Getting extra equation numbers using align environment

Just omit the line-break directive at the end of the final equation in a given align group. E.g.,

\begin{align} P(t) &= \tfrac{3}{2}[v_d(t)i_d(t)] \\ Q(t) &= \tfrac{3}{2}[-v_d(t)i_q(t)] % <- no "\\" directive \end{align} 

As the code shows, I would also (a) remove the \left and \right qualifiers as they actually don't do anything for the cases at hand and (b) replace \frac with \tfrac.

If you have a multi-line equation that should be assigned just one equation number, don't use an align environment. Instead, use a split environment inside an equation environment.

By the way, the arrows produced by \overrightarrow look disproportionately large; consider using \vec instead. For arrows (and other diacritics) set above the characters i and j, it's traditional to omit the "dot", i.e., to use a "dotless" i and j; this may be achieved in math mode by writing \imath and \jmath. Separately, I again would not use \left and \right to autosize the round parentheses and curly braces; consider using \bigl and \bigr instead. (By the way, the outermost round parentheses may be omitted in all three rows, right?)

\documentclass{article} \usepackage{amsmath} \numberwithin{equation}{section} \begin{document} \setcounter{section}{1} % just for this example \setcounter{equation}{31} \begin{align} P(t) &= \tfrac{3}{2}[v_d(t)i_d(t)] \\ Q(t) &= \tfrac{3}{2}[-v_d(t)i_q(t)] \end{align} \setcounter{equation}{20} % just for this example \begin{equation}\begin{split} P(t) &= \frac{ \Re\bigl\{\vec{v}(t)\vec{\imath}(t)\bigr\} + \Re\bigl\{\vec{v}(t)\vec{\imath}(t)^*\bigr\}}{2} \\ &\quad+ \frac{ \Re\bigl\{\vec{v}(t)\vec{\imath}(t)e^{-j\frac{4\pi}{3}}\bigr\} + \Re\bigl\{\vec{v}(t)\vec{\imath}(t)^*\bigr\}}{2} \\ &\quad+ \frac{ \Re\bigl\{\vec{v}(t)\vec{\imath}(t)e^{-j\frac{8\pi}{3}}\bigr\} + \Re\bigl\{\vec{v}(t)\vec{\imath}(t)^*\bigr\}}{2} \end{split}\end{equation} \end{document}