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Based on organic Rankine cycle (ORC), a trapezoidal cycle with theoretical model is proposed and built according to the trapezoidal configuration and the thermodynamic relation in T-s diagram. Simulations show that the relative deviation between trapezoidal cycle and ORC is lower than 5% within evaporation temperature of 5 °C lower than the critical temperature of the working fluids. Empirical equations to calculate the optimal evaporation temperature, the maximum net power output and the corresponding thermal efficiency are built, which relative deviations from ORC are lower than 4%. Trapezoidal cycle can break through the restrictions of the actual working fluids and the configuration of the ORC to extend the study of the ORC and investigate the general principle of the ORC (or the trapezoidal cycle). Trapezoidal cycle can develop to trilateral cycle or Carnot cycle, which are the boundary cycles of the trapezoidal cycle. Trapezoidal cycle can be used as a general cycle to investigate the relations and principles among the trilateral cycle, Carnot cycle and trapezoidal cycle (or ORC). The performance of these three cycles at maximum power and their relations are investigated in the same conditions of finite heat source. Results show that the maximum power and the corresponding thermal efficiency of the trapezoidal cycle are bounded between Carnot cycle and trilateral cycle. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]