Fit this equation code into column width

Question

Is there any way I can fit this equation into column width?

\begin{equation}\label{eq19}
\begin{aligned}
\frac{\partial P_k}{\partial V_{r_o}} = 
\begin{cases}
  & 2V_{r_k}G_{kk}(T) + \sum^{n}_{i=1} (G_{ki}(T)V_{r_i}-B_{ki}(T)V_{m_i}) \\
  & \sum_{o=1}^{n} (B_{ko}(T)V_{r_o}+G_{ko}(T)V_{m_o})
\end{cases}
\end{aligned}
\end{equation}

Because I am working on IEEEtrans style, every page is two columns and I want to fit it in single column width.

Thanks.

Update

This is what I am trying to get

\begin{equation}\label{eq19}
\frac{\partial P_k}{\partial V_{r_o}} =
\begin{dcases}
2V_{r_k}G_{kk}(T) + \sum^{n}_{i=1} (G_{ki}(T)V_{r_i}-B_{ki}(T)V_{m_i})         
\textnormal{for $o=k$}\\
\sum_{o=1}^{n} (B_{ko}(T)V_{r_o}+G_{ko}(T)V_{m_o}) \textnormal{for $o\neq k$}
\end{dcases}
\end{equation}

But the conditions need to be aligned and the entire equation, I was hoping, could be possibly fit in the column.

Update

This is where I am so far

\begin{equation}\label{eq19}
\frac{\partial P_k}{\partial V_{r_o}} =
\begin{dcases}
2V_{r_k}G_{kk}(T) + \sum^{n}_{i=1} (G_{ki}(T)V_{r_i}-B_{ki}      
(T)V_{m_i})~&\textnormal{for $o=k$} \\
(V_{r_k}G_{ko}(T)+V_{m_k}B_{ko}(T))~&\textnormal{for $o\neq k$}
\end{dcases}
\end{equation}

\begin{equation}
\frac{\partial P_k}{\partial V_{r_o}} =
\left\lbrace\begin{aligned}
&2V_{r_k}G_{kk}(T) + \sum^{n}_{i=1}(G_{ki}(T)V_{r_i}-B_{ki}(T)V_{m_i})~&&\textnormal{for $o=k$} \\
&\sum_{o=1}^{n} (B_{ko}(T)V_{r_o}+G_{ko}(T)V_{m_o})~&&\textnormal{for $o\neq k$}
\end{aligned}\right.
\end{equation}

Anyway now to fit them into the column width without multiline or splitting?

Answer 1

Since you still not provide a Minimal Working Example (MWE) which we can test, is difficult to help you. In your code and mentioned document class, which you should use, I found more issues:

• IEEEtrans is corrupted with message of the person who claim that he improved it. So, if you receive any result, than you didn't use it. To resolve this, please (I ask you again) complete your code snipped, that we can see, what is really going on in your document.
• From LaTeX aspect, if cases is real necessary, the use of aligned environment is surplus.
• From math aspect the use of cases is not complete: in it I miss condition when one of equations is valid.

To solve your basic problem, you need to break first equation in cases into two lines, for example as follows:

\begin{equation}\label{eq19}
\frac{\partial P_k}{\partial V_{r_o}} =
\begin{dcases}
\begin{multlined}[0.5\linewidth]
    2V_{r_k}G_{kk}(T)\\ + \sum^{n}_{i=1} (G_{ki}(T)V_{r_i}-B_{ki}(T)V_{m_i})
\end{multlined} \\
\sum_{o=1}^{n} (B_{ko}(T)V_{r_o}+G_{ko}(T)V_{m_o})
\end{dcases}
\end{equation}

which in my math testbed using \documentclass{IEEEtran} gives:

For any further help, please consider my comments above.

Addendum:

Considering David Carlisle assumption in his answer, you can rewrite your equation into following form:

by:

\documentclass{ieeetran}
\usepackage{mathtools}

\usepackage{lipsum}

\begin{document}
\lipsum*[1]
\begin{multline}\label{eq19}
\frac{\partial P_k}{\partial V_{r_o}} =
    2V_{r_k}G_{kk}(T) + \\
    \sum^{n}_{i=1} (G_{ki}(T)V_{r_i}-B_{ki}(T)V_{m_i}) + \\
    \sum_{o=1}^{n} (B_{ko}(T)V_{r_o}+G_{ko}(T)V_{m_o})
\end{multline}
\lipsum[2-9]
\end{document}

Edit:

After end it seems, that your equation will have some condition. For it writing in equation you need space, so the your problem can become more acute: for their writing is only for four letter space left! As possible solution you can write:

\documentclass{ieeetran}
\usepackage{mathtools}
\usepackage[T1]{fontenc}

\usepackage{lipsum}% for dummy text

\begin{document}
\lipsum*[1]
\begin{equation}\label{eq19}
\frac{\partial P_k}{\partial V_{r_o}} =
\begin{dcases}
\begin{multlined}
    2V_{r_k}G_{kk}(T)\\ + \sum^{n}_{i=1} (G_{ki}(T)V_{r_i}-B_{ki}(T)V_{m_i})
\end{multlined}                                     &   *   \\
\sum_{o=1}^{n} (B_{ko}(T)V_{r_o}+G_{ko}(T)V_{m_o})  &   **
\end{dcases}
\end{equation}
 where are * <condition 1> and **  <condition 2> respectively.

\lipsum[2-7]
\end{document}

Answer 2

How about dispensing with the dcases machinery entirely and using a simple array environment instead?

\documentclass[twocolumn]{IEEEtran}
\usepackage{array,amsmath}
\begin{document}
\begin{equation}\label{eq19}
\frac{\partial P_k}{\partial V_{r_o}} =
\left\{\begin{array}{@{\,}>{\displaystyle}l@{}}
2V_{r_k}G_{kk}(T) + \sum^{n}_{i=1} \bigl(G_{ki}(T)V_{r_i}\\[2.75ex]
\multicolumn{1}{r@{}}{{}-B_{ki}(T)V_{m_i}\bigr) \quad\text{for $o=k$}} \\[1ex]
\sum_{o=1}^{n} \bigl(B_{ko}(T)V_{r_o}+G_{ko}(T)V_{m_o}\bigr) \quad\text{for $o\neq k$}
\end{array}\right.
\end{equation}
\end{document}