Is it normal for a teenage girl to always experience heavy periods?

No : It is not normal for teenagers specifically to have heavy periods. She should schedule a visit and discuss the many many options for menstrual cycle regulation. Birth control pills, the patch and NuvaRing can decrease bleeding. Mirena (levonorgestrel) iud can minimize cycles. Lysteda is a nonhormonal medication which can help too. There are many options.

Can be normal...: If your periods are too painful/heavy, see a GYN and get an US to detect problems like cervical lesions, infections, polyps, or fibroids. If you don't have any of these, you may benefit from hormonal control using contraceptives like the pill/patch/ring. The best option is a hormonal IUD (Mirena), that thins the lining and decreases your flow significantly. Some women even stop having periods!