This paper presents a forward recursive procedure to calculate the exp
ected 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 approac
h is developed to compute the first and second derivatives of the expe
cted generation energy of a thermal unit with respect to the capacity
of all thermal units in the system. The salient feature of the propose
d approach is that it applies to hydro-thermal systems with multiple l
imited-energy hydro units.