When a common price signal is present, network topology leaves no fingerprint on a storage fleet's collective dynamics

Abstract

Price-based mean-field models of battery storage coordination usually assume that each agent responds to the true population-average charging power. Under that assumption, communication topology is irrelevant because the broadcast price already carries the coupling that matters. We study a nearby regime in which agents respond to a shared noisy forecast of the average, with correlation rho between agents' forecast errors. Analytically and in simulation, we find that topology remains undetectable in the effective-dimensional response of the fleet, even when neighbour observation is the only explicit communication signal. The mechanism is structural: the correlated forecast error projects onto the graph-invariant consensus mode, while topology acts through transverse modes. As rho N grows, the consensus-mode variance dominates and the spectral participation ratio approaches one independently of graph topology. Simulations on linear, star, and small-world graphs confirm that topology-induced variation is below the variation caused by redrawing the forecast noise. The result is not a claim that topology has no dynamical effect, but that shared stochastic forcing can mask topology-dependent modes in decentralized storage fleets.