Gap Analysis Step 1c: Alternative Methods for Calculating the AEP

%load_ext autoreload
%autoreload 2

This notebook provides an overview and walk-through of the augmented capabilities of the MonteCarloAEP analysis class, focusing on the application of various approaches within the AEP calculation, notably different time resolutions, regression inputs, and regression models. In this example, we’ll also be using the augmented approach to accessing the analysis class creation through the PlantData object.

Important

This example runs only 300 simulations for each analysis, and as such the results do not converge. In practice, users should expect to run each analysis with num_sim=1000 or greater.

import copy

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

import project_ENGIE

# Load plant object
project = project_ENGIE.prepare()

Comparison 1: AEP calculation using different regression models and different time resolution

The updated AEP class includes four different regression algorithms to calculate the long-term operational analysis (OA), accessible by the following reg_model inputs:

• Linear regression, reg_model="lin" (default)

• Generalized additive regression model, reg_model="gam"

• Gradient boosting regressor, reg_model="gbm"

• Extremely randomized trees model, reg_model="etr"

Linear regression can be selected without any parameter restrictions, but should only be used at monthly resolution because wind plant power curves are not linear at fine time resolutions. On the other hand, as advanced machine learning models are more suited for problems with a large number of data points, we have restricted the use of the “gam”, “gbm” and “etr” regressors to OA performed at daily and hourly resolution only.

Here, we’ll calculate AEP using all four regression models, using only wind speed as input (Comparison 2 will show an example of a multivariate regression). The linear regression model is run at monthly resolution; the GBM and ETR models at daily resolution; the GAM model at hourly resolution.

aep_lin = project.MonteCarloAEP(
    reanalysis_products=["merra2", "era5"],
    time_resolution="MS",
    reg_temperature=False,
    reg_wind_direction=False,
    reg_model="lin",
)

aep_gam = project.MonteCarloAEP(
    reanalysis_products=["merra2", "era5"],
    time_resolution="h",
    reg_temperature=False,
    reg_wind_direction=False,
    reg_model="gam",
)

aep_gbm = project.MonteCarloAEP(
    reanalysis_products=["merra2", "era5"],
    time_resolution="D",
    reg_temperature=False,
    reg_wind_direction=False,
    reg_model="gbm",
)

aep_etr = project.MonteCarloAEP(
    reanalysis_products=["merra2", "era5"],
    time_resolution="D",
    reg_temperature=False,
    reg_wind_direction=False,
    reg_model="etr",
)

As an example, the monthly data frame below includes wind speed averages for both the reanalysis products selected for the analysis.

# View the monthly data frame
aep_lin.aggregate.head()

	energy_gwh	energy_nan_perc	num_days_expected	num_days_actual	availability_gwh	curtailment_gwh	gross_energy_gwh	availability_pct	curtailment_pct	avail_nan_perc	curt_nan_perc	nan_flag	availability_typical	curtailment_typical	combined_loss_valid	merra2	era5
time
2014-01-01	1.279667	0.0	31	31	0.008721	0.000000	1.288387	0.006769	0.000000	0.0	0.0	False	True	True	True	7.227947	7.314878
2014-02-01	1.793873	0.0	28	28	0.005280	0.000000	1.799153	0.002934	0.000000	0.0	0.0	False	True	True	True	8.598686	8.347006
2014-03-01	0.805549	0.0	31	31	0.000151	0.000000	0.805700	0.000188	0.000000	0.0	0.0	False	True	True	True	5.207071	5.169673
2014-04-01	0.636472	0.0	30	30	0.002773	0.000000	0.639245	0.004338	0.000000	0.0	0.0	False	True	True	True	4.872304	4.756275
2014-05-01	1.154255	0.0	31	31	0.015176	0.000225	1.169656	0.012974	0.000192	0.0	0.0	False	True	True	True	6.351635	6.162751

Now, let’s run the Monte-Carlo AEP analysis for the four setups specified above, where the following cell runs each model for 300 simulations.

The following lines of code launch the Monte Carlo-based OA for AEP. We identify each source of uncertainty in the OA estimate and use that uncertainty to create distributions of the input and intermediate variables from which we can sample for each iteration of the OA code.

We repeat the OA process “num_sim” times using different sampling combinations of the input and intermediate variables to produce a distribution of AEP values. Running the OA with the machine learning models at daily resolution is significantly slower than the case of a simple linear regression. Therefore, we have reduced the num_sim parameter to speed up the computation here. Once again, for a detailed description of the steps in the OA process, please refer to the standard AEP example notebook.

aep_lin.run(num_sim=300)  # Monthly data, linear regression

100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 300/300 [00:00<00:00, 490.12it/s]

aep_gam.run(num_sim=300)  # Hourly data, generalized additive model

100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 300/300 [01:12<00:00,  4.12it/s]

aep_gbm.run(num_sim=300)  # Daily data, gradient boosting machine

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aep_etr.run(num_sim=300)  # Daily data, extra randomized trees

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The key results for the AEP analysis are shown below: distributions of AEP values from which uncertainty can be deduced. We can now compare the AEP distributions obtained for the four configurations of the OA.

# Create consistent axis limits between the plots to show the differences between the distributions
plotting_kwargs = {
    "xlim_aep": (8, 18),
    "xlim_availability": (0.8, 1.6),
    "xlim_curtail": (0.03, 0.08),
    "ylim_aep": (0, 0.6),
    "ylim_availability": (0, 9),
    "ylim_curtail": (0, 250),
}

# Plot a distribution of AEP values from the Monte-Carlo OA method - wind speed only
aep_lin.plot_result_aep_distributions(**plotting_kwargs)

# Plot a distribution of AEP values from the Monte-Carlo OA method - gam model
aep_gam.plot_result_aep_distributions(**plotting_kwargs)

# Plot a distribution of AEP values from the Monte-Carlo OA method - gradient boosting model
aep_gbm.plot_result_aep_distributions(**plotting_kwargs)

# Plot a distribution of AEP values from the Monte-Carlo OA method - extra randomized tree model
aep_etr.plot_result_aep_distributions(**plotting_kwargs)

For this specific case, we see a decrease in AEP uncertainty when the calculation is performed with a machine learning regression model at daily resolution, which becomes even more significant when performing the calculation at hourly resolution.

Our analysis on a larger set of wind plants (Bodini et al. 2021, Wind Energy) showed how the uncertainty component connected to the regression decreases by up to 60% (relative change) when moving from monthly to daily resolution, and by up to 80% (relative change) when moving from monthly to hourly resolution.

Finally, we note how the GBM and ETR regression models are more computationally expensive than the GAM regression model. However, as ensemble-based models, they are expected to be capable of better modeling complex relationships.

Results Stability and Number of Simulations

As mentioned at the beginning of the notebook, the results histograms appear to be quite unstable. To highlight how the number of simulations impacts the results, see below where 2000 simulations is run for the linear regression model.

aep_lin.run(num_sim=2000)

100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 2000/2000 [00:03<00:00, 546.92it/s]

aep_lin.plot_result_aep_distributions(**plotting_kwargs)

Comparison 2: AEP calculation using various input variables

The other class of augmented capabilities in the AEP class allow the user to include temperature and/or wind direction as additional inputs to the long-term OA, controlled by reg_temperature and reg_wind_direction, respectively.

Below, we will compute AEP using a multivariate hourly GAM regression, one including wind speed, temperature, and both as inputs, comparing the results with the univariate GAM applied in the previous comparison.

aep_gam_temp = project.MonteCarloAEP(
    reanalysis_products=["merra2", "era5"],
    time_resolution="h",
    reg_temperature=True,
    reg_wind_direction=False,
    reg_model="gam",
)

aep_gam_wd = project.MonteCarloAEP(
    reanalysis_products=["merra2", "era5"],
    time_resolution="h",
    reg_temperature=False,
    reg_wind_direction=True,
    reg_model="gam",
)

aep_gam_temp_wd = project.MonteCarloAEP(
    reanalysis_products=["merra2", "era5"],
    time_resolution="h",
    reg_temperature=True,
    reg_wind_direction=True,
    reg_model="gam",
)

We now run the Monte-Carlo based OA for this new setup:

aep_gam_temp.run(num_sim=300)
aep_gam_wd.run(num_sim=300)
aep_gam_temp_wd.run(num_sim=300)

100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 300/300 [02:12<00:00,  2.27it/s]
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And we can now take a look at the AEP distribution:

aep_gam_temp.plot_result_aep_distributions(**plotting_kwargs)

aep_gam_wd.plot_result_aep_distributions(**plotting_kwargs)

aep_gam_temp_wd.plot_result_aep_distributions(**plotting_kwargs)

In this case, only a slight reduction in AEP uncertainty is achieved when temperature is added as additional input to the hourly GAM regression. Our analysis (Bodini et al. 2021, Wind Energy) showed how adding temperature as additional input has the largest benefits for those wind plants that experience a strong seasonal cycle, which might not be the case for the specific wind plant considered in this example.