From personal experience I can say that it is necessary to keep the battery inserted into the laptop when the power is on. Lithium ion batteries lose their strength after a certain period to some 20% of capacity a year. On the old laptop I always just used the power without the battery in order to avoid overheating the battery, however, soon became useless.

On the second laptop I have used the power and battery at the same time in 2 years of using batteries barely had waned. Also please note that the laptop is on an average 15 hours a day.   
The point is that batteries have a number of charging and discharging using both batteries and battery, power is only slightly filled without having to empty the whole time and extends battery life.