Problem with { and } when splitting equation into two lines

Question

I am using the following equation which works perfect when it is a single-line equation:

\begin{equation}
    \mathrm{NPIF}^\ast_i \mathrel{\mathop:}= \sum_{j=1}^{\mathrm{N}_\mathrm{L}} \biggl\{ w_{\mathrm{L},j} \, \tilde{l}_j \left[ \mathrm{PTDF}^{\left[ k_+ \right]}_{ij} \, \bigl( x_{\mathrm{L,max},j}^{\left[ k_+ \right]} \bigr)^{\mathrm{n}_1} + \mathrm{PTDF}^{\left[ k_- \right]}_{ij} \, \bigl( x_{\mathrm{L,min},j}^{\left[ k_- \right]} \bigr)^{\mathrm{n}_1} \right] \biggr\}
\end{equation}

I would like to break this equation into two lines using the splitenvironment:

\begin{equation}
\begin{split}
    \mathrm{NPIF}^\ast_i \mathrel{\mathop:}= \sum_{j=1}^{\mathrm{N}_\mathrm{L}} \biggl\{ w_{\mathrm{L},j} \, \tilde{l}_j \left[ \mathrm{PTDF}^{\left[ k_+ \right]}_{ij} \, \bigl( x_{\mathrm{L,max},j}^{\left[ k_+ \right]} \bigr)^{\mathrm{n}_1} \\
    + \mathrm{PTDF}^{\left[ k_- \right]}_{ij} \, \bigl( x_{\mathrm{L,min},j}^{\left[ k_- \right]} \bigr)^{\mathrm{n}_1} \right] \biggr\}
\end{split}
\end{equation}

The last code gives me a ! Extra }, or forgotten \right. error. I tried to close the two brackets in the first line by using \right. \right. and a corresponding \left. \left. on the second line but this did not solve the error... Any ideas?

Answer 1

You have \left in one line and the matching \right in the other one: this is not allowed.

Also, there's no need that outer parentheses are larger than inner ones; in this case \Big size is enough; also the square brackets are in the same size for ease of reading. The alignment point can be at “PDTF”, in order to exploit the symmetry.

I introduced a shorthand for \mathrm; a more semantic command is better anyway (change the name into one that suits you best). I'm not sure about \mathrm applied to the exponent n_1, though. I'm also dubious about the usefulness of the braces.

\documentclass{article}
\usepackage{mathtools}

\newcommand{\rv}[1]{\mathrm{#1}}

\begin{document}

\begin{equation}
\begin{split}
\rv{NPIF}^\ast_i \coloneqq
  \sum_{j=1}^{\rv{N}_\rv{L}}
    \Bigl\{
      w_{\rv{L},j} \tilde{l}_j
      \Bigl[ & \rv{PTDF}^{[k_+]}_{ij} (x_{\rv{L,max},j}^{[ k_+]} )^{\rv{n}_1} \\
    {} + {}  & \rv{PTDF}^{[k_-]}_{ij}( x_{\rv{L,min},j}^{[k_-]})^{\rv{n}_1} \Bigr] \Bigr\}
\end{split}
\end{equation}

\end{document}

Answer 2

In your case you want to break the line at the + sign. Therefore you have one open \left in the first line and an open \right in the second line.

So you need one \right. in the first line and one \left. in the second line (see the marked lines <======== in the following MWE).

The following MWE compiles with no errors:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\begin{equation}
    \mathrm{NPIF}^\ast_i \mathrel{\mathop:}= 
    \sum_{j=1}^{\mathrm{N}_\mathrm{L}} \biggl\{ w_{\mathrm{L},j} \, \tilde{l}_j 
    \left[ \mathrm{PTDF}^{\left[ k_+ \right]}_{ij} \, 
    \bigl( x_{\mathrm{L,max},j}^{\left[ k_+ \right]} \bigr)^{\mathrm{n}_1} 
    + \mathrm{PTDF}^{\left[ k_- \right]}_{ij} \, 
    \bigl( x_{\mathrm{L,min},j}^{\left[ k_- \right]} \bigr)^{\mathrm{n}_1} \right] \biggr\}
\end{equation}

\begin{equation}
\begin{split}
    \mathrm{NPIF}^\ast_i \mathrel{\mathop:}= \sum_{j=1}^{\mathrm{N}_\mathrm{L}} 
      \biggl\{ w_{\mathrm{L},j} \, \tilde{l}_j 
      \left[ \mathrm{PTDF}^{\left[ k_+ \right]}_{ij} \, 
      \bigl( x_{\mathrm{L,max},j}^{\left[ k_+ \right]} \bigr)^{\mathrm{n}_1} 
      \right.\\ % <=====================================================
    + \left. % <========================================================
      \mathrm{PTDF}^{\left[ k_- \right]}_{ij} \, 
      \bigl( x_{\mathrm{L,min},j}^{\left[ k_- \right]} \bigr)^{\mathrm{n}_1} \right] \biggr\}
\end{split}
\end{equation}

\end{document}