Advanced Distributed Control of Parallel Resonant CLLC DAB Converters

Abstract

The integration of hybrid alternating current (AC) and direct current (DC) networks has gained relevance due to the growing demand for more flexible, efficient, and reliable electrical systems. A key aspect of this integration is the parallelization of power converters, which presents several technical challenges, such as current sharing imbalances, circulating currents, and control complexity. This paper proposes a distributed control architecture for parallel resonant CLLC dual active bridge (DAB) converters to address these issues in hybrid AC–DC networks and microgrids. The approach includes a master voltage controller to regulate the output voltage and distributed local current controllers to ensure load balance. The approach minimizes the difference between the output and input voltages, allowing for independent control of power flow. Simulation and experimental results show significant improvements. The system stability has been demonstrated experimentally. Transient response has been improved with response time 80% lower using the feed-forward term. The system maintained stability with current sharing deviations below 3% under full and low load conditions. Finally, scalability is ensured by the proposed distributed controller because the central power controller is not affected by the number of units in parallel used in the application. This solution is suitable for advanced hybrid networks and microgrid applications.

1. Introduction

In recent years, microgrids (MGs) have become increasingly important for improving the efficiency, reliability, and flexibility of electrical power systems. MGs integrate distributed generators, energy storage systems, loads, and control units that can operate independently or connected to the main grid, providing increased stability and resilience in the power supply [1]. The evolution of MGs has led to the development of various topologies, including AC, DC, and hybrid grids, which require advanced control strategies to optimally manage distributed resources [2].

Traditionally, secondary and tertiary control layers in MGs have been implemented using centralized control topologies, where a central controller manages all information and makes operational decisions for the microgrid [3]. However, this centralized approach presents several significant limitations, such as vulnerability to single-point failures and a lack of scalability when integrating new resources or adapting to changes in demand [4]. Furthermore, dependence on a single central unit for decision-making can compromise the robustness and responsiveness of the system to unexpected events [5].

Distributed control has emerged as a promising solution to overcome these limitations. Unlike centralized control, distributed control spreads control responsibility between several autonomous agents, which work cooperatively to achieve global objectives [6]. This approach offers several key advantages, such as increased robustness to failures, since the failure of a single agent does not lead to total system breakdown [7]. Moreover, distributed control improves scalability, allowing the seamless integration of new distributed energy resources (DERs), storage systems, and loads without affecting the overall operation of the microgrid [8].

The integration of hybrid AC-DC electrical grids has gained prominence in recent years due to the growing demand for more flexible, efficient, and reliable electrical systems. A key aspect of this integration is the parallelization of power converters, which poses several technical challenges, such as current sharing imbalances, circulating currents, and the complexity of control [9,10]. These issues can significantly affect the performance and reliability of hybrid networks, leading to inefficiencies and operational risks [11].

Various strategies have been proposed to address these challenges, including advanced control schemes, voltage droop control, and current droop control, as well as real-time communication between converters [12]. Recent trends emphasize the use of digital controllers, predictive algorithms, and artificial intelligence to improve system performance and scalability [13]. However, solutions based on centralized controllers, such as programmable logic controllers (PLCs), suffer from slow transient response and communication delays, which limit overall system stability [14].

The CLLC resonant converter has emerged as a promising solution to parallelize dual active bridge (DAB) converters in hybrid AC–DC networks, particularly in high-power applications [15]. The CLLC converter is known for its ability to operate with high efficiency in bidirectional modes, making it ideal for use in solid-state transformers (SSTs). However, parallel operation of multiple CLLC converters introduces significant technical challenges, such as unequal current sharing between converters at both the input and output stages and the precise control of circulating currents [16].

This paper proposes a novel distributed control strategy that eliminates the need for a global controller and instead relies on a local master controller installed on a single converter to regulate the output voltage. The remaining converters are controlled by distributed current controllers that share the load current equally, and feed-forward control is implemented to improve the system response time during transient events.

The remainder of this paper is organized as follows. Section 2 describes the materials and methods used, addressing the modeling of CLLC DAB resonant converters and the system architecture, and presents the traditional control strategies and the proposed distributed control methodology, including the master voltage controller and the distributed current controllers together with the feed-forward term in control. Section 3 shows the experimental results obtained in test configurations, including positive and negative AC power flow, response to nominal power and voltage variations, and the effect of the feed-forward term in the system. Section 4 discusses the impact of the distributed control strategy compared to traditional centralized systems, highlighting the improvements in terms of response time, stability, and current distribution under various load conditions. Finally, Section 5 concludes the paper by summarizing the main contributions and suggesting directions for future research, such as the integration of artificial intelligence to improve system adaptability.

2. Materials and Methods

2.1. Paper Preparation

During the preparation of this work, GenAI tools have been used to improve the paper. CHATGPT V4 has been used for preparing the reference list during the state of the art compilation and to improve English writing. The authors have reviewed and edited all the results and take full responsibility for the content of the publication.

2.2. Modeling of Resonant CLLC DAB Converters

Figure 1 illustrates the topology of a resonant CLLC DAB converter.

In this figure, $v_p$, $i_p$, $v_s$ and $i_s$ are the input and output voltages and currents, respectively. $L_1$, $C_1$, $L_2$ and $C_2$ are the inductance and capacitance of the primary and secondary resonant tank, respectively. $i_L$ is the primary current that circulates by inductance $L_1$. The voltages $v_1$ and $v_2$ are the alternating voltages of the primary H bridge and the secondary H bridge, respectively. Finally, n is the transform ratio between the primary and secondary.

The power converter can be modeled by a simple equivalent circuit, as depicted in Figure 2. For simplicity, no parasitic effects are considered (such as those that involve switches, inductance, or capacitance). Additionally, the magnetizing inductance is neglected.

In this figure, L represents the equivalent inductance $L=L_1+n^2{L}_2$, and C is the equivalent capacitance $C=C_1+n^2{C}_2$.

Depending on the application, the input voltage $v_p$ or the output voltage $v_s$ can be continuously maintained by a power supply or can be connected to a current source. In this case, a current source connected to the output is considered and the input voltage is constantly maintained.

In terms of the Laplace transformation, this system can be considered as two subsystems, as shown in Figure 3: the resonant tank subsystem and the RC output filter subsystem. In this figure, the variables in capital letters $V_1$, $V_2$, $I_L$, $I_s$ and $I_o$ represent the phasor name of the same lowercase letter defined previously. s is the Laplace symbol.

$V_1$ and $V_2$ are square waveforms shifted at $\varphi$ angle. Using the first-harmonic approximation, the first harmonic of the difference between $V_1$ and $V_2$ can be obtained using the Fourier series. The first harmonic is obtained in Equation (1):

$${(V_1-V_2)}_1={\displaystyle \frac{4{\mathrm{V}}_{\mathrm{s}}nsin\left(\varphi \right)}{\pi }}+{\displaystyle \frac{4cos\left(\varphi \right)\left({\mathrm{V}}_{\mathrm{p}}-{\mathrm{V}}_{\mathrm{s}}n\right)\mathrm{i}}{\pi }}.$$

(1)

In this equation, $V_p$ and $V_s$ are the DC component of the input and output voltage, respectively. i is the imaginary unity complex number. The admittance is obtained as follows:

$$G=-{\displaystyle \frac{C\omega \mathrm{i}}{CL{\omega }^2-1}}.$$

(2)

The current $I_L$ can be obtained by multiplying the admittance by the difference in voltages. The current $I_L$ results are obtained as follows:

$$I_L=G{(V_1-V_2)}_1={\displaystyle \frac{4C{\mathrm{V}}_{\mathrm{s}}nwsin\left(\varphi \right)}{\pi \left(CL{w}^2-1\right)}}-{\displaystyle \frac{4Cwcos\left(\varphi \right)\left({\mathrm{V}}_{\mathrm{p}}-{\mathrm{V}}_{\mathrm{s}}n\right)\mathrm{i}}{\pi \left(CL{w}^2-1\right)}}.$$

(3)

Using this expression, the output current $I_o$ can be obtained by projecting the current $I_L$ into the output voltage per unit $V_2\left(pu\right)$. This $V_2\left(pu\right)$ voltage can be expressed by first harmonic approximation as follows:

$$V_2\left(pu\right)={\displaystyle \frac{2\left(sin\left(\varphi \right)-cos\left(\varphi \right)\mathrm{i}\right)}{\pi }}.$$

(4)

The output current $I_s$ is a function of the phase angle $\varphi$ and can be obtained, as explained above, using the scalar product of $I_L$ by $V_2\left(pu\right)$. The result is as follows:

$$I_s=V_2\left(pu\right)·I_L={\displaystyle \frac{8C{\mathrm{V}}_{\mathrm{p}}\omega sin\left(\varphi \right)}{{\pi }^2\left(CL{\omega }^2-1\right)}}.$$

(5)

This approximate model considers the dynamic decomposition of the fast dynamic and slow one. This can be exploited for the design of distributed cascade controllers so that the dynamics of the current controller can be much faster than that of the output voltage controller.

2.3. System Architecture and CLLC Resonant Converters

The proposed system focuses on the parallelization of CLLC resonant converters within hybrid AC–DC microgrids. Figure 4 shows a photo of the power converter as a modular system which has been used for our experiments. The parallel connection of these modules is represented in Figure 5. These converters are essential in solid-state transformers (SSTs), which enable bidirectional power transfer with high efficiency. A key advantage of CLLC converters is their ability to operate in high-frequency transformer configurations, which are typically used in modular power systems with power ratings of around 25 kW per module. To achieve higher power levels, multiple converters need to be operated in parallel at the output stage.

2.4. Traditional Control Strategies

Traditional control strategies for parallel converters in SSTs typically rely on droop control, either based on voltage or current. In voltage droop control, the output voltage is adjusted based on load changes, while current droop control adjusts the current supplied by each converter depending on the system’s load demand. However, these approaches face several challenges when applied to large-scale, modular systems. In parallel systems, droop control can lead to unequal current sharing between converters, resulting in circulating currents and efficiency losses. Systems controlled via global controllers (e.g., PLC-based systems) often exhibit slow response times due to communication delays, especially during fast load changes.

Hybrid control schemes that combine voltage and current droop strategies have been proposed to mitigate these issues but continue to suffer from transient instability and require complex coordination across multiple units.

2.5. Proposed Control Methodology

To overcome the limitations of traditional control methods, this paper introduces a distributed control strategy that eliminates the need for a global controller and instead leverages local control at the converter level. The overall structure of this approach is illustrated in Figure 6, showing the simplified model of the resonant CLLC DAB converter with constant input and a resistive load.

2.5.1. Master Voltage Controller

As depicted in Figure 6, a master voltage PI controller is installed on one of the converters in the system. This controller is responsible for regulating the output voltage of the entire system, ensuring that the output voltage remains stable despite changes in load demand or fluctuations in input power. By localizing this control function to a single converter, the system avoids communication delays commonly associated with global controllers. This control strategy allows the system to emulate the behavior of an ideal transformer, where the voltage at the output can be dynamically adjusted to meet load requirements, regardless of the direction of power flow.

The master voltage controller operates by adjusting the output voltage reference for the system, allowing real-time regulation without relying on external communication links.

2.5.2. Distributed Current Controllers

Each remaining converter operates under a current PI control strategy (see Figure 6). The total load current is evenly distributed among the parallel converters, with each current controller regulating its assigned portion. This strategy ensures balanced current sharing and minimizes circulating currents, which are common in parallel converter systems.

The total load current is calculated by the system and divided equally between the active converters. Each converter is equipped with its own current PI controller, which adjusts its output current to match the reference value determined by the system. This distributed approach ensures that the converter is not overloaded and minimizes the risk of current imbalances.

As illustrated in Figure 6, the current controllers calculate their reference values by equally dividing the total $i_{total}$ load current among the active converters m, allowing dynamic load sharing without the need for extensive communication between units.

2.5.3. Converter Characteristics

The CLLC resonant converter used in this study operates with the following nominal design parameters.

Table 1. Nominal electrical specifications of the converter.

Parameter	Nominal Value
Input bus voltage ($V_{\mathrm{s}}$)	550 V
Output bus voltage ($V_{\mathrm{p}}$)	554 V
Input current ($I_{\mathrm{s}}$)	45 A
Output current ($I_{\mathrm{p}}$)	45 A
Output power ($P_{\mathrm{out}}$)	25 kW
Switching frequency ($f_{\mathrm{sw}}$)	80 kHz
Transformer turn ratio (n)	$n={\displaystyle \frac{N_{\mathrm{prim}}}{N_{\sec }}}=1.007$

lists the nominal electrical specifications of the converter, and

Table 2. Nominal PI controller parameters.

Controller	${\mathit{K}}_{\mathit{p}}$	${\mathit{K}}_{\mathit{i}}$
Master Voltage Controller	1.2	5.7 × 10−6
Distributed Current Controller	2.4	4 × 10−4

provides the parameters of PI controllers.

These nominal parameters were carefully selected to ensure stable and efficient system operation under the experimental and simulation conditions described in this work.

The oscillation method, also known as the Ziegler–Nichols method, was used to adjust PI controllers for voltage and current regulation in CLLC converters through phase-shift control between primary and secondary bridges, with a fixed duty cycle of 50% on both sides. Resonant converters operate near their natural frequency, where the dynamics tend to be oscillatory, allowing for the direct application of the oscillation method to identify critical stability parameters. In this method, the proportional gain $K_p$ is gradually increased until the system reaches the critical gain $K_c$ and exhibits sustained oscillations with a well-defined oscillation period $P_c$. The proportional gain is set as $K_p=K_c$, and the integral constant $K_i$ is calculated as

$$K_i={\displaystyle \frac{K_p}{T_i}},\mathrm{where}{T}_i=\alpha P_c,$$

and $\alpha$ is a chosen fraction of $P_c$. The procedure is applied sequentially: first, the voltage PI controller is tuned to regulate the output voltage, followed by the current PI controller, ensuring that the conditions set in the voltage loop are maintained. This approach provides an intuitive, yet robust, tuning process, improving system stability and dynamic performance by enabling precise regulation of voltage and current. The method’s effectiveness lies in its ability to optimize controller parameters without requiring complex mathematical models, enhancing the efficiency and control accuracy of the CLLC converter operating near its resonant frequency.

2.5.4. Feed-Forward Term in the Control Strategy

To further improve the transient response and enhance system stability, the proposed method incorporates feed-forward control into the current regulation scheme. Feed-forward control allows for faster responses to changes in load conditions by anticipating disturbances and adjusting the current output accordingly. This approach significantly reduces the reaction time of the system and prevents overshooting or instability during transient events.

By placing both voltage and current control functionalities locally within each converter, the system eliminates communication delays inherent in centralized control systems, making it more responsive to real-time changes in power demand and improving overall stability.

The feed-forward term in Equation (6) can be obtained by taking the inverse of Equation (5).

$${\varphi }_{\mathrm{ff}}=arcsin\left({\displaystyle \frac{{\pi }^2\left(CL{\omega }^2-1\right)I_{total}}{8C{\mathrm{V}}_{\mathrm{p}}\omega m}}\right).$$

(6)

In Equation (6), m is the number of converters in parallel, and $I_{total}$ is the total current that is measured by each converter.

2.6. Algorithm for Voltage and Current Regulation

The core of the proposed control strategy is a novel algorithm designed to manage both voltage regulation and current sharing. The algorithm is implemented across all converters, but its operation is divided between the master voltage controller and the individual current controllers.

2.6.1. Voltage Regulation Algorithm

The voltage regulation algorithm used by the master controller is based on continuous monitoring of input and output voltages. The difference between the output voltage and the input voltage, multiplied by the transformer ratio, is calculated in real-time. The controller then adjusts the output voltage to minimize this difference, ensuring that the system behaves as a transformer that can operate independently of the power flow direction.

2.6.2. Current Sharing Algorithm

The current sharing algorithm, implemented by the distributed current controllers, calculates the total load current and divides it evenly among the converters. The algorithm monitors the output current of each converter, comparing it with the reference current calculated from the total load. If discrepancies are detected, the current controller adjusts the output to ensure balanced sharing.

The inclusion of feedforward control in the current PI controller enhances this process by allowing the controllers to adjust the output pre-emptively when load changes are detected. This prevents sudden changes in the current distribution and ensures that the system remains stable under dynamic conditions.

3. Experimental Results

3.1. Experimental Setup

The experimental setup was designed to evaluate the performance of the proposed distributed control system for parallelized CLLC resonant converters within a hybrid AC–DC system. The test system included a combination of DC–DC converters, DC–AC converters, and a DC microgrid for load simulation and power distribution.

To ensure consistent operation and accurate evaluation, the parameters specified in Table 1 were applied during all experiments. These nominal values were carefully selected to match the requirements of the modular CLLC converters used in the tests.

The configuration is described as follows:

• A DC input bus was connected to a DC–AC converter. This converter allowed the DC bus to connect to the AC electrical grid, enabling bidirectional power flow and grid-tied operation.
• Multiple CLLC resonant DC–DC converters were connected in parallel. The converters shared the load current evenly and the proposed distributed control strategy was applied to regulate the sharing of voltage and current among these converters.
• The output of the DC–DC converters was connected to a DC microgrid, which represented the load of the system. This microgrid operated autonomously and was used to test the system’s performance under varying load conditions.
• The DC microgrid was stabilized using a battery storage system. The battery served as a voltage regulator for the microgrid, ensuring stable operation and preventing large voltage fluctuations under dynamic load conditions. The battery controlled the microgrid voltage, allowing smooth power flow and load balance.

This configuration was used to evaluate the voltage regulation, current sharing, and transient response of the proposed control strategy, focusing on the following key performance metrics:

• System stability during normal and dynamic load conditions.
• Transient response time to sudden changes in load.
• Performance of current sharing between parallel DC–DC converters.

3.2. Test 1: Positive AC Power Flow

In the first test, we assign a series of positive AC power references to the DC-AC converter to simulate an increase in power demand. Several increments were applied, and the system response was recorded. The following results were obtained:

• Figure 7: Graph of the individual currents of each converter when the power reference is positive, showing the percentage of current distributed between the three converters. The graph confirms that the current sharing between the converters is well balanced at different power levels.
• Figure 8: Oscilloscope capture of the total current flowing through the DC output bus. This image highlights the stability of the total current during load increments.

The results indicate that under positive AC power flow, the system maintained balanced current sharing among the three converters, with minor deviations remaining within acceptable limits. For positive current flow, the system maintained deviations less than 3% at full load and low load. During transient events, the deviations were slightly larger but remained below 8.15%.

3.3. Test 2: Negative AC Power Flow

In the second test, the DC–AC converter was assigned negative AC power references, simulating sending power back to the grid. Again, multiple power increments were applied, and the system response was recorded. The following results were obtained:

• Figure 9: Plot of the individual currents of each converter when the power reference is negative, showing the percentage of current distributed among the three converters.
• Figure 10: Oscilloscope capture of the total current flowing through the DC output bus, highlighting the stability of the total current during power surges with negative power flow.

For negative AC power flow, the results showed a similar balanced current sharing between the converters, confirming the system’s ability to effectively handle bidirectional power flow. For negative current flow, deviations were kept below 1% at full and low load and below 9.75% during transient events.

Summarizing the results, both tests performed with positive and negative power references confirmed the correct operation of the distributed control system for the parallelized CLLC converters. The key observations from the experiments are as follows:

• The current sharing between the converters remained within acceptable limits, with minimal deviations under all load conditions.
• The system maintained a stable power flow through the DC bus during both positive and negative power operations.
• The system responded smoothly to incremental changes in power demand, with stable voltage regulation and minimal fluctuations in current sharing.

The data from both tests are summarized in the consolidated

Table 3. Optimal and sub-optimal energy flow testing results.

Test	Current (A) Conv 1	Current (A) Conv 2	Current (A) Conv 3	Total Current (A)	% Share Conv 1	% Share Conv 2	% Share Conv 3	Max Difference (%)
1	5.94	5.76	5.96	17.66	33.64	32.62	33.75	1.13
1	11.01	10.64	11.56	33.21	33.15	32.04	34.81	2.77
1	3.67	3.54	4.41	11.62	31.58	30.46	37.95	7.49
1	3.64	3.42	4.35	11.41	31.90	29.97	38.12	8.15
2	−3.86	−3.95	−3.90	−11.71	32.96	33.73	33.30	0.77
2	−10.23	−10.15	−9.93	−30.31	33.75	33.49	32.76	0.99
2	−3.90	−4.02	−3.45	−11.37	34.30	35.36	30.34	5.01
2	−9.39	−6.97	−8.46	−24.82	37.83	28.08	34.09	9.75

, which shows the optimal and suboptimal results of each test in terms of the maximum difference between the percentages of sharing.

3.4. Test 3: System Response to Bidirectional Nominal Power Steps

This test scenario describes a step response test to evaluate the performance of the system’s power regulation. Applying a power step from −24 kW to +24 kW (a jump of 48 kW) tests the system’s ability to manage a rapid change in power demand. This shift corresponds to a current change of 87 A, challenging both the current control loop and the voltage stability mechanisms across converters and buses.

The test setup allows us to observe the following key response characteristics.

Current Response on the Internal Bus: Monitoring the total current through the internal bus provides insight into the dynamic response of the system. Specifically, observing the current rise, peak, and any oscillations or settling times helps assess whether the current control loop is appropriately tuned.

Voltage Stability Across Converter Buses: Monitoring the voltage across buses on either side of the converters reveals how effectively the converters manage energy during power transients. Stability in controlled voltage (Vs) is observed, with maximum deviations of 3 V, indicating an effective response of the system. Voltage spikes, drops, or prolonged settling times would signal the need to adjust converter control parameters or enhance energy storage/buffer capacity.

In this context, Figure 11 typically illustrates these dynamics, showing the following:

Rapid response of the total current in the internal bus, highlighting the overshoot and settling time following the power step. Voltage trends on both sides of the converters to verify that they remain within safe operating limits and promptly return to steady-state values after the step change, with controlled voltage (Vs) deviations remaining within 3 V. These data support diagnostics on the system’s robustness in handling significant power variations, ensuring stability and reliability under diverse operating conditions.

3.5. Test 4: System Response to Voltage Variations with and Without Power Reference

This test is designed to evaluate how the system responds to external bus voltage variations, both under load and nonload conditions. Four scenarios have been simulated, with changes in the external bus voltage of 20 V, both increases and decreases, and the behavior of the current control has been evaluated in two situations: with a power reference of 10 kW and without a power reference (0 W). The main objective has been to analyze the speed and stability of the system response under different conditions.

• Figure 12: Voltage rise from 543 V to 563 V without power reference (0 W). In this scenario, the system was subjected to an increase in the voltage on the external bus, from 543 V to 563 V, without applying any power reference. This first scenario evaluated how the current control performs when the system operates with no load and only focuses on stabilizing the internal voltage. Here, the speed with which the system balances the voltages, as well as the stability during the transition, were the main points to be analyzed.
• Figure 13: The voltage rises from 543 to 563 V with a power reference (10 kW). In this second scenario, the same 20 V voltage rise was repeated on the external bus, but this time, a power reference of 10 kW was maintained. The test allowed us to observe how the current control adjusts power sharing and current management in parallel connected converters under active load conditions. The interaction between voltage stabilization and power maintenance was key in this analysis.
• Figure 14: Voltage drop from 563 V to 543 V without power reference (0 W). In the third scenario, a 20 V voltage drop from 563 V to 543 V was simulated without a power reference (0 W). This scenario was designed to test how the system restores the voltage balance when the grid experiences a drop without the system operating under load. The speed of the reaction and the absence of oscillations in the internal bus are indicators of the efficiency of the control.
• Figure 15: Voltage drop from 563 V to 543 V with power reference (10 kW). Finally, in the fourth scenario, the 20 V voltage drop was repeated while keeping the power reference at 10 kW. This scenario tested the ability of the current control to simultaneously manage voltage stabilization and power sharing between the converters, keeping the load active without interruptions or significant fluctuations.

In the four scenarios evaluated, the system showed robust and stable behavior, responding quickly to external bus voltage changes, both during 20 V rises and falls. In all cases, the current control acted efficiently to stabilize the internal bus and ensure a smooth transition without significant fluctuations. The current distribution between the converters was balanced, which allowed system stability to be maintained throughout the voltage variations, ensuring continuous and reliable operation.

3.6. Test 5: Evaluating the Effect of Feed-Forward on System Control

In this test, the aim is to evaluate the influence of the feed-forward term in the control system in order to determine whether its incorporation improves its performance. To this end, a comparison will be made between the results obtained when carrying out the test with and without the feed-forward term, which will allow the reaction times of the control to be analyzed in each case, as shown in Figure 16 and Figure 17.

A current step has been applied, increasing from 4 A to 14 A, to observe the effect of this term on the dynamics of the system. This configuration will make it possible to evaluate the effectiveness of the feed-forward and its capacity to improve the response of the control to changes in the current.

The results show that the inclusion of the feed-forward term allows a significantly faster system response. Without feed-forward, the time to reach the reference was 0.222 s, while with feed-forward, the reaction time was reduced to 0.046 s. This difference highlights the effectiveness of feed-forward in improving control behavior to changes in current.

4. Discussion

The experimental results presented in the previous section validate the effectiveness of the proposed distributed control strategy for parallelized CLLC resonant converters. In this section, we discuss the significance of these results, the advantages of the proposed system over traditional control systems, and the potential impact of implementing external PLC-based control. Key performance metrics, such as response time, stability, and current sharing, are also addressed.

4.1. Improved Response Time and Stability

One of the most significant advantages of the proposed distributed control system is the fast response time and improved stability observed during both positive and negative power flow tests. The system was able to respond to dynamic load changes within 20 ms, significantly reducing transient time compared to traditional centralized control approaches, where communication delays often result in response times exceeding 150 ms.

The fast response time is largely due to the integration of local controllers within each converter, allowing real-time adjustments to current and voltage without relying on a central control unit. In contrast, a PLC-based system, where control decisions are made externally, would introduce communication delays that slow the system’s reaction to load changes. This delay can lead to instability during transient events, particularly when handling sudden changes in the direction of the load or power flow.

In the proposed system, the inclusion of feed-forward control further enhances the dynamic response by allowing the current controllers to anticipate disturbances and adjust their outputs pre-emptively. This proactive adjustment improves system stability during transitions, ensuring smooth operation even under challenging conditions, such as rapid load fluctuations.

4.2. Current Sharing and Load Balancing

Experimental results also confirmed that the system maintained a balanced current sharing between all converters in parallel, with deviations of less than 0.8% during negative current flow at full load and low load conditions. In transient events, deviations remained below 9.75% for all converters. For positive current flow, the system showed slightly larger deviations, with a deviation of 3% at both full and low load and deviations of up to 8.15% during transient conditions. These deviations, although somewhat larger than those of the negative current flow, remained within acceptable limits for safe and efficient operation.

The precise current-sharing performance of the system is a result of the distributed current control implemented within each converter. This distributed control allowed the system to divide the total load current equally among the converters without requiring continuous communication between them. In contrast, a centralized PLC-based control system would likely struggle to maintain such a high level of current sharing accuracy due to communication delays and the inherent limitations of a centralized architecture.

In a PLC-based centralized control system, current imbalances would be more likely, as the central controller would need to gather data from each converter, process them, and send appropriate control signals. These delays can cause circulating currents and uneven load distribution, particularly during rapid load changes, leading to reduced system efficiency and higher operational risks.

The distributed control system, by placing control responsibility at the converter level, effectively mitigates these issues. It ensures balanced current sharing even under dynamic conditions, without the need for extensive communication between converters, enhancing both efficiency and reliability.

4.3. Impact of Control Strategy on Power Flow

The system’s ability to handle bidirectional power flow effectively was demonstrated in both positive and negative AC power flow tests. This capability is essential for applications in hybrid AC–DC microgrids, where the direction of the power flow can change depending on the needs of the grid, for example, when feeding energy back into the grid or storing excess energy in a battery system.

The proposed voltage regulation algorithm, which continuously monitors and adjusts the output voltage, allowed the system to behave like an ideal transformer. This ensured that the system could regulate both the input and output voltage regardless of the direction of the power flow, maintaining stability and minimizing voltage fluctuations.

In contrast, a PLC-based control system would likely face challenges in maintaining stable voltage regulation during power flow reversal. The delays introduced by communication between the converters and the central controller could result in voltage oscillations and instability, particularly during transitions between power flow directions. These challenges are exacerbated in high-power systems, where even small voltage deviations can lead to significant inefficiencies and operational risks.

The results of the experiments confirm that the distributed control system offers superior performance in handling bidirectional power flow, making it a robust solution for applications in microgrids, renewable energy systems, and energy storage solutions.

4.4. Benefits of Local Control vs. External PLC-Based Control

The experimental results clearly show that the use of local control provides substantial benefits over traditional PLC-based control systems, particularly in terms of the following:

• Response time: Local control allows instantaneous adjustments to voltage and current without relying on external communication, which is crucial for maintaining system stability during transient events.
• Scalability: The plug-and-play nature of the distributed control system enables easy integration of new converters, while centralized control systems require significant reconfiguration and recalibration when expanding the system. With the proposed configuration, the central power plant controller is not affected by the number of units that are connected in parallel, and so this solution is more flexible and scalable if compared with centralized controller. Therefore, the proposed configuration is suitable for applications such as hybrid networks and microgrid applications, where any upgrade can be easily made, and a higher number of units in parallel is required.
• Robustness: By distributing control responsibility among individual converters, the system becomes more robust against failures. If one controller fails, the rest of the system can continue to operate without significant disruption. In a PLC-based system, the failure of the central controller could lead to a complete system shutdown.

In a scenario where external PLC control is used, the system would be limited by the communication latency between the converters and the PLC. These delays, although acceptable for some low-frequency applications, become problematic in high-frequency, high-power systems, such as those required for solid-state transformers (SSTs). In such systems, even small delays can lead to voltage instabilities and inefficient current sharing, increasing the risk of circulating currents and reducing overall system efficiency.

4.5. Comparison of Distributed and Centralized Control Methods in DC Microgrids

To evaluate the advantages of distributed control over traditional centralized methods, a comparison is made in four key aspects: system stabilization, current balancing, dynamic response to load and power variations, and computational complexity. The experimental results from [17] serve as a reference for this analysis.

It is important to highlight that traditional droop control presents significant limitations in DC microgrids. This method can lead to voltage deviations under heavy load conditions and inefficient power sharing during light load situations. Furthermore, the lack of proper regulation can result in system instabilities, especially in the presence of non-linear loads. These shortcomings make traditional droop control less effective in applications where high precision and stability in power supply are required [18].

In terms of stabilization, centralized control systems, such as those based on PLCs analyzed in [17], exhibit significant limitations due to their low sampling frequency, which is limited to 250 Hz. This frequency restricts how quickly the controller can adjust system variables, leading to delays in both current and voltage stabilization. Additionally, communication delays between the PLC and the local converters further exacerbate these limitations, as control commands and measurements must traverse the network, introducing latency [19]. In contrast, the distributed control proposed in this work leverages local PI controllers implemented in high-speed DSPs with a sampling frequency of 10 kHz. The key advantage of the decentralized system is that both the control commands and the measurements originate locally within each converter, eliminating communication delays and enabling a significantly faster response. The use of these DSPs, combined with data acquisition through high-frequency ADCs, ensures rapid adjustments and enhances overall system performance.

Current balancing is another critical aspect of parallel converters. In centralized systems utilizing droop control, as analyzed in [17], current imbalances are observed, especially under dynamic conditions. Experimental results show current deviations reaching up to 5–8%, particularly during load changes. Moreover, in the proposed centralized control, a low-pass filter (LPF) is included, which destabilizes the system below its cutoff frequency, and with low time constants, oscillations in the signal are produced, further aggravating stability issues.

In contrast, the proposed distributed control, with local PI controllers and a feed-forward term, anticipates load changes and precisely adjusts the converter output. This predictive capability ensures a robust system response, even during sudden power variations of −24 kW to +24 kW, maintaining voltage stability with deviations below 3 V. Additionally, the distributed system guarantees equitable current sharing between converters, keeping deviations below 3% in both steady-state and dynamic conditions. Current distribution eliminates unwanted oscillations and minimizes circulating currents.

The proposed distributed control method also reduces computational complexity compared to centralized approaches. In centralized systems, the computational load increases linearly with the number of converters, as a central controller must aggregate real-time data, solve global control equations, and dispatch control actions. This process becomes increasingly expensive and introduces delays as the system scales.

In contrast, the decentralized approach distributes control tasks among local PI controllers, which independently perform lightweight real-time computations for current regulation on digital signal processors (DSPs). The master voltage controller, responsible for the regulation of the output voltage, requires minimal computational resources due to the simplicity of PI operation. By eliminating the need for a central controller to process global system states, the proposed method ensures that computational resources scale efficiently with the number of converters, enhancing both system scalability and real-time performance.

5. Conclusions

This study presents a novel distributed control strategy for parallelizing CLLC resonant converters in hybrid AC-DC microgrids, addressing challenges like current sharing, voltage regulation, and system stability. The proposed approach eliminates the reliance on centralized control systems, replacing them with local controllers that allow faster and more accurate responses to changes in load conditions.

The experimental results demonstrated the following key findings:

• Improved Response Time: The distributed control system achieved significantly faster transient response times (15–20 ms) compared to the expected delays in PLC-based systems. The inclusion of feed-forward control further enhanced the system’s ability to anticipate and react to disturbances, maintaining system stability under both positive and negative power flow conditions.
• Balanced Current Sharing: The system maintained a balanced current distribution among the parallel converters, with deviations kept below 1% for negative current flow at full load and low load. For positive current flow, deviations were 3% at both full and low load. During transient events, the deviations remained below 8% for negative currents and below 8.15% for positive currents. This accurate current-sharing was achieved without the need for complex communication between converters, relying on local current controllers to manage load sharing autonomously.
• Scalability and Flexibility: The proposed distributed control strategy inherently provides scalability due to its modular architecture. Each converter operates independently with local controllers, enabling the seamless integration of additional converters to meet higher power demands without requiring a major reconfiguration of the system. This modularity ensures that the system can expand easily while maintaining stable and balanced operation. Furthermore, the system demonstrates flexibility in handling varying load conditions and bidirectional power flow. The experimental results confirm that the system maintains dynamic stability under sudden power reference changes and external voltage variations, highlighting its adaptability to dynamic operating scenarios.
• Voltage Stability: The system’s voltage regulation algorithm, which adjusts the output voltage in real-time based on the difference between the input and output voltages (scaled by the transformer ratio), ensured stable operation in all test scenarios. The system behaved like an ideal transformer, with minimal voltage fluctuations during both positive and negative power flows.

By distributing control responsibilities among individual converters, the system became more robust and adaptable, allowing it to continue operating even if one controller failed. This plug-and-play capability further enhances the system’s practical applicability, particularly in scenarios where fast response and high reliability are essential.

Future Work: Looking ahead, further research could focus on incorporating artificial intelligence (AI) or machine learning to enhance the control system’s ability to adapt to more complex conditions and predict potential problems, such as load variation and deviations of the parameters. Furthermore, the use of advanced communication protocols could improve coordination between distributed controllers, enabling even more precise current sharing and voltage regulation in larger-scale systems. Although the proposed distributed control strategy demonstrates significant improvements in current sharing, voltage regulation, and transient response, stability remains a critical factor in systems with parallel converters. Studies such as [20] have shown that interactions between impedance and control can lead to low-frequency oscillations (LFO) if not addressed properly.

In our work, the careful tuning of PI controller parameters and the inclusion of feed-forward control help mitigate these potential instabilities. The experimental results confirm stable operation under load variations and bidirectional power flow conditions. Nevertheless, for future studies, we aim to incorporate a more detailed stability analysis based on phase margin criteria and impedance-based methods to further enhance the system’s robustness.