Recently I have started meditating on my own, by observing my breath and rise and fall of abdomen. Half an hour in the morning and half an hour in the night before going to sleep. Sometimes sleep takes over and I go to sleep immediately after meditation. But when I try to concentrate more during meditation, my mind becomes charged and even when I sleep, my mind is awake , although body is resting. I aware that my mind has not shutdown. Is this normal? am I doing correctly? This wakefulness is there till next day. Is this some kind of alpha state of mind? Please help.
But when I try to concentrate more during meditation, my mind becomes charged...
If what you are describing here is concentrate with more effort (rather than meditating for a longer duration) then what you have described is a common symptom of concentrating with too much power & effort.
While beginner meditators often meditate with mental force to counter (suppress) discursive (habitual) thinking, ultimately, Buddhist meditation is based on letting go & emptying the mind (rather than pushing the mind with power & effort).
(thīna-middha) is one of the 5 hindrance of mind. I too experience the same way. I feels more alert after a good session of meditation. 5 hindrance and mediation are polar opposites. I think we are doing good, where Buddha compare self monitoring to being a great chef who watches king at his dinner table to figure out his personal palate and adjust the next meals accordingly. This kind of chef will reap rewards.
thīna-middha-heaviness of body and dullness of mind which drag one down into disabling inertia and thick depression or could even be sleepiness.