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Economic dispatch (ED) is an optimisation tool that is used to allocate active load demands to the generating units through optimising the fuel generation cost function subject to the different operational constraints. The high non-linearity of the power system imposes mathematical challenges in formulating the generation cost function models, which makes the ED problem hard to solve. This study introduces two ideas to solve issues related to the ED problem. First, a dynamic formulation technique is developed to optimally allocate the change in the total active load demand to the generating units. This technique is shown to be insensitive to the optimality of the initial active load distribution unlike the base point and participation factor method. Moreover, it guarantees an optimal distribution among the generating units due the change in the active load demand. Second, a novel approximation of the non-convex generation cost function is developed to solve non-convex ED problem with the transmission losses. This approximation enables the use of gradient and Newton techniques to solve the non-convex ED problem with valve point loading effect and transmission losses in an analytic approach. This approximation is compared with some heuristic optimisation techniques.