How did the great compromise represent the interests of those who wanted a strong national government?

Stronger Government

The Great Compromise set up the 3 branches of government.  It also put in place the Executive branch with a president and the Judicial branch with a court system.  Neither of these existed before.  Now we are able to enforce the laws and interpret the laws.  In addition, the compromise set up checks and balance so that no one branch had sole power.

States

The Great Compromise took the best of the New Jersey Plan and the Virginia Plan to create a bicameral Legislative branch.  The Senate and House of Representative was put in place.  To please the larger states the House of Representatives based representation on population.  To make the smaller states happy the Senate gave equal (2 per state) representation.