Combine vegetable broth, barley, tomatoes, carrots, celery, zucchini, onion, corn, bay leaves, salt, sugar, pepper, and garlic powder in a multi-functional pressure cooker (such as Instant Pot(R)). Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 20 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Unlock and remove the lid.