## 4 Experimental Analysis  
A typical building power system constitutes the experimental environment. The power line follows a typical tree topology model with a 500 m distribution radius. The power area includes a collection terminal, collectors, single-phase smart meters, and three-phase smart meters from different manufacturers. All carrier devices possess unique identification numbers and are interconnected via power lines. To account for differences in communication performance, devices are parameterized according to their characteristics. Variables are incorporated to characterize the effective communication radius under different channel conditions, capturing time-varying characteristics. The experiment employs the BPSK coding scheme \(L\) for carrier communication. MATLAB software 2025 edition is utilized to simulate the secure transmission method of high-speed power line carrier communication. The experimental simulation utilizes a communication network comprising 38 carrier devices distributed within a 500 m radius. Figure 4 illustrates the physical connections between the meters. The network consists of 1 collection terminal, 3 collectors, 30 single-phase smart meters, and 4 three-phase smart meters from different manufacturers. The carrier communication employs BPSK modulation, with an average effective communication distance of \(L=100\) m. The main reason for employing BPSK modulation technology lies in its straightforward implementation and excellent noise immunity, making it particularly suitable for power line carrier communication systems operating in complex noise environments. However, alternative modulation techniques, such as quadrature phase shift keying (QPSK), can enhance the data transmission rate. Nevertheless, in high-frequency bands, the bit error rate may increase significantly due to the inherent channel characteristics of power lines, potentially compromising communication reliability and stability. The network formation results, presented in Figure 4, are derived by implementing the proposed technique on the carrier equipment depicted in Figure 5 to establish a high-speed power line carrier communication network. Figure 5 demonstrates that the proposed method successfully establishes interconnections among all carrier nodes within the high-speed power line carrier network. Carrier devices numbered 38, 16, 17, 28, 31, and 37 are designated as cluster head nodes due to their superior communication performance. This selection criterion ensures network stability by minimizing frequent reconfigurations when channel conditions vary, thereby enhancing the overall reliability of the high-speed power line carrier communication system. For a chaotic mapping, its bifurcation diagram illustrates the trajectories under different parameters. The diagram visually demonstrates the traversal and non-periodicity properties of the chaotic mapping under various control parameters. Figure 6 shows the 3D view of the bifurcation diagram for the generalized 2D polynomial chaotic mapping employed in this study, with two parameters (taking parameters \(\alpha_{1}\) and \(\mu\) as examples). As shown in Figure 5, under the configuration of control parameters \(\alpha_{1}\) and \(\mu\), the state variables are uniformly distributed throughout the entire space, demonstrating that the generalized two-dimensional polynomial chaotic mapping technique adopted significantly enhances the security performance of high-speed power line carrier communication. This mapping method makes it extremely difficult to intercept information from transmitted signals, greatly improving the protection capabilities of the high-speed power line carrier communication network and ensuring the confidentiality and integrity of the transmitted data. Figure 4: Physical connection diagram of carrier energy meter. Among them, 1–38 respectively represent the carrier equipment number. Figure 5: Results of high-speed power line carrier communication network construction.