def test_plot_gradients():
x = np.arange(-3, 4, .1)
plt.plot(x, x**2)
plot_gradients(1.5**2, 3, 1.5, "test", 1)
if 0:
plt.show()
plt.close()
def test_set_gradients():
wt = IEA37_WindTurbines()
def dpctdu(ws, run_only):
if run_only == 0:
return np.where((ws > 4) & (ws <= 9.8),
100000 * ws, # not the right gradient, but similar to the reference
0)
else:
return np.full(ws.shape, 0)
wt.powerCtFunction.set_gradient_funcs(dpctdu)
with use_autograd_in([WindTurbines, iea37_reader, power_ct_functions, wind_turbines_deprecated]):
ws_lst = np.arange(3, 25, .1)
plt.plot(ws_lst, wt.power(ws_lst))
ws_pts = np.array([3., 6., 9., 12.])
dpdu_lst = autograd(wt.power)(ws_pts)
if 0:
for dpdu, ws in zip(dpdu_lst, ws_pts):
plot_gradients(wt.power(ws), dpdu, ws, "", 1)
plt.show()
dpdu_ref = np.where((ws_pts > 4) & (ws_pts <= 9.8),
100000 * ws_pts,
0)
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref)
def test_spline():
wt_tab = V80()
wt_spline = V80()
wt_spline.spline_ct_power(err_tol_factor=1e-2)
ws_lst = np.arange(3, 25, .001)
# mean and max error
assert (wt_tab.power(ws_lst) - wt_spline.power(ws_lst)).mean() < 1
assert ((wt_tab.power(ws_lst) - wt_spline.power(ws_lst)).max()) < 1400
# max change of gradient 80 times lower
assert np.diff(np.diff(wt_spline.power(ws_lst))).max() * 80 < np.diff(np.diff(wt_tab.power(ws_lst))).max()
ws_pts = [6.99, 7.01]
dpdu_tab_pts = np.diag(fd(wt_tab.power)(np.array(ws_pts)))
with use_autograd_in():
dpdu_spline_pts = np.diag(autograd(wt_spline.power)(np.array(ws_pts)))
npt.assert_array_almost_equal(dpdu_spline_pts, [205555.17794162, 211859.45965873])
if 0:
plt.plot(ws_lst, wt_tab.power(ws_lst))
plt.plot(ws_lst, wt_spline.power(ws_lst))
for wt, dpdu_pts, label in [(wt_tab, dpdu_tab_pts, 'V80 tabular'),
(wt_spline, dpdu_spline_pts, 'V80 spline')]:
for ws, dpdu in zip(ws_pts, dpdu_pts):
plot_gradients(wt.power(ws), dpdu, ws, label, 1)
ax = plt.gca().twinx()
ax.plot(ws_lst, wt.power(ws_lst) - wt_spline.power(ws_lst))
plt.figure()
plt.plot(np.diff(np.diff(wt_tab.power(ws_lst))))
plt.plot(np.diff(np.diff(wt_spline.power(ws_lst))))
plt.show()
def test_method():
wt_linear = V80()
wt_pchip = V80(method='pchip')
wt_spline = V80(method='spline')
ws_lst = np.arange(3, 25, .001)
for wt in [wt_linear, wt_pchip, wt_spline]:
wt.enable_autograd()
ws_pts = [6.99, 7.01]
with use_autograd_in():
dpdu_linear_pts = autograd(wt_linear.power)(np.array(ws_pts))
dpdu_pchip_pts = autograd(wt_pchip.power)(np.array(ws_pts))
dpdu_spline_pts = autograd(wt_spline.power)(np.array(ws_pts))
if 0:
wt_dp_label_lst = [(wt_linear, dpdu_linear_pts, 'linear'),
(wt_pchip, dpdu_pchip_pts, 'pchip'),
(wt_spline, dpdu_spline_pts, 'spline')]
for wt, dpdu_pts, label in wt_dp_label_lst:
c = plt.plot(ws_lst, wt.power(ws_lst), label=label)[0].get_color()
gradients.color_dict[label] = c
for ws, dpdu in zip(ws_pts, dpdu_pts):
plot_gradients(wt.power(ws), dpdu, ws, label)
plt.legend()
plt.figure()
for wt, dpdu_pts, label in wt_dp_label_lst:
plt.plot(ws_lst, wt_linear.power(ws_lst) - wt.power(ws_lst), label=label)
plt.legend()
plt.ylabel('Power difference wrt. linear')
plt.figure()
for wt, dpdu_pts, label in wt_dp_label_lst:
plt.plot(np.diff(np.diff(wt.power(ws_lst))), label=label)
plt.ylabel('Change of gradient')
plt.legend()
plt.show()
# mean and max error
for wt, mean_tol, absmean_tol, max_tol in [(wt_pchip, 213, 2323, 15632),
(wt_spline, 1, 1, 1380)]:
assert np.abs((wt_linear.power(ws_lst) - wt.power(ws_lst)).mean()) < mean_tol
assert np.abs((wt_linear.power(ws_lst) - wt.power(ws_lst)).mean()) < absmean_tol
assert np.abs((wt_linear.power(ws_lst) - wt.power(ws_lst)).max()) < max_tol
for wt, diff_grad_max, dpdu_pts, ref_dpdu_pts in [(wt_linear, 64, dpdu_linear_pts, [178000.00007264, 236000.00003353]),
(wt_pchip, 0.2, dpdu_pchip_pts, [
202520.16516056, 203694.66294614]),
(wt_spline, 0.8, dpdu_spline_pts, [205555.17794162, 211859.45965873])]:
assert np.diff(np.diff(wt.power(ws_lst))).max() < diff_grad_max
npt.assert_array_almost_equal(dpdu_pts, ref_dpdu_pts)
def test_dAEP_2wt():
site = Hornsrev1Site()
iea37_site = IEA37Site(16)
wt = IEA37_WindTurbines()
wfm = IEA37SimpleBastankhahGaussian(site, wt)
x, y = iea37_site.initial_position[np.array([0, 2, 5, 8, 14])].T
# plot 2 wt case
x, y = np.array([[0, 130 * 4], [0, 0]], dtype=np.float)
x_lst = np.array([0., 1.]) * np.arange(1, 600, 10)[:, na]
kwargs = {'ws': [10], 'wd': [270]}
_, (ax1, ax2) = plt.subplots(1, 2, sharey=False)
ax1.plot(x_lst[:, 1], [wfm.aep(x_, y, **kwargs) for x_ in x_lst])
ax1.set_xlabel('Downwind distance [m]')
ax1.set_ylabel('AEP [GWh]')
x_ = x_lst[20]
ax1.set_title("Center line")
for grad in [fd, cs, autograd]:
dAEPdx = wfm.dAEPdn(0, grad)(x_, y, **kwargs)[1]
npt.assert_almost_equal(dAEPdx / 360, 3.976975605364392e-06,
(10, 5)[grad == fd])
plot_gradients(wfm.aep(x_, y, **kwargs),
dAEPdx,
x_[1],
grad.__name__,
step=100,
ax=ax1)
y_lst = np.array([0, 1.]) * np.arange(-100, 100, 5)[:, na]
ax2.plot(y_lst[:, 1], [wfm.aep(x, y_, **kwargs) for y_ in y_lst])
ax2.set_xlabel('Crosswind distance [m]')
ax2.set_ylabel('AEP [GWh]')
y_ = y_lst[25]
ax2.set_title("%d m downstream" % x[1])
for grad in [fd, cs, autograd]:
dAEPdy = wfm.dAEPdn(1, grad)(x, y_, **kwargs)[1]
plot_gradients(wfm.aep(x, y_, **kwargs),
dAEPdy,
y_[1],
grad.__name__,
step=50,
ax=ax2)
npt.assert_almost_equal(dAEPdy / 360, 3.794435973860448e-05,
(10, 5)[grad == fd])
if 0:
plt.legend()
plt.show()
plt.close()
def test_gradients():
wt = IEA37_WindTurbines()
with use_autograd_in([WindTurbines, iea37_reader]):
ws_lst = np.arange(3, 25, .1)
plt.plot(ws_lst, wt.power(ws_lst))
ws_pts = np.array([3., 6., 9., 12.])
dpdu_lst = np.diag(autograd(wt.power)(ws_pts))
if 0:
for dpdu, ws in zip(dpdu_lst, ws_pts):
plot_gradients(wt.power(ws), dpdu, ws, "", 1)
plt.show()
dpdu_ref = np.where((ws_pts > 4) & (ws_pts <= 9.8),
3 * 3350000 * (ws_pts - 4)**2 / (9.8 - 4)**3, 0)
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref)
def test_set_gradients():
wt = IEA37_WindTurbines()
wt.set_gradient_funcs(lambda ws: np.where((ws > 4) & (ws <= 9.8),
100000 * ws, # not the right gradient, but similar to the reference
0), lambda ws: 0)
with use_autograd_in([WindTurbines, iea37_reader]):
ws_lst = np.arange(3, 25, .1)
plt.plot(ws_lst, wt.power(ws_lst))
ws_pts = np.array([3., 6., 9., 12.])
dpdu_lst = np.diag(autograd(wt.power)(ws_pts))
if 0:
for dpdu, ws in zip(dpdu_lst, ws_pts):
plot_gradients(wt.power(ws), dpdu, ws, "", 1)
plt.show()
dpdu_ref = np.where((ws_pts > 4) & (ws_pts <= 9.8),
100000 * ws_pts,
0)
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref)
def test_gradients():
wt = IEA37_WindTurbines()
wt.enable_autograd()
ws_lst = np.arange(3, 25, .1)
ws_pts = np.array([3., 6., 9., 12.])
dpdu_lst = autograd(wt.power)(ws_pts)
if 0:
plt.plot(ws_lst, wt.power(ws_lst))
for dpdu, ws in zip(dpdu_lst, ws_pts):
plot_gradients(wt.power(ws), dpdu, ws, "", 1)
plt.show()
dpdu_ref = np.where((ws_pts > 4) & (ws_pts <= 9.8),
3 * 3350000 * (ws_pts - 4)**2 / (9.8 - 4)**3, 0)
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref)
fd_dpdu_lst = fd(wt.power)(ws_pts)
npt.assert_array_almost_equal(fd_dpdu_lst, dpdu_ref, 0)
cs_dpdu_lst = cs(wt.power)(ws_pts)
npt.assert_array_almost_equal(cs_dpdu_lst, dpdu_ref)
WindTurbines, iea37_reader, power_ct_functions,
wind_turbines_deprecated
]):
if grad_method == autograd:
wt.enable_autograd()
ws_lst = np.arange(2, 25, .1)
kwargs = {k: 1 for k in wt.function_inputs[0]}
dpdu_lst = grad_method(wt.power)(ws_pts, **kwargs)
dctdu_lst = grad_method(wt.ct)(ws_pts, **kwargs)
if 0:
gradients.color_dict = {'power': 'b', 'ct': 'r'}
plt.plot(ws_lst, wt.power(ws_lst, **kwargs), label='power')
c = plt.plot([], label='ct')[0].get_color()
for dpdu, ws in zip(dpdu_lst, ws_pts):
plot_gradients(wt.power(ws, **kwargs), dpdu, ws, "power", 1)
ax = plt.twinx()
ax.plot(ws_lst, wt.ct(ws_lst, **kwargs), color=c)
for dctdu, ws in zip(dctdu_lst, ws_pts):
plot_gradients(wt.ct(ws, **kwargs), dctdu, ws, "ct", 1, ax=ax)
plt.title(case)
plt.show()
npt.assert_array_almost_equal(dpdu_lst, dpdu_ref,
(0, 4)[grad_method == autograd])
npt.assert_array_almost_equal(dctdu_lst, dctdu_ref,
(4, 6)[grad_method == autograd])
if __name__ == '__main__':
x = np.linspace(0, 2 * np.pi, 100)
def test_dAEP_2wt():
site = Hornsrev1Site()
iea37_site = IEA37Site(16)
wsp_cut_in = 4
wsp_cut_out = 25
wsp_rated = 9.8
power_rated = 3350000
constant_ct = 8 / 9
def ct(wsp):
wsp = np.asarray(wsp)
ct = np.zeros_like(wsp, dtype=float)
ct[(wsp >= wsp_cut_in) & (wsp <= wsp_cut_out)] = constant_ct
return ct
def power(wsp):
wsp = np.asarray(wsp)
power = np.where((wsp > wsp_cut_in) & (wsp <= wsp_cut_out),
np.minimum(
power_rated * ((wsp - wsp_cut_in) /
(wsp_rated - wsp_cut_in))**3,
power_rated), 0)
return power
def dpower(wsp):
return np.where((wsp > wsp_cut_in) & (wsp <= wsp_rated),
3 * power_rated * (wsp - wsp_cut_in)**2 /
(wsp_rated - wsp_cut_in)**3, 0)
def dct(wsp):
return wsp * 0 # constant ct
wt = DeprecatedOneTypeWindTurbines(name='test',
diameter=130,
hub_height=110,
ct_func=ct,
power_func=power,
power_unit='w')
wt.set_gradient_funcs(dpower, dct)
wfm = IEA37SimpleBastankhahGaussian(site, wt)
x, y = iea37_site.initial_position[np.array([0, 2, 5, 8, 14])].T
# plot 2 wt case
x, y = np.array([[0, 130 * 4], [0, 0]], dtype=float)
x_lst = np.array([0., 1.]) * np.arange(1, 600, 10)[:, na]
kwargs = {'ws': [10], 'wd': [270]}
_, (ax1, ax2) = plt.subplots(1, 2, sharey=False)
ax1.plot(x_lst[:, 1], [wfm.aep(x_, y, **kwargs) for x_ in x_lst])
ax1.set_xlabel('Downwind distance [m]')
ax1.set_ylabel('AEP [GWh]')
x_ = x_lst[20]
ax1.set_title("Center line")
for grad in [fd, cs, autograd]:
dAEPdx = wfm.dAEPdn(0, grad)(x_, y, **kwargs)[1]
npt.assert_almost_equal(dAEPdx / 360, 3.976975605364392e-06,
(10, 5)[grad == fd])
plot_gradients(wfm.aep(x_, y, **kwargs),
dAEPdx,
x_[1],
grad.__name__,
step=100,
ax=ax1)
y_lst = np.array([0, 1.]) * np.arange(-100, 100, 5)[:, na]
ax2.plot(y_lst[:, 1], [wfm.aep(x, y_, **kwargs) for y_ in y_lst])
ax2.set_xlabel('Crosswind distance [m]')
ax2.set_ylabel('AEP [GWh]')
y_ = y_lst[25]
ax2.set_title("%d m downstream" % x[1])
for grad in [fd, cs, autograd]:
dAEPdy = wfm.dAEPdn(1, grad)(x, y_, **kwargs)[1]
plot_gradients(wfm.aep(x, y_, **kwargs),
dAEPdy,
y_[1],
grad.__name__,
step=50,
ax=ax2)
npt.assert_almost_equal(dAEPdy / 360, 3.794435973860448e-05,
(10, 5)[grad == fd])
if 0:
plt.legend()
plt.show()
plt.close('all')
