Statistical Power Grid Observability under Finite Blocklength

We study the stochastic observability of the power grid system under communication constraints in the finite blocklength regime. Compared to the study under the assumption of infinite blocklength, we introduce two new elements: probability of decoding error and transmission delay. An optimization problem to maximize the observability of the smart grid over all possible bandwidth allocation is proposed, incorporating these two new elements. To solve the optimization problem, for a given bandwidth allocation, we first solve parallel subproblems, one for each synchronous phasor measurement unit (PMU), using alternating optimization, to find the optimal QoS exponent, transmission delay and probability of decoding error for each PMU. Then, simulated annealing method is used to find the optimal bandwidth allocation among PMUs. Numerical results verify that the assumption of infinite blocklength is indeed too optimistic and instead, finite blocklength should be studied. Large bandwidth saving gains of the proposed scheme are demonstrated compared to the equal bandwidth allocation scheme.