The article presents results of thermodynamic analysis using a zero-dimensional mathematical models of a negative CO₂ emission power plant. The developed cycle of a negative CO₂ emission power plant allows the production of electricity using gasified sewage sludge as a main fuel. The negative emission can be achieved by the use this type of fuel which is already a “zero-emissive” energy source. Together with carbon capture installation, there is a possibility to decrease CO₂ emission below the “zero” level. Developed models of a novel gas cycle which use selected codes allow the prediction of basic parameters of thermodynamic cycles such as output power, efficiency, combustion composition, exhaust temperature, etc. The paper presents results of thermodynamic analysis of two novel cycles, called PDF0 and PFD1, by using different thermodynamic codes. A comparison of results obtained by three different codes offered the chance to verify results because the experimental data are currently not available. The comparison of predictions between three different software in the literature is something new, according to studies made by authors. For gross efficiency (54.74%, 55.18%, and 52.00%), there is a similar relationship for turbine power output (155.9 kW, 157.19 kW, and 148.16 kW). Additionally, the chemical energy rate of the fuel is taken into account, which ultimately results in higher efficiencies for flue gases with increased steam production. A similar trend is assessed for increased CO₂ in the flue gas. The developed precise models are particularly important for a carbon capture and storage (CCS) energy system, where relatively new devices mutually cooperate and their thermodynamic parameters affect those devices. Proposed software employs extended a gas–steam turbine cycle to determine the effect of cycle into environment. First of all, it should be stated that there is a slight influence of the software used on the results obtained, but the basic tendencies are the same, which makes it possible to analyze various types of thermodynamic cycles. Secondly, the possibility of a negative CO₂ emission power plant and the positive environmental impact of the proposed solution has been demonstrated, which is also a novelty in the area of thermodynamic cycles.