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| # -*- coding: utf-8 -*- | ||||||
| """ | ||||||
| This module contains functions for inverter modeling, primarily conversion of | ||||||
| DC to AC power. | ||||||
| """ | ||||||
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| import numpy as np | ||||||
| import pandas as pd | ||||||
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| def sandia(v_dc, p_dc, inverter): | ||||||
| r''' | ||||||
| Convert DC power and voltage to AC power using Sandia's | ||||||
| Grid-Connected PV Inverter model. | ||||||
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| Parameters | ||||||
| ---------- | ||||||
| v_dc : numeric | ||||||
| DC voltage input to the inverter. [V] | ||||||
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| p_dc : numeric | ||||||
| DC power input to the inverter. [W] | ||||||
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| inverter : dict-like | ||||||
| Defines parameters for the inverter model in [1]_. See Notes for | ||||||
| required model parameters. A copy of the parameter database from the | ||||||
| System Advisor Model (SAM) [2]_ is provided with pvlib and may be read | ||||||
| using :py:func:`pvlib.pvsystem.retrieve_sam`. | ||||||
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| Returns | ||||||
| ------- | ||||||
| power_ac : numeric | ||||||
| AC power output. [W] | ||||||
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| Notes | ||||||
| ----- | ||||||
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| Determines the AC power output of an inverter given the DC voltage and DC | ||||||
| power. Output AC power is bounded above by the parameter ``Paco``, to | ||||||
| represent inverter "clipping". When `power_ac` would be less than | ||||||
| parameter ``Pso`` (startup power required), then `power_ac` is set to | ||||||
| ``-Pnt``, representing self-consumption. `power_ac` is not adjusted for | ||||||
| maximum power point tracking (MPPT) voltage windows or maximum current | ||||||
| limits of the inverter. | ||||||
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| Required model parameters are: | ||||||
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| ====== ============================================================ | ||||||
| Column Description | ||||||
| ====== ============================================================ | ||||||
| Paco AC power rating of the inverter. [W] | ||||||
| Pdco DC power input to inverter, typically assumed to be equal | ||||||
| to the PV array maximum power. [W] | ||||||
| Vdco DC voltage at which the AC power rating is achieved | ||||||
| at the reference operating condition. [V] | ||||||
| Pso DC power required to start the inversion process, or | ||||||
| self-consumption by inverter, strongly influences inverter | ||||||
| efficiency at low power levels. [W] | ||||||
| C0 Parameter defining the curvature (parabolic) of the | ||||||
| relationship between AC power and DC power at the reference | ||||||
| operating condition. [1/W] | ||||||
| C1 Empirical coefficient allowing ``Pdco`` to vary linearly | ||||||
| with DC voltage input. [1/V] | ||||||
| C2 Empirical coefficient allowing ``Pso`` to vary linearly with | ||||||
| DC voltage input. [1/V] | ||||||
| C3 Empirical coefficient allowing ``C0`` to vary linearly with | ||||||
| DC voltage input. [1/V] | ||||||
| Pnt AC power consumed by the inverter at night (night tare). [W] | ||||||
| ====== ============================================================ | ||||||
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| References | ||||||
| ---------- | ||||||
| .. [1] D. King, S. Gonzalez, G. Galbraith, W. Boyson, "Performance Model | ||||||
| for Grid-Connected Photovoltaic Inverters", SAND2007-5036, Sandia | ||||||
| National Laboratories. | ||||||
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| .. [2] System Advisor Model web page. https://sam.nrel.gov. | ||||||
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| See also | ||||||
| -------- | ||||||
| pvlib.pvsystem.retrieve_sam | ||||||
| ''' | ||||||
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| Paco = inverter['Paco'] | ||||||
| Pdco = inverter['Pdco'] | ||||||
| Vdco = inverter['Vdco'] | ||||||
| Pso = inverter['Pso'] | ||||||
| C0 = inverter['C0'] | ||||||
| C1 = inverter['C1'] | ||||||
| C2 = inverter['C2'] | ||||||
| C3 = inverter['C3'] | ||||||
| Pnt = inverter['Pnt'] | ||||||
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| A = Pdco * (1 + C1 * (v_dc - Vdco)) | ||||||
| B = Pso * (1 + C2 * (v_dc - Vdco)) | ||||||
| C = C0 * (1 + C3 * (v_dc - Vdco)) | ||||||
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| power_ac = (Paco / (A - B) - C * (A - B)) * (p_dc - B) + C * (p_dc - B)**2 | ||||||
| power_ac = np.minimum(Paco, power_ac) | ||||||
| power_ac = np.where(p_dc < Pso, -1.0 * abs(Pnt), power_ac) | ||||||
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| if isinstance(p_dc, pd.Series): | ||||||
| power_ac = pd.Series(power_ac, index=p_dc.index) | ||||||
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| return power_ac | ||||||
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| def adr(v_dc, p_dc, inverter, vtol=0.10): | ||||||
| r''' | ||||||
| Converts DC power and voltage to AC power using Anton Driesse's | ||||||
| Grid-Connected PV Inverter efficiency model | ||||||
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| Parameters | ||||||
| ---------- | ||||||
| v_dc : numeric | ||||||
| DC voltage input to the inverter, should be >= 0. [V] | ||||||
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| p_dc : numeric | ||||||
| DC power input to the inverter, should be >= 0. [W] | ||||||
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| inverter : dict-like | ||||||
| Defines parameters for the inverter model in [1]_. See Notes for | ||||||
| required model parameters. A parameter database is provided with pvlib | ||||||
| and may be read using :py:func:`pvlib.pvsystem.retrieve_sam`. | ||||||
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| vtol : numeric, default 0.1 | ||||||
| Fraction of DC voltage that determines how far the efficiency model is | ||||||
| extrapolated beyond the inverter's normal input voltage operating | ||||||
| range. 0.0 <= vtol <= 1.0. [unitless] | ||||||
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| Returns | ||||||
| ------- | ||||||
| power_ac : numeric | ||||||
| AC power output. [W] | ||||||
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| Notes | ||||||
| ----- | ||||||
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| Determines the AC power output of an inverter given the DC voltage and DC | ||||||
| power. Output AC power is bounded above by the parameter ``Pacmax``, to | ||||||
| represent inverter "clipping". AC power is bounded below by ``-Pnt`` | ||||||
| (negative when power is consumed rather than produced) which represents | ||||||
| self-consumption. `power_ac` is not adjusted for maximum power point | ||||||
| tracking (MPPT) voltage windows or maximum current limits of the inverter. | ||||||
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| Required model parameters are: | ||||||
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| ======= ============================================================ | ||||||
| Column Description | ||||||
| ======= ============================================================ | ||||||
| Pnom Nominal DC power, typically the DC power needed to produce | ||||||
| maximum AC power output. [W] | ||||||
| Vnom Nominal DC input voltage. Typically the level at which the | ||||||
| highest efficiency is achieved. [V] | ||||||
| Vmax Maximum DC input voltage. [V] | ||||||
| Vmin Minimum DC input voltage. [V] | ||||||
| Vdcmax . [V] | ||||||
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There was a problem hiding this comment. @adriesse for the ADR inverter model, what is the definition of the parameter Vdcmax? The definition is missing from the function docstring. I'm having trouble distinguishing Vdcmax from Vmax, which I understand to be the maximum DC input voltage. It look like Vdcmax is an alternate upper bound on DC voltage. |
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| MPPTHi Maximum DC voltage for MPPT range. [V] | ||||||
| MPPTLow Minimum DC voltage for MPPT range. [V] | ||||||
| Pacmax Maximum AC output power, used to clip the output power | ||||||
| if needed. [W] | ||||||
| ADRCoefficients A list of 9 coefficients that capture the influence | ||||||
| of input voltage and power on inverter losses, and thereby | ||||||
| efficiency. Corresponds to terms from [1]_ (in order): :math: | ||||||
| `b_{0,0}, b_{1,0}, b_{2,0}, b_{0,1}, b_{1,1}, b_{2,1}, b_{0,2}, | ||||||
| b_{1,2}, b_{1,2}`. See [1]_ for the use of each coefficient | ||||||
| and the associated unit. | ||||||
| Pnt AC power consumed by inverter at night (night tare) to | ||||||
| maintain circuitry required to sense PV array voltage. [W] | ||||||
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| ======= ============================================================ | ||||||
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There was a problem hiding this comment. This parameter table doesn't show up on RTD -- maybe it's the linebreaks? The table in There was a problem hiding this comment. Sphinx still doesn't like this. I'm not if all of these steps are necessary, but I got it working locally for me by:
Here's the text that works for me (with some text reflows to stay under 80 chars): There was a problem hiding this comment. Two more notes: Vdcmax is still undefined and |
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| References | ||||||
| ---------- | ||||||
| .. [1] Driesse, A. "Beyond the Curves: Modeling the Electrical Efficiency | ||||||
| of Photovoltaic Inverters", 33rd IEEE Photovoltaic Specialist | ||||||
| Conference (PVSC), June 2008 | ||||||
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| See also | ||||||
| -------- | ||||||
| pvlib.inverter.sandia | ||||||
| pvlib.pvsystem.retrieve_sam | ||||||
| ''' | ||||||
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| p_nom = inverter['Pnom'] | ||||||
| v_nom = inverter['Vnom'] | ||||||
| pac_max = inverter['Pacmax'] | ||||||
| p_nt = inverter['Pnt'] | ||||||
| ce_list = inverter['ADRCoefficients'] | ||||||
| v_max = inverter['Vmax'] | ||||||
| v_min = inverter['Vmin'] | ||||||
| vdc_max = inverter['Vdcmax'] | ||||||
| mppt_hi = inverter['MPPTHi'] | ||||||
| mppt_low = inverter['MPPTLow'] | ||||||
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| v_lim_upper = float(np.nanmax([v_max, vdc_max, mppt_hi]) * (1 + vtol)) | ||||||
| v_lim_lower = float(np.nanmax([v_min, mppt_low]) * (1 - vtol)) | ||||||
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| pdc = p_dc / p_nom | ||||||
| vdc = v_dc / v_nom | ||||||
| # zero voltage will lead to division by zero, but since power is | ||||||
| # set to night time value later, these errors can be safely ignored | ||||||
| with np.errstate(invalid='ignore', divide='ignore'): | ||||||
| poly = np.array([pdc**0, # replace with np.ones_like? | ||||||
| pdc, | ||||||
| pdc**2, | ||||||
| vdc - 1, | ||||||
| pdc * (vdc - 1), | ||||||
| pdc**2 * (vdc - 1), | ||||||
| 1. / vdc - 1, # divide by 0 | ||||||
| pdc * (1. / vdc - 1), # invalid 0./0. --> nan | ||||||
| pdc**2 * (1. / vdc - 1)]) # divide by 0 | ||||||
| p_loss = np.dot(np.array(ce_list), poly) | ||||||
| power_ac = p_nom * (pdc - p_loss) | ||||||
| p_nt = -1 * np.absolute(p_nt) | ||||||
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| # set output to nan where input is outside of limits | ||||||
| # errstate silences case where input is nan | ||||||
| with np.errstate(invalid='ignore'): | ||||||
| invalid = (v_lim_upper < v_dc) | (v_dc < v_lim_lower) | ||||||
| power_ac = np.where(invalid, np.nan, power_ac) | ||||||
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| # set night values | ||||||
| power_ac = np.where(vdc == 0, p_nt, power_ac) | ||||||
| power_ac = np.maximum(power_ac, p_nt) | ||||||
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| # set max ac output | ||||||
| power_ac = np.minimum(power_ac, pac_max) | ||||||
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| if isinstance(p_dc, pd.Series): | ||||||
| power_ac = pd.Series(power_ac, index=pdc.index) | ||||||
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| return power_ac | ||||||
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| def pvwatts(pdc, pdc0, eta_inv_nom=0.96, eta_inv_ref=0.9637): | ||||||
| r""" | ||||||
| Implements NREL's PVWatts inverter model [1]_. | ||||||
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| .. math:: | ||||||
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| \eta = \frac{\eta_{nom}}{\eta_{ref}} (-0.0162\zeta - \frac{0.0059} | ||||||
| {\zeta} + 0.9858) | ||||||
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| .. math:: | ||||||
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| P_{ac} = \min(\eta P_{dc}, P_{ac0}) | ||||||
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| where :math:`\zeta=P_{dc}/P_{dc0}` and :math:`P_{dc0}=P_{ac0}/\eta_{nom}`. | ||||||
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| Note that ``pdc0`` is also used as a symbol in | ||||||
| :py:func:`pvlib.pvsystem.pvwatts_dc`. ``pdc0`` in this function refers to | ||||||
| the DC power input limit of the inverter. ``pdc0`` in | ||||||
| :py:func:`pvlib.pvsystem.pvwatts_dc` refers to the DC power of the modules | ||||||
| at reference conditions. | ||||||
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| Parameters | ||||||
| ---------- | ||||||
| pdc: numeric | ||||||
| DC power. Same unit as ``pdc0``. | ||||||
| pdc0: numeric | ||||||
| DC input limit of the inverter. Same unit as ``pdc``. | ||||||
| eta_inv_nom: numeric, default 0.96 | ||||||
| Nominal inverter efficiency. [unitless] | ||||||
| eta_inv_ref: numeric, default 0.9637 | ||||||
| Reference inverter efficiency. PVWatts defines it to be 0.9637 | ||||||
| and is included here for flexibility. [unitless] | ||||||
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| Returns | ||||||
| ------- | ||||||
| power_ac: numeric | ||||||
| AC power. Same unit as ``pdc0``. | ||||||
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| References | ||||||
| ---------- | ||||||
| .. [1] A. P. Dobos, "PVWatts Version 5 Manual," | ||||||
| http://pvwatts.nrel.gov/downloads/pvwattsv5.pdf | ||||||
| (2014). | ||||||
| """ | ||||||
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| pac0 = eta_inv_nom * pdc0 | ||||||
| zeta = pdc / pdc0 | ||||||
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| # arrays to help avoid divide by 0 for scalar and array | ||||||
| eta = np.zeros_like(pdc, dtype=float) | ||||||
| pdc_neq_0 = ~np.equal(pdc, 0) | ||||||
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| # eta < 0 if zeta < 0.006. power_ac is forced to be >= 0 below. GH 541 | ||||||
| eta = eta_inv_nom / eta_inv_ref * ( | ||||||
| -0.0162 * zeta - np.divide(0.0059, zeta, out=eta, where=pdc_neq_0) | ||||||
| + 0.9858) # noQA: W503 | ||||||
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| power_ac = eta * pdc | ||||||
| power_ac = np.minimum(pac0, power_ac) | ||||||
| power_ac = np.maximum(0, power_ac) # GH 541 | ||||||
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| return power_ac | ||||||
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