**About the Special Issue Editors**

**Teen-Hang Meen** was born in Tainan, Taiwan, in 1967. He received his BSc from the Department of Electrical Engineering of National Cheng Kung University (NCKU), Tainan, Taiwan, in 1989, and his MSc and PhD from the Institute of Electrical Engineering, National Sun Yat-Sen University (NSYSU), Kaohsiung, Taiwan, in 1991 and 1994, respectively. He was the chairman of the Department of Electronic Engineering of National Formosa University, Yunlin, Taiwan, from 2005 to 2011. He recevied the Excellent Research Award from National Formosa University in 2008 and 2014. Currently, he is a Distinguished Professor with the Department of Electronic Engineering, National Formosa University, Yunlin, Taiwan. He is also the president of International Institute of Knowledge Innovation and Invention (IIKII) and the chair of the IEEE Tainan Section Sensors Council. He has published more than 100 SCI, SSCI and EI papers in recent years.

**Wenbing Zhao** is a Full Professor of Electrical Engineering and Computer Science (EECS) at Cleveland State University (CSU), Cleveland, Ohio, USA. He obtained his BSc and MSc in Physics from Peking University, Beijing, China, in 1990 and 1993, respectively, and his MSc and PhD in Electrical and Computer Engineering from the University of California, Santa Barbara, in 1998 and 2002, respectively. Prior to joining Cleveland State University in 2004, Dr. Zhao worked as a post-doctoral researcher at the University of California, Santa Barbara, and as Senior Research Engineer/Chief Architect at Eternal Systems, Inc. (now dissolved), which he co-founded in 2000. Dr. Zhao has conducted research in several different areas, including fault tolerance computing, computer and network security, smart and connected healthcare, machine learning, Internet of Things, quantum optics and superconducting physics. Currently, his research focuses on smart and connected healthcare. Dr. Zhao's recent research was funded by the National Science Foundation, the Ohio Bureau of Workers' Compensation, the Ohio Department of Higher Education, the Ohio Advancement Office (via the Ohio Third Frontier Program), the US Department of Transportation (via CSU Transportation Center), Cleveland State University, and private companies.

**Cheng-Fu Yang** was born in Taiwan in 1964. Yang received his MSc and PhD in 1988 and 1993, respectively, from the Department of Electrical Engineering of Cheng Kung University, Tainan, Taiwan. Yang entered professional academic life in 1993 with the Department of Electronic Engineering, Chinese Air Force Academy, and then, in 2000, as a professor. In 2004 he joined the faculty of the National University of Kaohsiung (NUK). Currently, he is a Professor of Chemical and Materials Engineering at NUK. He received the Outstanding Contribution Awards of the Chinese Ceramic Society in 2009. In 2010, he was the first (and only) person to receive the title of Distinguished Professor from NUK. In 2014, he became the Fellow of Taiwanese Institute of Knowledge Innovation (TIKI) and in 2015 the Fellow of the Institution of Engineering and Technology (IET). He was also labeled the Mingjiang Scholar and Chair Inviting Professor of Jimei University, Xiamen, Fujian, China.

### *Editorial* **Special Issue on Selected Papers from IEEE ICKII 2019**

**Teen-Hang Meen 1,\*, Wenbing Zhao <sup>2</sup> and Cheng-Fu Yang 3,\***


Received: 23 March 2020; Accepted: 3 April 2020; Published: 14 April 2020

**Abstract:** This Special Issue on "Selected papers from IEEE ICKII 2019" selected 13 excellent papers from 260 papers presented in IEEE ICKII 2019 on topics in energies. The fields include: energy fundamentals, energy sources and energy carriers, energy exploration, intermediate and final energy use, energy conversion systems, and energy research and development. The main goal of this Special Isue is to discover new scientific knowledge relevant to the topic of energies.

**Keywords:** energy sources and energy carriers; energy conversion systems; energy research and development

The 2nd IEEE International Conference on Knowledge Innovation and Invention 2019 (IEEE ICKII 2019) was held in Seoul, South Korea on 12–15 July 2019. It provided a unified communication platform for researchers in the topics of information technology, innovation design, communication science and engineering, industrial design, creative design, applied mathematics, computer science, electrical and electronic engineering, mechanical and automation engineering, green technology and architecture engineering, material science, and other related fields. This Special Issue on "Selected papers from IEEE ICKII 2019" selected 13 excellent papers from 260 papers presented in IEEE ICKII 2019 on topics in energies. The fields include: energy fundamentals, energy sources and energy carriers, energy exploration, intermediate and final energy use, energy conversion systems, and energy research and development. The main goal of this Special Issue is to discover new scientific knowledge relevant to the topic of energies.

#### **The Topic of Energies and its Applications**

This Special Issue on "Selected papers from IEEE ICKII 2019" selected 13 excellent papers from 260 papers presented in IEEE ICKII 2019 on topics in energies. The published papers are introduced as follows:

Hwang et al. reported on "Optimization and Application for Hydraulic Electric Hybrid Vehicle" [1]. In this research, the rule-based control strategy was implemented as the energy distribution management strategy first, and then the genetic algorithm was utilized to conduct global optimization strategy analysis. The results from the genetic algorithm were employed to modify the rule-based control strategy to improve the electricity economic performance of the vehicle. The simulation results show that the electricity economic performance of the designed hydraulic hybrid vehicle was improved by 36.51% compared to that of a pure electric vehicle. The performance of energy consumption after genetic algorithm optimization was improved by 43.65%.

Liao reported "A Step Up/Down Power-Factor-Correction Converter with Modified Dual Loop Control" [2]. In this study, A step up/down AC/DC converter with a modified dual loop control is proposed. The step up/down AC/DC converter features the bridgeless characteristic which can reduce bridge–diode conduction losses. Based on the step up/down AC/DC converter, a modified dual loop control scheme is proposed to achieve input current shaping and output voltage regulation. Fewer components are needed compared with the traditional bridge and bridgeless step up/down AC/DC converters. In addition, the intermediate capacitor voltage stress can be reduced. Furthermore, the top and bottom switches still have a zero-voltage turn-on function during the negative and positive half-line cycle, respectively. Hence, the thermal stresses can also be reduced and balanced. Simulation and experimental results are provided to verify the validity of the proposed step up/down AC/DC converter and its control scheme.

Wu et al., reported "The Optimal Control of Fuel Consumption for a Heavy-Duty Motorcycle with Three Power Sources Using Hardware-in-the-Loop Simulation" [3]. This study presents a simulation platform for a hybrid electric motorcycle with an engine, a driving motor, and an integrated starter generator (ISG) as three power sources. This platform also consists of the driving cycle, driver, lithium-ion battery, continuously variable transmission (CVT), motorcycle dynamics, and energy management system models. Two Arduino DUE microcontrollers integrated with the required circuit to process analog-to-digital signal conversion for input and output are utilized to carry out a hardware-in-the-loop (HIL) simulation. A driving cycle called the worldwide motorcycle test cycle (WMTC) is used for evaluating the performance characteristics and response relationship among subsystems. Control strategies called rule-based control (RBC) and equivalent consumption minimization strategy (ECMS) are simulated and compared with the purely engine-driven operation. The results show that the improvement percentages for equivalent fuel consumption and energy consumption for RBC and ECMS using the pure software simulation were 17.74%/18.50% and 42.77%/44.22% respectively, while those with HIL were 18.16%/18.82% and 42.73%/44.10%, respectively.

Tsai et al., reported "Optimal Configuration with Capacity Analysis of a Hybrid Renewable Energy and Storage System for an Island Application" [4]. This study uses a Philippine offshore island to optimize the capacity configuration of a hybrid energy system (HES). A thorough investigation was performed to understand the operating status of existing diesel generator sets and load power consumption, and to collect the statistics of meteorological data and economic data. Using the Hybrid Optimization Models for Energy Resources (HOMER) software we simulated and analyzed the techno-economics of different power supply systems containing stand-alone diesel systems, photovoltaic (PV)-diesel HES, wind-diesel HES, PV-wind-diesel HES, PV-diesel-storage HES, wind-diesel-storage HES, and PV-wind-diesel-storage HES. In addition to the lowest cost of energy (COE), capital cost, fuel saving and occupied area, the study also uses entropy weight and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to evaluate the optimal capacity configuration. The proposed method can also be applied to design hybrid renewable energy systems for other off-grid areas.

Li et al., reported "Integrated Analysis of Influence of Multiple Factors on Transmission Efficiency of Loader Drive Axle" [5]. In this study, a loader drive axle digital model was built using 3D commercial software. On the basis of this model, the transmission efficiency of the main reducing gear, the differential planetary mechanism, and the wheel planetary reducing gear of the loader drive axle were studied. The functional relationship of the transmission efficiency of the loader drive axle was obtained, including multiple factors: the mesh friction coefficient, the mesh power loss coefficient, the normal pressure angle, the helix angle, the offset amount, the speed ratio, the gear ratio, and the characteristic parameters. This revealed the influence law of the loader drive axle by the mesh friction coefficient, mesh power loss coefficient, and speed ratio. The research results showed that the transmission efficiency of the loader drive axle increased with the speed ratio, decreased when the mesh friction coefficient and the mesh power loss coefficient increased, and that there was a greater influence difference in the transmission efficiency of the loader drive axle.

Yu et al., reported "Management and Distribution Strategies for Dynamic Power in a Ship's Micro-Grid System Based on Photovoltaic Cell, Diesel Generator, and Lithium Battery" [6]. This study examines the stable parallel operation of a ship's micro-grid system through a dynamic power

management strategy involving a step change in load. With cruise ships in mind, the authors construct a micro-grid system consisting of photovoltaics (PV), a diesel generator (DG), and a lithium battery, and establish a corresponding simulation model. The authors analyze the system's operating characteristics under different working conditions and present the mechanisms that influence the power quality of the ship's micro-grid system. Based on an analysis of the power distribution requirements under different working conditions, the authors design a power allocation strategy for the micro-grid system. Next the authors propose an optimization allocation strategy for dynamic power based on fuzzy control and a load current feed-forward method, and finally, the authors simulate the whole system. Through this study, the authors prove that the proposed power management strategy not only verifies the feasibility and correctness of the ship's micro-grid structure and control strategy, but also greatly improves the reliability and stability of the ship's operation.

Lin et al., reported "Analysis of Energy Flux Vector on Natural Convection Heat Transfer in Porous Wavy-Wall Square Cavity with Partially-Heated Surface" [7]. This study utilizes the energy-flux-vector method to analyze the heat transfer characteristics of natural convection in a wavy-wall porous square cavity with a partially heated bottom surface. The effects of the modified Darcy number, modified Rayleigh number, modified Prandtl number, and length of the partially heated bottom surface on the energy-flux-vector distribution and mean Nusselt number are examined. The results show that when a low modified Darcy number with any value of modified Rayleigh number is given, the recirculation regions are not formed in the energy-flux-vector distribution within the porous cavity. Therefore, a low mean Nusselt number is presented. The recirculation regions still do not form, and thus the mean Nusselt number has a low value when a low modified Darcy number with a high modified Rayleigh number is given.

Luo et al., reported "Performance Enhancement of Hybrid Solid Desiccant Cooling Systems by Integrating Solar Water Collectors in Taiwan" [8]. In this study, a solar-assisted hybrid Solid Desiccant Cooling System (SDCS) was developed, in which solar-heated water is used as an additional heat source for the regeneration process, in addition to recovering heat from the condenser of an integrated heat pump. A solar thermal collector sub-system is used to generate solar regenerated water. Experiments were conducted in the typically hot and humid weather of Taichung, Taiwan, from the spring to fall seasons. The experimental results show that the overall performance of the system in terms of power consumption can be enhanced by approximately 10% by integrating a solar-heated water heat exchanger, in comparison to the hybrid SDCS system. The results show that the system performs better when the outdoor humidity ratio is high. In addition, regarding the effect of ambient temperature on the coefficient of performance (COP) of the systems, a critical value of outdoor temperature exists. The COP of the systems gradually rises with the increase in ambient temperature. However, when the ambient temperature is greater than the critical value, the COP gradually decreases with the increase in ambient temperature. The critical outdoor temperature of the hybrid SDCS is from 26 to 27 ◦C, and the critical temperature of the solar-assisted hybrid SDCS is from 27 to 30 ◦C.

Hsueh et al. reported "Condition Monitor System for Rotation Machine by CNN with Recurrence Plot" [9]. In this paper, the authors introduce an effective framework for the fault diagnosis of 3-phase induction motors. The proposed framework mainly consists of two parts. The first part explains the preprocessing method, in which the time-series data signals are converted into two-dimensional (2D) images. The preprocessing method generates recurrence plots (RP), which represent the transformation of time-series data such as 3-phase current signals into 2D texture images. The second part of the paper explains how the proposed convolutional neural network (CNN) extracts the robust features to diagnose the induction motor's fault conditions by classifying the images. The generated RP images are considered as input for the proposed CNN in the texture image recognition task. The proposed framework is tested on the dataset collected from different 3-phase induction motors working with different failure modes. The experimental results of the proposed framework show its competitive performance over traditional methodologies and other machine learning methods.

Chen et al., reported "Design of a Logistics System with Privacy and Lightweight Verification" [10]. This study designs a secure logistics system, with anonymous and lightweight verification, in order to meet the following requirements: mutual authentication, non-repudiation, anonymity, integrity, and a low overhead for the logistics environment. A buyer could check the goods and know if the parcel has been exchanged by a malicious person. Moreover, the proposed scheme not only presents a solution to meet the logistics system's requirements, but also to reduce both computational and communication costs.

Chang et al. reported on the "Current Control of the Permanent-Magnet Synchronous Generator Using Interval Type-2 T-S Fuzzy Systems" [11]. In this study, the current control of the permanent-magnet synchronous generator (PMSG) using an interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems is designed and implemented. PMSG is an energy conversion unit widely used in wind energy generation systems and energy storage systems. Its performance is determined by the current control approach. IT2 T-S fuzzy systems are implemented to deal with the nonlinearity of a PMSG system in this paper. First, the IT2 T-S fuzzy model of a PMSG is obtained. Second, the IT2 T-S fuzzy controller is designed based on the concept of parallel distributed compensation (PDC). Next, the stability analysis can be conducted through the Lyapunov theorem. Accordingly, the stability conditions of the closed-loop system are expressed in Linear Matrix Inequality (LMI) form. The AC power from a PMSG is converted to DC power via a three-phase six-switch full bridge converter. The six-switch full bridge converter is controlled by the proposed IT2 T-S fuzzy controller. The analog-to-digital (ADC) conversion, rotor position calculation and duty ratio determination are digitally accomplished by the microcontroller. Finally, the simulation and experimental results verify the performance of the proposed current control.

Lin et al., reported "The Optimal Energy Dispatch of Cogeneration Systems in a Liberty Market" [12]. This paper investigates the cogeneration systems of industrial users and collects fuel consumption data and data concerning the steam output of boilers. On the basis of the relation between the fuel enthalpy and steam output, the Least Squares Support Vector Machine (LSSVM) is used to derive boiler and turbine Input/Output (I/O) operation models to provide fuel cost functions. The CO2 emission of pollutants generated by various types of units is also calculated. The objective function is formulated as a maximal profit model that includes profit from steam sold, profit from electricity sold, fuel costs, costs of exhausting carbon, wheeling costs, and water costs. By considering Time-of-Use (TOU) and carbon trading prices, the profits of a cogeneration system in different scenarios are evaluated. By integrating the Ant Colony Optimization (ACO) and Genetic Algorithm (GA), an Enhanced ACO (EACO) is proposed to come up with the most efficient model. The EACO uses a crossover and mutation mechanism to alleviate the local optimal solution problem and to seek a system that offers an overall global solution using competition and selection procedures. The results show that these mechanisms provide a good direction for the energy trading operations of a cogeneration system. This approach also provides a better guide for operation dispatch to use in determining the benefits accounting for both cost and the environment in a liberty market.

Hsu et al. reported "Article Numerical Simulation of Crystalline Silicon Heterojunction Solar Cells with Different p-Type a-SiOx Window Layer" [13]. In this study, p-type amorphous silicon oxide (a-SiOx) films are deposited using a radio-frequency, inductively coupled plasma chemical vapor deposition system. Effects of the CO2 gas flow rate on film properties and crystalline silicon heterojunction (HJ) solar cell performance are investigated. The experimental results show that the band gap of the a-SiOx film can reach 2.1 eV at CO2 flow rate of 10 standard cubic centimeters per minute (sccm), but the conductivity of the film deteriorates. In the device simulation, the transparent conducting oxide and contact resistance are not taken into account. The electrodes are assumed to be perfectly conductive and transparent. The simulation result shows that there is a tradeoff between the increase in the band gap and the reduction in conductivity at an increasing CO2 flow rate, and the balance occurs at the flow rate of six sccm, corresponding to a band gap of 1.95 eV, an oxygen content of 34%, and a conductivity of 3.3 S/cm. The best simulated conversion efficiency is 25.58%, with an open-circuit voltage of 741 mV, a short-circuit current density of 42.3 mA/cm2, and a fill factor of 0.816%. **Author Contributions:** Writing and reviewing all papers, T.-H.M.; English editing, W.Z.; checking and correcting the manuscript, C.-F.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The guest editors would like to thank the authors for their contributions to this Special Issue and all the reviewers for their constructive reviews. We are also grateful to Chloe Wu, the Assistant Editor of *Energies*, for her time and efforts in the publication of this special issue for Energies.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Optimization and Application for Hydraulic Electric Hybrid Vehicle**

#### **Hsiu-Ying Hwang 1, Tian-Syung Lan 2,\* and Jia-Shiun Chen <sup>1</sup>**


Received: 27 November 2019; Accepted: 7 January 2020; Published: 9 January 2020

**Abstract:** Targeting the application of medium and heavy vehicles, a hydraulic electric hybrid vehicle (HEHV) was designed, and its energy management control strategy is discussed in this paper. Matlab/Simulink was applied to establish the pure electric vehicle and HEHV models, and backward simulation was adopted for the simulation, to get the variation of torque and battery state of charge (*SOC*) through New York City Cycle of the US Environmental Protection Agency (EPA NYCC). Based on the simulation, the energy management strategy was designed. In this research, the rule-based control strategy was implemented as the energy distribution management strategy first, and then the genetic algorithm was utilized to conduct global optimization strategy analysis. The results from the genetic algorithm were employed to modify the rule-based control strategy to improve the electricity economic performance of the vehicle. The simulation results show that the electricity economic performance of the designed hydraulic hybrid vehicle was improved by 36.51% compared to that of a pure electric vehicle. The performance of energy consumption after genetic algorithm optimization was improved by 43.65%.

**Keywords:** hydraulic hybrid vehicle; NYCC driving cycle; optimization; genetic algorithm

#### **1. Introduction**

The increasing demand for fossil fuels in different fields since the Industrial Revolution has led to increasing global CO2 emission and worsening global warming. Among all CO2 emission, the emission of means of transportation is only second to the industry. Now, the passenger vehicles all develop toward alternative energy, whereas the medium and heavy vehicles for goods transportation are still using gasoline or diesel engines as the main power source. With global warming and increasing stringent laws and regulations, they will definitely develop toward the same clean energy as the passenger vehicles. According to Navigant Research, the market survey company, hydraulic hybrid vehicles seldom known and underestimated in significance will gain a position in the heavy-duty truck market, and even can be expected to apply to the next generation of vehicles. Therefore, hydraulic electric hybrid vehicles (HEHV) will be the first choice for medium vehicles, heavy vehicles, and common carriers. With the DSHplus software simulation, Sokar [1] compared the fuel economy of the hydraulic transmission vehicles and hydraulic hybrid vehicles in urban and highway driving cycles. Chen [2] compared the energy consumption of different hydraulic hybrid configurations, and it showed the HEHV could have better energy efficiency over the pure EV system. The energy optimization can be divided to hardware optimization and control strategy optimization. As for hardware optimization, Ramakrishnan et al. [3] proposed the study on influence of system parameters in hydraulic system on the overall system power and established the series hydraulic hybrid power vehicle with LMS AMESim software. Change of size of accumulator and hydraulic motor/pump

and internal pressure greatly improves the output power of the whole system, which also reduces the fuel consumption and pollution of the hydraulic hybrid vehicles. The energy control strategy can be divided into two categories [4]: (1) rule-based strategy and (2) optimization-based strategy. For optimization strategy, Lu et al. [5] introduced the weighted-sum method and no-preference method to solve the multi-objective optimization problem of plug-in electric vehicles, and it was validated with ADVISOR software. Zeng et al. [6] proposed a different strategy, Equivalent Consumption Minimum Strategy (ECMS), to solve the optimization problem of PHEV, and the Simplified-ECMS strategy could effectively shorten the calculation time. Wang et al. [7] applied the Dynamic Programming for PHEV and received an approximately 20% improvement in fuel economy.

The rule-based control, featuring a smaller amount of calculation, is adopted by many studies, to design the energy management strategy. Yu et al. [8] developed a simulation model and rule-based control strategy for extended-range electric vehicle (E-REV) and showed that a small engine can be used to reduce the weight of vehicle and batteries of E-REV. Gao et al. [9] proposed two control strategies, thermostat and power follower. With dynamic programming, it showed that the thermostat control strategy optimized the operation of the internal combustion engine, and the power follower control strategy minimizes the battery-charging and -discharging operations. Konev et al. [10] developed a control strategy for series hybrid vehicle. The control strategy was to ensure gradual operation of the motor along the steady-state Optimal Operating Points Line (OOP-Line) in the engine speed–torque map, which could improve the efficiency of series hybrid vehicle. Liu et al. [11] developed a control strategy for a series hybrid vehicle which included two parts, constant *SOC* control, and driving-range optimization. Comparing to thermostat control strategy, the constant *SOC* control could have a longer driving range. Li et al. [12] proposed a fuzzy logic energy-management system, using the battery working state, which ensured that the engine would operate in the vicinity of its maximum fuel-efficiency region. The rule-based design is fast and easy and can be readily applied to real vehicle-control strategy. However, the rule-based control strategy is simple, so it cannot provide optimal power management to HEV in real time. Therefore, an optimization algorithm is required for rule-based control to improve the energy efficiency. Ho and Klong [13] introduced an optimization algorithm for series plug-in hybrid electric vehicles by utilizing the genetic algorithm (GA), which could determine the optimal driving patterns offline. Xu et al. [14] developed a fuzzy control strategy for parallel hybrid electric vehicle. The control strategy was adjusted with GA. It was verified that GA could effectively improve the efficiency of the engine and fuel consumption. Kaur et al. [15] proposed a control strategy to control the speed of a hybrid electric vehicle. The controller, which was using GA, could improve fuel economy and reduce pollution. Hu and Zhao [16] applied an adaptive based hybrid genetic algorithm to optimize the energy efficiency of parallel hybrid electric vehicles and presented the effectiveness of the hybrid genetic algorithm.

Therefore, global optimization, together with rule-based control method, are selected in this paper for medium and heavy vehicles in fixed driving route, to adjust the rule-based control strategy and improve the electricity economic performance of vehicles. The optimization approach selected in this paper is genetic algorithm (GA). With global optimization ability and probability optimization approach, GA can automatically obtain and instruct the optimized search space and adaptively adjust the search direction without the need of clear rules.

#### **2. Modeling**

In this study, Matlab/Simulink serves as the main simulation program, and backward simulation is used to establish the model. In order to compare the difference between an HEHV and a pure electric vehicle, subsystem models of the electric system are established, including models of electric motor, generator, and lithium ion battery. The subsystem models of hydraulic system include variable hydraulic motor/pump and accumulator models. The whole vehicle model can be divided into following subsystem models: (1) driver model; (2) vehicle dynamic model; (3) tyre and drive model; (4) power component element; and (5) energy storage component model. Driving cycle of the EPA NYCC is employed in this study to get the vehicle driving force, and then gear ratio of the transmission system is adopted to calculate the torque and speed needed for the motor. In HEHV, the electric motor does not function as the regenerative brake; rather the hydraulic pump is used for energy recovery. This is introduced in the following.

#### *2.1. Driver Model*

The EPA NYCC driving cycle for testing, as shown in Figure 1, is employed in this model. The total driving time is 599 s. The stop time accounts for 35.08% of the total driving time. The maximum speed and the average speed are 44.6 and 11.4 km/h, respectively.

**Figure 1.** United States Environmental Protection Agency New York City Cycle (US EPA NYCC) driving cycle.

#### *2.2. Vehicle Dynamic Model*

A vehicle dynamic model is applied to respond to the driving tractive effort and resistance needed for the simulation vehicle. The resistance included rolling resistance (*Rr*), aerodynamic resistance (*Ra*), grading resistance (*Rc*), and acceleration resistance *Rs*. The tractive effort for driving needed by the vehicle can be obtained with a vehicle dynamic model, which can be represented by Equation (1). The detailed calculation of resistance will be introduced in the following:

$$F\_t = R\_r + R\_a + R\_c + R\_s \tag{1}$$

#### 2.2.1. Rolling Resistance

During vehicle traveling, interaction force is produced in both radial and axial directions in the area where the wheels make contact with the ground, and there is also deformation between the tyre and the ground. The deformation process will be accompanied by a certain energy loss, regardless of whether or not it is in tyre or ground. This energy loss is the cause of rolling resistance during wheel turning. The rolling resistance can be represented by Equation (2), where μ*<sup>r</sup>* is the rolling resistance coefficient, and *W* is the vehicle weight:

$$R\_{\mathbf{r}} = R\_{\mathbf{r},\mathbf{A}} + R\_{\mathbf{r},\mathbf{B}} = \mu\_{\mathbf{r}} \cdot \mathbf{W} \tag{2}$$

#### 2.2.2. Aerodynamic Resistance

The aerodynamic resistance can be represented by Equation (3) as follows, where *CD* is the aerodynamic resistance coefficient, ρ is the air density, *Af* is the front area of the vehicle, *v* is the vehicle speed, and *vw* is the wind speed.

$$R\_{\mathfrak{a}} = \mathbb{C}\_{D} \cdot \frac{\rho}{2} \cdot A\_{f} \cdot \left(\upsilon - \upsilon\_{w}\right)^{2} \tag{3}$$

#### 2.2.3. Grading Resistance

During climbing, grading resistance is produced due to the influence of the vehicle weight. During downhill, this resistance becomes the driving force instead. It can be represented by Equation (4), where θ is the slope angle:

$$R\_{\mathbb{C}} = \mathcal{W}\text{sim}(\theta) \tag{4}$$

#### 2.2.4. Acceleration Resistance

The vehicle driving state covers the acceleration and deceleration for most of the time, except on highways, where it is fixed-speed driving. The required force for acceleration can be represented by Equation (5), where *a* is the acceleration, and *g* is the gravity acceleration:

$$R\_5 = W \cdot \frac{a}{\mathcal{S}} \tag{5}$$

#### *2.3. Tyre and Drive Model*

Vehicle dynamics is used to analyze the vehicle tyre model. The angular speed (ω*drive*) and the torque (*Tdrive*) of its transmission shaft can be represented by Equations (6) and (7), where GR is the final transmission gear ratio, *r* is the tyre radius, η*fd* is the transmission efficiency, and *Ftire* is the tyre force.

$$
\omega\_{d\text{riv}} = \text{GR} \cdot \frac{60}{2\pi \cdot r} v
\tag{6}
$$

$$T\_{d\text{rive}} = F\_{\text{tire}} \cdot r\_{\text{'}} \frac{\eta\_{fd}}{GR} \tag{7}$$

#### *2.4. Electric Motor Model*

A 150 kW permanent magnetic motor was applied in this study. An efficient map of the motor was reproduced from Autonomie simulation software. In simulation, the motor efficiency can be obtained from a 2D look-up table through the efficiency curve shown in Figure 2, based on the motor torque and speed.

**Figure 2.** Efficiency of electric motor.

#### *2.5. Variable Hydraulic Motor*/*Pump Model*

Axial slope plate plunger type of hydraulic motor/pump is applied in this study, and its efficiency is obtained through a look-up table, as shown in Figure 3. The fluid flow rate (*QP*/*M*) and output torque (*TP*/*M*) are calculated according to Equations (8) and (9), where *DP*/*<sup>M</sup>* is the maximum hydraulic motor displacement, *N* is the hydraulic motor speed, *Sp* is the plate angular position, η*vP*/*<sup>M</sup>* is the volumetric efficiency, Δ*PP*/*<sup>M</sup>* is the pressure difference at the entry and exit, and η*tP*/*<sup>M</sup>* is the mechanical efficiency.

$$Q\_{\rm P/M} = D\_{\rm P/M} N S\_p / \left(1000 \eta\_{\rm vP/M}\right) \tag{8}$$

$$T\_{P/M} = (S\_P \Delta P\_{P/M} D\_{P/M} \eta\_{tP/M}) / 63\tag{9}$$

**Figure 3.** Efficiency of hydraulic motor/pump [1].

#### *2.6. Battery Model*

The battery used in this study was a lithium ion battery. An RC circuit design was applied, as shown in Equation (10), where *Vt* is the battery terminal voltage, *Voc* is the battery open-circuit voltage, *Ibat* is the output current, and *Rint* is the internal resistance.

$$V\_t = V\_{\alpha \mathbf{c}} - I\_{\text{bat}} \cdot R\_{\text{int}} \tag{10}$$

Since the terminal voltage and the current can be measured, output of battery power *Pbat* can be received from Equation (11).

$$P\_{\text{flat}} = I\_{\text{flat}} \cdot V\_{\text{oc}} \tag{11}$$

Equation (12) can be obtained by substituting Equation (10) to Equation (11).

$$I\_{\rm bat} = \frac{V\_t - \left(V\_t^2 - 4 \cdot R\_{\rm int} \cdot P\_{\rm bat}\right)^{0.5}}{2R\_{\rm int}} \tag{12}$$

The battery *SOC* is expressed by the capacity ampere hour. Since *SOC* changes with the current charging and discharging, *SOC* can be obtained from Equation (13), where *SOCint* is the initial value of the battery.

$$SOC = SOC\_{int} - \frac{\int\_0^t I\_{bat} dt}{Ah} \tag{13}$$

#### *2.7. Accumulator Model*

For the accumulator model, the influence due to temperature change was not considered in this study, so the gas-state change is set to be adiabatic process (rapid change, *n* = 1.4). The relationship between the pressure and volume is shown in Equations (14) and (15), during actual expansion and compression of gas.

$$PV^n = \mathbb{C} \tag{14}$$

where *P* is pressure, *V* is volume of container area, and *C* is a constant value.

$$P\_0 V\_0^n = P\_1 V\_1^n = P\_2 V\_2^n = \mathbb{C} \tag{15}$$

where *P*<sup>0</sup> is initial pressure, *P*<sup>1</sup> is the maximum activate pressure of accumulator, *P*<sup>2</sup> is the minimum activate pressure of accumulator, *V*<sup>0</sup> is the total volume of accumulator, *V*<sup>1</sup> is the volume of air in accumulator when the pressure is *P*1, and *V*<sup>2</sup> is the volume of air in accumulator when the pressure is *P*2.

The boundary movement work, *Wb*, of the accumulator can be expressed by Equation (16).

$$\mathcal{W}\_b = \int\_1^2 P dV = P\_1 V\_1 \ln \frac{P\_1}{P\_2} \tag{16}$$

The inlet/outlet fluid, *Vf*, of the accumulator can be expressed by Equation (17).

$$V\_f = V\_1' - V\_2'$$

$$\dot{\rho} = (V\_0 - V\_1) - (V\_0 - V\_2) = V\_2 - V\_1 = P\_0^{\frac{1}{n}} V\_0 \left\{ \left(\frac{1}{P\_2}\right)^{\frac{1}{n}} - \left(\frac{1}{P\_1}\right)^{\frac{1}{n}} \right\} = \left(\frac{P\_0}{P\_1}\right)^{\frac{1}{n}} V\_0 \left\{ \left(\frac{P\_1}{P\_2}\right)^{\frac{1}{n}} - 1 \right\} \tag{17}$$

The accumulator *SOC* is expressed by the volume. Since the *SOC* changes with the volume flow rate, the accumulator *SOC* can be expressed by Equation (18).

$$\text{SOC} = \text{SOC}\_{\text{int}} - \frac{\int\_0^t \text{Qdt}}{V\_f} \tag{18}$$

#### *2.8. Vehicle Configurations*

Two vehicles configurations were applied in this study for energy-efficiency comparison. The electric vehicle (EV) configuration is shown in Figure 4, and the HEHV configuration is presented in Figure 5.

**Figure 4.** Electric vehicle (EV) configuration.

**Figure 5.** Hydraulic electric hybrid vehicle (HEHV) configuration.

#### **3. Optimization Control Strategy**

In this study, genetic algorithm (GA) was applied as the optimization function. The rule-based control was taken as the energy management strategy of HEHV first, and the simulation result was compared with the pure-electric-vehicle model. Then, the selected optimization approach was implemented for global optimization. From those results, together with a rule-based control approach, the optimal electricity economic performance was obtained.

The global optimization calculation was made by genetic algorithm. The objective of GA optimization was to minimize electricity consumption, and the objective function was set to be the reciprocal of the lithium ion battery's state of charge, SOL Li, as shown in Equation (19). The setting of objective function in GA could correspond to the fitness function, as shown in Equation (20). Parameters of GA set in this study are shown in Table 1.

$$\text{cost} = \min \left( 1 \Big/ \sum \text{(SOC Li)} \right) \tag{19}$$

$$\text{Fitness} = 1/\text{cost} \tag{20}$$


**Table 1.** Parameter settings of genetic algorithm (GA).

Two design variables (vehicle acceleration and accumulator *SOC*) were applied to judge the time to use the hydraulic system in control strategy. The thresholds of vehicle acceleration and accumulator *SOC* were set as selected variables *x* and *y* for optimization, respectively. If the vehicle acceleration was higher than the acceleration threshold and the accumulator *SOC* was higher than the accumulator threshold, the hydraulic pump provided the required power for vehicle acceleration. If the vehicle acceleration was lower than the acceleration threshold and the accumulator *SOC* was lower than the accumulator threshold, the electric motor provided the required acceleration power. If the vehicle acceleration was higher than the acceleration threshold and the accumulator *SOC* was lower than the accumulator threshold, the electric motor provided the major portion of required acceleration power. Some other detailed judgements of applying hydraulic pump and the overall control flow are shown

in Figure 6. To prevent the calculation of variables *x* and *y* from exceeding the maximum component scope, the setting constraints of the variables are shown in the constraint Equations (21) and (22).

0 < *x* ≤ 1(vehicle acceleration constraint) (21)

$$0 \le y \le 0.4(\text{accumulator constraint})\tag{22}$$

**Figure 6.** Control flow of genetic algorithm.

The fitness function was adapted to judge whether the solution of GA was suitable for the overall response of the hydraulic system. Values of acceleration threshold *x* and accumulator threshold *y* were recorded each time the GA was simulated. After the algorithm completed the iteration set of simulation, its fitness performance was looked up to ensure the value of fitness function was reasonable. The number of mutations and whether the optimization was convergence were checked during the operation of GA. In this study, the convergence of GA was judged by the difference of fitness values between the final four generations. If each difference was smaller than 1%, the optimization reached the convergence. From the solution of optimal fitness value, the recorded variables *x* and *y* were selected as the optimal set threshold. This set of variables could be implemented in rule-based control algorithm for real-time simulation and improve the energy consumption. With the implement of genetic algorithm, the rule-based control algorithm for real-time simulation could achieve the energy performance close to optimization.

The thresholds of vehicle acceleration and accumulator *SOC* calculated from the genetic algorithm were 0.9 and 0.1, respectively. The diagram of control strategy was modified, as shown in Figure 7.

**Figure 7.** Updated control strategy from genetic algorithm.

#### **4. Results**

The vehicle parameters of the simulated vehicle are presented in Table 2. The mass of vehicle includes the gross weight, which is 7200 kg, and 20 passengers, which is 1600 kg.


**Table 2.** Vehicle parameters.

In this section, simulation results of the pure electric vehicle and HEHV are compared, and that of the HEHV with optimized energy management strategy is explored. With the energy consumption of the NYCC driving cycle as the analysis basis, the difference of component performance is discussed. Firstly, the pure electric vehicle was established based on the set subsystem model, and it was taken as the basic model. Then the HEHV model was established based on the hydraulic components (hydraulic motor/pump and accumulator), and the rule-based control strategy was applied for the energy management of the power system. Finally, the rule-based control strategy was improved based on the results from the genetic algorithm, to get the HEHV with optimization energy management strategy.

#### *4.1. EV vs. HEHV (Rule-Based)*

This section compares the difference between the EV and HEHV and presents the causes of the differences. The operating points of the EV electric motor are presented in Figure 8, and those of HEHV electric motor are show in Figure 9. It is obvious that the HEHV electric motor does not work at heavy load and low speed, so it was replaced with a hydraulic motor/pump. Therefore, the operating efficiency points concentrate on the high-efficiency region, and the HEHV features better electricity economic performance than the pure electric vehicle.

**Figure 8.** Electric-motor operating points of EV.

**Figure 9.** Electric motor operating points of HEHV (rule-based).

In order to better understand the reason that the HEHV has a better economic performance than the pure electric vehicle, the power of electric motors is compared. As shown in Figure 10, the power of HEHV electric motor is smaller than that of pure electric vehicle. Figure 11 shows the comparison of battery *SOC*, where the electricity economic performance of HEHV is greatly improved.

**Figure 10.** Electric motor power comparison of EV and HEHV.

**Figure 11.** Battery *SOC* comparison of EV and HEHV.

Table 3 shows the electricity economic performance of the EV and HEHV (rule-based). Since a hydraulic motor functions as the drive at the HEHV's low speed, the use of an electric motor in the low-efficiency zone is reduced, and the electricity is optimized. The electricity economy of the HEHV has 36.5% improvement over that of EV.

**Table 3.** Comparison of electricity economic performance between the EV and HEHV (rule-based).


#### *4.2. HEHV (Rule-Based) vs. HEHV (GA)*

This research had taken the genetic algorithm (GA), together with rule-based control, to perform global optimization, and it got the optimal electricity economic performance. In this section, the HEHV with original rule-based control is compared with the HEHV with modified rule-based control based on the genetic algorithm optimization. The distribution of operating points of the HEHV (rule-based) and HEHV (GA) electric motors is presented in Figures 12 and 13, respectively. The distribution suggests that the operating points of the electric motor after being modified for optimization concentrate more on the high-efficiency region.

**Figure 12.** Efficiency points of the HEHV (rule-based) electric motor.

**Figure 13.** Efficiency points of the HEHV (GA) electric motor.

To understand the motor-use state, the power is compared in this paper, as shown in Figure 14. The usage rate of the electric motor after optimization is less than the original rule-based control strategy, so that better electricity economic performance is reached.

**Figure 14.** Power comparison between the HEHV (rule-based) and HEHV (GA) electric motors.

The reason why the electric-motor-usage rate after optimization is less can be explained with the help of a comparison of hydraulic motor power, as shown in Figure 15. It is found that the HEHV after optimization uses more hydraulic energy than the original control strategy.

**Figure 15.** Comparison between HEHV (rule-based) and HEHV (GA) hydraulic motor power.

As suggested by the comparison of operating-point distribution of hydraulic motor/pump of two control strategies (Figure 16) and state of accumulator use (Figure 17), there are more operating points for the hydraulic motor/pump after optimization than for the original strategy, and they tend to be in the high-efficiency zone. The accumulator is applied more completely due to the wider range of applications for the hydraulic motor/pump.

**Figure 16.** Comparison of operating-point distribution of hydraulic motor/pump (GA vs. rule-based).

**Figure 17.** Comparison between HEHV (rule-based) and HEHV (GA) accumulator *SOC*.

The analysis above indicates that the electricity economic performance of the HEHV after optimization is more improved. Figure 18 shows the battery *SOC* comparison of the EV and HEHV (Rule based) and HEHV (GA). It is clear that the HEHV after optimization is more improved than the HEHV with original strategy.

The electricity economic performance of the HEHV (rule-based) and HEHV (GA) is drawn in Table 4. Table 5 shows the percentage improvement of electricity in this study. The HEHV with original rule-based control shows 36.5% improvement over the EV, and the HEHV with modified rule-based control has 43.7% improvement.

**Figure 18.** Battery *SOC* comparison between HEHV (Rule based), HEHV (GA), and EV.




#### **5. Discussion**

This research mainly targeted the medium and large trucks for energy efficiency, and a hydraulic hybrid electric powertrain system was proposed to apply on the medium duty vehicle for energy efficiency. SimuLink simulation models of the EV and HHEV were built to evaluate the efficiency of the HHEV system. Compared to the EV system, the HHEV system had better energy efficiency, but the control algorithm was not optimized. To improve the efficiency, the genetic algorithm was implemented to achieve the optimized energy efficiency. Since GA was a global optimization algorithm which required longer CPU time for calculation and was not suitable for real-time control, the result of design variables of GA was required to apply on the real-time control strategy, rule-based control. In this research, two design variables of GA, thresholds of vehicle acceleration and hydraulic accumulator *SOC*, were optimized. These two optimized variables were applied in the HHEV simulation. From the simulation result, Tables 4 and 5, the rule-based model with GA could further improve the energy efficiency. The simulation results show that the electricity economic performance of the designed hydraulic hybrid vehicle was improved by 36.5% when compared to that of pure electric vehicle. The performance of energy consumption after genetic algorithm optimization was improved by 43.7%.

#### **6. Conclusions**

In this study, HEHV energy management strategy was applied, and Matlab/Simulink simulation program was utilized to establish a backward simulation model, to simulate the large-vehicle energy consumption. Movement situation of power components, *SOC* of energy storage components, and overall electricity economic performance of the pure electric vehicle and HEHV were obtained with the NYCC driving cycle. The following results can be achieved after simulation in this study:


**Author Contributions:** Conceptualization, T.-S.L.; investigation, T.-S.L.; methodology, H.-Y.H.; project administration, J.-S.C.; software, J.-S.C.; validation, H.-Y.H. and J.-S.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature**



#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **A Step Up**/**Down Power-Factor-Correction Converter with Modified Dual Loop Control**

#### **Yi-Hung Liao**

Department of Electrical Engineering, National Central University, Taoyuan City 32001, Taiwan; yhlmliao@gmail.com; Tel.: +886-3-4227151 (ext. 35153)

Received: 5 November 2019; Accepted: 29 December 2019; Published: 1 January 2020

**Abstract:** A step up/down AC/DC converter with modified dual loop control is proposed. The step up/down AC/DC converter features the bridgeless characteristic which can reduce bridge-diode conduction losses. Based on the step up/down AC/DC converter, a modified dual loop control scheme is proposed to achieve input current shaping and output voltage regulation. Fewer components are needed compared with the traditional bridge and bridgeless step up/down AC/DC converters. In addition, the intermediate capacitor voltage stress can be reduced. Furthermore, the top and bottom switches still have zero-voltage turn-on function during the negative and positive half-line cycle, respectively. Hence, the thermal stresses can also be reduced and balanced. Simulation and experimental results are provided to verify the validity of the proposed step up/down AC/DC converter and its control scheme.

**Keywords:** bridgeless; AC/DC converter; power factor correction; zero-voltage switching (ZVS)

#### **1. Introduction**

Power factor correction is very popular and necessary for modern power sources in the ac grid. It decreases line current harmonics, line losses, and increases system power capacity due to reducing system reactive power flow [1–3]. Today, boost rectifiers are the most commonly-used circuit structures implemented for power factor correction. However, some consumer electronic devices, portable devices and server power applications [4,5] require lower dc voltage level than the main ac voltage source. The dc output voltage in boost rectifiers is always higher than the peak value of the main input ac voltage. Therefore, in low dc voltage level applications, another dc-dc step-down converter is necessary that follows the boost rectifier to form a two-stage structure as shown in Figure 1. Because of the two-stage structure, power efficiency may degrade and the total number of components in the system is increased. Thus, the efficiency, cost, and volume of the two-stage power conversion system are not a good choice and need to be improved.

Step-down PFC rectifiers, such as buck converters are therefore considered. However, the buck rectifier input current is discontinuous. A dead angle also exists when the line input voltage is lower than the output voltage so that the input current cannot be easily shaped [6–8]. As a result, the step up/down AC-DC topologies are developed including buck-boost, Cuk, and Sepic type rectifiers [9–11]. The buck-boost rectifier also has inherent discontinuous input current like the buck converter, and needs an additional filter to smooth the input current. Although the Sepic rectifier has continuous input current, the output current is still discontinuous and easily causes output voltage ripples.

Bridgeless rectifier topologies are explored in [12,13] to reduce the diode bridge conduction losses and increase the conversion efficiency. The bridgeless PFC boost rectifiers, such as the dual boost rectifier and the totem-pole boost rectifier, have been discussed [14]. Due to the need for lower output voltage applications, the bridgeless Cuk/Sepic rectifiers [15,16] with two dc/dc Cuk/Sepic circuit structures were proposed. The bridgeless Cuk rectifier [16] is shown in Figure 2. However, four diodes are still needed to achieve step up/down output voltage. Other bridgeless Sepic [17] and Cuk [18] power-factor-correction rectifiers were also proposed with reduced number of components and conduction losses. These rectifiers were operated in discontinuous conduction mode without current loop control. A control method for bridgeless Cuk/Sepic power factor correction rectifier operated in continuous conduction mode was also proposed to achieve power decoupling [19]. Although, the bulky electrolytic capacitor can be replaced with a small film capacitor, this control method requires an extra voltage sensor for the intermediate capacitor and the system cost is increased.

Pulsating power buffering technology [8,20,21] has recently expanded, which can reduce the number of components including passive and active ones. Although rectifiers using pulsating power buffering technology have high power density, high conversion efficiency and high reliability, high voltage stress is still present in the switches and diodes [22], which leads to high switching and conduction losses and reduces the rectifier life-span.

This paper proposes a bridgeless Cuk rectifier with modified dual loop control scheme. The voltage stresses in the switches and diodes can be adjusted to low voltage levels by the proposed control scheme, which may reduce the switching and conduction losses and increase the rectifier life-span. The detailed operation principle and switching sequence of the bridgeless Cuk rectifier are explained. Simultaneously, a modified dual loop control scheme is also proposed to achieve input current shaping and output voltage regulation as well as voltage stress reduction.

**Figure 1.** Two-stage AC/DC conversion structure.

**Figure 2.** Bridgeless Cuk rectifier [16].

#### **2. Circuit Topology and Switching Sequence**

The bridgeless Cuk converter [19] discussed in this paper is shown in Figure 3. The proposed control switching sequence and key waveforms in one switching period during the positive and negative half line cycle are shown in Figure 4. For convenience of discussion the active switches are assumed to be ideal active switches with anti-paralleling body diode. Both the input inductor *Ls* and output inductor *Lo* are assumed to be operated in continuous conduction mode. The circuit operation can be divided into three operation states in one switching period T for both positive and negative half-line cycles. The circuit operation principle of the bridgeless Cuk converter during the positive half-line cycle is discussed first, as follows:

**Figure 3.** Bridgeless Cuk converter [19].

**Figure 4.** Control switching sequence and key waveforms in one switching period.

(1) State 1 (*t*<sup>0</sup> ≤ *t* <*t*1): In this state, as shown in Figure 5, both switches *S*<sup>1</sup> and *S*<sup>2</sup> are turned on. The zero-voltage switching of *S*<sup>2</sup> is obtained due to body diode conducting in switch *S*<sup>2</sup> in the pre-state, i.e., State 3. The input inductor *Ls* is magnetized by the input voltage *Vs* so as to increase the inductor current *iLs*. The inductor current *iLs* flows through diode *D*<sup>1</sup> and switch *S*<sup>1</sup> and goes back to the main ac source. Simultaneously, the intermediate capacitor *Cd* releases energy to the output inductor *Lo* and load. The equivalent circuit equations are described as Equations (1)–(4).

$$L\_s \frac{d\dot{q}\_{\rm Ls}}{dt} = v\_{\rm s,s} \tag{1}$$

$$L\_o \frac{d\dot{q}\_{Lo}}{dt} = v\_{Cd} - v\_{o\_2} \tag{2}$$

$$\mathbf{C}\_d \frac{dv\_{\mathbb{C}d}}{dt} = -\mathbf{i}\_{L\sigma} \tag{3}$$

$$C\_o \frac{dv\_0}{dt} = i\_{Lo} - \frac{v\_0}{R\_o} \tag{4}$$

**Figure 5.** Equivalent circuit of the bridgeless Cuk converter in State 1 during positive half line cycle.

(2) State 2 (*t*<sup>1</sup> ≤ *t* <*t*2): In this state, as shown in Figure 6, switch *S*<sup>1</sup> is turned on and switch *S*<sup>2</sup> is turned off. Switch current *ids*<sup>1</sup> is increasing. Input inductor *Ls* is still magnetized by the input voltage *Vs* so as to increase the inductor current *iLs* which still flows through diode *D*<sup>1</sup> and switch *S*<sup>1</sup> and then goes back to the main ac source. The voltage of intermediate capacitor *Cd* remains constant. Simultaneously, the output inductor *Lo* is demagnetized and releases energy to the load through the diode *Dd*. The equivalent circuit equations are expressed as Equations (5)–(8).

$$L\_s \frac{di\_{Ls}}{dt} = v\_{s\prime} \tag{5}$$

$$L\_{\upsilon} \frac{di\_{L\sigma}}{dt} = -v\_{\sigma} \tag{6}$$

$$C\_d \frac{dv\_{Cd}}{dt} = 0,\tag{7}$$

$$C\_o \frac{dv\_o}{dt} = i\_{Lo} - \frac{v\_o}{R\_o} \,\tag{8}$$

**Figure 6.** Equivalent circuit of the bridgeless Cuk converter in State 2 during positive half line cycle.

(3) State 3 (*t*<sup>2</sup> ≤ *t* <*t*3): In this state, as shown in Figure 7, switch *S*<sup>1</sup> is turned off and *S*<sup>2</sup> is also turned off. Input inductor *Ls* is demagnetized by the voltage −(*Vcd*−*Vs*) so as to decrease the inductor current *iLs* which flows through diodes *D*<sup>1</sup> and *Dd*, and the body diode of switch *S*<sup>2</sup> and goes back to the main ac source. The intermediate capacitor *Cd* is charged by the input inductor current *iLs*. Simultaneously, the output inductor *Lo* still releases energy to the load through diode *Dd*. The equivalent circuit equations are given by Equations (9)–(12).

$$L\_s \frac{di\_{Ls}}{dt} = v\_s - v\_{Cd} \tag{9}$$

$$L\_o \frac{d\dot{q}\_{Lo}}{dt} = -v\_{o\prime} \tag{10}$$

$$\mathbf{C}\_d \frac{dv\_{\rm Cd}}{dt} = \mathbf{i}\_{\rm Is,} \tag{11}$$

$$\mathbf{C}\_o \frac{dv\_o}{dt} = \dot{\mathbf{u}}\_o - \frac{v\_o}{R\_o} \,\tag{12}$$

**Figure 7.** Equivalent circuit of the bridgeless Cuk converter in State 3 during positive half line cycle.

Referring the gate signals shown in Figure 4, while the bridgeless Cuk converter is operated during the negative half line cycle, the circuit operation principle in the proposed control switching sequence can be described as follows:

(1) State 1 (*t*<sup>0</sup> ≤ *t* <*t*1): In this state, as shown in Figure 8, both the switches *S*<sup>1</sup> and *S*<sup>2</sup> are turned on. The zero-voltage switching of *S*<sup>1</sup> is obtained due to body diode conducting in switch *S*<sup>1</sup> in the pre-state, i.e., State 3. The input inductor *Ls* is magnetized by the input voltage *Vs* so as to increase the inductor current *iLs* in the inverse direction. The inductor current *iLs* flows through diode *D*<sup>2</sup> and switch *S*<sup>2</sup> and goes back to the main ac source. Simultaneously, the intermediate capacitor *Cd* releases energy to the output inductor *Lo* and load. The equivalent circuit equations are described as Equations (13)–(16).

$$L\_s \frac{di\_{Ls}}{dt} = v\_{s\prime} \tag{13}$$

$$L\_o \frac{d\dot{q}\_{Lo}}{dt} = v\_{Cd} - v\_{o\_2} \tag{14}$$

$$\mathbf{C}\_d \frac{dv\_{\rm Cd}}{dt} = -\mathbf{i}\_{\rm Lo} \tag{15}$$

$$C\_o \frac{dv\_0}{dt} = i\_{Lo} - \frac{v\_0}{R\_o} \,\tag{16}$$

**Figure 8.** Equivalent bridgeless Cuk converter circuit in State 1 during negative half line cycle.

(2) State 2 (*t*<sup>1</sup> ≤ *t* <*t*2): In this state, as shown in Figure 9, switch *S*<sup>2</sup> is turned on and switch *S*<sup>1</sup> is turned off. The switch current *ids*<sup>2</sup> is increasing. Input inductor *Ls* is still magnetized by the input voltage *Vs* so as to increase the inductor current *iLs* in the inverse direction which still flows through diode *D*<sup>2</sup> and switch *S*<sup>2</sup> and then goes back to the main ac source. The intermediate capacitor *Cd* voltage remains constant. Simultaneously, the output inductor *Lo* is demagnetized and releases energy to the load through diode *Dd*. The equivalent circuit equations are expressed as Equations (17)–(20).

$$L\_s \frac{di\_{ls}}{dt} = v\_{s,s} \tag{17}$$

$$L\_o \frac{di\_{Lo}}{dt} = -v\_{o\_1} \tag{18}$$

$$\mathbf{C}\_d \frac{dv\_{Cd}}{dt} = \mathbf{0},\tag{19}$$

*YV*

**Figure 9.** Equivalent circuit of the bridgeless Cuk converter in State 2 during negative half line cycle.

(3) State 3 (*t*<sup>2</sup> ≤ *t* <*t*3): In this state, as shown in Figure 10, switch *S*<sup>2</sup> is turned off and *S*<sup>1</sup> is also turned off. Input inductor *Ls* is demagnetized in the inverse direction by the voltage (*Vcd* + *Vs*) so as to decrease the inductor current *iLs* which flows through diodes *D*2, *Dd* and the body diode of switch *S*<sup>1</sup> and goes back to the main ac source. The intermediate capacitor *Cd* is charged by the input inductor current *iLs* in the inverse direction. Simultaneously, the output inductor *Lo* still releases energy to the load through diode *Dd*. The equivalent circuit equations are given by Equations (21)–(24).

$$L\_s \frac{di\_{Ls}}{dt} = v\_s + v\_{Cd'} \tag{21}$$

$$L\_o \frac{d\dot{q}\_{Lo}}{dt} = -v\_{o\prime} \tag{22}$$

$$\mathbf{C}\_d \frac{d\mathbf{v}\_{\rm Cd}}{dt} = -\mathbf{i}\_{\rm Ls} \tag{23}$$

$$C\_o \frac{dv\_o}{dt} = i\_{Lo} - \frac{v\_o}{R\_o} \,\tag{24}$$

**Figure 10.** Equivalent circuit of the bridgeless Cuk converter in State 3 during negative half line cycle.

To further reveal the potential merits of the proposed step up/down converter with modified dual loop control, Table 1 is provided to summarize comparisons for the bridge Cuk [11], bridgeless Cuk [16], and the proposed step up/down converter with modified dual loop control. It is worth mentioning that the power levels of the three converters in Table 1 are all at small power levels like the fly-back converter. Although the control methods may be different, the harmonics of the three converters all meet the IEC61000-3-2 Class D standard.


**Table 1.** Comparisons of step up/down converters.

#### **3. Control Scheme and Parameter Design**

#### *3.1. Control Scheme*

According to the circuit analysis in the previous section, assume the duty ratio *DW* = *D*<sup>1</sup> + *D*<sup>2</sup> and *D*<sup>0</sup> = *D*1. While the main ac voltage is operating in the positive half line cycle *vs* > *0*, by utilizing state-space averaged technique and flux balance theory in the input inductor *Ls* and output inductor *Lo*, one can obtain the equations

$$v\_{\rm Cd} = \frac{v\_{\rm S}}{(1 - D\_{\rm W})'} \tag{25}$$

$$v\_{Cd} = \frac{v\_o}{D\_o} \,\prime \tag{26}$$

Similarly, while the main ac voltage is operating in the negative half line cycle *vs* < 0, the corresponding symmetrical equations can also be obtained as

$$
\upsilon\_{\rm Cd} = \frac{-\upsilon\_{\rm S}}{(1 - D\_{\rm W})'} \tag{27}
$$

$$v\_{\rm Cd} = \frac{v\_o}{D\_o} \,\tag{28}$$

Merging Equations (25)–(28) in both the positive and negative half line cycles of the main ac voltage, the voltage gain of the bridgeless Cuk converter is obtained as

$$\frac{v\_o}{|v\_S|} = \frac{D\_o}{(1 - D\_W)'}\tag{29}$$

As can be observed from Equation (29), the output voltage is related to the two parameters *Do* and *DW*. If the input and output voltages are given, infinite different kinds of solutions exist in the Equation (29). However, in the same operation condition for the conventional dual loop control scheme shown in Figure 11, only one solution is obtained, i.e., *Do* = *DW*. Therefore, in order to reduce the voltage stresses of all switches and diodes in the circuit, the conventional dual loop control scheme is not suitable.

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**Figure 11.** Conventional dual loop control scheme.

*Energies* **2020**, *13*, 199

A modified dual loop control scheme is proposed. The proposed control scheme for the bridgeless Cuk converter is shown in Figure 12. The actual input current *iLs* compared with the current command *iLs\** to generate the current error as the input of the current controller and then produce the control signal *VDw*. The actual output voltage *Vo* compared with the output voltage command *Vo\** generates the voltage error as the voltage controller input. The voltage controller generates the current command amplitude and also the control signal *VDo*. In the conventional dual loop control scheme, only one control signal is produced to achieve both input current shaping and output voltage regulation. In the proposed control scheme, two control signals *VDw* and *VDo* are produced to control the input current shaping and output voltage regulation. Thus, the intermediate capacitor voltage is not fixed and can be adjusted to fit a better low voltage level. Hence, the intermediate capacitor voltage stress could be reduced and the adopted electrolytic capacitor life span could also be increased. According to the circuit analysis in Section 2, the voltage stresses of active switches *S*<sup>1</sup> and *S*2, diodes *D*1, *D*2, and *Dd* are clamped and equal to the intermediate capacitor voltage. The average switching power loss *Ps* in one switching period caused by transitions can be defined as

$$P\_s = 0.5V\_{DS}I\_{DS}[t\_{c(on)} + t\_{c(off)}]\_\prime \tag{30}$$

where *tc*(*on*) and *tc*(*off*) are the turn-on and turn-off crossover intervals, respectively. For simplification, the switches are operated in the same turn-on and turn-off crossover intervals and at the same switching frequency *fs*. The average switching power loss is then proportional to the voltage across the switch *VDS* and the entire current *IDS* which flows through the switch as

$$P\_s \propto V\_{DS} I\_{DS\_f} \tag{31}$$

According to the above equation, if the intermediate capacitor voltage is adjusted to fit a better low voltage level, the average switching power loss is also reduced. This is also true for the diodes. Therefore, the total losses in semiconductor devices can be reduced and the efficiency can be lifted.

**Figure 12.** Proposed modified dual loop control scheme.

#### *3.2. Parameter Design*

To verify the feasibility of the proposed step up/down AC/DC converter with modified dual loop control, a parameter design for inductor and capacitor is discussed. In order to find the boundary between the continuous and discontinuous modes for input inductor *Ls*, one can find that the critical value of *K*<sup>1</sup> at boundary between modes, *Kcrit*(*Dw*), is function of duty cycle *Dw* and can be expressed as

$$K\_1 > K\_{crit}(D\_w), \text{ where } K\_1 = \frac{2L\_s}{R\_s T\_s} \text{ and } K\_{crit}(D\_w) = \frac{\left(1 - D\_w\right)^2}{D\_w} \tag{32}$$

The critical value *Kcirt* (*Dw*) is plotted vs. duty cycle *Dw* in Figure 13. Consider inductor *Ls* is operated in CCM and the switching frequency is *fs*. The maximum input current ripple is less than 25% of the fundamental current. The minimum input inductor *Ls* value can be derived by the equation

$$L\_s \ge \frac{v\_{s,\text{max}}}{0.25 \cdot \Delta i\_{Ls,\text{BCM}}} \cdot \frac{D\_W}{f\_s} \,\tag{33}$$

where Δ*iLs*,*BCM* is the input current ripple while inductor *L*<sup>1</sup> is operated in BCM. Consider that inductor *Lo* is operated in BCM and one can find that the critical value for *K*<sup>2</sup> at the boundary between modes, *Kcrit*(*Do*), is function of the duty cycle *Do* and can be expressed as

**Figure 13.** Proposed step up/down AC/DC converter *Kcirt* (*Dw*) vs. *Dw*.

$$K\_2 > K\_{crit}(D\_o), \text{ Where } K\_2 = \frac{2L\_o}{R\_o T\_s} \text{ and } K\_{crit}(D\_o) = \frac{1 - D\_o}{2} \tag{34}$$

The critical value *Kcirt (Do)* is plotted vs. duty cycle *Do* in Figure 14. Similarly, the minimum value of inductor *Lo* also can be derived as

$$L\_o \ge \frac{\upsilon\_{Cd,\text{max}}}{\Delta i\_{Lo,\text{BCM}}} \cdot \frac{D\_o}{f\_s} \,. \tag{35}$$

where Δ*iLo*,*BCM* is the output current ripple while inductor *Lo* is operated in BCM.

**Figure 14.** Proposed step up/down AC/DC converter *Kcirt* (*Do*) vs. *Do*.

Consider the output capacitor and assume the switching ripple is neglected. The output capacitor must be large enough to minimize the output ripple because the output voltage ripple frequency is twice the input line frequency. The output filter capacitor can be determined by

$$\mathcal{C}\_{o} = \frac{\mathcal{P}\_{o}}{\omega V\_{o} (2\Delta V\_{o})'} \tag{36}$$

where Δ*Vo* is the output voltage ripple and ω is the input line angular frequency.

#### **4. Simulation and Experimental Results**

To verify the validity of the bridgeless step up/down AC/DC converter, some simulation results are executed and a prototype system is constructed to facilitate the theoretical results as verification. The simulation and experimental parameters are listed in Table 2. The input voltage is the AC grid with 110 Vrms and 60 Hz fundamental frequency. The controlled output voltage is 48 V and the load is 48 Ω. The assigned output power rating is 48 W. The simulation results for the input voltage *Vs*, input current *is* and the corresponding intermediate capacitor voltage *Vcd* are shown in Figure 15. It follows from Figure 15 that the input current shaping can be achieved. Figure 16 shows the switching control signals for switch *S*<sup>1</sup> and *S*<sup>2</sup> and the corresponding voltage and current of switch *S*<sup>2</sup> during the positive half-line cycle. As can be seen from Figure 16, the ZVS turn-on of switch *S*<sup>2</sup> is obtained during the positive half-line cycle. Similarly, Figure 17 shows the switching control signals for switch *S*<sup>1</sup> and *S*<sup>2</sup> and the corresponding voltage and current of switch *S*<sup>1</sup> during the negative half-line cycle. It also can be seen from Figure 17 that the ZVS turn-on of switch *S*<sup>1</sup> is obtained during the negative half-line cycle.

Consider that the load is a dynamic load and/or RL load such as a dc motor whose armature winding resistance is Ra = 0.5 Ω, armature winding inductance is La = 0.5 mH, back electromotive force is 47 V. Figure 18 shows the simulation results for the input voltage, input current and the corresponding intermediate capacitor voltage. As can be observed from Figure 18, the output power is about 120 W and the power factor correction is also achieved. Hence, the proposed converter can indeed be operated in the RL load. Consider the intermediate capacitor voltage which can be adjusted using the control signal *VDo* based on Equations (26) and (28). Figure 19 shows the simulation results for the input voltage and the corresponding input current, and the control signal *VDo* and the corresponding intermediate capacitor voltage *VCd* under the low control signal *VDo* value. Figure 20 shows the same simulated condition under the high control signal *VDo* value. It can be seen from Figures 19 and 20 that the lower the control signal *VDo* value, the higher the intermediate capacitor voltage *VCd*. That the duty ratio Do affects the intermediate capacitor voltage level and also the voltage stresses of the switches and diodes in the circuit is very important information. This also implies that the duty ratio Do affects the converter power losses and efficiency. Finally, to facilitate understanding of the proposed step up/down converter with modified dual loop control and as verification, a prototype is constructed with a TMS320F28335 digital signal processor (DSP). The experimental hardware construction block diagram is shown in Figure 21. Figures 22 and 23 show the experimental results for the switching control signals and the corresponding voltage and current of switches *S*<sup>2</sup> and *S*<sup>1</sup> during positive and negative half-line cycles, respectively. As can be observed from Figures 22 and 23, the ZVS soft switching of switches *S*<sup>2</sup> and *S*<sup>1</sup> were indeed achieved and agreed with the simulation results. The measured harmonic distribution of the input current is shown in Figure 24. One can find that the measured harmonic currents meet the IEC 61000-3-2 Class D harmonic standards.

In order to understand the total harmonic distortion *THDi* of the input currents in the three converters listed in Table 1, the PSIM software is adopted to carry out the simulation. The input voltage is 110Vrms, the output voltage is controlled at 48 V and the load is 2 A. The corresponding parameters and simulated results are shown in Table 3. As can be seen from Table 3, the input current *THDi* of the bridge Cuk [11] is better than that of the bridgeless Cuk [16] and the proposed Cuk with modified dual loop control scheme. Nevertheless, the parameter value of the bridge Cuk input inductor [11] is larger than those for the other two. Although the bridge Cuk [11] has the smallest input current *THDi*, the input inductor may make it appear bulky.

9FG

 

*VCd*


**Table 2.** Parameters of the bridgeless Cuk converter for simulation and experimentation.

**Figure 15.** Simulation results for (top) the input voltage *Vs*, current *is*, and (bottom) corresponding intermediate capacitor voltage.

**P6**

**Figure 16.** Simulation results for (top) switching control signals and (bottom) corresponding voltage and current of switch *S*<sup>2</sup> during positive half line cycle.

**Figure 17.** Simulation results for (top) switching control signals and (bottom) corresponding voltage and current of switch *S*<sup>1</sup> during negative half line cycle.

**Figure 18.** Simulation results for (top) the input voltage *Vs*, current *is*, and (bottom) corresponding intermediate capacitor voltage while the load is a dc motor.

**Figure 19.** Simulation results for (top) the input voltage *Vs*, current *is*, (middle) the control signal V*Do* with low parameter value, and (bottom) corresponding intermediate capacitor voltage.

**Figure 20.** Simulation results for (top) the input voltage *Vs*, current *is*, (middle) the control signal V*Do* with high parameter value, and (bottom) corresponding intermediate capacitor voltage.

**Figure 21.** Experimental hardware construction block diagram.

**Figure 22.** Experimental results for (top) switching control signals *S*1, *S*<sup>2</sup> and (bottom) corresponding voltage and current of switch *S*<sup>2</sup> during positive half line cycle.

**Figure 23.** Experimental results for (top) switching control signals *S*1, *S*<sup>2</sup> and (bottom) corresponding voltage and current of switch *S*<sup>1</sup> during negative half line cycle.

**Figure 24.** The measured harmonic distribution of the input current compared with IEC61000-3-2 Class D standard.

**Table 3.** Comparisons of the total harmonic distortion of the step up/down converters.


#### **5. Conclusions**

This paper presented a bridgeless step up/down converter with modified dual loop control scheme. The proposed system has ZVS soft switching in switches *S*<sup>1</sup> and *S*<sup>2</sup> during the negative and positive half-line cycle operation, respectively. Thus, the switching losses can be reduced and the thermal stress can be balanced between switches *S*<sup>1</sup> and *S*2. There are fewer components compared to the bridge Cuk and the bridgeless dual Cuk configuration. Therefore, the size and cost can be reduced. In addition, based on the proposed control scheme, the voltage stresses of the intermediate capacitor, active switches, and diodes can all be reduced. To verify the validity of the proposed step up/down converter, simulation, and experimental results are offered. From simulation and experimental results, the proposed bridgeless step up/down converter can indeed achieve input current shaping and output voltage regulation as well as reduce the switching and conduction losses.

**Author Contributions:** The author contributed to the theoretical analysis, modeling, simulation, experiment, and manuscript preparation. The author have read and agreed to the published version of the manuscript.

**Funding:** This research is sponsored by the Ministry of Science and Technology of R.O.C. under grant MOST 108-3116-F-008-001.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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