The paper considers real-time simulation over the operational timescales in an electrical power system and presents a mathematical technique for the decomposition of a set of nonlinear algebraic and differential equations, which result from the corresponding dynamic model. It is shown that the resulting algorithm is suitable for implementation on parallel processors with a 32-bit word capability. The results illustrate that the proposed decomposition technique results in a significant saving in simulation elapsed time, and can consequently be applied to the real-time simulation of large power systems, using relatively inexpensive microprocessor-based hardware.