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.