Decision Error Probability in a Two-stage Communication Network for   Smart Grids with Imperfect Data Links
  This paper analyzes a scenario where the distribution system operator needs to estimate whether the average power demand in a given period is above a predetermined threshold using an 1-bit memoryless scheme. Specifically, individual smart-meters periodically monitor the average power demand of their respective households to inform the system operator if it is above a predetermined level using only a 1-bit signal. The communication link between the meters and the operator occurs in two hops and is modeled as binary symmetric channels. The first hop connects individual smart meters to their corresponding aggregator, while the second connects different aggregators to the system operator. A decision about the power demand also happens in two stages based on the received information bit. We consider here three decision rules: AND, OR and MAJORITY. Our analytical results indicate the circumstances (i.e. how frequent the meters experience the consumption above the defined threshold) and the design setting (i.e. decision rules) that a low error probability can be attained. We illustrate our approach with numerical results from actual daily consumption from 12 households and 3 aggregators. 
Iran Ramezanipour, Mauricio C. Tom\'e, Pedro H. J. Nardelli, Hirley   Alves
cs.IT math.IT