I have three Google Ad Words vouchers but no account yet. Is it possible to combine these vouchers when I open my new account?
Not as far as I know. You can only use one voucher for one account. You could create 3 accounts and redeem one voucher on each account.
However in doing this, you are violating Google's terms and conditions. So although it will let you do this, your accounts will most likely be suspended.
I would just use one voucher :)
This post by a Google Employee touches on the subject of using multiple vouchers for multiple accounts here.
To put it another way, the same advertiser opening multiple accounts to use multiple vouchers is not acceptable - and it is the sort of things that might lead to accounts beings shut down.