add v_from_i, improve singlediode speed by 2x (#190)

* implement v_from_i

* add and use v_from_i, just add _dpower_dcurrent

* remove _dpower_dcurrent

* add notes to whatsnew

* remove _v_oc_optfcn

* fix doc typo

* add a v_from_i test representative of a cdte voc

Author: wholmgren

docs/sphinx/source/whatsnew/v0.3.3.txt

@@ -24,6 +24,10 @@ Enhancements
   (:issue:`169`)
 * Add ``__repr__`` method to PVSystem, LocalizedPVSystem, ModelChain,
   SingleAxisTracker, Location. (:issue:`142`)
+* Add ``v_from_i`` function for solving the single diode model.
+  (:issue:`190`)
+* Improve speed of ``singlediode`` function by using ``v_from_i`` to
+  determine ``v_oc``. Speed is ~2x faster. (:issue:`190`)
 
 
 Bug fixes

pvlib/pvsystem.py

@@ -1395,15 +1395,16 @@ def singlediode(module, photocurrent, saturation_current,
     i_sc = i_from_v(resistance_shunt, resistance_series, nNsVth, 0.01,
                     saturation_current, photocurrent)
 
+    # Find open circuit voltage using Lambert W
+    v_oc = v_from_i(resistance_shunt, resistance_series, nNsVth, 0.0,
+                    saturation_current, photocurrent)
+
     params = {'r_sh': resistance_shunt,
               'r_s': resistance_series,
               'nNsVth': nNsVth,
               'i_0': saturation_current,
               'i_l': photocurrent}
 
-    __, v_oc = _golden_sect_DataFrame(params, 0, module['V_oc_ref']*1.6,
-                                      _v_oc_optfcn)
-
     p_mp, v_mp = _golden_sect_DataFrame(params, 0, module['V_oc_ref']*1.14,
                                         _pwr_optfcn)
 
@@ -1534,13 +1535,70 @@ def _pwr_optfcn(df, loc):
     return I*df[loc]
 
 
-def _v_oc_optfcn(df, loc):
+def v_from_i(resistance_shunt, resistance_series, nNsVth, current,
+             saturation_current, photocurrent):
     '''
-    Function to find the open circuit voltage from ``i_from_v``.
+    Calculates voltage from current per Eq 3 Jain and Kapoor 2004 [1].
+
+    Parameters
+    ----------
+    resistance_shunt : float or Series
+        Shunt resistance in ohms under desired IV curve conditions.
+        Often abbreviated ``Rsh``.
+
+    resistance_series : float or Series
+        Series resistance in ohms under desired IV curve conditions.
+        Often abbreviated ``Rs``.
+
+    nNsVth : float or Series
+        The product of three components. 1) The usual diode ideal factor
+        (n), 2) the number of cells in series (Ns), and 3) the cell
+        thermal voltage under the desired IV curve conditions (Vth). The
+        thermal voltage of the cell (in volts) may be calculated as
+        ``k*temp_cell/q``, where k is Boltzmann's constant (J/K),
+        temp_cell is the temperature of the p-n junction in Kelvin, and
+        q is the charge of an electron (coulombs).
+
+    current : float or Series
+        The current in amperes under desired IV curve conditions.
+
+    saturation_current : float or Series
+        Diode saturation current in amperes under desired IV curve
+        conditions. Often abbreviated ``I_0``.
+
+    photocurrent : float or Series
+        Light-generated current (photocurrent) in amperes under desired
+        IV curve conditions. Often abbreviated ``I_L``.
+
+    Returns
+    -------
+    current : np.array
+
+    References
+    ----------
+    [1] A. Jain, A. Kapoor, "Exact analytical solutions of the
+    parameters of real solar cells using Lambert W-function", Solar
+    Energy Materials and Solar Cells, 81 (2004) 269-277.
     '''
-    I = -abs(i_from_v(df['r_sh'], df['r_s'], df['nNsVth'],
-                      df[loc], df['i_0'], df['i_l']))
-    return I
+    try:
+        from scipy.special import lambertw
+    except ImportError:
+        raise ImportError('This function requires scipy')
+
+    Rsh = resistance_shunt
+    Rs = resistance_series
+    I0 = saturation_current
+    IL = photocurrent
+    I = current
+
+    argW = I0 * Rsh / nNsVth * np.exp(Rsh *(-I + IL + I0) / nNsVth)
+    lambertwterm = lambertw(argW)
+
+    # Eqn. 3 in Jain and Kapoor, 2004
+
+    V = -I*(Rs + Rsh) + IL*Rsh - nNsVth*lambertwterm + I0*Rsh
+
+    return V.real
 
 
 def i_from_v(resistance_shunt, resistance_series, nNsVth, voltage,

pvlib/test/test_pvsystem.py

@@ -229,6 +229,16 @@ def test_PVSystem_calcparams_desoto():
     assert_almost_equals(nNsVth, 0.473)
 
 
+def test_v_from_i():
+    output = pvsystem.v_from_i(20, .1, .5, 3, 6e-7, 7)
+    assert_almost_equals(7.5049875193450521, output, 5)
+
+
+def test_v_from_i_big():
+    output = pvsystem.v_from_i(500, 10, 4.06, 0, 6e-10, 1.2)
+    assert_almost_equals(86.320000493521079, output, 5)
+
+
 def test_i_from_v():
     output = pvsystem.i_from_v(20, .1, .5, 40, 6e-7, 7)
     assert_almost_equals(-299.746389916, output, 5)
@@ -263,16 +273,16 @@ def test_singlediode_floats():
     module = 'Example_Module'
     module_parameters = sam_data['cecmod'][module]
     out = pvsystem.singlediode(module_parameters, 7, 6e-7, .1, 20, .5)
-    expected = {'i_xx': 4.2549732697234193,
+    expected = {'i_xx': 4.2685798754011426,
                 'i_mp': 6.1390251797935704,
-                'v_oc': 8.1147298764528042,
+                'v_oc': 8.1063001465863085,
                 'p_mp': 38.194165464983037,
                 'i_x': 6.7556075876880621,
                 'i_sc': 6.9646747613963198,
                 'v_mp': 6.221535886625464}
     assert isinstance(out, dict)
     for k, v in out.items():
-        assert_almost_equals(expected[k], v, 5)
+        yield assert_almost_equals, expected[k], v, 3
 
 
 def test_PVSystem_singlediode_floats():
@@ -281,16 +291,16 @@ def test_PVSystem_singlediode_floats():
     system = pvsystem.PVSystem(module=module,
                                module_parameters=module_parameters)
     out = system.singlediode(7, 6e-7, .1, 20, .5)
-    expected = {'i_xx': 4.2549732697234193,
+    expected = {'i_xx': 4.2685798754011426,
                 'i_mp': 6.1390251797935704,
-                'v_oc': 8.1147298764528042,
+                'v_oc': 8.1063001465863085,
                 'p_mp': 38.194165464983037,
                 'i_x': 6.7556075876880621,
                 'i_sc': 6.9646747613963198,
                 'v_mp': 6.221535886625464}
     assert isinstance(out, dict)
     for k, v in out.items():
-        assert_almost_equals(expected[k], v, 5)
+        yield assert_almost_equals, expected[k], v, 3
 
 
 def test_scale_voltage_current_power():
@@ -478,7 +488,7 @@ def test_PVSystem___repr__():
 
     assert system.__repr__()==('PVSystem with tilt:0 and azimuth:'+
     ' 180 with Module: blah and Inverter: blarg')
-    
+
 
 def test_PVSystem_localize___repr__():
     system = pvsystem.PVSystem(module='blah', inverter='blarg')
@@ -504,7 +514,7 @@ def test_LocalizedPVSystem_creation():
     assert localized_system.latitude == 32
     assert localized_system.longitude == -111
 
-    
+
 def test_LocalizedPVSystem___repr__():
     localized_system = pvsystem.LocalizedPVSystem(latitude=32,
                                                   longitude=-111,