High penetration of distributed renewable energy introduces significant uncertainties to active distribution networks. Optimal control methods accounting for inherent uncertainties are needed to facilitate economic and reliable operation of active distribution networks. This paper proposes a stochastic receding horizon control method based on modified stochastic model predictive control framework to integrate high penetration of distributed generation. Multiple controllable resources are jointly optimized over a finite prediction horizon while ensuring relevant security restrictions. The simplified Z-bus sensitivity for active distribution networks is developed for computationally efficient estimation of system nonlinearity with high accuracy, and is combined with the sequential linear programming to iteratively derive the linear state space model for compensation of cumulative modeling errors. Furthermore, the voltage limitations are reformulated as chance constraints to indicate the probabilistic reliability index of voltage qualification rate, and achieve tradeoffs between cost reduction and voltage regulation. The affine-disturbance feedback control policy is leveraged here to enforce close-loop control performance and analytically transform intractable chance constraints into second-order cone constraints. Comprehensive case studies based on 33-bus and 123-bus distribution systems are carried out to demonstrate the capability and effectiveness of the proposed approach in terms of modeling accuracy, control performance, cost reduction, and method scalability. The proposed approach can effectively enforce voltage regulation against uncertainties with the prescribed probability level. Control costs and constraint violation can be reduced compared with deterministic model predictive control and open-loop control strategies.