The ultrasonic features during the overcharge test are shown in Figure 7e,f. Figure 7e shows that the TOF shifts towards the lower value before 2.5 h, which is in agreement with [26] (due to the change of SOC). The TOF begins to increase at about 2.8 h. One possible interpretation of this increase is that the TOF has already indicated a tiny amount of gas generated inside the battery. In addition, an increase of the thickness of battery layers may also increase the value of TOF. Then, the TOF increases sharply in a similar time range as the temperature increases. Subsequently, the TOF shows the same decreasing trend as the temperature when the test is stopped. Figure 7f shows the change in the PA during the overcharge process. Similar to the cycling test results, the PA does not show a stable indication of the overcharge-induced battery failure.

**Figure 7.** *Cont*.

**Figure 7.** Overcharge test results for battery A1: (**a**) voltage and current profiles, (**b**) temperature profile, (**c**) photos of the battery (top view), (**d**) X-ray images of the battery (side view), (**e**) evolution of TOF, and (**f**) evolution of PA.

#### **5. Ultrasonic Health Monitoring for Lithium-Ion Batteries**

As summarized in the ultrasonic test results, the TOF was found to be highly related to the underlying degradation and failure process for the batteries, and therefore can be used for battery health monitoring. However, evaluation of battery degradation and failure will be arbitrary if a unique sensor is used because one sensor can have large uncertainties. Other than the ultrasonic signal, temperature is indicative of the health status of a battery, especially for some catastrophic failures such as thermal runaway. Therefore, to enhance the reliability of battery health monitoring, a data fusion method was developed that fuses the temperature with the ultrasonic signal.

#### *5.1. Methodology*

Mahalanobis distance (MD) is a distance measure with multivariate data that determine the similarity between an unknown sample and a collection of known samples [34]. It is sensitive to changes in different parameters because it considers the correlation among parameters, and it eliminates the scale problem by normalizing different parameters [35]. Due to these advantages, the MD approach was used as the data fusion method in this study. The MD values were calculated based on the temperature and ultrasonic features and used as the health indicators (HIs).

Figure 8 shows a flowchart of the MD-based battery health monitoring method. A dataset from the pristine battery (i.e., the healthy battery) was used as the training data to construct the baseline and determine the testing thresholds. Then, the MD value of the data from the test battery was calculated and compared with the thresholds to determine the health of the test battery.

**Figure 8.** Developed battery health monitoring method.

The data collected from the healthy battery are denoted *Xij*, where *i* = 1, ... , *m*; *j* = 1, ... , *n*; *m* is the dimension of the feature vector; and *n* denotes the number of the observations. Each observation is normalized using the mean (*Xi*) and the standard deviation (*Si*) of the feature calculated from the healthy data. Thus, a parameter's normalized value is:

$$Z\_{i\bar{j}} = \frac{\left(X\_{i\bar{j}} - \overline{X}\_i\right)}{S\_{\bar{i}}} \tag{4}$$

where

$$\overline{X}\_i = \frac{1}{n} \sum\_{j=1}^n X\_{ij} \tag{5}$$

$$S\_i = \sqrt{\frac{\sum\_{j=1}^{n} \left(X\_{ij} - \overline{X}\_i\right)^2}{(n-1)}} \tag{6}$$

Then, the MD value for the healthy data is calculated by the following equation:

$$\mathbf{^jMD\_j} = \mathbf{Z\_j^T C^{-1} Z\_j} \tag{7}$$

where *C* is the correlation matrix.

$$\mathcal{C} = \frac{1}{(n-1)} \sum\_{j=1}^{n} Z\_j Z\_j^T \tag{8}$$

Two types of test data were used to calculate the HIs for the purpose of health monitoring. To assess degradation, the HI was calculated based on the features at a specific state (the same SOC level) in order to eliminate the effect of SOC on the features. For the indication of early failure, the HI was obtained using the features, which were continuously monitored during the operating process, in order to provide an immediate response to a sudden failure. For different types of test data, different thresholds were established. For a battery, a degradation threshold is determined based on its

degradation criterion. Generally, it is suggested to replace a battery if the capacity is less than 80% of its initial value [36]. Thus, the MD value, which corresponded to SOH = 80%, was set as the threshold for the battery degradation assessment.

Determination of the early failure threshold is an important step in order to have advanced warning of failure. A fixed threshold is defined based on expert knowledge. However, this approach may not be able to indicate early failure when knowledge of failure is not available. Therefore, it is useful to implement the generalized probabilistic approach to determine the threshold. The MD values are always positive and do not follow a normal distribution. A Box–Cox transformation transforms the data with these kinds of characteristics into a normal distribution. Then the mean (μ) and standard deviation (σ) of the transformed data are obtained. Since the intervals (−∞, μ + 3σ) contain 99.9% of the MD data, the three standard deviation limit (μ + 3σ) was chosen as the threshold for failure indication, which has been demonstrated for various electronic products [35,37,38].

The Box–Cox transformation is defined as follows [39]:

$$\mathcal{Y}(\lambda) = \begin{cases} \frac{\left(y^{\lambda} - 1\right)}{\lambda}, & \lambda \neq 0 \\\ln(y), & \lambda = 0 \end{cases} \tag{9}$$

where *y* = *y*1, *y*2, ... , *y*n is the original MD value and *y*(λ) is the transformed MD value. The power λ is obtained by maximizing the log-likelihood function.

$$f(y,\lambda) = -\frac{n}{2} \ln \left[ \sum\_{i=1}^{n} \frac{\left( y\_i(\lambda) - \overline{y}(\lambda) \right)^2}{n} \right] + (\lambda - 1) \sum\_{i=1}^{n} \ln(y\_i) \tag{10}$$

where

$$\overline{y}(\lambda) = \frac{1}{n} \sum\_{i=1}^{n} y\_i(\lambda) \tag{11}$$

The mean (μ) and standard deviations (σ) of the transformed healthy MD values are used to determine the failure threshold. The upper bound (μ + 3σ) is used as a threshold for failure indication [38].

For a test battery, each observation is normalized using the mean and standard deviation from the healthy data. Then, the MD value for each observation is calculated using Equation (7) and transformed using Equation (9). When the transformed test MD values cross the thresholds, a failure is considered to occur.

#### *5.2. Battery Health Monitoring Results*

As shown in Section 4, battery A1 underwent a period of cycling test and an overcharge test, sequentially. It is used as a case study to evaluate the developed health monitoring method. Figure 9a shows a scatter plot of the TOF and temperature for battery A1. First, the baseline data correspond to the first 10 data points from the cycling test. They refer to 100% to 98% SOH and are all measured at 0% SOC. Then, the test data 1 are extracted from the subsequent cycling test. They are also measured at 0% SOC but used for degradation assessment. Finally, the test data 2 correspond to the data measured during the 5 V overcharge process after 210 cycles. They are used for failure indication. Here, since tests were conducted under the well-controlled lab conditions, the data are used without a denoising process. In practice, the measured data may contain noise, these data are denoised before calculating the MD values.

The MD values corresponding to the training (baseline) data and the test data 1 for degradation assessment are shown in Figure 9b. These MD values were transformed into normally distributed variables using Box–Cox. To set the degradation threshold (DT), a linear model between the SOH and TOF was built based on the training data. Then, the estimated TOF value (TOF\_DT) corresponding to SOH = 80% was obtained based on the linear model. In addition, the average value of the temperatures (T\_DT) from the training data was calculated. The MD value between (TOF\_DT and T\_DT) and the baseline was calculated and set as the DT. In order to quantify the degree of degradation, the MD values were normalized using the DT value. The range of the normalized MD value is from zero to one. A larger MD value indicates greater degradation, i.e., one means the battery degrades severely and is not able to be used and zero means the battery is healthy. According to Figure 9b, the normalized MD value shows an increasing tendency with the increasing cycle number, which means the battery degrades with the increasing cycle number. The MD value does not reach the degradation threshold until the end of the cycling test. The battery capacity is 96% of the initial capacity at the end of the cycling test, which also indicates the battery does not reach its degradation criterion (80% of its initial capacity). Therefore, the degradation assessment based on the proposed HI is consistent with the capacity test result.

**Figure 9.** Health monitoring for battery A1: (**a**) scatter plot of the TOF and temperature, (**b**) degradation assessment result based on Mahalanobis distance (MD) values, (**c**) failure indication result based on MD values, and (**d**) failure indication result based on the temperature change rate.

The transformed MD values corresponding to test data 2 for failure indication are shown in Figure 9c. The failure threshold (FT) is plotted as the dashed line in Figure 9c. The temperature change rate (d*T*/d*t*) is plotted in Figure 9d. These two figures compare the indication time of failure by using the MD values and the temperature change rate, respectively. As shown in Figure 9c, when the MD value exceeded the failure threshold, the failure was indicated at 2.825 h. This time corresponds to the battery voltage at 4.564 V and the surface temperature at 46.86 ◦C. However, if the failure time is determined only in terms of the first peak of d*T*/d*t*, the battery failure was only identified at 3.642 h, which corresponds to close to 5 V voltage and a temperature of 55.65 ◦C. After that point, the temperature increased sharply, which means there was little time to prevent the battery from swelling. Therefore, the MD-based HI provides earlier failure indication time and a longer time margin for countermeasures to prevent further catastrophic failure as compared with monitoring only the temperature.

#### **6. Conclusions**

This paper developed an ultrasonic health monitoring method for lithium-ion batteries. To begin with, the feasibility of using ultrasonic sensing to probe the health status of a lithium-ion battery was demonstrated through battery cycling tests and an overcharge abusive test (up to 5 V). The ultrasonic results from the cycling test showed a strong dependence between the ultrasonic TOF and battery degradation. The overcharge test results showed that the ultrasonic TOF is sensitive to the battery swelling, which offers the potential for battery failure indication.

More importantly, an effective method for battery health monitoring was developed, which offers a significant improvement over the state-of-the-art ultrasonic techniques in terms of providing an early indication of sudden failure. A new data fusion MD-based health indicator was constructed by integrating the data from the temperature sensor and the ultrasonic transducer. The effectiveness of the health indicator was verified by the case study of battery A1, which underwent a cycling test followed by an overcharge test. The cycling test showed that the MD value increases with the battery aging. This means it can be used to determine battery degradation straightforwardly without the information on the battery's discharge capacity. The overcharge test (up to 5 V) showed that the health indicator can indicate battery failure 0.872 h ahead of battery swelling and 0.817 h earlier than the temperature-based method. In comparison to the temperature-based method, the developed method provides earlier warning of catastrophic failure and a longer time margin for failure prevention.

The developed ultrasonic health monitoring method can assess battery degradation as well as indicate battery sudden failure without needing the battery to be fully charged/discharged. This health monitoring method can be applied to batteries during their operation by integrating simple and small equipment (a pulser-receiver module and a piezoelectric transducer) into the existing battery management system. Similar techniques can be extended and applied to batteries with different chemistries, scales, and form factors. In future research, we will investigate the feasibility of using an ultrasonic inspection method to identify different aging mechanisms of the lithium-ion batteries.

**Author Contributions:** Investigation, M.P.; methodology, Y.W. (Yi Wu); writing—original draft, Y.W. (Yi Wu); writing—review and editing, Y.W. (Youren Wang) and M.P.; supervision, M.P.; funding acquisition, W.K.C.Y.

**Funding:** This work was supported by the National Natural Science Foundation of China (grant number 61473242); funding for Outstanding Doctoral Dissertation in NUAA (grant number BCXJ14-04); and the Fundamental Research Funds for the Central Universities and Funding of Jiangsu Innovation Program for Graduate Education (grant number KYLX\_0251).

**Acknowledgments:** The authors would like to thank the more than 150 companies and organizations that support research activities at the Center for Advanced Life Cycle Engineering (CALCE) at the University of Maryland.

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

#### **References**

© 2019 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* **Battery Charger Based on a Resonant Converter for High-Power LiFePO4 Batteries**

**Christian Brañas 1,\*, Juan C. Viera 2, Francisco J. Azcondo 1, Rosario Casanueva 1, Manuela Gonzalez 2 and Francisco J. Díaz 1**

**Abstract:** A new battery charger, based on a multiphase resonant converter, for a high-capacity 48 V LiFePO4 lithium-ion battery is presented. LiFePO4 batteries are among the most widely used today and offer high energy efficiency, high safety performance, very good temperature behavior, and a long cycle life. An accurate control of the charging current is necessary to preserve the battery health. The design of the charger is presented in a tight correlation with a battery model based on experimental data obtained at the laboratory. With the aim of reducing conduction losses, the general analysis of the inverter stage obtained from the parallel connection of *N* class D *LCpCs* resonant inverters is carried out. The study provides criteria for proper selection of the transistors and diodes as well as the value of the DC-link voltage. The effect of the leakage inductance of the transformer on the resonant circuit is also evaluated, and a design solution to cancel it is proposed. The output stage is based on a multi-winding current-doubler rectifier. The converter is designed to operate in open-loop operation as an input voltage-dependent current source, but in closed-loop operation, it behaves as a voltage source with an inherent maximum output current limitation, which provides high reliability throughout the whole charging process. The curve of efficiency of the proposed charger exhibits a wide flat zone that includes light load conditions.

**Keywords:** lithium-ion battery; battery modeling; battery chargers; power supplies; resonant inverters; phase control

#### **1. Introduction**

Lithium iron phosphate (LiFePO4) batteries have a great electrochemical performance and a good thermal stability, which makes them safer and more robust. This lithium-based technology exhibits a very low internal resistance offering a high current rating. Their cycle life is significantly longer compared to other technologies [1,2]. The applications of LiFePO4 batteries are, among others, for storage systems in renewable energy facilities, powering electric vehicles and uninterruptible power supplies (UPS) in data centers, telecommunications, and hospitals. A battery model is an important tool for designing the charger allowing the study of the dynamic response of the battery-charger system along the whole charging process, wherein the converter load, i.e., the equivalent resistance of the battery, varies from almost short-circuit to open-circuit values. Most of the battery models are aimed to improve the battery management system (BMS) performance, providing information about important parameters of the battery such as the state of charge (*SOC*) [3]. The estimation of the battery *SOC* and power capacity is usually solved by applying three methods, i.e., the look-up table method, the model-based method, and the artificial intelligence method [4–7]. In addition to that, the BMS is responsible for ensuring the battery operation within safety margins of temperature and sets the overvoltage and

**Citation:** Brañas, C.; Viera, J.C.; Azcondo, F.J.; Casanueva, R.; Gonzalez, M.; Díaz, F.J. Battery Charger Based on a Resonant Converter for High-Power LiFePO4 Batteries. *Electronics* **2021**, *10*, 266. https://doi.org/ 10.3390/ electronics10030266

Received: 21 December 2020 Accepted: 21 January 2021 Published: 23 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 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 (https:// creativecommons.org/licenses/by/ 4.0/).

under voltage protection limits. In this work, the battery modeling is presented in a tight correlation with the battery charger design.

The technology of resonant converters is chosen to implement the proposed battery charger. The advantages of the resonant conversion of energy, such as high frequency of operation, sinusoidal waveforms, and low switching losses are well known [8]. Among all possible configurations of resonant converters, the series resonant converter and the *LLC* converter have been widely used [9–12]. Usually, the converter is designed to operate as a voltage source with some kind of control to limit the charging current. In this work, the converter is designed as a voltage-dependent current source. In this approach, the circuit presents an inherent maximum current limitation, which is a safer operation mode. The LiFePO4 technology reaches current rates as high as hundreds of amps. In circuit design for high-current applications, conduction losses are a major design limitation [13,14]. In high-current resonant converters, increasing the dc-link voltage, *Vdc*, and using a stepdown transformer (*n* > 1) reduces the amplitude of the resonant currents in the inverter stage, minimizing the conduction loss in transistors and resonant inductors. New Wide Band Gap (WBG) devices enable the operation at an 800 V to 1700 V dc-link voltages range [15]. WBG devices achieve high performance at high current levels with important simplifications in the power circuit. However, the cost of WBG devices limits their use for certain applications.

In this work, a generalized design method aimed at minimizing the conduction loss is presented for multiphase resonant converters [16]. The number of parallel branches and therefore phases, *N*, in the inverter stage is calculated according to the maximum output power and the expected efficiency. This alternative offers another degree of freedom for achieving efficiencies higher than 90% even at relatively low values of *Vdc* and using low-cost transistors. Moreover, the multi-phase structure makes it possible to regulate the charging current at constant switching frequency by shifting the phase of the output voltages of each class D section of the inverter.

This paper is organized as follows: After the introduction, Section 2 describes the charging profile of the target LiFePO4 battery, which is oriented to obtain a fast charge without reducing its lifetime. The battery model is presented in Section 3. The analysis of the proposed charger and main design equations are developed in Section 4. The efficiency of the charger is studied in Section 5. A detailed step-by-step design sequence of the proposed charger is explained in Section 6. In Sections 7 and 8, the results obtained for the modeling of the battery and experimental waveforms to verify the performance of the prototype are presented, ending with a discussion about Si vs. SiC solutions and concluding remarks.

#### **2. Charging Method**

The main characteristics of the commercial 48NPFC50 LiFePO4 battery (Narada Power Source Co., Ltd., Hangzhou, China) [17] used in this work are 48 V nominal voltage and 50 Ah nominal capacity (*Cn*) i.e., 2.4 kWh of power capacity. The battery consists of fifteen (*Ns* = 15) stacked cells in series and incorporates a BMS that guarantees the right balanceof-charge of all cells. Thus, the voltage across each cell is assumed identical to any other. The battery charger is designed to meet all operational limits settled by the BMS.

The charging protocol recommended for LiFePO4 batteries is the well-known [18] constant current (CC)–constant voltage (CV) method (i.e., CC–CV). During the CC stage, the battery is charged at the maximum current rate, which depends on the battery capacity and technology. Once the battery voltage reaches its maximum charging voltage specified in the battery data sheet, the CV stage begins. At this point, the power drawn from the charger is the maximum, which happens at 90% of the *SOC* approximately. During the CV stage, the charging current diminishes. Three experimental charging profiles are carried on at the battery laboratory facility shown in Figure 1. They are evaluated at room temperature (25 ◦C) using the battery test equipment PEC SBT-10050 (PEC, Leuven, Belgium) and taking into account that the battery is fully discharged as the initial condition.

**Figure 1.** (**Left**) Laboratory facility for battery testing. (**Right**) Battery connected to SBT-10050 test equipment.

Those profiles correspond to the battery charge at current rates equal to *Cn*/5, *Cn*/2, and *Cn* during the CC stage. The results are shown in Figure 2.

**Figure 2.** Experimental charging profiles at 10, 25, and 50 A for a 48NPFC50 LiFePO4 battery.

The temperature is observed by the BMS during the whole charging process, and it implements the corresponding protection (maximum value 55 ◦C for charging) to prevent the battery aging. Electro-thermal models for studying the temperature of a lithium-ion cell as a function of the charging/discharging current have been reported in [19,20]. The user manual recommends a conservative value, *Cn*/5, for the charging current rate; however, LiFePO4 technology tolerates fast-charging protocols [21–24]. In this work, in order to shorten the charging time, a maximum charging current rate of 20 A (approximately *Cn*/2) is chosen the charger design. According to the experimental characterization of the battery, charging at *Cn*/2 keeps the temperature of the battery well below 55 ◦C.

#### **3. Battery Model**

Although the LiFePO4 cell is a complex physical system with several variables involved, a good trade-off among simplicity, accuracy, and insight information is obtained with the electrical parameters-based models [25], as shown in Figure 3. The single cell

model is generalized by affecting all parameters by the total number of cells, *Ns*, under the assumption that all cells are identical, as shown in Figure 3.

**Figure 3.** Battery model considering *Ns* stacked cells in series.

The state of charge (*SOC*) [26] of the battery is defined as the ratio of the battery charge, *Q*, to the nominal capacity, *Cn*.

$$\text{SOC} = \frac{\text{Q}}{\text{C}\_{\text{H}}} \cdot 100\% \tag{1}$$

The model calculates the *SOC* [26], integrating the battery current-dependent current source, *ibat*, which charges/discharges the capacitor *Cn*. The *SOC* is equal to the voltage across the capacitor *Cn*, *vCn* varying from zero to one corresponding to exhausted to fully charged battery, respectively.

$$SOC(t) = SOC(t\_o) + \frac{1}{\mathcal{C}\_{\text{u}}} \int\_{t\_o}^{t} i\_{bat}(t)dt\tag{2}$$

The voltage-controlled voltage source, *Nsvqoc*(*SOC*), dependent on the voltage *vCn*, represents the quasi-open-circuit battery voltage, where *vqoc*, is the quasi-open-circuit voltage across one single cell. The experimental measurement of *vqoc* as a function of the *SOC* is a time-consuming task because it should be obtained while keeping the cell in electrochemical equilibrium [27], charging and discharging the cell at a very low current rate. From the experimental study of one single cell, the *vqoc* as a function of the *SOC* was obtained by charging and discharging the cell at *Cn*/50. This test required 100 h. The result is shown in Figure 4.

**Figure 4.** Quasi-open-circuit voltage of the cell as a function of the state of charge (*SOC*) obtained at *Cn*/50 for a complete charge/discharge cycle. Solid line: Charge trajectory. Dashed line: Discharge trajectory.

As it is observed in Figure 4, the quasi-open-circuit cell voltage, *vqoc*, incorporates the effect of the voltage hysteresis caused by the battery structure [27]. The maximum hysteresis is about ≈ 40 mV within the 30% *SOC* region, and the average is ≈ 20 mV within the 40% to 80% SOC region. The experimental test results show a cell capacity *Cn* = 50 Ah, which is represented in the model by a capacitance *Cn* = 180,000 F.

The electrolyte and electrode resistance are modeled by *R*Ω. In addition to that, the model also includes two time constants, which are modeled by networks *RtCt* and *RdCd*. The time constant *RtCt* is associated to chemical reactions and charge transportation phenomenon in the electrodes. This time constant is within the range from milliseconds to a few seconds. In contrast, the time constant *RdCd* governs the mass diffusion in the electrolyte and electrodes and is within the tens of seconds range [27]. From the point of view of the battery charger design, the electrical parameters of the battery at the end of the CC stage are of interest. At this point, the power supplied by the charger is the maximum. For a given *SOC*, the battery model can be simplified to a resistance, *rBat*, in series with a voltage source equal to the quasi-open-circuit voltage *NsVqoc*. Assuming the battery is in steady state, *rbat* is obtained from the model shown in Figure 3 as

$$r\_{Bat} = N\_s \cdot (R\_\Omega + R\_l + R\_d). \tag{3}$$

The specific values *Rt* and *Rd* for a given *SOC* should be obtained from the dynamic study of the battery, once the time constants associated with transport and diffusion phenomena were obtained. Finally, the battery voltage is obtained as:

$$V\_{Bat} = N\_s V\_{qoc} + I\_{Bat} r\_{Bat} \,\text{.}\tag{4}$$

#### **4. Multiphase** *LCpCs* **Resonant Converter**

The proposed battery charger is a multiphase resonant converter. The general form of the circuit is shown in Figure 5, where the battery is modeled in steady state by its internal impedance, *rBat*, in series with the quasi-open-circuit battery voltage *NsVqoc*.

**Figure 5.** General architecture of the battery charger based on an *N*-phase *LCpCs* resonant inverter with an *M*-winding current-doubler rectifier as output stage. Multiple configurations are possible according to the *N* and *M* values.

The AC side is a multiphase resonant inverter, which consists of *N* paralleled *LCpCs* class D sections [16,28]. Among the possible configurations of the resonant network, the configuration *LCpCs* of the *LCC* family is chosen to achieve a current source behavior while preserving the zero voltage switching (ZVS) mode of transistors [8,29]. Unlike the *LLC* converter, the proposed *LCpCs* does not require a gapped-core transformer [30], so the magnetizing inductance, *LM*, is high enough to neglect its impact in the later analysis.

The DC side consists of an *M*-winding current multiplier, which is derived from the parallel connection of an *M* current-doubler rectifier [31,32]. The low output voltage of this application recommends the use of Schottky diodes without any control circuit in the secondary side, which is a simplification in comparison to solutions based on synchronous rectification (SR).

#### *4.1. Resonant Inverter Stage*

The converter is analyzed considering the general case, where each midpoint voltage *vi* of all class D sections has associated a phase-angle Ψ0, Ψ1, ... , Ψi−1. To illustrate this assumption, the midpoint voltages, *vi*, are shown in Figure 6.

**Figure 6.** Output voltages of each inverter section obtained in the midpoint of the transistors leg.

Using the fundamental approximation, the input voltages, *vi*, are represented with the exponential form given in (5),

$$\mathbf{V}\_{\mathbf{i}} = \frac{2V\_{d\varepsilon}}{\pi} \cdot e^{-j\mathbf{V}\_{i-1}},\tag{5}$$

where *i* ∈ [1, 2, ... , *N*] is the phase number. In steady state and using the low ripple approximation, the *M*-winding output rectifier is reduced to an equivalent impedance *Rac* [8,29]. The resonant inverter stage is analyzed using the simplified circuit model shown in Figure 7.

**Figure 7.** Simplified model using the fundamental approximation for circuit analysis purposes of the inverter stage.

The parallel parameters of the resonant inverter are defined in Table 1.

#### 4.1.1. AC Side Output Current

During the CC stage of the charging process, the converter provides an inherent current limitation, protecting the battery and extending its life. The current source behavior of the resonant converter is achieved by fixing the switching frequency at *ω* = *ωp*, where *ωp* is the parallel resonant frequency, as given in Table 1. Once the switching frequency is fixed at *ω* = *ωp*, the output current, seen from the primary side of the transformer, i.e., through *Cs*, **Iac**, is calculated by (6).

$$\mathbf{I}\_{\mathbf{ac}} = -\frac{2V\_{dc}}{\pi Z\_p} \left\{ \sum\_{m=1}^{N} \sin \Psi\_{m-1} + j \sum\_{m=1}^{N} \cos \Psi\_{m-1} \right\} \tag{6}$$

From (6), the current source behavior is verified, given that **Iac** has no dependence on the load.

#### 4.1.2. Switching Mode

The switching losses are minimized by ensuring the zero voltage switch (ZVS) on the primary side of the converter [8,29]. The ZVS mode requires sufficient phase-delay of the resonant current with respect to the input voltage. A high value of *Qp* reduces the reactive energy in the resonant converter, which is beneficial from the point of view of reducing the conduction loss. However, some reactive energy must be accepted for ensuring the ZVS mode of all transistors. The complex form, **Ii**, of each resonant current is given in (7) as a function of the angles Ψ0, Ψ1,... , ΨN−1.

$$\mathbf{I}\_{\mathbf{i}} = \frac{2V\_{dc}}{\pi \mathbf{Z}\_p} \times \left\{ \begin{array}{c} \frac{Q\_p}{N} \sum\_{m=1}^{N} \cos \Psi\_{m-1} - \left( \frac{\mathbf{C}\_p}{\mathbf{N} \mathbf{C}\_s} - \frac{L\_l}{L} \right) \sum\_{m=1}^{N} \sin \Psi\_{m-1} - \sin \Psi\_{i-1} \\\\ -j \left[ \frac{Q\_p}{N} \sum\_{m=1}^{N} \sin \Psi\_{m-1} + \left( \frac{\mathbf{C}\_p}{\mathbf{N} \mathbf{C}\_s} - \frac{L\_l}{L} \right) \sum\_{m=1}^{N} \cos \Psi\_{m-1} + \cos \Psi\_{i-1} \right] \end{array} \right\} \tag{7}$$

In order to determine the power factor angle, *φi*, of each transistor's leg, the input impedance **Zi** = **Vi**/**Ii**, of each phase is calculated. The power factor angle, *φi* is obtained using *φi* = angle(*Zi*) as a function of the control angles, Ψ0, Ψ1, ... , ΨN−1, the number of phases, *N*, and the quality factor, *Qp*. Upon substitution of Ψ0 = Ψ1 = ... ΨN−1 = 0◦ in (5) and (7), *φi* at the maximum output current is obtained:

$$\phi\_i = \arctan\left(\frac{1 + \frac{C\_p}{C\_s} - N\frac{L\_k}{L}}{Q\_p}\right). \tag{8}$$

From (8), it can be observed that the effect of leakage inductance referred to the primary side of the transformer, *Lk*, is more significant for high-power as well as for highfrequency designs, where the value of inductance of the resonant circuit, *L*, is usually low, and a high value of leakage inductance could produce the loss of the ZVS mode. However, the series disposition of *Lk* and *Cs* enables the cancelation of the *Lk* effect on the AC side by calculating *Cs* to achieve, at the switching frequency, the series resonance with *Lk*. According to this proposal, *Cs* is obtained from (9).

$$\mathbb{C}\_{\mathfrak{s}} = \frac{L}{N L\_{\mathfrak{k}}} \mathbb{C}\_{p} \tag{9}$$

With the cancellation of the *Lk* effect, the value of the power factor angle, *φi*, depends essentially on the value of the quality factor *Qp*, which is set during the design process of the converter. The minimum value of power factor angle for achieving ZVS, *φ*zvs, depends on the dead time, *td*, of the transistors' driver and the switching frequency *ωp* [33].

$$
\varphi\_{z\upsilon s} = \frac{t\_d \omega\_p}{2\pi} \cdot 360^{\circ} \tag{10}
$$

As design criteria, a value of power factor angle *φi* = 2*φzvs* is assumed at nominal conditions for achieving a reliable operation of the converter. This is the most restrictive design condition for operating in ZVS mode for the whole range of variation of the control angle Ψ. From (8) to (10), the value of the quality factor at nominal conditions, *QpN*, is obtained:

$$Q\_{pN} = \frac{1}{\tan 2\varphi\_{z\nu s}}\tag{11}$$

4.1.3. Variation of the Quality Factor and Transformer Turns Ratio

During the charging process, the equivalent impedance of the battery, *RBat*, changes depending on *VBat* and *IBat*, whose relationship is given by the charging profile of the battery, as shown in Figure 1. At the end of the CC stage, *VBat* = *VBat*(*Max*) and the power supplied to the battery reaches the maximum, *PBat* = *VBat*(*Max*)*IBat*(*Max*). The specifications of the point of maximum output power are used for defining the nominal value of the quality factor, *QpN*. Thus, during the CC stage of the charging profile, the converter works with a quality factor lower than the nominal one, which strengthens the inductive behavior of the resonant tank, assuring the ZVS mode.

During the CV stage, the reduction of the charging current leads to a significant increment in the equivalent resistance *RBat* and consequently, the reflected impedance on the AC side, *Rac*, and the quality factor *Qp* also increase. Assuming that *VBat*(*Max*) is constant and working with (6), the quality factor as a function of Ψ is obtained in (12),

$$Q\_{\mathcal{P}} = \frac{n\pi^2 V\_{\text{Bat}(\text{Max})}}{2V\_{\text{dc}}} \frac{N}{\sqrt{\left(\sum\_{m=1}^{N} \sin \Psi\_{m-1}\right)^2 + \left(\sum\_{m=1}^{N} \cos \Psi\_{m-1}\right)^2}} \tag{12}$$

The increment of *Qp*, as a consequence of the reduction of the charging current during the CV stage could put at risk the ZVS mode of the transistors of the converter. However, it is beneficial from the point of view of achieving waveforms with low distortion and increases the converter efficiency. The nominal value of quality factor is obtained by evaluating (12) for Ψ0 = Ψ1 = ΨN−1 = 0◦.

$$Q\_{pN} = \frac{n\pi^2 V\_{Bat(Max)}}{2V\_{dc}}\tag{13}$$

From (13) and (11), the transformer's turns ratio (*n*:1) can be obtained:

$$m = \frac{2V\_{dc}}{\pi^2 V\_{Bat(Max)} \tan 2\varphi\_{zvs}}.\tag{14}$$

#### *4.2. Output Current Multiplier*

In order to analyze the output current multiplier stage, first, a single-winding currentdoubler rectifier with an ideal transformer, as seen in Figure 8, is considered. The quasisinusoidal voltage *vac* at parallel capacitor *Cp* drives the current multiplier stage. The diodes *D*1 and *D*2 turn on alternatively according the positive or negative cycle of *vac*, respectively.

**Figure 8.** (**Left**) Current-doubler rectifier considering the positive semi-cycle of the drive voltage *vac*. (**Right**) Theoretical voltage waveform at the filter inductors.

The diodes conduction time, *t*1, is obtained from the volts–seconds balance across the inductors. The areas are calculated according to the approximation shown in Figure 8 right.

$$t\_1 = \frac{n\pi}{1 + n\pi}T\tag{15}$$

The average current through each inductor, *Lo*1,2, is equal to one-half of the charging current *IBat*. The amplitude of the current ripple in each inductor is determined by

$$
\Delta \dot{\mathbf{u}}\_L = \frac{n\pi^2 V\_{\text{Bat}(Maxx)}}{(1 + n\pi)\omega\_P L\_o}.\tag{16}
$$

The total ripple current through the filter capacitor *Co* is calculated considering *M* parallel rectifiers and taking into account the ripple cancellation effect due to the 180◦ phase displacement between the current through each inductor [31,32] in the current-doubler structure; thus,

$$
\Delta i\_{\mathbb{C}} = \frac{n\pi^2 MV\_{\text{But}(\text{Max})}}{2(1 + n\pi)\omega\_p L\_o} \tag{17}
$$

The output voltage ripple is

$$
\Delta v\_{Bat} = \frac{n\pi^3 MV\_{Bat(Max)}}{16(1 + n\pi)\omega\_p^2 L\_o C\_o} \tag{18}
$$

From (18), the ripple of the charging current is a function of the switching frequency, output filter components, and battery parameters.

$$
\Delta i\_{\rm Bat} = \frac{n\pi^3 MV\_{\rm Rat}(\rm Max)}{16(1 + n\pi) r\_{\rm Bat} \omega\_p^2 L\_o C\_o} \tag{19}
$$

The limitation of the output current ripple, Δ*iBat*, is mandatory in order to avoid the battery degradation [12].

Reflected Impedance on the Primary Side of the Transformer

Since the output filter removes the high-frequency ripple, the low ripple approximation [29] is used to study the proposed rectifier in steady state. Considering the total current in the primary side and using the first harmonic of the square waveform, the relationship between the AC and DC currents is given in (20).

$$\mathcal{I}\_{\rm ac} = \frac{2I\_{\rm Bat}}{n\pi} \tag{20}$$

where *Îac* is the amplitude of the transformer's primary current. From (20) and (6), the charging current is obtained as a function of the angles Ψ0, Ψ1,... , ΨN−1,

$$I\_{Bat} = \frac{nV\_{dc}}{Z\_p} \sqrt{\left(\sum\_{m=1}^{N} \sin \Psi\_{m-1}\right)^2 + \left(\sum\_{m=1}^{N} \cos \Psi\_{m-1}\right)^2} \tag{21}$$

The normalized amplitude of the charging current, *IBat*, is depicted in Figure 9 as a function of the control angle, Ψ, and considering the modulation pattern where all phases are evenly shifted.

**Figure 9.** Amplitude of the normalized charging current, *IBat*, as a function of the control angle, Ψ, for *N* = 2, 3, and 4. All phases are evenly shifted, Ψ0 = 0◦, Ψ1 = Ψ, Ψ2 = 2Ψ,... , ΨN−1 = (*N*–1)Ψ.

Working with (21), the maximum charging current is achieved at Ψ0 = Ψ1 = ΨN−1 = 0◦ and is given by

$$I\_{\text{Bat}(\text{Max})} = \frac{nV\_{dc}}{Z\_p} \cdot N \tag{22}$$

From (22), it can be observed that the output current capability of the multiphase converter is enhanced by increasing the number, *N*, of paralleled phases. An accurate acquisition of the modulation angle, covering the whole range over the entire battery charging process, facilitates the computation of ampere-hours in order to calculate the supplied capacity.

The amplitude of the voltage in the primary side of the transformer is obtained from the power balance in the windings. Assuming a lossless transformer,

$$P\_{\rm ac} = P\_{\rm Bat} = \frac{I\_{\rm ac} \mathcal{V}\_{\rm ac}}{2} = I\_{\rm Bat} V\_{\rm Bat} \tag{2.3}$$

and substituting (20) into (23),

$$
\hat{\mathcal{V}}\_{\rm ac} = n\pi V\_{\rm Bat} = n\pi r\_{\rm Bat} \cdot I\_{\rm Bat} + n\pi \cdot V\_{\rm Bat} \,. \tag{24}
$$

From (20) and (24), the battery is modeled from the AC side by

$$
\hat{\mathcal{V}}\_{\rm ac} = \frac{n^2 \pi^2}{2} r\_{\rm But} \cdot \hat{\mathcal{I}}\_{\rm ac} + n \,\pi \cdot V\_{\rm But}.\tag{25}
$$

The reflected impedance of the current multiplier and load, *Rac*, into the AC side of the converter defines important characteristics of the resonant inverter, such as the switching mode of the transistors, the distortion of the waveforms, and the efficiency [11]. From (25), the rectifier stage is reflected into the AC side as the equivalent resistance *Rac* in (26),

$$R\_{\rm ac} = \frac{\pi^2}{2} n^2 R\_{\rm Bat} = \frac{\pi^2}{2} n^2 \left( r\_{\rm Bat} + \frac{V\_{\rm Bat}}{I\_{\rm Bat}} \right) \tag{26}$$

Assuming an ideal transformer, where the leakage inductance reflected in the secondary side is *Lks* = 0, the maximum voltage across the diodes is *VB* = −*nπVBat*. However, in practice, *Lks* is in series with the junction capacitance of the reverse-biased diode, *Cj*, causing a high-frequency oscillation or ringing. The selection of the Schottky devices takes into account the minimization of this effect.

#### **5. Efficiency of the Multiphase** *LCpCs* **Resonant Converter**

The overall efficiency of the converter is calculated by

$$
\eta = \eta\_I \cdot \eta\_{R\prime} \tag{27}
$$

where *ηI* is the efficiency of the resonant inverter stage and *ηR* is the efficiency of the output current multiplier stage.

#### *5.1. Efficiency of the Inverter Stage*

Taking into account the ZVS mode operation of the converter, the switching loss is considered negligible in comparison to the conduction loss. The efficiency of the resonant inverter stage, *ηI*, considering the conduction loss only [16] is

$$\eta\_I = \frac{1}{1 + \frac{r}{\mathbb{R}\_{\text{ac}}} \cdot \frac{\sum\_{i=1}^{N} I\_i^2}{I\_{\text{ac}}^2}} \tag{28}$$

where *Îi* is the amplitude of each resonant current given in (7). The resistance *r* represents the *rdson* of the transistors as well as the ESR of the inductors. The highest efficiency, *ηI*(*Max*), is achieved with Ψ0 = Ψ1 = ... = ΨN−1 = 0◦. Upon substitution of Ψ0 = Ψ1 = ... = ΨN−1 = 0◦ in (28) and under the assumption that *Cs* is calculated according to (9), the maximum efficiency as a function of the ratio *r*/*Rac*, the nominal value of the quality factor, *QpN*, and the number of phases, *N*, is obtained.

$$\eta\_{I(\text{Max})} = \frac{1}{1 + \frac{r}{N R\_{\text{ac}}} \cdot \left[1 + Q\_{pN}^2\right]} \tag{29}$$

From (28), it is observed that *ηI*(*Max*) is improved by increasing *Rac*. The straightforward way to increase *Rac* is through the larger transformer turns ratio, *n*. However, it should be considered that *QpN* increases with *n*, according to (12), which could jeopardize the ZVS mode of the converter transistors. Taking into account the tight correlation among, *N*, *QpN*, *n*, and *r*/*Rac*, the design process oriented to find a suitable value of these parameters involves iterative cycles. Upon the substitution of (12) and (20) into (29), *ηI*(*Max*) is obtained as a function of the converter parameters,

$$\eta\_{I(\text{Max})} = \frac{1}{1 + \frac{\pi^2 r I\_{\text{Bat}(\text{Max})} V\_{\text{Bat}(\text{Max})}}{2N V\_{d\varepsilon}^2} + \frac{2r I\_{\text{Bat}(\text{Max})}}{n^2 \pi^2 N V\_{\text{Bat}(\text{Max})}}} \approx \frac{1}{1 + \frac{2r I\_{\text{Bat}(\text{Max})}}{n^2 \pi^2 N V\_{\text{Bat}(\text{Max})}}} \tag{30}$$

The maximum efficiency of the resonant inverter stage, *ηI*(*Max*), improves, approaching one asymptotically as the number of phases, *N*, increases.

#### *5.2. Efficiency of the Output Current Multiplier*

Limiting the current level through the output rectifier stage is a major design challenge oriented to reduce the conduction loss. The proposed *M*-windings output current multiplier lowers the amplitude of the current through diodes by a factor *M* and the average current through filters inductors by a factor 2*M*. An expression for the rectifier efficiency, *ηR*, only including the conduction loss, is obtained from the analysis of the current paths shown in Figure 7. Considering a lossless transformer, the total power, *PT*, in the secondary side of the current multiplier is

$$P\_T = P\_{Bat} + M\left(\frac{V\_D I\_{Bat}}{M} + \frac{I\_{Bat}^2 r\_D}{M^2} + \frac{I\_{Bat}^2 r\_{LF}}{4M^2}\right),\tag{31}$$

where *PBat* is the output power, *PBat* = *VBat*·*IBat*, *VD* and *rD* are the voltage and dynamic resistance of the linear model of the diode, and *rLF* is the ESR of the filter inductor *Lo*. The efficiency, *ηR*, is calculated with *ηR* = *PBat*/*PT*,

$$\eta\_{\mathcal{R}} = \frac{1}{1 + \frac{V\_D}{V\_{\text{Rat}}} + \frac{\left(\frac{V\_D}{R} + \frac{V\_{\text{Rat}}}{R}\right)I\_{\text{Rat}}}}.\tag{32}$$

The efficiency of the output current multiplier, *ηR*, is improved by increasing the number of secondary windings, *M*. The theoretical limit *ηR*(*Max*) of *ηR* is obtained letting *M*→∞,

$$\eta\_{R(\text{Max})} = \frac{1}{1 + \frac{V\_D}{V\_{\text{Rat}(\text{Max})}}}.\tag{33}$$

From (32) and (33), it can be observed that the ratio *VD*/*VBat*(*Max*) should be minimized, which confirms the benefit of using Schottky diodes or sync rectifiers to improve the efficiency of the rectifier stage.

#### *5.3. Optimum N and M of Parallelized Stages*

The expressions (30) to (33) are used as a criterion to define the appropriate number of phases, *N*, of the resonant inverter stage as well as the number of secondary windings, *M*, of the output current multiplier. The maximum efficiency of the inverter section, *ηI*(*Max*), and the efficiency of the current multiplier, *ηR*, are depicted in Figure 10 as a function of *N* and *M*.

**Figure 10.** Maximum efficiency of the resonant inverter stage, *ηI*(*Max*), and efficiency of the output current multiplier, *ηR*, as a function of the number of phases, *N*, and secondary windings *M*. The following typical values are assumed: *n* = 2, *r* = 1.7 Ω, *IBat*(*Max*) = 20 A, 2*rIBat*(*Max*)/π2*V*Bat*(*Max*)* = 0.5, *VD*/*VBat*(*Max*) = 0.05 and *rD = rLF* = 0.1.

From a practical point of view, the asymptotic variation of *ηR* and *ηI*(*Max*), shown in Figure 10, limits the maximum values of *M* and *N*. The criterion for choosing the suitable values of *M* and *N* is a tradeoff between the increment of the efficiency and the circuit complexity. It is assumed that if the increment of efficiency achieved is barely 1%, a higher number of secondary windings *M* or phases, *N*, is not justified.

#### **6. Design of the Multiphase** *LCpCs* **Resonant Converter**

#### **7. Control Circuit and Battery Modeling**

During the CV stage, the charging current must be regulated to avoid the voltage of the battery exceeding *VBat*(*Max*). The current is modulated through the phase-angles Ψ0, Ψ1, and ΨN−1, while keeping the switching frequency constant. Different patterns are possible for adjusting Ψ1, Ψ2, and Ψ*N*−1. For any value of *N*, the full control of the charging current is achieved if the phase shift is evenly distributed among all *N* phases, e.g., Ψ0 = 0◦, Ψ1 = Ψ, Ψ2 = 2Ψ ... Ψ*N*–1 = (*N*–1)Ψ. In this case, the minimum current *IBat* = 0 A is achieved at Ψ = 360◦/*N*. This pattern requires *N* control signals. For this design, where *N* = 4, the control angles are adjusted as follows: Ψ0 = Ψ1 = 0◦ and Ψ2 = Ψ3 = Ψ. For this approach, the minimum *IBat* = 0 A is achieved at Ψ = 180◦, and only two control signals are required, which implies a simplification of the control circuit.

Once the converter is designed, the battery-charger system is completed with a control loop to limit the output voltage of the charger to the maximum value recommended for the battery. The action of the control loop transforms the circuit's open-loop current source behavior into a voltage source. A type I error amplifier is enough for this action. The scheme of the charger-battery system, modeled in Simulink, is shown in Figure 11. In the voltage mode, the battery imposes the dynamic response of the converter-battery system [27].

**Figure 11.** Control loop for limiting the maximum battery voltage, *VBat*(*Max*).

The Simulink® model of the battery [34,35] is shown in Figure 12. The look-up tables include the quasi-open circuit voltage of a basic cell for the charge and discharge trajectories as a function of the *SOC*.

**Figure 12.** Simulink® model of the battery.

The different parameters of the model can be tuned using curve fitting. The data used as reference for adjusting the model were obtained from the experimental characterization of the battery charging at 25 A, which has been shown in Figure 1. The time constant for charge transportation and diffusion phenomena are 1 s and 100 s, respectively. The impedance for the charge transport is *Rt* = 0.7 mΩ and the capacitance is *Ct* = 1428 F. The impedance of the diffusion is *Rd* = 0.6 mΩ and the corresponding capacitance is *Cd* = 166,000 F. The impedance due to electrodes and electric connections is *R*Ω =1mΩ. The impedance of the battery pack is obtained from (4), *rbat* = 34.5 mΩ. This value of *rBat* includes the impedance of connectors and cables, which is used to conform to the battery by the series connection of the 15 cells.

The variation of the battery voltage, obtained from the simulation of the system in Figure 11, is shown in Figure 13. It can be observed that simulation and experimental results are in good agreement for the three charging profiles in Figure 2 that were evaluated experimentally.

**Figure 13.** Charging profiles at 10, 25, and 50 A. Solid lines: Experimental battery voltage. Dashed lines: Simulation result. Dot lines: Charging current.

#### **8. Results of the Experimental Prototype**

An experimental prototype, shown in Figure 14, has been built to validate the theoretical proposal.

**Figure 14.** Details of the experimental prototype of the charger. (**Left**) Four-phase resonant inverter stage. (**Right**) Currentdoubler rectifier.

When connecting the battery to the charger, an initial frequency sweep is programmed to ensuring the gradual growth of the charging current to prevent the occurrence of an overvoltage across the discharged battery. The experimental waveforms in different circuit sections are shown in Figures 15–17. In order to demonstrate the charger performance at different operation points, the waveforms for full load and 70% of full load operation are

shown. In Figure 15, it is observed that the resonant current has a phase lag with respect to the input voltage. At full load condition, *ϕi1,2* = *ϕi3,4* = 54◦, which is in good agreement with the theoretical value, and at 70% of the full load condition, *ϕi1,2* = 54◦, *ϕi3,4* = 72◦. The ZVS mode operation was verified for all phases of the resonant inverter section.

**Figure 15.** From top to bottom: Midpoint voltages of phases 1 and 2, *v1,2*. Midpoint voltages of phases 3 and 4, *v3,4*. Resonant current of phases 1 and 2, *i1,2*. Resonant current of phases 3 and 4, *i3,4*. (**Left**) Full load condition (Ψ0 = Ψ1 = Ψ2 = Ψ3 = 0◦). (**Right**) 70% of full load condition (Ψ0 = Ψ1 = 0◦, Ψ2 = Ψ3 = 90◦).

**Figure 16.** From top to bottom: Output current through the primary side of the transformer, *iac*. Output voltage applied to the primary side of the transformer, *vac*. (**Left**) Full load condition (Ψ0 = Ψ1 = Ψ2 = Ψ3 = 0◦). (**Right**) 70% of full load condition (Ψ0 = Ψ1 = 0◦, Ψ2 = Ψ3 = 90◦).

In Figure 16, the current and voltage at the primary side of the transformer are shown. The amplitude of the current square waveform is half (10 A) of the battery charging current. In Figure 17, the charging current at full load (20 A) and at 70% of full load are shown. The results are in good agreement with the theoretical value according to the control angle Ψ. It can be observed that the charging current ripple is negligible as it is required for this application. The experimental efficiency of the prototype measured at the point of maximum load (*IBat* = 20 A, *PBat* = 1.07 kW) was η = 91.3%. The efficiency at 70% and 50% of the full load was η = 90.2% and η = 88%, respectively. The experimental efficiency is slightly lower than the theoretical due to the switching losses, the power dissipation at the transistors drive circuit, and the auxiliary power supply loss.

**Figure 17.** From top to bottom: Midpoint voltages of phases 1 and 2, *v1,2*. Midpoint voltages of phases 3 and 4, *v3,4*. Charging current *iBat*. (**Left**) Full load condition (Ψ0 = Ψ1 = Ψ2 = Ψ3 = 0◦). (**Right**) 70% of full load condition (Ψ0 = Ψ1 = 0◦, Ψ2 = Ψ3 = 90◦).

#### **9. Discussion**

In this work, the general design method of the proposed charger has been explained, but the particular configuration of the final solution depends on the chosen technology. One key decision is the most suitable value of the dc-link voltage. The solution for an dc-link voltage *Vdc* = 400 V, which was obtained from a single-phase power factor corrector (PFC) based on a Boost Converter, and using the CoolMOSTM SPA11N60C3 MOSFET transistor and the STPS30M60S Schottky diode has been fully developed. As alternative, a solution with *Vdc* = 800 V, obtained from a three-phase PFC and using silicon carbide (SiC) components is also assessed. For this case, the third-generation C3M0065100K MOSFET transistor (Wolfspeed, Research Triangle Park, USA) with the CGD15SG00D2 driver (Wolfspeed, Research Triangle Park, USA) is used in the inverter section. As the voltage, current, and power at the circuit output are the same, the silicon (Si) Schottky diode STPS30M60S is used in both cases. For a better comparison, both designs are summarized in Table 2.

As it can be seen in Table 2, both designs achieve a similar theoretical efficiency, but the SiC technology uses only two phases for the resonant inverter stage.

#### *Considerations about the Solution Cost*

SiC technology for power devices is becoming more competitive in technical performance and cost. Important advances have been reported in terms of increasing the wafer diameter and minimization of the defect density [36], which contribute to lowering the cost of the devices, so it is worth comparing the cost of the proposed alternatives. Focusing on the inverter section of the described designs, i.e., *Vdc* = 400 V for the four-phase Si inverter and *Vdc* = 800 V for the two-phase SiC inverter, the cost assessment reveals that at present, the solution based on SiC components is more expensive despite requiring fewer transistors. The cost of the third-generation SiC MOSFET C3M0065100K is five times (5 ×) that of the SPA11N60C3 Si MOSFET. On the other hand, in contrast to the simplicity of the half-bridge driver, based on the integrated circuit IR2111, the complexity and cost of the selected driver CGD15SG00D2 for SiC MOSFETS are also significantly higher [37]. In addition, the PFC section adds a cost difference in favor of the *Vdc* = 400 V four-phase Si

design. For illustrating the analysis, in Tables 3 and 4, the cost of the SiC components and its Si counterparts are summarized [38]. Differences in the magnetic elements, capacitors, and control circuit have less impact on cost.

**Table 3.** SiC resonant inverter.

Nowadays, for a given architecture, the use of SiC MOSFETs could be recommended if the maximum current, voltage, and temperature limits of the Si MOSFETs are compromised, e.g., for charging currents and powers higher than 50 A and 2.5 kW, respectively.

#### **10. Conclusions**

The general design procedure of a multiphase resonant converter for battery charger applications has been presented. Since the output current on the AC side is shared among *N* equal inverter sections, the circuit presents high output current capability using low-cost power MOSFETs, and the design of the resonant inductors is simplified. The proposed output rectifier is based on an *M*-winding current-doubler rectifier that also diminishes the conduction loss by using passive components. The efficiency curve of the proposed charger exhibits a wide flat zone, assuring a constant value of efficiency even at light load conditions. This feature is very interesting for the battery charger applications, taking into account that high efficiency is desirable along the whole charging process, despite the heavy load variation. The effect on the AC side of the leakage inductance of the transformer *Lk* is canceled out by the series capacitor *Cs*. The maximum charging current is limited by the circuit in an inherent manner, without the necessity of any control. However, the output voltage is limited to the maximum value recommended for the battery by a voltage control loop with a type I error amplifier. The control action is performed keeping constant the switching frequency by adjusting the control angle, Ψ, while maintaining the ZVS mode at any operation point. The general proposal has been validated by implementing an experimental prototype for charging a commercial 48 V LiFePO4 battery with 50 Ah of capacity. The achieved efficiency of the *N* = 4 inverter with *Vdc* = 400 V using Si MOSFETs is similar to the predicted with an *N* = 2 inverter with *Vdc* = 800 V using SiC MOSFETs.

**Author Contributions:** The battery characterization and the experimental evaluation of the different charging profiles were carried out at the Batteries Laboratory of University of the Oviedo by J.C.V. and M.G. The proposed charger was developed at the Power Electronics Laboratory of the University of Cantabria by C.B., F.J.A., R.C. and F.J.D. Conceptualization, C.B. and J.C.V.; methodology, C.B. and J.C.V.; validation, C.B., J.C.V., R.C. and F.J.D.; formal analysis, C.B. and J.C.V.; investigation, C.B., J.C.V. and F.J.A.; writing—original draft preparation, C.B. and J.C.V.; writing—review and editing, F.J.A., M.G., R.C. and F.J.D.; project administration, F.J.A. and M.G.; funding acquisition, F.J.A. and M.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Spanish Ministry of Science and the EU through the projects RTI2018-095138-B-C31: "Power Electronics for the Grid and Industry Applications", TEC2016- 80700-R (AEI/FEDER/UE), PID2019-110955RB-I00, and by the Principality of Asturias via Project FC-IDI/2018/000226.

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

#### **References**

*Article*

## **A Novel High-E**ffi**ciency Double-Input Bidirectional DC**/**DC Converter for Battery Cell-Voltage Equalizer with Flyback Transformer**

**Fengdong Shi 1,2 and Dawei Song 1,2,\***

Received: 30 October 2019; Accepted: 27 November 2019; Published: 29 November 2019

**Abstract:** Large-scale battery cells are connected in series, which inevitably leads to a phenomenon that the cell voltage is unbalanced. With a conventional equalizer, it is challenging to maintain excellent characteristics in terms of its size, design cost, and equalization efficiency. In order to improve the defects in the above equalization circuit, a novel voltage equalization circuit is designed, which can work in two modes. A bidirectional direct current–direct current (DC–DC) equalization structure is adopted, which can quickly equalize two high or low-power batteries without using an external energy buffer. In order to verify the effectiveness of the proposed circuit, a 12-cell battery 2800-MAh battery string was applied for experimental verification. Computer monitoring (LabVIEW) was adopted in the whole system to intelligently adjust the energy imbalance of the battery pack. The experimental results showed excellent overall performance in terms of equalization was achieved through the newly proposed method. That is, the circuit equalization speed, design cost, and volume have a good balance performance.

**Keywords:** battery equalization; flyback transformer; topology

#### **1. Introduction**

Lithium-ion batteries have been widely used in the field of electric vehicles due to their high charging–discharging times and high energy efficiency. Since the battery pack in a pure electric vehicle is connected in series and in parallel through a large number of battery cells, some of the battery cells may be unbalanced during the continuous charging and discharging process of the battery. The overall performance of the battery pack will be restricted by the battery cells with the lowest battery capacity, which will seriously affect the service life of the battery pack and reduce the battery life of the electric vehicle [1,2]. Battery equalization technology can suppress imbalance in the battery pack, leading to improved work consistency. The battery management system is able to operate well, which can ensure safe driving of new energy vehicles, and the working principle is shown in Figure 1. Excess energy (Converted Energy in the legend) can be transferred from cell 1 to cell 2 through the energy converter. A relatively balanced state is achieved between the two cells, and so on, resulting in consistent energy obtained by the entire battery pack.

In recent years, plenty of battery pack equalization methods have been proposed [3–6]. The equalization method has been divided into different categories according to various criteria. The energy dissipation has two types [7,8]: switch shunt and fixed shunt. This equalization circuit with a simple structure was easy to control. However, the converted heat will result in increased temperature in the entire battery pack, and the system will require extra energy. Compared with the energy dissipation type, a peripheral energy conversion circuit was applied to balance the voltage of the

battery through the non-energy dissipation equalization method. Although the circuit is more complex, it is more efficient and safe according to the different means of energy transmission. These methods are further subdivided into four types: cell-to-cell equalization methods, cell-to-pack equalization methods, pack-to-cell equalization methods, and cell-to-pack to cell equalization methods, as shown in Figure 2.

**Figure 1.** Battery balance diagram.

In the above equalization method, the monomer-to-monomer equalization method and the monomer-to-battery equalization method can effectively prevent overcharging and over-discharging of the battery. Even if the energy overlap and high-pressure stress in the equilibrium process are considered, the equilibrium efficiency cannot be guaranteed. In contrast, cell-to-cell equalization methods with short and efficient transmission paths are ideal choices. These methods are further subdivided into three types: transmission equalization methods, a non-isolated direct current–direct current (DC–DC) equalization method [9], and an isolated DC–DC equalization method [10]. One of the most conventionally used topologies of the transmission equalization methods is the bidirectional buck-boost converter [11]. Every two adjacent cells have a common buck-boost converter to achieve energy transfer. However, when the positions of the unbalanced batteries are not adjacent, the path of energy transfer becomes long. In order to compensate for the shortcomings of such equalization methods, Li, Y proposed a structure of an equalization method [12].

**Figure 2.** Battery balance-type diagram.

This circuit transfers energy from the most charged unit to the least charged unit to have higher equalization efficiency, but at the expense of lower equalization speed. Another direct cell-to-cell equalization method which uses an inductor as the energy storage component has fast equalization. However, each battery has two directional transmission channels, which require a large number of switches and diodes. Similarly, the direct inter-cell equalization method using a transformer ensures a fast equalization speed [13], but the use of a large number of transformers is costly. Obviously, the aforementioned direct cell-to-cell equalization method cannot achieve fast equalization speed and high efficiency, and relatively low cost.

In order to improve the deficiencies of these defects, a dual-winding battery equalizer with energy bidirectional flow was proposed. The advantage is that the cells with low energy are supplemented, and the cells with high electric quantity are effectively weakened. The principle of operation is an equalization structure using bidirectional forward and flyback equalization. Any two high-energy cells or low-energy cell in the battery pack was quickly equalized without external energy buffer. To realize the effective balance of the whole battery pack.

#### **2. Proposed Equalization Topology**

#### *2.1. Proposed Equalizer*

The proposed voltage equalizer is composed of a left and right sides interleaved switching network and an isolated double winding DC–DC converter. Figure 3 shows an equalization structure based on a flyback coaxial multi-winding output, which is mainly composed of a flyback transformer *T*1 and a battery pack *B*1-*Bn* circuit. The battery pack as a whole and single cells form a loop through the output winding of each channel. Energy is transmitted to the battery cell from one direction.

**Figure 3.** Coaxial multi-winding equalizer.

The equilibrium method proposed in this paper could be extended from the original single-to-single equilibrium to the multi-to-two equilibrium structure. The staggered switching network is combined with the two operation modes. Bidirectional equalization is realized in the energy-transfer process as shown in Figure 4. The left and right sides are staggered control switches by the application of a two-winding flyback transformer for output isolation. The bidirectional equalization equivalent circuit is shown in Figure 5.

**Figure 4.** New voltage equalizer.

**Figure 5.** Equalization equivalent circuit.

Each cell is connected with a control switch. The control switch *K*1-*K*2*n*+1 is on the left side of the battery pack. The corresponding cell is *A*1-*A*2*n*+1. The control switch *K*0-*K*2*n* is on the right side of the battery pack and the corresponding cell is *A*0-*A*2*n*. The control switch network on the left is connected to the output side winding *A2N*−*1* of the flyback transformer. The control switch network on the right side is connected to the output side winding *A*2, the battery pack is integrally connected to the *L*0 end of the flyback transformer.

The flyback mode was applied when the number of unbalanced battery cells in the battery pack increased, which indicated that the energy of the battery pack and the battery cells are directly subjected to two-way energy transfer. There are two kinds of equilibrium situations. One is that the excess energy in the high-power battery cell was transferred to the positive battery pack, eliminating the effect of excessive power. The other is that the energy was provided by the battery cell with low battery capacity, so that the damage of the battery itself induced by over flushing or over discharging of an individual cell can be avoided.

When the energy difference between the individual cells in the battery pack is large, and the equalization mode will adopt forward operation mode, the cell can be directly connected to the *A*2*N*−1 and *A*2 windings on the output side for fast equalization.

The new battery equalizer uses the two modes of operation to work together. Flyback mode is "rough-tuning" and Forward mode is "fine-tuning" synergism, which achieves the goal of efficient and balanced, making efficient use of energy.

#### *2.2. Equilibrium Process Analysis*

According to the voltage difference in different single cells as the judgment basis. The equalization method was proposed in this paper to select forward operation mode or flyback operation mode. Finally, efficient and fast equalization of the battery pack was realized, and the specific balancing strategy will be discussed in detail as follows.

Case 1: when the batteries in the group are unbalanced and the voltage difference is large (less than 0.4 V), the operation flyback mode timing is as shown in Figure 6a. In a work cycle, the working process of the flyback transformer can be divided into two stages according to the difference between the control signal and the current path in the circuit. During the process of charging, the energy was transferred from the primary side *L*0 of the transformer to the secondary sides *L*1 and *L*2. The drop of conduction voltage in the control switch is *VD*1 and *VD*2. The overall primary side voltage *VL*0 of the battery pack and the output side voltage are *VL*1, *VL*2. The energy was transferred from the secondary side of the transformer to the primary side during discharge.

**Figure 6.** Flyback transition timing diagram. (**a**) Flyback converter energy forward flow timing diagram; (**b**) Flyback converter energy reverse flow timing diagram.

The following circuit workings in detail were defined as follows: the leakage inductance of the multi-winding transformer is *Lk*, the magnetizing inductance denotes Lm. In the primary winding of the transformer, the voltage at the input port is *VL*0, the output port voltage is *VL*1 and *VL*2.

$$V\_{L1} = -(\frac{N\_{L0}}{N\_{L0}})V\_{L0} \tag{1}$$

$$V\_{L2} = -(\frac{N\_{L2}}{N\_{L0}})V\_{L0} \tag{2}$$

The coefficient of leakage inductance for *VL*0 is *K*, which can be expressed as:

$$K = \frac{L\_k}{L\_m} \tag{3}$$

The energy is transmitted from the primary side to the secondary side, which was shown in Figure 6b. It is divided into the following two modes.

Model 1 (*t*0~*t*1): the *Q*1 switch is turned on, the current *Ip* in the primary side *L*0 of the transformer increases. When *t* = *to*ff, *IQ* reaches the maximum value. The energy is stored in the magnetizing inductance *Lm* of the transformer. Where in the exciting inductor current *iLM* is:

$$i\_{Lm} = i\_{Lk} = \frac{V\_{L0} - V\_D}{L\_m + L\_k} t\_{\text{ou}} \tag{4}$$

The peak value of the inductor current at the time of *ton* is:

$$i\_{pk} = i\_{LK} I\_{t = t\_{on}} = \frac{(V\_{L0} - V\_D)DT}{L\_m(K+1)} \tag{5}$$

where *D* is the duty cycle of the control switch. *T* is the turn-on switching period of the flyback converter, the energy stored E in the transformer is:

$$E = \frac{1}{2} L\_{\text{ll}} i\_{\text{pk}}^2 = \frac{(V\_{L0} - V\_D)^2 D^2 T^2}{2L\_m (K+1)^2} \tag{6}$$

In this process, the iron core of the transformer is magnetized. Wherein the increase in the magnetic flux Φ is:

$$
\Delta\Phi\_{(+)} = \frac{V\_{L0}}{N\_{L0}} D t\_{\rm ou} \tag{7}
$$

Model 2 (*t*1~*t*2): the *Q*1 switch is turned off, the secondary side switches *Q*2 and *Q*3 are both open. Its current is slowly reduced to Ismin, *iD*2 and *iD*3, charge capacitors *C*1 and *C*2. The energy in the stored primary side is transferred to the low-energy cell for charge equalization. The secondary inductor current gradually decreases and the falling slope is:

$$\frac{d i\_{L1k}}{dt} = -\frac{V\_{L1} + V\_{D1}}{L\_1 + L\_{1k}}\tag{8}$$

$$\frac{di\_{L2k}}{dt} = -\frac{V\_{L2} + V\_{D2}}{L\_2 + L\_{2k}}\tag{9}$$

In this process, the core of the transformer is demagnetized. The magnetic flux Φ is also linearly reduced, where the reduction Φ is:

$$
\Delta\Phi\_{(-)} = \frac{\mathcal{U}\_{L1}}{N\_{L0}} (1 - D) t\_{\text{on}} \tag{10}
$$

The process of turning on and off the energy from the secondary side to the primary side, in principle, is the same as the above process. Therefore, the description is not repeated.

Case 2: when the cells in the group are unbalanced, the voltage difference becomes large (no less than 0.4 V). A forward operating mode was applied in the topology without the output of inductance, considering that the selected battery cells *A*2*N*−1 and *A*2 are monomers with a large difference in power. The circuit topology is shown with the dotted line in Figure 5. The specific working process of this model is analyzed as follows. The working sequence diagram is shown in Figure 7.

**Figure 7.** Forward transition timing diagram.

(1) Model 1(*to*~*t*1): when *t* = 0, the switch tubes *Q*2 and *Q*3 are turned on. The voltages of the battery cells *A*2*n*−1 and *A*2 are applied across the output windings *L*1 and *L*2 of the flyback converter, respectively. Battery *A*2*n*−1 charges the primary winding Lm1 through *Q*2 as shown in Figure 5. The voltage across Lm is *VA*2*n*−1-*VD*2 where the direction is up and down. Meanwhile, the induced voltage across the winding *Lm*2 is *VA*2*n*-1-*VD*2 due to the coupling relationship of the voltage transformation, its direction is up and down. A peak current of *I*0 was produced from the secondary winding circuit under the turn-on instant. The core is magnetized and the magnetic flux is maximized during this process. The current on winding *L*1 and winding *L*2 increases and the voltage across the battery is directly parallel balanced.

$$I\_0 = \frac{V\_{L1} - V\_{D1} - V\_{A2}}{R\_{eq}} \tag{11}$$

where *Req* denotes the equivalent resistance of the battery *A*2 loop, then the voltage across the secondary winding *L*2 is clamped at *VA*2 + *VD*2. The inductance current in the circuit decreases linearly.

Its slope is:

$$\frac{d\dot{l}\_{L2k}}{dt} = -\frac{V\_{A2} + V\_{D2}}{L\_2 + L\_{2k}}\tag{12}$$

During the period of *t*0-*t*1, the currents of windings *L*1 is:

$$i\_{L1}(t) = I\_0 - \frac{V\_{A2N-1} + V\_{D1}}{L\_1 + L\_{1K}}(t - t\_0) \tag{13}$$

At time *t*1, the bidirectional switches *Q*1 and *Q*2 are turned off. The mode ends and the current of the winding *L*1 at time *t*1 is:

$$i\_{L1}(t1) = I\_0 - \frac{V\_{A2N-1} + V\_{D1}}{L\_1 + L\_1 K} DT \tag{14}$$

The current of the primary winding at time *t*1 is:

$$i\_{L1k}(t\_1) = I\_{\max} + \frac{V\_{A2N-1} - V\_{D1}}{L\_{1m}(1+K)}DT\tag{15}$$

The energy stored in the transformer at this time is:

$$\mathcal{W}\_{L1m} = \frac{\left(V\_{A2N-1} - V\_D\right)^2}{2L\_{1M}(1+K)^2}D^2T^2\tag{16}$$

(2) Model 2 (*t*1~*t*2): at *t* = *ton* time. Turn off the switch tubes *Q*2 and *Q*3. Switch tubes *Q*2 and *Q*3 is turned off when *t* is at *ton.* There is no current flowing through the winding *L*1 and *L*2. At this point, the transformer conducts magnetic reset through the reset winding. The excitation current is fed back to the whole battery pack through the primary side. Finally, the reset of the magnetic flux is realized.

$$\frac{d\dot{q}\_{L2k}}{dt} = -\frac{V\_{A2} + V\_{D2}}{L\_2 + L\_{2k}}\tag{17}$$

$$i\_{L2}(t) = I\_{L2}(t\_1) - \frac{V\_{A2} + V\_{D2}}{L\_2 + L\_2 K}(t - t\_1) \tag{18}$$

At this point, the energy is completely transferred at time *t*2. The current *iL*2(t) becomes zero and the transformer completes the magnetic reset.

#### *2.3. Design Consideration of the Main Circuit*

This article uses a two-winding bidirectional flyback converter. Whether energy is from *Vin* to *Vout*, or energy is from *Vout* to *Vin*, the switch *Q*1 is turned on when the diode *D*1 opposite to it is energized. The switch tube *Q*2 is turned on. When the *D*2 is energized and all the zero-voltage switching (ZVS) are turned on. In the bidirectional flyback converter, the current alternates and the current work continuously. Let *Q*1 have a duty cycle of *DQ*1. When the energy flows *Vin* to *Vout1*, the input voltage and output port voltage are expressed as:

$$\frac{V\_{IN}}{V\_{out1}} = \frac{L\_2}{L\_1} \times \frac{D\_{Q1}}{1 - D\_{Q2}}\tag{19}$$

If *DQ*2 is the duty cycle of *Q*2, when energy flows from *Vout*1 to *Vin*1:

$$\frac{V\_{\text{out1}}}{V\_{in1}} = \frac{L1}{L2} \times \frac{D\_{Q2}}{1 - D\_{Q1}}\tag{20}$$

Assuming that the input voltage Vin is 30–45 V, the output voltage Vout is 3.8–5 V and the switching period *T* is 40 μs. And then the duty ratio *D* can be derived to be 68%. The average equalization current *Ipk* is calculated to be 1.52 A.

The peak equalization current is expressed as follows:

$$I\_{pk} = \frac{2P\_{in}}{D\_{\text{max}}V\_{\text{irmin}}} \tag{21}$$

The input power is expressed as follows:

$$P\_{\rm in} = \frac{p\_0}{E\_{ff}} = \frac{\mathcal{U}\_{out1} \times I\_{w1} + \mathcal{U}\_{out2} \times I\_{w2}}{E\_{ff}} \tag{22}$$

Considering the energy storage and conversion of the flyback converter. The primary inductance is expressed as follows:

$$L\_m = \frac{V\_{\text{inmin}} \times D\_{\text{max}}}{I\_{pk} \times f\_{\text{s}} K\_{RF}} = \frac{V\_{\text{inmin}} \times D\_{\text{max}}}{\left(\frac{2P\_{\text{in}}}{D\_{\text{max}}V\_{\text{inmin}}}\right) \times f\_{\text{s}} K\_{RF}} = \frac{\left(V\_{\text{inmin}} \times D\_{\text{max}}\right)^2}{2P\_{\text{in}}f\_{\text{S}}K\_{RF}}\tag{23}$$

The flyback transformer is equivalent to a coupled inductor. In the process of transferring energy from the primary side to the secondary side, because the coil has magnetic flux leakage the magnetic flux leakage energy cannot be transferred to the secondary party thereby causing the switching tube voltage to rise further. The clamp circuit connected to the primary and secondary sides of the bidirectional flyback transformer. This limits the switching tube voltage to the maximum value. This article uses the RCD (Resistance Capacitance Diode) absorption circuit, as shown in Figure 8.

$$R\_{\mathbb{C}} = \frac{V\_{\mathbb{C}}^2}{P\_{\mathbb{R}}} = \frac{2 \times V\_{\mathbb{C}}^2}{L\_{i\mathbb{K}} l\_p^2 f\_s} \tag{24}$$

$$C\_{\mathbb{C}} \ge \frac{V\_{\mathbb{C}}}{\Delta V\_{\mathbb{C}} R\_{\mathbb{C}} f\_s} \tag{25}$$

**Figure 8.** RCD absorption circuit.

The clamp capacitor *C* has the same voltage as the resistor *R*. The relationship between *R* and *C* can be obtained by the relationship between voltage and power transition. According to the above analysis, during the working process of the clamp circuit, the energy stored in the capacitor is consumed by the resistor. That is, the power consumed by the resistor is equal to the energy stored by the capacitor.

#### *2.4. Equalization Strategy*

The new voltage equalization structure was proposed in this paper. During the process of equalizing the battery pack, it is necessary to control the DC–DC converter in different operating modes. This can become an essential basis for working mode matching by the amount of cell voltage difference. Meanwhile, the corresponding control method was adopted to control the equalization switch network. The balancing strategy is shown in Figure 9. The strategy of equalization control should pay attention to the following points:

A. Selected battery port voltage as a criterion for equalization.

B. In the process of energy transfer, when the current is not zero, it will cause irreversible losses to the elements of the switch array in the long-term equalization process.

C. Balanced operation modes are divided into two types, which are switched according to the distribution of different battery voltages.

For A: the equalization control uses the battery port voltage as a reference. The equalization mode is selected according to the voltage dispersion degree of different unit cells. The highest voltage and the lowest voltage of the battery cells are *Vmax* and *Vmin*, and the difference between them is *Vd*. The difference between the voltages is:

$$V\_d = V\_{\text{max}} - V\_{\text{min}} \tag{26}$$

For B: when the switch network is switching. It is necessary to keep the flyback isolation converter off. Prevents damage to circuit components, which is caused by inrush current during switching.

For C: when the allowable difference *Vd* set by *Vd* is equalized, the balance is stopped until *Vd* is less than *Vd*. The specific equalization process is played by two working modes, which will be described in detail below as follows.

**Figure 9.** Equalization strategy flow chart.

Flyback mode: the problem of the voltage difference *Vd* has been addressed when this difference of each battery in the battery pack is no less than 0.4V. The battery pack as a whole was applied as energy input and only the battery pack was used as energy output through the flyback mode of operation. Due to the special two-winding output structure. The battery pack can simultaneously charge balance two low-power batteries, or two high-energy batteries can be fed as energy input for the entire battery pack.

Forward mode: when the pressure difference *Vd* of each cell in the battery pack is less than 0.4V, in forward mode select two low-power battery cells by connecting the two output windings of the transformer. Point-to-point supplementation of energy for fast balancing purposes.

#### **3. Experimental Results**

#### *3.1. Voltage Equalization System*

Figure 10 shows the structure of the voltage equalization system designed by the new voltage equalization structure proposed in this paper. Because the car power battery pack is composed of series batteries. Therefore, this article uses 12 battery cells in series for voltage equalization experiments. the battery voltage of the series can be monitored in real-time using the battery detection chip LTC6803. The main control unit communicates with the LTC6803 through SPI (Serial Peripheral Interface) to obtain the voltage of the battery cells of the battery pack and control the LTC6803. The master passes the output control signal. The LTC6803 controls the two-sided interleaved switching network through the S1, S2, S3...S12 pins. The master provides control and drives signals for the flyback isolation converter.

**Figure 10.** Voltage equalization system.

#### *3.2. Main Circuit Design*

In the new voltage equalization system, real-time acquisition and analysis for parameters of battery voltage and temperature parameters were performed by the main controller and voltage detection chip LTC6803. Different equalization modes are selected according to the number of unbalanced monomers, thus the equalization control was efficiently implemented. The switch array has a function of selecting a path, and the battery cells are connected to the double-winding flyback isolating converter by the switches on the left and right sides. The switch consists of a bidirectional MOS (Metal-Oxide-Semiconductor) tube. The six cells A1, A2, A3, A4, A5 and A6 at the bottom of the pool group are connected to the N-MOS (N-Metal-Oxide-Semiconductor) switch tube respectively. The left battery cells A7–A12 are connected to the P-MOS (P-Metal-Oxide-Semiconductor) switch tube, the specific working circuit is shown in Figure 11. The battery cell is connected to the switch tube through the optocoupler, the switch is connected to the gate of four MOS transistors, the first four switches of the battery pack are Sa12, Sb12, Sa11, Sb11, the gate of each set of switches is connected to the c-pole of the phototransistor in the optocoupler, the e pole is connected to the negative electrode of the battery cell, which possessed the lower three positions of the battery cell. For example, the switch corresponding to the battery unit A12 is Sa12. The gate of the four PMOS transistors is connected to the c pole of the optocoupler OPa12, and the e pole is connected to the negative electrode of the battery unit A9. The switch corresponding to the A1 battery cell is OPb1 on the right side in the switch array, the gates of the four N-MOS transistors are connected to the e-pole of the optocoupler OPb. The c pole is connected to the battery cell A4. The connection method is the same as the above discussion when the control switches of the remaining battery units are applied. An additional complicated switch drive circuit is not required for the structure, the driving voltage of MOS is directly provided by the battery pack, the optocoupler is connected to the left and right switch arrays for signal control, which acts as a signal isolation function, the battery structure is simple and efficient.

The circuit of the flyback isolation converter is shown in Figure 12. The output winding of the flyback converter is connected to two battery cells of different potentials in the battery pack. The corresponding equalization mode was adopted through different modes. The isolation between the battery pack and battery can be realized by the flyback transformer T. The optocoupler OPT, MOS transistor S3 and S4 formed an isolation driver. The 5V power supply was provided by an isolated power supply. Current is detected by current sensor ACS712. The control switches in the circuit are *Q*1, *Q*2, *Q*3 respectively. If switch *Q*1 is turned on, meanwhile *Q*2 and *Q*3 are off, and the duty cycle PWM pulse can be adjusted by the main controller according to the output of the equalization circuit. The signal that controls the output was divided three ways: one way was to control *Vg*1 and the two external signals were connected to one inverter to control the opposite signals of *Vg*2 and *Vg*3. The driving circuits of *Q*2 and *Q*3 shown in Figure 12 are the same as the working principle, which thus was simplified in the circuit diagram.

When the input signal *Vg* is high, the LED (Light Emitting Diode) in the optocoupler did not work. The phototransistor is turned off, resulting in a high-level output of optocoupler.  The output voltage of the isolated power supply is applied for the gate level of the switch *Q*1 through the resistor *R*3. When it turns off, a small amount of charge left to generate a voltage difference with the S4 gate voltage, S4 is turned on due to the influence of the *Q*1 gate capacitance. Then the *Q*1 gate is discharged, and *Q*1 is turned off. The main component parameters of the system are shown in Table 1.

**Figure 11.** Switching network diagram.

**Table 1.** Main component parameters of equalizing circuit system.

**Figure 12.** Flyback switch drive circuit.

#### *3.3. Experimental Verification*

To verify the performance of the proposed voltage equalizer, a prototype was built and tested. Figure 13 shows a photograph of the experimental prototype and associated instruments. The experiment uses a "DELI PU BATTERY" 18650 Li-ion Battery with a capacity of 2800-mAh, a rated voltage of 3.7 V, a discharge cut-off voltage of 2.75 V, and an equivalent series resistance of 80 mΩ. The standard charging voltage is 0.5 C (1400 mA), the operating temperature is 0–45 ◦C in the state of charge, and the discharge state is −(20–60) ◦C. the battery pack consists of 12 batteries of 2800-mAh battery strings which can store 10.36 Ah and 124.32 Wh. When the experiment is carried out, the voltage detection frequency is 50 Hz. The switching frequency of the left and right switches is 1 Hz, the operating frequency of the bidirectional winding flyback converter is 25 kHz and the voltage difference between the beginning and the ending equalization is 30 mV.

**Figure 13.** (**a**) Voltage acquisition circuit; (**b**) experimental prototype and associated instruments.

Figure 14 shows the voltage variation of the battery cells during the overall equalization process of the battery pack. It can seem that the highest and lowest voltage of the single battery was 3.98 V and 2.78 V respectively. The entire energy transfer and conversion process can be realized by bidirectional transfer, and a gradual reduction in high voltage cells was achieved. The low voltage gradually rises and cycles in sequence until all voltages were up to the set equilibrium voltage.

**Figure 14.** Voltage curve during forward go equalization.

Figure 15 shows a schematic diagram of voltage changes during battery pack equalization. In this mode of operation, 12 cells with large energy differences are selected for direct equalization. From the analysis of the graph, a relatively balanced state can be gradually obtained between the highest-energy battery cells and the lowest-connected battery cells, and the remaining energy was also in accordance with this equalization mode.

**Figure 15.** Voltage curve during equalization process.

Figure 16 shows the voltage distribution before and after the battery voltage equalization. The horizontal axis represents different monomers and the vertical axis denotes the cell voltage. It can be noted clearly that the voltage of each cell in the battery pack is unbalanced. The voltages tend to be consistent upon equalization, which indicates that the new voltage equalization structure can effectively realize the function of voltage equalization.

**Figure 16.** Voltage distributions of the battery pack.

#### **4. Discussion**

A comparative study of the proposed equalization method is shown in Table 2. Through comparing and analyzing the new equalizer with other equalization networks, the proposed equalizer has relative advantages in size, cost and equalization rate. The output structure of double windings is utilized to realize efficient operation in two working modes of forward and reverse excitation. It is suitable for a large-scale battery

A pack-to-cell equalization mode was formed, which has great potential in promotion and application [14]. With the coaxial winding structure, the equalization function can be realized without additional control in the whole process, but the disadvantage is that it is difficult to accurately adjust the voltage of the battery pack in actual work. The parasitic inductance and mutual inductance of the circuit cannot be accurately controlled, which influenced the operation of the circuit. This leads to the difficult consistency of battery packs for the battery management system (BMS). Additionally, this structure is not suitable for a large number of battery cells. It is challenging to wind too many windings on the same core. Finally, the true energy balance of the battery pack made it difficult to achieve balance from the battery pack to the single unit [15]. It cannot directly reduce the monomer with the highest energy and directly supplement the monomer with the lowest energy. Energy can only be transferred from the whole battery pack.

Energy can only be transferred in the whole battery pack one by one during the equalization process. However, the equalization speed is relatively slow for most batteries connected in series. A point-to-point balanced supplement can be realized by the proposed point-to-point balanced structure, but the number of switch groups is huge. If a small pressure difference has existed between the two equalization monomers in the equalization process, the equalization time is not dominant. The equalizer is based on the equalization of coaxial windings. At the same time, the advantages of a high-frequency switch of the forward converter and the small volume of flyback converter were retained. The number of switches was relatively small and the control method was flexible. In addition, in order to prevent the surge impact of high voltage and high current on the cells during the charging and discharging process of the pack, a Zener diode with an anti-parallel protection function on every single cell was applied in the new equalization structure, and the battery pack module was also equipped with fuses to ensure the safe operation of the battery pack. the proposed equalizer exhibited higher stability and better equalization by this method.

#### *Electronics* **2019** , *8*, 1426

#### **5. Conclusions**

In order to solve the problem of inconsistency between the single cell in the actual use process of the power lithium-ion battery pack, this paper displays a new type of voltage equalization circuit. Comparing with the traditional equilibrium structure, the balanced mode adopted was divided into two working modes. The control method is flexible and the volume occupied by the space volume is relatively small. The balanced structure of the two windings could allow the fast equalization of two battery cells simultaneously. Meanwhile, the designed switch array circuit has a simple control mode with low energy loss. In this paper, the working principle and equalization control strategy of the voltage equalization circuit was introduced in detail and analyzed. A voltage equalization system for 12 batteries of 2800-mAh battery strings was designed in a targeted manner and a voltage equalization experiment was performed. The results show that voltage equalization of series battery packs can be realized efficiently and quickly by the proposed equalizer. The circuit became simple and efficient using a flexible control mode. It is beneficial to improve the overall performance of the battery pack, meanwhile guaranteeing the healthy operation of the battery pack.

**Author Contributions:** F.S. designed the study, D.S. designed the experiments and wrote the manuscript. All authors have read and approved the manuscript.

**Funding:** Research funded by National Natural Science Foundation of China (57807138).

**Acknowledgments:** Thank you for the experimental instrument support and financial support provided by the Engineering Training Center of Tianjin University of Technology.

**Conflicts of Interest:** This article has no conflict of interest.

#### **References**

© 2019 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* **Semiactive Hybrid Energy Management System: A Solution for Electric Wheelchairs**

#### **Sadam Hussain, Muhammad Umair Ali, Sarvar Hussain Nengroo, Imran Khan, Muhammad Ishfaq and Hee-Je Kim \***

School of Electrical Engineering, Pusan National University, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan 46241, Korea<EMAIL_ADDRESS>(S.H<EMAIL_ADDRESS>(M.U.A<EMAIL_ADDRESS>(S.H.N<EMAIL_ADDRESS>(I.K<EMAIL_ADDRESS>(M.I.) **\*** Correspondence<EMAIL_ADDRESS>Tel.: +82-51-510-2364

Received: 21 February 2019; Accepted: 20 March 2019; Published: 21 March 2019

**Abstract:** Many disabled people use electric wheelchairs (EWs) in their daily lives. EWs take a considerable amount of time to charge and are less efficient in high-power-demand situations. This paper addresses these two problems using a semiactive hybrid energy storage system (SA-HESS) with a smart energy management system (SEMS). The SA-HESS contained a lithium-ion battery (LIB) and supercapacitor (SC) connected to a DC bus via a bidirectional DC–DC converter. The first task of the proposed SEMS was to charge the SA-HESS rapidly using a fuzzy-logic-controlled charging system. The second task was to reduce the stress of the LIB. The proposed SEMS divided the discharging operation into starting-, normal-, medium-, and high-power currents. The LIB was used in normal conditions, while the SC was mostly utilized during medium-power conditions, such as starting and uphill climbing of the EW. The conjunction of LIB and SC was employed to meet the high-power demand for smooth and reliable operation. A prototype was designed to validate the proposed methodology, and a comparison of the passive hybrid energy management system (P-HESS) and SA-HESS was performed under different driving tracks and loading conditions. The experimental results showed that the proposed system required less charging time and effectively utilized the power of the SC compared with P-HESS.

**Keywords:** electric wheelchair; lithium-ion battery; supercapacitor; semiactive hybrid energy storage system; smart energy management system

#### **1. Introduction**

Currently, there are an estimated 600 million people aged 60 years or older in the world [1]. In addition, people disabled due to traffic and lower-limb accidents add another 9 million to the count, with an increasing rate of 500,000 per year. The quality of life of elderly or disabled people is restricted. However, advancements in different assistive devices, such as wheelchairs, has led to an increase in their range of activities [2]. While using electric wheelchairs (EWs), people want to travel greater distances and reduce the amount of time it takes to charge the battery [3].

Various technologies have been employed for EWs, but their efficiency greatly depends on the characteristics of their energy storage system (ESS) [4,5]. Various ESSs, including lithium-ion batteries (LIBs), lead–acid batteries, and nickel metal hydride batteries, are used in vehicular applications [6,7]. Among these, LIBs are a widely used energy source due to their attractive properties such as high energy density, low self-discharge rate, and long lifecycle [8–10]. A comparison of different properties of batteries is shown in Figure 1. On the other hand, in vehicular applications, the battery faces many challenges, such as the need for high power demand during acceleration or uphill climbing modes. Although a high-power battery is possible to tackle this problem, these batteries are quite bulky and

expensive [11,12]. The power specifications of the LIB are very low, and the peak-to-average-power ratio ranges between 0.5 to 2 [13], which makes LIBs unpromising in high-power-demand situations. Therefore, supercapacitors (SCs) can be used as a secondary ESS.

**Figure 1.** Comparison of different battery storage systems [14,15].

The power and energy density of SCs range from 1000 to 5000 W/kg and 1 to 10 Wh/kg, respectively [16]. SCs have charging and discharging capabilities of 10–20 times more than LIBs [17]. SCs are not a replacement for LIBs but provide the power needed for EW systems when accelerating up a slope. In addition, they have a longer lifecycle and a wider range of operating temperatures (−4 to +70 ◦C) than LIBs, although they do have low energy density [18]. In electric vehicles (EVs), the stress on the battery is higher than that in a hybrid electric vehicle (HEV) due to deep discharging (~80% for EVs and ~10% for HEVs) [19]. A hybrid energy storage system (HESS) is a combination of SC and LIB, which combines the advantages of both devices to fulfill the requirements of high energy and power densities. SCs are normally used for high power storage, and LIBs are used as a high-energy-storage unit. The SC is utilized for the high power demand of the powertrain, while the LIB is used in low-power situations [20].

An energy management system (EMS) is required to fully utilize the energy of both storage units effectively [21]. The EMS presented in [22,23] is based on the frequency decoupling method to protect the battery from abrupt changes in the load. HESSs can be easily divided into three main topologies: passive HESS (P-HESS), semiactive HESS (SA-HESS), and fully active HESS [24]. A P-HESS is the direct coupling of two or more energy storage devices without a power converter [25]. This has several benefits over a standalone LIB as a power source (e.g., higher peak power capability, higher efficiency, and long battery lifecycle) [26]. Although it is simple to implement, there are some limitations. Power sharing is uncontrollable because the two storage systems are not decoupled [27,28]. Napoli et al. [17] used an ultracapacitor connected in parallel to a battery with no power converter between the two sources. In a P-HESS, power sharing between the LIB and SC is determined by their respective resistance, and the resulting terminal voltage follows the discharge curve of a battery [16]. The energy storage device should be decoupled for efficient operations with respect to its characteristics [29]. In contrast, the degree of controllability is increased using a fully active HESS, but there are some disadvantages, such as increased system losses, weight, and cost. In addition, efficiency also decreases because of the additional converter [20]. Similarly, a modular multilevel fully active HESS also adds complexity and cost. This will also affect the sensitivity of the system, with a failure of one DC–DC converter causing system failure [30]. The SA-HESS is a tradeoff between cost and performance. This system employs only one DC–DC converter and most control strategies can be implemented on this topology [31].

The cell voltage of an LIB is very low. Therefore, a string of batteries is generally used. An imbalanced cell voltage because of the series connection of LIBs causes an increase in temperature, deep discharging, overcharging, and reduced lifecycle and capacity of the battery [32]. Different engineering techniques have been used to control and monitor battery parameters (e.g., state of charge (SOC), voltage, current, and temperature) [33]. For voltage balancing, a special type of charging circuit is required [34,35]. Various fast-charging techniques are used to charge LIBs, such as constant current and constant voltage (CC/CV), a multistage current charging algorithm, model-based charging, a pulse charging algorithm, and a fuzzy logic controller (FLC) [36–38]. The CC/CV technique is simple and computationally efficient [39]. This method has two modes. First, it reaches the defined voltage level while providing a CC to the battery. In the second step, a CV is supplied, and the battery current begins to decrease exponentially [40]. This procedure requires a high current if the battery needs to be charged in a short time, but this increases the battery temperature dramatically, which reduces the lifecycle. In contrast, it takes more time to charge a battery if the current is lower. Huang et al. introduced different intervals to determine the optimal current using FLC [41].

This paper proposes a semiactive hybrid energy management system comprised of SA-HESS and a smart energy management system (SEMS). The proposed methodology charges the HESS smartly using an FLC. The temperature is used as a feedback, which is thermally and electrically favorable to achieve a long lifetime for the ESS. The proposed SEMS discharges the SA-HESS smartly according to the desired load current. Several experiments have been performed to compare the proposed technique with P-HESS.

The rest of the paper is organized into five sections. Section 2 describes an overview and the methodology of the proposed system. Section 3 presents the experimental installation. Section 4 reports the results from the experimental study. Section 5 is the discussion of the results, and Section 6 concludes the paper.

#### **2. Methodology**

#### *2.1. Overview of the Proposed Methodology*

This section provides an overview of the proposed SA-HESS for EWs. At high power/current demand, the use of only an LIB is ineffective and the LIB discharges very rapidly because of the lower power density. Therefore, in the proposed technique, an SC was used as a parallel controlled power source in the SA-HESS. The required power was determined according to the SOC/voltage of the SC and LIB. Figure 2 presents the proposed system for EWs. In the SA-HESS, the LIB was used as a high energy unit, which was connected in parallel to the load via a bus link. The SC was used as a high-power unit, which was connected to the DC bus via a bidirectional converter. The CC/CV charging system was replaced with a temperature (Tbat) feedback FLC charging system. The controlled current (Icontrolled) was supplied as the optimal charging current to the LIB. The SC and LIB provided the desired current to the load, which was controlled using an Arduino microcontroller. A bidirectional converter was used in boost mode, whereas discharging and buck mode were used in charging mode [42]. The output voltage of SC (VSC) varied according to its state of charge, while the battery voltage (Vbat) remained almost constant. The boost converter was used to maintain the VSC relative to the reference (bus/battery) voltage. The converter generated the pulse width modulation (PWM) signal according to the reference value [43]. The load current (IL) was sensed using a current sensor and applied as a feedback signal for the SC (ISC) and LIB (Ibat) current. The ISC and Ibat smartly contributed according to the requirement of IL.

**Figure 2.** Overview of the proposed methodology. Battery voltage (VBat), controlled current (Icontrolled), battery temperature (Tbat), lithium-ion battery (LIB), electric wheelchair (EW), pulse width modulation (PWM) and supercapacitor (SC).

#### *2.2. Fast-Charging System for EW*

FLC is well suited to anticipating a battery's nonlinear behavior because it is robust, easily adaptive, and does not require any mathematical model. The FLC is classified into four parts [44]: Fuzzifier—in the fuzzifier, linguistic fuzzy sets are obtained from the truth value of the membership function. Fuzzy rule base—the fuzzy rule base is designed from professional experience and controls the system operation. Fuzzy interface engine—the fuzzy linguistic input is transformed into a fuzzy linguistic output with respect to the controlled law stated in the fuzzy rule set. Defuzzifier—this maps the fuzzy output from the inference engine to a crisp or real value by using membership functions. The fast-charging methodology was designed using the same rule base as discussed in a previous study [45]. However, in this work, the FLC-based, fast-charging methodology was designed for a series and parallel cell combination of an LIB pack. The lowest single-cell voltage and the highest voltage difference between the two cells of the string were the inputs of the FLC to find the optimal value of the charging current. When the voltage difference between the two cells was high, then a high current was inserted to charge the LIB pack in less time.

However, at the same time, it was essential to control the temperature in order to ensure that this high current value did not affect the battery life. The threshold value and operation of the temperature control unit are shown in Figure 3. The temperature threshold value was set to 39 ◦C. If the temperature was below the threshold value, Icontrolled was supplied to the battery. When it crossed the threshold value, then the controller compared Ibat with the range defined in the flowchart. The value of the charging current changed according to the value shown in the flowchart.

**Figure 3.** Flowchart for temperature control.

#### *2.3. Smart Energy Management System for the SA-HESS*

The power requirement for EWs motion is totally different when traveling on a flat surface than when moving on an inclined surface. A SEMS was designed to overcome the power demand. Two tracks were taken into consideration to implement the SEMS on the SA-HESS. Figure 4a,b present the normal plain track-AB and inclination track-ABCD, respectively. On track-AB, the motor of the EW did not require much power and current; however, for track-ABCD, the motor required high current/power.

**Figure 4.** The logic for the smart energy management system (SEMS): (**a**) normal plaint track-AB; (**b**) uphill climbing steep track-ABCD.

The load on the EW's motor can be calculated by using the following equations [46,47]:

$$F = ma - f\_{\mathbf{x}} - mg\sin\Theta\tag{1}$$

$$P = \frac{F \times v}{\eta} \tag{2}$$

$$I = \frac{P}{V\_{bus}}\tag{3}$$

where *F* and *fx* are the propulsion and friction force, respectively; *m* is the mass of the person and EW; and *v* and *I* are the values of the velocity and current of the EW, respectively. These equations correlated the load/power of the EW motor with the electrical current, as the bus voltage of the SA-HESS almost remains constant. So, the proposed algorithm mainly depended upon electrical current values. Figure 5 shows a flowchart of the proposed algorithm. This methodology was implemented in the Arduino MEGA 2560 interface with MATLAB (R2017a, MathWorks, Natick, MA, USA). The microcontroller, which works as a SEMS, decided the operation mode based on the sensing and analyzing HESS and load parameters (currents, SOC, and voltage). When the EW motor started, most of the power/current was supplied by the SC. VSC and IL were monitored and analyzed. If the SEMS sensed a small current that was less than the first threshold value (ITH1 = 2.5 A), it switched on the LIB circuitry to supply the required current to the load. This condition occurred when the EW was traveling along track-AB. When EW reached point B (see Figure 4b), the SEMS controller sensed a higher value of current compared with ITH1 and one lower than a second threshold current (ITH2 = 3.5 A). Soon after, SEMS would check VSC. If VSC was higher than the threshold (VTH =10 V) value, the SC supplied power to the load; otherwise, the LIB and SC supplied power together to the EW motor. Similarly, when EW was at point C (i.e., the current required to the load was more than the ITH2), the controller would switch on both the LIB and SC to fulfill the desired power demands of the load.

**Figure 5.** Algorithm for the SEMS.

Figure 6 presents a simplified block of a hardware implementation for the SEMS algorithm. Solid lines represent energy flow lines, and dotted lines show the control signal flow lines. The microcontroller sent a control signal to the switch based on the condition provided by the algorithm and opened a path for the storage system to supply the desired power to the load. Three switches that connected HESS to the EW motor were used: switch SW1 connected the SC and LIB to the motor, SW2 was the interface between the SC and load, and SW3 was between the LIB and load, as shown in Figure 6.

**Figure 6.** Hardware implementation of the SEMS algorithm.

The voltage requirement and maximum power demand determined the number of series and parallel connected branches of the devices in the storage system. The number of cells in series (*Nbat*\_*s*) and parallel (*Nbat*\_*p*) of the LIB was computed using Equations (4) and (5) [48]:

$$N\_{\text{bat\\_s}} = \frac{V\_{\text{bus}}}{V\_{\text{bat}}} \tag{4}$$

$$N\_{bat\\_p} = \frac{Total\ Ah}{cell\ Ah} \tag{5}$$

Similarly, the number of series and parallel SCs was calculated as [48]

$$N\_{SC\\_s} = \frac{V\_{bus}}{V\_{SC}}\tag{6}$$

$$N\_{\rm SC\\_p} = \frac{I.N\_{\rm SC\\_s}}{\Delta V} \left(\frac{\Delta t}{\rm C} + ESR\right) \tag{7}$$

where *NSC*\_*s* and *NSC*\_*p* are the number of supercapacitors connected in series and parallel, respectively, and *VSC* is the voltage of the supercapacitor. ESR represents the equivalent series resistance, where Δ*V* and Δ*t* are the voltage drop and discharging time of the supercapacitor depending upon the output current.

#### **3. Experimental Setup**

Figure 7 presents the experimental setup of the proposed SA-HESS prototype for an EW. A Samsung 18650 LIB (Samsung, Yongin-si, South Korea) was used in the current experiment. An SC bank with a capacitance of 350 F was used. A liquid crystal display (20 × 4 dimension) was used to indicate the mode of the HESS. The SEMS algorithm implemented in Arduino Mega 2560 was connected to the monitoring system. Different sensors were used to measure and monitor the parameters, such as the HESS temperature, current, and voltage. ACS712-20A hall effect current sensors were used for current sensing. An F30S60S power diode (ON Semiconductor, Phoenix, AZ, USA) was used. A DC motor was used as a load in this prototype.

**Figure 7.** Experimental setup of the prototype.

#### **4. Results**

#### *4.1. Performance Evaluation of Smart Energy Management System*

#### 4.1.1. Charging System Using SEMS

Figure 8 shows the voltages and temperature profiles of an LIB pack, where V1, V2, V3, V4, and Vt are the first, second, third, fourth, and overall voltages of the LIB pack, respectively. T1, T2, T3, T4, T5, T6, and T7 denote the value of different temperature sensors. The voltage and temperature were monitored to obtain the optimal value of the charging current for an LIB. At 3498 s, the temperature (T2) increased from the threshold value. To compensate for this effect, the current was reduced, as described in Section 2.2 and shown in the magnified graph.

**Figure 8.** Voltage and temperature profile of the Li-ion battery (LIB).

#### 4.1.2. Discharging System Using SEMS

Two tracks were used to validate the SEMS methodology for SA-HESS, as shown in Figure 9. The EW needed a high current value to start, which was provided by the SC at the time (t) = 9 s. At t = 11 s, the EW started moving on a flat surface. On a normal surface, the EW motor required less current, which was supplied by the LIB at t = 11–50 s. At t = 51 s, the EW started to climb uphill. The EW drew more current, which was provided by the SC. Here, the stress on the LIB was reduced using the SC instead of the LIB. At t = 100 s, the EW reached the middle of the inclined surface and required more power to reach the top surface. In this case, both the LIB and SC supplied power to the load. These timeframes are discussed in detail below in the test cases considering the proposed algorithm, as described in Section 2.3.

**Figure 9.** Experimental results of the SEMS on the electric wheelchair (EW) motor.

Case—EW Start (t = 0–11 s)

At the start, the EW motor required a high current for a small amount of time. The current profile in Figure 10 shows a spike at t = 10 s, indicating that the EW motor drew 6 A. The SC supplied this high pulse current. The voltage of the SC showed small variations (0.6 V), but the DC–DC converter maintained a constant voltage for smooth power transfer.

**Figure 10.** The experimental results at the start of the EW movement.

Case—Plain Track (t = 11–50 s)

From t = 11 to 50 s, the EW traveled on track-AB (from Figure 4a). The EW motor drew a 1.9-A current. SEMS enabled the LIB to supply this small amount of power to the load. The current profile in Figure 11 reveals the SC to have had an almost zero current, while the current of the LIB was 1.3 A. This confirms that only the LIB supplied a small amount of power to the load.

**Figure 11.** Experimental results for track-AB.

Case—Climbing Uphill (t = 51–150 s)

As shown in Figure 12, from t = 51 to 100 s, the EW traveled from points B to C (as described in Figure 4b). On this track, a 3-A current was drawn by the load. The proposed system enabled SC to supply a high power/current to the load. The SC current increased to 3 A to fulfill the power requirement of the load shown in the current of a supercapacitor in Figure 12. The voltage of the SC started decreasing, but the DC–DC converter maintained a constant voltage to fully utilize the SC. The current profile of the LIB confirmed that the LIB supplied an almost zero current, even at a high load current.

**Figure 12.** Experimental results for track-ABCD (points B–C).

Figure 13 shows the current and voltage profile of the EW traveling from points C to D from t = 100 to 150 s. At the peak load, the proposed system supplied power from both sources. The experimental results showed that at point C, the LIB supplied approximately 1–1.7 A and the SC supplied 4 A, as shown in the current profile of the LIB and SC in Figure 13. The terminal voltage of the SC decreased from 12.9 to 11.9 V, but the DC–DC converter provided a constant voltage to the load. Regardless of acceleration, the proposed system supplied a constant LIB voltage to the load and less current, which improved the LIB lifecycle. This should also increase the traveling range of the EW.

**Figure 13.** Experimental results for track-ABCD (points C–D).

#### *4.2. Performance Evaluation of P-HESS*

The same tests were performed on a P-HESS for track-ABCD. Figure 14 shows the experimental results of the P-HESS. At t = 11 s, the EW motor started, and an approximately 3.5-A current was supplied by the LIB and 3.1 A was supplied by the SC, as shown in the current profiles of the LIB and SC, respectively, in Figure 14. From t = 12 to 50 s, the passive system traveled on a flat surface. The EW motor drew an average of 1.9 A, which was supplied by the LIB, whereas the SC current was almost zero. From t = 51 to 101 s, when it started traveling on an inclined surface, it drew 4.5 A. The LIB and SC supplied 3- and 1.5-A currents, respectively. Similarly, at t = 101–150 s, the passive system traveling on an inclined surface required more current, which was again supplied by the LIB. The current profile of the EW motor increased from 5 to 6 A. The LIB current also increased from 4 to 5 A. The SC supplied 1 A, as shown in the graph of the current of a supercapacitor (Figure 14).

**Figure 14.** Experimental results of the passive hybrid energy storage system (P-HESS).

#### **5. Discussion**

To validate the proposed technique, several experiments were performed to compare the result of SA-HESS and P-HESS under different conditions. The average current values of different track experiments are presented in Figure 15. It can be noted that by adopting the proposed technique, the stress of the LIB was reduced. In high-power-demanding conditions, the proposed technique effectively used the SC as compared with P-HESS to enhance the lifecycle of the LIB. Some of the results of real-time testing under different tracks are shown in Figure A1 of Appendix A.

**Figure 15.** Comparison of the proposed semiactive (SA)-HESS and P-HESS.

The validation of the proposed system was also done under different load conditions. Figure 16 shows some of the experimental results of the proposed system and the P-HESS under different loading conditions. The superiority of the proposed algorithm under different loading conditions can be seen in Figure 16. The efficiency of the SA-HESS was 97.6% in the EW application. The proposed methodology does not have any significant effect on the cost of the system.

**Figure 16.** Comparison of the proposed SA-HESS and P-HESS during different loads: (**a**) 35-W load; (**b**) 25-W load.

Renewable energy resources can be used to charge the HESS. The installation of a regenerative braking system in EWs is a good option to charge the SC during the downslope. The discharging efficiency of the HESS can be enhanced by using a smart controller such as an FLC.

#### **6. Conclusions**

This paper introduced a new hybrid energy management system for EWs. The SA-HESS was implemented using a smart energy management system algorithm. The proposed system ensured effective use of the SC and decreased the stress of the LIB to extend the battery life under demanding conditions. Five different tracks and two different loads were used to ensure the practicability of the proposed hybrid energy management system and to compare it with the passive system. The experimental results confirmed that the proposed system provided a more effective charging and discharging management system at high power demand compared with the conventional P-HESS.

**Author Contributions:** Conceptualization, S.H., M.U.A., and H.-J.K.; Formal analysis, S.H., S.H.N., and M.I.; Funding acquisition, H.-J.K.; Investigation, S.H.; Methodology, S.H. and M.U.A.; Software, M.U.A. and I.K.; Supervision, H.-J.K.; Validation, M.U.A., S.H.N., and M.I.; Writing—original draft, S.H., S.H.N., and I.K.; Writing—review & editing, H.-J.K.

**Funding:** This research was supported by Brain Korea 21 Center for Creative Human Resource Development Program for IT Convergence of Pusan National University.

**Acknowledgments:** This research was supported by Brain Korea 21 Center for Creative Human Resource Development Program for IT Convergence of Pusan National University.

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

#### **Appendix A**

Figure A1 shows the current profiles of the proposed system and P-HESS while traveling in different surface conditions.

**Figure A1.** Comparison of the proposed SEMS and P-HESS during different modes: (**a**) start–high climbing–low climbing–plain; (**b**) start–low climbing–plain–high climbing; (**c**) start–low climbing–high climbing–plain; (**d**) start–plain–high climbing–low climbing.

#### **References**

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