# pvl_est_kappa_IEC60891_2

PVL_EST_KAPPA_IEC60891_2 Estimate the curve correction factor kappa for IEC 60891 method 2.

## Contents

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

## Syntax

`kappa = pvl_est_kappa_IEC60891_2(IVCurves, aIsc, bVoc, Rs)`

## Description:

Methods 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). A value for the curve correction factor interpreted as the temperature coefficient of the series resistance is found by interative search using a set of IV curves measured at different cell temperatures and at a common irradiance: first, voltage and current for each IV curve are translated to a common temperature, then kappa is found by minimizing the variance of Pmp of the translated IV curves.

`pvl_est_kappa_IEC60891_2` assumes that the IV curves have been translated to a common irradiance.

## 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).
- `Rs` - the series resistance estimated for curve translation in ohms, see `pvl_est_Rs_IEC60891_2`

## Outputs:

- `kappa` - the curve correction factor in ohm/K.

## 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 = 1000;
    Tc = 25:1:35;
    nPts = 100;
    for i=1:length(Tc)
        [IL, I0, Rs, Rsh1, nNsVth] = pvl_calcparams_desoto(Ee, Tc(i), 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(Tc)
        IVcurves(i).Ee = Ee;
        IVcurves(i).Tc = Tc(i);
    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;

    % Use known Rs for the curve correction factor. Otherwise, estimate Rs from
    % a set of IV curves with fixed temperature and varying irradiance, using
    % pvl_est_Rs_IEC60891_2
    Rs_est = param.Rs_ref;

    % Estimate kappa
    kappa = pvl_est_kappa_IEC60891_2(IVcurves, aIsc_rel, bVoc_rel, Rs_est)

    kappa =

       -0.0045

## 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_Rs_IEC60891_2`, `pvl_translate_IV_curve_IEC60891_2`

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