Abstract- With the cabling reconstruction of urban medium voltage distribution network, three-core cables are gradually used to replace overhead lines. Theoretically due to the zero-sequence current of three-core cable is zero in steady state, the traditional ferromagnetic current transformer cannot be applied to the non-intrusive arc grounding fault detection of three-core cable. Therefore, this paper proposes a method to measure the zero-sequence current of 10 kV three-core cable by using magnetic sensor array. The magnetic field intensity is detected by the sensor to invert each phase current, which is used to detect arc grounding fault. First of all, the structure of a 10 kV three-core cable is briefly introduced, as shown in Fig. 1. It is mainly composed of conductor core, semiconductor shield, insulating layer, copper tape screen, steel tape armor, sheath and so on. Secondly, on the basis of Maxwell equations, the three-core cable model is established, and then, the surface magnetic field distribution is simulated by finite element method (FEM). In the simulation model, the three-phase sinusoidal current signal is set with frequency of 50 Hz and peak value of 200 A. The variation of the tangential magnetic field intensity on six equidistant points of the cable surface with time is shown in Fig. 2. It can be seen that the tangential magnetic field intensity shows a sinusoidal change with the current change, which indicates that the relationship between the magnetic field intensity and three-phase current can be quantitatively analyzed. Next, combined with the Ampere circuital theorem, the nonlinear equations of each phase current and the tangential magnetic field intensity at measured points are constructed. So that, each phase current can be obtained by inverse calculation. In practice, the installation position of the sensor array has a direct impact on the current calculation results. On the one hand, due to the unknown distribution of the three-phase position inside the cable, the magnetic sensor usually cannot be accurately installed at the intersection of the cable center and the phase center. On the other hand, there may be eccentricity between the cable center and the sensor array center. Therefore, establishing the analytical model of the tangential magnetic field intensity on the surface of the three-core cable, as shown in Fig. 3. In order to solve the influence of the installation position of the sensor array on the result, ultimately, designing a circular sensor array with six equidistant measurement points, numbered N1~N6, which is used to solve six unknown variables: A-phase current, B-phase current, C-phase current, rotation angle α and eccentric distance x, y. Finally, the feasibility of the method can be verified by simulation. Using EMTP software to simulate the arc grounding fault, the fault occurs in A-phase at 0.1 s, and the each phase current waveform is obtained, as shown in Fig. 4. It can be seen that after the arc grounding fault occurs, the current values change abruptly. By extracting the tangential magnetic field intensity at measured point, the inversion solution of fault current waveform can be used to detect the occurrence of arc grounding fault.