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So I have a A1502 Late 2013 and Early 2015 with me at the moment. If I unplug the battery they won’t power on without a 85 Watt charger? Is this normal?
Review the required charger here: Find the right power adapter and cable for your Mac notebook You do need to use the correct charger for your system as the wattage needs to be equal or larger than what the system requires. Did someone alter your MagSafe charger cable? The MagSafe & MagSafe2 chargers offer out different voltages. Update (01/24/2019) So you need a new battery! You’ll need to do that. No matter what charger you use. Here’s the needed part MacBook Pro 13" Retina (Late 2013-Mid 2014) Battery and here’s the IFIXIT guide to put it in MacBook Pro 13" Retina Display Late 2013 Battery Replacement
In some macs lower voltage chargers are not capable of charging so you require a high voltage charger for charging or switch on the computer as required by the system however high voltage doesn’t help you to charge faster and neither do it will harm the computer on long life may be you see an effect.