The method of adjustment of a double-circuit closed loop robust system of active silencing of the magnetic field generated by double-circuit overhead transmission lines with a “Barrel” type arrangement of wires in multy-storey residential building based on experimental measurements magnetic field space-time characteristics developed at first time. The adjustment of the channel regulators carried out in such a way that their magnetic field space-time characteristics are orthogonal to each other with separate operation of only the first and only the second channels. The problem of design of two degree of freedom robust two circuit system of active shielding of initial magnetic field comes down to a decision of the multi-criteria game. The payoff vector game calculated based on Ampere-Laplace law. The game solution calculated based on the stochastic particles multiswarm optimization algorithms. Experimental adjustment of the model of double circuit system of active silencing of magnetic field, generated by double-circuit overhead transmission lines with a “Barrel” type arrangement of wires in multy-storey residential building based on experimental measurements space-time characteristics are given. The possibility of initial magnetic flux density level reducing to the living safe level has been experimentally shown.