Analytic Conditions for Energy Neutrality in Uniformly-Formed Wireless Sensor Networks

Future deployments of wireless sensor network (WSN) infrastructures for environmental or event monitoring are expected to be equipped with energy harvesters (e.g. piezoelectric, thermal, photovoltaic) in order to substantially increase their autonomy. In this paper we derive conditions for energy neutrality, i.e. perpetual energy autonomy per sensor node, by balancing the node's expected energy consumption with its expected energy harvesting capability. Our analysis assumes a uniformly-formed WSN, i.e. a network comprising identical transmitter sensor nodes and identical receiver/relay sensor nodes with a balanced cluster-tree topology. The proposed framework is parametric to: (i) the duty cycle for the network activation; (ii) the number of nodes in the same tier of the cluster-tree topology; (iii) the consumption rate of the receiver node(s) that collect (and possibly relay) data along with their own; (iv) the marginal probability density function (PDF) characterizing the data transmission rate per node; (v) the expected amount of energy harvested by each node. Based on our analysis, we obtain the number of nodes leading to the minimum energy harvestingrequirement for each tier of the WSN cluster-tree topology. We also derive closed-form expressions for the difference in the minimum energy harvesting requirements between four transmission rate PDFs in function of the WSN parameters. Our analytic results are validated via experiments using TelosB sensor nodes and an energy measurement testbed. Our framework is useful for feasibility studies on energy harvesting technologies in WSNs and for optimizing the operational settings of hierarchical WSN-based monitoring infrastructures prior to time-consuming testing and deployment within the application environment.