In this paper, an advanced zero emission plant using oxy-fuel combustion is presented and compared with a reference plant (a) without $CO2$ capture and (b) with $CO2$ capture via chemical absorption. A variation of the oxy-fuel plant with a lower $CO2$ capture percentage (85%) is also presented, in order to (1) evaluate the influence of $CO2$ capture on the overall performance and cost of the plant and (2) enable comparison at the plant-level with the conventional method for $CO2$ capture: chemical absorption with monoethanolamine. Selected results of an advanced exergetic analysis are also briefly presented to provide an overview of further development of evaluation methodologies, as well as deeper insight into power plant design. When compared with the reference case, the oxy-fuel plants with 100% and 85% $CO2$ captures suffer only a relatively small decrease in efficiency, essentially due to their more efficient combustion processes that make up for the additional thermodynamic inefficiencies and energy requirements. Investment cost estimates show that the membrane used for the oxygen production in the oxy-fuel plants is the most expensive component. If less expensive materials can be used for the mixed conducting membrane reactor used in the plants, the overall plant expenditures can be significantly reduced. Using the results of the exergoeconomic analysis, the components with the higher influence on the overall plant are revealed and possible changes to improve the plants are suggested. Design modifications that can lead to further decreases in the costs of electricity and $CO2$ capture, are discussed in detail. Overall, the calculated cost of electricity and the cost of avoided $CO2$ from the oxy-fuel plants are calculated to be competitive with those of chemical absorption.

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