The lack of comprehensive monitoring equipment in low voltage (LV) residential feeders, impedes a near-term deployment of centralized schemes for the integration of domestic-scale distributed generation (DG). In this context, this paper introduces a technique that generates a set of fitted polynomials, derived from offline simulations and regression analysis, that characterise the magnitude of representative network variables (i.e. key for network operation) as a direct analytical expression of the controllable local conditions of any DG unit (i.e. active and reactive power injections). Crucially, the coefficients of these polynomials can be estimated, autonomously at the location of each DG unit, without the need for remote monitoring (i.e. using only locally available measurements). During online implementation, the method consists only of direct calculations (i.e. non-iterative), facilitating real-time operation. The accuracy of the polynomials to estimate the magnitude of the network variables is assessed under multiple scenarios on a representative radial LV feeder. Furthermore, the robustness of the method is demonstrated under the presence of new generation and electric vehicles.