A Low-Voltage Back-to-Back Converter Interface for Prosumers in a Multifrequency Power Transfer Environment

Abstract

The research demonstrates, through simulation and laboratory validation, the development of a low-voltage DC-link (LVDC) back-to-back converter system that enables multi-frequency power transfer. The system operates in two distinct modes, which include a three-phase grid-connected converter transferring fundamental and 5th and 7th harmonic power to a three-phase residential inverter supplying a clean 50 Hz load and another mode that uses a DC–DC buck–boost converter to integrate a battery storage unit for single-phase load supply. The system allows independent control of each harmonic component and maintains a clean sinusoidal voltage at the load side through DC-link isolation. The LVDC link functions as a frequency-selective barrier to suppress non-standard harmonic signals on the load side, effectively isolating the multi-frequency power grid from standard-frequency household loads. The proposed solution fills the gap between the multi-frequency power systems and the single-frequency loads because it allows the transfer of total multi-frequency grid power to the traditional household loads with pure fundamental frequency. Experimental results and simulation outcomes demonstrate that the system achieves high efficiency, robust harmonic isolation, and dynamic adaptability when load conditions change.

1. Introduction

The modern power grid transforms into complex networked systems that combine high percentages of renewable energy sources with energy storage capabilities. The hybrid AC/DC microgrid architecture has received substantial interest because it enables the combination of different energy sources and loads while improving system flexibility and efficiency. The introduction of multi-frequency power transfer represents a new method to shape the voltage peak, which results in increased RMS voltage without violating the peak limits. This, in turn, leads to the power capacity increase without the need to uprate distribution system lines. Also, it reduces network congestion through the simultaneous utilization of various frequency components across AC lines. The approach involves adding specific harmonic frequencies to the 50 Hz fundamental waveform to establish additional power channels through intentional harmonic signal superposition. The method draws inspiration from communication systems that use frequency-division multiplexing, and researchers have applied it to the “energy internet” for enabling bidirectional energy packet transfer through existing power lines [1,2,3,4,5].

The use of low-voltage DC links has become more common for connecting different grid-tied converters, photovoltaic (PV) generators, and battery energy storage systems (BESS) to a single bus. A hybrid AC/DC system is formed by a bidirectional inverter that connects the DC-link to the AC grid and other converters that connect PV and battery units to the DC bus [3]. The DC-link functions as the central power exchange system between sources and loads to enhance renewable energy integration and storage capabilities [6].

The conventional power systems operate at a single fundamental frequency (50 or 60 Hz), and any harmonic components are usually mitigated to maintain power quality. However, researchers have recently started to explore multi-frequency power transfer as a paradigm shift, using specific harmonic frequencies to transfer power simultaneously with the fundamental. This idea was first inspired by waveform peak-shaping techniques that showed that adding harmonics does not increase peak voltage [4,5]. Rather than filtering out harmonics, the multi-frequency approach treats them as independent channels for energy transfer. Ref. [4] showed one of the early demonstrations of a single-phase islanded multi-frequency grid, where a 50 Hz base waveform and its 3rd, 5th, and 7th harmonics were superimposed to increase the RMS voltage while maintaining peak voltage. Thus, for the same amount of power, the current would be smaller, which reduces the losses in the system.

The multi-frequency concept has moved past single-phase experiments during recent years. A thorough assessment implemented the “orthogonal power transfer” principle, allowing separate power distribution between different frequencies. The experimental findings showed that renewable and storage sources can utilize the same three-phase line without any form of interference, which leads to better line utilization [1].

Research has shown that multi-frequency power transfer systems can independently manage multiple frequency components. The first single-phase converter, which injected fundamental and 150 Hz harmonics, led to the development of a three-phase, two-frequency system. A three-phase, three-frequency system, which uses positive-sequence 50 Hz, zero-sequence 3rd, and negative-sequence 5th harmonics, has been proposed to create three parallel power channels from a single line. The added harmonic channels can be controlled such that they do not interfere with the fundamental component, thus partitioning the power flow by frequency. The system achieved increased RMS voltages through harmonic amplitude adjustments, which stayed below peak limits. The experimental results, together with simulation outcomes, showed that orthogonal decomposition simplified control while eliminating network congestion according to [2,7,8].

Multi-frequency systems continue to develop as an emerging field because multiple challenges persist despite recent advancements. Research in this field primarily investigates conceptual feasibility through studies that use single-phase systems and simplified conditions [4,7]. Three-phase implementations and complex harmonic combinations became the focus of research only in recent times. The integration of distributed generation systems and storage facilities into multi-frequency power grids has not received enough research attention. The integration of PV panels and batteries into multi-frequency buses has been proposed, but effective control systems for this application are hard to find. The analysis of PV and BESSs connected through a DC link requires studying AC-side multiple frequency power interactions, DC-link behavior, and device connectivity. The integration of these elements requires interdisciplinary control approaches that combine power quality management with power electronics and microgrid energy management principles [1,2,8].

A low-voltage DC link enables a hybrid AC/DC microgrid that combines the strengths of both systems. The main AC grid is connected to local AC networks via a back-to-back converter, and the DC link integrates PV, batteries, other DC sources, or DC networks via DC/DC converters. This architecture improves efficiency, simplifies power flow coordination, and enables bidirectional energy exchange between AC and DC subsystems [3,9]. The stability of the DC link becomes a problem when multiple converters, such as PV inverters and BESS converters, are exchanging power. Several control strategies have been proposed to coordinate these units. A unified control method has been proposed to enable smooth transitions between grid-connected and islanded modes, thus providing resiliency during grid outages and seamless resynchronization when the grid returns [10,11].

Integrating a photovoltaic source and a battery energy storage system into a shared DC-link improves microgrid performance by enabling local renewable supply and buffering power fluctuations. The PV operates under maximum power point tracking (MPPT), while the BESS smooths DC-link variations by charging or discharging. To ensure stable operation in both grid-connected and autonomous modes, mode-adaptive control is used: the battery inverter operates in current-control mode during grid connection and switches to voltage-control mode during islanding [12]. Energy management strategies are critical for real-time control of BESS charging and discharging. Hierarchical control methods allocate power between PV and BESS based on forecasts and demand [13], while centralized EMS monitors battery state-of-charge and DC-link status to optimize energy flow and support peak shaving [14]. These strategies ensure that the PV and battery jointly maintain DC-link stability, store surplus energy during peak production, and supply power during high demand or transient events [15].

The stability of DC-link voltage represents a fundamental operational challenge for standalone and grid-forming inverter systems, especially when designers implement reduced-capacitance solutions to enhance reliability and lifespan. Research indicates that sliding mode control successfully controls voltage instabilities that occur from small film capacitors in standalone photovoltaic systems to improve system dynamics and maintain power quality [16,17]. The improper adjustment of PI-based DC-link controllers in grid-forming inverters creates transient instability because unstable limit cycles appear even though small-signal stability remains intact. A bifurcation-based analysis was proposed to guide parametric selection and ensure synchronism under large disturbances [18].

An important aspect is the control of the BESS converter, typically a bidirectional DC/DC unit connected to the DC-link. Its role is to regulate battery charging and support DC-link voltage stability alongside the grid-tied inverter. A PI-based current control loop has been used to enable rapid battery response to DC-link deviations. The BESS could also help balance harmonic power in multi-frequency systems by absorbing oscillatory components, acting as an active damping element against low-frequency voltage oscillations caused by 5th or 7th harmonic interactions [19].

The integration of PV-BESSs in a properly coordinated way improves microgrid reliability through peak shaving, load leveling, and frequency regulation. Including additional storage components such as supercapacitors and flywheels can enhance the dynamic response by handling fast transients. A holistic energy management strategy is required to dispatch multiple storage units effectively so that PV operates at maximum power, BESS maintains DC-link stability, and both respond to grid-side or EMS requirements [20,21]. The grid-side bidirectional inverter controls the DC-link voltage and controls AC-side power quality. It operates in grid-following mode and uses a PI-controlled dq-frame or resonant controller to inject the required currents. Standard controllers regulate fundamental currents, but specialized harmonic compensators are needed to control significant harmonic components at frequencies like 5th or 7th. Therefore, the inverter can cancel distortion or precisely control harmonic power flow [9,19].

The extraction and control of specific harmonic components requires multiple techniques. The proportional-resonant (PR) controllers operate in the stationary frame to extract specific harmonic frequencies such as 250 Hz (the 5th harmonic) and 350 Hz (the 7th harmonic). The PR controllers provide easier tuning procedures and successful harmonic targeting compared to multi-reference-frame transformations. The repetitive control (RC) method provides harmonic cancellation of integer harmonics across cycles, yet it experiences slow responses and stability problems. The standard implementation in practice involves using a PI controller for fundamental 50 Hz frequency control alongside PR controllers for specific harmonic frequencies [22,23,24].

The load side of the DC link consists of a load inverter that functions in grid-forming mode to regulate voltage and frequency for supplying local loads with a pure 50 Hz sinusoidal output. It provides voltage isolation from multi-frequency distortions during grid-connected operation and creates a stable AC subsystem and decouples the load-side from grid-side disturbances (e.g., unbalance, harmonics, voltage sags and swells, or over- and undervoltage). This setup is often called a back-to-back converter system or AC/AC isolation via DC link [9,10]. The control of grid-forming inverters has been studied extensively because inverter-based resources need to regulate the grid voltage. A grid-forming inverter has an inner current loop and an outer voltage loop, which is often based on droop control or virtual synchronous machine (VSM) principles. For single-inverter systems, stable voltage reference and fast transient response are key, while droop control becomes more important when paralleling sources. Virtual impedance or damping further improves stability when supplying nonlinear or motor loads [10].

A key scenario occurs when the main grid connection is lost. The load-side grid-forming inverter must continue to supply the local loads using the PV and BESS through the DC link, effectively forming an islanded microgrid. This requires close coordination between the grid-forming inverter and the BESS. Recent studies have shown that a BESS inverter can switch from current-controlled to voltage-controlled mode during islanding, allowing a smooth transition without large transients. Also, PV-battery inverters with suitable control algorithms can maintain stable operation through such mode changes [12,25].

The load-side grid-forming inverter needs to separate loads from upstream harmonic disturbances during typical operation. The system filters higher-frequency disturbances through voltage controllers that operate at a 50 Hz bandwidth. The inverter needs to reject DC-link ripples, which represent harmonic disturbances from the grid, to produce a clean output. The system can reject grid harmonics through feed-forward cancellation or by using an adequate DC-link capacitor. The inverter controls the voltage reference, so external synchronization is not required, but phase and frequency synchronization with the grid-tied inverter can be useful when reconnecting. Virtual oscillator control and self-synchronization methods can be used to enable DC-link-based coordination between systems [10].

The modern distribution network adopts LVDC systems as flexible alternatives to AC systems because they support renewable generation and provide better energy efficiency and lower conversion losses. ETAP simulations demonstrated that LVDC architectures operating at 110 V, 250 V, and 320 V outperform traditional AC systems by delivering superior voltage drop performance and harmonic distortion reduction and power quality improvement [26]. The review of LVDC microgrids demonstrated their importance for urban applications and prosumer integration and decentralized energy systems [27].

The implementation of advanced power electronic interfaces boosts the functionality of LVDC systems within hybrid power grids. The technological advancement of power converter topologies for electric vehicles and microgrids has been documented in recent research, which demonstrates how multilevel, bidirectional, and modular converters serve as fundamental enablers for grid flexibility [28]. The combination of LVAC–LVDC–HVDC architectures has been proven to decrease energy losses while enhancing DER-rich network hosting capacity [29].

A bipolar modular multilevel DC–DC converter functions as a connection between MVDC and LVDC subsystems by providing galvanic isolation and self-balancing control for decoupled power flow [30]. The research investigated power transmission boundaries of back-to-back converter systems together with PLL dynamics effects on weak grid conditions [31].

The survey of DC microgrid protection identified fast communication-less fault management strategies as essential for improving reliability in modular LVDC architectures [32]. The IDBS-MPET proposes a multiport power electronic transformer structure with isolated LVDC ports and maximum power transfer capability through a single converter [33]. The SiC-based single-to-three-phase converter has been tested for rural LVDS environments to provide a three-phase power supply under nonlinear and unbalanced load conditions [34]. Research on multi-frequency AC/DC systems demonstrates that BTB and AC/DC converters can successfully control power transfer between grids with different frequencies through unified power flow models. The models include converter control strategies, system constraints, and voltage regulation to enable accurate and flexible operation in hybrid power networks [35].

The main objective of this research is to facilitate the integration and control of multi-frequency power in low-voltage networks through a back-to-back converter structure with a shared DC-link. The proposed system includes a grid-side inverter that feeds fundamental and harmonic components into the DC link and a load-side inverter that reconstructs a pure 50 Hz voltage for residential loads. The DVR generates harmonic components on purpose to enable power transfer between different frequency channels without disrupting sensitive end-users. The DC-link functions as a frequency-selective barrier to protect the load from upstream harmonic distortions while enabling total power transmission, including harmonic contributions through controlled conversion.

The research demonstrates that LVDC systems, together with modular converter topologies and harmonically decoupled back-to-back interfaces, form essential building blocks for future multifrequency power transfer networks.

The research introduces a back-to-back converter system with a low-voltage DC-link (LVDC), which functions to separate residential loads from power grids with multiple frequency components. The system enables controlled power transfer across a three-phase AC network, which contains both the 50 Hz fundamental component and the 5th and 7th harmonic voltages. The simulation includes two operating modes. The first one is called grid-connected mode, and the second one is called storage-supported mode, which combines a grid-connected multi-frequency inverter with a household inverter for three-phase load supply, and the second mode includes a battery energy storage system (BESS) connected to the DC-link for power flow regulation and voltage stability during dynamic load conditions. The system architecture enables support for upcoming multi-frequency power systems and maintains optimal power quality for connected loads.

The main contributions of this work are as follows:

• Development and laboratory implementation of a back-to-back converter system with LVDC-link, which is able to isolate the non-standard-compliant voltage used in multi-frequency power systems from the standard-compliant voltage required by the residential loads, while transferring the total multi-frequency power to the load side.
• Validation of two operating modes: (i) a baseline mode with a three-phase balanced load fed through a clean inverter output and (ii) a BESS-supported mode where the battery system interacts with the DC-link to absorb or supply power dynamically under changing load conditions.

2. Methodology

The architecture of the proposed system is illustrated in Figure 1. It consists of a low-voltage DC-link interconnecting two independent three-phase inverters: one interfacing with the grid side and the other supplying the customer side. This structure enables the decoupling of grid-side disturbances from the sensitive customer loads while supporting multi-frequency power transfer and efficient energy management. The growing use of distributed energy resources (DERs), including PV systems and BESSs, has prompted the creation of hybrid AC/DC microgrid architectures that provide better flexibility and efficiency. LVDC links have established themselves as essential components for linking various power sources while enabling independent management of power generation and load consumption. The idea of multi-frequency power transfer has received notable interest because researchers intentionally add the 5th and 7th harmonic frequencies to the fundamental component to create multiple parallel energy paths in one network structure.

Traditional systems approach harmonics as unwanted disturbances that need to be eliminated. Research shows that superimposing frequency components enables better transmission capacity usage while creating possibilities for energy packet transfer. This research develops an innovative system design that uses an LVDC link to divide grid functionality from customer functionality and enables multi-frequency operation.

A three-phase inverter on the grid side maintains DC-link voltage stability and performs power exchange with the grid through fundamental frequency and 5th and 7th harmonic operations. The implementation of a Dynamic Voltage Restorer (DVR) at the point of common coupling (PCC) allows active harmonic voltage injection for proper control of multi-frequency signals. A different three-phase inverter located on the consumer side generates a pure fundamental-frequency (50 Hz) voltage supply to loads while blocking upstream voltage disturbances but transferring total power from the grid side. The system design provides sensitive customer loads with high power quality through fundamental-frequency supply while maintaining flexible and efficient grid interaction.

The multi-frequency grid voltage consists of 50 Hz and 350 Hz positive sequence, and 250 Hz negative sequence, which maintains a balanced three-phase configuration. The grid voltage after harmonic injection can be formulated by these relations:

$$v_a\left(t\right)=V_1\mathit{sin}\left(\omega t\right)+V_5\mathit{sin}\left(5\omega t\right)+V_7\mathit{sin}\left(7\omega t\right)$$

$$v_b\left(t\right)=V_1\mathit{sin}\left(\omega t-120°\right)+V_5\mathit{sin}\left(5\omega t+120°\right)++V_7\mathit{sin}\left(7\omega t-120°\right)$$

(1)

$$v_c\left(t\right)=V_1\mathit{sin}\left(\omega t+120°\right)+V_5\mathit{sin}\left(5\omega t-120°\right)++V_7\mathit{sin}\left(7\omega t+120°\right)$$

where V₁, V₅, and V₇ are the fundamental, fifth, and seventh harmonic voltage amplitudes, respectively, and ω is the fundamental angular frequency.

The proposed system allows PV and BESS components to be integrated into the DC-link through bidirectional energy flow, which improves microgrid resilience. The system maintains strong decoupling between grid dynamics and end-user environment by using multi-frequency control for grid-side operations combined with fundamental-frequency regulation for customer-side operations. Through its LVDC link function, the system creates both an energy storage capability and an interface that splits areas with harmonic presence from areas without harmonics.

The research describes modeling approaches alongside control design methods and analysis for this architecture while discussing difficulties and resolution strategies related to multi-frequency power transfer and DC-link voltage stability and DVR-based harmonic injection and customer-side voltage regulation.

2.1. Grid-Side Converter Control

As shown in Figure 2, the primary objective of the outer loop is to maintain the DC-link voltage $V_{\mathrm{D}\mathrm{C}}$ at its reference value $V_{\mathrm{D}\mathrm{C},\mathrm{r}\mathrm{e}\mathrm{f}}$.

$$e_{v_{\mathrm{d}\mathrm{c}}}\left(t\right)=V_{\mathrm{D}\mathrm{C},\mathrm{r}\mathrm{e}\mathrm{f}}-V_{\mathrm{D}\mathrm{C}}\left(t\right)$$

(2)

This error is processed through a Proportional-Integral (PI) controller to generate the reference d-axis current $i_{d_{-}ref}$:

$$i_{d\_ref}(t)=K_{p_{-}v}{e}_{v_{\mathrm{d}\mathrm{c}}}(t)+K_{i_{-}v}\int e_{v_{\mathrm{d}\mathrm{e}}}(\tau )d\tau$$

(3)

where

• $K_{p\_v}$ is the proportional gain.
• $K_{i\_v}$ is the integral gain of the DC voltage controller.

The current control loop is implemented in the synchronous rotating dq-frame synchronized to the fundamental frequency.

The inverter output current $i_{\mathrm{cv}}$ is measured and transformed into the dq-frame components $i_{d_{-}cv}$ and $i_{q_{-}cv}$.

The $d$-axis and $q$-axis control objectives are as follows:

• D-axis: track $i_{d\_\mathrm{ref}}$ to regulate active power (and indirectly DC-link voltage).
• Q-axis: track $i_{q_{-}ref}$ (typically set to zero to achieve unity power factor or adjusted for reactive power exchange).

The control errors are as follows:

$$\begin{array}{r}{e}_{i_d}\left(t\right)=i_{d_{-}ref}-i_{d_{-}cv}\\ e_{i_q}\left(t\right)=i_{q_{-}ref}-i_{q_{-}cv}\end{array}$$

(4)

Each error signal is processed through independent PI controllers as follows:

For the d-axis

$$v_{d_{\_}cv}(t)=K_{p_{-}i}{e}_{i_d}(t)+K_{i_{-}i}\int e_{i_d}(\tau )d\tau +v_{d_{-}ff}$$

(5)

For the $q$-axis

$$v_{q_{-}cv}(t)=K_{p_{-}i}{e}_{i_q}(t)+K_{i_{-}i}\int e_{i_q}(\tau )d\tau +v_{q_{-}ff}$$

(6)

where

• $K_{p_{-}i}$ and $K_{i_{-}i}$ are the proportional and integral gains of the current controllers.
• $v_{d_{-}ff}=\omega L{i}_{q_{-}cv}$ is the feedforward voltage term to compensate for the coupling between d and q axes.
• $v_{q_{-}ff}=-\omega L{i}_{d_{-}cv}$ is the corresponding feedforward term for the q-axis.

Thus, the decoupled control ensures dynamic and independent regulation of both current components.

The grid-side converter (GSC) and the customer-side inverter (CSI) operate in synchronous rotating reference frames. The GSC uses phase-locked loop (PLL) synchronization. A synchronous reference frame PLL operates on the grid side. The structure provides enhanced tracking performance when dealing with harmonic-rich and distorted grid conditions through improved filtering and reduced phase error. The d-axis points towards the voltage vector at the point of common coupling (PCC) using the filtered grid voltage (V_g). The system enables precise synchronization for multi-frequency operation, which allows independent control of fundamental and harmonic components through resonant controllers in the d/q frame.

The CSI is a grid-forming inverter that outputs proper fundamental voltage because end-user loads receive sinusoidal waveforms without harmonic distortion.

2.2. Customer-Side Inverter Control

The customer-side inverter (shown in Figure 2) operates in a grid-forming mode, providing a stable 50 Hz voltage to local loads. The control structure is based on cascaded voltage and current controllers implemented in the synchronous $dq$-frame.

The inverter’s outer voltage control loop ensures that the output voltage $V_L$ tracks the desired sinusoidal reference.

The voltage error in the $dq$-frame is as follows:

$$\begin{gathered} e_{v_d}\left(t\right)=V_d^{*}-V_d\left(t\right) \\ {e}_{v_q}\left(t\right)=V_q^{*}-V_q\left(t\right) \end{gathered}$$

(7)

where

• $V_d^{*}$ and $V_q^{*}$ are the d- and q-axis voltage references;
• $V_d$ and $V_q$ are the measured voltages in the $dq$-frame.

Each error is fed into a Proportional-Integral (PI) controller to produce the reference inverter currents:

$$\begin{gathered} i_{cv,d}^{*}(t)=K_{p_{-}v}{e}_{v_d}(t)+K_{i-v}\int e_{v_d}(\tau )d\tau \\ {i}_{cv,q}^{*}(t)=K_{p_{-}v}{e}_{v_q}(t)+K_{i\_v}\int e_{v_q}(\tau )d\tau \end{gathered}$$

(8)

where

• $K_{p\_v}$ and $K_{i\_v}$ are the voltage controller gains.

The inner current loop tracks the reference currents $i_{cv,d}^{*}$ and $i_{cv,q}^{*}$ by controlling the inverter output voltages.

The current tracking errors are defined as follows:

$$\begin{gathered} e_{i_d}\left(t\right)=i_{cv,d}^{*}-i_{cv,d} \\ {e}_{i_q}\left(t\right)=i_{cv,q}^{*}-i_{cv,q} \end{gathered}$$

(9)

These are fed into separate PI controllers.

For d-axis

$$v_{cv,d}^{*}(t)=K_{p_{i}i}{e}_{i_d}(t)+K_{i\_i}\int e_{i_d}(\tau )d\tau +v_{d_{-}ff}$$

(10)

For q-axis

$$v_{cv,q}^{*}(t)=K_{p_{-}i}{e}_{i_q}(t)+K_{i\_i}\int e_{i_q}(\tau )d\tau +v_{q_{-}ff}$$

(11)

where

• $K_{p\_i} K_{i\_i}$ are the Pl gains for current control;
• $v_{d_{-}ff}=\omega L_f{i}_{cv,q}$ and $v_{q_{-}ff}=-\omega L_f{i}_{cv,d}$ are feedforward decoupling terms to compensate for the $dq$ cross-coupling.

The control structure provides exact voltage regulation and effective harmonic isolation, which allows the inverter to produce high-quality 50 Hz sinusoidal output despite upstream disturbances and ensures stable operation of residential loads in the proposed LVDC back-to-back system.

2.3. Control Strategy for DVR with Multi-Frequency Injection

Figure 1 presents the structure employed in the DVR for multi-frequency voltage injection at the PCC [36]. The primary objective of the voltage loop is to maintain the load-side voltage at a predefined reference composed of the fundamental, 5th, and 7th harmonic components. The instantaneous voltage error is formulated as follows:

$$e_v\left(t\right)=V_{ref,\alpha \beta }-V_{pcc,\alpha \beta }$$

(12)

where $V_{ref,\alpha \beta }$ is the desired voltage reference, including the 50 Hz fundamental and selected harmonic contents, and $V_{pcc,\alpha \beta }$ is the measured PCC voltage.

This error is regulated by a multi-resonant proportional-resonant (PR) controller, which provides high gain at the targeted frequencies while maintaining stability across the operating range. The voltage controller transfer function is defined as follows:

$$G_{PR,v}(s)=k_{pv}+\sum _{n\in \{\mathrm{1,5},7\}} {\displaystyle \frac{2k_{rv,n}s}{s^2+{\omega }_n^2}}$$

(13)

where

• $k_{pv}$ is the proportional gain for the voltage loop;
• $k_{rv,n}$ are the resonant gains at the respective harmonic frequencies ${\omega }_n$ (fundamental ${\omega }_1$, 5th ${\omega }_5$, and 7th ${\omega }_7$).

The controller output generates the reference current signal for the current regulation stage:

$$i_{cv,\alpha \beta }^{ref}=G_{PR,v}(s)\cdot e_{v,\alpha \beta }$$

(14)

This ensures that the injected DVR voltage compensates for disturbances at the targeted frequencies, maintaining voltage quality at the PCC. The current control loop ensures accurate tracking of the DVR output current according to the reference generated by the voltage controller. The current error is defined as follows:

$$e_{i,\alpha \beta }=i_{cv,\alpha \beta }^{ref}-i_{cv,\alpha \beta }$$

(15)

where $i_{cv,\alpha \beta }$ is the measured converter output current.

A dedicated multi-resonant PR controller is employed in the current loop to enforce accurate current tracking across the fundamental, 5th, and 7th harmonic frequencies [36]. The current controller transfer function is expressed as follows:

$$G_{PR,i}(s)=k_{pc}+\sum _{n\in \{\mathrm{1,5},7\}} {\displaystyle \frac{2k_{rc,n}s}{s^2+{\omega }_n^2}}$$

(16)

where

• $k_{pc}$ is the proportional gain for the current loop;
• $k_{rc,n}$ are the resonant gains for the selected harmonic frequencies.

The output of the current controller defines the inverter voltage reference:

$$v_{cv,\alpha \beta }^{ref}=G_{PR,i}(s)\cdot e_{i,\alpha \beta }$$

(17)

which is then used for PWM generation to control the inverter switching states.

The control strategy provides precise voltage tracking and selective harmonic injection at the point of common coupling to synthesize the desired multi-frequency voltage profile while maintaining system stability and improving power transfer flexibility across harmonic channels.

2.4. System and Control Strategy with Energy Storage

The system configuration with DC-Link storage integration is shown in Figure 3. The three-phase grid-connected converter remains unchanged from the previous configuration and retains full control over regulating the DC-link voltage by managing the fundamental power exchange. The added components in this setup include (1) a single-phase residential inverter that delivers a clean 50 Hz voltage to the load and (2) a DC–DC buck-boost converter connected to a battery-based storage unit. The reason for choosing a single-phase inverter is that the number of analog inputs needed by the controller algorithm would have exceeded the number of inputs in the hardware in the laboratory if a three-phase inverter had been used. The storage system is not responsible for DC-link voltage regulation but dynamically supports or consumes power based on system conditions, enabling energy balancing and improving flexibility under varying load or injection scenarios.

3. Simulation Results

MATLAB/Simulink R2023b runs time-domain simulations to validate the proposed system. The model contains two operational modes, which include direct supply of a three-phase residential load without storage and supply of a single-phase consumer through an integrated storage system for power management. The grid-side converter generates three voltage signals that include a 50 Hz fundamental at 120 V RMS and a 5th harmonic (negative sequence) at 50 V RMS, and a 7th harmonic (positive sequence) at 25 V RMS. The first operational mode delivers 100 V RMS per phase to a balanced three-phase load, which starts at 1 kW before increasing to 1.5 kW for dynamic testing. The second operational mode uses a single-phase inverter to supply power to a 70 V RMS, 650 W load, while a bidirectional buck-boost converter connects to a battery system that can discharge at 3 A and charge at 2 A. The three-phase grid-connected converter controls DC-link voltage regulation, while the storage system provides power support for system flexibility and energy equilibrium.

The system uses the electrical parameters that are listed in

Table 1. System parameters.

Component	Symbol	Value
Grid voltage	$V_{\mathrm{grid} }$	$100 \mathrm{V},50 \mathrm{H}\mathrm{z}$
Switching frequency	$f_{sw}$	20 kHz
DC-link voltage reference	$U_{\mathrm{dcref} }$	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	$R_f$	$22 \mathrm{m}\Omega$
Line resistance	$R_{\mathrm{line} }$	$0.36 \Omega /\mathrm{k}\mathrm{m}$

. The system parameters include inverter-side output filter components, DC-link voltage and capacitance, battery emulator specifications, and realistic line impedances. The inductance L used in the feedforward voltage term of the implemented control scheme refers to the inverter-side filter inductance and does not include the line inductance. The same parameter set was used in both the simulation studies and the laboratory experimental validation to ensure consistency and credibility of the results.

3.1. 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 5th and 7th harmonic components under normal and increased load conditions is summarized in

Table 2. Power distribution and efficiency under different load conditions.

Condition	Power (W)					Efficiency (%)
	Grid	Load	Fundamental	5th Harmonic	7th Harmonic
Normal Load (1 kW)	1015	999.2	685.1	185.4	144.1	98.44
Load Increase (1.5 kW)	1513	1499	1002.1	277.9	233.7	99.07

, which shows the system’s high efficiency and effective harmonic-based power transfer.

Figure 6 presents the total sent power, received load power, and the contributions from the fundamental, 5th, and 7th 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 5th and 7th 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, 5th, and 7th 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.

The power transfer efficiency during the increased load condition reached approximately 99.07%, calculated from a total sent power of 1513 W and a received load power of 1499 W. The system maintains excellent efficiency at the higher transfer level, validating the capability of multi-frequency power boosting without compromising performance. The DC bus voltage measurement in Figure 7 shows a load increase at t = 1.2 s, resulting in a transient voltage dip. The voltage drops from its nominal value of approximately 400 V to a minimum of around 375 V, then begins to recover. The system successfully stabilizes the DC voltage within approximately 300 ms (by t ≈ 1.5 s), demonstrating fast and reliable dynamic response. This confirms robust system performance under load transients and harmonic-rich grid conditions, with effective DC-link voltage regulation throughout the event.

The step increase in power demand results in the grid voltage and current waveforms, which are displayed in Figure 8. The voltage waveform shows no change in amplitude or shape while maintaining its harmonic content and staying within peak limits. The grid current shows an increase in magnitude after the load change because the system starts transmitting more power. The proposed method demonstrates an essential benefit because it allows power transfer increases through current amplification without changing the voltage envelope structure or exceeding peak constraints. The system operates safely through changing loads because voltage-sensitive components remain within safe limits.

The inverter load voltage and current responses to the load increase are depicted in Figure 9. The voltage remains sinusoidal and stable, which means that the inverter maintains a clean 50 Hz output. The current increases smoothly in response to the higher load, which confirms that the system delivers more power without affecting voltage quality or waveform shape.

According to the simulation results, the proposed LVDC-link control system transfers the total power from the multi-frequency grid to the load as standard signals. This proves that this device can precisely play the role of the frequency changers when connecting the multi-frequency systems to the loads that are not addressed so far in the multi-frequency power transfer system research topic.

3.2. Storage-Supported Mode

Figure 10 shows the dynamic power profiles of the fundamental, 5th harmonic, 7th harmonic, house-load inverter (HLI), and battery power over time under the storage-supported mode. The battery starts discharging (magenta line rises to around +300 W) at the beginning (t = 0.8 s) to help supply the load while the fundamental (cyan) and harmonic components (orange for 5th and blue for 7th) initially remain low. The HLI power (green line) remains nearly constant around 650 W, indicating stable delivery to the single-phase load.

Between t = 1.6 s and 1.7 s, the system undergoes a mode transition: the battery switches to charging mode (the magenta line drops to around −500 W), and the power contribution from the grid (fundamental and harmonic components) increases sharply to take over the full load and supply additional power to charge the battery. This dynamic demonstrates how the harmonic-based power transfer adjusts to maintain system balance without affecting the load. The HLI power remains unaffected throughout the transitions, confirming that the DC-link isolation and inverter regulation maintain pure sinusoidal power at the load end. The system effectively demonstrates flexible energy sharing between the harmonics, the fundamental component, and the battery unit.

The DC-link voltage stays close to constant at 400 V throughout the simulation period, including load transients, according to Figure 11.

Figure 12 shows the voltage and current waveforms at the single-phase HLI output. The top subplot shows the HLI voltage, while the bottom subplot shows the corresponding load current. Both signals are perfectly sinusoidal at 50 Hz, which means that the inverter is delivering clean fundamental frequency power to the load. The absence of visible harmonic distortion confirms that the DC-link and inverter stages are effective in isolating the load from any grid-side harmonic components, thus ensuring high power quality.

Figure 13 shows the grid voltage and current waveforms when the 5th and 7th harmonics are injected during battery charge and discharge transitions. The upper plot shows the three-phase grid voltages, which are visibly distorted due to the injected harmonics, combining the 50 Hz fundamental with the 5th and 7th harmonics. The lower plot shows the corresponding grid currents, which also reflect harmonic content and dynamic behavior associated with the transition between charging and discharging modes. These current waveforms demonstrate the system’s ability to manage harmonic-rich conditions while adjusting power exchange with the battery.

Figure 10, Figure 11, Figure 12 and Figure 13 show that the storage-integrated mode is able to support the DC-link during load transitions and maintain stable voltage and a clean 50 Hz supply to the HLI. The system effectively isolates the load from the injected 5th and 7th harmonics on the grid side and demonstrates robust harmonic decoupling and energy support from the battery.

4. Hardware and Implementation Results

The experimental validation of the grid-connected mode was performed using Imperix modular power converters from Imperix, Sion, Switzerland, with two independent 3-leg modules configured for grid-side and load-side operations, as shown in Figure 14. An Imperix pre-charge unit was used to safely energize the DC-link capacitors during startup. Real-time voltage and current measurements were acquired through Imperix measurement units and a DEWE PA7 analyzer from Dewetron, Grambach, Austria, to monitor the system’s operation. A programmable residential inverter emulated the customer-side load, ensuring complete isolation from the grid-side harmonics.

Figure 15 presents the laboratory measurements for the system operating under fundamental frequency (50 $\mathrm{H}\mathrm{z})$ conditions. The top left graph shows the three-phase grid voltages $U_{g,a}{U}_{g,b}$, and $U_{g,c}$, highlighting a typical balanced three-phase waveform. The middle-left graph illustrates the HLI side voltages $U_{L,a^{\prime }}{U}_{L,b}$, and $U_{L,c^{\prime }}$ where clean 50 Hz voltage signals are maintained through the DC-link isolation. The bottom left graph compares the phase-a currents, showing the grid current $I_{g,a}$ (red) and the HLI current $I_{L,a}$ (blue), demonstrating effective current transfer between the two sides.

On the top right, the frequency spectrum analysis shows a sharp dominant peak at 50 Hz for all measured quantities, with negligible harmonic content at 250 Hz (5th harmonic) and 350 Hz (7th harmonic), confirming the absence of multi-frequency injection in this mode. The table below the spectrum quantifies the RMS values of voltages and currents for both the grid and HLI sides. The middle right section reports the active power measurements, where the total and fundamental active powers at the grid side ($P_{t,g}{P}_{\mathrm{fund},g}$) and load side ($P_{t,L},P_{\mathrm{fund},L}$) are nearly identical, confirming minimal losses and efficient power transfer. Finally, the bottom right plot depicts the DC-link voltage $U_{dc}$, regulated around 376 V, ensuring stable energy exchange across the system.

The results presented in Figure 16 reveal the system response to a 5th harmonic voltage component (negative sequence, 250 Hz) applied to the grid. The grid voltages show clear signs of distortion because the injected harmonic exists, while the House Load-Inverter (HLI) voltages stay purely sinusoidal at 50 Hz, which proves the low-voltage DC-link provides effective isolation. The grid current waveforms show visible distortion because of the harmonic injection, yet the HLI load currents remain clean, sinusoidal shapes. The spectral analysis shows that the grid voltages and currents contain a substantial 5th harmonic component, yet the HLI side shows no harmonic presence. The total active power on the grid side reaches 735 W, but the fundamental active power decreases to 687 W because of the injected distortion. The HLI side demonstrates no power difference between total and fundamental measurements because the customer receives power without distortion. The DC-link voltage operates at a stable 375 V level, which provides reliable operation and complete electrical isolation between the distorted grid and customer load.

The experimental results presented in Figure 17 show the effects of injecting both the 5th harmonic (negative sequence, 250 Hz) and 7th harmonic (positive sequence, 350 Hz) voltage components into the grid. The grid voltages become more severely distorted compared to the case of only 5th harmonic injection, confirming the simultaneous presence of two harmonic orders. The House Load-Inverter (HLI) voltages remain clean and purely sinusoidal at 50 Hz, demonstrating continued effective isolation through the low-voltage DC-link. The grid current shows greater distortion, while the HLI load currents stay unaffected. The harmonic spectrum reveals prominent peaks at both 250 Hz and 350 Hz for the grid-side measurements, while the HLI side remains free of harmonic content. The total active power on the grid side is about 738 W, but the fundamental active power drops significantly to around 566 W due to the added harmonic distortion, whereas the HLI side maintains stable power values with negligible difference between total and fundamental powers. The DC-link voltage is consistently regulated around 376 V, ensuring reliable and isolated operation under severe harmonic grid conditions.

The proposed system introduces a new architecture that enables controlled multi-frequency power transfer through a low-voltage DC back-to-back converter interface while conventional LVDC or hybrid AC/DC systems operate at the fundamental frequency only. The system actively controls harmonic components, including the 5th and 7th harmonics together with the fundamental frequency, to enable parallel power channels without exceeding peak voltage limits. The system improves line utilization while maintaining high power quality on the load side through DC-link isolation and grid-forming inverter operation. The dual-mode capability, which combines grid-connected and battery-supported operations, has been experimentally validated under dynamic load conditions to demonstrate both technical feasibility and practical robustness. This paper presents the first experimental proof of a multi-frequency three-phase LVDC system that uses decoupled harmonic power routing and delivers clean-load voltage.

The simulation results, together with experimental data, show that the proposed system enables controlled multi-frequency power transfer and maintains strict load-side power quality. The LVDC link architecture proved successful in isolating harmonic-rich grid voltages from sensitive customer loads because it produced a clean 50 Hz output throughout both steady-state and dynamic operating conditions. The DVR-based harmonic injection strategy with multi-resonant controllers achieved exact synthesis of 5th and 7th harmonic voltages, which allowed improved line utilization without reaching peak voltage boundaries. The system maintained strong operation during mode changes and load variations, which confirmed the effectiveness of the control system design and the practicality of using DC-link isolation for multi-frequency energy transfer.

The proposed system uses 5th (negative-sequence) and 7th (positive-sequence) harmonics together with the fundamental component to create parallel power channels without raising peak voltage levels. The selected harmonics function as orthogonal components to both the fundamental frequency and each other in sequence terms. The independent control of each frequency component becomes possible through dedicated resonant controllers because they prevent mutual interference during power transfer. The control structure includes dedicated resonant controllers that maintain system stability for each harmonic. The harmonic voltages injected into the system maintain the peak amplitudes to ensure compatibility with grid-side equipment insulation levels. However, the harmonic content will be greater than the levels set by grid codes and standards (e.g., EN50160). Therefore, in these multi-frequency systems, we propose an LVDC back-to-back converter interface that decouples the load from the grid. Thus, the load will be isolated from the harmonics, and a standard-compliant voltage will be ensured for the loads. The DC-link operates as a frequency-selective barrier, which enables the load-side inverter to produce a clean 50 Hz output that protects end-user loads from harmonic effects. And a series voltage generator, such as a DVR, can be utilized to add the harmonics for use in multi-frequency systems [2,36,37]. The simulation results, together with laboratory data, show that harmonic injection maintains voltage stability and load quality throughout all dynamic scenarios, including load changes and mode transitions.

The proposed LVDC back-to-back system architecture includes modular design features that enable future scalability for connecting higher-capacity loads and additional distributed energy resources (DERs), including photovoltaic (PV) arrays and battery storage systems, and electric vehicle charging units. System expansion can be achieved through converter parallel operation or by upgrading existing power stage capacities while preserving the established control strategy and multi-frequency coordination.

The system uses industrial components that are widely available, including standard three-phase inverters together with LC filters and digital control platforms. The control software manages harmonic injection and separation operations without requiring special hardware components, thus minimizing both capital costs and system flexibility.

A comprehensive economic evaluation exceeds the current study boundaries, yet preliminary assessments indicate that the power routing complexity from harmonic-based control methods provides multiple operational advantages. The system achieves better power transfer efficiency through harmonic channels without raising peak voltage levels and optimizes line capacity utilization, and delivers high-quality 50 Hz voltage to loads. The system operates in dual mode to enable peak load reduction and self-consumption optimization, which leads to long-term operational cost savings.

The proposed system presents beneficial features for real-world implementation in smart distribution systems and flexible microgrids because it offers modularity and high-power quality together with efficient infrastructure utilization.

5. Conclusions

The research introduced and experimentally validated a 3-phase 3-wire LVDC back-to-back converter architecture for use in multi-frequency power systems. The system allows the grid-side converter to receive fundamental, 5th (negative sequence), and 7th (positive sequence) harmonic voltages for power transfer enhancement, while the load receives only a clean 50 Hz sinusoidal voltage from the DC-link and inverter. The system operated in two modes, which included a configuration without energy storage and a configuration with a battery unit connected at the DC-link for bidirectional power flow. The laboratory tests showed that the system provided stable voltage together with clean waveforms at the load and maintained high efficiency across steady and dynamic operating conditions. The LVDC-link successfully isolated the multi-frequency grid side from the sensitive household load side while transferring the total multi-frequency power to the load side. The proposed device confirms the system’s capability to be connected as an interface between multi-frequency networks and standard 50 Hz applications.

The experimental and simulation results confirmed the core functionalities while demonstrating multiple essential outcomes, which demonstrate the practical value and technical novelty of the proposed architecture:

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The 5th and 7th harmonic components functioned as active power transfer channels on the grid side without reaching the load, which improved line utilization while preserving high power quality.

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The LVDC link functioned as a strong frequency-selective barrier that maintained complete harmonic decoupling throughout all dynamic mode transitions.

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The system works on increasing total power transfer through voltage harmonic injection while peak voltage stays within limits, thus maximizing existing infrastructure potential.

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The load-side inverter produced pure 50 Hz sinusoidal voltage throughout all operating conditions to fulfill the strict power quality requirements.