Compact Representation of Nodal Prices in a Distribution Grid

As distributed generation becomes more widespread, distribution network management methods need to be adapted. To achieve an optimal network management, the resolution of the optimal power flow (OPF) problem indicates that it is necessary to use a minimum number of decision variables equal to the number of buses making up the network. However, a real deployment is likely to be limited to sending one or a few variables to the agents connected to the network, as shown by the rich literature currently devoted to this subject. A key question is then to know the optimality gap between the optimal solution and the one using a reduced number of variables. Based on the control variables derived from the OPF and using principal component analysis (PCA), this contribution proposes the construction of new variables, known as latent variables, which are decorrelated from one another. The control of the network by these variables shows, for the test case considered, that only 30% of the variables are necessary to obtain near-optimal control. This finding makes it possible to consider learning these variables for networks in which their operational calculation is impossible in real time.