This paper proposes a mixed‐integer non‐linear programming (MINLP) model for the multi‐period active low voltage (LV) distribution network expansion planning problem, which can be solved by off‐the‐shelf optimization solvers. In addition, the wide‐spread penetration of solar resources, optimal loading of transformers, and modeling of the multiple solar generation patterns are considered in the model. The solar resources are of roof‐top household‐scale photovoltaic panel type, developed using a host‐owned business model and are able to exchange energy with the distribution company (DISCO). This model enables the DISCO, as the owner of the network, to minimize the investment and operation costs while being able to determine the optimal location and capacity of the distribution transformers, the service zone of distribution transformers, the optimal route of the distribution lines, and the total and annual planning costs. In order to check the efficiency of the proposed model, a 0.4 kV distribution test network is considered to plan the LV network of a residential district over a planning horizon of 5 years. Results show the effectiveness of the proposed model in dynamic expansion planning of the active LV distribution network. Also, results illustrates that the penetration of solar sources can be a great tool to improve the technical, economic, and environmental criteria for planning studies. Specifically while reducing the billing costs of customers, it favors the government to reduce the pollution costs, and it enables the DISCO to reduce the loss costs and maintain the voltage in the standard boundaries.