The easiest method is to power off your internet modem overnight. Depending on your ISP lease time, you will be assigned a new IP.
If your ISP has set a long IP lease time, this method will not work. The IP is bound to the MAC address of your router.
Generally, changing the MAC address means a new IP. So if your router has the option of MAC cloning, this could be a solution.
If your computer is assigned the external IP directly, you can follow the steps below.
(How to determine if you computer is assigned the external ip)
1. Hit Win-R, type 'cmd' and hit enter (or Start > Run > All programs > Accessories > Command prompt)
2. Type ipconfig /release and hit enter
3. Click Start, Control Panel, and open Network Connections (Vista and Win 7: Network and Sharing Center)
4. Find and Right click on the active Local Area Connection and choose Properties
5. Double-click on the correct Internet Protocol (TCP/IP)
6. Click on Use the following IP address
7. Make up a false IP, for example 18.104.22.168
8. Press Tab and the Subnet Mask section will populate with default numbers
9. Hit OK twice
10. Right click the active Local Area Connection again and choose Properties
11. Double-click on the Internet Protocol (TCP/IP)
12. Choose Obtain an IP address automatically
13. Hit OK twice
14. Go to http://www.clientip.net to check if you have a new IP address.