## 3 Reconstruction Method and Protection Algorithm
### Reconstructing Current Trajectory in Two-Dimensional Space  
As a new power system with a high proportion of new energy is affected by the control system, the amplitude of the fault current is limited, the phase changes, and the equivalent impedance property of the system changes, and the difficulty of accurately identifying the fault is significantly increased by the traditional differential protection that relies on the analysis of the power frequency characteristics of the fault current. As shown in Figure 2, the characteristics of the transient quantity after the fault is considered, combining new energy control collaboration and deep learning to construct a new principle of protection.  
From [11], the differential current of a photovoltaic parallel network is summarized in Formula (3). It can be seen that the differential current consists of power frequency and DC attenuation, including all the information of the fault current on the PV side and the grid side, which can be used to construct a new protection principle.  
\[\begin{array}{l}i_{dx}=i_{px}+i_{gx}=I_{P}\cos(\omega_{0}t+\varphi_{p})\\ \phantom{i_{px}}+I_{\overline{g}}\cos(\omega_{0}t+\theta_{0})+I_{\overline{g}}e ^{-t/T_{a}}\end{array} \tag{3}\]  
In Formula (3), \(I_{p}\) is the current amplitude on the PV side, \(I_{g}\) is the current amplitude on the PV side, \(\omega_{0}\) is the power frequency, \(\psi_{p}\) is the current phase angle on the PV side, and \(I_{\overline{g}}\) and \(I_{\overline{g}}\) denote the amplitudes of the alternating current (AC) and direct current (DC) components of the grid-side current, respectively. \(\theta_{0}\) is the initial angle, and \(T_{a}\) is the decay time constant of the DC component.  
In the two-dimensional space plane coordinate system, the PV side current \(I_{p}\) is taken as the X-axis independent variable, and the system side current \(I_{\overline{g}}\) is taken as the Y-axis dependent variable. Over time, the two will draw a trajectory curve image in the coordinate system. The trajectory image contains all characteristic information of phase electrical quantities and sequence electrical quantities, such as amplitude, phase, and power of the current at both ends of transmission lines.  
The continuous waveform is essentially composed of the point set with a certain sampling frequency. It is assumed that the point sets \(I_{p}\) and \(I_{g}\) with N data points can be expressed as Formula (4); \(I_{p}(k)\) and \(I_{g}(k)\) denote the \(k\)-th sampled current values on the PV side and the grid side, respectively:  
\[\begin{array}{l}I_{p}=\left[i_{p}(1)\cdots i_{p}(k)\cdots i_{p}(N)\right]\\ I_{g}=\left[i_{g}(1)\cdots i_{g}(k)\cdots i_{\overline{g}}(N)\right]\end{array} \tag{4}\]  
The data points sampled at the same time in the two sets form \(N\) data pairs in one-to-one correspondence [18], such as in (5).  
\[D=\left[\left(i_{p}(1),i_{\overline{g}}(1)\right)\cdots\left(i_{p}(k),i_{ \overline{g}}(k)\right)\cdots\left(i_{p}(N),i_{\overline{g}}(N)\right)\right] \tag{5}\]  
This paper uses a 2 kHz sampling frequency. For the 50 Hz power system, 40 data points are sampled in one cycle (20 ms), forming 40 data pairs. All data pairs are mapped to a two-dimensional space plane to obtain the current characteristic trajectory image, as shown in Figure 8. Figure 8 demonstrates the methodology for reconstructing two-dimensional spatial current trajectory images, which serve as the critical input for the proposed deep learning-based protection algorithm. This process transforms raw current signals from photovoltaic stations and grid-side systems into time-domain spatial features,enabling A-CNN to extract fault characteristics without relying on predefined thresholds or grid models.