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The operational stability of a power transformer exerts an extremely important impact on the power symmetry, balance, and security of power systems. When the grid load fluctuates greatly, if the load factor of the transformer cannot be maintained within a reasonable range, it leads to increased instability in grid operation. Adjusting the transformer capacity based on load changes is of great significance. The existing control methods for on-load capacity-regulating (OLCR) transformers have low timeliness, and the daily switching frequency of the capacity-regulating switch is not controlled. To ensure the safe and stable operation of transformers, this paper proposes a control method for OLCR transformers based on load prediction and fuzzy control. Firstly, the operating principle of OLCR transformers is analyzed, and a multi-strategy enhanced dung beetle optimizer (MSDBO) combined with a CNN−LSTM model is proposed for load forecasting. On this basis, the daily switching frequency of the capacity-regulating transformer is introduced, and hesitant fuzzy control is used to select the optimal capacity-regulating strategy relying on three factors: loss, economy, and switching frequency. Finally, simulation models are constructed using the MATLAB/SIMULINK platform and simulation analysis is conducted to verify the effectiveness and superiority of the proposed control method. For the three scenarios in this paper, the method reduces daily power loss by 28.5% to 56.3% and daily operating costs by 25.4% to 50.8%. The method used in this paper can sacrifice 3.5% to 9.2% of the loss reduction capability in exchange for reducing the number of switch operations by 28.6% to 57.1%, significantly extending the lifespan of the switches and thereby increasing the operational lifespan of the transformer. [ABSTRACT FROM AUTHOR]