What is the grammatical system in which sentence structures are derived by transforming kernel sentences?

The grammatical system you are referring to is known as Transformational Grammar. This theory, developed by Noam Chomsky in the 1950s, posits that all sentences in a language can be generated by applying a series of transformational rules to basic underlying structures called kernel sentences. These transformations allow for the generation of complex sentences from simpler ones, providing a framework for understanding the syntax of a language.