An efficient controller design of a PV integrated single inductor multiple output DC–DC converter for dynamic voltage and low power applications

Abstract

In this article, a Single Inductor Multiple Output (SIMO) DC–DC boost converter for driving independent three outputs of dynamic voltage and low power is proposed. Compared with the traditional SIMO DC–DC converter, the proposed work accomplishes (i) independent control of power at each output, (ii) small switch count, (iii) relatively better scalability with increasing output channel, (iv) fast response time, and (v) relatively better efficiency. The core aim of the current article is to implement an efficient controller design of the SIMO DC converter circuit operating in continuous conduction mode for dynamic voltage applications. The SIMO circuit comprises a photovoltaic (PV) array as a renewable energy harvesting source at the input. A hysteretic controller based on direct control with seamless transition control topology is implemented in this model for SIMO operation. This scheme is popular due to its less cost, simple, easy-to-use design architecture, and fast speed of close loop control. The configuration of the solar array is designed to deliver maximum power on the input of the SIMO DC–DC converter. For tracking the maximum power point, incremental conductance with integral control configuration is applied on the PV array with fast speed and efficiency. The MATLAB/Simulink environment is utilized for model configuration. The simulation results show that the proposed SIMO configuration with the PV array provided 100.5 W and 21.7 W for 1000 W/m² and 250 W/m², respectively.

Introduction

The growing market is leading towards a battery-operated system, and its optimization is required for power consumption in multiprocessor voltage regulation purposes.^1,2 Portable products’ power management systems need efficient power conversion techniques, rapid load/line response, and a small volume of the power module. Digital cameras, Personal Digital Assistants and other portable products require a dynamic voltage/current level of the power supply system to provide different voltages/currents to the subsystem in the module.^3–5 Figure 1 shows different schemes for obtaining varied voltage/current levels. ⁶ The low dropout regulator array is one of the techniques for dynamic current/voltage levels as shown in Figure 1(a). However, low dropout regulators lead toward less power conversion efficiency and a greater reduction in the size of the battery. Another technique to achieve multiple outputs is to use a combination of inductor switching circuits as illustrated in Figure 1(b). These switching circuits are capable of achieving high power conversion efficiency. In the same system, the requirement of multiple output voltages without Single Inductor Multiple Output (SIMO) leads to a large Printed Circuit Board (PCB) surface area, more components, increased fabrication cost, and reliability problems when using multiple inductors.^6,7

Figure 1.

Different multiple output DC–DC converter topologies.

SIMO DC converter provides a low-cost and compact-size solution for digital electronics application that requires various independent voltage supplies. For DC voltage transformation, power electronics devices (buck converter, boost converter) are used for such purposes. For multiple output voltages, the energy stored in a single inductor is shared with all outputs by using control switch techniques. The schematic diagram of the SIMO is shown in Figure 1(c). With a single inductor component, the topology can generate various current/voltage levels for portable devices.

The SIMO DC to DC converter reduces the PCB chip's fabrication cost as well as size and provides greater power conversion efficiency to the system. ⁸ SIMO has additional control components with the main output circuit to regulate multiple output structures efficiently. ⁹ The key challenges in SIMO DC converter operation are current control configuration, controller complexity, and less response time. ¹⁰ Compared to other techniques,^11–13 the hysteretic controller configuration has some key advantages, such as ease of implementation as well as fast response.^14–17

Another application of the SIMO converter is a multicoil wireless power transmission system using single inductor-based power converters. Wireless power transmission is one of the most rapidly growing technologies with larger industrial and academic players. ¹⁸ It enables power delivery to various consumer devices such as tablets, mobile phones, wearable sensors, and scientific biomedical implants. The major drawback of the conventional use of Wireless Power Transmission (WPT) is that only one device can avail charging facility at a time. ¹⁹

Since the efficiency of power transfer capability is highly dependent on the operating distance between the coils and the alignment of the coils. Therefore, this technique suffers random inductive link performances. To achieve maximum power transfer capability, optimized current tuning in a magnetic field is required. This simple topology has a very limited range of design parameters (coupling k and quality factor) and it leads toward reduced power transfer efficiency. ²⁰

In recent years, the multi-coil system has been trending for WPT technology to provide services for multiple devices at a time. This time-effective technique consists of a coil array having multiple coil transmitters. ²¹ In this topology, one transmitter coil in the charging circuit is properly aligned with the end device receiving coil. It leads to the positioning freedom of users’ devices without compromising the power transfer efficiency of the system. It makes the charging system capable of charging multiple devices simultaneously with different power levels and different charging speeds. The major drawback of using multi-coil topology is its complex design and high cost. ²² This challenge has been overcome by using the SIMO DC–DC converter for a multicoil wireless power transmission system. After converting DC voltage into higher/lower voltage in buck, boost, or buck-boost scheme, the resonant circuit converts DC supply into AC supply for WPT operation. ²³

A DC–DC converter switching regulator shares the inductor current among various loads by using a time-sharing technique. DC converters have two categories for their operation: continuous mode of conduction and discontinuous mode of conduction. ²⁴ Figure 2 illustrates the basic circuit construction of the Single Inductor Dual Output (SIDO) DC converter. The circuit contains three time slots. In the first time slot, the inductor is energized through the power supply, and the rest of the two slots are used to de-energize the inductor across the loads connected to the circuit.

Figure 2.

SIDO DC–DC converter circuit.

SIDO: Single Inductor Dual Output.

The SIMO converter is used for many applications such as portable devices, Light Emitting Diode (LED) lighting, and many other systems. ²⁵ Multiple-output voltage technologies depend on multi-output topology for driving different demands of loads. ²⁶ The nth number of Single Inductor Single Output DC–DC converter for N number of output channels with various voltage levels is one way to achieve multiple output supply. Another method to achieve multiple output voltages is to utilize SIMO topology.^27,28 In recent studies,^29,30 digital control has been considered in depth. Specifically, the cross-voltage problem has been digitally controlled based on Model Predictive Control (MPC). Lee et al. ³¹ proposed a dead-beat method by considering the regulation of source current and load terminal voltage. These two methods suffer less response time and complex mathematical calculations relatively. Chen et al. ³² proposed the DC–DC converter with boost, buck–boost with inverting, and noninverting operation. These converter operations involve only three steps and fewer conduction losses. This scheme requires a greater number of active switches and the switching frequency is comparatively low. A Bipolar DC Micro Grid system-based Dual Input Dual Output (DIDO) DC converter having low voltage is presented by Prabhakaran and Agarwal. ³³ This converter scheme is cost-effective, compact in size, and has fewer switches. It can change its operation mode from DIDO to SIDO. The principal disadvantages of this scheme are low power at the load terminal and less efficiency. Moreover, this scheme requires start-up time to supply power.

The time multiplexing method that controls the discontinuous conduction mode (DCM) SIMO DC–DC converter is proposed Waters et al. ³⁴ The drawback of this scheme is that the SIMO suffers surge currents in DCM mode in case of heavy load conditions. Another research proposed by Shi et al. ³⁵ suggested the pseudo conduction mode for SIMO circuit topology to reduce the large peak current during heavily loaded conditions. This scheme needed an extra switch for a freewheeling operation that consumes considerable power, and the power loss is greater in case of unbalanced loading. Johari et al. ³⁶ focused on a high-speed comparator for dynamic adjustment of the duty cycle switching sequence of a heavily loaded branch. This method is helpful to reduce the large ripple current produced in the circuit. The drawback of this scheme is that it lowers voltage branches’ stability and the chances of topology failure are more when most of the branches suffer the heavily loaded conditions.

Güler and Irmak ³⁷ implemented a MPC. This topology efficiently selects the modes of operation by tracking input voltage levels. MPC has the best capability of current tracking under both variant and steady-state conditions. Besides the advantages, switching frequency is a major drawback of this scheme. A typical variation in switching frequency entirely affects the component size and circuit response time.

Fong et al. ³⁸ presented the charge control method with adoptive average current control. However, this method requires a large number of external equipment for voltage compensation. For particular regulation purposes, a digital control-based method is adopted for differential and common mode operation. ³⁹ In this method, the voltage of the mth branch is linearly dependent on the voltage of the (m-1)th branch. Therefore, in this scenario, the method leads toward the failure of the voltage supply to the mth branch of the circuit. To improve efficiency under lightly loaded conditions and suppress the ripple voltage among the outputs, Goh and Ng ⁴⁰ proposed a control method for SIDO. A flying capacitor is employed to reduce ripples. However, this leads to the worst cross-regulation problem in the circuit. Further improvement is suggested with the adaptive Pseudo Continuous Conduction Mode (PCCM) method by Zhang and Ma. ⁴¹ Freewheeling current adjustment with an additional charge meter made this topology complicated.

Shen et al. ⁴² presented the predictive current control method. In this method, the individual branch duty cycle is calculated based on a linear equation. However, unbalancing loading minimizes the efficiency of the circuit, and this scheme works only when the inductor current is greater than some specific threshold limit. The state feedback mechanism with cross derivative based on inductor ripple current small-signal model has been proposed by Patra et al. ⁴³ The key aspect of this method is the placement of poles and zeros around the operating point. The circuit's performance may be influenced by the variation of input parameters and the components of the circuits. Dasika et al. ⁴⁴ proposed a methodology based on the digital multivariable design of the controller. In this methodology, the variation in input parameters of the operational point of the circuit is adjusted by gradually decoupling the output voltages so that it satisfies the demand of the load. However, the circuit topology configuration restricts the output voltages of one channel to be, always, less than the other channels. A SIDO power factor correction buck–boost converter has been suggested Liu et al. ⁴⁵ Each circuit output level is regulated independently by the time-division multiplexing of a single inductor. However, this circuit configuration works in critical conduction mode (CCM) and the peak inductor current is linearly varied with the load. The heavily loaded circuit may suffer a high peak inductor current.

Although the conventional converter technology deals with controller design and power stages related to DC–DC power conversion, multiple output DC sources can be generated with the help of a single input power source. However, the key concept of SIMO is not only related to DC–DC power conversion. Some literature and techniques discuss the SIMO in DC–AC and AC–DC power conversion with efficient control design. The LED driver scheme has been proposed by Guo ⁴⁶ where a single-stage single inductor multiple output AC–DC topology is under consideration. The multi-string LED panel is excited by multiple independent control DC sources transformed by AC supply. The SIMO topology is very useful for wireless power transmission. Wai and Liaw ⁴⁷ and Lucia et al. ⁴⁸ used the simple approach of implementing multiple wireless transmitters using an individual power inverter for each stage. The main drawback of this topology is that the number of inverter circuits linearly increases with the output. Conventional DC–AC power inverter topology for the wireless power transmission system is presented by Yao et al. ⁴⁹ The power stage of each output consists of a single inductor and an LC-tuned circuit. However, this leads to an increase in the cost of the system, and there is no coordination of switches among different outputs.

Another scheme for driving a multi-stage transmitter has been proposed by Sarnago et al. ⁵⁰ The full-wave inverter (bridge type) is used to convert DC supply into AC, and the de-multiplexer circuit is used to distribute supply among the various outputs. In this scheme, there are two drawbacks: (1) two different sets of controller circuits are needed for the inverter, and de-multiplexer circuits (2) to control de-multiplexer digital logic gates, discrete relays, and Field Effect Transistor (FET) switches are needed. ⁵¹ Although only one bridge inverter is used for three outputs, the digital control of de-multiplexer with an increased number of outputs is not simple and cost-effective. The preceding discussion leads to the consideration of a single inductor three output (SITO) which has been recently proposed by Lee et al. ⁵² The power stage of this circuit consists of a single inductor to provide three outputs. Compared with existing technologies, this method has a single inductor, fewer power switches, and other passive components. ⁵³ Despite the advantage of a single controller requirement to regulate three outputs, there are two major drawbacks in this scheme: (1) only 8.4 W power is available for each channel which may not meet power demand requirements and (2) the number of switches required for this scheme is 2(N + 1), where N is the number of outputs. Table 1 shows the core literature survey of SIMO DC–DC converters.

Table 1.

Core literature survey of SIMO DC–DC converters.

Reference	Control philosophy	Key contributions	Research limitations
28	Average inductor current control	Controls current prediction	Less output power.
			More driver circuit.
			Slow response time.
30	Model predictive control	Digitally controls cross regulation	Large no. of switches.
			Complex control circuit.
31	Dead beat control method	Source current and terminal voltage regulation.	Less response time.
			Complex calculations.
33	Closed-loop controller	Cost effective.	Requires start time.
		Compact size.	Low power.
		Fewer switches.	Less efficiency.
37	Model predictive control	Best current tracking. Efficient selection of operation modes.	Switching frequency variation. More response time.
40	Phase-lock loop, finite state machine (FSM) controller.	Suppresses ripple voltages.	Worst cross-regulation.
		Improved efficiency	Slow response time.
			Work under light load.
41	Adapted digital control	Current adjustment using online meter. Improved regulation.	Complex circuit. Ripples at the output. Less efficiency
42	Predictive current control	Batter response time. Fewer switches. Better regulation.	Less power. Unbalanced loading. Minimizes efficiency.

SIMO: Single Inductor Multiple Output; PV: photovoltaic.

The hysteretic controller named as bang-bang controller circuit, or ripple regulator circuit is designed to maintain DC–DC converter output voltages within the limit of the hysteretic band. This scheme is popular due to its less cost, simple, and easy-to-use design architecture. ⁵⁴ The key advantage of this direct control scheme is the speed of close-loop control. To overcome the frequency variation problem, many control topologies use additional circuitry with a pure hysteretic controller.^55,56 Keeping in view of the proceeding literature survey, in this paper, we proposed a model of SIMO DC boost converter with PV integration and Direct Control with Seamless Transition (DCS)-based hysteretic control and its implementation is under consideration.

The model introduces a novel approach to designing efficient controllers for SIMO DC–DC converters powered by solar energy. The proposed topology of the SIMO DC converter utilizes a time-sharing technique among multiple output channels, optimizing power delivery at the output. This paper presents an effective design for a hysteretic controller, employing direct control with seamless transition control topology. The output power for each channel achieves output power values of 100.5 W and 21.7 W for 1000 and 250 W/m² irradiance, respectively, which are significantly higher than proposed in the existing literature. The proposed model aims to minimize the number of switches necessary for efficient circuit operation, achieving the required power output. Consequently, the model offers a reduced count of switching components. Additionally, the proposed controller demonstrates robust control operation, exhibiting improved settling time, response time, and minimal steady-state error. Moreover, under both balanced and unbalanced loading conditions, the proposed control model effectively monitors the peak current limit of the inductor current and seamlessly switches between output channels.

This article is organized as follows: Section 1 discusses the need, importance, and applications of a multi-output DC converter. Theoretical background knowledge of the SIMO DC converter is also a part of this section. Section 2 covers the discussion of the photovoltaic cell with complete working equations and IC maximum power point tracking (MPPT) techniques. Section 3 discusses the proposed DCS control-based circuit, switching pattern, control configuration of the circuit, and mathematical modeling. Section 4 discusses the scalability of the proposed controller configuration. Section 5 consists of semiconductor stresses and switching losses in the proposed converter model. Section 6 contains simulation verification and result discussion. In section 7, the conclusion based on the findings and the future scope of work with existing limitations is discussed.

Research gap

From the above literature survey, the research gap finding is as follows.

• The SIMO DC converter suggested by many authors has much less output power,^28,30,34,36 which is insufficient for many applications. The efficient utilization of SIMO topology with increment in output power is a key challenge for many applications.

• The number of switches required for the optimal power flow operation linearly increases with an increase in output channels.^30,35,36,52 Reduction in the number of switches leads toward less switching losses and better efficiency.

• Loading effect that leads towards instability and efficiency reduction,^40,42 less response time,^28,33,40 poor efficiency, and regulation.

Key contributions

The efficient controller design of solar-powered single inductor multiple output DC–DC converters is proposed in the model. The key contributions of this proposed model are as follows:

• The SIMO DC converter topology utilizes a time-sharing technique among various output channels to deliver maximum power at the output. This article proposes an efficient hysteretic controller design based on direct control with seamless transition control topology. The output power for each channel is 100.5 W and 21.7 W for 1000 and 250 W/m², respectively, which is significantly higher than 8.4 W in the recent proposed work in Zheng et al., ²⁸ Jung et al., ³⁰ Waters et al., ³⁴ Johari et al., ³⁶ Zhang and Ma, ⁴¹ and Lee et al. ⁵²

• The number of switches required for the efficient circuit operation is (N + 1), where N is the number of output channels. Reducing the number of switches by meeting power requirements is the main aspect of the proposed model. The proposed model has a smaller count of switching components compared with Jung et al., ³⁰ Lee et al., ³¹ Shi et al., ³⁵ Johari et al., ³⁶ Güler and Irmak, ³⁷ Zhang and Ma, ⁴¹ and Lee et al. ⁵²

• The proposed controller has robust control operation with better settling time, response time, and less steady-state error compared with references Zheng et al., ²⁸ Lee et al., ³¹ Waters et al., ³⁴ Shi et al., ³⁵ and Zhang and Ma. ⁴¹

• The proposed control model efficiently tracks the peak current limit of the inductor current and switches the output channel under balanced and unbalanced loading conditions.

PV array and incremental control MPPT algorithm

PV generation based on the PV effect is to convert the heat or light energy directly available from the sun to electrical energy. Sunlight strikes at the surface of the PV panel and surface materials like silicone absorb this light. Electrons lose their atomic shell and provide a path to produce electrical energy. The whole process is known as the PV effect. ⁵⁷ The open-circuit voltage is mathematically written as. ⁵⁸

$$V_{oc.}=a{V}_{Th}\left({\displaystyle \frac{I_{ph}}{I_o}+1}\right)$$ (1)

As expressed in (1), the value of open-circuit voltages highly depends upon the temperature due to the factor Io. The open-circuit voltages are inversely proportional to the temperature and at standard testing conditions, the value of open-circuit voltage is 600 mV/cell. The per degree increment in temperature can cause a −0.35% or −2.2 mV change in voltages. ⁵⁹ In the present work, the Incremental Conductance plus integral method ⁶⁰ is used to evaluate the maximum power point. An integral controller incorporated with this algorithm is helpful in steady-state error reduction and it speeds up the process by reducing the convergence time. ⁶¹ The maximum power point (MPP) slope tracking is the basic principle of the incremental conductance method. The working flow chart of the IC and the integral method ⁶² is shown in Figure 3.

Figure 3.

IC MPPT algorithm flow chart.

The factor dρ/dv is equal to zero, positive and negative when the power is at maximum level, before MPP, and after the maximum point, respectively. The general equation used by this algorithm dρ/dv is expressed in terms of V and I. ⁵⁹

$${\displaystyle \frac{d\rho }{dv}={\displaystyle \frac{d(VI)}{dv}=I.{\displaystyle \frac{dv}{dv}+V.{\displaystyle \frac{dI}{dv}}}}}$$ (2)

$${\displaystyle \frac{d\rho }{dv}\cong I+V.{\displaystyle \frac{dI}{dv}}}$$ (3)

Therefore, at V_max. and I_max, the value of dρ/dv is zero. Rearranging (3)

$$-\left[{\displaystyle \frac{I}{V}}\right]={\displaystyle \frac{dI}{dv}}$$ (4)

Practically this requirement for the tracking of MPP is not achieved. Therefore, a little margin $\in$ is introduced. ⁶¹ Now the condition will be

$${\displaystyle \frac{d\rho }{dv}=\pm \in }$$ (5)

Table 2 shows the PV module parameters under standard test conditions.

Table 2.

Characteristics of the PV module.

Module	Sun power SPR-305-WHT
VOC	54.2V
ISC	2.58A
Vmp	49.25V
Imp	2.23A
RS	0.037998Ω
RP	993.51Ω
Iph	2.58A

PV: photovoltaic.

Proposed controller model and mathematical analysis

The hysteretic-based controller also called the ripple regulator circuit is designed to maintain DC–DC converter output voltages within the limit of the hysteretic band. This scheme is popular due to its less cost, simple and easy to use design architecture. The key advantage of this direct control scheme is the speed of close loop control, better efficiency, and better regulation. In this article, the proposed model (Figure 4) of the SIMO DC converter with PV integration and hysteretic control is implemented. The principle working of SIMO is based on the time-sharing technique among the N loads connected at the output. The switching pattern and width of the duty cycle for various switches are controlled by an efficient DCS-based controller design.

Figure 4.

DCS control-based hysteretic controller.

DCS: Direct Control with Seamless Transition.

The output voltage at each output channel is multiplexed and converted into a digital signal for controller operation. The error detector and amplifier circuit compare the output voltage with a reference voltage and provide an error voltage to the compensation network. The compensator circuit conditions at the input regulate the signal for the controller circuit. The peak detector circuit compares the output with the inductor threshold and generates the high and low signal for the gate driver circuit. There are three inputs of the DCS-based hysteretic controller. The first input is an adjusted duty cycle variable that is used to generate the pulses with 20 kHz frequency. The second input is the feedback signal extracted from the outputs of the SIMO circuit. Voltages V_out1, V_out2, and V_out3 are connected at the input of the mux for timely providing the feedback signal as per the selection of the output. The multiplexed signal is then fed as the second input of the hysteretic controller where it is compared to the saw-tooth signal and pulses are generated at this stage. These pulses are connected at the Reset and Set input of SR flip flops one and two, respectively. The third input is the inductor current that is acting as a controlling agent for the output voltage level. By comparing I_L with the threshold or any reference value, we can control the width of pulses generated by the control signal. The proposed SIMO model is illustrated in Figure 4.

When the main switch receives an enable pulse from the control circuit based on the decision of the MPPT algorithm, it allows the inductor to store energy in its magnetic field. When the gate pulse is at its negative value and MOSFET acts as an open switch, the inductor supplies energy to the rest of the circuit connected as a load. The values of resistance and capacitance are identical for each load. The on/off state of switches S_1, S₂, and S₃ is entirely controlled by the controller circuit through the value of inductor current and feedback. The inductor current is acting as a controlling agent for the output voltage level. By comparing I_L with a reference value, we can control the width of pulses generated by the control signal. The proposed model works on balanced and unbalanced loading modes of operation. If the reference value is zero, voltages at the outputs are equal and this condition shows a balanced loading condition with the same resistive load. On the other hand, if the reference voltages are different for each case, the output voltages for three distinct outputs are unequal in magnitude irrespective of the equal value of resistance connected as load. The working of SIMO is divided into two modes of operation.

• Mode 1

In this operational mode, all switches are closed except S_main. The inductor is fully energized in this mode and when it is reached to peak limit, the switch S_main is turned off by the controller circuit. The mathematical expression for inductor current is

$$I_{l,peak}={\displaystyle \frac{V_{in}}{L}DTs+I_{l,dc}}$$ (6)

Where D is the duty cycle of the SIMO boost DC converter and I_{L, dc} is the DC offset of the inductor current.

• Mode 2

In the second mode of operation, the S_main shows the characteristics of the OFF state. The inductor energy and source supply flow toward the first load segment through S₁ MOSFET. In this operation, all other switches behave like open circuits because no gating pulse is provided on their gate terminal. The inductor current decreases with slope.

$$m={\displaystyle \frac{V_{out1}}{L}}$$ (7)

V_out1 is the output voltage of the first stage. The mathematical expression for output voltage is written as

$$V_{out1}={\displaystyle \frac{1}{D_{12}{T}_S}{\int }_{D_1{T}_s}^{(D_{11}+D_{12})T_s}{V}_{out1}dt}$$ (8)

When the inductor is fully de-energized, the switch S₁ is turned OFF and again S_main is switched ON by the controller to energize the inductor. When the inductor is fully energized and the peak inductor current is detected by the controller, the switch S_main is turned off and power is supplied to the second output channel through the inductor. The whole process is repeated for the third output channel. The sequence for switching operation of the main switch and load connected to the switch is illustrated in Figure 5.

Figure 5.

Switching arrangement of various switches.

The whole process of this inductor energizing and de-energizing shuffles between loads 1, 2, and 3 is based on the time-sharing technique controlled by the hysteretic controller circuit. DCS control system defines the switching pattern of three switches S₁, S₂, and S₃ connected at the output. The switching pattern of three MOSFETs connected at the output is defined by the control system. The switching frequency is set at 20 KHz. The control unit has three inputs. The first input adjusts the duty cycle variable to generate pulses with a frequency of 20 KHz. By comparing the inductor current (I_L) with a threshold or reference value, the width of the pulses generated by the control signal can be controlled. In the first mode of operation, the main switch receives a pulse from the control circuit, and the inductor is energized through the input source. In the second mode of operation, the main switch acts as an open switch, and switch S1 receives pulses from the control system. The entire inductor energy is transferred to the load through S1. In the third segment, the main switch is closed, and all other switches are open. The inductor is energized through the input source. In the fourth segment of operation, only switch S2 is closed by the control pulse, and load 2 receives the inductor energy. In various time slots, the inductor receives energy from the source and simultaneously using time division provides distinct output loads through high-frequency switching. The time-sharing switching pattern generated by the control circuit for a balanced loading condition is illustrated in Figure 6. The duty cycle and on/off time of any switch can be controlled by controlling the threshold value of the inductor current.

Figure 6.

Gating pulses for the proposed SIMO model.

SIMO: Single Inductor Multiple Output.

Mathematical modeling of the proposed controller circuit

In mathematical analysis, all circuit elements present in Figure 7 must be considered ideal. Let the capacitor voltage be V_K. V_H is the higher threshold voltage level and V_L is the lower level of a comparator. V_V is the comparator output voltage. Figure 7 illustrates the schematic arrangement of a hysteretic-based control design system. Whereas, the Figure 8 presents the Pole Zero map of the proposed circuit.

• First state: 0 < t < T_on

Figure 7.

DCS control-based hysteretic controller.

DCS: Direct Control with Seamless Transition.

Figure 8.

PZ map of the proposed circuit.

The comparator's output signal is at a lower level during this interval.

$${\displaystyle \frac{V_k-V_{ref}}{R}+i+{\displaystyle \frac{V_k-(-V_v)}{R_k}}}$$ (9)

$$C_k{\displaystyle \frac{d{V}_k}{dt}={\displaystyle \frac{V_{ref}-V_k}{R}+{\displaystyle \frac{V_k+V_v}{R_k}}}}$$ (10)

Let R_s= RR_k /R + R_K, using e ^{∫ 1 / C}_k^R_k an integral factor ⁴⁶ and by putting R_S value (10) is written as

$$\int {\displaystyle \frac{d}{dt}\left(e^{\int C_k{R}_{s}dt}{V}_f\right)={\displaystyle \frac{1}{C_k}(\int {\displaystyle \frac{V_{ref}}{R}-{\displaystyle \frac{V_v}{R_k})e^{\int C_k{R}_s}}}}}$$ (11)

(11) reduces to

$$V_k=\left({\displaystyle \frac{V_{ref}}{R}-{\displaystyle \frac{V_v}{R_k}}}\right)R_k+X1$$ (12)

X₁ is constant. During V_K (T_on)=V_H initial condition, we obtained the following equation.

$$V_H=\left({\displaystyle \frac{V_{ref}}{R}-{\displaystyle \frac{V_v}{R_s}}}\right)R_s+X1$$ (13)

Evaluating and putting X₁ in (13), we obtain

$$V_k={\displaystyle \frac{V_{ref}{R}_s}{R}-{\displaystyle \frac{V_v{R}_s}{R_s}+\left(V_H-V_{ref}{\displaystyle \frac{R_s}{R}+V_v{\displaystyle \frac{R_s}{R_k}}}\right)e^{\frac{-t}{C_k{R}_s}}}}$$ (14)

V_K should be smaller than V_L for this case. Therefore, the condition is

$$V_{ref}{\displaystyle \frac{R_s}{R}-V_v{\displaystyle \frac{R_s}{R_k}<V_L}}$$ (15)

By putting V_K= V_L and t = t_on in (15), we obtain

$$V_L=V_H{e}^{\left(\frac{-ton}{C_k{R}_s}\right)}+V_{ref}{\displaystyle \frac{R_s}{R}\left(1-e^{\left(\frac{-ton}{C_k{R}_s}\right)}\right)-V_v{\displaystyle \frac{R_s}{R_k}\left(1-e^{\left(\frac{-ton}{C_k{R}_s}\right)}\right)}}$$ (16)

Let V_H -V_L << V_H -V_ref (R_s/R)+V_v(R_s/R_v), on-time is written as

$$t_{on}=C_k{R}_s{\displaystyle \frac{V_{H.}-V_{L.}}{V_L-V_{ref}{\displaystyle \frac{R_s}{R}+V_v{\displaystyle \frac{R_s}{R_k}}}}}$$ (17)

• Second state: T_on< t < T_S

The comparator's output signal is at a higher level during this interval. Thus, by using KVL the following equations are found.

$${\displaystyle \frac{V_k-V_{ref}}{R}+i+{\displaystyle \frac{V_k-V_v}{R_k}=0}}$$ (18)

$$C_k{\displaystyle \frac{d{V}_k}{dt}+V_k{\displaystyle \frac{R+Rk}{RRk}={\displaystyle \frac{V_{ref}}{R}+{\displaystyle \frac{V_v}{R_k}}}}}$$ (19)

Putting the value of R_S and using e ^{∫ 1 / C}_k^R_k an integral factor

$$\int {\displaystyle \frac{d}{dt}\left[e^{\int \frac{1}{C_k{R}_s}}{V}_k\right]=\int \left[{\displaystyle \frac{V_{ref}}{C_{k}R}+{\displaystyle \frac{V_v}{C{R}_k}}}\right]e^{\int \frac{1}{C_k{R}_s}}}$$ (20)

$$V_k=V_{ref}{\displaystyle \frac{R_s}{R}+V_v{\displaystyle \frac{R_s}{R_k}+X{e}^{\frac{-t}{C_k{R}_s}}}}$$ (21)

Taking initial condition V_K (0) = V_L. and substitute X in (21).

$$V_k=V_L{e}^{\frac{-t}{C{R}_f}}+V_{ref}{\displaystyle \frac{R_s}{R}\left(1-e^{\frac{-t}{C_k{R}_s}}\right)+V_v{\displaystyle \frac{R_a}{R_k}\left(1-e^{\frac{-t}{C_k{R}_s}}\right)}}$$ (22)

To ensure that the comparator state is inverted, it is compulsory that V_K> V_H. By putting V_K= V_H, t_off can be obtained

$$t_{off}=C_k{R}_s{\displaystyle \frac{V_H-V_L}{V_H-V_{ref}{\displaystyle \frac{R_s}{R}-V_v{\displaystyle \frac{R_s}{R_k}}}}}$$ (23)

(17) and (23) show on- and off-time expressions respectively. The frequency and duty cycle can be evaluated by further solving these equations. T = t_on + t_off is the total period and frequency can be obtained from f = 1/T.

$$f={\displaystyle \frac{\left(V_H-V_{ref}{\displaystyle \frac{R_s}{R}-V_v{\displaystyle \frac{R_s}{R_k}}}\right)\left(V_H-V_{ref}{\displaystyle \frac{R_s}{R}+V_v{\displaystyle \frac{R_s}{R_k}}}\right)}{CkRS(VH-VL)\left(VH+VL-2VREF{\displaystyle \frac{RS}{R}}\right)}}$$ (24)

The duty cycle is obtained from D = t_on/T.

$$D={\displaystyle \frac{V_L-V_{ref}{\displaystyle \frac{R_s}{R}+V_v{\displaystyle \frac{R_s}{R_k}}}}{V_H+V_L-2V_{ref}{\displaystyle \frac{R_s}{R}}}}$$ (25)

From (25) we determine the threshold limit of the duty cycle in the proposed converter circuit. The variation in duty cycle is restricted from 0.445 to 0.5 with 20–40 MPPT range input PV voltages.

Pole zero map of the proposed controller circuit

The transfer function of the proposed controller circuit with PI control compensation at the output channel is mathematically expressed in (26). Figure 8 shows the PZ map of the proposed SIMO circuit having pole and zero on the left half plane of the PZ map. This shows the stability and underdamped response of the system.

$${\displaystyle \frac{V_o(s)}{V_i(s)}={\displaystyle \frac{(k_{p}R)+(R.k_i/s)}{s^{2}cL+sRC+k_{p}R+R.k_i/s}}}$$ (26)

Scalability of the proposed model

The scalability of the proposed SIMO with the N output channel is investigated in this paper. For scalability, it is assumed that the circuit is operated under balanced loading conditions and that all channels have equal power delivered through the inductor. For each output, the inductor current (or input current) is

$$I_{in}=I_l={\displaystyle \frac{1}{T}{\int }_{n{T}_s}^{(n+D_{on)}{T}_s}{I}_{l}d(t)}$$ (27)

The value of the duty cycle is identical for each output. Therefore, (26) can be written as

$$I_{l.}={\displaystyle \frac{V_{in}{D}^2{T}_s^2+2DL{T}_s}{2LT}}$$ (28)

Assuming that SIMO is ideal and lossless. The input power expression is

$$P_i=V_{in}{I}_l={\displaystyle \frac{V{n}_i^2{D}^2{T}_s^2+2V_{i}DL{T}_s}{2LT}}$$ (29)

Input and output power is the same in ideal condition. The mathematical expression for output power is

$$P_o=V_{in}{I}_l={\displaystyle \frac{V_{in}^2{D}^2{T}_s^2+2V_{in}DL{T}_s}{2LT}}$$ (30)

Rearrange (30) and put T = mT.

$$2L{P}_o{m}^2-2V_{in}DLm-V_{in}^2{D}^{2}T$$ (31)

Taking discriminant $\mathrm{\Delta }$ of (31)

$$\mathrm{\Delta }=4D^2{V}_{in}^2(L^2+2L{P}_{o}T)>0$$ (32)

By taking the discriminant $\mathrm{\Delta }$ positive value, the two real roots of the (31) are

$$r_a{r}_b={\displaystyle \frac{D{V}_{in}\left(1\pm \sqrt{1+{\displaystyle \frac{2P_{o}T}{L}}}\right)}{2P_o}}$$ (33)

The maximum number of output channels is always a positive integer. Therefore, in (32) only positive roots are considered. ⁵²

$$m=floor.\left({\displaystyle \frac{D{V}_{in}\left(1\pm \sqrt{1+{\displaystyle \frac{2P_{o}T}{L}}}\right)}{2P_o}}\right)$$ (34)

By using volt second balance ⁵² the duty cycle in mode 1 and mode 2 is expressed as

$$m_{1}D{T}_s=m_2(1-D)T_s$$ (35)

During on state of a switch, the mathematical expression for the duty cycle is

$$D={\displaystyle \frac{V_{0ut}}{V_{in}+V_{out}}}$$ (36)

Substitute (36) in (34), we get

$$m=floor\left({\displaystyle \frac{Vout{V}_{in}\left(1\pm \sqrt{1+{\displaystyle \frac{2P_{o}T}{L}}}\right)}{2(Vout+Vin)P_o}}\right)$$ (37)

Assume that each output channel contains only resistive load, therefore, the expression for real output power can be written as

$$P_o={\displaystyle \frac{V^2}{R}}$$ (38)

By putting V_i= 30 V, R_L= 50Ω, and f = 20 kHz the analytical numbers of output channels for power are shown in Figure 9. The number of output channels can be increased by the trade-off power output at each channel.The Figure 10 provides power losses of different components at various duty cycles.

Figure 9.

The number of output channels with the power output.

Figure 10.

Power losses of different components at various duty cycles.

Semiconductor stresses and power loss analysis

Voltage stress:

By applying the voltage second balance law, the semiconductor switch voltage stress in the proposed SIMO DC converter can be written as

$$V_{D1}={\displaystyle \frac{V_i}{1-D}}$$ (39)

$$V_{Sw}={\displaystyle \frac{V_i}{1-D}}$$ (40)

Current stress:

In order to evaluate the current analysis and investigate the current stress of semiconductor devices, a bounded resonance (0.51T_R= DT_s) is considered. The average and the maximal values of the magnetizing inductor are also assumed same. Since the filter capacitors are series connected, the load current I_L is equal to the switching current at each output channel. Table 3 shows the current and voltage stress of the semiconductor. By using the charge balance on the series capacitor, the current expression can be written as

$$I_i\cong I_{i(avg)}=D{I}_o$$ (41)

Table 3.

Semiconductor stresses in the proposed circuit.

	Voltage stress	Current stress
Smain	Vi	IL
S1, D1	Vo1	Io
S2, D2	Vo2	Io
S3, D3	Vo3	Io

The semiconductor switches current in turned off operation is flowing through the diode and approximately equal to the current in (40). The maximum current through the series-connected diode and load resistor can be calculated by

$$I_{Ds}=I_{S(peak)}\cong {\displaystyle \frac{M+n{I}_o}{2n}}$$ (42)

Where n is inductor turns and M is voltage gain. The switching current can be expressed as

$$I_s=I_{in}+I_L+{\displaystyle \frac{M+n\pi T_s{I}_o}{2n}}$$ (43)

For boundary-operated condition, the 0.51T_R= DT_S peak switching current in terms of the duty cycle can be written as

$$I_{s(max)}\cong {\displaystyle \frac{((3-\pi )n+1)D+n\pi }{2D(1-D)}}$$ (44)

From (39), (40), and (44), when we increase the duty cycle from 0 to 1, the voltage and current stress or peak current across the switch also increases. The lowest value of current stress through the semiconductor main switch and output switches S₁, S₂, and S₃ can obtained in 0.4–0.55 duty cycle range. At the output of each channel, a series connected capacitor circuit with ESR and RC Snubber circuits across the semiconductor is used to minimize the stresses.

Power loss analysis:

The power losses in the proposed circuit configuration can be divided into three types: (a) switch loss, (b) diode switching loss, and (c) ESR loss in capacitor. Switch loss includes both conduction and switching power losses. Conduction losses can be evaluated by

$$P_{cond.}=R_{ds(On)}\times I^2$$ (45)

Switching losses can be calculated by

$$P_{switch}=({\displaystyle \frac{1}{2}{V}_s\times I_s\times t_{delay})f_{sw}}$$ (46)

Power loss in the diode depends on the voltage across the diode and current passing through it to the rest of the circuit element. So loss in diode can be written as

$$P_{Diode}=V_F\times I_{(D)}$$ (47)

Power loss due to the parasitic elements can be calculated by

$$P_{{}_C}=ESR\times I_c^2$$ (48)

Table 4 presents the numerical calculations of all the above losses of the proposed converter circuit

Table 4.

various losses in the proposed converter.

Operating duty cycle	D = 0.4	D = 0.5	D = 0.6
Ploss (conduction)	1.089W	0.87 W	0.76W
Ploss (Switch)	0.51W	0.29W	0.34W
Ploss(Diode)	1.12W	1.12W	1.12W
Ploss (Capacitor)	0.75W	0.68W	0.82W

Simulation results and discussion

To validate the result of the proposed PV-sourced SIMO DC converter, three different levels of irradiance are provided by the PV array. The circuit parameters are listed in Table 5.

Table 5.

Circuit parameters.

Circuit parameters	Value
Input filter	100µF
Inductor	500µH
Switches (Smain, S1, S2, and S3)	IRF540
Vout	42 V – 50V
Vin	25V-29V
Output current	2.5A
Switching frequency	20KHz
Diode	IN4007
Filters (output at each channel) with ESR	680µF, 20mΩ
Resistors (R1, R2, and R3)	10Ω
Voltage sensor gain	0.24
Snubber capacitor	10nf
Snubber Resistance	5Ω

When the irradiance level has changed, the characteristics of the PV panel vary due to the tracking of optimal MPP. Figure 11 shows theV_PV and I_PV characteristics of PV cells.

Figure 11.

(a) V_PV characteristics at different irradiance levels and (b) I_PV characteristics at a different irradiance level.

Irradiance level varies with respect to time and for each change in irradiance level the algorithm tries to achieve the MPP rapidly. Figure 12 illustrates the variation in incremental conductance by the irradiance level. The negative output value of instantaneous conductance fluctuates near the change in irradiance and approaches zero when the maximum power point is achieved.

Figure 12.

Incremental conductance and instantaneous conductance.

To examine the characteristics of the MPPT algorithm with a balanced loading condition, different irradiance levels are provided as a source at the PV array input. Figure 13 shows the irradiance and variance in the duty cycle due to MPP tracking. When irradiance from the PV source varies, the SIMO boost DC converter changes its duty cycle in order to maintain the desired voltage level at the output channel. The Duty cycle varies from 44.3% (minimum value) to 50% (maximum value) in different irradiance levels.

Figure 13.

(a) Irradiance level provided to the PV array and (b) variance in the duty cycle due to MPP.

MPP: maximum power point; PV: photovoltaic.

With the change in the irradiance level, the algorithm tries to locate another local MPP for the circuit and stabilizes the output for this MPP. If the same irradiance level control values are provided to all three stages, the output sequence for turning MOSFETs ON/OFF must be equal to obtain the same voltages. In the controller circuit, the inductor current is compared to any given threshold value for different outputs at various output stages. If the threshold value for all three output stages is zero and in a generic view approaches zero, this condition shows the balanced loading condition and the output voltage amplitude of all outputs connected to the circuit must be equal to (49.91 V) as shown in Figure 14.

Figure 14.

Balance loading condition: (a) first output stage voltages, (b) second output stage voltages, and (c) third output stage voltages.

In the unbalanced loading condition case, reference voltages or threshold voltages are different for each case. Therefore, the output voltages for three distinct outputs are unequal in magnitude irrespective of the equal value of resistance connected as load. Figure 15 shows the unbalanced loading effect of the SIMO converter circuit entirely controlled by the hysteretic-based system. At different irradiance levels, V_OUT1, V_OUT2, and V_OUT3 are 49.91 V, 46.66 V, and 42.11 V respectively.

Figure 15.

Output voltages in unbalanced loading condition.

When changing behavior of irradiance is applied at the input of the PV array, it alters the flow of current towards the boost converter input. The variation in irradiance directly affects the output power of the circuit. The response time of the controller circuit is significantly high. When applied input is changed, the MPPT algorithm efficiently locates the maximum power point. The DCS-based hysteretic controller quickly variates the duty cycle to change the voltage magnitude accordingly. The rise time is high and the controller achieves the output voltage level with less (2%) steady-state error. Figure 16 illustrates the behavior of output power. At 1000 W/m² irradiance, the output power is 100.5 W and slightly decreases to 21.7 W with decreasing behavior of irradiance from 1000 to 250 W/m². The efficiency of the proposed DCS-based single inductor multiple output DC–DC converters is 90.90%.

Figure 16.

Output power at various irradiances.

To assess the scalability of the proposed converter circuit, we evaluate the model under three, four, and six output channel (load) conditions. As the number of channels increased, the time slot for each switch connected to an output channel decreased, resulting in a significant reduction in PV output current and power supplied to the load. This phenomenon is also mathematically explained in section 4. When we used three output channels under 1000 W/m² irradiance, the output current was 3.9A with a power of 100.5 W. However, these values slightly decreased to 0.95A and 21.7 W respectively, due to the decreasing behavior of irradiance from 1000 to 250 W/m². Under four output load conditions at 1000 W/m² irradiance, the PV current and power were reduced to 3.5A and 85.5 W respectively. Similarly, under 250 W/m² irradiance, these values further decreased to 0.82A and 17.7 W. In the case of six output load conditions, the output power and current experienced a further decrease. At 1000 W/m² irradiance, the PV current and power were 3A and 80.5 W respectively, while under 250 W/m² irradiance, they were 0.68A and 9.7 W.

The above statistics demonstrate that as the connected load on the output increases, the power and current provided by the PV module decrease. There is a trade-off between the number of output channels and the power required at the output. The authors suggested that a converter design based on three output channels is the optimal solution to meet the requirements of the digital electronic industry. Figures 17 and 18 illustrate the output power and PV current for the cases of three, four, and six output channels connected to the proposed DC Converter circuit.

Figure 17.

Output power at various irradiances in three, four, and six channel conditions.

Figure 18.

I_PV at various irradiances in three, four, and six output channel conditions.

Table 6 consists of a power stage comparison between the proposed SIMO DC converter with previous literature (Zheng et al.,28 Jung et al.,30 Lee et al.,31 Chen et al. ³² Waters et al.,34 Shi et al.,35 Johari et al., ³⁶ Güler and Irmak, ³⁷ Zhang and Ma,41. Lee et al. ⁵² ) in the scenario of the class of power amplifier, no. of switches, controller complexity, driver circuit, efficiency, and power output available at each output channel. As compared in Table 6, the proposed SIMO DC converter has a smaller number of power switches and other passive equipment. The proposed SIMO topology has higher output power (100.7 W), fast response time, less controller complexity, only one driver circuit, and supports the scalability of three-channel to multichannel configuration.

Table 6.

Comparison of the proposed SIMO with the existing literature.

Reference	Power amplifier	Controller complexity	Response time	Switching frequency	Driver circuits	No. of switches	Output power	Efficiency
28	Class E	Medium	Slow	2 MHz	3	2	6 W	84%
30	SIMO	High	Medium	25 KHz	2	9	462 mW	89.2%
31	DIDO	High	Slow	10 KHz	2	6	<15 W	92.5%
32	SIMO	Low	Fast	25 KHz	1	4	12 W	91.9%
34	Class E	High	Slow	20 KHz	1	2	5 W	82%
35	Class D	Low	Slow	10 KHz	2	24	18 W	78%
36	Class A	Low	Medium	10 KHz	2	8	<1 W	80%
37	SITO	High	Medium	5–10 KHz	2	6	195 W	87%
41	SITO	Low	Slow	500 KHz	2	6	2.4 W	88.75%
52	SITO	Low	Fast	80 KHz	2	9	8.4 W	84.6%
This work	SITO	Low	Fast	20 KHz	1	4	100.7, 21.7 W	90.90%

SITO: single inductor three output; SIMO: Single Inductor Multiple Output.

Conclusion

In this article, a SITO DC converter operated in continuous conduction mode is proposed which enables a DC–DC power conversion from a PV source to multiple independently controlled DC output voltage channels. A DCS-based hysteretic controller circuit is used to control the flow of power from the source to three distinct output channels. It is capable of independent power control at each output channel with fast response time, lesser switch count, and better efficiency. The number of switches required for this SITO circuit network is N + 1, where N is the number of outputs (three in this proposed work). By adjusting the threshold limit for inductor current, balanced loading condition as well as unbalanced loading condition with the same and distinct output level for each channel is simulated. In the proposed model, under balanced loading conditions, the output voltage amplitude of all outputs is 49.91 V. However, in an unbalanced loading scenario, the voltages V_OUT1, V_OUT2, and V_OUT3 are 49.91 V, 46.66 V, and 42.11 V, respectively with the same resistive load. At 1000 W/m² irradiance, the output power is 100.5 W and decreases to 21.7 W with decreasing irradiance behavior from 1000 to 250 W/m². The duty cycle variation is 44.5% to 50% under different irradiance levels. The peak efficiency of the proposed model is 90.90%. The current model is useful for a multi-transmitter wireless power transfer, digital module, computer hardware applications, space crafts, and uninterruptable supply sources, where the dynamic supply level is the key requirement. The simulation results illustrate the controller design effectiveness for the SIMO DC model among various output channels. The PV array is implemented in the proposed model without the partial shading effect on the PV cell. Investigation of the partial shading effect on the PV array with this model is recommended for future work. The proposed SIMO model may be implemented on hardware structure for real-time verification scenarios in future applications.

Author biographies

Mudassar Usman is an Electrical Engineer. He received a master's degree in electrical engineering from Bahria University Islamabad, Pakistan with specialization in power systems. His research interests include renewable energy, Power Electronics and control systems. Currently he is working as Lecturer in the department of Electrical, Electronics and Telecommunication Engineering at University of Engineering and Technology Lahore, Pakistan.

Furqan Asghar received the BS degree in Electrical Engineering from The University of Faisalabad and M.S. leading to Ph.D. degree in Electrical, Electronics and Control Engineering from Kunsan National University, South Korea in 2018. From 2014 to 2018, he was a Research Assistant with the Factory Automation and Intelligent Control Laboratory (FAIC), Korea. Since July 2018, he has been working as an Assistant Professor in the Department of Energy Systems Engineering, University of Agriculture, Faisalabad.

Muhammad Rameez Javed received BSc and MSc degree in Electrical Engineering from University of Engineering and Technology, Taxila. He is currently serving as Lecturer in University of Engineering and Technology, Lahore since 2017.

Umar Siddique Virk received his BSc degree in Mechatronics & Control Engineering from University of Engineering and Technology, Lahore, Pakistan in 2015. He later received his M.Sc. degree in Mechanical Engineering from The Hong Kong University of Science and Technology (HKUST), Hong Kong in 2016. He joined the Department of Mechanical, Mechatronics & Manufacturing Engineering, UET Lahore (Faisalabad Campus) as Lecturer in September 2016.

Muhammad Yasir Jamal received his BS and MS in Electrical Engineering from UET Lahore in 2009 and 2015 respectively and PhD from The University of Hong Kong in January 2021. He joined Faisalabad Campus of UET Lahore in 2009.

Aashir Waleed received his BS and MS degree in Electrical Engineering from University of Engineering and Technology, Lahore, Pakistan in 2009 and 2014 respectively. He joined UET Lahore (FSD campus) in September 2009. He finished his Ph.D. studies in Electronic and Computer Engineering with energy concentration specialization from The Hong Kong University of Science and Technology (HKUST), Hong Kong in 2017. He is currently working as an Assistant Professor in UET Lahore.