AbstractPower transmission line management presents unique challenges, and a smart grid approach could effectively reduce costs and improve reliability. For years, wireless mesh networks have been studied because of their capability of providing good performance with low deployment cost even in environments with scarce communication infrastructure. Because of these characteristics, the employment of wireless mesh networks as a communication infrastructure for monitoring power transmission lines has gained popularity. While mesh networks allow organic growth, for this application, ana priorinetwork planning is mandatory to ensure the required levels of performance and fault tolerance while maintaining deployment costs within a specified budget. This paper studies the problem of wireless mesh network planning in that environment, that is, how to deploy a minimum number of wireless mesh nodes along a power transmission line (or any linear system) so that coverage and connectivity constraints are met. We show that the linearity of power transmission lines and the large distances between towers result in networks with very particular characteristics and that previous proposals found in the literature cannot be readily adapted for these scenarios. We then propose both an integer programming model and a polynomial‐time heuristic for this particular version of the planning problem. Our evaluation shows that the proposed heuristic is able to closely match the optimal results obtained with the integer programming model while being more scalable and easily allowing the addition of more constraints that can be useful in practice. Copyright © 2016 John Wiley & Sons, Ltd.