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To reduce the electric field distortion and increase the thermal conductivity of the dielectric materials in cable accessories, this paper proposes a method to prepare composites with good nonlinear electrical conductivity and high thermal conductivity. Silver nanoparticles grown on hexagonal boron nitride (AgNPs/BN) were prepared as a powder and introduced into ethylene propylene diene monomer (EPDM) to obtain AgNPs/BN/EPDM composites. The nonlinear electrical conductivity, thermal conductivity and breakdown field strength of the composites were investigated at different temperatures. The nonlinear electrical conductivity and thermal conductivity of the composites increased with increasing AgNPs content grown on BN. Moreover, the breakdown field strength decreased with increasing AgNPs, and exhibited a weaker temperature dependence than neat EPDM. Simulations showed that the composites could improve the electric field distribution in a cable accessory. [ABSTRACT FROM AUTHOR]