When the alkaline electrolysis hydrogen production system is coupled with renewable energy sources with strong fluctuation, intermittency and stochasticity, ensuring the safety and efficiency of the system operation has become a world problem. The traditional PID algorithms are having a hard time to adapt to today's brand-new application scenarios of off-grid hydrogen energy system. In this work, the fuzzy logic and back propagation neural network have been successfully introduced to the traditional PID algorithm to realize the precise control of the operating temperature of the alkaline water electrolysis system, which show superior control performance against fluctuations under the actual wind power. The fuzzy PID algorithm reduces the overshooting amount to 40.4% of the traditional algorithm; BP-PID algorithm reduces the rise time, peak time and overshooting amount to 98.3%, 66.7% and 5.5% of the traditional algorithm, respectively. Through a bunch of simulation analyses, the effectiveness and advancement of the proposed controllers is quantitatively verified, which outperform in several performance indexes and provide new tools and ideas for the improvement of the fluctuation-resistance of alkaline water electrolyzers to operate more efficiently and safely when coupled with fluctuating renewable energy sources, and to promote the intelligence of the design, operation and maintenance process of hydrogen energy systems.