# pvl_est_Rs_Bowden

PVL_EST_RS_BOWDEN Estimate Rs using the method of Bowden and Rohatgi.

## Contents

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

## Syntax

- `[Rs, errest] = pvl_est_Rs_Bowden(Vocs, Iscs, V, I)`
- `[Rs, errest] = pvl_est_Rs_Bowden(Vocs, Iscs, V, I, Rshf, Rshs, Io, nNsVth)`

## Description:

The method of Bowden and Rohatgi estimates a value for series resistance using values from two IV curves, one under 'shaded' conditions, anticipated to be ~100 W/m2, and another at 'full-sun' conditions, anticipated to be ~1000 W/m2. The cell temperature is assumed to be the same for both IV curves. Voc and Isc from the shaded IV curve are used with Isc from the full sun IV curve to locate the desired point on the full sun IV curve. If optional arguments are provided, the difference between the returned Rs value and the Rs parameter for the single diode equation is estimated, see [2].

## Inputs:

- `Vocs` - open circuit voltage on the shaded (low irradiance) IV curve, in V.
- `Iscs` - short circuit current on the shaded (low irradiance) IV curve, in A.
- `V` - a vector of voltages for the full sun IV curve. It is assumed that V(1) = 0.
- `I` - a vector of currents for the full sun IV curve. It is assumed that I(1) = Isc.
- `Rshs` - (optional) shunt resistance, in ohms, for the shaded IV curve.
- `Rshf` - (optional) shunt resistance, in ohms, for the full-sun IV curve.
- `nNsVth` - (optional) the product n (diode factor) x Ns (cells in series) x Vth (thermal voltage per cell) for both IV curves.
- `Io` - (optional) the dark current, in A, for both IV curves.

## Outputs:

- `Rs` - the series resistance value in ohms.
- `errest` - the estimated difference between Rs and the series resistance parameter for the single diode equation.

## 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 full sun IV curve
    Ee = 1000;
    Tc = 25;
    nPts = 100;
    [IL, I0, Rs, Rshf, nNsVth] = pvl_calcparams_desoto(Ee, Tc, param.aIsc, param, EgRef, dEgdT);
    fullsunIVcurve = pvl_singlediode(IL, I0, Rs, Rshf, nNsVth, nPts);

    % Calculate shaded IV curve
    Ee = 200;
    [IL, I0, Rs, Rshs, nNsVth] = pvl_calcparams_desoto(Ee, Tc, param.aIsc, param, EgRef, dEgdT);
    shadedIVcurve = pvl_singlediode(IL, I0, Rs, Rshs, nNsVth, nPts);

    % Estimate Rs
    Rs = pvl_est_Rs_Bowden(shadedIVcurve.Voc, shadedIVcurve.Isc, fullsunIVcurve.V, fullsunIVcurve.I)

    Rs =

        0.2051

## References:

- [1] S. Bowden and Rohatgi, A., “Rapid and Accurate Determination of Series Resistance and Fill Factor Losses in Industrial Silicon Solar Cells”, in 17th European Photovoltaic Solar Energy Conference, Munich, Germany, 2001.

- [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_Swanson` , `pvl_est_Rs_sunsVoc` , `pvl_est_Rs_Pysch` , `pvl_est_Rs_IEC60891_1` , `pvl_est_Rs_IEC60891_2`

Copyright 2018 Sandia National Laboratories