Powerline communication networks assume an interesting position in the communication network space: Similarly to wireless networks, powerline networks are based on a shared broadcast medium; unlike wireless networks , however, the signal propagation is constrained to the power lines of the electrical infrastructure, which is essentially a graph. This article presents an algorithmic model to study the design of communication services over powerline communication networks. As a case study, we focus on the fundamental broadcast problem, and present and analyze a distributed algorithm COLORCAST which terminates in at most n communication rounds, where n denotes the network size, even in a model where link qualities are unpredictable and time-varying. For comparison, the achieved broadcast time is lower than what can be achieved by any unknown-topology algorithm (lower bounds Ω(n log n/ log(n/D)) and Ω(n log D) are proved in [22] resp. [10] where D is the network diameter). Moreover, existing known-topology broadcast algorithms often fail to deliver the broadcast message entirely in this model. This article also presents a general broadcast lower bound for the powerline model.