在“双碳”战略背景下，综合能源系统（integrated energy system, IES）需要结合经济性和低碳性进行多能协同优化。碳交易机制作为衔接环境效益与经济效益的关键纽带，其价格波动特性对综合能源系统的规划决策有显著影响。本文针对碳交易价格不确定性给综合能源系统低碳规划带来的决策问题，提出了一种考虑碳交易价格不确定性的综合能源系统扩展规划模型。首先，构建基于长短期记忆网络-宽度学习系统的碳价预测模型，提升对未来碳价分布的评估能力。随后结合核密度估计方法刻画碳价非参数概率分布特性，通过拒绝抽样与后向缩减技术生成典型场景集。在此基础上，建立考虑奖惩阶梯式碳交易机制的IES低碳扩展规划模型。实验结果表明，所提模型提升了碳交易价格预测的准确性，为碳市场波动条件下的能源系统扩展规划提供了决策依据。

Under the “dual-carbon” strategy, integrated energy systems must pursue multi-energy coordination that balances economic efficiency and low-carbon performance. The carbon-trading mechanism, acting as a critical bridge between environmental and economic benefits, introduces price volatility that significantly influences IES planning decisions. To address the decision-making challenges posed by uncertain carbon-trading prices, this paper proposes an IES expansion-planning model that explicitly accounts for carbon-price uncertainty. First, a carbon-price forecasting model based on a long short-term memory network-broad learning system is developed to enhance the assessment of future carbon-price distributions. Kernel density estimation is then employed to characterize the non-parametric probability distribution of carbon prices, and a representative scenario set is generated via rejection sampling combined with backward reduction. On this basis, a low-carbon IES expansion-planning model incorporating a reward-punishment stepped carbon-trading mechanism is established. Experimental results demonstrate that the proposed model improves the accuracy of carbon-price forecasting and provides a reliable decision-making basis for energy-system expansion planning under volatile carbon-market conditions.