With the integration of a large number of the intermittent distributed generators such as wind turbine generators（WTG） into distributed system， the influences brought by random and correlated variables have to be taken into consideration in the reactive power optimization of distribution network. Firstly， rank correlation coefficient is used to represent the the correlations between wind speed and load demand， and the initial correlated samples are generated by means of Latin hypercube sampling（LHS） techniques. In addition， the simultaneous backward reduction is applied to reduce the scenarios to improve the computation efficiency. Secondly， a reactive power optimization model based on multiple scenarios is proposed， considering the volt/var control devices such as shunt capacitor（SC）， static var compensation （SVC）， on-load tap changer（OLTC）. And then， second order cone（SOC） relaxation is applied to transform the traditional reactive power optimization model to mixed integer second order cone programming（MISOCP） model， which can be tractably solved. Finally， the rationality of the proposed model is verified by the improved IEEE 33 node distribution network， and the effects of correlations on the reactive power optimization are emphatically studied.