analysis of results 3rd campaign

experimental_setup/experiments/campaign3_20180124/s_Cp_TSR.m

+## Copyright (C) 2018 Juan Pablo Carbajal
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+## Author: Juan Pablo Carbajal <ajuanpi+dev@gmail.com>
+## Created: 2018-02-02
+
+## Script to preprocess measured data
+#
+
+## Load Friction
+# Torque due to friction as indentified independently, see |s_friction.m| for
+# the generation of the file used here
+fname_F = '../campaign1_20180110/tauF.dat';
+load (fname_F)
+
+## Load pre-processed data
+# The raw data, collected with |s_rawdata.m|, is pre-processed in the script
+# |s_preprocess_rawdata.m|.
+fname_vp  = @(w) sprintf ("vp%s.dat", strrep (num2str (w), '.', '_'));
+fname_raw = @(w) sprintf ("rawdata_vp%s.dat", strrep (num2str (w), '.', '_'));
+
+##
+# We load the data form the two wind speeds we used
+vp = 6;
+for i=1:length(vp)
+  load (fname_raw(vp(i)),'Temp', 'Hum', 'Pres','v','v_std');
+  load (fname_vp(vp(i)));
+  A         = 2 * radiusR * HR;
+  A_std_rel = dr/radiusR + dH / HR;
+   
+  v_w{i}      = v;
+  v_w_std_rel = v_std ./ v_w{i};
+  
+  vt{i}      = vtR_data;
+  vt_std{i}  = vtR_data_std;
+  
+  tsr{i}     = vt{i} / v_w{i};
+  tsr_std{i} = (vt_std{i} ./ vt{i} + v_w_std_rel) .* tsr{i};
+
+  tau{i}     = - tauR - tauF(omegaR);
+  tau_std{i} = tauR_std; % + tauF_std; # TODO
+
+  rho{i} = air_density (Temp, Pres, Hum);
+
+  Pw{i}      = 0.5 * A * v_w{i}^3 * rho{i};
+  Pw_std_rel = 3 * v_w_std_rel + A_std_rel;
+  
+  Cp{i}     = tau{i} .* omegaR ./ Pw{i};
+  Cp_std{i} = (tau_std{i} ./ tau{i} + omegaR_std ./ omegaR + Pw_std_rel) .* Cp{i};
+endfor
+
+## Plots
+#
+txt_label = @(v) {sprintf('%.1f m/s down',v), sprintf('%.1f m/s up',v)};
+figure (1)
+clf
+h1  = errorbar (vt{1}, tau{1}, vt_std{1}, tau_std{1}, '~>o');
+hold on
+vtf = linspace (0, max (vt{1})*1.5, 100).';
+h3 = plot (vtf, -tauF(vtf/radiusR),'k-');
+hold off
+axis tight
+xlabel ('Tangential speed rotor [m/s]')
+ylabel ('\tau_W [Nm]')
+set (h1, 'markerfacecolor', 'auto')
+legend ([h1; h3], {txt_label(v_w{1}){:}, '\tau_F'}, ...
+'Location', 'NorthOutside','Orientation', 'horizontal');
+
+print ('-dpng', 'TauW_vs_vt.png');
+%print ('-dpng', 'TauW_vs_tsr.png');
+
+figure (2)
+clf
+h1 = errorbar (tsr{1}, Cp{1}, tsr_std{1}, Cp_std{1}, '~>o');
+axis tight
+xlabel ('TSR [a.u.]')
+ylabel ('C_p [a.u.]')
+legend (h1, txt_label(v_w{1}), ...
+'Location', 'NorthOutside','Orientation', 'horizontal');
+
+print ('-dpng', 'Cp_vs_tsr.png');

experimental_setup/experiments/campaign3_20180124/s_preprocess_rawdata.m

+## Copyright (C) 2018 Juan Pablo Carbajal
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+## Author: Juan Pablo Carbajal <ajuanpi+dev@gmail.com>
+## Created: 2018-02-02
+
+## Script to preprocess measured data
+#
+# add folder with data analysis functions
+
+fname_raw = @(w) sprintf ("rawdata_vp%s.dat", strrep (num2str (w), '.', '_'));
+fname     = @(w) sprintf ("vp%s.dat", strrep (num2str (w), '.', '_'));
+vars      = {'gearGP52', 'radiusR', 'HR', 'dr', 'dH', ...
+             'tauM', 'tauR', 'tauM_std', 'tauR_std', ...
+             'omegaM', 'omegaR', 'omegaM_std', 'omegaR_std', ...
+             'omegaR_data', 'omegaR_data_std', ...
+             'vtR', 'vtR_std', 'vtR_data', 'vtR_data_std', 'v'};
+
+txt_label = @(v) {sprintf('%.1f m/s down',v), sprintf('%.1f m/s up',v)};
+
+vp = 6;
+load (fname_raw(vp))
+
+if ~exist ('vtR', 'var')
+  # properties of gearbox installed in motor
+  gearGP52 = struct ('ratio', 4.3, 'efficiency', 0.91);
+  # Properties of the rotor
+  radiusR  = 0.35; # in meters
+  dr       = 0.01;
+  HR       = 0.50;
+  dH       = 0.01;
+  # Error of the mean from interval
+  # Measurements are consider 0.99 confidence intervals
+  coeff = 1 ./ erfinv (0.99);
+  lu2std = @(LU) squeeze (std (LU, 0, 2)) * coeff / sqrt (2);
+
+  ##
+  # Motor/rotor torque and rotation
+  [TM, WM, TR, WR]         = maxonRE50_model (U, I, gearGP52);
+  [TMlu, WMlu, TRlu, WRlu] = maxonRE50_model (U, I_lu, gearGP52);
+
+  tauM = TM; tauM_std = lu2std (TMlu);
+  tauR = TR; tauR_std = lu2std (TRlu);
+  omegaM = WM; omegaM_std = lu2std (WMlu);
+  omegaR = WR; omegaR_std = lu2std (WRlu);
+  
+  omegaR_data      = 2 * pi * fe;
+  omegaR_data_std  = 2 * pi * fe_err;
+  vtR_data         = omegaR_data * radiusR;
+  vtR_data_std     = omegaR_data_std * radiusR .* ones(size(fe));
+
+endif
+
+## Plots
+#
+
+##
+# Motor voltage and current at stead state
+# The voltage was scanned with increasing (up) and decreasing values (down)
+# for two values of the wind speed.
+figure (1)
+clf
+h = plot (U,I,'o-');
+axis tight
+xlabel ('Voltage [V]')
+ylabel ('Current [A]')
+legend (h, txt_label(v));
+
+##
+# Motor rotational frequency as measured from the encoder and
+# as caculated using the manufacturer's model.
+# The plots show that the error propagated through the model 
+# is an over estimation of the uncertainty in the angular speed.
+# Therefore we assign the erro of th emeasured speed to the model output.
+
+figure (2)
+clf
+fm  = omegaM / 2 / pi; 
+if ~exist ('vtR', 'var')
+  subplot (1,2,1)
+  errf = omegaM_std / 2 / pi;
+  h   = errorbar (fm, fe, errf, fe_err*ones(size(errf)),'~>o');
+  ff  = [fm(:) fe(:)]; ff(!isfinite(ff(:,2)),:) = [];
+  vax = [min(ff(:)) max(ff(:))];
+  vax = vax([1 2 1 2]);
+  axis (vax);
+  line (vax(1:2), vax(3:4));
+  xlabel ('Freq. motor (model) [Hz]')
+  ylabel ('Freq. encoder (measured) [Hz]')
+  legend (h, txt_label(v), ...
+  'Location', 'NorthOutside','Orientation', 'horizontal');
+
+  omegaM_std  = fe_err * 2 * pi;
+  omegaR_std = omegaM_std / gearGP52.ratio;
+
+  subplot (1,2,2)
+endif
+
+ferr = fe_err * ones(size(fm));
+h = errorbar (fm, fe, ferr, ferr,'~>o');
+if exist ('vtR', 'var')
+  axis tight; 
+  vax = axis (); 
+else
+  axis (vax);
+endif
+line (vax(1:2), vax(3:4));
+xlabel ('Freq. motor (model) [Hz]')
+ylabel ('Freq. encoder (measured) [Hz]')
+legend (h, txt_label(v), ...
+'Location', 'NorthOutside','Orientation', 'horizontal');
+
+print ('-dpng', sprintf('freqR_vs_freqRmodel_%d.png',v))
+##
+# Torque of the motor applied to the turbine rotor vs. tangential speed of
+# turbine rotor
+# Tangential speed
+vtR     = omegaR * radiusR;
+vtR_std = omegaR_std * radiusR;
+
+figure (3)
+clf
+errV = vtR_std * ones (size (vtR));
+h    = errorbar (vtR, tauR, errV, tauR_std, '~>o');
+axis tight
+xlabel ('Tangetial speed rotor (model) [rad/s]')
+ylabel ('\tau_M [Nm]')
+legend (h, txt_label(v), ...
+'Location', 'NorthOutside','Orientation', 'horizontal');
+
+
+figure (4)
+clf
+h  = errorbar (vtR_data / v, tauR, vtR_data_std / v, tauR_std, '~>o');
+axis tight
+xlabel ('TSR [a.u.]')
+ylabel ('\tau_M [Nm]')
+legend (h, txt_label(v), ...
+'Location', 'NorthOutside','Orientation', 'horizontal');
+
+print ('-dpng', sprintf('tauR_vs_tsr_%d.png',v))
+
+## Save data
+#
+fn = fname (vp);
+save (fn, vars{:});
+printf ("Saved to %s\n", fn); fflush (stdout);

experimental_setup/experiments/campaign3_20180124/s_rawdata.m

+## Copyright (C) 2018 Juan Pablo Carbajal
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 3 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program. If not, see <http://www.gnu.org/licenses/>.
+
+## Author: Juan Pablo Carbajal <ajuanpi+dev@gmail.com>
+## Created: 2018-02-02
+
+## Script to collect and save measured data
+#
+fname = @(w) sprintf ("rawdata_vp%s.dat", strrep (num2str (w), '.', '_'));
+vars  = {'vp', 'v', 'v_std', 'U', 'I', 'I_lu', 'fe', 'fe_err', 'Temp', 'Pres', 'Hum'};
+
+## Voltage ramp up and down
+# Last index is down (=1) and up (=2)
+nU = 7;
+U      = zeros (nU,2);
+U(:,1) = [30 26 22 18 14 10 6].';
+U(:,2) = flipud (U(:,1));
+
+## Wind power 6 %
+# Wind speed from anemometer @ 12.5 %
+vp = 6;
+v = 1.9;  # m/s
+v_std = 0.1;
+
+## 
+# Current @ 6 %
+I_lu        = zeros (nU,2,2);
+I_lu(:,:,1) = [18.8 19.9;15.8 17.0; 12.2 13.6; 9 10; 7.3 7.8; ...
+               5.7 6.3; 4.4 5.1] * 1e-2.';
+;
+I_lu(:,:,2) = [4.3 5.1; 6.2 6.8; 7.1 7.9; 9.2 10; 10.7 12; ...
+              15.8 16.2; 19.4 20]*1e-2;
+I           = squeeze (mean (I_lu, 2));
+
+##
+# Encoder rotation frequency
+fe      = NA (nU,2);
+fe(:,1) = [19.1; 16.5; 14.0; 11.5; 8.8; 6.3; 3.7];
+fe(:,2) = [3.6; 6.3; 8.9; 11.4; 14; 16.6; 19.1].';
+# Resolution in frequency measurement [Hz]
+fe_err = 0.1; 
+
+##
+# Temprature, Pressure and Relative humidity
+Pres = 978.1e2 * [1 1];  #Pa
+Hum  = [0.52 0.53];
+Temp = [11.7 10.3];     #C
+
+fn = fname (vp);
+save (fn, vars{:});
+printf ("Saved to %s\n", fn); fflush (stdout);