Design and Control of Four-Port Non-Isolated SEPIC Converter for Hybrid Renewable Energy Systems

Abstract

A new four-port non-isolated SEPIC converter intended for hybrid renewable energy systems is presented in this study. The suggested converter minimizes space and expense by integrating two inputs and two outputs in a single-stage structure with fewer components. The converter retains important characteristics including continuous input current, buck/boost capability, non-inverting output, and enhanced power factor because it is based on the fundamental SEPIC topology. It effectively combines an energy storage system (ESS) with a variety of energy sources that have different voltage and current characteristics. The converter can be configured to operate in unidirectional or bidirectional topologies depending on whether storage elements are included. Performance is examined in two operating modes, with an emphasis on the ESS’s charging and discharging processes. System equations are produced by steady-state analysis, and the design of a closed-loop controller for accurate input power and output voltage regulation is informed by dynamic analysis performed with the state-space approach. Through real-time hardware implementation and MATLAB/Simulink simulations, the efficacy of the suggested design is verified, demonstrating the open-loop unidirectional topology’s theoretical and practical validity.

1. Introduction

Power electronics have advanced significantly as a result of the growing need for renewable energy sources, with DC-DC converters being essential for effective energy transmission in a variety of applications [1,2]. These converters are vital parts of LED lighting solutions, computer systems, medical devices, renewable energy technologies, and power factor correction systems [3]. The industry is dominated by two main types of DC-DC converters: isolated and non-isolated converters [4]. High-frequency transformers used in isolated converters provide electrical isolation, but because of higher switching losses, electromagnetic interference (EMI), larger size, and higher prices, their efficiency frequently suffers [5,6]. Conversely, non-isolated converters, like a buck, boost, buck-boost, zeta, cuk, and Single Ended Primary Inductor Converter (SEPIC), eliminate the requirement for transformers and offer greater efficiency with fewer parts, which makes them perfect for contemporary applications that value performance and compactness [7,8].

Among them, the SEPIC converter has become popular due to its distinct benefits, which include its low EMI, power factor correction capability, non-inverting output, and decreased switch-driving needs [9]. Because of these qualities, SEPIC converters are especially appealing for use in renewable energy applications, where system viability depends on high efficiency and affordable solutions [10]. DC-DC converters that can effectively manage numerous energy sources are becoming more and more necessary as the need for sustainable energy systems rises, particularly in hybrid renewable energy systems.

Either hybrid or single-source renewable energy systems can be used to integrate renewable energy [11,12]. A hybrid system combines several renewable energy sources—like wind turbines and solar panels—to increase overall efficiency, dependability, and power quality. Because these systems can offset the erratic nature of renewable energy sources and guarantee a steady and uninterrupted power supply even in the event that one of the energy sources is unavailable, they are more appropriate for use in real-world scenarios [13]. Furthermore, energy storage components like batteries or supercapacitors, which store surplus energy and supply it during times of low renewable energy generation, are frequently included in hybrid systems [14,15]. Yet, improved power electronics are needed to manage power flow between various sources and energy storage devices in a hybrid system, with Multi-Port Converters (MPCs) playing a crucial role in guaranteeing smooth energy integration.

A multi-port converter, which can transmit electricity in both directions, is a crucial component for integrating various energy sources and loads in renewable energy systems [16,17]. Conventional methods of combining renewable energy sources usually depend on having a separate converter for every source, which raises the number of components, power losses, bulkiness, and expense of the system. By combining several energy sources into a single power structure, MPCs assist in addressing these issues by lowering system complexity and increasing efficiency [18]. The goal of this study is to enhance the overall performance of hybrid renewable energy systems by managing two input and two output ports using a Four-Port Non-Isolated SEPIC Converter. This application is especially well-suited for the SEPIC converter architecture because of its non-inverting output, buck/boost capabilities, and continuous input current maintenance. In renewable energy systems, these qualities are essential for preserving power quality and guaranteeing dependable energy delivery, particularly in applications involving solar photovoltaic (PV) arrays, batteries, and other energy storage devices [19,20]. By eliminating switching losses and lowering the total number of components, the suggested converter’s design maximizes power flow between the various energy sources and storage components, resulting in a more economical and compact design.

Precise regulation of power flow between various sources and loads is one of the primary issues in hybrid renewable energy systems. Even in the face of variations in input power, the proposed Four-Port SEPIC Converter’s unique control method guarantees consistent voltage regulation throughout the system [21]. This is particularly crucial for solar-powered systems since the output of the PV panels might fluctuate greatly based on the meteorological circumstances. The controller guarantees that the system functions effectively even in times of low renewable energy output in addition to controlling the flow of power between the various ports [22,23]. The energy storage component, which is usually a battery, makes sure that power is delivered to the load even in the event that the PV input is unavailable. This emphasizes the significance of a dependable control method in hybrid renewable energy systems.

The controller is made to control both unidirectional and bidirectional power flows in addition to guaranteeing steady operation [24]. This feature enables the system to store extra energy in the battery during times of strong renewable energy generation and release it when required [25,26]. This adaptability is essential to preserving system stability and guaranteeing that the renewable energy system can always supply the load’s power requirements. Non-isolated SEPIC converters are a great option for hybrid renewable energy systems because of their many benefits, such as their low component count, high efficiency, and capacity to handle diverse power sources [27]. These built-in advantages are combined with a cutting-edge control system in the suggested Four-Port Non-Isolated SEPIC Converter, which provides an incredibly effective and adaptable way to integrate renewable energy sources [28]. With this method, the design and control of MPCs for renewable energy applications have advanced significantly, laying the groundwork for further study and advancement in this area.

The growing integration of renewable energy systems into contemporary power networks highlights the necessity for effective power electronics solutions capable of smoothly integrating various energy sources [29,30]. The Four-Port Non-Isolated SEPIC Converter presents a viable option in this regard, simplifying conventional systems while enhancing overall effectiveness and dependability [27,31]. The suggested converter offers a versatile and scalable framework for integrating renewable energy sources in a range of applications, from home solar systems to large-scale renewable energy plants, by utilizing the intrinsic benefits of the SEPIC topology [32,33]. Developing high-performance converters, such as the Four-Port Non-Isolated SEPIC Converter, is crucial to developing renewable energy technologies and accomplishing sustainable development objectives worldwide [34,35]. These converters aid in ensuring that renewable energy systems can function dependably and effectively even in the face of fluctuating energy generation by optimizing power flow between renewable energy sources and storage devices [36,37]. Furthermore, the suggested converter’s modest size and low component count make it a desirable choice for a variety of applications, from big grid-tied installations to tiny off-grid devices [38,39].

In summary, the Four-Port Non-Isolated SEPIC Converter, which provides an incredibly dependable and effective means of controlling several energy sources, is a noteworthy addition to the field of power electronics for renewable energy systems [40,41,42]. The suggested converter facilitates the shift to a more sustainable energy future by resolving issues with conventional converter designs and opening the door for wider adoption of hybrid renewable energy systems [43,44]. The potential of renewable energy systems can be fully realized by ongoing research and development in this field, spurring innovation and advancement toward a cleaner, more efficient global energy landscape [45,46].

To sum up, the integration of renewable energy sources has advanced significantly with the introduction of the Four-Port Non-Isolated SEPIC Converter. With its creative design, which is based on the SEPIC topology, it provides a low-cost, high-efficiency solution for contemporary power systems. This research confirms the efficacy of the converter and lays the groundwork for upcoming advancements in the field of renewable energy integration through thorough study and validation. The major contribution of the proposed work is as follows:

• By lowering the total number of components, the suggested four-port non-isolated SEPIC converter represents a major improvement. Compared to traditional multi-port converter systems, which usually require more components, this decrease increases system efficiency, reduces the size of the converter, and cuts costs.
• The converter makes it possible to integrate several renewable energy sources—like solar, wind, and energy storage systems—effectively. For hybrid energy systems that must both supply and store energy based on demand and supply situations, their design must handle both unidirectional and bidirectional power flows.
• A reliable closed-loop PI controller, like the one found in renewable energy sources like solar power, is important to the converter’s ability to maintain steady output voltages under variable input conditions. In order to maintain a consistent output despite large fluctuations in the input, this controller dynamically modifies the duty cycles.
• Thorough steady-state and dynamic evaluations are used to validate the suggested design. The theoretical feasibility of the system is demonstrated by MATLAB/Simulink simulations supporting these assessments. In addition, real-time hardware implementation validates the converter’s practical applicability and efficacy in real-world scenarios, guaranteeing that the system is not only theoretically sound but also practically dependable for energy management.

The format of this document is as follows: In Section 2, the suggested Four-Port SEPIC unidirectional converter’s steady-state analysis is examined, and the design parameters are described in detail using a small ripple approximation model. This study is extended to the Four-Port bidirectional converter in Section 3. The Four-Port converter’s state-space modeling is covered in Section 4, where the transfer function is used to validate the model. The controller’s architecture to maintain a consistent output voltage despite input fluctuations is covered in Section 5. The results of the MATLAB/Simulink simulation, which examined the converter’s performance in a variety of scenarios, are shown in Section 6. In conclusion, Section 7 delineates the hardware configuration and its association with the simulation outcomes.

2. Proposed Structure

2.1. Four Port Non-Isolated Unidirectional Converter

The structure of the proposed Four-Port SEPIC unidirectional converter is shown in Figure 1. According to Figure 1; the proposed converter consists of two power switches, three inductors, four capacitors, and two diodes. For convenient analysis, the proposed converter is assumed to be in the Continuous Conduction Mode (CCM). Since this is a unidirectional converter, both the inputs are considered to be solar.

The energy flows from source to load. Assume that the first source voltage is $V_a$ and the second source voltage is $V_b.$ Consider $D_a$ as the duty cycle of the first input source and $D_b$ as the duty cycle of the second input source. If $V_a$ is greater than $V_b$, then the duty cycle $D_a$ should be less than $D_b$. If $V_a$ is less than $V_b$, then the duty cycle $D_a$ should be greater than $D_b$. If $V_a$ is equal to $V_b$, then the duty cycle $D_a$ should be equal to $D_b$.

2.2. Operation Modes

The operation of the proposed topology can be categorized into four modes. Here Deff is the effective duty ratio of PVSC₂, D_eff = D₂ − D_1, and DD is the duty ratio for which the diode conducts, DD = D₄ − D₃. Equivalent circuits of the proposed converter under CCM are shown in Figure 2. The CCM consists of four operating modes as compared in

Table 1. Different Modes of Operation.

Mode	Switches on	Switches off	L1	L2	L	C1	C2	C3	C4	Power Flow
I	S1	S2, S3, S4	C	D	C	C	D	D	D	Source to load
II	S2	S1,S3, S4	D	C	C	D	C	D	D	Source to load
III	S3, S4	S1, S2	D	D	C	D	D	C	C	Source to load
IV	S4	S1,S2,S3	D	D	D	D	D	D	C	Source to load

C—Charging, D—Discharging.

.

Mode 1: Switch S₁is ON and switches S₂, S_3, and S₄ are OFF. The topology of mode 1 is shown in Figure 2a. It is assumed that voltage V_a is greater than V_b, so the duty cycle D_a should be less than D_b. The inductor L₁ is charged from source V_a as the switch S₁ is closed, which forms a closed path. The capacitors C₃ and C₄ maintain the load. The inductor L gets charged from the capacitor C₁ and the capacitors C₃ and C₄ are discharged to the load side.

Mode 2: Switch S2 is ON and switches S1, S3, and S4 are OFF. The topology of mode 2 is shown in Figure 2b. The inductor L2 is charged from the source Vb as the switch S2 is closed, which forms a closed path. The load current is maintained by the capacitors C3 and C4. The inductor L is charged from the discharging capacitor C2.

Mode 3: Switches S3 and S4 are ON and switches S1 and S2 are OFF. The topology of mode 3 is shown in Figure 2c. In this mode, the load side switches are operating and the source side switches are not operating. The load is directly connected to sources Va and Vb through the energy storage elements. Load side capacitors C3 and C4 are charged from the sources Va and Vb. The inductors L1 and L2 discharge the stored energy to the capacitors.

Mode 4: Switch S4 is ON and switches S1, S2, and S3 are OFF. The topology of mode 4 is shown in Figure 2d. Capacitor C4 is charged by the two sources Va and Vb, but the capacitor C3 is discharged to the load.

The four modes of operations are considered to be in CCM assuming the ripple voltage and ripple current to be negligible. The output voltages V₀₁ and V₀₂ are given below.

$${\mathrm{V}}_{01}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{a}}{\mathrm{D}}_1}{{\mathrm{D}}_3}}+{\displaystyle \frac{{\mathrm{V}}_{\mathrm{b}}{\mathrm{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{{\mathrm{D}}_3}}-{\displaystyle \frac{{\mathrm{V}}_{02}[1-\left({\mathrm{D}}_2+{\mathrm{D}}_3\right)]}{{\mathrm{D}}_3}}$$

(1)

$${\mathrm{V}}_{02}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{a}}{\mathrm{D}}_1+{\mathrm{V}}_{\mathrm{b}}{\mathrm{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{\left(1-{\mathrm{D}}_2\right)}}$$

(2)

2.3. Small Ripple Approximation of the Proposed Four-Port Converter

The expressions of L₁, L₂, L, C₁, C₂, C_3, and C₄ with respect to current and voltage ripples are described below. The ripple current and ripple voltage are assumed to be 0.5. The circuit parameters are

$${\mathrm{L}}_1={\displaystyle \frac{{\mathrm{V}}_{\mathrm{a}}{\mathrm{D}}_1}{\mathrm{f}∆\mathrm{I}{\mathrm{L}}_1}}$$

(3)

$${\mathrm{L}}_2={\displaystyle \frac{{\mathrm{V}}_{\mathrm{b}}{\mathrm{D}}_2}{\mathrm{f}∆\mathrm{I}{\mathrm{L}}_2}}$$

(4)

$$\mathrm{L}={\displaystyle \frac{{\mathrm{V}}_{\mathrm{C}3}{\mathrm{D}}_3}{\mathrm{f}∆\mathrm{I}\mathrm{L}}}$$

(5)

$${\mathrm{C}}_1={\displaystyle \frac{{\mathrm{I}}_{\mathrm{L}1}(1-{\mathrm{D}}_1)}{\mathrm{f}∆{\mathrm{V}}_{\mathrm{C}1}}}$$

(6)

$${\mathrm{C}}_2={\displaystyle \frac{{\mathrm{I}}_{\mathrm{L}2}({\mathrm{D}}_1+{\mathrm{D}}_4)}{\mathrm{f}∆{\mathrm{V}}_{\mathrm{C}2}}}$$

(7)

$${\mathrm{C}}_3={\displaystyle \frac{{\mathrm{V}}_{\mathrm{C}3}({\mathrm{D}}_2+{\mathrm{D}}_{\mathrm{D}})}{\mathrm{f}\mathrm{R}∆{\mathrm{V}}_{\mathrm{C}3}}}$$

(8)

$${\mathrm{C}}_4={\displaystyle \frac{{\mathrm{V}}_{\mathrm{C}4}{\mathrm{D}}_2}{\mathrm{f}\mathrm{R}∆{\mathrm{V}}_{\mathrm{C}4}}}$$

(9)

3. Four-Port Bi-Directional Converter

3.1. Four Port Non-Isolated Bidirectional Converter

Topology-2 is a bidirectional converter as shown in Figure 3, utilizing solar as the primary source and a battery for energy storage. This configuration is applied when the back EMF exceeds the battery voltage, allowing energy to flow from the load back to the source. It supports bidirectional power transfer, enabling the battery to be charged from both the solar source and the back EMF.

There are two possible conditions for the bi-directional topology

• Va > E, charging condition
• Va < E, discharging condition

3.2. Power Flow Analysis from Source to Load for Four Port Non-Isolated Converter for Bi-Directional Topology

Mode 1: Switch S₁ is ON and switch S₂ is OFF. The battery is charged through the energy stored in the inductor $L_2$. When switch $S_1$ is closed, the inductor $L_1$ gets charged from the source $V_a$ and capacitor $C_1$ gets discharged through a switch $S_1$. The load current is supplied by individual capacitors $C_3$ and $C_4$. The switching waveform is shown in Figure 4 and Figure 5 and the modes of operation are represented in Figure 6.

Mode 2: Switch S₁ and S₂ are OFF. In this mode of operation, all the switches are OFF because the battery has to charge. The capacitor C₁ is charged from the source voltage V_a and capacitor C₂ is discharged through the inductor L₂ and the battery gets charged. The loads are maintained by the output capacitors. The switching waveform is shown in Figure 5.

The two modes of operations are considered to be in CCM assuming the ripple voltage and ripple current to be negligible. The steady-state equations of each mode are described below.

$${\mathrm{L}}_1{\displaystyle \frac{\mathrm{d}{\mathrm{i}}_{\mathrm{L}1}}{\mathrm{d}\mathrm{t}}}={\mathrm{D}}_1{\mathrm{V}}_{\mathrm{a}}+\left(1-{\mathrm{V}}_{\mathrm{a}}\right)\left({\mathrm{V}}_{\mathrm{a}}-{\mathrm{V}}_{\mathrm{C}1}-{\mathrm{V}}_{\mathrm{C}3}-{\mathrm{V}}_{\mathrm{C}4}\right)$$

(10)

$${\mathrm{L}}_2{\displaystyle \frac{\mathrm{d}{\mathrm{i}}_{\mathrm{L}2}}{\mathrm{d}\mathrm{t}}}=-{\mathrm{D}}_1\mathrm{E}+\left(1-{\mathrm{D}}_1\right)\left({\mathrm{V}}_{\mathrm{C}2}-\mathrm{E}-{\mathrm{V}}_{\mathrm{C}3}-{\mathrm{V}}_{\mathrm{C}4}\right)$$

(11)

$$\mathrm{L}{\displaystyle \frac{\mathrm{d}{\mathrm{i}}_{\mathrm{L}}}{\mathrm{d}\mathrm{t}}}={{\mathrm{D}}_1\mathrm{V}}_{\mathrm{C}1}+\left(1-{\mathrm{D}}_1\right)\left({(\mathrm{V}}_{\mathrm{C}2}-\mathrm{E}\right)-{\mathrm{V}}_{\mathrm{C}3}-{\mathrm{V}}_{\mathrm{C}4})$$

(12)

$${\mathrm{C}}_3{\displaystyle \frac{\mathrm{d}{\mathrm{V}}_{\mathrm{C}3}}{\mathrm{d}\mathrm{t}}}=-{\displaystyle \frac{{\mathrm{V}}_{\mathrm{C}3{\mathrm{D}}_1}}{{\mathrm{R}}_1}}$$

(13)

$${\mathrm{C}}_4{\displaystyle \frac{\mathrm{d}{\mathrm{V}}_{\mathrm{C}4}}{\mathrm{d}\mathrm{t}}}=-{\displaystyle \frac{{\mathrm{V}}_{\mathrm{C}4{\mathrm{D}}_1}}{{\mathrm{R}}_2}}$$

(14)

In steady state condition, ${\displaystyle \frac{\mathrm{d}{\mathrm{i}}_{\mathrm{L}}}{\mathrm{d}\mathrm{t}}}=0$, V_C1 = V_C2 = V_a and V_C3 = V_C4 = V_O

The output voltage expressions will be

$${\mathrm{V}}_{\mathrm{O}}={\mathrm{V}}_1={\mathrm{V}}_2={\displaystyle \frac{{\mathrm{D}}_1\mathrm{V}\mathrm{a}+(1-{\mathrm{D}}_1)(\mathrm{V}\mathrm{a}-\mathrm{E})}{1-{\mathrm{D}}_1}}$$

(15)

3.3. Power Flow Analysis from Load to Source for Four Port Non-Isolated Converter for Bi-Directional Topology

Mode 1: Switch S₃ is OFF and switch S₄ is ON. The proposed topology is shown in the Figure 7a. It is assumed that the back emf is greater than the battery voltage. So, the power will flow from load to source through the path $E_b$, $S_4$, $D_2$, $L_2$ and charges the battery E. In this case, some anti-parallel diodes are taken in order to divert the path of energy flow which makes capacitors open circuits.

Mode 2: Switch S₂ is ON and switches S₁, S₄, and S₃ are OFF: The proposed topology of this mode is shown in Figure 7b. The stored energy in inductor L₂ is discharged and it charges the battery as the switch S₂ makes a closed path.

The battery discharging condition is the same as the unidirectional topology. The modes of operation of the discharging battery are shown in Figure 8.

The output voltage equation is the same as the unidirectional topology since the battery is discharging.

$${\mathrm{V}}_{\mathrm{O}}={\mathrm{V}}_1={\mathrm{V}}_2={\displaystyle \frac{{\mathrm{D}}_2\mathrm{E}+{\mathrm{D}}_{\mathrm{e}\mathrm{f}\mathrm{f}}\mathrm{V}}{1-{\mathrm{D}}_1}}$$

(16)

where, D_eff = D₁ − D₂, V = Supply source voltage, E = Battery nominal voltage.

3.4. State Space Analysis of Four Port SEPIC Converter

State space analysis can be explained by using modern theory which is applicable to all types of systems like SISO, MIMO, MISO, SIMO, time-variant and time-invariant systems, linear, and non-linear systems. By using state space analysis, we can find the stability of the system (whether the system is stable or unstable). The state space analysis is used to analyze the system response for all modes of operation.

The state space model is represented as,

$$\dot{\mathrm{x}}=\mathrm{A}\mathrm{x}+\mathrm{B}\mathrm{u}$$

(17)

$$\mathrm{y}=\mathrm{C}\mathrm{x}+\mathrm{D}\mathrm{u}$$

(18)

where, x = state variable matrix, u = input matrix, y = output matrix

$$\mathrm{x}={\displaystyle \frac{\mathrm{d}}{\mathrm{d}\mathrm{t}}}\left[\begin{array}{c}{\mathrm{i}}_{\mathrm{L}1}\\ {\mathrm{i}}_{\mathrm{L}2}\\ {\mathrm{i}}_{\mathrm{L}}\\ {\mathrm{V}}_{\mathrm{C}1}\\ {\mathrm{V}}_{\mathrm{C}2}\\ {\mathrm{V}}_{\mathrm{C}3}\\ {\mathrm{V}}_{\mathrm{C}4}\end{array}\right] \mathrm{u}=\left[\begin{array}{c}{\mathrm{V}}_{\mathrm{a}}\\ {\mathrm{V}}_{\mathrm{b}}\end{array}\right] \mathrm{y}=\left[\begin{array}{c}{\mathrm{V}}_{\mathrm{o}}\\ {\mathrm{I}}_{\mathrm{o}}\end{array}\right]$$

(19)

V_a and V_b are the source voltages. Vo and Io are the output voltage and output current, respectively. The transfer function (TF) of the system is defined as,

$$\mathrm{T}\left(\mathrm{s}\right)=\mathrm{C}{(\mathrm{s}\mathrm{I}-\mathrm{A})}^{-1}\mathrm{B}+\mathrm{D}$$

(20)

$$A=\left[\begin{array}{ccccccc}0& 0& 0& {\displaystyle \frac{\left({\mathrm{D}}_1-D_2-D_3-D_4\right)}{L_1}}& {\displaystyle \frac{\left(D_2-D_1\right)}{L_1}}& {\displaystyle \frac{D_3}{L_1}}& {\displaystyle \frac{-D_4}{ L_1}}\\ 0& 0& 0& {\displaystyle \frac{D_3}{L_2}}& -{\displaystyle \frac{\left({\mathrm{D}}_1-D_2-D_3-D_4\right)}{L_2}}& {\displaystyle \frac{-D_3}{L_2}}& {\displaystyle \frac{-D_4}{ L_2}}\\ 0& 0& 0& {\displaystyle \frac{D_1}{L}}& {\displaystyle \frac{D_2}{L}}& {\displaystyle \frac{-D_3}{L}}& {\displaystyle \frac{-D_4}{L}}\\ {\displaystyle \frac{\left(D_2+D_3\right)}{C_1}}& {\displaystyle \frac{D_1}{C_1}}& 0& 0& 0& 0& 0\\ {\displaystyle \frac{\left(D_2-D_1\right)}{C_2}}& {\displaystyle \frac{\left(D_1+D_4\right)}{C_2}}& {\displaystyle \frac{\left(D_2-D_1\right)}{C_2}}& 0& 0& 0& 0\\ {\displaystyle \frac{D_3}{2C_3}}& {\displaystyle \frac{D_3}{2C_3}}& {\displaystyle \frac{D_3}{2C_3}}& 0& 0& {\displaystyle \frac{\left({-\mathrm{D}}_1+2D_3-D_4\right)}{R_{01}{C}_3}}& 0\\ {\displaystyle \frac{D_4}{2C_4}}& {\displaystyle \frac{D_4}{2C_4}}& {\displaystyle \frac{D_4}{2C_4}}& 0& 0& 0& {\displaystyle \frac{-\left(D_2+D_4\right)}{R_{02}{C}_4}}\end{array}\right]$$

(21)

$$B=\left[\begin{array}{cc}{\displaystyle \frac{\left({\mathrm{D}}_1-D_2-D_3-D_4\right)}{L_1}}& 0\\ 0& {\displaystyle \frac{\left({\mathrm{D}}_1-D_2-D_3-D_4\right)}{L_{21}}}\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& 0\\ 0& 0\end{array}\right]$$

(22)

$$C=\left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 1\end{array}\right]$$

(23)

$$D=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$$

(24)

By substituting the entire matrix in Equation (17), we can obtain the transfer function of the proposed converter. Transfer functions of the system are given below.

$${\displaystyle \frac{V_{01}}{V_a}}={\displaystyle \frac{1.136\mathrm{e}005 \mathrm{s}^5+3.616\mathrm{e}007 \mathrm{s}^4+7.379\mathrm{e}010 }{\mathrm{s}^7 - 4.539\mathrm{e}005 \mathrm{s}^6 - 1.437\mathrm{e}008 \mathrm{s}^5 - 3.464\mathrm{e}011 }}{\displaystyle \frac{\mathrm{s}^3+2.348\mathrm{e}013 \mathrm{s}^2+9.465\mathrm{e}015 \mathrm{s}+3.012\mathrm{e}018}{\mathrm{s}^4 - 9.365\mathrm{e}013 \mathrm{s}^3 - 8.526\mathrm{e}016 \mathrm{s}^2 - 1.804\mathrm{e}019 \mathrm{s} - 4.298\mathrm{e}021}}$$

(25)

$${\displaystyle \frac{V_{02}}{V_a}}={\displaystyle \frac{ 1.136\mathrm{e}005 \mathrm{s}^5 - 5.162\mathrm{e}010 \mathrm{s}^4+7.379\mathrm{e}010 }{\mathrm{s}^7 - 4.539\mathrm{e}005 \mathrm{s}^6 - 1.437\mathrm{e}008 \mathrm{s}^5 - 3.464\mathrm{e}011 }}{\displaystyle \frac{\mathrm{s}^3 - 3.352\mathrm{e}016 \mathrm{s}^2+9.465\mathrm{e}015 \mathrm{s} - 4.299\mathrm{e}021}{\mathrm{s}^4 - 9.365\mathrm{e}013 \mathrm{s}^3 - 8.526\mathrm{e}016 \mathrm{s}^2 - 1.804\mathrm{e}019 \mathrm{s} - 4.298\mathrm{e}021}}$$

(26)

$${\displaystyle \frac{V_{01}}{V_b}}={\displaystyle \frac{1.136\mathrm{e}005 \mathrm{s}^5+3.616\mathrm{e}007 \mathrm{s}^4+4.099\mathrm{e}010 }{\mathrm{s}^7 - 4.539\mathrm{e}005 \mathrm{s}^6 - 1.437\mathrm{e}008 \mathrm{s}^5 - 3.464\mathrm{e}011 }}{\displaystyle \frac{\mathrm{s}^3+1.304\mathrm{e}013 \mathrm{s}^2+4.732\mathrm{e}015 \mathrm{s}+1.506\mathrm{e}018}{\mathrm{s}^4 - 9.365\mathrm{e}013 \mathrm{s}^3 - 8.526\mathrm{e}016 \mathrm{s}^2 - 1.804\mathrm{e}019 \mathrm{s} - 4.298\mathrm{e}021}}$$

(27)

$${\displaystyle \frac{V_{02}}{V_b}}={\displaystyle \frac{1.136\mathrm{e}005 \mathrm{s}^5 - 5.162\mathrm{e}010 \mathrm{s}^4+4.099\mathrm{e}010 }{\mathrm{s}^7 - 4.539\mathrm{e}005 \mathrm{s}^6 - 1.437\mathrm{e}008 \mathrm{s}^5 - 3.464\mathrm{e}011 }}{\displaystyle \frac{\mathrm{s}^3 - 1.862\mathrm{e}016 \mathrm{s}^2+4.732\mathrm{e}015 \mathrm{s} - 2.15\mathrm{e}021}{\mathrm{s}^4 - 9.365\mathrm{e}013 \mathrm{s}^3 - 8.526\mathrm{e}016 \mathrm{s}^2 - 1.804\mathrm{e}019 \mathrm{s} - 4.298\mathrm{e}021}}$$

(28)

The control design of the Four-Port Non-Isolated SEPIC Converter is tightly linked to its hardware system. Transfer functions govern the relationship between the input voltages, V₀₁ and V₀₂, and the output voltages, V₀₁ and V₀₂. By modifying the duty cycles D₁ and D₂, a closed-loop PI controller controls the output. It minimizes deviations by comparing the actual output to reference values (200 V, 240 V). Through real-time feedback, the PI controller’s integral (K_I) and proportional (K_P) components maintain stability while enabling rapid response to large fluctuations and long-term error correction. Saturation blocks shield the system from instability and component failure by capping the duty cycle at 80%. This architecture ensures steady and dependable operation while effectively managing voltage swings from hybrid renewable energy sources.

4. Design of Controller

4.1. Closed Loop Unidirectional Controller

The reliability of the Four-Port Non-Isolated SEPIC Converter design is largely dependent on the ability to maintain a steady output voltage in the face of input voltage variations. The converter has a closed-loop control system using a proportional-integral (PI) controller to accomplish this. The principal duty cycle of the switching pulses is modified by the PI controller in order to regulate the output voltages by comparing them to predetermined reference values. The two input voltage sources that the converter uses are identified as V₁ and V₂. The output voltage is usually affected by variations in various input sources, which might have an impact on the system’s performance. To keep the system operating effectively and dependably, the PI controller’s job is to reduce these variations and maintain steady output voltages.

The second input voltage source (V₂) is positioned between the output and the PI controller in the controller design. With this configuration, the controller may compare the output voltage to a reference value and monitor it in real-time. The system strives to maintain the reference voltage at the output, which is a predetermined value. An error signal is produced if there is a difference between the reference voltage and the actual output voltage. This error signal alerts the controller to the output voltage deviation from the required level so that corrective action can be taken. The PI controller applies integral and proportional control actions to process the error signal. Two constants are used to fine-tune it: the integral constant (KI) and the proportional constant (KP). These constants are essential to the controller’s general functionality. KI, the integral constant, is set to 0.005, and KP, the proportional constant, is set to 0.0001. These numbers were selected with care to guarantee system stability, reduce steady-state error, and preserve fast response times to changes in input voltage.

Large differences in the output voltage are corrected instantly by the controller’s proportional component (KP), which responds to the error signal. As this is going on, the integral component (KI) corrects more minor but long-term faults, gradually getting rid of any lingering differences and making sure the system eventually reaches the required voltage level. When combined, these elements enable the PI controller to respond to voltage variations in a balanced manner, maintaining output voltage stability in the face of fluctuating circumstances. After the error signal is processed by the PI controller, a saturation block is applied to the output. This block’s function is to restrict the duty cycle of the switching pulses produced by the converter, shielding the system from harsh operating circumstances that can cause instability or component failure. In this design, the saturation block’s upper limit is set to 0.8 to guarantee that the duty cycle does not go above 80%. By shielding the switch from undue strain, this safety feature increases the converter’s lifespan and guards against future faults.

The signal is routed to a pulse generation circuit, also known as the pulse width modulation (PWM) block, after it has passed through the saturation block. Based on the input voltages V₁ and V₂, the PWM block creates the switching pulses D₁ and D₂, which regulate the converter’s functioning. The PI controller efficiently controls the power flow inside the system and keeps the output voltages at the appropriate levels by varying the duty cycles of these pulses. The reference voltages in this specific design are 200 V and 240 V. In order to guarantee that the output voltages stay at these levels despite fluctuations in the input voltages, the PI controller continuously modifies the duty cycles of the switching pulses. This unidirectional closed-loop control topology offers a reliable means of preserving constant output voltages in spite of changes in the input supply from V₁ and V₂. In general, the Four-Port Non-Isolated SEPIC Converter’s controller design guarantees dependable and effective functioning, which makes it an excellent choice for incorporating hybrid renewable energy sources into a steady power system. The converter delivers excellent performance and smooth energy management by making use of the PI controller’s capacity to control output voltages. This helps current power systems make efficient use of renewable energy sources.

4.2. Closed Loop Bi-Directional Controller

• Case 1: When both PV and battery are active

An error signal is produced when the battery and photovoltaic (PV) system are both operating. The actual output voltage is compared to a predetermined reference value. A proportional-integral (PI) controller receives this error and is calibrated with specified values for the integral constant (K_I) and proportional constant (K_P). After processing the error, the PI controller emits a signal that is routed via a saturation block. To guarantee that the switch functions within a safe duty cycle of up to 80%, this block’s maximum limit is set at 0.8. The pulse production circuit, sometimes referred to as the Pulse Width Modulation (PWM) block, receives the output signal from the saturation block and uses it to create the switching pulses D₁ and D₂ that are required for the system switches.

• Case 2: When Just PV Is Inactive

The Maximum Power Point Tracking (MPPT) controller is disabled and the PI controller is positioned between the load and the PV input when maximum solar power is available and sufficient to meet the load requirement. In this case, the switch for the battery port (S₂) is switched off to allow the battery to charge from the PV source if it is not fully charged. A breaker can be used to remove the battery from the system after it has reached full charge. Even with variations in solar irradiation, the output is guaranteed to stay stable by the PI controller attached to the PV input.

• Case 3: When There is Just a Battery

When photovoltaic electricity is unavailable, as it often is in overcast or dark conditions, the load is powered solely by the battery, which keeps the output voltage steady. In these circumstances, a breaker is used to cut the PV system off from the circuit. The load and the battery source are connected to the PI controller. An error signal is produced every time the reference voltage and actual output voltage are compared. The PI controller, which is calibrated with the proper values for K_P and K_I, handles this error. A saturation block is traversed by the PI controller’s processed signal. The resulting signal is then routed to the PWM block, which ensures consistent power delivery to the load by producing the switching pulses V₁ and V₂ for the system switches.

The suggested control technique efficiently handles various hybrid renewable energy system operating scenarios. The system compares the actual and reference voltages using the PI controller when the PV and batteries are both operating, modifying the output through the PWM block to preserve stability. The system prioritizes battery charging and keeps output stable even with changes in solar power when it is just using PV. The PI controller modifies the output as necessary, but since the battery is the only source of power, the system depends entirely on it to maintain a steady output voltage. This all-encompassing strategy guarantees dependable and effective power management across a range of operating circumstances.

5. Results and Discussions

Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 show the state space model with equal and unequal inputs for the loads. The output voltage when the inputs are equal is 240 V, and the response of unequal inputs is 220 V. It is concluded that the output voltages of the system vary if the input voltage changes. So, the system requires a suitable closed-loop control design. So that the output voltages will be constant even if there is any change in voltage input.

The output voltage and current waveforms for the PVLC-1 and PVLC-2 closed-loop unidirectional topologies are displayed in Figure 15 and Figure 16. V01 = 240 V and V02 = 200 V are the generated outputs, and the inputs are assumed to be V1 = 70 V and V2 = 80 V. It can be deduced from the closed loop simulation results that the converter’s output voltage stays constant despite changes in the input source. 200 V and 240 V are the reference output voltage settings. The maximum overshoot and steady-state error are also reduced to 0% by the closed-loop system.

The output voltage waveforms for PVLC-1 and PVLC-2 in a closed-loop bidirectional topology are shown in Figure 14 and Figure 15. The inputs in this scenario are a 120 V photovoltaic (PV) source and a 100 V energy source. It is expected that the battery is 80% charged at the initial state of charge (SOC). According to the results of the closed-loop simulation, the output voltages of the converter stay constant at the 200 V and 220 V set points. The load is powered in part by the battery and the PV. When the PV source is operating and the battery’s state of charge is 30%, Figure 16 shows the output of the system. Because of the low initial SOC of 30%, the PV source, which is kept at 120 V, must both supply the load and charge the battery in this instance. The output voltages are maintained at the predetermined levels of 200 V and 220 V during the battery’s charging process. When the PV source is operating and the battery’s state of charge is 65% as shown in Figure 17. In this case, the 120 V PV supply is sufficient to meet the demands of the load. The battery’s initial state of charge (SOC) is 65%. The battery continues to charge while the output voltages are once more kept constant at 200 V and 220 V. The output when the battery is used alone is displayed in Figure 18. When the irradiation level falls to zero or the PV source is unavailable, this condition occurs. The battery takes over the load supply with an initial state of charge (SOC) of 80%. The findings show that the output voltages of the converter stay steady at the 200 V and 220 V set points. The PV supply is disconnected during this time, and the battery empties to power the load. To sum up, the system’s performance under different operating conditions—whether the battery is the only active component, the PV source is the only active component, or both are active—illustrates its consistent output voltage maintenance and strong control. Regardless of variations in the input sources or shifts in the state of charge (SOC) of the battery, the closed-loop bidirectional topology guarantees that the output voltages stay at their predetermined levels. This efficient power source management demonstrates how dependable and effective the system is at consistently supplying the load with power under various conditions.

6. Experimental Results

Figure 19 shows the hardware setup for the four-port unidirectional converter. The proposed converter has dual input and dual output- two PV inputs, a universal motor, and a rheostat as the load. Two PV panels are 100 W each and are connected in series for each of the inputs. The converter consists of a controller circuit and two driver circuits. The main component present in the controller circuit is the micro-controller. The micro-controller used in this circuit is a programmable interface controller which consists of 28 pins. The controller has 6 PWM signal pins which are obtained across the pins 21–26. The 16th pin is grounded. The 9th and 10th pins are connected to the crystal oscillator which generates a frequency of 10 MHz. This 10 MHz frequency acts as the operating frequency for the micro-controller. The input side driver circuit receives the pulses from the control circuit which is generated using the micro-controller. The operating voltage for the micro-controller is 5 V. The main component present in the driver circuit is the opto-coupler which has two primary functions- it separates the high-power IGBT from the low-power control circuit, also it provides an operating voltage of 9–12 V for the IGBT.

Table 2. Design Parameters.

Component	Value
Inductor L1 at PVSC1	15 mH
Inductor L2 at PVSC2	15 mH
Inductor L at PVLC	15 mH
Capacitor C1 at PVSC1	0.54 mF
Capacitor C2 at PVSC2	0.54 mF
Capacitor C at PVLC	0.54 mF
Switching frequency, f	5000 Hz

mention the experimental parameters value and Figure 20 shows the experimental setup.

Table 3. Test Inputs.

PV source 1, V1	35 V
PV source 1, V2	42 V
Duty cycle of PVSC1, D1	67%
Duty cycle of PVSC2, D2	50%
Switching frequency, f	5000 Hz

and

Table 4. Comparison of output results from Hardware, Simulation, and Mathematical analysis.

PV source 1, V1	35 V
PV source 1, V2	42 V
Duty cycle of PVSC1, D1	67%
Duty cycle of PVSC2, D2	50%
Switching frequency, f	5000 Hz
V01, V02 from hardware setup	79 V, 81 V
V01, V02 from MATLAB simulation	79 V, 80.5 V
V01, V02 from mathematical formula	80.66 V, 82.22 V

shows the input and output results of the proposed converter. The hardware arrangement was powered by 35 V and 42 V solar PV sources, with duty cycles of 67% and 50%, respectively, for the system. The hardware configuration yielded output voltages of 81 V and 79 V. The 79 V and 80.5 V outputs from the MATLAB simulation and the 80.66 V and 82.22 V outputs from the mathematical model roughly match these values. The measured results are presented in Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26 and Figure 27. This consistency proves that the simulation and quantitative analysis were accurate in forecasting the hardware performance and shows that the system is dependable in maintaining steady output voltages under given circumstances.

Losses and Efficiency of Four-Port Topology

Important factors like conduction losses and switching losses for diodes and Insulated Gate Bipolar Transistors (IGBTs) are taken into account while analyzing losses and efficiency for the Four-Port Non-Isolated SEPIC Converter. The corresponding device datasheets provided the values needed for these computations.

Conduction and Switching Losses for IGBT (FGA15N120FTD)

The conduction losses in an IGBT are calculated based on the on-state voltage V_CE(sat), the collector current I_C, and the on-state resistance R_ON. The formula for conduction losses is given as:

$$\mathrm{Conduction} \mathrm{losses}={ V}_{CE\left(sat\right)}\times I_C+R_{ON}\times {I_C}^2$$

For the IGBT (FGA15N120FTD), the following values are used:

• V_CE(sat) = 1.58 V
• I_C = 15 A
• R_ON = 0.001 Ω

Thus, the conduction losses are:

Conduction losses = 1.58 × 15 + 0.001 × 15²

Conduction losses = 23.7 + 0.225 = 23.925 W

Next, the switching losses are calculated based on the energy losses during turn-on (EON) and turn-off (E_OFF) and the switching frequency $f_{sw}$. The formula for switching losses is:

Switching losses = (E_ON + E_OFF) × fsw

For the IGBT (FGA15N120FTD): Switching losses = 4.4 W

Conduction and Switching Losses for IGBT/Diode (H15R1203)

Similarly, for the IGBT/Diode (H15R1203), the conduction losses are calculated using the same formula:

$$\mathrm{Conduction} \mathrm{losses}=V_{CE\left(sat\right)}\times I_C+R_{ON}\times {I_C}^2$$

$$\mathrm{Conduction} \mathrm{losses}=23.925 \mathrm{W}$$

$$\mathrm{Switching} \mathrm{losses}=({\mathrm{E}}_{\mathrm{ON}}+{\mathrm{E}}_{\mathrm{OFF}}){\mathrm{f}}_{\mathrm{sw}}= 4.4W$$

Total Losses = Switching losses+ Conduction losses

= 23.925 + 4.4 + 22.425 + 3.5

= 54.25 W

$$\mathrm{Output} \mathrm{power}=V_O\times I_O=255 \mathrm{W}$$

$$\mathrm{Efficiency}={\displaystyle \frac{\mathrm{O}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t} \mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}}{\mathrm{O}\mathrm{u}\mathrm{t}\mathrm{p}\mathrm{u}\mathrm{t} \mathrm{p}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}+\mathrm{L}\mathrm{o}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{s}}}\times 100=82.46\%$$

Thus, the efficiency of the Four-Port Non-Isolated SEPIC Converter is approximately 82.46%.

7. Conclusions

The closed-loop controller topologies for the suggested unidirectional and bidirectional four-port converters are described in this paper. A PV source and a battery are employed in the bidirectional topology, and to keep the output voltage at a constant reference value, a PI controller and an MPPT controller are integrated into the PV source. The study examined the output responses of both closed-loop and open-loop systems, showing that the proportional and integral actions of the PI controller enable the closed-loop topology to maintain a constant output in the face of input changes. With MATLAB simulations, the performance and functionality of the converter were verified. Furthermore, real-time hardware configuration was used to validate the simulation findings and mathematical analysis of the suggested unidirectional open-loop architecture. The hardware configuration was powered by 35 V and 42 V solar PV sources that ran at 50% and 67% duty cycles, respectively. The results of the mathematical model and simulation were quite similar to the output voltages of 79 V and 80.5 V. Moreover, hardware results were used to validate the modes of operation for both open and closed-loop topologies, confirming the dependability and efficiency of the suggested system.