Cogeneration systems with the use of microturbines are appropriate for the use of low quality energy that is normally wasted in conventional power generation systems technologies. The aim of this research is perform a thermodynamic, exergy and exergoeconomic assessment of a system of combined heat and electrical power using a Capstone 30 kW microturbine, considering first and second law efficiencies and the total cost rates of the system. This analysis is done through an interface designed that linked HYSYS with Matlab which allow the evaluation of these three parameters in a simplified way, this interface is validated by the simulation of other cogeneration system proposed by Adrian Bejan and George Tsatsaron .The results show that the highest rate of destruction is in the combustion chamber, then the compressor and heat recovery respectively. In the analysis the highest exergoeconomic costs is taken into flow from the compressor outlet, it is because all the exergy supplied to this flow is given by the mechanical power of the compressor. To evaluate the effect of varying the design parameters of this system functions in the three objectives functions, a parametric study is conducted. The results reveal that by increasing the compression ratio, the compressor and gas micro turbine efficiency improve thermodynamic system performance, however, increasing the compression ratio of the compressor increases the rate of system costs per unit time, on the other hand, the compressor and gas micro turbine efficiency and the outlet temperature of the preheater will be useful for the system in thermal and exergoeconomic terms.