Abstract: For the combined heat and power (CHP) unit featuring a gas-steam combined cycle with an unfired heat recovery boiler, this study establishes fundamental thermodynamic relationships. Firstly, based on energy conservation principles, equivalent relationships between gas mass flow rate and electrical parameters are derived. Subsequently, a comprehensive equivalent circuit model is developed to characterize the gas-to-electricity conversion process, incorporating the physical characteristics of power transformation. Furthermore, mathematical formulations are established to describe the system's gas-heat conversion efficiency, exhaust gas emissions, and operational heat losses, accounting for the thermodynamic principles governing energy transfer and dissipation processes. Accordingly, the CHP's physical characteristic equivalence model can be established, and its control parameters under strategies of "electricity determined by heat" and "heat determined by electricity" are defined. Then, using the Newton method and the principle of pipe-network hydraulic calculation, the correction equations for the power flow and the energy flows of gas and heat systems, as well as their Jacobian element expressions, are derived, thereby proposing a unified analysis method for gas-electricity-heat hybrid energy flow considering the CHP's inherent characteristic parameters varying with the operating conditions of the hybrid system. Finally, the effectiveness and feasibility of the proposed method are validated by the gas-electricity-heat hybrid systems with different control strategies of CHP.