The French system's losses rise nearly up to 12 TWh per year, attributed to the Joule effect. Therefore, the purchase of losses is of high importance from both a technical and an economic point of view, as they are valued up to several hundreds MEuros per year. The problem addressed in this paper is the calculation of transmission loss coefficients when the only information available are active injections measurements and active balance sheets.Index Terms-power losses, transmission loss coefficients, weighted least absolute value estimation I. CONTEXTAs the French TSO, and according to French Law, RTE has to compensate for electrical losses on the EHV and HV networks (especially the current squared resistive losses ). These losses amount to around 12 TWh per year. In order to do this, in France, RTE buys from various sources (from the yearly horizon to D-2) the volume corresponding to the predicted losses. The challenge, therefore, is to secure predictions for these losses for the year down to 2 days. The functional analysis of theses questions is presented in [11]. We focus here on the detailed presentation of one of the models, which can be used for losses estimations (and then predictions). II. POLYNOMIAL LOSS MODELSWhen the network topology is perfectly known and remains constant, the transmission losses can be evaluated efficiently as a quadratic function of generating units through a set of ``A coefficients``. Nanda and all showed that these ``A-coefficients'' are robust and don't have to be re-evaluated, even for large changes in loading pattern of the system [1]. This approach requires a representative snapshot of system operating conditions used as a reference base case and a perturbation technique of the power generation at every plant bus. However the short term forecasts require the identification of transmission loss coefficients from active generation measurements covering a wide operation range of the EHV/HV network. This paper combines the idea of piece-wise analytical loss model [2] and a parameter state estimation, the goal is an improvement of empirical equivalent hours loss factors [3,4] when the transmission losses depends significantly on generation schedules and wheeling. The practical use of the polynomial loss models is limited by the topology changes which affect the "commons" defined as the sets of contiguous busses supplied by the same generators [5]. A consequence is, for example, that the branch power losses cannot be approximated by one set of ``A-coefficients`` when the time sample topologies do not share the same "connection key" which is simply composed of the numbers of generators connected on each plant of primary importance. This fact leads us to approximate the square root of global losses as the sum of piece-wise polynomial function of the active power generation at every aggregate. A generating plant having identical generating units acts as an aggregate. The net MW interchange can be thought of as power flowing into or out of the network from an aggregate of the tie lines....