Based on loop-analysis method, a theoretical formulation of the forward/backward sweep with compensation power flow method is presented. The reason, why the convergence of this widely used method deteriorates when the network becomes more meshed, is also well analyzed. Subsequently, a novel solution of unbalanced three-phase power systems based on loop-analysis method is developed in this paper. The convergence speed of this algorithm remains very well even when network become more meshed. Furthermore, the implementation of this algorithm is similar with that of the forward/backward sweep with compensation method with the characteristic of understandability. This proposed method has clear theory foundation and takes full advantage of the radial (or weakly meshed) structure of distribution systems. The numerical test proves this new method is very robust and has excellent convergence characteristics.