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Scientific Reports volume 14, Article number: 30195 (2024 ) Cite this article high power capacitor
The main difficulties facing the operation of parallel converters in DC microgrids (DCMGs) are load sharing, circulation current, and bus voltage regulation. A droop controller is commonly used to control current sharing among parallel DC–DC converters due to its simplicity. However, the values of droop parameters impact both bus voltage regulation and the error in current sharing among converters. This study introduces an adaptive and straightforward droop control mechanism designed to estimate droop parameters. The algorithm aims to enhance both bus voltage regulation and load sharing performance within DCMGs. Additionally, to mitigate bus voltage deviation in DCMGs, the second loop shifts the droop lines to maintain voltage regulation at rated values. The proposed method has been compared with the conventional droop controller under variable input voltage and load resistance conditions. Simulation results demonstrate that the presented method outperforms the traditional control approach, achieving superior performance.
In recent years, there has been a growing interest among researchers in DCMGs, despite the predominant focus of microgrid literature being on AC microgrids ACMGs due to the reliance of existing power systems on AC systems1. DCMGs present numerous benefits compared to ACMGs, including the elimination of challenges like reactive power control, skin effect, and frequency-related issues, as well as the utilization of simpler control algorithms2. As a result, when AC and DCMGs are compared, the latter is generally considered more efficient, reliable, easy to control, and cost-effective due to lower distribution losses It should be noted that while DCMGs offer numerous advantages such as reduced energy losses and costs3, these benefits are dependent on the use of appropriate control methods. Additionally, DCMGs have found widespread applications in commercial sectors, data centers, and electronic ships. The typical structure of a DCMG system is illustrated in Fig. 1.
However, there are certain limitations and constraints associated with DCMGs, particularly concerning voltage control during parallel operations4. Sudden variations in input power, changes in load, and errors in voltage or current feedback can lead to DC bus voltage variations5. Variations in converter output voltages can also lead to circulating current. The main control objectives of DCMGs involve maintaining bus voltage within acceptable bounds and facilitating efficient load sharing. Failure to achieve these objectives can lead to a deterioration in system performance, as both effects work together to undermine the system’s stability6.
DCMGs configuration for a variety of distributed power resources.
Several strategies for controlling parallel DC/DC converters have been widely discussed in the literature. The most widely used techniques include active current sharing7,8, droop control9,10,11, and the Master-Slave Current (MSC) sharing scheme, described in7, is part of the first approach, which utilizes a common current sharing bus to generate the reference voltage. However, one significant drawback of this method is that if the current sharing bus signal fails, it can lead to the entire system being disabled. In8, the control of parallel converters is achieved through the droop control technique with automatic master control. However, this method fails to consider the impact of connected line resistances. Each converter is equipped with a droop voltage corrector individually. However, employing a parallel master and slave controller has its drawbacks, including increased complexity, reduced reliability, and higher overall cost.
The droop control strategy, as a second approach, is commonly employed for achieving sharing of the current among different resources, primarily due to its simplicity of implementation. However, this method has some limitations, including an increase in deviation of the DC bus voltage from its nominal value4,5,6, due to large droop resistances. This strategy can be classified into distributed control with communication, centralized with communication, and decentralized control12. The current droop control methods used in DC microgrids suffer from significant drawbacks, such as poor voltage regulation, the use of fixed droop values regardless of the instantaneous voltage deviation, and unequal load sharing. A secondary control loop is employed for regulating the load voltage to minimize voltage fluctuations in small DC grids13,14. Various strategies exist in the literature to address current sharing discrepancies, including optimized droop control parameters15 and adaptive droop control16. The droop resistance is dynamically adjusted for each unit within the microgrid via current sharing loops in adaptive control, necessitating low-bandwidth communication networks for sharing unit currents among droop controllers. Traditional PI controllers are utilized to fine-tune the droop parameters. Consequently, during significant fluctuations in system parameters or load conditions, the system may struggle to meet the specified requirements. An alternative method involves offline optimization techniques like particle swarm optimization (PSO) and genetic algorithms to determine optimal droop resistor values that reduce current sharing errors. While this approach circumvents the need for communication networks, the intensive computational load of the optimization algorithms hinders real-time implementation. Within the microgrid central controller (MGCC), a PI controller manages the voltage error, transmitting its output to each converter’s local controller through a connection17. Consequently, each converter can adjust its output voltage reference in the local controller to rectify the DC bus voltage fluctuation detected by the secondary (common) controller. While the centralized approach diminishes reliability due to a single point of failure18,19, decentralized control methods20,21, along with a sparse communication network and consensus-based algorithms22,23, have been suggested to address voltage variations in DC microgrids. Nonetheless, these control strategies still necessitate communication links for information exchange among converters, either directly or with neighboring units, in the microgrid to calculate the appropriate voltage adjustment by averaging the DC bus voltage and load current values.
To address the identified constraints, this research introduces an adaptive droop methodology to mitigate bus voltage deviations in DCMGs and ensure alignment with rated values. Furthermore, the proposed approach aims to achieve smooth current distribution from all power sources to the load, thereby enhancing overall system efficiency. By incorporating a secondary loop mechanism, adjustments to the offsets of the droop lines are implemented, facilitating the maintenance of bus voltage stability through the utilization of an FPI (Fuzzy Proportional-Integral) controller. This proposed method offers superior precision in regulating bus voltage deviations and optimizing current distribution across diverse operational scenarios, encompassing both steady-state and transient conditions.
In this section, the limitations of conventional droop control in DC microgrids are discussed and addressed. The equivalent circuit for distributed sources connected in parallel is shown in Fig. 224. The figure includes parameters such as \(\:\:{I}_{o1}\) , \(\:{I}_{o2},\) \(\:{{R}_{line1},\:{R}_{line2},\:\:V}_{o1}\) , \(\:{V}_{o2}\:\) and \(\:{R}_{di}\) , representing output currents, cable lines, output voltages, and virtual resistances, respectively. Any voltage difference between the converters can lead to uneven current sharing among them. This imbalance is evident in the combined load voltage Eq.
Where \(\:{{\text{R}}_{\text{o}i}={\text{R}}_{\text{d}\text{i}}+R}_{line\text{i}},\:\:\:\:\:\left(i=\text{1,2}\right)\)
Model of an equivalent circuit representation for parallel converters17.
In Fig. 2, Kirchoff’s voltage law is applied.
Hence, the relationship between virtual resistances and current sharing in steady-state can be expressed as:
The utilization of virtual resistances plays a crucial role in achieving controlled current sharing among the resources in DC microgrids. Figure 3 illustrates the droop control configuration employed in these DCMGs25. To accomplish this, the output currents from all converters are fed back and multiplied by the corresponding droop gain value, denoted as \(\:{R}_{di}\) . The resulting signal is then subtracted from the reference voltage, \(\:{V}_{ref,i}\) of all converters, resulting in new reference signals denoted as \({V}^{*}_{o,i}\) . In a more general form, this relationship can be expressed as follows:
The value of Rdi must be limited to the value of the maximum current and voltage deviation.
Where, the symbol ∆Vdc,max represents the permissible extent of fluctuation from the DC bus voltage, as indicated in references6,26. Additionally, \(\:{i}_{\:o,i}^{max}\) refers to the current rating of the source converter. These values are essential in determining the operational limits and constraints within the system.
Implementation of droop control for the ith converter in DC microgrids18.
The classical droop control method encounters two primary limitations that need to be addressed. The first limitation pertains to the decrease in the accuracy of sharing of the current, as depicted in Fig. 4. Meanwhile, the V–I droop control effectively influences various currents Io1 and Io2, and the deviation in the DC bus remains minimal at low droop gain. However, this limited drooping gain leads to a decrease in the accuracy of current sharing among the converters. The second limitation arises from the presence of voltage deviation caused by the application of a large droop action, even when the current sharing I′(o1), I′(o2) is relatively small. This discrepancy between voltage deviation and current sharing poses challenges to the performance and stability of the system27. Therefore, finding a solution to overcome these limitations is crucial for effective operation and control of DC microgrids.
Current-voltage (I-V) characteristics of two Distributed Energy Resources (DERs) in a DC Microgrid (DCMG).
In this work, 48 V is taken as the DC microgrid voltage level, which is generally considered for DC systems along with other voltage levels such as 400, 325, 230, and 120 V. The telecommunication industry typically employs 48 V, which is deemed optimal for Low Voltage (LV) DC distribution systems. The issue of circulating current arises when converters are connected in parallel, as illustrated in Fig. 5, due to mismatches in their output voltages. Even a little deviation in output voltages (± 1%) can trigger circulating currents, leading to increased current flow through switches, thereby raising power electronic switch ratings and losses. Circulating current also causes disparities in current sharing, overloading the converters, and collectively deteriorating system performance. In Fig. 2, the load resistance \(\:{\text{R}}_{\text{L}}\) compared to the cable resistor product can render it negligible, thereby enabling the derivation of the converter’s output current, where RL is substantial, due to the deviation in converters’ output voltages being the primary cause of current circulating between DC sources.
The second part of the equation represents the circulating current induced by the influence of the first source on the second, while the first part (left side) denotes the load current.
The current flowing between DC sources can be derived, as they arise due to unequal nominal voltages, resulting in unequal sharing of the current.
The parallel connection of two boost converters.
The drawbacks of the traditional droop control method mentioned previously can be addressed by adopting an automatic droop control approach, which functions independently of communication and adjusts as needed. Figure 6, a block diagram illustrating the system designed for DCMGs. The system achieves exceptional precision in current sharing by aligning the nominal voltages of the converters. To ensure accurate current distribution and minimize sharing discrepancies, the nominal voltage of all converters is dynamically modified through local control methods. As a result, converters with higher voltage deviation and lower nominal voltage exhibit diminished current value sharing. To mitigate this issue, the controller adjusts the nominal DC voltage incrementally, taking into account the sharing of the load current and bus voltage deviation. This optimization process enhances the overall performance of the system.
Figure 7 illustrates the droop characteristics of the suggested adaptive control system for DCMGs. To enhance the sharing of the current and maintain vector voltage within acceptable limits, significant virtual resistance is employed, and all converters are compensated based on the voltage deviation value, \(\:{\varDelta \text{V}}_{MG}\) (± ∆V,i). Additionally, Eq. (4) depicts the augmentation of the conventional droop control approach with ± ∆V,i to improve the DC bus voltage.
The FPI controller, as shown in Fig. 8, compares the required value \({V}_{MG,ref}\) with the measured bus voltage \({V}_{MG}\) to derive the bus voltage deviation signal. Through the secondary loop, the voltage reference of the droop line is adjusted along the voltage axis by adding \(\:{\varDelta V}_{i}\) , as explained in (4), to effectively manage and stabilize the bus voltage, compensating for deviations from the DCMGs. The magnitude of bus voltage deviation is contingent upon the load and/or discrepancies in current or voltage feedback. The primary loop employs a substantial virtual resistance to guarantee precise load distribution among all converters in DCMGs. Figure 9 illustrates the flowchart sequence for the proposed strategy.
Diagram illustrating the control system of parallel converters in DC microgrids (DCMGs).
A high droop resistance and a voltage offset of DCMGs.
Flowchart of the suggested method.
FPI controller, which is a hybrid controller combining elements of the Mamdani method-based fuzzy controller and the conventional PI controller. The process of fuzzy inference, as described in references28,29, can be executed in three steps. The initial step, known as fuzzification, involves converting crisp inputs into a set of fuzzy membership values ranging from 0 to 1, corresponding to the respective fuzzy sets. For this investigation, triangular membership functions are employed for two inputs, change in error (CE) and namely voltage error (E), as well as one output. Each input and output variable is represented by seven membership functions, namely +B (positive big), −B (negative big), +S (positive small), −S (negative small), +M (positive medium), −M (negative medium) and Z (zero), as depicted in Fig. 10.
The generation of decisions is facilitated by the utilization of fuzzy aggregation, implication, and the fuzzy logic rules of inference at the fuzzy logic rule inference level. Table 1 provides a linguistic explanation of the fuzzy rules: When both E and CE are classified as +B, the corresponding output is also classified as +B. The FPI controller’s mathematical representation, as depicted in Fig. 8, can be articulated as.
Where \(\:\left[\:e=\:{V}_{MG,ref}-\:{V}_{mG\:}\right]\) , The FLC is represented by the non-linear function F, whereas the scale factors force and e are \(\:{K}_{ce}\) and \(\:{K}_{e}\) . \(\:{K}_{i}\) and \(\:{K}_{p}\) are gains from PI controllers.
WOA is a form of optimization that draws inspiration from the humpback whale’s social behavior. This method can address various optimization problems, including controlling voltage in Microgrod30. By formulating voltage control as an optimization task, it becomes possible to reduce the “integral of time multiplied by absolute error (ITAE)” performance measure.
Where e(t) represents the discrepancy between\(\:{\:V}_{m}\) and \(\:{V}_{ref}\) at the time (t). The flow chart of WOA is illustrated in Fig. 11. This algorithm can be represented by the following equations31:
Flow chart of the WOA.
Where, X(t) symbolizes the position vectors of the whale, prey, and random whale, labeled as \({X}_{p}\left(t\right)\) (t), and \({X}_{r}\left(t\right)\) , respectively, at the current iteration, denoted as t. Coefficient vectors are represented by the symbols A and C. The value of (a) undergoes a consistent linear decrease from 2 to 0 throughout the iterations. The constant (b) defines the value that determines the spiral logarithmic form, while the random vector (r) fluctuates between 0 and 1. The random number (l) ranges from − 1 to 1, and ε denotes the probability number within the interval [0, 1].
To assess the limitations of the conventional droop control method, a simulation was conducted. The simulation utilized a parallel-connected boost converter, as shown in Fig. 12. The MATLAB program was used to conduct the simulations. Table 2 provides a comprehensive list of the parameter values that were incorporated within the system for the simulation.
DCMGs employed in the simulation.
To illustrate the limitations of the conventional droop control method, simulations were conducted using different droop gain values. Specifically, the effects of low droop gain values were investigated, with Rd1 = Rd2 = 0.2Ω. These simulations allowed for the observation and analysis of the specific limitations that arise when utilizing little droop gains in the classical droop control methodology.
Figure 13 illustrates various parameters and simulation results under different conditions. Figure 13a represents the input voltage, while Fig. 13b shows the output voltage of the converter. The DC bus voltage is depicted in Fig. 13c, and Fig. 13d displays the output currents for each converter during two different time intervals: from 0 to .5s and from 0.5 to 1s. These intervals correspond to light-load and heavy-load conditions, respectively, with \(\:{\text{R}}_{\text{L}\text{o}\text{a}\text{d}1}=4{\Omega\:}\:\) and \(\:{\text{R}}_{\text{L}\text{o}\text{a}\text{d}2}=4{\Omega\:}\:\) . The cable resistance values used\(\:{\:\:\text{R}}_{\text{L}\text{i}\text{n}\text{e}1}=0.1{\Omega\:}\:\text{a}\text{n}\text{d}\:{\text{R}}_{\text{L}\text{i}\text{n}\text{e}2}=0.3{\Omega\:}\) . The simulation results demonstrate the limitations of the conventional control method. In this case, the output currents for every converter were found to be 7.96 and 3.44 A, deviating by 39.6% from their ideal values. Ideally, each current should have been 5.7 A. These results highlight the significant discrepancies in load current sharing that arise when using small virtual resistance values, despite achieving good voltage regulation. Thus, it becomes evident that the conventional control method falls short of ensuring satisfactory load current distribution within the system.
Conventional droop control with a small virtual resistance.
Conventional droop control with a high virtual resistance.
In the second scenario, values of high droop gain of \(\:{\text{R}}_{\text{d}1}={\text{R}}_{\text{d}2}=1.8{\Omega\:}\:\) were implemented, as illustrated in Fig. 14. Under these conditions, each converter generated currents of 5.1 A and 4.2 A, respectively, exhibiting a deviation of 9.6% from their ideal values. Ideally, each current was expected to reach 4.65 A. Notably, the observed current deviation ratio in this case was significantly lower compared to the previous scenario depicted in Fig. 13. Despite the improved current sharing, an issue arose with the voltage of the DC bus, which surpassed its permissible maximum threshold of ∆Vmax = 45.6 V. This highlights a trade-off between current deviation and voltage regulation when employing the classical droop gain approach. For a comprehensive summary of the results obtained through this approach, as illustrated in Table 3.
The effectiveness of the proposed droop control methodology was assessed and compared to the conventional method under identical operating conditions. The proposed method underwent testing under conditions of unequal linear resistances for \(\:{R}_{Line1}\ne\:{R}_{Line2}\) , and variable input voltage. Figure 15 presents the output and input voltages of the converters Fig. 15a, b, the voltage of the DC bus Fig. 15c, and the currents generated by every converter. During the heavy load duration between zero and 0.06 s, the currents generated by every converter were measured at 5.88 A and 6.12 A, demonstrating a current sharing difference of 2% and an improvement in voltage of the DC bus to remain constant at the nominal voltage of 48. In contrast, the current sharing error for the traditional method was approximately 39.6% during the same period, highlighting the superiority of the suggested approach. Table 4 provides a comprehensive summary of all the results obtained through the proposed method.
The input voltage of the first and second converters remains constant, while the load changes from 4 to 1.33 ohms, considering different line cables.
Gradual changes in input voltage for the transient response of converters one and two, along with a load change from 4 to 1.33 Ω.
To assess the efficiency of the proposed method across diverse operational scenarios, encompassing variations in input voltages and loads. In Fig. 16, the voltage input for the first converter \(\:{V}_{S1}\) was raised by 12.5% from the 24 V base value, while for the second converter \(\:{V}_{S2}\) , it was reduced by an equivalent percentage. The purpose was to examine how well the proposed method could maintain current sharing and regulate the deviation of the bus voltage.
The results demonstrate the success of the proposed strategy in achieving its intended objectives. Regardless of the changes in input voltages, the method effectively ensures the desired current engagement and effectively regulates the bus voltage deviation. These findings highlight the effectiveness of the proposed approach in enhancing load current sharing and stabilizing the DC vector voltage under varying operating conditions. For a comprehensive summary of the output results obtained under different operating conditions, as illustrated in Table 4.
As depicted in Figs. 17 and 18, the secondary loop effectively maintains the voltage of the DC bus at a consistent 48 V. This resolves the issue of voltage deviation when employing identical cable line impedances and suggests minimal current sharing error across different operational scenarios. Figure 17 demonstrates that the currents of the converters are equivalent, and the DC bus voltage remains constant at its nominal value, ensuring stable bus voltage for DCMGs across various operating conditions. The proposed method underwent testing under conditions of equal linear resistances for \(\:{\text{R}}_{\text{L}\text{i}\text{n}\text{e}1}={\text{R}}_{\text{L}\text{i}\text{n}\text{e}2}\) , variable load resistance, and input voltage. In32, the system relies on low-bandwidth communication channels to transmit current and voltage data at the DC bus of the microgrid. It utilizes an adaptive PI controller to eliminate current sharing errors and another for the secondary loop to regulate the DC bus voltage of the microgrid. Communication failure can result in a system-wide failure. The parameters Kc, α1, and α2 are adjusted through trial and error to achieve satisfactory dynamic responses from the adaptive PI controllers used in the current sharing loops and the secondary loop.
This paper introduces a secondary voltage correction approach using FPI, providing a correction signal for the primary loop without relying on low-bandwidth communication channels. Traditional methods like PI control often necessitate manual tuning and may lack adaptability in change dynamic. FPI, on the other hand, permits dynamic parameter adjustments, enhancing adaptability to changing conditions.
Based on the results shown in Table 5, the proposed approach has the ability to maintain and stabilize the DC bus voltage while reducing the current sharing error.
The input voltage of the first and second converters remains constant, while the load changes from 4 to 1.33 ohms, considering matched line cables.
Gradual changes in input voltage for the transient response of converters one and two, along with a load change from 4 to 1.33 Ω.
This study introduces an adaptive droop controller aimed at overcoming the limitations of classical droop control. The proposed method stands out for its simplicity, complemented by an online adaptation algorithm developed to facilitate its functionality. Rigorous testing and evaluation under diverse operational conditions have been undertaken to assess the effectiveness of this approach, including a comparative analysis with classical droop control methods. The results obtained from these evaluations highlight the proposed algorithm’s efficacy in enhancing current load distribution among converters and mitigating output voltage fluctuations in response to variations in input voltage and load. Overall, the outcomes of this investigation affirm the viability of the proposed adaptive droop controller as a solution to address the challenges associated with classical droop control, particularly in its ability to optimize current load distribution and stabilize output voltage levels.
All data generated or analysed during this study are included in this published article.
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The authors also acknowledge technical support received from the Renewable Energy Lab at Prince Sultan University, Riyadh, Saudi Arabia.
This study is supported via funding from Prince sattam bin Abdulaziz University project number (PSAU/2024/R/1446).
Process Control Technology Department, Faculty of Technology and Education, Beni-Suef University, Beni-Suef, Egypt
Samir A. Hamad & Mohamed Ali Ghalib
Renewable Energy Lab., College of Engineering, Prince Sultan University, Riyadh, Saudi Arabia
Electrical Power and Machines Engineering Department, Faculty of Engineering, Tanta University, Tanta, 31733, Egypt
Department of Electrical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj, 16273, Saudi Arabia
Sulaiman Z. Almutairi & Mohammed H. Alqahtani
Energy Management Department, Luminous Energy Solutions, Calgary, Canada
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S.A. writing, reviewing, Methodology; M.A. Validation, Formal analysis, overall editing; M.F. Formal analysis, editing the manuscript; S.Z. Formal analysis, Software, Writing & editing; M.H. Investigation, Formal analysis, Software; H. H. original draft, Editing, Reviewing. All authors reviewed the manuscript.
Correspondence to Mohamed Ali Ghalib.
The authors declare no competing interests.
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Hamad, S.A., Ghalib, M.A., Elmorshedy, M.F. et al. Optimizing power sharing accuracy in low voltage DC microgrids considering mismatched line resistances. Sci Rep 14, 30195 (2024). https://doi.org/10.1038/s41598-024-74682-0
DOI: https://doi.org/10.1038/s41598-024-74682-0
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