The discrete-time representation of a broadband powerline channel as a linear periodically time variant system poses serious problems in terms of computational complexity. In this paper we exploit the principles of the Zadeh's series expansion to devise a new discrete-time system model, characterized by a limited computational complexity and particularly suitable for an implementation on embedded programmable hardware. Then, we illustrate simple methods for estimating the parameters of the proposed model and apply them to the development of a broadband channel sounding tool for powerlines. Our experimental and numerical results show that the proposed model is able to provide a faithful representation of the periodically time varying behavior of indoor powerline channels.