Optimal statistical calculation of underground cable bundles positions for time-varying currents

Optimal statistical calculation of power cables disposition in tunnels, for reducing magnetic fields and costs

“…• DetSymmetric: deterministic calculation of the optimal configuration, solving once the optimization problem (1)- (17). As presented in Fig.…”

“…In [14][15][16], several shielding solutions are presented, assuming as known the dispositions of underground cables. In [17], the cost of the disposition is introduced, in order to calculate the optimal position of cables. In this algorithm, all continuous variables are used, calculating optimal geometry of cables and phase arrangement of currents in one unique step.…”

“…For given specified currents in the cables and specified magnetic field limits in the two measurement areas, the proposed optimization problem is summarized in Eqs. ( 1)- (17). s.t.…”

“…For security and construction reasons, the minimum depth allowed for the ceiling of the tunnel y supgalmin is 0.5 m and the maximum depth for the floor of the tunnel y maxgal is 5 m, ( 15) and (16). Because of the nature of urban terrain, maximum distance between walls of tunnel is limited to 8 m, (17), where l max is 4 m. For maintenance reasons, cable bundles are allocated at a minimum distance of the floor (d floor = 0.2 m) and the ceiling (d ceiling = 0.2 m) of the tunnel, ( 18) and ( 19).…”

“…s.t.Eqs. ( 6)- (17). , , , .Where the variables are: (x il ,y il ), mean coordinates of the l-cable in the i-bundle of cables of the optimal mean arrangement; and , horizontal and vertical difference from (x il ,y il ) to each one of the ( ) coordinates of centers of the l-cable in the i-bundle of cables, for the m sample of currents.…”