Considering the uncertainty of renewable energy output

the current carbon trading response to the consumption of new energy in the park's integrated energy system has poor dynamic adjustment capability

with issues of non-real-time trading and static nature. To more effectively facilitate carbon trading and optimize the low-carbon dispatch strategy of park-integrated energy systems

this paper proposes a time-sharing stepped carbon trading optimization model with a dynamic incentive mechanism and a solution method for a two-stage nonlinear robust optimization model. First

a park integrated energy system model with multi-energy coupling is established

and a model of combined heat and power units with adjustable heat-to-power ratios is constructed to ensure the flexibility of electricity and heat energy output. Then

by utilizing the real-time rolling incentive of renewable energy consumption capacity from the previous period to adjust the carbon trading parameters for the next period

a time-sharing stepped carbon trading model with a dynamic incentive mechanism and a min-max-min nonlinear optimization model is established. Furthermore

a linearization method is employed for step-wise functions

which considers a multidimensional 0-1 variable matrix and the Hadamard product

along with the McCormick envelope tightening strategy

to ensure the model's linearization and accuracy. Afterwards

the karush-kuhn-tucker (KKT) conditions method is proposed to transform the piecewise decoupled two-stage inner model

thereby avoiding the inapplicability of traditional dual transformations under complex nonlinear objective functions

and solving for the renewable energy output under the worst-case scenario for different photovoltaic scenarios. Finally

taking a certain park as an example

the case study analysis verifies that the proposed model

compared to the traditional stepped carbon trading model without incentive mechanisms reduce economic costs by 5.97% and 1.88% under worst-case scenarios and optimal scenarios

respectively

while decreasing system carbon emissions by 1

440 kg and 466.4 kg

thereby improving the renewable energy consumption capacity of the system while ensuring the real-time and dynamic nature of carbon trading.