# pvl_est_Rs_IEC60891_2

PVL_EST_RS_IEC60891_2 Estimate Rs using method 2 of IEC60891.

## Contents

- Syntax
- Description:
- Inputs:
- Outputs:
- Example
- References:
- See also

## Syntax

`Rs = pvl_est_Rs_IEC60891_2(IVCurves, aIsc, bVoc)`

## Description:

Method 2 in IEC60891 translates a point on an IV curve measured at irradiance G1 and cell temperature Tc1 to the corresponding point on an unobserved IV curve at irradiance G2 and cell temperature Tc2. The translation reduces the voltage value by a voltage drop across the ‘internal series resistance’ of the module ([IEC 60891], Eq. 2). The resistance Rs is found by an iterative search over a set of IV curves measured at different irradiance levels and constant cell temperature: first, current for each IV curve is translated linearly to a common irradiance, then a fitting parameter is found by translating Voc to a common value, and finally Rs is found by minimizing the variance of Pmp of the translated IV curves. Method 2 differs from Method 1 by allowing greater variation in irradiance among the IV curves.

`pvl_est_Rs_IEC60891_2` assumes that the IV curves are measured at, or have been translated to a common cell temperature.

## Inputs:

- `IVCurves` - A structure array with the following fields:
- * `IVCurves.Isc` - short circuit current in amperes.
- * `IVCurves.Voc` - open circuit voltage in volts.
- * `IVCurves.Imp` - current at maximum power point in amperes.
- * `IVCurves.Vmp` - voltage at maximum power point in volts.
- * `IVCurves.Pmp` - power at maximum power point in watts.
- * `IVCurves.V` - vector of voltage in volts.
- * `IVCurves.I` - vector of current in amperes.
- * `IVCurves.Ee` - Effective irradiance (W/m2).
- * `IVCurves.Tc` - cell temperature (C).
- `aIsc` - relative temperature coefficient for short circuit current in 1/C (not A/C).
- `bVoc` - relative temperature coefficient for open circuit voltage in 1/C (not V/C).

## Outputs:

- `Rs` - the series resistance value in ohms.

## Example

    clearvars

    % Set up parameters for a representative 60 cell cSi module using the Desoto model
    Const.q = 1.60218E-19;
    Const.k = 1.38066E-23;
    Const.E0 = 1000;
    Const.T0 = 25;

    param.aIsc = 0.0008;  % A/C
    param.bVoc = -0.1900; % V/C

    param.Rs_ref = 0.2;
    param.Rsh_ref = 1000;
    param.IL_ref = 8.0;
    param.I0_ref = 5e-10;

    param.a_ref = 1.05 * 60 * Const.k/Const.q * (273.15 + Const.T0);

    EgRef = 1.121;
    dEgdT = -0.0002677;

    % Calculate set of IV curves
    Ee = 900:20:1100;
    Tc = 25;
    nPts = 100;
    for i=1:length(Ee)
        [IL, I0, Rs, Rsh1, nNsVth] = pvl_calcparams_desoto(Ee(i), Tc, param.aIsc, param, EgRef, dEgdT);
        IVcurves(i) = pvl_singlediode(IL, I0, Rs, Rsh1, nNsVth, nPts);
    end

    % Add Ee and Tc to IVcurves
    for i=1:length(Ee)
        IVcurves(i).Ee = Ee(i);
        IVcurves(i).Tc = Tc;
    end

    % Calculate relative temperature coefficients

    STC_Isc = IVcurves(6).Isc;
    STC_Voc = IVcurves(6).Voc;
    aIsc_rel = param.aIsc / STC_Isc;
    bVoc_rel = param.bVoc / STC_Voc;

    % Estimate Rs and a
    [Rs, a] = pvl_est_Rs_IEC60891_2(IVcurves, aIsc_rel, bVoc_rel)

    Rs =

        0.1996

    a =

        0.0428

## References:

- [1] IEC60891 Ed. 2 2009. Procedures for temperature and irradiance corrections to measured I-V characteristics of crystalline silicon photovoltaic (PV) devices.

- [2] C. Hansen and B. King, "Determining series resistance for equivalent circuit models of a PV module", in 45th IEEE Photovoltaic Specialist Conference, Waikoloa, HI, 2018.

## See also

`pvl_est_kappa_IEC60891_2`, `pvl_translate_IV_curve_IEC60891_2`

Copyright 2018 Sandia National Laboratories