<p>This work proposes a novel primal-dual dynamical model for affinely constrained convex optimization and presents a unified convergence analysis for a class of new accelerated primal-dual methods. In the continuous level, exponential decay of a novel Lyapunov function is established and in the discrete level, implicit, semi-implicit and explicit numerical discretizations for the continuous model are considered sequentially and lead to several accelerated primal-dual methods. To weaken the strong convexity assumption on the objective, we adopt the idea of quadratic penalty. Special structures of the corresponding subproblems are utilized to develop efficient inner solvers. In addition, nonergodic sublinear and linear rates in terms of the primal-dual gap, the objective residual and the feasibility violation are proved via a discrete Lyapunov function. Numerical results are provided to verify the practical performances of the proposed methods.</p>