Method, implemented by computer means, for determining a voltage state of a power supply network comprising at least one low-voltage branch, and at least one high-voltage branch, the low-voltage branch comprising a plurality of nodes at which said voltage state is to be determined, the determination of said voltage state being performed at at least one transformer station, the determination of the voltage state being used to regulate the voltage on the low-voltage network, the method comprising: - a definition of a value of a real target voltage for each node, said real target value representing the voltage value to be reached by the regulation; - an estimation of an active power and of a reactive power for each node; characterised in that it subsequently comprises the implementation, by a processing unit, of the following steps: - constructing a first system of Kirchhoff equations linking complex voltages to the active and reactive powers of the plurality of nodes, - respectively formulating said active and reactive powers in the form of a quadratic function for each node, said quadratic functions linking complex voltages of the plurality of nodes to complex symmetrical matrices from a complex admittance matrix of the network, said quadratic functions being substituted in the first system of equations in such a way as to obtain a second system of equations in real numbers, equivalent to the first system of equations, - formulating an optimisation problem in the form of an auxiliary function from the second system of equations, whereof an approached optimum solution, in particular a global minimum of said auxiliary function, corresponds to a solution of the second system of equations, - iteratively minimising said auxiliary function, whereof an initial solution to the first iteration is the target voltage, until an approximation is obtained of the global minimum of said auxiliary function representing a solution close to the global minimum of said auxiliary function, - and applying to the second system of equations an iterative method by successive linearisations, having as initial solution to the first iteration said approached global minimum, until a value of a complex voltage is obtained in each node. - a definition of a value of a real target voltage for each node, said real target value representing the voltage value to be reached by the regulation; - an estimation of an active power and of a reactive power for each node; characterised in that it subsequently comprises the implementation, by a processing unit, of the following steps: - constructing a first system of Kirchhoff equations linking complex voltages to the active and reactive powers of the plurality of nodes, - respectively formulating said active and reactive powers in the form of a quadratic function for each node, said quadratic functions linking complex voltages of the plurality of nodes to complex symmetrical matrices from a complex admittance matrix of the network, said quadratic functions being substituted in the first system of equations in such a way as to obtain a second system of equations in real numbers, equivalent to the first system of equations, - formulating an optimisation problem in the form of an auxiliary function from the second system of equations, whereof an approached optimum solution, in particular a global minimum of said auxiliary function, corresponds to a solution of the second system of equations, - iteratively minimising said auxiliary function, whereof an initial solution to the first iteration is the target voltage, until an approximation is obtained of the global minimum of said auxiliary function representing a solution close to the global minimum of said auxiliary function, - and applying to the second system of equations an iterative method by successive linearisations, having as initial solution to the first iteration said approached global minimum, until a value of a complex voltage is obtained in each node. - constructing a first system of Kirchhoff equations linking complex voltages to the active and reactive powers of the plurality of nodes, - respectively formulating said active and reactive powers in the form of a quadratic function for each node, said quadratic functions linking complex voltages of the plurality of nodes to complex symmetrical matrices from a complex admittance matrix of the network, said quadratic functions being substituted in the first system of equations in such a way as to obtain a second system of equations in real numbers, equivalent to the first system of equations, - formulating an optimisation problem in the form of an auxiliary function from the second system of equations, whereof an approached optimum solution, in particular a global minimum of said auxiliary function, corresponds to a solution of the second system of equations, - iteratively minimising said auxiliary function, whereof an initial solution to the first iteration is the target voltage, until an approximation is obtained of the global minimum of said auxiliary function representing a solution close to the global minimum of said auxiliary function, - and applying to the second system of equations an iterative method by successive linearisations, having as initial solution to the first iteration said approached global minimum, until a value of a complex voltage is obtained in each node.