This paper reports a new kind of exergetic performance analysis for a general cogeneration system model. In the model considered, the irreversibilities due to finite rate heat transfer, internal dissipations and the possible heat leakage between heat source and heat sink are taken into account. A new exergetic performance criterion named the exergy density has been proposed as an objective function which can include the consideration of the system sizes in the analysis. The exergy density function is defined as the ratio of total exergy rate to the maximum volume in the cycle. The general and optimal performances based on the exergy density objective have been investigated. The effects of the design parameters such as the ratio of the generated power to the produced heat rate and consumer temperature ratio on the global and optimal performance have been discussed. The obtained results based on the exergy density criterion are compared with the total exergy rate in terms of the exergy efficiency and system sizes. The comparisons show that design parameters at the maximum exergy density conditions lead to smaller and more efficient cogeneration system.