This paper presents a forward recursive procedure to calculate the expected system marginal cost curve (EMC). The EMC formulation allows for multi-state and multi-block dispatch of generating units and is used to determine the optimal energy of pumped-storage units. A new approach is developed to compute the first and second derivatives of the expected generation energy of a thermal unit with respect to the capacity of all thermal units in the system. The salient feature of the proposed approach is that it applies to hydro-thermal systems with multiple limited-energy hydro units.
Shahidehpour, S. M.,
& Xiang, N.
(1995). Power Systems Marginal Cost Curve and its Applications. IEEE Transactions on Power Systems, 10 (3), 1321-1328.