Polyester resin, water dispersion of polyester resin and method for preparing water dispersion

A polyester resin represented by the following chemical structure of formula (I) and having an acid value of 250 to 2,500 eq/106 g and a number-average molecular weight of 2,000 to 50,000:

• (X—O)r—W—(O—(CO—Z—CO—O—Y—O)p—X)q (I)
• wherein W is a (q+r)-valent organic group;
• (CO—Z—CO—O—Y—O) is a skeleton of polyester resin prepared by polymerization using a polyvalent carboxylic acid ingredient Z and a polyhydric alcohol ingredient Y as polymerizing ingredients;
• X is a residue of polybasic acid having two or more carboxyl groups or is hydrogen (except the case wherein all of X in numbers of (q+r) are hydrogen);
• X, Y and Z each may be the same as or different from each other and, even in the same repetitive unit, X, Y and Z each may be the same as or different from each other;
• average value of p is 3 or more, average value of q is more than 0 and is 15 or less, average value of r is 0 or more and is less than 15, and (q+r) is 3 or more and 15 or less.