Amidst the intensifying global warming, China is actively pursuing the national strategic goals of "carbon peaking" and "carbon neutrality" to expedite the development of an efficient, low-carbon, safe, and clean new energy structure. This necessitates the establishment of a distribution network investment model that better aligns with the requirements of carbon emission reduction and verifying the impact of carbon emission reduction-related factors on investment outcomes. This paper initially employs grey relational analysis to develop an evaluation index system for distribution network investment under the context of carbon emission reduction, and utilizes an explanatory model to elucidate the relationship between various indicators. A GM(1,N) model is constructed to analyze and forecast the investment demand in the distribution network sector, with simulation tests conducted to assess investment predictions under different factor scenarios. The study reveals that increasing the weight of internal demand characteristics such as total electricity consumption can effectively enhance the accuracy of investment demand forecasts for distribution networks under the carbon emission reduction backdrop. Considering carbon emission reduction-related factors aligns more closely with actual investment demands, thereby aiding power grid enterprises in better grasping distribution network investment needs and achieving precise investments.