The rising penetration of intermittent renewable distributed generation leads to uncertainties in the planning of electric distribution networks. Fully considering the uncertainties pertinent to wind power generation

photovoltaic power generation and load demand

this paper proposes a scenario-based model for the planning of active distribution systems. The solution obtains the optimal capacities and locations of wind and photovoltaic based distributed generators in the distribution system

whilst minimizing the active and reactive power losses as well as voltage deviation. A scenario matrix is generated using the heuristic moment matching technique that captures the stochastic moments and correlation among historical wind and photovoltaic power

and electricity demand. The scenario matrix is then incorporated to propose a stochastic planning model that considers a multi-objective index for minimizing power losses and voltage deviation. Finally

the effectiveness of the proposed planning model is confirmed using case-studies in 53-bus and IEEE 123-bus distribution systems.