Example 2 Given non-zero numbers $a, b$ satisfy
$$
|2 a-4|+|b+2|+\sqrt{(a-3) b^{2}}+4=2 a \text {. }
$$

Then the value of $a+b$ is ( ).
(2]
(A) -1
(B) 0
(C) 1
(D) 2
（2009, "Mathematics Weekly" Cup National Junior High School Mathematics Competition）
From the non-negativity of the radicand in the square root, we have
$$
\begin{array}{l}
(a-3) b^{2} \geqslant 0 \\
\Rightarrow a \geqslant 3 \\
\Rightarrow|2 a-4|=2 a-4 .
\end{array}
$$

Thus, the original expression becomes
$$
\begin{array}{l}
|b+2|+\sqrt{(a-3) b^{2}}=0 \\
\Rightarrow b+2=0,(a-3) b^{2}=0 \\
\Rightarrow b=-2, a=3 \\
\Rightarrow a+b=1 .
\end{array}
$$

Therefore, the answer is (C).