The energy system requires meticulous planning to achieve low-carbon development goals cost-effectively. However, optimizing large-scale energy systems with high spatial-temporal resolution and a rich variety of technologies has always been a challenge due to limited computational resources. Therefore, this study proposes a soft-linkage framework to deconstruct large-scale energy system optimization models based on sectors while ensuring the total carbon emission limit and the electricity supply-demand balance. Using China's energy system as a case study, the impact of uncertainty on emission reduction targets is analyzed. A long-term emission target curve is only described by the total carbon budget and its temporal distribution. Results show that different carbon budget time series can lead to total transition cost variations of up to nearly 100 trillion yuan. Moreover, although a lower carbon budget would increase the total cumulative transition cost quadratically, excessively high carbon budgets raise national natural gas demand, threatening energy security.