We study the problem of scheduling a set of jobs with release dates, deadlines and processing requirements (works), on parallel speed-scalable processors so as to minimize the total energy consumption. We consider that both preemption and migration of jobs are allowed. We formulate the problem as a convex program and we propose a polynomial-time combinatorial algorithm which is based on a reduction to the maximum flow problem. We extend our algorithm to the multiprocessor speed scaling problem with preemption and migration where the objective is the minimization of the maximum lateness under a budget of energy.