Future electrical low voltage (LV) distribution networks are expected to have higher penetration of distributed generation (DG) systems, e.g. small wind turbines (SWTs), and battery electric vehicles (BEVs). The intermittent and time-varying characteristics of wind speed and BEV charging bring difficulties in evaluating the adverse performance, e.g. voltage violation and unbalance, on the residential distribution networks (RDNs). This thesis develops two probabilistic power flow methods, i.e. statistical time series (STS) and point estimate method (PEM), for evaluating voltage violation and voltage unbalance in RDNs caused by integration of SWTs and BEVs. The STS method combines statistical distribution analysis (SDA) and time series analysis (TSA). PEM is an approximation method using deterministic routines for solving probabilistic problems. The STS supports the Distribution Network Operators (DNOs) to obtain daily probability of voltage violations in RDNs, considering the time varying characteristics of network load, wind speed and BEV charging in a statistical manner. In PEM, evaluating the voltage unbalance takes into account the disparity of the loads at the three phases and also the unbalanced distribution of SWT outputs. The PEM calculation can also obtain daily probability of voltage unbalance factor in RDNs. The results presented prove that STS and PEM can provide faster evaluation of the probability of voltage violation and unbalance of a RDN than TSA. Based on the statistics of one year's seasonal load, wind data, at the same level of time granularity, the STS method can reduce computational power by over 98%. The assessment difference is approximately 6%. PEM evaluation, using one year's load and wind speed data, without distinguishing these data into seasonal categories or weekdays and weekends, reduces the computational power required by over 97.8%. The evaluation estimate is within 16%. The proposed methods can provide DNOs with a global picture of the voltage violation and unbalance profiles of RDNs under various SWT and BEV penetrations. For the distribution network planning, the quick evaluation of voltage violation and unbalance can help DNOs determine the maximum capacity of SWTs and BEVs a network can accommodate without voltage violation or unbalance.