Developing a general and stable numerical interface for power hardware-in-the-loop (PHIL) applications is a major challenge. This paper proposes a stable, robust and precise implementation of a multi-time-step interface for a PHIL simulator based on the Bergeron transmission line model (BTLM). Two limitations of the transmission-line-based interface were identified, and remedial strategies were formulated in order to ensure that the interface was compatible with the PHIL application. Stability and passivity analyses were then conducted on the resulting interface to verify its performance. The proposed interface was implemented in an experimental 3-kVA PHIL setup, using a custom-made switching power amplifier (PA). Multiple tests were performed in order to demonstrate the stability and accuracy of the closed-loop system under a wide range of operating conditions and with various devices under test (DUTs). Experimental results were obtained from islanding tests involving different simulated load configurations and solar inverter responses to network disturbance while operating in a closed-loop configuration.

This paper presents a new validation method to demonstrate the stability, and accuracy of a discretized system using multiple sampling rates. Such multi-rate simulations are often encountered in real-time simulation application, where large power systems are coupled with circuit containing power electronics devices. Multi-rate simulation should not be confused with variable-step simulation, which is a single-rate simulation type. In single-rate simulation, the discretized system is stable when its discrete poles are within the unitary circle. When using multirate solvers state-variables are discretized with different sampling rates and poles location analysis for the system’s equations cannot be used. This paper introduces a formal mathematical analysis demonstrating stability of multi-rate real-time simulation. System state-variables, regardless of their discretization time-step, are found in a single matrix. Classical pole analyses are thereafter used to test stability with poles location analysis. The method is given in a generalized form, and can be applied to various multi-rate solvers. The proposed method was found accurate and reliable using numerical examples.

At high frequency, power losses of a winding due to eddy currents becomes significant. Moreover, the skin and proximity AC resistances are influenced by the width of printed circuit board (PCB) conductors and distance between the adjacent tracks which causes many difficulties to design windings with lowest AC resistances. To clarify this phenomenon, this paper focuses on modeling the influence of skin and proximity effects on AC resistance of planar PCB winding, thereby providing guidelines to reduce the winding AC resistance. An approximate electromagnetic calculation method is proposed and it shows that when the winding proximity AC to DC ratio $\left(F_{proximity}\right)$ is equal to $\frac{1}{3}$ the AC on DC ratio caused by skin effect $\left(F_{skin}\right)$ , the winding is optimized and it has lowest AC resistance. 3-D finite element simulations of 3, 7 and 10-Turn windings, which are divided into 3 groups with the same footprint, are presented to investigate the lowest AC resistance when the track width varies from 3 mm to 5 mm and the frequency range is up to 700 kHz. In order to verify the theoretical analysis and simulation results, an experiment with 3 simulated groups, (9 prototypes in total) is built and has a very good fit with simulation results. Experimental results show that at the optimal width, the AC resistance of the windings can be reduced up to $16.5\%$ in the frequency range from 200 kHz to 700 kHz.

At high frequency, AC resistance of a printed circuit board (PCB) winding becomes important and accounts for a large proportion of planar transformer losses. The winding is then influenced by both skin and proximity phenomenon, which makes the current distribution uneven resulting in an increased resistance. The study of improving AC resistance of a PCB winding has been tackled by many researchers. However, the lack of an overview and comparison among improvements has made it difficult to apply those methods to a specific winding. To overcome the above limitations, this paper investigates the pros and cons of three popular AC resistance optimizing methods: optimizing track width of a solid PCB winding, using multi-strands and using Litz style PCB winding. To verify the theoretical analysis, a total of 12 PCBs are simulated by finite element (FEM) and tested in the laboratory. Five criteria are analyzed, including skin resistance, proximity resistance, AC to DC ratio, total AC resistance and complexity are taken into consideration. The results of this study show that optimizing track width method has a significant improvement on AC resistance while the use of Litz PCB is effective for applications that need stable AC resistance in a wide frequency range. The use of parallel strands winding should be carefully considered as there is not significant benefit in both reducing the AC resistance and AC to DC ratio.

Managing parallel−connected single−phase distributed generators in low−voltage microgrids is challenging due to the volatility of renewable energy sources and fluctuating load demands. Traditional droop control struggles to maintain precise power sharing under dynamic conditions and varying line impedances, leading to inefficiency. This paper presents a novel adaptive droop control strategy integrating artificial neural networks and particle swarm optimization to enhance microgrid performance. Unlike prior methods that optimize artificial neural network parameters, the proposed approach uses particle swarm optimization offline to generate optimal dq−axis voltage references that compensate for line effects and load variations. These serve as training data for the artificial neural network, which adjusts voltage in real time based on line impedance and load variations without online optimization. This decoupling ensures computational efficiency and responsiveness, maintaining voltage and frequency stability during rapid load changes. Addressing dynamic load fluctuations and line impedance mismatches without inter−generator communication enhances reliability and reduces complexity. Simulations demonstrate that the proposed strategy maintains stability, achieves accurate power sharing with errors below 0.5%, and reduces total harmonic distortion, outperforming conventional droop control methods. These findings advance adaptive control in microgrids, supporting seamless renewable energy integration and enhancing the reliability and stability of distributed generation systems.

The three-phase dual active bridge (3p-DAB) converter is widely considered in next-generation DC grid applications. As for traditional AC grids, the successful integration of power electronic converters in DC grids requires accurate time-domain system-level studies. As demonstrated in the existing literature, the development and efficient implementation of large-signal models of 3p-DAB converters are not trivial. In this paper, a generalized average model is developed, which enables system-level simulation of DC grids with 3p-DAB converters in electromagnetic transient type (EMT-type) programs. The proposed model is rigorously compared with alternative modeling techniques: ideal-model, switching-function and state-space averaging. It is concluded that the generalized average model provides an optimal solution when accuracy of transient response, reduction in computation time, and wideband response factors are considered.