Against the backdrop of global climate change, renewable energy (RE) performs significant effects in reducing carbon emissions. Nevertheless, volatile RE sources disrupt the energy supply-demand balance (ESDB) in the energy market. Flexible energy (FE) can effectively mitigate the problem with high flexibility and controllability. FE sources are widely distributed in integrated energy systems (IESs). However, existing methods guide scattered FE in IESs with insufficient accuracy. To accurately guide FE, this study proposes an improved long-term price guidance mechanism (ILPGM) based on gated recurrent unit (GRU)- vision Transformer (ViT) prediction and fractional-order stochastic dynamic calculus (FSDC) control. The ILPGM combines GRU and ViT for baseline load forecasting and applies the FSDC method. The ILPGM can optimize the energy consumption of IESs and promote the ESDB while decreasing energy costs. The ILPGM is applied to the IES at Arizona State University-Tempe. The experimental results indicate that: the average coefficient of determination of electrical and heat energy under ILPGM is 97.69 %, realizing flexible regulation of energy consumption; the ILPGM can save 26.36 % actual cost and 94.62 % potential cost savings for the IES; compared to the previous long-term price guidance mechanism, the ILPGM provides an additional 5.87 % total cost savings and 28.65 % potential savings.
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