From 5359efe3cd564807792cd99f6a80647928736859 Mon Sep 17 00:00:00 2001 From: Felix Korbelius <75846164+FelixKoTU@users.noreply.github.com> Date: Mon, 18 Nov 2024 13:46:22 +0100 Subject: [PATCH] fix: missing subscript for number of cells in series (N_s) in equations --- docs/sphinx/source/user_guide/singlediode.rst | 28 +++++++++---------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/docs/sphinx/source/user_guide/singlediode.rst b/docs/sphinx/source/user_guide/singlediode.rst index 2fafa7d9f5..085b0b66cc 100644 --- a/docs/sphinx/source/user_guide/singlediode.rst +++ b/docs/sphinx/source/user_guide/singlediode.rst @@ -24,7 +24,7 @@ diode model equation. .. math:: - I = I_L - I_0 \left(\exp \left(\frac{V + I R_s}{n Ns V_{th}} \right) - 1 \right) + I = I_L - I_0 \left(\exp \left(\frac{V + I R_s}{n N_s V_{th}} \right) - 1 \right) - \frac{V + I R_s}{R_{sh}} Lambert W-function is the inverse of the function @@ -36,8 +36,8 @@ a form that can be expressed as a Lambert W-function. .. math:: - z = \frac{R_s I_0}{n Ns V_{th} \left(1 + \frac{R_s}{R_{sh}} \right)} \exp \left( - \frac{R_s \left( I_L + I_0 \right) + V}{n Ns V_{th} \left(1 + \frac{R_s}{R_{sh}}\right)} + z = \frac{R_s I_0}{n N_s V_{th} \left(1 + \frac{R_s}{R_{sh}} \right)} \exp \left( + \frac{R_s \left( I_L + I_0 \right) + V}{n N_s V_{th} \left(1 + \frac{R_s}{R_{sh}}\right)} \right) Then the module current can be solved using the Lambert W-function, @@ -46,7 +46,7 @@ Then the module current can be solved using the Lambert W-function, .. math:: I = \frac{I_L + I_0 - \frac{V}{R_{sh}}}{1 + \frac{R_s}{R_{sh}}} - - \frac{n Ns V_{th}}{R_s} W \left(z \right) + - \frac{n N_s V_{th}}{R_s} W \left(z \right) Bishop's Algorithm @@ -60,7 +60,7 @@ by a zero diode voltage and an estimate of open circuit voltage given by .. math:: - V_{oc, est} = n Ns V_{th} \log \left( \frac{I_L}{I_0} + 1 \right) + V_{oc, est} = n N_s V_{th} \log \left( \frac{I_L}{I_0} + 1 \right) We know that :math:`V_d = 0` corresponds to a voltage less than zero, and we can also show that when :math:`V_d = V_{oc, est}`, the resulting @@ -73,24 +73,24 @@ between 0 and :math:`V_{oc, est}` will always find any desired condition in the .. math:: - I = I_L - I_0 \left(\exp \left(\frac{V_{oc, est}}{n Ns V_{th}} \right) - 1 \right) + I = I_L - I_0 \left(\exp \left(\frac{V_{oc, est}}{n N_s V_{th}} \right) - 1 \right) - \frac{V_{oc, est}}{R_{sh}} \newline - I = I_L - I_0 \left(\exp \left(\frac{n Ns V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{n Ns V_{th}} \right) - 1 \right) - - \frac{n Ns V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline + I = I_L - I_0 \left(\exp \left(\frac{n N_s V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{n N_s V_{th}} \right) - 1 \right) + - \frac{n N_s V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline I = I_L - I_0 \left(\exp \left(\log \left(\frac{I_L}{I_0} + 1 \right) \right) - 1 \right) - - \frac{n Ns V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline + - \frac{n N_s V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline I = I_L - I_0 \left(\frac{I_L}{I_0} + 1 - 1 \right) - - \frac{n Ns V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline + - \frac{n N_s V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline I = I_L - I_0 \left(\frac{I_L}{I_0} \right) - - \frac{n Ns V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline + - \frac{n N_s V_{th} \log \left(\frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline - I = I_L - I_L - \frac{n Ns V_{th} \log \left( \frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline + I = I_L - I_L - \frac{n N_s V_{th} \log \left( \frac{I_L}{I_0} + 1 \right)}{R_{sh}} \newline - I = - \frac{n Ns V_{th} \log \left( \frac{I_L}{I_0} + 1 \right)}{R_{sh}} + I = - \frac{n N_s V_{th} \log \left( \frac{I_L}{I_0} + 1 \right)}{R_{sh}} References ---------- @@ -111,4 +111,4 @@ Clifford W. Hansen, Sandia `Report SAND2015-2065 [4] "Computer simulation of the effects of electrical mismatches in photovoltaic cell interconnection circuits" JW Bishop, Solar Cell (1988) -:doi:`10.1016/0379-6787(88)90059-2` \ No newline at end of file +:doi:`10.1016/0379-6787(88)90059-2`