def test_IEA37_ex16(deficitModel, aep_ref):
site = IEA37Site(16)
x, y = site.initial_position.T
windTurbines = IEA37_WindTurbines()
wf_model = PropagateDownwind(site,
windTurbines,
wake_deficitModel=deficitModel,
superpositionModel=SquaredSum(),
turbulenceModel=GCLTurbulence())
aep_ilk = wf_model(x, y, wd=np.arange(0, 360, 22.5),
ws=[9.8]).aep_ilk(normalize_probabilities=True)
aep_MW_l = aep_ilk.sum((0, 2)) * 1000
# check if ref is reasonable
aep_est = 16 * 3.35 * 24 * 365 * .8 # n_wt * P_rated * hours_pr_year - 20% wake loss = 375628.8
npt.assert_allclose(aep_ref[0], aep_est, rtol=.11)
npt.assert_allclose(aep_ref[1], [
9500, 8700, 11500, 14300, 21300, 25900, 39600, 44300, 23900, 13900,
15200, 33000, 72100, 18300, 12500, 8000
],
rtol=.15)
npt.assert_almost_equal(aep_MW_l.sum(), aep_ref[0], 5)
npt.assert_array_almost_equal(aep_MW_l, aep_ref[1], 5)
def test_fuga_downwind_vs_notebook():
powerCtFunction = PowerCtTabular([0, 100], [0, 0], 'w',
[0.850877, 0.850877])
wt = WindTurbine(name='',
diameter=80,
hub_height=70,
powerCtFunction=powerCtFunction)
path = tfp + 'fuga/2MW/Z0=0.00001000Zi=00400Zeta0=0.00E+00'
site = UniformSite([1, 0, 0, 0], ti=0.075)
wfm_ULT = PropagateDownwind(site, wt, FugaYawDeficit(path))
WS = 10
p = Path(tfp) / "fuga/v80_wake_4d_y_no_deflection.csv"
y, notebook_deficit_4d = np.array(
[v.split(",") for v in p.read_text().strip().split("\n")],
dtype=float).T
sim_res = wfm_ULT([0], [0], wd=270, ws=WS, yaw=[[[17.4493]]])
fm = sim_res.flow_map(XYGrid(4 * wt.diameter(), y=y))
npt.assert_allclose(fm.WS_eff.squeeze() - WS,
notebook_deficit_4d,
atol=1e-6)
if 0:
plt.plot(y, notebook_deficit_4d, label='Notebook deficit 4d')
plt.plot(y, fm.WS_eff.squeeze() - WS)
plt.show()
plt.close('all')
def test_GenericWindTurbine():
for ref, ti, cut_in, cut_out, p_tol, ct_tol in [(V80(), .1, 4, None, 0.03, .14),
(WindTurbine.from_WAsP_wtg(wtg_path +
"Vestas V112-3.0 MW.wtg"), .05, 3, 25, 0.035, .07),
(DTU10MW(), .05, 4, 25, 0.06, .12)]:
power_norm = ref.power(np.arange(10, 20)).max()
wt = GenericWindTurbine('Generic', ref.diameter(), ref.hub_height(), power_norm / 1e3,
turbulence_intensity=ti, ws_cutin=cut_in, ws_cutout=cut_out)
if 0:
u = np.arange(0, 30, .1)
p, ct = wt.power_ct(u)
plt.plot(u, p / 1e6, label='Generic')
plt.plot(u, ref.power(u) / 1e6, label=ref.name())
plt.ylabel('Power [MW]')
plt.legend(loc='center left')
ax = plt.twinx()
ax.plot(u, ct, '--')
ax.plot(u, ref.ct(u), '--')
ax.set_ylim([0, 1])
plt.ylabel('Ct')
plt.show()
u = np.arange(5, 25)
p, ct = wt.power_ct(u)
p_ref, ct_ref = ref.power_ct(u)
# print(np.abs(p_ref - p).max() / power_norm)
npt.assert_allclose(p, p_ref, atol=power_norm * p_tol)
# print(np.abs(ct_ref - ct).max())
npt.assert_allclose(ct, ct_ref, atol=ct_tol)
def test_iea37_distances():
from py_wake.examples.data.iea37 import IEA37Site
n_wt = 16 # must be 9, 16, 36, 64
site = IEA37Site(n_wt)
x, y = site.initial_position.T
lw = site.local_wind(x_i=x, y_i=y,
wd=site.default_wd,
ws=site.default_ws)
dw_iil, hcw_iil, _, _ = site.wt2wt_distances(
x_i=x, y_i=y,
h_i=np.zeros_like(x),
wd_il=lw.WD_ilk.mean(2))
# Wind direction.
wdir = np.rad2deg(np.arctan2(hcw_iil, dw_iil))
npt.assert_allclose(
wdir[:, 0, 0],
[180, -90, -18, 54, 126, -162, -90, -54, -18, 18, 54, 90, 126, 162, -162, -126],
atol=1e-4)
if 0:
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.scatter(x, y)
for i, txt in enumerate(np.arange(len(x))):
ax.annotate(txt, (x[i], y[i]), fontsize='large')
def test_deficitModel_wake_map_convection(deficitModel, ref):
site = IEA37Site(16)
x, y = site.initial_position.T
windTurbines = IEA37_WindTurbines()
wf_model = PropagateDownwind(site, windTurbines, wake_deficitModel=deficitModel, superpositionModel=WeightedSum(),
turbulenceModel=GCLTurbulence())
x_j = np.linspace(-1500, 1500, 200)
y_j = np.linspace(-1500, 1500, 100)
flow_map = wf_model(x, y, wd=0, ws=9).flow_map(HorizontalGrid(x_j, y_j))
X, Y = flow_map.X, flow_map.Y
Z = flow_map.WS_eff_xylk[:, :, 0, 0]
mean_ref = [3.2, 4.9, 8., 8.2, 7.9, 7.4, 7., 7., 7.4, 7.9, 8.1, 8.1, 8., 7.8, 7.9, 8.1, 8.4]
if 0:
flow_map.plot_wake_map()
plt.plot(X[49, 100:133:2], Y[49, 100:133:2], '.-')
windTurbines.plot(x, y)
plt.figure()
plt.plot(Z[49, 100:133:2], label='Actual')
plt.plot(ref, label='Reference')
plt.plot(mean_ref, label='Mean ref')
plt.legend()
plt.show()
# check that ref is reasonable
npt.assert_allclose(ref[2:], mean_ref[2:], atol=2.6)
npt.assert_array_almost_equal(Z[49, 100:133:2], ref, 2)
def test_yaw_tilt(yaw, tilt, cx, cz):
site = IEA37Site(16)
x, y = [0], [0]
windTurbines = V80()
D = windTurbines.diameter()
wfm = IEA37SimpleBastankhahGaussian(
site, windTurbines, deflectionModel=JimenezWakeDeflection())
x_lst = np.linspace(-200, 1000, 100)
y_lst = np.linspace(-100, 100, 201)
z_lst = np.arange(10, 200, 1)
fm_yz = wfm(x, y, wd=270, ws=10, yaw=yaw,
tilt=tilt).flow_map(YZGrid(x=5 * D, y=y_lst, z=z_lst))
fm_xz = wfm(x, y, wd=180, ws=10, yaw=yaw,
tilt=tilt).flow_map(YZGrid(x=0, y=x_lst, z=z_lst))
fm_xy = wfm(x, y, wd=270, ws=10, yaw=yaw,
tilt=tilt).flow_map(XYGrid(x=x_lst))
if 0:
axes = plt.subplots(3, 1)[1].flatten()
fm_xy.plot_wake_map(ax=axes[0])
axes[0].axvline(5 * D)
fm_xz.plot_wake_map(ax=axes[1])
axes[1].axvline(5 * D)
fm_yz.plot_wake_map(ax=axes[2])
plt.show()
wake_center = fm_yz.WS_eff.where(fm_yz.WS_eff == fm_yz.WS_eff.min(),
drop=True).squeeze()
npt.assert_allclose(wake_center.y, cx, atol=.1)
npt.assert_allclose(wake_center.h, cz, atol=.24)
def test_fuga_wake_center_vs_notebook():
p = Path(tfp) / "fuga/v80_wake_center_x.csv"
x, notebook_wake_center = np.array([v.split(",") for v in p.read_text().strip().split("\n")], dtype=float).T
powerCtFunction = PowerCtTabular([0, 100], [0, 0], 'w', [0.850877, 0.850877])
wt = WindTurbine(name='', diameter=80, hub_height=70, powerCtFunction=powerCtFunction)
path = tfp + 'fuga/2MW/Z0=0.00001000Zi=00400Zeta0=0.00E+00'
site = UniformSite([1, 0, 0, 0], ti=0.075)
wfm = PropagateDownwind(
site,
wt,
wake_deficitModel=FugaYawDeficit(path),
deflectionModel=FugaDeflection(path, 'input_par')
)
WS = 10
sim_res = wfm([0], [0], yaw=[17.4493], wd=270, ws=[WS])
y = wfm.wake_deficitModel.mirror(wfm.wake_deficitModel.y, anti_symmetric=True)
fm = sim_res.flow_map(XYGrid(x=x[1:], y=y[240:271]))
fuga_wake_center = [np.interp(0, InterpolatedUnivariateSpline(ws.y, ws.values).derivative()(ws.y), ws.y)
for ws in fm.WS_eff.squeeze().T]
if 0:
plt.plot(x, notebook_wake_center, label='Notebook deflection')
plt.plot(x[1:], fuga_wake_center)
plt.show()
plt.close('all')
npt.assert_allclose(fuga_wake_center, notebook_wake_center[1:], atol=.14)
def test_wake_radius(deficitModel, wake_radius_ref):
mean_ref = [105, 68, 135, 93, 123]
# check that ref is reasonable
npt.assert_allclose(wake_radius_ref, mean_ref, rtol=.5)
npt.assert_array_almost_equal(deficitModel.wake_radius(
D_src_il=np.reshape([100, 50, 100, 100, 100], (5, 1)),
dw_ijlk=np.reshape([500, 500, 1000, 500, 500], (5, 1, 1, 1)),
ct_ilk=np.reshape([.8, .8, .8, .4, .8], (5, 1, 1)),
TI_ilk=np.reshape([.1, .1, .1, .1, .05], (5, 1, 1)),
TI_eff_ilk=np.reshape([.1, .1, .1, .1, .05], (5, 1, 1)))[:, 0, 0, 0],
wake_radius_ref)
# Check that it works when called from WindFarmModel
site = IEA37Site(16)
windTurbines = IEA37_WindTurbines()
wfm = PropagateDownwind(site, windTurbines, wake_deficitModel=deficitModel, turbulenceModel=GCLTurbulence())
wfm(x=[0, 500], y=[0, 0], wd=[30], ws=[10])
if 0:
sim_res = wfm([0], [0], wd=[270], ws=10)
sim_res.flow_map(HorizontalGrid(x=np.arange(-100, 1500, 10))).WS_eff.plot()
x = np.arange(0, 1500, 10)
wr = deficitModel.wake_radius(
D_src_il=np.reshape([130], (1, 1)),
dw_ijlk=np.reshape(x, (1, len(x), 1, 1)),
ct_ilk=sim_res.CT.values,
TI_ilk=np.reshape(sim_res.TI.values, (1, 1, 1)),
TI_eff_ilk=sim_res.TI_eff.values)[0, :, 0, 0]
plt.title(deficitModel.__class__.__name__)
plt.plot(x, wr)
plt.plot(x, -wr)
plt.axis('equal')
plt.show()
def test_two_turbine_case0_time_series():
# same as test_two_turbine_case0
ws, ti, shear, wdir, dist = [10.9785338191, 0.2623204277, 0.4092031776, -38.4114616871 % 360, 5.123719529]
# ref from simulation statistic (not updated yet)
ws_ref = 1.103937e+01
thrust_ref = 4.211741e+02
power_ref = 3.399746e+06
ref_dels = [4546, 5931, 11902, 7599, 2407]
wt = IEA34_130_2WT_Surrogate()
site = UniformSite(p_wd=[1], ti=ti, ws=ws)
wfm = NOJ(site, wt, turbulenceModel=STF2017TurbulenceModel())
sim_res = wfm([0, 0], [0, dist * 130], wd=wdir, time=True, Alpha=shear)
assert sim_res.dw_ijl.dims == ('wt', 'wt', 'time')
npt.assert_allclose(ws, ws_ref, rtol=.006)
# npt.assert_allclose(ti, ws_std_ref / ws_ref, atol=.19)
npt.assert_allclose(sim_res.Power.sel(wt=0), power_ref, rtol=0.002)
npt.assert_allclose(sim_res.CT.sel(wt=0), thrust_ref * 1e3 / (1 / 2 * 1.225 * (65**2 * np.pi) * ws_ref**2),
rtol=0.03)
sim_res['duration'] = ('time', [3600 * 24 * 365 * 20])
loads = sim_res.loads(method='TwoWT')
npt.assert_allclose(loads.DEL.sel(wt=0).squeeze(), ref_dels, rtol=.05)
f = 20 * 365 * 24 * 3600 / 1e7
m = loads.m.values
npt.assert_array_almost_equal(loads.LDEL.sel(wt=0).squeeze(), (loads.DEL.sel(wt=0).squeeze()**m * f)**(1 / m))
loads = sim_res.loads(method='TwoWT', softmax_base=100)
npt.assert_allclose(loads.DEL.sel(wt=0).squeeze(), ref_dels, rtol=.05)
npt.assert_array_almost_equal(loads.LDEL.sel(wt=0).squeeze(), (loads.DEL.sel(wt=0).squeeze()**m * f)**(1 / m))
def test_time_series_aep():
d = np.load(os.path.dirname(examples.__file__) + "/data/time_series.npz")
wd, ws = [d[k][::100] for k in ['wd', 'ws']]
wt = V80()
site = Hornsrev1Site()
x, y = site.initial_position.T
wfm = NOJ(site, wt)
sim_res = wfm(x, y, ws=ws, wd=wd, time=True, verbose=False)
npt.assert_allclose(sim_res.aep().sum(), 545, atol=1)
def test_two_turbine_case0():
if 0:
i = 0
f = r'C:\mmpe\programming\python\Topfarm\iea-3_4-130-rwt\turbine_model\res/'
print(list(pd.DataFrame(eval(Path(f + 'input_two_turbines_dist.json').read_text())).iloc[i]))
# [10.9785338191, 0.2623204277, 0.4092031776, -38.4114616871, 5.123719529]
print(pd.concat([pd.read_csv(f + 'stats_two_turbines_mean.csv').iloc[i, [12, 14, 322]],
pd.read_csv(f + 'stats_two_turbines_std.csv').iloc[i, [12, 14, 322]]],
axis=1))
# Free wind speed Abs_vhor, gl. coo, of gl. pos ... 1.103937e+01 0.914252
# Aero rotor thrust 4.211741e+02 41.015962
# generator_servo inpvec 2 2: pelec [w] 3.399746e+06 3430.717100
print(pd.read_csv(f + 'stats_two_turbines_del.csv').iloc[i, [28, 29, 1, 2, 9]])
# MomentMx Mbdy:blade1 nodenr: 1 coo: blade1 blade root moment blade1 4546.998501
# MomentMy Mbdy:blade1 nodenr: 1 coo: blade1 blade root moment blade1 5931.157693
# MomentMx Mbdy:tower nodenr: 1 coo: tower tower bottom moment 11902.153031
# MomentMy Mbdy:tower nodenr: 1 coo: tower tower bottom moment 7599.336676
# MomentMz Mbdy:tower nodenr: 11 coo: tower tower top/yaw bearing moment 2407.279074
ws, ti, shear, wdir, dist = [10.9785338191, 0.2623204277, 0.4092031776, -38.4114616871 % 360, 5.123719529]
# ref from simulation statistic (not updated yet)
ws_ref = 1.103937e+01
ws_std_ref = 0.914252
thrust_ref = 4.211741e+02
power_ref = 3.399746e+06
ref_dels = [4546, 5931, 11902, 7599, 2407]
wt = IEA34_130_2WT_Surrogate()
site = UniformSite(p_wd=[1], ti=ti, ws=ws)
sim_res = NOJ(site, wt, turbulenceModel=STF2017TurbulenceModel())([0, 0], [0, dist * 130], wd=wdir, Alpha=shear)
npt.assert_allclose(ws, ws_ref, rtol=.006)
# npt.assert_allclose(ti, ws_std_ref / ws_ref, atol=.19)
npt.assert_allclose(sim_res.Power.sel(wt=0), power_ref, rtol=0.002)
npt.assert_allclose(sim_res.CT.sel(wt=0), thrust_ref * 1e3 / (1 / 2 * 1.225 * (65**2 * np.pi) * ws_ref**2),
rtol=0.03)
loads = sim_res.loads(method='TwoWT')
npt.assert_allclose(loads.DEL.sel(wt=0).squeeze(), ref_dels, rtol=.05)
f = 20 * 365 * 24 * 3600 / 1e7
m = loads.m.values
npt.assert_array_almost_equal(loads.LDEL.sel(wt=0).squeeze(), (loads.DEL.sel(wt=0).squeeze()**m * f)**(1 / m))
loads = sim_res.loads(method='TwoWT', softmax_base=100)
npt.assert_allclose(loads.DEL.sel(wt=0).squeeze(), ref_dels, rtol=.05)
npt.assert_array_almost_equal(loads.LDEL.sel(wt=0).squeeze(), (loads.DEL.sel(wt=0).squeeze()**m * f)**(1 / m))
def test_neighbour_farm_speed():
# import and setup site and windTurbines
site = IEA37Site(16)
# setup current, neighbour and all positions
wt_x, wt_y = site.initial_position.T
neighbour_x, neighbour_y = wt_x - 4000, wt_y
all_x, all_y = np.r_[wt_x, neighbour_x], np.r_[wt_y, neighbour_y]
windTurbines = WindTurbines.from_WindTurbines([IEA37_WindTurbines(), IEA37_WindTurbines()])
windTurbines._names = ["Current wind farm", "Neighbour wind farm"]
types = [0] * len(wt_x) + [1] * len(neighbour_x)
wf_model = PropagateDownwind(site, windTurbines,
wake_deficitModel=BastankhahGaussianDeficit(use_effective_ws=True),
superpositionModel=LinearSum())
# Consider wd=270 +/- 30 deg only
wd_lst = np.arange(240, 301)
sim_res, t = timeit(wf_model, verbose=False)(all_x, all_y, type=types, ws=9.8, wd=wd_lst)
if 1:
ext = 100
flow_box = wf_model(neighbour_x, neighbour_y, wd=wd_lst).flow_box(
x=np.linspace(min(wt_x) - ext, max(wt_x) + ext, 53),
y=np.linspace(min(wt_y) - ext, max(wt_y) + ext, 51),
h=[100, 110, 120])
wake_site = XRSite.from_flow_box(flow_box)
wake_site.save('tmp.nc')
else:
wake_site = XRSite.load('tmp.nc')
wf_model_wake_site = PropagateDownwind(wake_site, windTurbines,
wake_deficitModel=BastankhahGaussianDeficit(use_effective_ws=True),
superpositionModel=LinearSum())
sim_res_wake_site, _ = timeit(wf_model_wake_site, verbose=False)(wt_x, wt_y, ws=9.8, wd=wd_lst)
npt.assert_allclose(sim_res.aep().sel(wt=np.arange(len(wt_x))).sum(), sim_res_wake_site.aep().sum(), rtol=0.0005)
npt.assert_array_almost_equal(sim_res.aep().sel(wt=np.arange(len(wt_x))), sim_res_wake_site.aep(), 2)
def test_fuga_deflection_vs_notebook():
p = Path(tfp) / "fuga/v80_deflection_x.csv"
x, notebook_deflection = np.array([v.split(",") for v in p.read_text().strip().split("\n")], dtype=float).T
path = tfp + 'fuga/2MW/Z0=0.00001000Zi=00400Zeta0=0.00E+00'
fuga_deflection = -FugaDeflection(path).calc_deflection(dw_ijl=np.reshape(x, (1, 41, 1)),
hcw_ijl=np.reshape(x * 0, (1, 41, 1)),
dh_ijl=np.reshape(x * 0, (1, 41, 1)),
WS_ilk=np.array([[[9.5]]]),
WS_eff_ilk=np.array([[[9.5]]]),
yaw_ilk=np.array([[[17.4493]]]),
ct_ilk=np.array([[[0.850877]]]) *
np.cos(0.30454774)**2,
D_src_il=np.array([[80]]))[1].squeeze()
if 0:
plt.plot(x, notebook_deflection, label='Notebook deflection')
plt.plot(x, fuga_deflection)
plt.show()
plt.close('all')
npt.assert_allclose(fuga_deflection, notebook_deflection, atol=1e-5)
def test_GlobalWindAtlasSite():
ref = Hornsrev1Site()
lat, long = 55.52972, 7.906111 # hornsrev
site = GlobalWindAtlasSite(lat, long, height=70, roughness=0.001, ti=0.075)
ref_mean = weibull.mean(ref.ds.Weibull_A, ref.ds.Weibull_k)
gwa_mean = weibull.mean(site.ds.Weibull_A, site.ds.Weibull_k)
if 0:
plt.figure()
plt.plot(ref.ds.wd, ref_mean, label='HornsrevSite')
plt.plot(site.ds.wd, gwa_mean, label='HornsrevSite')
for r in [0, 1.5]:
for h in [10, 200]:
A, k = [site.gwc_ds[v].sel(roughness=r, height=h) for v in ['Weibull_A', 'Weibull_k']]
plt.plot(site.gwc_ds.wd, weibull.mean(A, k), label=f'{h}, {r}')
plt.legend()
plt.show()
npt.assert_allclose(gwa_mean, ref_mean, atol=1.4)
for var, atol in [('Sector_frequency', 0.03), ('Weibull_A', 1.6), ('Weibull_k', 0.4)]:
npt.assert_allclose(site.ds[var], ref.ds[var], atol=atol)
def test_one_turbine_case0():
ws, ti, shear = 9.2984459862, 0.0597870198, 0.2
if 0:
f = r'C:\mmpe\programming\python\Topfarm\iea-3_4-130-rwt\turbine_model\res/'
print(pd.concat([pd.read_csv(f + 'stats_one_turbine_mean.csv').iloc[0, [10, 14, 322]],
pd.read_csv(f + 'stats_one_turbine_std.csv').iloc[0, [10, 14, 322]]],
axis=1))
# Free wind speed Vy, gl. coo, of gl. pos 0.00... 9.309756e+00 0.401308
# Aero rotor thrust 5.408776e+02 11.489005
# generator_servo inpvec 2 2: pelec [w] 2.931442e+06 116491.192548
print(pd.read_csv(f + 'stats_one_turbine_del.csv').iloc[0, [28, 29, 1, 2, 9]])
# MomentMx Mbdy:blade1 nodenr: 1 coo: blade1 blade root moment blade1 1822.247387
# MomentMy Mbdy:blade1 nodenr: 1 coo: blade1 blade root moment blade1 5795.166623
# MomentMx Mbdy:tower nodenr: 1 coo: tower tower bottom moment 4385.405881
# MomentMy Mbdy:tower nodenr: 1 coo: tower tower bottom moment 2468.357017
# MomentMz Mbdy:tower nodenr: 11 coo: tower tower top/yaw bearing moment 1183.884786
ws_ref = 9.309756e+00
ws_std_ref = 0.401308
power_ref = 2.931442e+06
thrust_ref = 5.408776e+02
ref_dels = [1822, 5795, 4385, 2468, 1183]
wt = IEA34_130_1WT_Surrogate()
assert wt.loadFunction.output_keys[1] == 'del_blade_edge'
assert wt.loadFunction.wohler_exponents == [10, 10, 4, 4, 7]
site = UniformSite(p_wd=[1], ti=ti, ws=ws)
sim_res = NOJ(site, wt, turbulenceModel=STF2017TurbulenceModel())([0], [0], wd=0, Alpha=shear)
npt.assert_allclose(ws, ws_ref, rtol=.0013)
npt.assert_allclose(ti, ws_std_ref / ws_ref, atol=.02)
npt.assert_allclose(sim_res.Power, power_ref, rtol=0.003)
npt.assert_allclose(sim_res.CT, thrust_ref * 1e3 / (1 / 2 * 1.225 * (65**2 * np.pi) * ws_ref**2), rtol=0.011)
loads = sim_res.loads(method='OneWT')
npt.assert_allclose(loads.DEL.squeeze(), ref_dels, rtol=.11)
f = 20 * 365 * 24 * 3600 / 1e7
m = np.array([10, 10, 4, 4, 7])
npt.assert_array_almost_equal(loads.LDEL.squeeze(), (loads.DEL.squeeze()**m * f)**(1 / m))
loads = sim_res.loads(method='OneWT_WDAvg')
npt.assert_allclose(loads.DEL.squeeze(), ref_dels, rtol=.11)
npt.assert_array_almost_equal(loads.LDEL.squeeze(), (loads.DEL.squeeze()**m * f)**(1 / m))
