Introduction

The increasing global emphasis on sustainable energy has accelerated the adoption of electric vehicles (EVs) as a key solution for reducing carbon emissions and reliance on fossil fuels. As the demand for EVs grows, the need for efficient energy management systems within these vehicles has become paramount. A critical component in achieving this efficiency is the DC-DC converter, which plays a vital role in managing and distributing electrical energy from the primary energy storage system (typically a battery) to various vehicle subsystems, including the driving motor, lighting, air conditioning, and infotainment systems1,2 The complexity of modern EVs requires that power be delivered reliably and efficiently to multiple loads, each with its own voltage and current requirements. This paper introduces a novel DC-DC converter topology: The Single Source Multi-Load (SSML) and Multi-Source Single Load (MSSL) converter, designed to optimize power distribution in EV applications.

A typical EV relies on a high-capacity battery as its primary energy source, with power drawn to drive the motor and operate other vehicle systems. However, as EVs evolve, there is increasing interest in integrating secondary power sources, such as solar panels, to enhance energy efficiency and vehicle range3,4. With this integration, the need for advanced power conversion and management systems becomes critical to ensure that energy from both the battery and auxiliary sources is distributed efficiently across multiple subsystems. For this purpose, a DC-DC converter is essential to manage the flow of energy, regulate voltage levels, and optimize the overall energy usage within the vehicle5,6.

Traditional DC-DC converters used in EVs face several limitations when managing multiple loads or integrating multiple energy sources. Conventional single-input, single-output (SISO) converters are typically optimized for a single power path, often leading to inefficiencies when powering multiple subsystems with diverse power demand7,8. Additionally, conventional multi-port converters used for integrating multiple energy sources and delivering power to various loads encounter issues such as inductor current management, duty cycle regulation, and significant cross-regulation, which can negatively impact the system’s efficiency and reliability9.

Multi-port DC-DC converters, which are designed to handle multiple input and output paths, are a crucial element in EV energy management systems where energy from renewable sources like solar panels is combined with the primary battery system10,11. However, these conventional systems face several inherent challenges that limit their effectiveness, particularly in automotive applications.

One of the primary challenges is the issue of inductor charging current. In a multi-port converter, the inductor must be carefully regulated to prevent excessive current, which can lead to inefficiencies and even damage the system12 Conventional designs often employ complex control algorithms to manage the inductor current and balance power distribution, but these systems tend to introduce operational complexity and increased costs. Furthermore, as the loads vary dynamically (for example, with changes in motor speed or the activation of other subsystems), the duty cycle of the converter must adapt to maintain system stability. However, fluctuations in load demand often lead to cross-regulation, where changes in one load adversely affect the performance of other loads13.

Cross-regulation in conventional converters results in output voltage ripples and degraded performance across the entire system, making it difficult to achieve the high levels of efficiency and stability required for EV applications14. Addressing these issues has been a focus of research in recent years, with several strategies proposed to mitigate cross-regulation and improve system stability. For example, some researchers have suggested using interleaved converter topologies to reduce output voltage ripple15,16. However, while these solutions provide improvements, they often introduce additional complexity and may not fully resolve the underlying issues of load disturbance and cross-regulation17.

In recent years, numerous studies have made significant contributions to the development of efficient power converters for electric vehicles (EVs) and other renewable energy systems. These contributions are crucial as EV adoption grows and the demand for scalable and efficient power management solutions increases.

Vishnuram et al. (2023) offer a comprehensive review on EV power converter topologies, charger types, and communication techniques. They emphasize the increasing role of power electronics converters in improving energy efficiency and scalability for EV systems, particularly in incorporating renewable energy sources like solar power. Their work highlights the integration of these technologies to meet the rising demand for efficient and sustainable transportation solutions18.

Building on this, Panchanathan et al. (2023) extend the discussion by focusing on bidirectional converter topologies for Vehicle-to-Grid (V2G) systems. Their review demonstrates the importance of bidirectional converters in maintaining efficient power flow between EVs and the grid, especially in renewable energy systems. The combination of DC-bus systems and bidirectional converters, as discussed by both Vishnuram and Panchanathan, is essential for reducing energy conversion losses and achieving higher system efficiency19. Together, these reviews lay the foundation for understanding how bidirectional power flow can revolutionize EV systems by enabling them to not only consume energy but also supply it back to the grid, thus increasing flexibility and grid stability.

Kumar et al. (2023) propose a modified Ferdowsi Converter framework designed to enhance power quality during EV battery charging. Their design focuses on addressing voltage stability and power factor correction, which are critical for large-scale EV deployment. This framework aligns with the bidirectional converter concepts discussed by Panchanathan, as both address power flow optimization and the need for seamless integration with the grid. The combination of Kumar’s power quality framework with the efficiency-focused designs from previous studies further strengthens the potential for scalable EV infrastructures20.

Suresh et al. (2024) further contribute by designing a universal converter for microgrid applications, which utilizes approximate dynamic programming and artificial neural networks (ANN). This converter’s adaptability to different load conditions and its AI-driven control system create opportunities for both EV and broader renewable energy applications. The work builds on earlier studies by highlighting how artificial intelligence can enhance converter efficiency and scalability, addressing key limitations in conventional designs21.

Singh et al. (2024) develop a poly-input boost converter specifically tailored for energy storage and EV applications. This work focuses on maximizing the efficiency and scalability of converters in handling multiple energy sources, including renewable energy systems. When considered alongside Vishnuram’s review of topologies and Panchanathan’s work on bidirectional systems, Singh et al. extend the discussion by offering a solution that is not only efficient but also flexible, capable of managing the diverse energy demands of modern EV and energy storage systems22.

Moreover, Kambhampati et al. (2022) introduce a bidirectional DC-DC converter designed for hybrid electric drive systems, particularly in dual-battery configurations. Their design enhances energy management in EVs by offering greater control over battery energy storage, thus increasing overall system efficiency. This converter aligns with Singh’s poly-input converter and builds on the bidirectional topologies discussed by Panchanathan by improving energy management in complex multi-battery EV setups23.

Similarly, Karthikeyan et al. (2022) propose a dual-input single-output converter for multi-source EV applications. This converter allows for the integration of multiple power sources, such as solar energy and battery systems, providing greater flexibility in managing energy flows within EVs. When linked with the work of Suresh and Singh, this design emphasizes the importance of handling multiple energy sources efficiently, contributing to the broader discussion of flexible, scalable power converters for EV systems24.

Finally, Azib et al. (2023) contribute a reduced switch converter topology for double traction motor EVs, which optimizes the number of switches required for power conversion. This reduction in switch count decreases system complexity and cost, offering a practical solution for simplifying EV powertrain designs. This development complements the efficiency goals discussed in previous studies by streamlining the power conversion process while maintaining high performance25.

Together, these studies offer a comprehensive look at how modern power converter designs are evolving to meet the demands of electric vehicles and renewable energy systems. By focusing on efficiency, scalability, and flexibility, these works highlight the potential for advanced power management systems to transform the EV and energy sectors18,19,20,21,22,23,24,25.

Despite significant advancements in converter technologies, there remains a gap in developing a solution that can efficiently manage multiple loads from a single source, or multiple sources to a single load, without the drawbacks associated with conventional designs. Specifically, conventional multi-port converters struggle to provide stable and efficient power delivery in scenarios where loads have fluctuating demands, such as in EVs. The issues of inductor current control, cross-regulation, and voltage ripple continue to limit the performance of these systems, particularly when scalability and simplicity are required for real-world automotive applications26.

To address these challenges, this paper proposes a novel DC-DC converter topology: the SSML/MSSL converter. The primary objective of this research is to develop a converter capable of minimizing cross-regulation during load control, simplifying control operations by eliminating constraints related to inductor current and duty cycle, and ensuring stable power delivery to all loads27. The SSML/MSSL converter isolates each load or source, providing independent control over power distribution, which prevents disturbances in one load from affecting the others. This architecture not only improves efficiency but also enhances the reliability and scalability of the power management system.

The proposed SSML/MSSL converter offers several key innovations over traditional multi-port converters. First, it is designed to handle multiple outputs, such as 24 V and 48 V, from a single 12 V input, which is essential in EV applications where different subsystems require different voltage levels28,29. Additionally, the converter architecture allows for flexible extension, making it scalable to accommodate a wide range of vehicle applications, from compact EVs to larger electric trucks with more demanding power requirements.

Moreover, the SSML/MSSL converter is designed to eliminate duty cycle constraints, ensuring consistent performance even under fluctuating load conditions. By implementing a novel control strategy that independently regulates each output, the converter effectively eliminates cross-regulation, preventing voltage ripples and enhancing overall system stability30. The research also includes a comprehensive analysis of the converter’s performance through both simulation and experimental validation. A test bench model with a power rating of 100 W has been developed to verify the practical feasibility of the design, demonstrating its effectiveness in delivering 24 V and 48 V outputs from a 12 V input.

The remainder of this paper is organized as follows: Section II provides a detailed literature review, outlining existing multi-port converter designs and highlighting the limitations that the proposed SSML/MSSL converter addresses. Section III presents the design and operational principles of the proposed converter, including its key features and advantages. Section IV describes the experimental setup used to validate the converter, along with the results of the experimental model. Section V offers a comprehensive analysis of the results, comparing the performance of the SSML/MSSL converter with conventional designs. Finally, Section VI concludes the paper by summarizing the key contributions of the research and suggesting potential areas for future work.

Proposed topology

The proposed converter is designed for bidirectional operation, making it versatile and efficient for various power management applications, particularly in electric vehicles. This bidirectional capability allows the converter to operate effectively in both step-up (boost) and step-down (buck) modes, providing flexibility in power conversion and distribution. In boost mode, the converter operates in two distinct conduction modes: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). In CCM, the current through the inductors never falls to zero, ensuring a smooth and continuous energy transfer from the input to the output. This mode is particularly advantageous for applications requiring steady power delivery, as it minimizes ripple in the output voltage and current, thereby improving overall efficiency. On the other hand, DCM occurs when the inductor current drops to zero during each switching cycle. Conventional energy storage systems are typically designed with multiple converters, with each appliance connected to a separate converter. The proposed single source multi-load DC-DC converter block diagram is shown in Fig. 1. In multiphase converters for DC-DC operations, various appliances such as sound systems, lighting systems, wiper motors, and the main drive in vehicles require independent operation. Multiphase input/output converters are needed to meet a variety of practical needs. This converter can be realized in different topologies, one of which is the flyback converter, known for its simplicity in design. A block diagram of a multi-input, multi-output topology for DC-DC conversion in electric vehicles is shown in Fig. 2.

Fig. 1
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Single source multi-load DC-DC converter block diagram1.

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Fig. 2
figure 2

Multi-source multi-load DC-DC converter block diagram.

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Various single-input dual-output converters have been presented in previous research for electric vehicle applications; some of these converters are shown in Fig. 3. While these converters can maintain continuous current and high voltage, they encounter operational challenges. While DCM is less efficient due to increased ripple, it offers benefits such as reduced core losses in the inductors and lower electromagnetic interference (EMI), making it suitable for low-power or light-load conditions. The proposed Single Source Multi-Load (SSML) and Multi-Source Single Load (MSSL) converter topology, depicted in Fig. 4, incorporates five switches with anti-parallel diodes (S1-S5), two inductors, and capacitors. These components work together to manage energy flow and conversion efficiently. R-loads are used in the experimental setup to simulate real-world load conditions. One of the key features of this topology is its ability to control output voltages both independently and simultaneously. By adjusting the duty cycles D2 and D4, the converter can regulate the output voltages to the desired levels, ensuring that different loads receive the appropriate voltage regardless of variations in input power or load conditions. This capability is crucial for maintaining optimal performance and efficiency in complex systems with multiple power demands.

Fig. 3
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Existing topology.

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Fig. 4
figure 4

Proposed SSML DC-DC converter topology.

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The proposed topology is scalable and can be extended to support up to N levels, meaning it can accommodate N number of loads as illustrated in Fig. 5. As the number of connected loads increases, the circuit components will proportionally scale up to N times to maintain efficient operation across all loads. Each of these N loads can be operated independently or simultaneously, providing remarkable flexibility in managing multiple power demands within a single system. One of the key advantages of this converter is its simplified structure, which reduces complexity and eases implementation. Unlike conventional designs, this topology does not impose strict constraints on the duty cycle, allowing for more straightforward control and operation. Additionally, the output voltages for each load are independent of one another, which ensures that variations in one load do not adversely affect the others. This independence is crucial for applications requiring stable and precise voltage regulation across multiple outputs. Another significant benefit is the absence of ground loop problems during control, which enhances the reliability and safety of the system. This feature is particularly important in complex power systems where ground loops can lead to noise, interference, and potential damage to components. In terms of operational modes, the boost mode of the proposed topology is especially beneficial for energy storage system applications, where it can efficiently step up the voltage to store energy for later use. Conversely, the buck mode is advantageous for fast charging applications, allowing the converter to step down the voltage to safely and quickly charge batteries or other energy storage devices. This dual-mode capability makes the converter highly versatile, catering to a wide range of power management needs.

Fig. 5
figure 5

Proposed SSML N-stage DC-DC converter topology.

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CCM switching mode 1

When switches S1 and S4 are in the ON state, the current flows as illustrated in Fig. 6. Both inductors are energized by separate sources of equal value, which in turn charge the battery. The equations for inductor current and capacitor voltage are provided in Eqs. (1) and (2).

$$\:\begin{array}{c}{I}_{L1}\left(t\right)=\:\frac{{V}_{d}}{{R}_{1}}+{e}^{-\propto\:1t}\left[{c}_{1}{cos\omega\:}_{1}\left(t\right)+{c}_{2}{cos\omega\:}_{1}\left(t\right)\right]\\\:{I}_{L2}\left(t\right)=\:\frac{{V}_{d}}{{R}_{1}}+{e}^{-\propto\:2t}\left[{c}_{1}{cos\omega\:}_{2}\left(t\right)+{c}_{2}{cos\omega\:}_{2}\left(t\right)\right]\end{array}\:$$
(1)
Fig. 6
figure 6

Buck duty interval mode 1.

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$$\:\begin{array}{c}{V}_{C1}\left(t\right)={V}_{d}-\:\frac{{L}_{1}}{2{c}_{1}}{e}^{-\propto\:1t}\left[\begin{array}{c}({\omega\:}_{1}{c}_{1}+\frac{{}_{1}{c}_{1}}{{R}_{1}}){cos\omega\:}_{1}t\\\:\left(\frac{{\omega\:}_{1}{c}_{1}}{{R}_{1}}+{}_{1}{c}_{1}\right){sin\omega\:}_{1}t\end{array}\right]\\\:{V}_{C2}\left(t\right)={V}_{d}-\:\frac{{L}_{2}}{2{c}_{2}}{e}^{-\propto\:1t}\left[\begin{array}{c}({\omega\:}_{1}{c}_{2}+\frac{{}_{1}{c}_{2}}{{R}_{1}}){cos\omega\:}_{1}t\\\:\left(\frac{{\omega\:}_{2}{c}_{2}}{{R}_{1}}+{}_{2}{c}_{2}\right){sin\omega\:}_{2}t\end{array}\right]\end{array}$$
(2)

CCM switching mode 2

When switches S1 and S4 are in the OFF state, the current flow within the circuit undergoes a significant change, as illustrated in Fig. 7. In this state, both inductors, which were previously energized, begin to de-energize. As the inductors release their stored energy, the current finds an alternative path through the diodes connected across switches S2, S3, and S5. This process is commonly referred to as freewheeling, where the inductors maintain current continuity by discharging their energy through the diodes, thereby preventing abrupt changes in current that could otherwise lead to voltage spikes and potential damage to the circuit components. The freewheeling diodes play a critical role in ensuring that the energy stored in the inductors is effectively transferred to the battery. As the inductors de-energize, the current flows through these diodes and into the battery, contributing to its charging process. This mechanism not only aids in efficient energy transfer but also helps in maintaining the stability and longevity of the circuit by preventing unnecessary energy dissipation. The behavior of the inductor current and capacitor voltage during this phase is governed by specific equations. The initial conditions for the inductor current and capacitor voltage when switches S1 and S4 are ON are described by Eqs. (1) and (2). However, when these switches are turned OFF, the circuit dynamics change, and the inductor current and capacitor voltage follow a different set of equations, given by (3) and (4). These equations account for the freewheeling process and the energy transfer from the inductors to the battery. Equation (3) describes the inductor current as it decreases during the de-energizing phase, while Eq. (4) outlines the corresponding voltage across the capacitor as it stabilizes or adjusts based on the energy flow. The relationship between the inductor current and capacitor voltage in these equations is crucial for understanding the circuit’s overall behavior and performance during the OFF state of switches S1 and S4. In summary, when switches S1 and S4 are turned OFF, the inductors de-energize, and the current flow is redirected through the freewheeling diodes associated with S2, S3, and S5, thereby continuing to charge the battery. The inductor current and capacitor voltage during this phase are accurately modeled by Eqs. (3) and (4), reflecting the circuit’s response to the change in switch states.

Fig. 7
figure 7

Boost freewheeling interval mode 2.

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$$\:\begin{array}{c}{I}_{L1}\left(t\right)={e}^{-\propto\:1t}\left[{c}_{1}{cos\omega\:}_{1}\left(t\right)+{c}_{2}{cos\omega\:}_{1}\left(t\right)\right]\\\:{I}_{L2}\left(t\right)=\:{e}^{-\propto\:2t}\left[{c}_{1}{cos\omega\:}_{2}\left(t\right)+{c}_{2}{cos\omega\:}_{2}\left(t\right)\right]\end{array}\:$$
(3)
$$\:\begin{array}{c}{V}_{C1}\left(t\right)=-{e}^{-\propto\:1t}{L}_{1}\left[\begin{array}{c}({\omega\:}_{1}{c}_{1}+\frac{{}_{1}{c}_{1}}{{R}_{1}}){cos\omega\:}_{1}t\\\:\left(\frac{{\omega\:}_{1}{c}_{1}}{{R}_{1}}+{}_{1}{c}_{1}\right){sin\omega\:}_{1}t\end{array}\right]\\\:{V}_{C2}\left(t\right)=-{e}^{-\propto\:1t}{L}_{2}\left[\begin{array}{c}({\omega\:}_{1}{c}_{2}+\frac{{}_{1}{c}_{2}}{{R}_{1}}){cos\omega\:}_{1}t\\\:\left(\frac{{\omega\:}_{2}{c}_{2}}{{R}_{1}}+{}_{2}{c}_{2}\right){sin\omega\:}_{2}t\end{array}\right]\end{array}\:$$
(4)

During CCM modes during switches S1, S4 are ON, inductor voltages VL1 and VL2. Inductor voltage from leg1 is VL1 = V1 –VDC and voltage from leg2 is VL2 = V2 –VDC. Output voltage during mode 1 is given in Eq. (5).

$$\:\begin{array}{c}{V}_{DC}=\:{{V}_{1}D}_{1}\\\:{V}_{DC}=\:{{V}_{2}D}_{2}\end{array}\:$$
(5)

DCM switching mode

The waveforms of the proposed circuit during boost or step-up mode 1 and mode 2 are illustrated in Figs. 8 and 9. These figures provide a visual representation of the circuit’s behavior in these operational modes, where the goal is to increase the output voltage beyond the input voltage level. In boost mode, the operation of the circuit is driven by the coordinated switching of S2, S3, and S5. During the charging interval, when these switches are turned ON, both inductors are energized simultaneously from the same input source. This results in a linear increase in the inductor currents as they ramp up from their minimum values to their maximum levels. The inductors store energy during this period, which is crucial for the subsequent step-up process. The waveform in this phase reflects the gradual build-up of current within the inductors, as depicted by the rising slope in the current traces. This linear increase continues until the end of the charging interval, at which point the inductors have accumulated sufficient energy to contribute to the step-up in voltage. During the duty cycle interval, when the switches are turned OFF, the stored energy in the inductors is released. This energy release is where the boost or step-up operation occurs. The voltage across each inductor is added to the input source voltage, effectively increasing the total voltage that appears across the output. This additive process is the fundamental principle behind the boost mode, enabling the circuit to step up the input voltage to a higher level, which is then delivered to the load. The waveforms during this interval show the voltage across the inductors and the output voltage rising as the inductors release their stored energy. This step-up in voltage is a key feature of the boost mode, allowing the circuit to meet higher voltage requirements at the output, which is especially important in applications requiring efficient power conversion. Figures 8 and 9 illustrate these waveforms in detail, showcasing how the inductor currents and voltages evolve during the operation. The smooth transition between the charging and duty intervals, as well as the linear increase in inductor current, underscores the efficiency and effectiveness of the proposed circuit in achieving the desired voltage boost. V1 = VDC +VL1 in leg1 and V2 = VDC +VL2 in leg2. Output voltage equations are given in (6).

Fig. 8
figure 8

Boost charging interval mode.

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Fig. 9
figure 9

Boost duty interval mode 2.

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$$\:\begin{array}{c}{V}_{1}=\frac{{V}_{d}}{1-{D}_{1}}\:\\\:{V}_{2}=\:\frac{{V}_{d}}{1-{D}_{2}}\end{array}\:$$
(6)

The output voltage equation for the buck operation during buck mode is provided in Eq. (7), which describes the relationship between the input voltage and the output voltage when the circuit is stepping down the voltage. This equation is fundamental in understanding how the buck converter regulates the output voltage to a lower level, suitable for various applications where reduced voltage is needed. The output current, which is a critical parameter for determining the load current supplied by the converter, is derived in Eq. (8). This equation helps in calculating the amount of current delivered to the load, ensuring that the converter meets the power requirements of the connected devices. The peak inductor current, an important factor in assessing the performance and design of the inductor within the circuit, is given in Eq. (9). This value is crucial for sizing the inductor correctly to avoid saturation and to ensure efficient energy storage and transfer during operation. Finally, the duty cycle during circuit operation is expressed in Eq. (10). The duty cycle, which is the ratio of the on-time of the switch to the total switching period, plays a significant role in controlling the output voltage and current. It directly affects the efficiency and stability of the buck converter. The switching model waveform, which visually represents the circuit’s operation during the buck mode, is shown in Fig. 10. This waveform illustrates how the switch’s on and off states control the inductor current and output voltage, providing a clear understanding of the converter’s dynamic behavior during buck operation.

$$\:{(V}_{d}-{V}_{1}){D}_{11}{T}_{s}=\:{{V}_{2}D}_{10}{T}_{s}\:$$
(7)
$$\:{{I}_{2}=\:\frac{1}{T}\:{\int\:}_{0}^{{T}_{s}}{I}_{L1}dt=\frac{{(D}_{11}+{D}_{10})\varDelta\:{I}_{L1}}{2}\:}_{.}\:$$
(8)
$$\:\varDelta\:{I}_{L1}=\frac{(1-{A}_{V1}){{V}_{1}D}_{11}}{{L}_{1}}\:$$
(9)
$$\:{D}_{10}=\sqrt{1+\frac{8f{L}_{1}}{{{R}_{1}{D}_{11}}^{2}}\:}\:$$
(10)
Fig. 10
figure 10

Switching waveform.

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Transfer function model

The design of the converter is based on the principles outlined in Ref.30. The dynamic behavior of the system is captured through the state-space equation, which is presented in Eq. (11). In this equation, X represents the state vector, encompassing variables such as inductor currents and capacitor voltages, which describe the internal state of the converter. The vector denotes the input variables, typically including the input voltage and control signals that influence the converter’s operation. The output vector y reflects the desired outputs, such as the regulated voltage or current delivered to the load. Equation (11) specifically applies to one switching interval, meaning it describes the system’s dynamics during the period when the switching elements, such as transistors or MOSFETs, are either turned on or off. This equation is crucial for understanding how the converter transitions from one state to another within a single switching cycle, which in turn affects the overall performance of the power conversion process. Further expanding on this, the state and output equations, provided in Eq. (12), offer a more detailed look at how the state variables evolve over time and how they relate to the output vector y. These equations are fundamental in the design and analysis of the converter, as they allow for the prediction and control of the converter’s behavior under different operating conditions. By solving these state and output equations, designers can optimize the converter’s performance, ensuring that it meets the desired specifications for efficiency, stability, and output regulation.

$$\:\begin{array}{c}\frac{{d}_{x}}{dt}\:=bx+cu\\\:y=\:Ex+Fu\end{array}\:$$
(11)
$$\begin{array}{*{20}c} {\:\dot{x} = b_{n} x + c_{n} u} \\ {\:y = E_{n} x + F_{n} u} \\ \end{array}$$
(12)
$$\:\:C = \left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\frac{1}{{L_{2} }}} \\ {\:\frac{{D_{2} }}{{L_{2} }}} \\ \end{array} } \\ {\:\begin{array}{*{20}c} 0 \\ {\:0} \\ \end{array} } \\ \end{array} } \right]\:\:\:\:\:\:\:\:E = \left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} 0 & {\:0} \\ {\:0} & {\:0} \\ \end{array} } & {\:\begin{array}{*{20}c} 1 & {\:0} \\ {\:0} & {\:1} \\ \end{array} } \\ \end{array} } \right]\:\:$$
(13)

To linearize the voltage, duty cycle, and current for small perturbations, the above Eq. (12) is modified and expressed in Eqs. (13) and (14). These new equations account for small deviations from the steady-state values, allowing for a more accurate analysis of the system’s dynamic response to changes in operating conditions.

$$\:\dot{b=\left[\begin{array}{cc}\begin{array}{cc}0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:&\:0\\\:0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:&\:0\end{array}&\:\begin{array}{cc}\frac{-(1-{D}_{1})}{{L}_{1}}&\:0\\\:0&\:\frac{(1-{D}_{2})}{{L}_{2}}\end{array}\\\:\begin{array}{cc}\frac{(1-{D}_{1})}{{c}_{1}}\:\:\:\:\:\:\:&\:0\\\:0\:\:\:\:\:\:\:&\:\frac{(1-{D}_{2})}{{c}_{2}}\end{array}&\:\begin{array}{cc}\frac{-1}{{R}_{1}{C}_{1}}&\:\:\:\:\:\:\:\:\:\:\:\:\:0\\\:0&\:\:\:\:\:\:\:\:\:\:\frac{-1}{{R}_{2}{C}_{2}}\end{array}\end{array}\right]\:\:\:\left(14\right)\:\:}$$
(14)

Controller design

The proposed converter for closed-loop control operation is depicted in Fig. 11. This converter’s design incorporates a Proportional-Integral-Derivative (PID) controller, which is a widely used control strategy in power electronics to maintain system stability and achieve desired output levels31,32. The tuning of the PID controller is based on the Zeigler-Nichols method, a standard approach for determining optimal control parameters. This method involves setting the proportional gain to a level where the system oscillates continuously and then using this information to determine the proportional, integral, and derivative gains33. Once the PID controller is tuned using the Zeigler-Nichols method, the combined gain of the system is calculated, with the results summarized in Table 1. The tuning process is crucial as it directly impacts the performance of the converter. Proper tuning ensures that the converter responds quickly to changes in input or load conditions while maintaining stability and minimizing overshoot or oscillations. The output of the converter, following the application of the tuned PID controller, meets the desired value, demonstrating the effectiveness of the control strategy. The performance of the closed-loop system is further analyzed using Bode plots, which provide a graphical representation of the system’s frequency response. Bode plots are an essential tool in control system design as they allow engineers to assess the gain margin and phase margin, key indicators of system stability34. In the open-loop operation, the Bode plot reveals a gain margin of 0.98 dB and 1.03 dB, with a phase margin ranging between 130 and 145 degrees. These values indicate the system’s stability and response characteristics without the influence of feedback control35. However, open-loop systems are generally less robust to disturbances and changes in operating conditions. When the system is transitioned to closed-loop control, significant improvements are observed. The gain margins increase to 3.15 dB and 1.52 dB, while the phase margin is found to range between 115 and 131 degrees. These enhanced margins reflect the increased stability and improved dynamic performance of the converter under closed-loop control. The increased gain margin indicates that the system can tolerate larger variations in gain before becoming unstable, while the phase margin suggests better damping and reduced likelihood of oscillations. The closed-loop control operation thus provides a more robust and reliable system, capable of maintaining the desired output even in the presence of disturbances or variations in input voltage. The use of a PID controller tuned via the Zeigler-Nichols method ensures that the system is both responsive and stable, with sufficient gain and phase margins to handle real-world operating conditions. The performance improvements seen in the Bode plot analysis confirm the effectiveness of the proposed converter design for applications requiring precise and stable voltage regulation.

Table 1 Gain values from Zeigler-Nichols tuning method.
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Fig. 11
figure 11

Closed-loop-control operation.

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The current and voltage analysis for the proposed converter was conducted following the methodology outlined in Ref.17. This analysis is critical for understanding the performance of the converter, particularly in terms of the stress experienced by the circuit components, such as switches and diodes, and the behavior of inductors and capacitors under different operating conditions. Voltage stress across the switches and diodes was analyzed using specific equations. In mode 1, the current through the switches is found to be equal to the current through the inductors, indicating a direct relationship between the switching devices and the energy storage components. This relationship is important because it helps in determining the maximum current that the switches must handle, ensuring that they are appropriately rated to avoid failure under peak load conditions. During mode 2, the current through the diodes is equal to the inductor currents. This scenario is crucial for assessing the diode ratings, as diodes must be capable of conducting the full current without excessive losses or overheating. Proper selection of diodes based on this analysis ensures efficient operation and longevity of the converter. The design of the inductors and capacitors was carried out using the equations provided in Eq. (15). These equations take into account factors such as the desired ripple current, energy storage requirements, and voltage ratings. The inductors were sized to ensure they could handle the maximum expected current without saturating, while the capacitors were chosen to provide adequate filtering to maintain a stable output voltage. Inductor ripple current and peak-to-peak ripple voltages were calculated using Eq. (16). These ripple values are critical parameters in converter design, as they influence the quality of the output voltage and the overall efficiency of the converter. High ripple currents can lead to increased losses in the inductors and capacitors, as well as generate unwanted noise that can interfere with other components in the system. Therefore, minimizing these ripples is a key design objective. The component specifications derived from the analysis are summarized in Table 2. This table lists the values and ratings for the inductors, capacitors, switches, and diodes, ensuring that each component is properly matched to the demands of the converter’s operation. Accurate component selection based on thorough analysis is essential for achieving optimal performance and reliability in the final design. The output voltage variation as a function of other parameters, such as load and input voltage, is illustrated in Fig. 12. This figure shows how the output voltage responds to changes in these parameters, providing insight into the converter’s regulation capability. Understanding this relationship is important for applications where stable output voltage is required despite fluctuations in load or input conditions. By conducting a comprehensive current and voltage analysis, the proposed converter is optimized to handle the demands of real-world applications. The analysis ensures that the components are properly rated and that the converter can deliver reliable performance with minimal ripple and voltage stress. This careful consideration of electrical stresses and component behavior underpins the robustness and efficiency of the proposed design.

Fig. 12
figure 12

Output voltage variation with function of other parameters.

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$$\:\begin{array}{*{20}c} {\:L_{{1~\min }} = \:L_{{2~\min }} = \frac{{R_{{\max }} (1 - D_{{\min }} )}}{{2f}}\:} \\ {\:C_{{1~\min }} = \:C_{{2~\min }} = \frac{{D_{{\max }} }}{{2fR_{c} }}} \\ \end{array} \:$$
(15)
$$\:\begin{array}{c}\varDelta\:\:{L}_{1max}=\:\varDelta\:{L}_{2max}=\frac{{V}_{out}(1-{D}_{min})}{Lf}\:\\\:\:{V}_{C}=\frac{{V}_{r}}{2}\end{array}\:$$
(16)

The efficiency of the proposed system is determined by calculating the total power losses within the circuit. These losses are primarily attributed to the components such as switches, diodes, inductors, and capacitors. Each of these components contributes to the overall power dissipation, which in turn affects the system’s efficiency. The calculation of these power losses is based on specific equations, provided in Eqs. (17) and (18). These equations consider factors such as the conduction losses in the switches and diodes, the core and copper losses in the inductors, and the equivalent series resistance (ESR) losses in the capacitors. By summing these individual losses, the total power loss of the system is obtained. Once the total power loss is calculated, the efficiency of the converter is determined by comparing the output power to the input power, accounting for the losses. This approach provides a clear understanding of how much of the input energy is effectively converted to useful output, which is crucial for evaluating the performance of the converter in practical applications.

$$\:\begin{array}{c}\:{P}_{loss\_switch}=\:{P}_{conduction\:loss}+{P}_{switching\:loss}\:\\\:\:{P}_{conduction\:loss}=\:\frac{1}{T}\:{\int\:}_{0}^{T}({R}_{d}{i}_{f}+{V}_{f0}\:){I}_{f}dt\end{array}\:$$
(17)
$$\:\begin{array}{c}\:{P}_{loss\_switch}=f \times (\:{P}_{los{s}_{ON}}+{P}_{los{s}_{OFF}})\:\\\:\:{\eta\:}_{total}=\:\frac{{P}_{out}}{{P}_{out}+{P}_{loss\_switch}+{P}_{conduction}}\:\end{array}\:$$
(18)
Table 2 Parameters/components specification.
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Experimental and results discussion

A 300 W prototype model was developed to evaluate the performance of the proposed converter in real-time conditions. The components utilized in the circuit construction are listed in Table 2. This table provides detailed specifications for each component used in the prototype, ensuring that the design meets the required operational standards and performance criteria. The experimental setup for testing the prototype is depicted in Fig. 13. This setup includes all the necessary elements for verifying the converter’s functionality, including the test bench, measurement instruments, and the control system. The control signals for the converter’s switches are generated using a DsPIC30F411 controller. This microcontroller is tasked with managing the operation of the switches, specifically Insulated Gate Bipolar Transistors (IGBTs) model STGW30NC120HD. These IGBTs are chosen for their suitability in handling high power and voltage levels required by the prototype. The performance of the proposed converter was tested over a range of duty cycles from 30 to 50%. During these tests, the output voltages across two separate loads (Load 1 and Load 2) were measured. The output voltages, V1 and V2, were observed and recorded under these conditions. When the input voltage was set to 40 V (Vdc), the converter successfully maintained an output voltage of 20 V for both V1 and V2, despite using the same duty cycle for both outputs. This demonstrates the converter’s ability to regulate the output voltage effectively, even when subjected to varying input conditions. The output voltages obtained during the tests are illustrated in Fig. 14. This figure shows the relationship between the input and output voltages and provides a visual representation of the converter’s performance under the specified operating conditions. The results confirm the effectiveness of the proposed converter design in achieving stable and reliable voltage regulation.

Fig. 13
figure 13

Experiment setup.

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Fig. 14
figure 14

Buck mode from V1 and V2 to Vdc.

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In the analysis of the proposed converter’s performance, several key aspects highlight its efficiency and capability to handle varying conditions. Two significant scenarios have been evaluated: dynamic output voltage and static waveform of the output voltage. These scenarios illustrate the converter’s ability to regulate output voltage across different input voltages and power transitions. The dynamic performance of the converter is assessed by examining its response to changes in input voltage and power levels. In one particular test scenario, the dynamic output voltage achieved is 90 V when the input voltage is set to 24 V at Vdc. This result was obtained while maintaining the same duty cycle for both output voltages, V1 and V2. This scenario reflects the converter’s ability to handle dynamic conditions and deliver a stable output voltage despite changes in input power and conditions. The converter was subjected to a power transition, where the power level was adjusted from 100 W to 180 W. This transition is crucial for assessing how well the converter can handle varying loads and maintain stable output voltage. Figure 15 illustrates this power transition and shows the converter’s performance during the change. The ability of the converter to maintain a dynamic output voltage of 90 V while managing this significant power variation indicates its robust performance and effectiveness in real-time applications. Dynamic output voltage testing is essential to understand how the converter responds to real-world operating conditions where input voltages and power levels can fluctuate. A converter that can effectively manage these changes and provide a consistent output voltage is highly valuable in practical applications, ensuring reliable operation and performance. In contrast to the dynamic testing, static waveform analysis involves assessing the converter’s performance under steady-state conditions. One such test scenario involves the converter providing an output voltage of 80 V when the input voltage is 40 V. This steady-state operation is illustrated in Fig. 16. The static waveform shows how the converter maintains a constant output voltage of 80 V with a stable input voltage of 40 V. This scenario demonstrates the converter’s ability to regulate voltage effectively in a steady-state condition, providing reliable output without fluctuations. Steady-state performance is critical for applications requiring consistent voltage levels and stable operation. The waveform in Fig. 16 offers a visual representation of the output voltage behavior over time when subjected to a constant input voltage. This static analysis is essential for validating the converter’s capability to provide reliable performance under steady conditions, ensuring that it meets the desired specifications for output voltage regulation. Both dynamic and static analyses are integral to understanding the full performance capabilities of the proposed converter (Fig. 17). The dynamic output voltage test, with a result of 90 V at an input of 24 V and a power transition from 100 W to 180 W, highlights the converter’s ability to handle varying input conditions and power levels effectively. The static waveform analysis, showing a stable 80 V output from a 40 V input, confirms the converter’s reliability and stability under steady-state conditions. These analyses are crucial for ensuring that the converter performs well in both real-time and steady-state scenarios, providing stable and reliable voltage regulation across different operating conditions. The performance data and waveforms obtained from these tests offer valuable insights into the converter’s efficiency and effectiveness, validating its suitability for practical applications where both dynamic and static performance are critical. Figures 18 and 19 shows switching waveforms, input and output voltages.

Fig. 15
figure 15

Dynamic output boost mode from Vdc to V1.

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Fig. 16
figure 16

Static output boost mode from Vdc to V1.

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Fig. 17
figure 17

Dynamic output boost mode from Vdc to V1.

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Fig. 18
figure 18

Switching pulse.

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Fig. 19
figure 19

Switching pulse with output and input voltages.

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Fig. 20
figure 20

Efficiency vs. Load current.

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In the proposed circuit, power losses are a critical aspect of evaluating the efficiency and performance of the converter. Understanding these losses is essential for optimizing the design and ensuring that the system operates within its desired specifications. The losses are calculated for different components in the circuit, and these are detailed in Fig. 19. The total power loss in the circuit is given as 21 W. This total represents the cumulative energy dissipated as heat by various components within the converter. Accurate calculation and analysis of these losses help in assessing the efficiency of the converter and identifying areas where improvements can be made. Inductors are vital components in DC-DC converters, serving to store and transfer energy. However, they also contribute to power losses due to factors such as core losses and copper losses. In the proposed circuit, losses from the inductors amount to 25% of the total power loss. Given the total power loss of 21 W, this translates to 5.25 W lost in the inductors. These losses primarily arise from resistive heating in the inductor windings (copper losses) and hysteresis or eddy current losses in the magnetic core material. Reducing these losses involves selecting inductors with lower resistance and using high-quality core materials to minimize core losses. Diodes are used for rectification and controlling the direction of current flow in the converter. In the proposed circuit, the power losses from the five diodes account for 33% of the total power loss. With a total power loss of 21 W, this results in 6.93 W lost in the diodes. Diode losses occur due to forward voltage drops and reverse recovery characteristics. The forward voltage drops results in power dissipation as heat whenever current flows through the diode. Additionally, during switching operations, diodes experience reverse recovery losses, which contribute further to power dissipation. Minimizing these losses involves choosing diodes with lower forward voltage drops and optimizing the switching characteristics to reduce reverse recovery effects. Insulated Gate Bipolar Transistors (IGBTs) are crucial components for switching operations in DC-DC converters. In this circuit, losses from the five IGBTs account for 34% of the total power loss. With the total power loss being 21 W, this amounts to 7.14 W lost in the IGBTs. IGBT losses are typically due to conduction losses and switching losses. Conduction losses occur when the IGBT is in the ‘on’ state, and the current flowing through it causes resistive heating. Switching losses occur during the transition between the ‘on’ and ‘off’ states, where energy is dissipated as the IGBT switches on and off. To reduce these losses, IGBTs with lower on-state resistance and optimized switching speeds can be used. Capacitors play a role in filtering and smoothing the voltage within the converter. In the proposed circuit, losses from the two capacitors represent 8% of the total power loss. This translates to 1.68 W lost in the capacitors. Capacitor losses are primarily due to Equivalent Series Resistance (ESR), which results in resistive heating as current flows through the capacitor. High ESR values lead to greater power dissipation and reduced overall efficiency. Using capacitors with lower ESR values can significantly decrease power losses and improve the efficiency of the converter. The analysis of power losses across different components in the circuit reveals the following distribution: Inductors: 5.25 W (25% of total power loss), Diodes: 6.93 W (33% of total power loss), IGBTs: 7.14 W (34% of total power loss) and Capacitors: 1.68 W (8% of total power loss). This detailed breakdown provides valuable insights into where power losses are occurring and helps in identifying areas for potential improvement. The losses in IGBTs and diodes are the most significant, highlighting the need for optimization in these components to enhance overall efficiency. Efforts to reduce losses should focus on selecting components with better efficiency characteristics and improving the design to minimize resistive and switching losses. By addressing these losses, the overall performance and efficiency of the proposed converter can be improved, leading to better thermal management and reduced power dissipation. This optimization is crucial for ensuring the converter operates efficiently and reliably in practical applications, ultimately contributing to the effectiveness of the power management system.

Fig. 21
figure 21

Power loss distribution.

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The proposed converter operates in a closed-loop configuration, which ensures that the system can regulate its output effectively despite variations in load and input conditions. This closed-loop control is crucial for maintaining stable performance and efficient operation in practical applications. The experiment was conducted to test the converter’s performance under varying load conditions, from 120 W to 200 W, while boosting the voltage from 40 V to an output of 80 V. The results of these experiments, including efficiency calculations and power loss distributions, are illustrated in Figs. 20 and 21. In a closed-loop system, feedback is used to continuously adjust the operation of the converter to maintain the desired output. The proposed converter was tested by varying the load from 120 W to 200 W while boosting the input voltage of 40 V to achieve an output voltage of 80 V. This testing is crucial for evaluating how well the converter adapts to changes in load and maintains the desired output voltage. Figure 17 demonstrates the converter’s performance during these load variations. The converter successfully maintained the output voltage at 80 V across the different load conditions, indicating that the closed-loop control effectively compensates for changes in load. This stability is essential for applications requiring consistent voltage regulation despite fluctuating load demands. Figures 18 and 19 provide insights into the converter’s efficiency and the distribution of power losses among various components. Efficiency is a key performance metric for any converter, as it determines how effectively the converter transforms input power into usable output power. Higher efficiency means less power is wasted as heat, leading to better overall performance and reduced cooling requirements. Efficiency Calculations: The efficiency of the converter under different load conditions was calculated based on the ratio of output power to input power. By comparing these values, the efficiency of the converter at various loads can be assessed. The efficiency data helps in understanding how well the converter performs under real-world conditions and whether it meets the required performance standards. Power Loss Distributions: Power loss distributions are evaluated to identify where energy dissipation occurs within the converter. By analyzing the losses associated with different components, such as switches, diodes, inductors, and capacitors, it is possible to pinpoint which components contribute most to overall power loss. This analysis helps in optimizing the design to minimize losses and improve efficiency.

Losses in Inductors: Inductors typically experience losses due to resistance and core material properties. These losses can affect overall efficiency and should be minimized by selecting high-quality components and optimizing their design. Losses in Diodes: Diodes contribute to power loss through forward voltage drops and reverse recovery effects. Using diodes with lower forward voltage drops and optimizing switching characteristics can reduce these losses. Losses in IGBTs: IGBTs experience conduction losses and switching losses. Minimizing these losses involves using IGBTs with low on-state resistance and optimizing switching speeds. Losses in Capacitors: Capacitors contribute to power loss through Equivalent Series Resistance (ESR). Selecting capacitors with low ESR values can reduce power dissipation. Load Control and Cross-Regulation. The proposed converter allows for separate and simultaneous control of different outputs using various duty cycles. This capability is essential for applications requiring multiple output voltages or load-specific regulation. The ability to control each output independently helps in optimizing performance and meeting the specific needs of different loads. During the experiments, it was observed that other voltages in the outputs remained negligible when the load was varied. This indicates that cross-regulation issues were effectively eliminated in the proposed converter. Cross-regulation refers to the phenomenon where changes in one output voltage affect the other output voltages. By minimizing cross-regulation, the proposed converter ensures that each output voltage remains stable and unaffected by variations in other outputs. The closed-loop operation of the proposed converter was successfully demonstrated through experiments involving load variations and voltage boosting. The converter maintained a stable output voltage of 80 V across a range of load conditions from 120 W to 200 W, highlighting the effectiveness of the closed-loop control in managing real-time variations. Efficiency calculations and power loss distributions provided a comprehensive understanding of the converter’s performance. By analyzing losses in various components, opportunities for design optimization were identified to enhance overall efficiency. The ability to control loads separately and simultaneously, along with the elimination of cross-regulation issues, underscores the converter’s effectiveness in practical applications. Overall, the experimental results validate the proposed converter’s capability to deliver reliable and efficient performance across different operating conditions, making it suitable for applications requiring precise voltage regulation and efficient power conversion.

Conclusion and future research directions

This paper presented a novel Single Source Multi-Load (SSML) and Multi-Source Single Load (MSSL) DC-DC converter designed for electric vehicles (EVs), addressing the critical need for efficient power management across various subsystems. The SSML/MSSL converter eliminates common challenges in conventional multi-port converters, such as cross-regulation and inductor current constraints, while providing stable power distribution to multiple loads with independent control. The key contributions of this work include the converter’s ability to integrate multiple energy sources, such as a primary battery and a secondary solar source, enhancing overall energy efficiency in EV applications. Simulation and experimental validation using a 100 W test bench confirmed the converter’s ability to deliver stable output voltages (24 V and 48 V from a 12 V input), demonstrating its effectiveness for real-world applications. The proposed converter’s design offers flexibility and scalability, making it applicable not only to electric vehicles but also to other industries that require reliable multi-load power distribution. The results highlight its potential to improve energy management in EVs, contributing to more sustainable and efficient transportation systems.

Future research on the proposed Multi-Load and Multi-Source DC-DC converter will focus on several key areas to enhance its performance and broaden its applicability. One important direction is optimizing control strategies to further improve energy efficiency, particularly under variable load conditions and in real-world electric vehicle (EV) applications where power demands can fluctuate significantly. Additionally, research will explore the integration of advanced materials and thermal management techniques to enhance the converter’s durability and reliability in extreme environmental conditions, such as wide temperature ranges and high humidity. Further, investigating the economic feasibility of scaling the converter for mass production will be a priority, including studies on cost-effective manufacturing processes and component selection. Finally, expanding the potential use cases of the converter beyond EVs, particularly in renewable energy systems and industrial power supplies, will provide opportunities for more diverse applications. These future directions will not only address current limitations but also open new avenues for optimizing power management solutions in sustainable energy systems.