Due to the high-measuring cost, the monitoring of power quality (PQ) is nontrivial. This paper is aimed at reducing the cost of PQ monitoring in power network. Using a real-world PQ dataset, this paper adopts a learn-from-data approach to obtain a device latent feature model, which captures the device behavior as a PQ transition function. With the latent feature model, the power network could be modeled, in analogy, as a data-driven network, which presents the opportunity to use the well-investigated network monitoring and data estimation algorithms to solve the network quality monitoring problem in power grid. Based on this network model, algorithms are proposed to intelligently place measurement devices on suitable power links to reduce the uncertainty of PQ estimation on unmonitored power links. The meter placement algorithms use entropy-based measurements and Bayesian network models to identify the most suitable power links for PQ meter placement. Evaluation results on various simulated networks including IEEE distribution test feeder system show that the meter placement solution is efficient, and has the potential to significantly reduce the uncertainty of PQ values on unmonitored power links.Index Terms-Bayesian networks (BNs), conditional entropy (CE), Monte Carlo (MC) simulations, power quality (PQ) monitoring.