name == name]

longitude = ex_site['longitude'].values[0]
latitude = ex_site['latitude'].values[0]
altitude = ex_site['altitude'].values[0]

Input data: weather and electricity price

For each site a csv input file is provided. This file contains the weather and the spot market electricity prices.

The columns required are:

• Wind speed at multiple heights (WS_hh, where hh is the height in meters). In order to estimate the PV cell temperature, it is important to have a wind speed close to the ground (WS_1).

• (optional) Wind direction at multiple heights (WD_hh, where hh is the height in meters). Wind directions can be used when the layout of the wind farm is known and therefore the wind generation depends on the wind direction.

• Air temperature in Kelvin close to the ground (temp_air_1)

• Global horizontal irradiance (ghi).

• Direct normal irradiance (dni).

• Diffuse horizontal irradiance (dhi).

• Spot market electricity prices (Price)

input_ts_fn = examples_filepath+ex_site['input_ts_fn'].values[0]

input_ts = pd.read_csv(input_ts_fn, index_col=0, parse_dates=True)

required_cols = [col for col in input_ts.columns if 'WD' not in col]
input_ts = input_ts.loc[:,required_cols]
input_ts

	WS_1	WS_50	WS_100	WS_150	WS_200	temp_air_1	ghi	dni	dhi	Price
2012-01-01 00:00:00	3.816262	9.189450	11.084209	12.271178	13.193283	284.873662	0.10670	0.0	0.10670	32.685
2012-01-01 01:00:00	3.433942	8.425198	10.193588	11.295483	12.177159	284.759079	0.05335	0.0	0.05335	32.685
2012-01-01 02:00:00	3.401840	8.457382	10.257751	11.500057	12.475967	284.682409	0.00000	0.0	0.00000	32.685
2012-01-01 03:00:00	3.552851	8.750878	10.595812	11.846432	12.862474	284.804835	0.00000	0.0	0.00000	32.685
2012-01-01 04:00:00	3.563602	8.849321	10.730704	12.023872	13.075707	284.912742	0.00000	0.0	0.00000	32.685
...	...	...	...	...	...	...	...	...	...	...
2012-12-30 19:00:00	3.431328	8.738007	10.644316	11.514788	12.815824	281.205509	0.00000	0.0	0.00000	37.591
2012-12-30 20:00:00	3.522005	8.956219	10.906332	11.806788	13.153907	281.139846	0.00000	0.0	0.00000	35.839
2012-12-30 21:00:00	3.546788	9.081438	11.071820	12.064809	13.412334	280.716650	0.00000	0.0	0.00000	35.362
2012-12-30 22:00:00	3.613134	9.352224	11.424145	12.542857	13.966094	280.646177	0.00000	0.0	0.00000	34.468
2012-12-30 23:00:00	3.672954	9.526146	11.639926	12.831741	14.247031	280.627905	0.00000	0.0	0.00000	33.417

8760 rows × 10 columns

Additional data

Each region has a different hybrid power plant evaluation parameter file (hpp_pars.yml). This file contains all the assumptions on the valuation of a hyrbid power plant.

In the examples, the Indian sites have specified a requiredment to provide power at peak hours. This requirement is specified by setting the minimum number of full power hours at peak prices times per day.

For example the Indian case penalty has expected hours of 0.85*3= 2.55:

n_full_power_hours_expected_per_day_at_peak_price: 2.55

While the Europe sites have no penalty.

n_full_power_hours_expected_per_day_at_peak_price: 0

sim_pars_fn = examples_filepath+ex_site['sim_pars_fn'].values[0]

with open(sim_pars_fn) as file:
    sim_pars = yaml.load(file, Loader=yaml.FullLoader)

print(sim_pars_fn)
sim_pars

c:/sandbox/repo/topfarm/hydesign/hydesign/examples/Europe/hpp_pars.yml

{'G_MW': 300,
 'year': '2012',
 'N_life': 25,
 'wind_turbine_cost': 640000,
 'wind_civil_works_cost': 260000,
 'wind_fixed_onm_cost': 12600,
 'wind_variable_onm_cost': 1.35,
 'd_ref': 145,
 'hh_ref': 100,
 'p_rated_ref': 5.0,
 'wpp_efficiency': 1,
 'wind_deg_yr': [0, 25],
 'wind_deg': [0, 0.25],
 'share_WT_deg_types': 0.5,
 'solar_PV_cost': 110000,
 'solar_hardware_installation_cost': 100000,
 'solar_inverter_cost': 20000,
 'solar_fixed_onm_cost': 4500,
 'land_use_per_solar_MW': 0.01226,
 'tracking': 'No',
 'pv_deg_yr': [0, 1, 25],
 'pv_deg': [0.03, 0.03, 0.28],
 'latitude': None,
 'longitude': None,
 'altitude': None,
 'battery_energy_cost': 62000,
 'battery_power_cost': 16000,
 'battery_BOP_installation_commissioning_cost': 80000,
 'battery_control_system_cost': 2250,
 'battery_energy_onm_cost': 0,
 'battery_depth_of_discharge': 0.9,
 'battery_charge_efficiency': 0.985,
 'battery_price_reduction_per_year': 0.05,
 'min_LoH': 0.7,
 'n_full_power_hours_expected_per_day_at_peak_price': 0,
 'peak_hr_quantile': 0.9,
 'price_H2': 5,
 'storage_eff': 0.9,
 'ptg_deg': 0.99,
 'hhv': 39.3,
 'water_consumption': 9.4,
 'electrolyzer_capex_cost': 800000,
 'electrolyzer_opex_cost': 16000,
 'electrolyzer_power_electronics_cost': 0,
 'water_cost': 4,
 'water_treatment_cost': 2,
 'H2_storage_capex_cost': 300,
 'H2_storage_opex_cost': 3,
 'H2_transportation_cost': 5,
 'H2_transportation_distance': 0,
 'penalty_factor_H2': 0,
 'electrolyzer_eff_curve_name': 'PEM electrolyzer H2 production',
 'min_power_standby': 0.0,
 'hpp_BOS_soft_cost': 119940,
 'hpp_grid_connection_cost': 50000,
 'land_cost': 300000,
 'wind_WACC': 0.06,
 'solar_WACC': 0.06,
 'battery_WACC': 0.06,
 'tax_rate': 0.22,
 'ptg_WACC': 0.08,
 'phasing_yr': [-1, 0],
 'phasing_CAPEX': [1, 1],
 'inflation_yr': [-3, 0, 1, 25],
 'inflation': [0.1, 0.1, 0.06, 0.06],
 'ref_yr_inflation': 0,
 'depreciation_yr': [0, 25],
 'depreciation': [0, 1],
 'bi_directional_status': 0,
 'penalty_BM': 2000,
 'era5_zarr': '/groups/reanalyses/era5/app/era5.zarr',
 'ratio_gwa_era5': '/groups/INP/era5/ratio_gwa2_era5.nc',
 'era5_ghi_zarr': '/groups/INP/era5/ghi.zarr',
 'elevation_fn': '/groups/INP/era5/SRTMv3_plus_ViewFinder_coarsen.nc'}

Wind Turbine parameters:

1. Hub height [m]

2. Rotor diameters [m]

3. Rated power of the wind turbine [MW] (p_rated)

PV parameters:

4. Surface tilt [deg] (surface_tilt)

5. Surface azimuth [deg] (surface_azimuth)

6. DC-AC ratio [-] (solar_DCAC): This parameter controls how much over-planting of PV (in DC power) is connected to the inverters. It is common practice in PV design to have solar_DCAC = 1.5.

rotor_diameter_m = 220
hub_height_m = 130
wt_rated_power_MW = 10
surface_tilt_deg = 35
surface_azimuth_deg = 180
DC_AC_ratio = 1.5

Initializing the HPP model

Initialize the HPP model (hpp_model class) with the coordinates and the necessary input files.

hpp = hpp_model(
        latitude=latitude,
        longitude=longitude,
        altitude=altitude,
        rotor_diameter_m = rotor_diameter_m,
        hub_height_m = hub_height_m,
        wt_rated_power_MW = wt_rated_power_MW,
        surface_tilt_deg = surface_tilt_deg,
        surface_azimuth_deg = surface_azimuth_deg,
        DC_AC_ratio = DC_AC_ratio,
        num_batteries = 5,
        work_dir = './',
        sim_pars_fn = sim_pars_fn,
        input_ts_fn = input_ts_fn,
)

Fixed parameters on the site
-------------------------------
longitude = -0.864258
latitude = 48.744116
altitude = 302.0

Extract data from DTU’s ERA5 database

# price_fn = examples_filepath+ex_site['price_fn'].values[0]
# price = pd.read_csv(price_fn,index_col=0, parse_dates=True)[ex_site.price_col.values[0]]

# hpp = hpp_model_simple(
#         latitude,
#         longitude,
#         altitude,
#         rotor_diameter_m = rotor_diameter_m,
#         hub_height_m = hub_height_m,
#         wt_rated_power_MW = wt_rated_power_MW,
#         surface_tilt_deg = surface_tilt_deg,
#         surface_azimuth_deg = surface_azimuth_deg,
#         DC_AC_ratio = DC_AC_ratio,
#         num_batteries = 1,
#         work_dir = './',
#         sim_pars_fn = sim_pars_fn,
#         input_ts_fn=None,
#         price_fn=price,
# )

Evaluating the HPP model

start = time.time()

Nwt = 20
wind_MW_per_km2 = 7
solar_MW = 150
b_P = 20
b_E_h  = 3
cost_of_batt_degr = 5
clearance = hub_height_m - rotor_diameter_m / 2
sp = 4 * wt_rated_power_MW * 10 ** 6 / np.pi / rotor_diameter_m ** 2

x = [# Wind plant design
    clearance, sp, wt_rated_power_MW, Nwt, wind_MW_per_km2,
    # PV plant design
    solar_MW,  surface_tilt_deg, surface_azimuth_deg, DC_AC_ratio,
    # Energy storage & EMS price constrains
    b_P, b_E_h, cost_of_batt_degr]

outs = hpp.evaluate(*x)

hpp.print_design(x, outs)

end = time.time()
print(f'exec. time [min]:', (end - start)/60 )

Design:
---------------
clearance [m]: 20.000
sp [W/m2]: 263.066
p_rated [MW]: 10.000
Nwt: 20.000
wind_MW_per_km2 [MW/km2]: 7.000
solar_MW [MW]: 150.000
surface_tilt [deg]: 35.000
surface_azimuth [deg]: 180.000
DC_AC_ratio: 1.500
b_P [MW]: 20.000
b_E_h [h]: 3.000
cost_of_battery_P_fluct_in_peak_price_ratio: 5.000


NPV_over_CAPEX: 0.716
NPV [MEuro]: 242.707
IRR: 0.115
LCOE [Euro/MWh]: 35.589
Revenues [MEuro]: 33.246
CAPEX [MEuro]: 339.079
OPEX [MEuro]: 5.647
Wind CAPEX [MEuro]: 222.901
Wind OPEX [MEuro]: 4.635
PV CAPEX [MEuro]: 50.250
PV OPEX [MEuro]: 1.012
Batt CAPEX [MEuro]: 6.374
Batt OPEX [MEuro]: 0.000
Shared CAPEX [MEuro]: 59.553
Shared Opex [MEuro]: 0.000
penalty lifetime [MEuro]: 0.000
AEP [GWh]: 874.413
GUF: 0.333
grid [MW]: 300.000
wind [MW]: 200.000
solar [MW]: 150.000
Battery Energy [MWh]: 60.000
Battery Power [MW]: 20.000
Total curtailment [GWh]: 27.870
Total curtailment with deg [GWh]: 5.017
Awpp [km2]: 28.571
Apvp [km2]: 1.839
Plant area [km2]: 28.571
Rotor diam [m]: 220.000
Hub height [m]: 130.000
Number of batteries used in lifetime: 2.000
Break-even PPA price [Euro/MWh]: 23.787
Capacity factor wind [-]: 0.391

exec. time [min]: 0.17602744897206624

Understanding the sub-models

Plot an interactive N2 diagram (or N-squared diagram) to explore all components and interfaces between system elements.

Hydesign consists of several submodels:

Wind turbines/plant:

• genericWT: generic wind turbine model

• genericWake: generic wake losses model

• wpp: wind power plant

• wpp_cost: wind power plant cost model

PV plant:

• pvp: PV power plant

• pvp_degradation_linear: PV degradation model

• pvp_cost: PV power plant cost model

Battery:

• battery_degradation: Battery degradation model

• battery_cost: Battery cost model

HPP operation

• ems: (Energy Management System) Idealized hpp operation design. This component optimizes the operation of a HPP without considering degradation (PV nor Battery).

• ems_long_term_operation: This component executes the hpp operation changes in expected generation profiles and/or degradation on battery. This component tries to follow the operation plan (results of ems).

HPP

• shared_costs: Shared HPP infrastructure cost model

• finance: HPP financial performance metrics model

from openmdao.visualization.n2_viewer.n2_viewer import n2
#n2(hpp.prob) ## execute to generate an interactive diagram

# Static view
from IPython import display
display.Image("./n2.png")

Plot the HPP operation

b_E_SOC_t = hpp.prob.get_val('ems.b_E_SOC_t')
b_t = hpp.prob.get_val('ems.b_t')
price_t = hpp.prob.get_val('ems.price_t')

wind_t = hpp.prob.get_val('ems.wind_t')
solar_t = hpp.prob.get_val('ems.solar_t')
hpp_t = hpp.prob.get_val('ems.hpp_t')
hpp_curt_t = hpp.prob.get_val('ems.hpp_curt_t')
grid_MW = hpp.prob.get_val('ems.G_MW')

n_days_plot = 14
plt.figure(figsize=[12,4])
plt.plot(price_t[:24*n_days_plot], label='price')
plt.plot(b_E_SOC_t[:24*n_days_plot], label='SoC [MWh]')
plt.plot(b_t[:24*n_days_plot], label='Battery P [MW]')
plt.xlabel('time [hours]')
plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.15),
           ncol=3, fancybox=0, shadow=0)

plt.figure(figsize=[12,4])
plt.plot(wind_t[:24*n_days_plot], label='wind')
plt.plot(solar_t[:24*n_days_plot], label='PV')
plt.plot(hpp_t[:24*n_days_plot], label='HPP')
plt.plot(hpp_curt_t[:24*n_days_plot], label='HPP curtailed')
plt.axhline(grid_MW, label='Grid MW', color='k')
plt.xlabel('time [hours]')
plt.ylabel('Power [MW]')
plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.15),
           ncol=5, fancybox=0, shadow=0)

<matplotlib.legend.Legend at 0x1ec5a82fed0>

Plot battery, wind and PV degradation

A yearly loss factor is computed to plot the wind and battery degradation.

N_life = hpp.sim_pars['N_life']
life_h = N_life*365*24
age = np.arange(life_h)/(24*365)

SoH = hpp.prob.get_val('battery_degradation.SoH')
SoH_all = np.copy(hpp.prob.get_val('battery_loss_in_capacity_due_to_temp.SoH_all'))

wind_t_ext = hpp.prob.get_val('ems_long_term_operation.wind_t_ext')
wind_t_ext_deg = hpp.prob.get_val('ems_long_term_operation.wind_t_ext_deg')

solar_t_ext = hpp.prob.get_val('ems_long_term_operation.solar_t_ext')
solar_t_ext_deg = hpp.prob.get_val('ems_long_term_operation.solar_t_ext_deg')

hpp_t = hpp.prob.get_val('ems.hpp_t')
hpp_t_with_deg = hpp.prob.get_val('ems_long_term_operation.hpp_t_with_deg')

df = pd.DataFrame(
    index=pd.date_range(start='2023-01-01',end='2048-01-01',freq='1H'),
    )
df['wind_t_ext'] = np.NaN
df['wind_t_ext_deg'] = np.NaN
df['solar_t_ext'] = np.NaN
df['solar_t_ext_deg'] = np.NaN
df['hpp_t'] = np.NaN
df['hpp_t_with_deg'] = np.NaN

df.iloc[:len(age):,0] = wind_t_ext
df.iloc[:len(age):,1] = wind_t_ext_deg
df.iloc[:len(age):,2] = solar_t_ext
df.iloc[:len(age):,3] = solar_t_ext_deg
df.iloc[:len(age):,4] = hpp_t
df.iloc[:len(age):,5] = hpp_t_with_deg

df = df.dropna(axis=0)

df_year = df.groupby(df.index.year).mean()
df_year['age'] = np.arange(len(df_year))+0.5


df_year['eff_wind_ts_deg'] = df_year.wind_t_ext_deg.values/df_year.wind_t_ext.values
df_year['eff_solar_ts_deg'] = df_year.solar_t_ext_deg.values/df_year.solar_t_ext.values
df_year['eff_hpp_ts_deg'] = df_year.hpp_t_with_deg.values/df_year.hpp_t.values

C:\Users\mikf\AppData\Local\Temp\ipykernel_3116\3601579617.py:2: FutureWarning: 'H' is deprecated and will be removed in a future version, please use 'h' instead.
  index=pd.date_range(start='2023-01-01',end='2048-01-01',freq='1H'),

plt.figure(figsize=[12,4])
plt.plot(df_year.age.values, df_year.eff_wind_ts_deg.values, label='Wind degr.')
plt.plot(df_year.age.values, df_year.eff_solar_ts_deg.values, label='Solar degr.')
plt.plot(df_year.age.values, df_year.eff_hpp_ts_deg.values,  '--', label='HPP degr.')
plt.plot( age, SoH, label='Battery degr.')
plt.plot( age, SoH_all, label='Battery degr. and low temp. losses', alpha=0.5)

plt.legend()

plt.xlabel('age [years]')
plt.ylabel('CF_deg/CF for wind, solar and hpp [-] \n Battery loss of storing capacity [-]')

Text(0, 0.5, 'CF_deg/CF for wind, solar and hpp [-] \n Battery loss of storing capacity [-]')

Compare ideal operation (ems) wit h actual long-term opertation with degradation

#solar_t = hpp.prob.get_val('ems.solar_t_ext')
b_E_SOC_t = hpp.prob.get_val('ems.b_E_SOC_t')
hpp_t = hpp.prob.get_val('ems.hpp_t')
hpp_curt_t = hpp.prob.get_val('ems.hpp_curt_t')

b_E_SOC_t_with_deg = hpp.prob.get_val('ems_long_term_operation.b_E_SOC_t_with_deg')
hpp_t_with_deg = hpp.prob.get_val('ems_long_term_operation.hpp_t_with_deg')
hpp_curt_t_with_deg = hpp.prob.get_val('ems_long_term_operation.hpp_curt_t_with_deg')

price_t_ext = hpp.prob.get_val('ems_long_term_operation.price_t_ext')

# Plot the HPP operation in the 7th year (with and without degradation)
n_start = int(24*365*7.2)
n_days_plot = 14

plt.figure(figsize=[12,4])

plt.plot(price_t_ext[n_start:n_start+24*n_days_plot], label='price')

plt.plot(b_E_SOC_t[n_start:n_start+24*n_days_plot], label='SoC [MWh]')
plt.plot(b_E_SOC_t_with_deg[n_start:n_start+24*n_days_plot], label='SoC with degradation [MWh]')
plt.xlabel('time [hours]')
plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.15),
           ncol=5, fancybox=0, shadow=0)

plt.figure(figsize=[12,4])
plt.plot(hpp_t[n_start:n_start+24*n_days_plot], label='HPP')
plt.plot(hpp_t_with_deg[n_start:n_start+24*n_days_plot], label='HPP with degradation')

plt.plot(hpp_curt_t[n_start:n_start+24*n_days_plot], label='HPP curtailed')
plt.plot(hpp_curt_t_with_deg[n_start:n_start+24*n_days_plot], label='HPP curtailed with degradation')

plt.axhline(grid_MW, label='Grid MW', color='k')
plt.xlabel('time [hours]')
plt.ylabel('Power [MW]')
plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.15),
           ncol=6, fancybox=0, shadow=0)

<matplotlib.legend.Legend at 0x1ec5a34d950>

Compare battery degradation results by changing the cost of battery fluctuations factor

cost_of_battery_P_fluct_in_peak_price_ratio = 0.0
x = [clearance, sp, wt_rated_power_MW, Nwt, wind_MW_per_km2,
    solar_MW,  surface_tilt_deg, surface_azimuth_deg, DC_AC_ratio,
    b_P, b_E_h, cost_of_battery_P_fluct_in_peak_price_ratio]
outs = hpp.evaluate(*x)

SoH = np.copy(hpp.prob.get_val('battery_degradation.SoH'))

cost_of_battery_P_fluct_in_peak_price_ratio_B = 5
x = [clearance, sp, wt_rated_power_MW, Nwt, wind_MW_per_km2,
    solar_MW,  surface_tilt_deg, surface_azimuth_deg, DC_AC_ratio,
    b_P, b_E_h, cost_of_battery_P_fluct_in_peak_price_ratio_B]
outs = hpp.evaluate(*x)
SoH_B = np.copy(hpp.prob.get_val('battery_degradation.SoH'))

cost_of_battery_P_fluct_in_peak_price_ratio_C = 20
x = [clearance, sp, wt_rated_power_MW, Nwt, wind_MW_per_km2,
    solar_MW,  surface_tilt_deg, surface_azimuth_deg, DC_AC_ratio,
    b_P, b_E_h, cost_of_batt_degr]
outs = hpp.evaluate(*x)
SoH_C = np.copy(hpp.prob.get_val('battery_degradation.SoH'))

plt.figure(figsize=[12,3])
plt.plot( age, SoH, label=r'$C_{bfl}=0$')
#plt.plot( age, SoH_B, label=f'{cost_of_battery_P_fluct_in_peak_price_ratio_B}*Pr_Peak')
plt.plot( age, SoH_C, label=r'$C_{bfl}=$'+f'{cost_of_battery_P_fluct_in_peak_price_ratio_C}')#label=f'{cost_of_battery_P_fluct_in_peak_price_ratio_C}*Pr_Peak')
plt.plot( age, 0.7*np.ones_like(age), label=r'$min(1-L) = 0.7$', color='r',alpha=0.5)
plt.xlabel('age [years]')
plt.ylabel(r'Battery State of Health, $1-L(t)$ [-]')
plt.legend(title='Cost of Battery fluctuations',
           loc='upper center', bbox_to_anchor=(0.5, 1.27),
           ncol=3, fancybox=0, shadow=0)

<matplotlib.legend.Legend at 0x1ec5a896ed0>