## 3 Simulation Results
### Grid-Connected Mode  
The phase-to-phase voltage waveform shows grid voltage and current behavior after adding harmonic components, as shown in Figure 4. The voltage waveform shows harmonic distortion, yet the current remains well-controlled, which demonstrates effective harmonic management through control and filtering. The system operates safely within its limits despite its distorted appearance. The controlled harmonic injection using both positive- and negative-sequence components proved effective for the benefits of multi-frequency systems in [36; 37]. The measurement of load voltage and current waveforms appears after the DC link and inverter stage in Figure 5. The load receives a pure 50 Hz three-phase voltage despite the grid-side multi-frequency signals. The inverter uses the smoothed DC signal to produce a sinusoidal voltage, which keeps the load current free of harmonics. The power quality at the load remains completely unaffected by harmonic injection because the DC-link isolation, together with inverter reconstruction, maintains perfect power quality. The power distribution among fundamental 5 th and 7 th harmonic components under normal and increased load conditions is summarized in Table 2, which shows the system's high efficiency and effective harmonic-based power transfer. \begin{table}
\begin{tabular}{c c c} \hline
**Component** & **Symbol** & **Value** \\ \hline Grid voltage & \(V_{\text{grid}}\) & 100 V, 50 Hz \\ Switching frequency & \(f_{sw}\) & 20 kHz \\ DC-link voltage reference & \(U_{\text{d}cef}\) & 300–400 V \\ DC-link capacitance per leg & \(C_{dc}\) & 260 μF \\ Filter inductance & \(L_{f}\) & 2.5 mH \\ Filter capacitance & \(C_{f}\) & 10 μF \\ Filter resistance & \(R_{f}\) & 22 m\(\Omega\) \\ Line resistance & \(R_{\text{line}}\) & 0.36 \(\Omega/\text{km}\) \\ \hline \end{tabular}
\end{table} 
Table 1: System parameters. Figure 4: Grid voltage and current. (red: phase a, green: phase b, blue: phase c). Figure 6 presents the total sent power, received load power, and the contributions from the fundamental, 5 th, and 7 th harmonic components. The data clearly shows that while the system transmits total power close to 1000 W, the load receives slightly less, indicating minor losses due to conversion and system impedance. The power breakdown highlights that the fundamental component is responsible for the majority of power delivered to the load, while the 5 th and 7 th harmonics contribute meaningfully to the total transmitted power without reaching the load. This confirms the core advantage of the proposed method: harmonics are used to boost power transfer across the multi-frequency grid yet are fully decoupled from the load side through the DC link and inverter reconstruction, ensuring both high efficiency and standard power delivery. The following stage requires laboratory implementation of this setup to confirm simulation results and evaluate actual system performance, together with its precision and practical constraints. Figure 6 illustrates the power profile during a dynamic load increase from 1 kW to 1.5 kW. This step change occurs around 1.2 s, and the response clearly shows that the total sent power, received power, and the individual contributions from the fundamental, 5 th, and 7 th harmonic components all adjust proportionally to support the higher load demand. The simulation confirms that the injected harmonics are not static but dynamically participate in power sharing as load conditions vary. This reinforces the flexibility and scalability of the proposed approach, ensuring that both fundamental and harmonic components can actively contribute to increased power transfer while maintaining system stability and power quality.