Abigail is Theresa's grandmother. Her Pikachu, Sugar, ran away to try and find a way to toast Aspear Berries for a bake-off that she is competing in. Sugar saved Pikachu and found Ash and his friends and found her way back to Abigail.
Abigail owns a Pikachu that she uses to toast Aspear Berries. It went away after it thought it was useless, but came back, stronger than ever, and evolved into Raichu.