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High penetration of renewable generation poses great challenge to power system operation due to its uncertain nature. In droop-controlled microgrids, the voltage volatility induced by renewable uncertainties is aggravated by the high droop gains. This paper proposes a chance-constrained optimal power flow (CC-OPF) problem with power flow routers (PFRs) to better regulate the voltage profile in microgrids. PFR refer to a general type of network-side controller that brings more flexibility to the power network. Comparing with the normal CC-OPF that relies on power injection flexibility only, the proposed model introduces a new dimension of control from power network to enhance system performance under renewable uncertainties. Since the inclusion of PFRs complicates the problem and makes common solvers no longer apply directly, we design an iterative solution algorithm. For the subproblem in each iteration, chance constraints are transformed into equivalent deterministic ones via sensitivity analysis, so that the subproblem can be efficiently solved by the convex relaxation method. The proposed method is verified on the modified IEEE 33-bus system and the results show that PFRs make a significant contribution to mitigating the voltage volatility and make the system operate in a more economic and secure way.