Based on the cavity-mode model, we have developed a fast algorithm for calculating power bus impedance in multilayer printed circuit boards. The fast algorithm is based on a closed-form expression for the impedance Z matrix of a rectangular power bus structure; this expression was obtained by reducing the original double infinite series into a single infinite series under an approximation. The convergence of the single series is further accelerated analytically. The accelerated single summation enables much faster computation, since use of only a few terms is enough to obtain good accuracy. In addition, we propose two ways to compensate for the error due to the approximation involved in the process of reducing the double series to the single series, and have demonstrated that these two techniques are almost equivalent.