Reliability
Evaluating the performance of a hybrid power plant including availability time series
[ ]:
# Install hydesign if needed
import importlib
if not importlib.util.find_spec("hydesign"):
!pip install git+https://gitlab.windenergy.dtu.dk/TOPFARM/hydesign.git
[1]:
import time
import numpy as np
import pandas as pd
import os
import matplotlib.pyplot as plt
from hydesign.assembly.hpp_assembly import hpp_model
from hydesign.examples import examples_filepath
Reliability time series
It is important that the reliability time series is provided for the specific plant configuration. In this example we proved a realization of the reliability of 500W solar panels connected to 1MW inverters and we have 100 inverters. The PV-reliability time series is then the combined realiability of this setup. Here we assume that failing panels will be bypassed with bypass diodes. The reliability time series provided for the wind turbines i for a realization with 50 turbines.
[3]:
name = 'France_good_wind'
examples_sites = pd.read_csv(f'{examples_filepath}examples_sites.csv', index_col=0, sep=';')
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]
sim_pars_fn = examples_filepath+ex_site['sim_pars_fn'].values[0]
input_ts_fn = examples_filepath+ex_site['input_ts_fn'].values[0]
reliability_ts_battery=pd.read_csv(os.path.join(examples_filepath, 'reliability', 'battery_seed_0.csv'), index_col=0, sep=',').values.squeeze()
reliability_ts_trans=pd.read_csv(os.path.join(examples_filepath, 'reliability', 'transformer_seed_0.csv'), index_col=0, sep=',').values.squeeze()
reliability_ts_wind=pd.read_csv(os.path.join(examples_filepath, 'reliability', 'wt_seed_0_50_turbines.csv'), index_col=0, sep=',').values.squeeze()
reliability_ts_pv=pd.read_csv(os.path.join(examples_filepath, 'reliability', 'pv_seed_0_100_inverters_of_1MW_500W_panels.csv'), index_col=0, sep=',').values.squeeze()
hpp = hpp_model(
latitude=latitude,
longitude=longitude,
altitude=altitude,
num_batteries = 10,
work_dir = './',
sim_pars_fn = sim_pars_fn,
input_ts_fn = input_ts_fn,
reliability_ts_battery=reliability_ts_battery,
reliability_ts_trans=reliability_ts_trans,
reliability_ts_wind=reliability_ts_wind,
reliability_ts_pv=reliability_ts_pv,
)
Fixed parameters on the site
-------------------------------
longitude = -0.864258
latitude = 48.744116
altitude = 302.0
[4]:
wt_rated_power_MW = 4
surface_tilt_deg = 35
surface_azimuth_deg = 180
DC_AC_ratio = 1.5
Nwt = 50
wind_MW_per_km2 = 7
solar_MW = 100
b_P = 20
b_E_h = 3
cost_of_batt_degr = 5
clearance = 20
sp = 350
D = np.sqrt(4 * wt_rated_power_MW * 10 ** 6 / np.pi / sp)
hh = clearance + D / 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]
[5]:
start = time.time()
outs = hpp.evaluate(*x)
hpp.print_design(x, outs)
end = time.time()
print('exec. time [min]:', (end - start)/60 )
print(hpp.prob['NPV_over_CAPEX'])
Design:
---------------
clearance [m]: 20.000
sp [W/m2]: 350.000
p_rated [MW]: 4.000
Nwt: 50.000
wind_MW_per_km2 [MW/km2]: 7.000
solar_MW [MW]: 100.000
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: 0.054
NPV [MEuro]: 13.641
IRR: 0.064
LCOE [Euro/MWh]: 55.396
Revenues [MEuro]: 15.781
CAPEX [MEuro]: 252.993
OPEX [MEuro]: 3.777
Wind CAPEX [MEuro]: 153.566
Wind OPEX [MEuro]: 3.102
PV CAPEX [MEuro]: 33.500
PV OPEX [MEuro]: 0.675
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]: 426.593
GUF: 0.162
grid [MW]: 300.000
wind [MW]: 200.000
solar [MW]: 100.000
Battery Energy [MWh]: 60.000
Battery Power [MW]: 20.000
Total curtailment [GWh]: 0.000
Total curtailment with deg [GWh]: 0.000
Awpp [km2]: 28.571
Apvp [km2]: 1.226
Plant area [km2]: 28.571
Rotor diam [m]: 120.629
Hub height [m]: 80.314
Number of batteries used in lifetime: 2.000
Break-even PPA price [Euro/MWh]: 35.354
Capacity factor wind [-]: 0.269
exec. time [min]: 0.17982743978500365
[0.05391978]
Transformer failure event example
[6]:
trans_fail_index = int(np.argwhere(reliability_ts_trans==0)[0][0])
[7]:
b_t = hpp.prob.get_val('battery_with_reliability.b_t')
wind_t = hpp.prob.get_val('wpp_with_reliability.wind_t')
solar_t = hpp.prob.get_val('pvp_with_reliability.solar_t')
b_t_rel = hpp.prob.get_val('battery_with_reliability.b_t_rel')
wind_t_rel = hpp.prob.get_val('wpp_with_reliability.wind_t_rel')
solar_t_rel = hpp.prob.get_val('pvp_with_reliability.solar_t_rel')
hpp_t = hpp.prob.get_val('ems_long_term_operation.hpp_t_with_deg')
grid_MW = hpp.prob.get_val('ems.G_MW')
n_days_plot = 14
idx_from = int(trans_fail_index-24*n_days_plot/2)
idx_to = int(trans_fail_index+24*n_days_plot/2)
plt.figure(figsize=[12,4])
plt.plot(b_t[idx_from:idx_to], label='battery power w/o reliability')
plt.plot(wind_t[idx_from:idx_to], label='wind power w/o reliability')
plt.plot(solar_t[idx_from:idx_to], label='solar power w/o reliability')
plt.plot(b_t_rel[idx_from:idx_to], label='battery power with reliability')
plt.plot(wind_t_rel[idx_from:idx_to], label='wind power with reliability')
plt.plot(solar_t_rel[idx_from:idx_to], label='solar power with reliability')
plt.plot(hpp_t[idx_from:idx_to], label='HPP power with reliability')
plt.xlabel('time [hours]')
plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.15),
ncol=3, fancybox=0, shadow=0)
[7]:
<matplotlib.legend.Legend at 0x24fa2607b10>
Generating availability time series
You can also generate your own availability data by supplying the mean time to fail and repair and probability distribution sampling constants:
[8]:
from hydesign.reliability import generate_availability_ensamble
N_seeds = 2
inputs = {
"WT": {"MTTF": 1.10e4,
"MTTR": 1.10e2,
"N_components": 200,
"sampling_const": 50.4,},
"PV": {"MTTF": 3.53e4,
"MTTR": 2.18e3,
"N_components": 400*2,
"sampling_const": 1000},
"inverter": {"MTTF": 3.01e4,
"MTTR": 7.20e2,
"N_components": 20,
"sampling_const": 328.8},
"transformer": {"MTTF": 1.77e4,
"MTTR": 6*30*24,
"N_components": 1,
"sampling_const": 1972},
"BESS": {"MTTF": 7.09e4,
"MTTR": 1.68e2,
"N_components": 1,
"sampling_const": 76.8}
}
for k, v in inputs.items():
ds_out = generate_availability_ensamble(component_name=k,
MTTF = v['MTTF'],
MTTR = v['MTTR'],
N_components = v['N_components'],
sampling_const = v['sampling_const'],
seeds=range(N_seeds),
)
print(k)
print(ds_out)
WT
<xarray.Dataset> Size: 129kB
Dimensions: (seed: 2, sample: 20, component: 200)
Coordinates:
* sample (sample) int32 80B 0 1 2 3 4 5 6 7 ... 13 14 15 16 17 18 19
* component (component) int32 800B 0 1 2 3 4 5 ... 195 196 197 198 199
N_components int32 4B 200
ts_start <U16 64B '2030-01-01 00:00'
ts_end <U16 64B '2054-12-31 23:00'
ts_freq <U2 8B '1h'
N_sample int32 4B 100407
N_sample_needed (seed) int32 8B 20 17
component_name <U2 8B 'WT'
* seed (seed) int32 8B 0 1
Data variables:
TTF_indices (seed, sample, component) float64 64kB 8.754e+03 ... nan
TTR_indices (seed, sample, component) float64 64kB 8.914e+03 ... nan
C:\Users\mikf\Anaconda3\envs\sesame2\Lib\site-packages\xarray\core\dataset.py:4789: UserWarning: No index created for dimension batch_no because variable batch_no is not a coordinate. To create an index for batch_no, please first call `.set_coords('batch_no')` on this object.
warnings.warn(
C:\Users\mikf\Anaconda3\envs\sesame2\Lib\site-packages\xarray\core\dataset.py:4789: UserWarning: No index created for dimension batch_no because variable batch_no is not a coordinate. To create an index for batch_no, please first call `.set_coords('batch_no')` on this object.
warnings.warn(
PV
<xarray.Dataset> Size: 258kB
Dimensions: (seed: 2, batch_no: 2, sample: 10, component: 400)
Coordinates:
* batch_no (batch_no) int32 8B 0 1
* sample (sample) int32 40B 0 1 2 3 4 5 6 7 8 9
* component (component) int32 2kB 0 1 2 3 4 5 ... 395 396 397 398 399
N_components int32 4B 400
ts_start <U16 64B '2030-01-01 00:00'
ts_end <U16 64B '2054-12-31 23:00'
ts_freq <U2 8B '1h'
N_sample int32 4B 100524
N_sample_needed (seed, batch_no) int32 16B 10 8 8 7
component_name <U2 8B 'PV'
* seed (seed) int32 8B 0 1
Data variables:
TTF_indices (seed, batch_no, sample, component) float64 128kB 3.742e...
TTR_indices (seed, batch_no, sample, component) float64 128kB 3.809e...
final_seed (seed, batch_no) int32 16B 1000 2000 1001 2001
inverter
<xarray.Dataset> Size: 5kB
Dimensions: (seed: 2, sample: 8, component: 20)
Coordinates:
* sample (sample) int32 32B 0 1 2 3 4 5 6 7
* component (component) int32 80B 0 1 2 3 4 5 6 ... 14 15 16 17 18 19
N_components int32 4B 20
ts_start <U16 64B '2030-01-01 00:00'
ts_end <U16 64B '2054-12-31 23:00'
ts_freq <U2 8B '1h'
N_sample int32 4B 100075
N_sample_needed int32 4B 8
component_name <U8 32B 'inverter'
* seed (seed) int32 8B 0 1
Data variables:
TTF_indices (seed, sample, component) int64 3kB 23955 3181 ... 253722
TTR_indices (seed, sample, component) int64 3kB 24357 3768 ... 253970
transformer
<xarray.Dataset> Size: 568B
Dimensions: (seed: 2, sample: 10, component: 1)
Coordinates:
* sample (sample) int32 40B 0 1 2 3 4 5 6 7 8 9
* component (component) int32 4B 0
N_components int32 4B 1
ts_start <U16 64B '2030-01-01 00:00'
ts_end <U16 64B '2054-12-31 23:00'
ts_freq <U2 8B '1h'
N_sample int32 4B 100035
N_sample_needed (seed) int32 8B 5 10
component_name <U11 44B 'transformer'
* seed (seed) int32 8B 0 1
Data variables:
TTF_indices (seed, sample, component) float64 160B 1.409e+04 ... 9.5...
TTR_indices (seed, sample, component) float64 160B 1.822e+04 ... 1.0...
BESS
<xarray.Dataset> Size: 212B
Dimensions: (seed: 2, sample: 1, component: 1)
Coordinates:
* sample (sample) int32 4B 0
* component (component) int32 4B 0
N_components int32 4B 1
ts_start <U16 64B '2030-01-01 00:00'
ts_end <U16 64B '2054-12-31 23:00'
ts_freq <U2 8B '1h'
N_sample int32 4B 100180
N_sample_needed int32 4B 1
component_name <U4 16B 'BESS'
* seed (seed) int32 8B 0 1
Data variables:
TTF_indices (seed, sample, component) int64 16B 56427 38258
TTR_indices (seed, sample, component) int64 16B 56509 38275
These data sets can be converted to time series of availability. However these time series are memory intensive. The higher level HPP model for reliability can be used instead. ## Evaluation with HPP reliability model This model will also run multiple realizations and aggregate the results together:
[9]:
from hydesign.assembly.hpp_assembly_reliability import ReliabilityModel
[10]:
n_reliability_seed = 2
inverter_size = 1000 # [kW]
panel_size = 500 # [W]
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,
# Reliability inputs
inverter_size, panel_size,
]
RM = ReliabilityModel(hpp_model,
latitude=latitude,
longitude=longitude,
altitude=altitude,
num_batteries = 10,
sim_pars_fn = sim_pars_fn,
input_ts_fn = input_ts_fn,
n_reliability_seed=n_reliability_seed,
)
start = time.time()
outs = RM.evaluate(*x)
end = time.time()
RM.print_design(x, outs)
print('exec. time [min]:', (end - start)/60 )
Fixed parameters on the site
-------------------------------
longitude = -0.864258
latitude = 48.744116
altitude = 302.0
Fixed parameters on the site
-------------------------------
longitude = -0.864258
latitude = 48.744116
altitude = 302.0
Fixed parameters on the site
-------------------------------
longitude = -0.864258
latitude = 48.744116
altitude = 302.0
Design:
---------------
clearance [m]: 20.000
sp [W/m2]: 350.000
p_rated [MW]: 4.000
Nwt: 50.000
wind_MW_per_km2 [MW/km2]: 7.000
solar_MW [MW]: 100.000
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
inverter_size [kW]: 1000.000
panel_size [W]: 500.000
NPV_over_CAPEX: 0.333
NPV [MEuro]: 84.182
IRR: 0.086
LCOE [Euro/MWh]: 45.153
Revenues [MEuro]: 19.399
CAPEX [MEuro]: 252.993
OPEX [MEuro]: 3.777
Wind CAPEX [MEuro]: 153.566
Wind OPEX [MEuro]: 3.102
PV CAPEX [MEuro]: 33.500
PV OPEX [MEuro]: 0.675
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]: 521.445
GUF: 0.198
grid [MW]: 300.000
wind [MW]: 200.000
solar [MW]: 100.000
Battery Energy [MWh]: 60.000
Battery Power [MW]: 20.000
Total curtailment [GWh]: 0.000
Total curtailment with deg [GWh]: 0.000
Awpp [km2]: 28.571
Apvp [km2]: 1.226
Plant area [km2]: 28.571
Rotor diam [m]: 120.629
Hub height [m]: 80.314
Number of batteries used in lifetime: 2.000
Break-even PPA price [Euro/MWh]: 28.932
Capacity factor wind [-]: 0.269
Inverter size nominal [kW]: 1000.000
Panel size nominal [W]: 500.000
Number of inverters [-]: 100.000
Inverter size real [kW]: 1000.000
Number of panels per inverter [-]: 2000.000
Panel size real [W]: 500.000
exec. time [min]: 0.44130285978317263