Low-carbon economic optimization for flexible DC distribution networks based on the hiking optimization algorithm

The integration of large-scale renewable energy into the grid has significantly advanced research on flexible DC distribution networks. However, the potential of flexible loads—possessing both source and load characteristics—in supporting the low-carbon economic operation of integrated energy systems (IES) remains underexplored. Furthermore, the optimization of IES scheduling is inherently a multi-dimensional nonlinear problem, where traditional intelligent optimization methods struggle to achieve satisfactory solution accuracy. In this paper, an IES model is developed based on the concept of an energy hub, incorporating elements such as wind turbine output, photovoltaics, energy storage systems, gas turbines, and flexible loads, while considering the transferability, interruptible nature, and reverse energy flow characteristics of demand-side flexible loads. To address the current challenges in balancing environmental and economic benefits in IES, a carbon trading strategy and demand response mechanisms are applied to the optimization scheduling process, with the objective of achieving low-carbon and low-cost operations. The proposed model is solved using a novel Hiking Optimization Algorithm (HOA), and comparative analysis across different scenarios is conducted to investigate the impact of the carbon trading strategy on low-carbon operation, alongside an evaluation of the system’s economic and environmental performance under reasonable scheduling of both the carbon trading strategy and flexible loads. The results indicate that the total cost and carbon emissions of the system decreased by 8.98% and 15.13%, respectively, indicating that appropriate scheduling of the carbon trading mechanism and flexible loads effectively improves the system’s economic and environmental performance. In addition, a comparative study with traditional particle swarm and genetic algorithms demonstrates that the HOA, by incorporating adaptive mechanisms for both search space resolution and speed adjustment, enhances both global exploration and local exploitation, effectively avoiding local optima traps. This leads to improved optimization accuracy, further validating its effectiveness in IES optimization.