Full Current-Type Control-Based Hybrid Energy Storage System

: With greater power density, a hybrid power source that combines supercapacitors and batteries has a wide range of applications in pulse-operated power systems. In this paper, a superca-pacitor/battery semi-active hybrid energy storage system (HESS) with a full current-type control strategy is presented. The studied HESS is composed of batteries, supercapacitors, and a bidirectional buck–boost converter. The converter is controlled such that supercapacitors supply load power pulses, and batteries provide the power in steady state. To realize the fast compensation of the supercapacitors to the load power pulses, a power distribution module based on hysteresis control theory is designed in the control system. Moreover, the control strategy does not require the model parameters of the converter and supercapacitors, so the control system is simpliﬁed. A complete conﬁguration scheme and cost analysis of the proposed HESS are also presented. Obtained results show that the proposed supercapacitor/battery semi-active HESS has good performance in terms of dynamic response, weight, and energy utilization coefﬁcient (EUC). converter to compensate for the peak load power. The converter operates in buck mode when the supercapacitor is charged while operating in boost mode when the supercapacitor discharges.


Introduction
The battery energy storage system (BESS) with a Li-ion battery as the core device has become the mainstream power supply scheme, due to its high energy density and decreasing cost [1]. However, limited by the low power density of Li-ion batteries, BESS used for pulsed power loads such as electric vehicles and satellites faces the problems of excessive battery size and weight [2,3]. Since supercapacitors have high specific power and can be charged and discharged quickly, which are very suitable for the pulsed loads, the HESS combining Li-ion batteries and supercapacitors has been widely studied [4].
In HESS, supercapacitors provide load current pulses instead of batteries, so the battery pack can be miniaturized. Proper energy management strategy (EMS) and component configuration can reduce the weight and lifecycle cost of the energy storage system while improving the payload capabilities and capacity utilization [1,5].
The topology, control strategy, and optimal configuration of HESS have always been important research content. In recent years, several topologies have been proposed, which can be divided into passive topology, semi-active topology, and fully active topology according to the combination mode of battery and supercapacitor [5][6][7]. The battery is directly paralleled with the supercapacitor as the DC power source in passive HESS, without any power converters. This topology is very simple, but due to the lack of control, the power compensation effect of the supercapacitor is relatively poor [6,8]. In contrast, fully active HESS has the best performance, as it employs two DC-DC converters for energy management of the battery and the supercapacitor, respectively. Nonetheless, this topology has high costs, and the real-time interaction control between the two converters is complex [9][10][11]. The semi-active HESS only employs one power converter, and although its control performance is not perfect, the cost and complexity of the system are greatly reduced. Furthermore, most control strategies can be applied to this topology. Due to these advantages, semi-active HESS is currently the most popular topology [12,13]. There are two semi-active HESS topologies. One topology is to connect a DC-DC converter between the supercapacitor and the DC bus, connecting the Li-ion battery directly to the DC bus. This configuration efficiently utilizes the energy of the supercapacitor, but the DC bus voltage cannot be changed. Another topology is to connect a DC-DC converter between the Li-ion battery and the DC bus, connecting the supercapacitor directly to the DC bus. This structure protects the battery but limits the operating range of the supercapacitor [5].
A variety of control strategies have been designed and studied, and the basic principles of these strategies are similar due to the simple structure of HESS. In [14], a current-type polynomial dynamic control strategy for supercapacitor/battery semi-active HESS was proposed, and the output power of the DC-DC converter was regulated by controlling the supercapacitor current. This strategy calculates the supercapacitor current reference using the DC-DC converter model, and the converter efficiency parameters in the model are corrected online. Since the efficiency parameters of the converter are simultaneously affected by many factors such as duty cycle, input power, voltage, and current, the output power of the DC-DC converter may not be precisely controlled using the supercapacitor current as a reference. In [15], a control algorithm based on power filter theory was presented, and the high-and low-frequency components of the load power were allocated to the supercapacitor and battery, respectively. Since the equivalent series resistance (ESR) of the supercapacitor pack is introduced into the control loop, the accuracy of this control algorithm may be affected when the supercapacitor cells increase. In [16], a control strategy based on the current filter algorithm was designed, which limited the battery current by adjusting the cut-off frequency. In addition, some online high-performance control algorithms have also been applied to HESS, such as model predictive control and fuzzy logic control [17][18][19].
The optimal configuration of HESS mainly considers cost, battery lifetime, and the total weight of the energy storage devices. In [11,12], the operation cost of HESS was considered as the optimization object, which could be reduced by 50%, compared with that of BESS. The authors of [3] proposed a hybrid optimization algorithm to calculate the feasible optimal solution under the joint constraints of weight, cost, and battery lifetime. In [1], an optimization algorithm based on the Hamiltonian function was designed to solve the optimal pack size of the HESS configuration. In addition, the dynamic programming algorithm and Pontryagin's minimum principle were also used to reduce the operation cost and size of HESS [20].
Since most of the energy management strategies of HESS rely on the model of power converters, it is necessary to modify the model parameters online for ensuring the control accuracy, which increases the computational cost. In this paper, an improved full currenttype polynomial control strategy is proposed for semi-active HESS. This method takes the bidirectional DC-DC converter as the controlled object and directly controls the converter current, which simplifies the control system, and the control accuracy is independent of the model parameters.
This paper is organized as follows: First, combining the HESS model with the optimization objective of the total weight of the energy storage devices, a conventional configuration scheme is established. Then, a full current-type DC-DC converter control strategy is proposed for energy management. Finally, simulation and experiment are used to evaluate the proposed control strategy and configuration scheme. Figure 1 shows the basic topology of supercapacitor/battery semi-active HESS. In this paper, a non-isolated, bidirectional buck-boost converter was employed. The Li-ion battery is directly connected to the DC bus to provide energy and stabilize the DC bus voltage, while the supercapacitor is interfaced to the DC bus with a bidirectional DC-DC Energies 2022, 15, 2910 3 of 13 converter to compensate for the peak load power. The converter operates in buck mode when the supercapacitor is charged while operating in boost mode when the supercapacitor discharges. Figure 1 shows the basic topology of supercapacitor/battery semi-active HESS paper, a non-isolated, bidirectional buck-boost converter was employed. The Litery is directly connected to the DC bus to provide energy and stabilize the DC b age, while the supercapacitor is interfaced to the DC bus with a bidirectional DC-D verter to compensate for the peak load power. The converter operates in buck mod the supercapacitor is charged while operating in boost mode when the superca discharges.

Battery Pack Design Considerations
The power allocation rules should be established first. A typical approach is t the high-frequency component of the load power through a signal filter and then the supercapacitor to output this high-frequency power and the battery pack to the remaining low-frequency power [11,15]. However, the battery current of this is indeterminate and depends on the filter cut-off frequency and the actual load Therefore, the distribution method based on the current level was adopted. In the of HESS providing a power pulse, the battery current is fixed, and the supercapaci puts most of the pulse current via the converter.
The battery pack was designed according to the DC bus voltage, the total consumption during the load operation, and the maximum power allocated.
The voltage of the DC bus is fixed by the battery pack, and the battery pack is obtained using the following equation, where Vpack,Li is the battery pack volta Vdcbus is the DC bus voltage: The battery pack should provide the energy consumed by the pulsed power a mission. In order to ensure the performance and lifetime, the depth of discharge of the Li-ion battery pack cannot exceed 80% [21]. The rated energy of the batte can be denoted as in (2), where Epack,Li is the energy of the battery pack; PL,norm and P the normal power and peak power of the pulsed load, respectively. ηconv is the pow verter efficiency, I is the duration of load operation, DODpack,Li is the DOD of batte and kLi is the margin coefficient of battery pack.
The battery power is composed of the normal load power and the charging p the supercapacitor, which can be expressed as follows, where PSC,charge is the superca charging power:

Battery Pack Design Considerations
The power allocation rules should be established first. A typical approach is to obtain the high-frequency component of the load power through a signal filter and then control the supercapacitor to output this high-frequency power and the battery pack to output the remaining low-frequency power [11,15]. However, the battery current of this method is indeterminate and depends on the filter cut-off frequency and the actual load power. Therefore, the distribution method based on the current level was adopted. In the process of HESS providing a power pulse, the battery current is fixed, and the supercapacitor outputs most of the pulse current via the converter.
The battery pack was designed according to the DC bus voltage, the total energy consumption during the load operation, and the maximum power allocated.
The voltage of the DC bus is fixed by the battery pack, and the battery pack voltage is obtained using the following equation, where V pack,Li is the battery pack voltage, and V dcbus is the DC bus voltage: The battery pack should provide the energy consumed by the pulsed power during a mission. In order to ensure the performance and lifetime, the depth of discharge (DOD) of the Li-ion battery pack cannot exceed 80% [21]. The rated energy of the battery pack can be denoted as in (2), where E pack,Li is the energy of the battery pack; P L,norm and P L,peak are the normal power and peak power of the pulsed load, respectively. η conv is the power converter efficiency, I is the duration of load operation, DOD pack,Li is the DOD of battery pack, and k Li is the margin coefficient of battery pack.
The battery power is composed of the normal load power and the charging power of the supercapacitor, which can be expressed as follows, where P SC,charge is the supercapacitor charging power:

Supercapacitor Pack Design Considerations
Since the supercapacitor has a strong instantaneous power capability, its design mainly considers the maximum load energy pulse and voltage constraints [22,23]. Additionally, the rated energy of the supercapacitor pack can be described as where E pack,SC is the rated energy of supercapacitor pack; t peak is the duration of single peak power; DOD pack,SC and k SC are the DOD and margin coefficient of supercapacitor pack, respectively. Since the charging and discharging of supercapacitors is a physical process, supercapacitors can theoretically be fully discharged. Generally, the DOD pack,SC can reach more than 90%. Limited by the power loss and cooling system of the DC-DC converter, the voltage of the supercapacitor pack should not be too low, and a reasonable voltage range is as follows [1], where V min,conv is the minimum voltage of the supercapacitor pack that the DC-DC converter can operate safely, and V pack,SC is the rated supercapacitor pack voltage:

Configuration Scheme
Regardless of V dcbus , the configuration of the battery pack and supercapacitor pack are unrelated. Assuming homogeneity of Li-ion cell and supercapacitor cell, combining (1)-(3), the cell numbers and structure of the battery pack should satisfy the constraints in (6), where N s,Li is the number of Li-ion cells in series, N p,Li is the number of Li-ion cells in parallel; V cell,Li and C cell,Li are the rated voltage and capacity of a single Li-ion cell, respectively. Additionally, µ is the discharge rate of the battery.
In the same way, combining (4) and (5), the constraints on the cell numbers and structure of the supercapacitor pack can be obtained with the equation below, where N s,SC is the number of supercapacitor cells in series, N p,SC is the number of supercapacitor cells in parallel, and V cell,sc and C cell,sc are the rated voltage and capacitance of a single supercapacitor cell, respectively.
According to the constraint conditions in (6) and (7), the optimal configuration can be obtained as Additionally, the minimum weight of the battery pack and the supercapacitor pack can be expressed as (9). Notably, the weights of the battery management system (BMS) and assembly box were not included. where W pack,Li and W pack,SC are the weights of the Li-ion battery pack and supercapacitor pack, respectively. Additionally, W cell,Li and W cell,SC are the weights of Li-ion cell and supercapacitor cell, respectively.

Converter Topology
In this paper, a bidirectional synchronous rectifier buck-boost converter was adopted to improve efficiency [24], and the topology is shown in Figure 2. During buck mode, Q 1 was used as the main switch and Q 2 served as the assistant free-wheeling switch. While during boost mode, Q 2 was the main switch, and Q 1 served as the assistant switch. In the continuous conduction mode (CCM), the driving signals of Q 1 and Q 2 were complementary. pack, respectively. Additionally, Wcell,Li and Wcell,SC are the weights of Li-ion cell and supercapacitor cell, respectively.

Converter Topology
In this paper, a bidirectional synchronous rectifier buck-boost converter was adopted to improve efficiency [24], and the topology is shown in Figure 2. During buck mode, Q1 was used as the main switch and Q2 served as the assistant free-wheeling switch. While during boost mode, Q2 was the main switch, and Q1 served as the assistant switch. In the continuous conduction mode (CCM), the driving signals of Q1 and Q2 were complementary.
It should be noted that both battery and supercapacitor are active loads, during soft starting, the converter will operate in discontinuous conduction mode (DCM) due to the small duty cycle of the main switch. In DCM, if the auxiliary switch is not turned off in time, the inductor current will flow backward; consequently, the converter efficiency is diminished, and the battery and switches will also be damaged as the current backflow increases. Different from the absolutely complementary drive of CCM, in DCM, the auxiliary switch needs to be turned off when the inductor current returns to zero [25].  Figure 3 shows a simple equivalent circuit model of the supercapacitor pack, which consists of the capacitor C, the equivalent series resistor Res, and the equivalent parallel It should be noted that both battery and supercapacitor are active loads, during soft starting, the converter will operate in discontinuous conduction mode (DCM) due to the small duty cycle of the main switch. In DCM, if the auxiliary switch is not turned off in time, the inductor current will flow backward; consequently, the converter efficiency is diminished, and the battery and switches will also be damaged as the current backflow increases. Different from the absolutely complementary drive of CCM, in DCM, the auxiliary switch needs to be turned off when the inductor current returns to zero [25]. Figure 3 shows a simple equivalent circuit model of the supercapacitor pack, which consists of the capacitor C, the equivalent series resistor R es , and the equivalent parallel resistor R ep [26]. According to this model, the relationship between the supercapacitor pack voltage V SC and the voltage V C representing the real energy can be obtained with (10), where I SC is the supercapacitor current, and since R ep is very large, its influence on V SC is neglected. It must be noted that when I SC is not zero, the directly measured V SC cannot reflect the actually stored energy of the supercapacitor. Therefore, it is necessary to combine V SC and I SC to calculate accurate ultracapacitor charging status.

Supercapacitor Model
Energies 2022, 15, x FOR PEER REVIEW resistor Rep [26]. According to this model, the relationship between the superca pack voltage VSC and the voltage VC representing the real energy can be obtained wi where ISC is the supercapacitor current, and since Rep is very large, its influence o neglected. It must be noted that when ISC is not zero, the directly measured VSC reflect the actually stored energy of the supercapacitor. Therefore, it is necessary t bine VSC and ISC to calculate accurate ultracapacitor charging status.

Control Strategy
The bidirectional buck-boost converter is controlled according to the control s described in Figure 4a. In buck operation mode, the supercapacitor pack is cha ensure that there is enough energy to support the load power pulse later, and ISC

Control Strategy
The bidirectional buck-boost converter is controlled according to the control strategy described in Figure 4a. In buck operation mode, the supercapacitor pack is charged to ensure that there is enough energy to support the load power pulse later, and I SC is controlled in a closed loop. In boost operation mode, I conv is closed-loop controlled to satisfy the peak current requirement of the load. Since the load current I load is given, the battery current I bat is also controlled using (11).

Control Strategy
The bidirectional buck-boost converter is controlled according to the control strategy described in Figure 4a. In buck operation mode, the supercapacitor pack is charged to ensure that there is enough energy to support the load power pulse later, and ISC is controlled in a closed loop. In boost operation mode, Iconv is closed-loop controlled to satisfy the peak current requirement of the load. Since the load current Iload is given, the battery current Ibat is also controlled using (11).
The power allocation system shown in Figure 4b determines the operation mode of the DC-DC converter, and the reference currents of the converter and supercapacitors (Iconv,ref and ISC,ref, respectively) are also given. As the bus voltage is fixed, a controller based on the hysteresis comparison principle is applied to the load current to assess the load power level.  Figure 4b determines the operation mode of the DC-DC converter, and the reference currents of the converter and supercapacitors (I conv,ref and I SC,ref , respectively) are also given. As the bus voltage is fixed, a controller based on the hysteresis comparison principle is applied to the load current to assess the load power level. Figure 5 demonstrates a complete flowchart of the proposed power allocation system. Define I th1 and I th1 as the lower threshold and upper threshold of the hysteresis comparator. If I load < I th1 , the load runs at normal power, and at this stage, the converter should operate in buck mode to charge the supercapacitors. The charging process can be divided into two phases. In the first phase, the commonly used constant current charging is employed, and the supercapacitors' current reference ISC,ref = Iref is obtained. According to the previous analysis, due to the influence of Res, the charging status calculated by the measured VSC is slightly less than the target charging status. Therefore, a second stage of charging is required after the measured VSC reaches the target voltage Vref. During the second phase, the charging current gradually decreases, and ISC,ref is calculated as where f(t) is a decreasing linear function, with an initial value of 1 and a final value of 0. The maximum battery current Ibat,max can be described as If Iload > Ith2, the load operates at peak power, and at this stage, the converter should operate in boost mode and the supercapacitor pack starts discharging. The purpose of this stage is to replace the battery pack with the supercapacitors to provide the peak load current, so the battery current Ibat is limited as Ibat,ref, and the converter current reference Iconv,ref In the first phase, the commonly used constant current charging is employed, and the supercapacitors' current reference I SC,ref = I ref is obtained. According to the previous analysis, due to the influence of R es , the charging status calculated by the measured V SC is slightly less than the target charging status. Therefore, a second stage of charging is required after the measured V SC reaches the target voltage V ref . During the second phase, the charging current gradually decreases, and I SC,ref is calculated as where f(t) is a decreasing linear function, with an initial value of 1 and a final value of 0. The maximum battery current I bat,max can be described as If I load > I th2 , the load operates at peak power, and at this stage, the converter should operate in boost mode and the supercapacitor pack starts discharging. The purpose of this stage is to replace the battery pack with the supercapacitors to provide the peak load current, so the battery current I bat is limited as I bat,ref , and the converter current reference I conv,ref is obtained as I conv,re f = I load − I bat,re f ,

Simulation Results
To verify the performance of the control strategy proposed in Section 3, a supercapacitor/battery HESS shown in Figure 1 was established in the MATLAB/SIMULINK. The peak load power was 2 kW, and the normal load power was 0.12 kW. The load cycle duration was 40 s, P L,peak duration was 5 s, P L,norm duration was 35 s, and the load ran continuously for one hour under the above conditions. The battery pack had a rated voltage of 72 V and a rated capacity of 9.6 Ah, the rated voltage of the supercapacitor pack was 56 V, and the capacitance was 17.5 F. Table 1 shows the values of the main circuit parameters.  Figure 6 shows the simulation result of the supercapacitor's current control in buck mode. In the beginning, the supercapacitor current reference I SC,ref was fixed at 8 A, and then I SC,ref gradually reduced from 8 A to 0 A. This figure shows that the supercapacitor's current-control strategy is satisfactory.  Figure 7 shows the simulation result of the converter's current control in boost mode In this paper, the peak load power was intended to be provided by the supercapacitor pack alone, so the battery current reference Ibat,ref was fixed at 0 A, and the sampled load current Iload was taken as the converter current reference Iconv,ref. Since the battery pack was connected to the load, the control accuracy was bound to be affected. However, it can be seen from Figure 7 that almost all of the peak load current was provided by the converter meaning that the converter's current-control strategy was satisfactory.    Figure 7 shows the simulation result of the converter's current control in boost mode. In this paper, the peak load power was intended to be provided by the supercapacitor pack alone, so the battery current reference I bat,ref was fixed at 0 A, and the sampled load current I load was taken as the converter current reference I conv,ref . Since the battery pack was connected to the load, the control accuracy was bound to be affected. However, it can be seen from Figure 7 that almost all of the peak load current was provided by the converter, meaning that the converter's current-control strategy was satisfactory.

Output capacitor
C 220 μF Switching frequency fs 50 kHz  The simulation results of battery current and load current in a load cycle are sh in Figure 8. The peak load current was 24.92 A, while the maximum output current o battery pack was only 7.36 A, which was reduced by 17.57 A, compared with the for These results mean that the peak current stress of the battery pack greatly decreased using HESS. The simulation results of battery current and load current in a load cycle are shown in Figure 8. The peak load current was 24.92 A, while the maximum output current of the battery pack was only 7.36 A, which was reduced by 17.57 A, compared with the former. These results mean that the peak current stress of the battery pack greatly decreased by using HESS.

Experimental Results
To evaluate the supercapacitor/battery semi-active HESS with a full current-type trol strategy, an experimental platform was built, which consists of the pulsed power l a Li-ion battery pack, a supercapacitor pack, a bidirectional buck-boost converter, and control system based on STM32F103C8T6 microprocessor. The 2kw peak power exp mental platform is shown in Figure 9. All circuit parameters are consistent with Tabl

Experimental Results
To evaluate the supercapacitor/battery semi-active HESS with a full current-type control strategy, an experimental platform was built, which consists of the pulsed power load, a Li-ion battery pack, a supercapacitor pack, a bidirectional buck-boost converter, and the control system based on STM32F103C8T6 microprocessor. The 2 kw peak power experimental platform is shown in Figure 9. All circuit parameters are consistent with Table 1.
For safety reasons, the supercapacitor pack voltage ranged from 40 V to 56 V in the experiment, so the current through the DC-DC converter was not more than 50 A. Figure 10 shows the experimental waveforms of battery current and load current in a load cycle. The normal current of the pulse load was 1.55 A, and the peak current was 25.6 A. When the load was running at normal power, the battery provided the power for charging the supercapacitors and normal operation of the load. Considering the current ripple, the maximum battery current I bat,max was 8.5 A. When the load was running at peak power, the battery current was successfully limited to around 0 A, and almost all of the peak load current was provided by the supercapacitors with the boost converter.

Experimental Results
To evaluate the supercapacitor/battery semi-active HESS with a full current-type control strategy, an experimental platform was built, which consists of the pulsed power load, a Li-ion battery pack, a supercapacitor pack, a bidirectional buck-boost converter, and the control system based on STM32F103C8T6 microprocessor. The 2kw peak power experimental platform is shown in Figure 9. All circuit parameters are consistent with Table 1. For safety reasons, the supercapacitor pack voltage ranged from 40 V to 56 V in the experiment, so the current through the DC-DC converter was not more than 50 A. Figure 10 shows the experimental waveforms of battery current and load current in a load cycle. The normal current of the pulse load was 1.55 A, and the peak current was 25.6 A. When the load was running at normal power, the battery provided the power for charging the supercapacitors and normal operation of the load. Considering the current ripple, the maximum battery current Ibat,max was 8.5 A. When the load was running at peak power, the battery current was successfully limited to around 0 A, and almost all of the peak load current was provided by the supercapacitors with the boost converter.
The voltage and current experimental waveforms of the supercapacitors in a load cycle are shown in Figure 11. The initial voltage of the supercapacitor pack was 40 V, and it was charged to the target voltage of 54 V at a constant current of 8 A. After that, the charging current gradually decreased, and the charging process was terminated immediately when the voltage reached the upper limit of 56 V. Five seconds after the end of charging, the load current suddenly increased, the DC-DC converter switched from buck mode to boost mode, and the supercapacitors began to discharge. The initial discharge current was 40.5 A, and the maximum discharge current was 48.1A.
At the moment when the supercapacitors discharge started and ended, the terminal voltage VSC dropped and rose suddenly, with amplitudes of 3.1 V and 4.0 V, respectively. This phenomenon is mainly caused by the equivalent series resistance Res of the supercapacitors. As described in (10), at the moment of supercapacitors discharge, due to the sudden increase in the current ISC, the voltage drop on Res increased, so VSC dropped. Similarly, when the discharge ended, the voltage drop on Res was reduced to 0 V, so VSC suddenly increased.   Figure 12a shows the experimental waveforms during the dynamic process through which the DC-DC converter switched from buck mode to boost mode. Within 4 milliseconds after the load current increased, the supercapacitors had completely replaced the battery pack to provide peak load power. Figure 12b shows the experimental results during the dynamic process through which the DC-DC converter switched from boost mode to buck mode. Within 3 milliseconds after the load current decreased, the supercapacitors could stop discharging entirely, and the battery and the output capacitor provided normal load power and then charged the supercapacitors. These results show that the power allocation strategy based on the hysteretic control principle has good dynamic-response ability. Figure 13 shows the efficiency of the converter (buck mode) during the supercapacitor charging process. Since the charging current was fixed, the charging power depended on the supercapacitor pack voltage VSC. In the voltage range from 40 V to 56 V, the converter maintained a charging efficiency above 95.84%. Figure 14 shows the efficiency of the converter (boost mode) at different levels of load power during the supercapacitor's discharging process. When the output power was constant at 2kW, the efficiency during the entire discharge process was not less than 96.89%. The voltage and current experimental waveforms of the supercapacitors in a load cycle are shown in Figure 11. The initial voltage of the supercapacitor pack was 40 V, and it was charged to the target voltage of 54 V at a constant current of 8 A. After that, the charging current gradually decreased, and the charging process was terminated immediately when the voltage reached the upper limit of 56 V. Five seconds after the end of charging, the load current suddenly increased, the DC-DC converter switched from buck mode to boost mode, and the supercapacitors began to discharge. The initial discharge current was 40.5 A, and the maximum discharge current was 48.1A. to boost mode, and the supercapacitors began to discharge. The initial discharge current was 40.5 A, and the maximum discharge current was 48.1A.
At the moment when the supercapacitors discharge started and ended, the terminal voltage VSC dropped and rose suddenly, with amplitudes of 3.1 V and 4.0 V, respectively. This phenomenon is mainly caused by the equivalent series resistance Res of the supercapacitors. As described in (10), at the moment of supercapacitors discharge, due to the sudden increase in the current ISC, the voltage drop on Res increased, so VSC dropped. Similarly, when the discharge ended, the voltage drop on Res was reduced to 0 V, so VSC suddenly increased.   Figure 12a shows the experimental waveforms during the dynamic process through which the DC-DC converter switched from buck mode to boost mode. Within 4 milliseconds after the load current increased, the supercapacitors had completely replaced the battery pack to provide peak load power. Figure 12b shows the experimental results during the dynamic process through which the DC-DC converter switched from boost mode to buck mode. Within 3 milliseconds after the load current decreased, the supercapacitors could stop discharging entirely, and the battery and the output capacitor provided normal load power and then charged the supercapacitors. These results show that the power allocation strategy based on the hysteretic control principle has good dynamic-response At the moment when the supercapacitors discharge started and ended, the terminal voltage V SC dropped and rose suddenly, with amplitudes of 3.1 V and 4.0 V, respectively. This phenomenon is mainly caused by the equivalent series resistance R es of the supercapacitors. As described in (10), at the moment of supercapacitors discharge, due to the sudden increase in the current I SC , the voltage drop on R es increased, so V SC dropped. Similarly, when the discharge ended, the voltage drop on R es was reduced to 0 V, so V SC suddenly increased. Figure 12a shows the experimental waveforms during the dynamic process through which the DC-DC converter switched from buck mode to boost mode. Within 4 milliseconds after the load current increased, the supercapacitors had completely replaced the battery pack to provide peak load power. Figure 12b shows the experimental results during the dynamic process through which the DC-DC converter switched from boost mode to buck mode. Within 3 milliseconds after the load current decreased, the supercapacitors could stop discharging entirely, and the battery and the output capacitor provided normal load power and then charged the supercapacitors. These results show that the power allocation strategy based on the hysteretic control principle has good dynamic-response ability.     Figure 13 shows the efficiency of the converter (buck mode) during the supercapacitor charging process. Since the charging current was fixed, the charging power depended on the supercapacitor pack voltage V SC . In the voltage range from 40 V to 56 V, the converter maintained a charging efficiency above 95.84%. Figure 14 shows the efficiency of the converter (boost mode) at different levels of load power during the supercapacitor's discharging process. When the output power was constant at 2 kW, the efficiency during the entire discharge process was not less than 96.89%.      Figure 15 shows the total weight and energy utilization coefficient (EUC) of BESS and HESS under the same load, where the EUC is defined as the ratio of the total energy consumed by the load to the rated energy of the battery pack.  In BESS, the Li-ion battery pack with a rated capacity of 28.8 Ah was used to satisfy the peak load current, with a total weight of 9.3 kg, and the EUC was only 17.12%. In HESS, the battery pack with a rated capacity of 9.6 Ah was sufficient, so the EUC increased to 51.36%. The total weight of HESS was 7.45 kg, consisting of the Li-ion battery pack with a weight of 3.5 kg, the supercapacitor pack with a weight of 2.25 kg, and the DC-DC converter and control system with a total weight of 1.7 kg. The weight distribution of each device in HESS is shown in Figure 16.  Figure 17 shows the cost comparison between BESS and HESS. A 72V/28.8Ah Li-ion battery was used in BESS to meet the pulse power requirements of the load. In HESS, the capacity of a Li-ion battery was only 9.6 Ah, and the cost of a Li-ion battery was only 36.68% of BESS. Although the supercapacitor module and the bidirectional DC-DC converter were added to HESS, the total cost of HESS was only 59.07% of the cost of BESS due to the dramatic drop in the cost of Li-ion battery. In BESS, the Li-ion battery pack with a rated capacity of 28.8 Ah was used to satisfy the peak load current, with a total weight of 9.3 kg, and the EUC was only 17.12%. In HESS, the battery pack with a rated capacity of 9.6 Ah was sufficient, so the EUC increased to 51.36%. The total weight of HESS was 7.45 kg, consisting of the Li-ion battery pack with a weight of 3.5 kg, the supercapacitor pack with a weight of 2.25 kg, and the DC-DC converter and control system with a total weight of 1.7 kg. The weight distribution of each device in HESS is shown in Figure 16. In BESS, the Li-ion battery pack with a rated capacity of 28.8 Ah was used to satisfy the peak load current, with a total weight of 9.3 kg, and the EUC was only 17.12%. In HESS, the battery pack with a rated capacity of 9.6 Ah was sufficient, so the EUC increased to 51.36%. The total weight of HESS was 7.45 kg, consisting of the Li-ion battery pack with a weight of 3.5 kg, the supercapacitor pack with a weight of 2.25 kg, and the DC-DC converter and control system with a total weight of 1.7 kg. The weight distribution of each device in HESS is shown in Figure 16.  Figure 17 shows the cost comparison between BESS and HESS. A 72V/28.8Ah Li-ion battery was used in BESS to meet the pulse power requirements of the load. In HESS, the capacity of a Li-ion battery was only 9.6 Ah, and the cost of a Li-ion battery was only 36.68% of BESS. Although the supercapacitor module and the bidirectional DC-DC converter were added to HESS, the total cost of HESS was only 59.07% of the cost of BESS due to the dramatic drop in the cost of Li-ion battery.  Figure 17 shows the cost comparison between BESS and HESS. A 72V/28.8Ah Li-ion battery was used in BESS to meet the pulse power requirements of the load. In HESS, the capacity of a Li-ion battery was only 9.6 Ah, and the cost of a Li-ion battery was only 36.68% of BESS. Although the supercapacitor module and the bidirectional DC-DC converter were added to HESS, the total cost of HESS was only 59.07% of the cost of BESS due to the dramatic drop in the cost of Li-ion battery. Figure 17 shows the cost comparison between BESS and HESS. A 72V/28.8Ah Li-ion battery was used in BESS to meet the pulse power requirements of the load. In HESS, the capacity of a Li-ion battery was only 9.6 Ah, and the cost of a Li-ion battery was only 36.68% of BESS. Although the supercapacitor module and the bidirectional DC-DC converter were added to HESS, the total cost of HESS was only 59.07% of the cost of BESS due to the dramatic drop in the cost of Li-ion battery. Figure 17. The cost comparison between BESS and HESS. Figure 17. The cost comparison between BESS and HESS.

Conclusions
In this paper, a supercapacitor/battery semi-active HESS with a full current-type control strategy was proposed for pulsed power loads. The peak load power was allocated to the supercapacitors, and the normal load power was provided by the batteries. By directly controlling the output current of the DC-DC converter, the control system was simplified, and the model parameters were needless. The rated capacity of the battery pack was greatly reduced because the peak load power was allocated to the supercapacitors. The experimental results show that the full current-type control strategy has good control performance. Compared with the traditional BESS, the total weight of HESS was reduced by 19.89%, the energy utilization coefficient increased by 34.24%, and the cost was only 59.07% of the cost of BESS.