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This paper proposes a modeling and analysis method for a Caputo–Fabrizio (C-F) definition-based fractional-order Boost converter with fractional-order inductive loads. The proposed method analyzes the system characteristics of a fractional-order circuit with three state variables. Firstly, this paper constructs a large signal model of a fractional-order Boost converter by taking advantage of the state space averaging method, providing accurate analytical solutions for the quiescent operating point and the ripple parameters of the circuit with three state variables. Secondly, this paper constructs a small signal model of the C-F definition-based fractional-order Boost converter by small signal linearization, providing the transfer function of the fractional-order system with three state variables. Finally, this paper conducts circuit-oriented simulation experiments where the steady-state parameters and the transfer function of the circuit are obtained, and then the effect of the order of capacitor, induced inductor, and load inductor on the quiescent operating point and ripple parameters is analyzed. The experimental results show that the simulation results are consistent with those obtained by the proposed mathematical model and that the three fractional orders in the fractional model with three state variables have a significant impact on the DC component and steady-state characteristics of the fractional-order Boost converter. In conclusion, the proposed mathematical model can more comprehensively analyze the system characteristics of the C-F definition-based fractional-order Boost converter with fractional-order inductive loads, benefiting the circuit design of Boost converters. [ABSTRACT FROM AUTHOR]

International cooperation for renewable energy under the Belt and Road Initiative (BRI) plays a pivotal role in the transition to low-carbon energy in BRI developing countries. However, the rise in energy, debt, food, and geopolitical crises, along with the unique internal challenges found in different BRI developing countries, introduce multiple uncertainties to international renewable energy cooperation (IREC). Therefore, it is crucial to analyze the risks associated with IREC across different BRI countries by incorporating international cooperation theory. This study proposes an analytical framework comprising cooperation consensus–state capacity–institutional environment, which encompasses the willingness to cooperate, national capabilities, and international institutional considerations. An evaluation indicator system is constructed based on this framework. The study optimizes the indicator weights obtained from expert surveys using the analytic hierarchy process and the criteria importance through intercriteria correlation method. A quantitative assessment of IREC risks was conducted for 114 BRI countries from 2010 to 2020. The results indicate a gradual reduction in IREC risks between China and BRI countries. Regional risk assessments reveal that Southeast Asia exhibits the lowest average risk, while Africa not only records the highest average risk but also indicates substantial cooperation potential. Therefore, we recommend a comprehensive approach to risk mitigation. Such an approach would include gradually improving cooperation mechanisms, promoting both top-down and bottom-up cooperation, encouraging the involvement of multiple stakeholders, and prioritizing early-stage risk assessments and research. • A new analytical framework based on international cooperation theories. • A dynamic risk map for Belt and Road renewable energy cooperation. • The combination of AHP and CRITIC. • Tailored risk mitigation strategies for different regions. [ABSTRACT FROM AUTHOR]