The paper is devoted to the development of a neural network architecture which implements the Newton-Raphson algorithm for solving the set of nonlinear equations of power-system load-flow analysis. The principal context is that of online network analysis in energy management systems with particular reference to the optimal power-flow function. The author shows that the complete Newton-Raphson load-flow formulation maps into an array of two-layer neural networks. The development starts from a formulation for solving as a minimisation problem the linearised equation system to which the Newton-Raphson sequence leads at each iteration. For that purpose, an objective function in quadratic form is derived. A neural network structure is given which implements the steepest descent method for minimising this objective function. It is shown that the weighting coefficients of neural networks are formed from element values in the Jacobian matrix of Newton-Raphson load-flow analysis. When the Jacobian matrix is nonsingular, the quadratic objective function derived has a unique and global minimum. A principal feature of the extensive parallel processing capability of the architecture developed is that the computing time of load-flow analysis is independent of the number of nodes in the power network for which analysis is carried out. For a sample section of a power network, and by software simulation, the architecture which the paper seeks to report gives solutions which are identical with those from a standard sequential processor load-flow program.