With the fast expansion of the power grid and increasing complexity due to modern equipment, power flow models with non-convexity and long computing time are not suitable for network calculation and optimization problems. Therefore, this paper proposes a linearized branch flow model (LBF) considering line shunts (LBFS). The strength of LBF lies in its linear mathematical structure, and hence the convex nature, which is primarily achieved by regarding the apparent power flow as the branch current magnitude. Moreover, the calculation accuracy in nodal voltage magnitude is significantly improved by appropriately modeling line shunt admittances and network equipment like transformers, shunt capacitors and distributed generators (DG). We show the application scope of LBFS by controlling the network voltages through a two-stage stochastic optimization Volt/VAr control (VVC) problem considering DG output uncertainty. Since LBFS results in a linear VVC program, the global solution is guaranteed. Simulations show that VVC framework can optimally dispatch the discrete control devices, viz. substation transformers and shunt capacitors, and also optimize the decision rules for real time reactive power control of DGs. Besides, the computing efficiency is significantly improved compared to traditional VVC methods.