Dafür gibt es eine spezielle batchInsert-Methode:
Yii::$app->db->createCommand()->batchInsert('tableName', ['id', 'title', 'created_at'], [
[1, 'title1', '2015-04-10'],
[2, 'title2', '2015-04-11'],
[3, 'title3', '2015-04-12'],
])->execute();