You need
\subfigure[<caption>]{<image>\label{..}}
not
\subfigure[<caption>]{<image>}\label{..}
Note that the \label is placed before the last closing brace. Complete example below. I also replaced the center environment with \centering, cf. Weird figure numbering in RevTeX article
\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{subfigure}
\begin{document}
\begin{figure}
\centering
\subfigure[]{\includegraphics[height=4cm,width=4.5cm]{Fig_10(a)_Current_NLL_Sag}\label{subfig:real time single phase current NLL sag}}
\subfigure[]{\includegraphics[height=4cm,width=4.5cm]{Fig_10(b)_Current_NLL_LL_Sag}\label{subfig:real time single phase current NLL LL sag}}
\subfigure[]{\includegraphics[height=4cm,width=4.5cm]{Fig_10(c)_Voltage_NLL_LL_Sag}\label{subfig:real time single phase voltage NLL LL sag}}
\caption{\small \slshape Opal-RT results under voltage sag condition: $(a)$ load, source and compensating current with NLL only $(b)$ load, source and compensating current with NLL and LL $(c)$ source, load and series injected voltage with NLL and LL}
\label{Fig:real time single phase sag}
\end{figure}
Fig.~\ref{Fig:real time single phase sag} has
\ref{subfig:real time single phase current NLL sag},
\ref{subfig:real time single phase current NLL LL sag}, and
\ref{subfig:real time single phase voltage NLL LL sag}
\end{document}
But note that the subfigure package is considered deprecated, so it's generally recommended to move to the newer subcaption package (or possibly subfig). That package has a different syntax though. Here is one example with subcaption:
\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{subcaption}
\captionsetup[figure]{textfont={small,sl}}
\begin{document}
\begin{figure}
\centering
\subcaptionbox{\label{subfig:real time single phase current NLL sag}}{\includegraphics[height=4cm,width=4.5cm]{Fig_10(a)_Current_NLL_Sag}}
\subcaptionbox{\label{subfig:real time single phase current NLL LL sag}}{\includegraphics[height=4cm,width=4.5cm]{Fig_10(b)_Current_NLL_LL_Sag}}
\subcaptionbox{\label{subfig:real time single phase voltage NLL LL sag}}{\includegraphics[height=4cm,width=4.5cm]{Fig_10(c)_Voltage_NLL_LL_Sag}}
\caption{Opal-RT results under voltage sag condition: $(a)$ load, source and compensating current with NLL only $(b)$ load, source and compensating current with NLL and LL $(c)$ source, load and series injected voltage with NLL and LL}
\label{Fig:real time single phase sag}
\end{figure}
Fig.~\ref{Fig:real time single phase sag} has
\ref{subfig:real time single phase current NLL sag},
\ref{subfig:real time single phase current NLL LL sag}, and
\ref{subfig:real time single phase voltage NLL LL sag}
\end{document}
\begin{center}should be\centeringand\end{center}should be removed. If you really want additional vertical space (I doubt it),\labelshould be before\end{center}. Commands such as\slhave been deprecated for more than 20 years. – egreg Jan 02 '17 at 17:34