What conditions must be satisfied for parallel operation of transformers?

For successful parallel operation: same voltage ratio (to prevent circulating current at no-load), same percentage impedance (for proper load sharing), same phase shift (for three-phase), same polarity, and same phase sequence. Transformers with unequal impedances share load inversely proportional to their per-unit impedances. Equal impedance ensures equal loading. Vector groups must be compatible (same clock number or phase displacement). Small voltage ratio differences cause large circulating currents.