MHKiT WEC-Sim Example

This notebook demonstrates using the MHKiT wave module and WEC-Sim together to perform a resource characterization study in MHKiT, simulate representative cases with WEC-Sim, and visualize the results in MHKiT to estimate MAEP (Mean Annual Energy Production).

  1. Characterize the available resource at a location

    • See the PacWave example notebook

  2. Write a WEC-Sim batch file for the given clusters

  3. Simulate the device in WEC-Sim.

    • Ensure that the spectra used in WEC-Sim is identical to the one used in MHKiT.

  4. Load WEC-Sim batch results

  5. Assess results and visualize quantities of interest

This example uses WEC-Sim to simulate the Oscillating Surge Wave Energy Converter (OSWEC), a flap-type device.

Start by importing MHKiT and the necessary python packages (e.g.scipy.io, matplotlib.pyplot, pandas, numpy).

[1]:

from mhkit import wave
import scipy.io as sio
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

1. Characterize the available resource at a location

This example will use an abbreviated version of PacWave_resource_characterization_example.ipynb. For full details on downloading, calculating, and visualizing the k-means clusters representation of the site’s wave resouce, see that example.

We select the N=32 cluster as it’s total energy flux is closet to the total energy flux of the site considering all wave conditions. We will load the PacWave example output, which can be easily saved after running the example with the command results[32].to_csv("pacwave_cluster_32.csv"). We will start this example by reading in that csv output and formatting it for WEC-Sim.

[2]:

results = pd.read_csv("data/wave/pacwave_cluster_32.csv", index_col=0)
results

[2]:
Te Hm0 weights Tp J
0 7.974491 1.253970 0.058861 9.294279 6031.115427
1 10.794533 2.641403 0.035216 12.581041 37004.325098
2 6.901979 1.953122 0.052001 8.044264 12516.214519
3 12.667628 7.310116 0.005070 14.764135 367451.945581
4 12.893701 2.262294 0.016046 15.027624 36455.136139
5 10.557621 4.754297 0.017311 12.304920 116784.361789
6 8.766664 2.739380 0.043646 10.217557 31825.667989
7 6.537403 1.305578 0.050746 7.619350 5272.441394
8 9.666291 1.340694 0.037070 11.266073 8443.649821
9 12.787307 3.920397 0.016464 14.903621 107680.986511
10 11.605879 1.821016 0.022323 13.526666 19446.169168
11 7.584082 1.878735 0.054624 8.839256 12827.143861
12 10.175411 6.133932 0.008836 11.859453 188189.689187
13 9.319357 4.587432 0.018817 10.861722 95155.068368
14 7.228996 1.256691 0.057692 8.425403 5449.034309
15 5.646967 1.339107 0.032118 6.581547 4750.825175
16 7.615980 2.634620 0.036497 8.876433 25339.645267
17 9.460406 3.381147 0.033824 11.026114 52508.670941
18 16.000441 3.044223 0.004295 18.648532 87446.895732
19 10.550343 1.563634 0.030265 12.296437 12622.321616
20 11.817436 2.982923 0.021717 13.773236 53748.089829
21 12.101122 5.305727 0.014540 14.103872 177305.220432
22 10.400035 3.588297 0.032312 12.121253 65405.272028
23 9.132540 2.011568 0.048130 10.643986 17913.129344
24 9.880296 2.462908 0.050634 11.515496 29157.316025
25 8.321803 2.003080 0.054171 9.699071 16104.920042
26 6.131352 1.794449 0.035429 7.146098 9295.960216
27 11.430727 3.979891 0.025331 13.322525 90734.821382
28 14.263809 2.781733 0.009359 16.624486 66183.179571
29 13.744161 5.465225 0.007518 16.018835 240475.837506
30 8.735251 1.270630 0.047066 10.180945 6821.344537
31 8.301748 3.676767 0.022070 9.675697 54122.886646

2. Write a WEC-Sim batch file for the given clusters

WEC-Sim MCR (multiple condition run) files should contain a structure mcr that contains two variables: header and cases. Each column of header and cases denotes a variable and it’s value respectively. Each row is another simulation. WEC-Sim defines waves using the significant wave height and peak period. We will isolate these values from the results of the cluster analysis and create a dictionary that is written to the .mat file.

[3]:

ws_mcr_cases = results[["Hm0","Tp"]]
ws_mcr_header = np.array(["waves.height","waves.period"], dtype='object')
ws_mcr_out = {'mcr': {'header': ws_mcr_header, 'cases': ws_mcr_cases}}
sio.savemat('mcr_mhkit.mat', ws_mcr_out)

3. Simulate the device in WEC-Sim

Now that the MCR file is created, we need to go simulate WEC performance in these wave conditions using WEC-Sim. To recreate the data used in the next step, use the created MCR file with WEC-Sim’s OSWEC example. For an accurate comparison to the power calculated in the resource characterization, we should ensure that the WEC-Sim cases use irregular JONSWAP wave spectra as in the PacWave example.

For convenience in this demonstration, we enforce OSWEC model stability in the extreme wave conditions by arbitrarily applying a large PTO stiffness and damping:

pto(1).stiffness = 1e5;
pto(1).damping = 5e7;

To reduce the amount of extranenous data saved for this example, we limit the WEC-Sim output to the PTO’s power output in the userDefinedFunctions.m script:

if exist('imcr','var')
    if imcr == 1
        nmcr = size(mcr.cases,1);
        power = nan(1, nmcr);
    end

    iRampEnd = simu.rampTime./simu.dtOut + 1;
    power(imcr) = -mean(output.ptos(1).powerInternalMechanics(iRampEnd:end,5));

    if imcr == nmcr
        % Save output
        save('mcr_mhkit_power.mat', 'power');
    end
end

4. Load WEC-Sim batch results

Note that in this example we do not save the entire WEC-Sim output structure for each case. See the wecsim_example.ipynb for information on loading that WEC-Sim data. Here the output is one array of average power output that we will load and compare to the resource characterization.

Note that the power output [W] is significantly larger than the energy flux [W/m] due to the width of the OSWEC.

[4]:

# Relative location and filename of simulated WEC-Sim data (run with mooring)
filename = "./data/wave/mcr_mhkit_power.mat"

# Load data using the `wecsim.read_output` function which returns a dictionary of Datasets.
wecsim_data = sio.loadmat(filename)
results['P'] = wecsim_data['power'][0]
results

[4]:
Te Hm0 weights Tp J P
0 7.974491 1.253970 0.058861 9.294279 6031.115427 6.861312e+04
1 10.794533 2.641403 0.035216 12.581041 37004.325098 3.873519e+05
2 6.901979 1.953122 0.052001 8.044264 12516.214519 1.923400e+05
3 12.667628 7.310116 0.005070 14.764135 367451.945581 1.951187e+06
4 12.893701 2.262294 0.016046 15.027624 36455.136139 3.115873e+05
5 10.557621 4.754297 0.017311 12.304920 116784.361789 8.410281e+05
6 8.766664 2.739380 0.043646 10.217557 31825.667989 3.398579e+05
7 6.537403 1.305578 0.050746 7.619350 5272.441394 8.332614e+04
8 9.666291 1.340694 0.037070 11.266073 8443.649821 6.951609e+04
9 12.787307 3.920397 0.016464 14.903621 107680.986511 5.068824e+05
10 11.605879 1.821016 0.022323 13.526666 19446.169168 1.601980e+05
11 7.584082 1.878735 0.054624 8.839256 12827.143861 2.112478e+05
12 10.175411 6.133932 0.008836 11.859453 188189.689187 2.402013e+06
13 9.319357 4.587432 0.018817 10.861722 95155.068368 1.067714e+06
14 7.228996 1.256691 0.057692 8.425403 5449.034309 6.414256e+04
15 5.646967 1.339107 0.032118 6.581547 4750.825175 7.328911e+04
16 7.615980 2.634620 0.036497 8.876433 25339.645267 3.671972e+05
17 9.460406 3.381147 0.033824 11.026114 52508.670941 4.020208e+05
18 16.000441 3.044223 0.004295 18.648532 87446.895732 2.414505e+05
19 10.550343 1.563634 0.030265 12.296437 12622.321616 1.335059e+05
20 11.817436 2.982923 0.021717 13.773236 53748.089829 3.552203e+05
21 12.101122 5.305727 0.014540 14.103872 177305.220432 1.343228e+06
22 10.400035 3.588297 0.032312 12.121253 65405.272028 7.368317e+05
23 9.132540 2.011568 0.048130 10.643986 17913.129344 1.998769e+05
24 9.880296 2.462908 0.050634 11.515496 29157.316025 2.715734e+05
25 8.321803 2.003080 0.054171 9.699071 16104.920042 2.319710e+05
26 6.131352 1.794449 0.035429 7.146098 9295.960216 1.478045e+05
27 11.430727 3.979891 0.025331 13.322525 90734.821382 9.391133e+05
28 14.263809 2.781733 0.009359 16.624486 66183.179571 2.000335e+05
29 13.744161 5.465225 0.007518 16.018835 240475.837506 8.686179e+05
30 8.735251 1.270630 0.047066 10.180945 6821.344537 8.550423e+04
31 8.301748 3.676767 0.022070 9.675697 54122.886646 7.578856e+05

5. Assess results and visualize quantities of interest

Now that we have loaded the OSWEC’s modeled power, we can assess it’s performance relative to the incoming wave and calculate the mean annual energy production (MAEP) using MHKiT.

[5]:

results['CW'] = wave.performance.capture_width(results['P'], results['J'])
oswec_width = 18
results['CWR'] = results['CW'] / oswec_width
results

[5]:
Te Hm0 weights Tp J P CW CWR
0 7.974491 1.253970 0.058861 9.294279 6031.115427 6.861312e+04 11.376523 0.632029
1 10.794533 2.641403 0.035216 12.581041 37004.325098 3.873519e+05 10.467747 0.581542
2 6.901979 1.953122 0.052001 8.044264 12516.214519 1.923400e+05 15.367264 0.853737
3 12.667628 7.310116 0.005070 14.764135 367451.945581 1.951187e+06 5.310048 0.295003
4 12.893701 2.262294 0.016046 15.027624 36455.136139 3.115873e+05 8.547144 0.474841
5 10.557621 4.754297 0.017311 12.304920 116784.361789 8.410281e+05 7.201547 0.400086
6 8.766664 2.739380 0.043646 10.217557 31825.667989 3.398579e+05 10.678736 0.593263
7 6.537403 1.305578 0.050746 7.619350 5272.441394 8.332614e+04 15.804090 0.878005
8 9.666291 1.340694 0.037070 11.266073 8443.649821 6.951609e+04 8.232943 0.457386
9 12.787307 3.920397 0.016464 14.903621 107680.986511 5.068824e+05 4.707260 0.261514
10 11.605879 1.821016 0.022323 13.526666 19446.169168 1.601980e+05 8.238022 0.457668
11 7.584082 1.878735 0.054624 8.839256 12827.143861 2.112478e+05 16.468814 0.914934
12 10.175411 6.133932 0.008836 11.859453 188189.689187 2.402013e+06 12.763787 0.709099
13 9.319357 4.587432 0.018817 10.861722 95155.068368 1.067714e+06 11.220783 0.623377
14 7.228996 1.256691 0.057692 8.425403 5449.034309 6.414256e+04 11.771363 0.653965
15 5.646967 1.339107 0.032118 6.581547 4750.825175 7.328911e+04 15.426605 0.857034
16 7.615980 2.634620 0.036497 8.876433 25339.645267 3.671972e+05 14.491015 0.805056
17 9.460406 3.381147 0.033824 11.026114 52508.670941 4.020208e+05 7.656274 0.425349
18 16.000441 3.044223 0.004295 18.648532 87446.895732 2.414505e+05 2.761110 0.153395
19 10.550343 1.563634 0.030265 12.296437 12622.321616 1.335059e+05 10.576970 0.587609
20 11.817436 2.982923 0.021717 13.773236 53748.089829 3.552203e+05 6.608984 0.367166
21 12.101122 5.305727 0.014540 14.103872 177305.220432 1.343228e+06 7.575793 0.420877
22 10.400035 3.588297 0.032312 12.121253 65405.272028 7.368317e+05 11.265631 0.625868
23 9.132540 2.011568 0.048130 10.643986 17913.129344 1.998769e+05 11.158124 0.619896
24 9.880296 2.462908 0.050634 11.515496 29157.316025 2.715734e+05 9.314074 0.517449
25 8.321803 2.003080 0.054171 9.699071 16104.920042 2.319710e+05 14.403735 0.800207
26 6.131352 1.794449 0.035429 7.146098 9295.960216 1.478045e+05 15.899861 0.883326
27 11.430727 3.979891 0.025331 13.322525 90734.821382 9.391133e+05 10.350087 0.575005
28 14.263809 2.781733 0.009359 16.624486 66183.179571 2.000335e+05 3.022422 0.167912
29 13.744161 5.465225 0.007518 16.018835 240475.837506 8.686179e+05 3.612080 0.200671
30 8.735251 1.270630 0.047066 10.180945 6821.344537 8.550423e+04 12.534806 0.696378
31 8.301748 3.676767 0.022070 9.675697 54122.886646 7.578856e+05 14.003052 0.777947 
[6]:

MAEP = wave.performance.mean_annual_energy_production_matrix(results['CW'], results['J'], results['weights']) / 1000 # kWh
MAEP = np.round(MAEP, 0).item()
MAEP

[6]:

2865149.0