The city’s new parking rates will go into effect this week. Beginning Thursday, the on-street parking limit will be increased from two to three hours and the meter rate will increase from $1 an hour to $1.50 per hour on “high-occupancy” streets. In the High-Hanover parking garage, there will be no charge for the first hour and 75 cents per hour for any additional time. Parking will be free in the garage for Portsmouth residents on Sundays. The fines for parking at expired meters will increase from $10 to $15, and late-payment fines will rise from $25 to $30.