A direct Newton-Raphson economic dispatch

The authors present a method to solve the real-time economic dispatch problem using an alternative Jacobian matrix considering system constraints. The transmission loss is approximately expressed in terms of generating powers and the generalized generation shift distribution factor. Based on this expression, a set of simultaneous equations of the Jacobian matrix are formulated and solved by the Newton-Raphson method. The proposed method eliminates the penalty factor calculation and solves the economic dispatch directly. The method resulted in a very fast solution speed and maintained good accuracy in test examples. It is a good approach to solve the economic dispatch problem