Heightened environmental concerns have arisen the urge for low-carbon power systems. Existing literatures on low-carbon dispatching have fully studied how to reduce carbon emissions on generation side or demand side. But, carbon emissions related to network power losses (i.e., network-side carbon emissions), especially in distribution system (DS), significantly affects the whole carbon distributions as well. However, the objective of conventional low-carbon economic dispatching fails to precisely reduce this part of carbon emissions. To address this issue, we propose a network-side carbon emission reduction method. After determining active power flows by the day-ahead economic dispatching, this method innovatively explores utilizing reactive power compensation capability of some emerging power electronic devices in AC-DC hybrid DS for reducing network-side carbon emissions. First, the traditional Var compensation devices and the emerging voltage source converters (VSCs) with specific control strategies are modelled. Second, models of inverter-based PV units and the aggregated feasible power region (AFPR) of PV aggregators are also proposed. Finally, the low-carbon dispatching model for network-side carbon emission reduction is established, and an ALSO-X+ method is used to solve joint chance constraints (JCC) on the AFPR caused by the uncertainties of PV generation. Case studies on AC-DC test systems with different scales verify that dispatching reactive power can also influences carbon intensities among the whole distribution network. Moreover, our proposed method could effectively reduce network-side carbon emissions and demand-side carbon emissions.