Q:

Problem with { and } when splitting equation into two lines

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?

A:

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}

