1

I have a large fraction containing very similar parts in both the numerator and denominator, but since the denominator has additional variables, the similar parts are not aligned together. Here is the picture:

enter image description here

I want is align similar parts of both numerator and denominator as in this (photo-edited) picture:

enter image description here

My source code:

\documentclass[]{report}

\usepackage{amsmath}

\begin{document}

\begin{equation}
    I_{rs} = \frac{ y^{2} I_{sc,ref}
        \bigg[
        1 + \frac{\alpha}{100} (T_{op}-T_{ref})
        \biggl]
    }
    {exp
        \left
        ( \displaystyle \frac{V_{oc,ref} \bigg[  1 + \frac{\beta}{100} (T_{op}-T_{ref}) \biggl]}   {a \thinspace V_{t}}
        \right)  - 1 
    }
    %
    \label{eq:I_rs_trans}
\end{equation}

\end{document}
2

I wouldn't align these as structurally aligning the terms seems confusing, but...

enter image description here

\documentclass[]{report}

\usepackage{amsmath}

\def\posA{0sp}\def\posB{0sp}
\begin{document}

\begin{equation}\makeatletter
    I_{\mathrm{rs}} = \frac{ y^{2} I_{\mathrm{sc}sc,\mathrm{ref}}
\pdfsavepos\write\@auxout{\gdef\string\posA{\the\pdflastxpos sp}}% 
        \biggl[
        1 + \frac{\alpha}{100} (T_{\mathrm{op}}-T_{\mathrm{ref}})
        \biggr]\kern2\dimexpr\posA-\posB\relax
    }
    {\exp
        \left
        ( \displaystyle \frac{V_{\mathrm{oc},\mathrm{ref}}
\pdfsavepos\write\@auxout{\gdef\string\posB{\the\pdflastxpos sp}}% 
\biggl[  1 + \frac{\beta}{100} (T_{\mathrm{op}}-T_{\mathrm{ref}}) \biggr]}   {a \thinspace V_{t}}
        \right)  - 1 
    }
    %
    \label{eq:I_rs_trans}
\end{equation}

\end{document}

It takes two runs to stabilize. Note using \mathrm and \bigl on the left not the right.

2

I suspect your readers won't gain much, in terms of really understanding what's going on in the equation, if the two terms in square brackets are aligned. In fact, they might become confused, or at least distracted.

Your readers might, instead, appreciate something that's more compact:

enter image description here

\documentclass{report}
\usepackage{amsmath}
\begin{document}

\begin{equation} \label{eq:I_rs_trans}
    I_{\mathrm{rs}} = 
    \frac{ y^2 I_{\mathrm{sc},\mathrm{ref}}
            \bigl[ 1+\frac{\alpha}{100} (T_{\mathrm{op}}-T_{\mathrm{ref}}) \bigr] 
         }
         { \exp\bigl\{ 
            (a V_{t}{)}^{-1}V_{\mathrm{oc},\mathrm{ref}} 
            \bigl[ 1+\frac{\beta}{100} (T_{\mathrm{op}}-T_{\mathrm{ref}}) \bigr] 
            \bigr\}  - 1  
         }
\end{equation}

\end{document}

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