# A Modern Simple Power Prediction Index for Improving Battery Life

Authors: Masoud Dahmardeh; Pouria Rahimirad; Masoud Masih-Tehrani
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Prediction of available energy storage power is essential for increasing the energy management performance of fuel cell hybrid electric systems (FCHES). A simple yet effective power prediction index is proposed to estimate the supercapacitor state of power. It prevents the supercapacitor’s total depletion in the battery/supercapacitor combination. Modern energy management is equipped with an equivalent consumption minimization strategy. The power prediction index is simple compared with other predictive algorithms while providing excellent efficiency compared with supercapacitor-based management strategies. A supercapacitor-based strategy is presented which extends battery life, at the cost of increased fuel consumption. However, it cannot predict the future low state of charge for the supercapacitor. In such conditions, the battery provides the demand power while fuel cells generate more current. On the other hand, the modern power prediction index energy management strategy significantly increases battery life without adding extra hardware. Moreover, fuel consumption decreased by 15.1 percent. The results show that the modern energy management strategy provides outstanding performance for battery life and fuel consumption compared with other energy management strategies due to its power limitation prediction.


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## Body

## 1. Introduction

Nowadays, fuel cell hybrid electric system (FCHES) is employed for various applications, from fuel cell hybrid electric vehicle (FCHEV) to aircraft, as a way to cope with environmental pollution regulations. They offer high-efficiency electrical power [1], less noise, and almost zero-emission compared with conventional internal combustion engines [2]. Usually, FCHES consists of a battery, supercapacitor (SC), and fuel cell (FC) [3]. The benefit of employing SC in FCHES is to moderate the current stresses of the battery [4], which leads to increased battery lifetime [5]. However, the performance of FCHES is significantly dependent on its energy management system [6], which is used for electric power distribution between fuel cell, battery, and SC [7].The energy management strategy is responsible for controlling the key performance values, such as battery state of charge (SOC), SC voltage, power demand, or DC bus voltage [8]. In an equivalent consumption minimization strategy (ECMS), energy management is based on the minimization of an immediate cost function, which includes fuel consumption of fuel cell system and equivalent consumption of other sources [9]. In supercapacitor-based (SB) energy management, ECMS is employed for calculating fuel cell power. SB strategy is among the supercapacitor-based strategies in which the main energy source is the SC [10]. What is less discussed in the literature is the employment of state of available power (SOP) for energy management strategies. On one hand, the modern approach combines the ECMS method with the SOP strategy to achieve high performance. On the other hand, SOP is a method for the safe operation of energy storage.Plett [11] proposed a new method for the available power estimation of the battery. Considering SOP is beneficial for the energy management system in order to prevent sudden drop of power. The prediction methods of the state-of-available-power (SOP) for the battery are divided into three categories: the characteristic card-based techniques [12], the ANFIS-based method [13], and the dynamic battery model [14]. The dynamic battery model is more common among these methods. The proposed models include Rint, resistor-capacitor (RC) network, Randles, and Hysteresis models. The RC model is capable of providing a reasonable estimation of the dynamic behavior with acceptable accuracy [15]. Masih-Tehrani and Dahmardeh [16] employed this strategy for the SC (instead of the battery) to be employed for a hybrid energy storage system (HESS).This study analyzes different energy management strategies in order to investigate battery life and fuel consumption improvement for two different load profiles and proposes a method for controlling FCHES. A case study of FCHES for aircraft applications is presented. A modern simple power prediction index strategic energy management is developed for this system and is compared with the equivalent consumption minimization strategy (ECMS) [17] and SC-based energy management system [10]. Detailed models for each of the subsystem components are developed, based on the experimental results validations [18]. Wanget al. [19] assessed the aging procedures of LiFePO4 battery cells. The battery life model employed in this research is developed in 2011 and employed by many models recently [20, 21]. Although there are newer models [22], the one reported by Wang proposes a formula for battery life assessment.The main contributions of the article are summarized as follows:(i)
The modern simple power prediction index strategic energy management combines the ECMS method with the SOP method to improve battery life and fuel consumption, simultaneously.(ii)
The state of available power (SOP) for supercapacitor is proposed for a fuel cell hybrid electric system. The SOP algorithm prediction helps preventing supercapacitor from depletion for the battery/supercapacitor combination.(iii)
Battery life and fuel consumption of a fuel cell hybrid electric system are determined.(iv)
The basic energy management of the FCHES is an equivalent consumption minimization strategy.(v)
For implementing the proposed method, no new hardware and extra cost are needed.The article structure is as follows: in Section2 the FCHES is described. The energy management of FCHES is presented in Section 3. A new approach to SOP energy management is proposed in Section 4. Results and Discussion is presented in Section 5. Conclusion is presented in Section 6.


## 2. Methodology

A modern simple power prediction index for improving battery life is proposed for a fuel cell hybrid electric system. SOP algorithm is proposed to estimate supercapacitor state of power for a specific time. Therefore, SOP helps preventing the depletion of supercapacitor for the battery/supercapacitor combination. The proposed modern simple power prediction index strategic energy management combines the ECMS method with the SOP strategy to achieve high performance. Moreover, SOP is a method for the safe operation of energy storage. A graphical abstract of the proposed method is shown in Figure1.Figure 1
A modern simple power prediction index strategic energy management consisting of ECMS method and SOP.As shown in Figure1, the hybrid electric system contains fuel cell, battery, and supercapacitor. The hybrid electric system model is explained in detail in subsection 2.1. Fuel cell and battery pack are equipped with a controllable DC/DC converter, and supercapacitor is directly connected to the DC bus. Therefore, each component can contribute to the generation of the demand power independently using this configuration. This topology is typically used for similar applications, due to the power-split factor which controls fuel cell and supercapacitor power share [23].Two energy management methods are introduced in the next subsections (2.2 and 2.3), as the base for designing the proposed method, as well as a reference method for performance comparison. The modern approach using SOP energy management is explained thoroughly in Section 3.


### 2.1. Fuel Cell Hybrid Electric System Model

For the FCHES, fuel cell is designed for the average power demand (7.5 kW), while the battery and SC are designed to help the latter with a continuous and transient request. FCHES is designed according to [24], and the topology detail and sizing are discussed in [25].The system has a 48 V LiPO4 battery rated at 40 Ah, as well as 6 NESSCAP supercapacitors (48.6 V and 88 F). The fuel cell stack contains a hydroponics fuel cell, proton exchange membrane (PEM) type, and a power rating of 12.5 kW. As shown in Figure2, the energy of fuel cell is controlled by the DC/DC converters using NI PXI-8108, as an integrated internal controller [26]. A reference voltage of the output and the maximum current reference input/output is required for the DC/DC converters, which is determined by the energy management system (implemented in the controller). The efficiency of DC/DC converters is considered as 95%. The focus of this research is development and performance comparison of a modern simple power prediction index strategic energy management with other methods. The network losses are not considered. It is assumed the demand power is supplied by the HESS. Investigation is carried out for the power supplied by the battery/ultracapacitor. This approach is reported for similar applications [23]. Two power demand profiles that are considered to evaluate the energy management system are shown in Figure 3. This load profile is regenerative with low fluctuations compared with an aircraft emergency load profile [26]. The load profile used for performance comparison is obtained by repeating the profile shown in Figure 3(a) for 30 min. The load profile of Figure 3(b) is the same as the one for Figure 3(a) for the interval of 0–130 seconds, plus repeating the interval of 130–245 seconds for fifteen times [17]. These load profiles are selected for comparison of battery life in stressful cycles. The chosen load profile is reported by the relative research works [17, 23, 26] as a representative profile which considers the extremum and average behavior of real conditions, in the specific application of FCHES (electric aircraft). Therefore, the optimization based on the chosen load profiles has good accuracy for real-world conditions (nondeterministic scenarios) of the FCHES in the same applications.Figure 2
Schematic of the fuel cell hybrid electric system.Figure 3
(a). Load profile A in 350 seconds (b). Load profile B in 1800 seconds.
(a)(b)These load profiles contain variant responses on hybrid energy storage and many battery applications are repetitive. These two-load profiles are stressful and simple; therefore, these can be used for comparison of energy management by focusing on battery life in real-time systems.For similar applications, such as hybrid electric vehicle, using driving cycles and cycle-based optimization is popular. This approach is validated by testing nondeterministic scenarios, after optimization in the lab using an appropriate driving cycle.PEMs are the most common fuel cells used for automotive applications. This is mainly because they operate at wide temperature range as well as at low temperatures (−20°C to 100°C); therefore, fast-starting can be realized from idle to full load mode. The hybrid system model is developed in MATLAB/Simulink using the SimPowerSystems (SPS) toolbox. The FC dynamic model is a modified version of the model developed by Padullés et al. [27], where the dynamics of the reactant flow inside the electrode is not considered. Therefore, the determination of the reagent partial pressure is decoupled from the characteristics of the electrode (such as the anode/cathode volume and the orifice area). An interesting feature of this model is that parameters can be obtained from a simple polarization curve test or the data provided by the manufacturer. The transient and steady-state error is very low, which shows the accuracy of the developed fuel cell system model [28].Choosing the best type of the battery for the HESS is very important [29]. The battery type employed in the FCHES is LiFePO4, due to its safety and high energy efficiency compared to other battery types [30]. These specifications are essential for aerospace and automotive applications. The battery model is developed in the SPS environment based on an improved Shepherd model. The voltage polarization expression of the battery discharge voltage shows the effect of the battery SOC more efficiently and ensures the high reliability of the model stability [31]. The catalog data and some results of the dynamic experiments are used for determining the parameters of the battery model [26]. The proposed model has a good correlation with the experiment results [32].The battery life model provides cyclic test results from a long-term battery life study of a commercial lithium battery. The effects of the test parameters (time, temperature, depth of charge, and flow) are studied and described. The results indicate that the loss of capacity is strongly influenced by the degradation and thermal condition, whereas the load depth influence is lower with the rate ofCrate/2 [33]. The model of life loss is developed to express the dependence of degradation sand thermal condition. The capacity loss Qloss model is presented by equations (1) and (2) [33]. These equations are expressed to calculate battery life in a year and are valid for all C-rates, where C-rate is a measure of the rate at which a battery is being charged or discharged. As Qloss reaches 20 percent of the nominal battery capacity, the battery life is considered as over. The battery life model is derived from the popular model derived based on experimental results on the capacity fade of LiFePO4 battery [19]. Extensive cycle-tests are performed to take into account the temperature effect (−30 to 60°C), as well as the effect of depth of discharge (DOD) (90–10%), and also sudden charge and discharges of up to 10 Crate. This battery life model is used in recent research works [34, 35].(1)Qloss=B×exp31700+370.3×CrateR×TAh0.55,Lifebatyear=0.2CbatQloss∗ti3600∗8∗250.whereB is a constant and is shown for different C-rates in Table 1. R is the ideal gas constant, T is the battery temperature, Ah is the battery capacity, Cbat is the nominal battery capacity, and ti is the time duration of the sample cycle. Equation (1) shows that as the Crate increases, the battery capacity loss increases exponentially. Therefore, SC can help reduce the stress on the battery and improve battery lifetime significantly.Table 1
The value ofB.
Crate/22Crate6Crate10CrateB values31630216811293415512Electrical double-layer capacitors (EDLCs), supercapacitors, are similar to conventional capacitors, with the improvement of capacity for charge and discharge [35].The SC model is developed using Helmholtz and Gouy-Chapman-Stern diffusion model [36]. The basic model parameters are determined according to the experimental results and the datasheet (capacitance, nominal voltage, and DC resistance) [26].


### 2.2. Equivalent Consumption Minimization Strategy

The equivalent consumption minimization strategy (ECMS) minimizes the fuel consumption of the FC by handling its power and keeping battery SOC in a certain range [27, 37]. In this strategy, SC provides the remaining power demand and engages at peak powers, although it is not completely controllable. The ECMS algorithm flowchart is shown in Figure 4. The ECMS optimization problem in this application is proposed as follows. Find an optimal solution x=Pfc,α,Pbat, which minimizes [27]:(2)F=Pfc+αPbat×ΔT,where Pfc and Pbat are the fuel cell and battery powers, respectively. ΔT is the simulation sample time. α is the penalty coefficient, and μ is a predefined value which is used to specify the contribution of the battery for the energy minimization. In this application, it is tuned to 0.6 for better battery SOC control.Figure 4
The equivalent consumption minimization strategy (ECMS).Minimizing equation (2) can minimize total energy that is produced by the battery and fuel cell. Under the equality constraints:(3)Pload=Pfc+Pbat,α=1−2μSOCbat−0.5SOCbat−max+SOCbat−minSOCbat−max+SOCbat−min,where Pload is the load power, taking into account the DC/DC converter losses.Considering the boundary conditions as:(4)Pfc−min≤Pfc≤Pfc−max,Pbat−min≤Pfc≤Pbat−max,0≤α≤100,where SOCbat−min and SOCbat−max are the minimum and maximum battery SOC, respectively. Pbat−min and Pbat−max are the minimum and maximum battery power, respectively. Pfc−min and Pfc−max are the minimum and maximum FC power, respectively.In the proposed optimization problem, SC power is not considered, due to its low effect on the DC bus voltage of the electric motor DC/AC converter [27]. Therefore, when the supercapacitor is at low SOC, it is charged by the battery. The primary approach of this strategy is power-sharing between the battery and FC without directly considering the SC.


### 2.3. Supercapacitor-Based Energy Management

Supercapacitor-based (SB) energy management is chosen to compare the energy management of the proposed method with other energy management method reported in the literature. In this method, ECMS is used for calculating the power of fuel cell. Power distribution system calculates an efficient distribution for the battery/SC combination. It is among the latest strategies that work mainly on the battery and supercapacitor [10]. It is among supercapacitor-based strategies such as the one reported by Rezzak and Boudjerda [38]. The supercapacitor-based management algorithm is shown in Figure 5.Figure 5
Supercapacitor-based (SB) energy management governing algorithm.Case 1.
(charging mode): If FC power is more than the demand power by0.98Pfc≥Pload, supercapacitor is set to be in the charging mode.
When the charging current of the supercapacitor reaches the low threshold value of around 0.5 A, it is assumed that it is fully chargedSOCSC=100%. Consequently, the power distribution system terminates the SC charge mode and activates the battery charge mode.Case 2.
(discharging mode): If FC power is lower than the demand power by0.98Pfc<Pload, supercapacitor is set to be in the discharge mode.
When the SC discharge current reaches the lower threshold current of around 0.5 A, SC is considered as fully dischargedSOCSC=0%. Consequently, power distribution system terminates the SC discharge mode and activates the battery discharge mode.


## 2.1. Fuel Cell Hybrid Electric System Model

For the FCHES, fuel cell is designed for the average power demand (7.5 kW), while the battery and SC are designed to help the latter with a continuous and transient request. FCHES is designed according to [24], and the topology detail and sizing are discussed in [25].The system has a 48 V LiPO4 battery rated at 40 Ah, as well as 6 NESSCAP supercapacitors (48.6 V and 88 F). The fuel cell stack contains a hydroponics fuel cell, proton exchange membrane (PEM) type, and a power rating of 12.5 kW. As shown in Figure2, the energy of fuel cell is controlled by the DC/DC converters using NI PXI-8108, as an integrated internal controller [26]. A reference voltage of the output and the maximum current reference input/output is required for the DC/DC converters, which is determined by the energy management system (implemented in the controller). The efficiency of DC/DC converters is considered as 95%. The focus of this research is development and performance comparison of a modern simple power prediction index strategic energy management with other methods. The network losses are not considered. It is assumed the demand power is supplied by the HESS. Investigation is carried out for the power supplied by the battery/ultracapacitor. This approach is reported for similar applications [23]. Two power demand profiles that are considered to evaluate the energy management system are shown in Figure 3. This load profile is regenerative with low fluctuations compared with an aircraft emergency load profile [26]. The load profile used for performance comparison is obtained by repeating the profile shown in Figure 3(a) for 30 min. The load profile of Figure 3(b) is the same as the one for Figure 3(a) for the interval of 0–130 seconds, plus repeating the interval of 130–245 seconds for fifteen times [17]. These load profiles are selected for comparison of battery life in stressful cycles. The chosen load profile is reported by the relative research works [17, 23, 26] as a representative profile which considers the extremum and average behavior of real conditions, in the specific application of FCHES (electric aircraft). Therefore, the optimization based on the chosen load profiles has good accuracy for real-world conditions (nondeterministic scenarios) of the FCHES in the same applications.Figure 2
Schematic of the fuel cell hybrid electric system.Figure 3
(a). Load profile A in 350 seconds (b). Load profile B in 1800 seconds.
(a)(b)These load profiles contain variant responses on hybrid energy storage and many battery applications are repetitive. These two-load profiles are stressful and simple; therefore, these can be used for comparison of energy management by focusing on battery life in real-time systems.For similar applications, such as hybrid electric vehicle, using driving cycles and cycle-based optimization is popular. This approach is validated by testing nondeterministic scenarios, after optimization in the lab using an appropriate driving cycle.PEMs are the most common fuel cells used for automotive applications. This is mainly because they operate at wide temperature range as well as at low temperatures (−20°C to 100°C); therefore, fast-starting can be realized from idle to full load mode. The hybrid system model is developed in MATLAB/Simulink using the SimPowerSystems (SPS) toolbox. The FC dynamic model is a modified version of the model developed by Padullés et al. [27], where the dynamics of the reactant flow inside the electrode is not considered. Therefore, the determination of the reagent partial pressure is decoupled from the characteristics of the electrode (such as the anode/cathode volume and the orifice area). An interesting feature of this model is that parameters can be obtained from a simple polarization curve test or the data provided by the manufacturer. The transient and steady-state error is very low, which shows the accuracy of the developed fuel cell system model [28].Choosing the best type of the battery for the HESS is very important [29]. The battery type employed in the FCHES is LiFePO4, due to its safety and high energy efficiency compared to other battery types [30]. These specifications are essential for aerospace and automotive applications. The battery model is developed in the SPS environment based on an improved Shepherd model. The voltage polarization expression of the battery discharge voltage shows the effect of the battery SOC more efficiently and ensures the high reliability of the model stability [31]. The catalog data and some results of the dynamic experiments are used for determining the parameters of the battery model [26]. The proposed model has a good correlation with the experiment results [32].The battery life model provides cyclic test results from a long-term battery life study of a commercial lithium battery. The effects of the test parameters (time, temperature, depth of charge, and flow) are studied and described. The results indicate that the loss of capacity is strongly influenced by the degradation and thermal condition, whereas the load depth influence is lower with the rate ofCrate/2 [33]. The model of life loss is developed to express the dependence of degradation sand thermal condition. The capacity loss Qloss model is presented by equations (1) and (2) [33]. These equations are expressed to calculate battery life in a year and are valid for all C-rates, where C-rate is a measure of the rate at which a battery is being charged or discharged. As Qloss reaches 20 percent of the nominal battery capacity, the battery life is considered as over. The battery life model is derived from the popular model derived based on experimental results on the capacity fade of LiFePO4 battery [19]. Extensive cycle-tests are performed to take into account the temperature effect (−30 to 60°C), as well as the effect of depth of discharge (DOD) (90–10%), and also sudden charge and discharges of up to 10 Crate. This battery life model is used in recent research works [34, 35].(1)Qloss=B×exp31700+370.3×CrateR×TAh0.55,Lifebatyear=0.2CbatQloss∗ti3600∗8∗250.whereB is a constant and is shown for different C-rates in Table 1. R is the ideal gas constant, T is the battery temperature, Ah is the battery capacity, Cbat is the nominal battery capacity, and ti is the time duration of the sample cycle. Equation (1) shows that as the Crate increases, the battery capacity loss increases exponentially. Therefore, SC can help reduce the stress on the battery and improve battery lifetime significantly.Table 1
The value ofB.
Crate/22Crate6Crate10CrateB values31630216811293415512Electrical double-layer capacitors (EDLCs), supercapacitors, are similar to conventional capacitors, with the improvement of capacity for charge and discharge [35].The SC model is developed using Helmholtz and Gouy-Chapman-Stern diffusion model [36]. The basic model parameters are determined according to the experimental results and the datasheet (capacitance, nominal voltage, and DC resistance) [26].


## 2.2. Equivalent Consumption Minimization Strategy

The equivalent consumption minimization strategy (ECMS) minimizes the fuel consumption of the FC by handling its power and keeping battery SOC in a certain range [27, 37]. In this strategy, SC provides the remaining power demand and engages at peak powers, although it is not completely controllable. The ECMS algorithm flowchart is shown in Figure 4. The ECMS optimization problem in this application is proposed as follows. Find an optimal solution x=Pfc,α,Pbat, which minimizes [27]:(2)F=Pfc+αPbat×ΔT,where Pfc and Pbat are the fuel cell and battery powers, respectively. ΔT is the simulation sample time. α is the penalty coefficient, and μ is a predefined value which is used to specify the contribution of the battery for the energy minimization. In this application, it is tuned to 0.6 for better battery SOC control.Figure 4
The equivalent consumption minimization strategy (ECMS).Minimizing equation (2) can minimize total energy that is produced by the battery and fuel cell. Under the equality constraints:(3)Pload=Pfc+Pbat,α=1−2μSOCbat−0.5SOCbat−max+SOCbat−minSOCbat−max+SOCbat−min,where Pload is the load power, taking into account the DC/DC converter losses.Considering the boundary conditions as:(4)Pfc−min≤Pfc≤Pfc−max,Pbat−min≤Pfc≤Pbat−max,0≤α≤100,where SOCbat−min and SOCbat−max are the minimum and maximum battery SOC, respectively. Pbat−min and Pbat−max are the minimum and maximum battery power, respectively. Pfc−min and Pfc−max are the minimum and maximum FC power, respectively.In the proposed optimization problem, SC power is not considered, due to its low effect on the DC bus voltage of the electric motor DC/AC converter [27]. Therefore, when the supercapacitor is at low SOC, it is charged by the battery. The primary approach of this strategy is power-sharing between the battery and FC without directly considering the SC.


## 2.3. Supercapacitor-Based Energy Management

Supercapacitor-based (SB) energy management is chosen to compare the energy management of the proposed method with other energy management method reported in the literature. In this method, ECMS is used for calculating the power of fuel cell. Power distribution system calculates an efficient distribution for the battery/SC combination. It is among the latest strategies that work mainly on the battery and supercapacitor [10]. It is among supercapacitor-based strategies such as the one reported by Rezzak and Boudjerda [38]. The supercapacitor-based management algorithm is shown in Figure 5.Figure 5
Supercapacitor-based (SB) energy management governing algorithm.Case 1.
(charging mode): If FC power is more than the demand power by0.98Pfc≥Pload, supercapacitor is set to be in the charging mode.
When the charging current of the supercapacitor reaches the low threshold value of around 0.5 A, it is assumed that it is fully chargedSOCSC=100%. Consequently, the power distribution system terminates the SC charge mode and activates the battery charge mode.Case 2.
(discharging mode): If FC power is lower than the demand power by0.98Pfc<Pload, supercapacitor is set to be in the discharge mode.
When the SC discharge current reaches the lower threshold current of around 0.5 A, SC is considered as fully dischargedSOCSC=0%. Consequently, power distribution system terminates the SC discharge mode and activates the battery discharge mode.


## 3. A Modern Simple Power Prediction Index Strategic Energy Management

A modern simple power prediction index strategic energy management is proposed by using SOP for energy management of FCHES. It combines ECMS method with the SOP strategy to achieve high performance power management system. Although SOP is a method for safe operation of the energy storage system, knowing SOP is used in the energy management to prevent a sudden drop in power.This strategy is employed to be used in FCHES. Figure6 shows the proposed energy management governing algorithm flowchart. At first, PFC is calculated using ECMS algorithm. Supercapacitor is used as the main energy storage, considering its state of available power limit. The remaining power is drawn from the battery which is limited by Pbat−min and Pbat−max. Afterwards, PSC is recalculated based on the value of Pbat. It should be noted that PSC is limited by PSC−min and PSC−max which are the minimum and maximum levels of power for the SC, respectively, provided by the manufacturer data sheet. The new value of Pbat is then limited by Pbat−min and Pbat−max. The rate limits that are considered for fuel cell, battery, and supercapacitor are 25, 45, and 4 amperes per second, respectively.Figure 6
A modern simple power prediction index strategic energy management consisting of ECMS method with SOP strategy.The state-of-available-power (SOP) is a method for estimating available power for a battery within a future specified time period. It determines the power boundaries of an energy storage system to avoid harmful conditions during a future period. In a battery/SC combined system, the battery energy capacity is higher than that for the SC. Hence, SC is more liable to reach its limit based on the voltage and SOC boundaries. The battery state of health (SOH) is strongly dependent on the SC behavior. Battery SOH is improved by employing SC efficiently. A key parameter in improving battery SOH is to remove peak power demands, as well as stresses from the battery. The main role of SC is the limitation of SOP. Due to the simple structure of supercapacitor, compared with the complex electrochemical batteries, as well as SC thermal stability, supercapacitor is a good choice to move the power demand from the battery to it. In other words, SC SOP is appropriate to be used as a powerful tool for calculating SC limit based on voltage and SOC for a future time period.The ultimate SC current boundaries for a certain future time periodΔt in second) based on the predicted supercapacitor SOC SOCSC are expressed in equations (5) and (6). For discharge mode, ISC−maxdis−SOC by equation (5) and for charge mode, ISC−minchg−SOC by equation (6) [16].(5)ISC−maxdis−SOC=SOCSC+SOCSC−minΔt/CSC,(6)ISC−minchg−SOC=SOCSC+SOCSC−maxΔt/CSC,where SOCSC−min and SOCSC−max are the minimum and maximum limits of supercapacitor SOC, respectively. These values are selected as 20% and 98% for the discharge mode and charge mode, respectively.The ultimate SC current boundaries for a certain future time periodΔt in second) based on the predicted voltage of the SC VSC are expressed by equation (7) for the discharge mode ISC−maxdis−v and by equation (8) for charge mode ISC−minchg−v.(7)ISC−maxdis−v=VOC−SC+VSC−minΔt/CSC×VOC−SC−rate+Rin−SC,(8)ISC−minchg−v=VOC−SC+VSC−maxΔt/CSC×VOC−SC−rate+Rin−SC,VOC−SC is the open circuit voltage of the supercapacitor when ISC=0, VSC−min and VSC−max are the minimum and maximum voltage limits of SC and are set to 9.7 V and 48.6 V, for the discharge and charge modes, respectively. VOC−SC−rate is the supercapacitor voltage curve rate versus SOCSC. Rin−SC is the SC internal resistance.The ultimate SC current boundaries based on both SOC and voltage of the SC are expressed by equation (9) (for the discharge mode ISC−maxdis−tot and equation (10) (for the charge mode ISC−maxchg−tot.(9)ISC−maxdis−tot=minISC−max,ISC−maxdis−SOC,ISC−maxdis−v,(10)ISC−minchg−tot=maxISC−min,ISC−minchg−SOC,ISC−minchg−v,The permissible SC power insight of the SOP is calculated by simultaneously considering the current limits (equations (9) and (10) and the predicted SC voltage Vter−SCt+Δt. Equation (11) calculates the maximum (discharge) power PSC−maxdis−SOP and equation (12) calculates the minimum (charge) power PSC−minchg−SOP. These SC power boundaries are used by the HESS power distribution system (Figure 6, SOP check block).(11)PSC−maxdis−SOP=ISC−maxdis−tot×Vter−SCt+Δt,=ISC−maxdis−tot,VOC−SCSOCSC−ISC−maxdis−tot×ΔtCSC−Rin−SC×ISC−maxdis−tot,(12)PSC−minchg−SOP=ISC−minchg−SOP×Vter−SCt+Δt,=ISC−minchg−SOP,VOC−SCSOCSC−ISC−minchg−SOP×ΔtCSC−Rin−SC×ISC−minchg−SOP,


## 4. Results and Discussion

Performance results of different energy management systems are simulated in this section. Figure7 shows the (a) voltage, (b) current, (c) and SOC of the battery for load profile A. Energy management systems are ECMS (solid lines), SB (dotted lines), and modern simple power prediction index strategic energy management of the SOP strategy (dashed lines). The battery curves show that the ECMS strategy engages the battery more compared with other strategies. Specifically, the more voltage drops (Figure 7(a)), the more discharge current (Figure 7(b)), and more SOC drop (Figure 7(c)) is evident for this strategy. Consequently, battery capacity loss is higher for the ECMS strategy compared with other methods. A significant difference between the modern simple power prediction index strategy and supercapacitor-based energy management is the battery charging strategy. For the latter one, the priority for charging is battery, whereas in the former one, the priority for charging is supercapacitor. Therefore, battery voltage and SOC are higher for the supercapacitor-based strategy, compared with the modern simple power prediction index strategy, due to the higher battery charge current. This leads to more battery capacity loss for the SB method, compared with the proposed method.Figure 7
Comparison of battery. (a) Voltage. (b) Current and (c) SOC for different energy management systems for load profile A.
(a)(b)(c)Figure8 shows the (a) voltage, (b) current, and (c) SOC of supercapacitor for load profile A. The energy management systems are ECMS (solid lines), supercapacitor-based (dotted lines), and the modern simple power prediction index strategic energy management of the SOP strategy (dashed lines). Although the strategies and models are the same for battery and SC, the results for the SC are not the same. Supercapacitor is not equipped with a DC/DC converter, and it provides the remaining demand power. Supercapacitor curves show that ECMS strategy engages SC less compared with other strategies. It is obvious from less voltage fluctuations (Figure 8(a)), less discharge current (Figure 8(b)), and less SOC variations (Figure 8(c)). This SC behavior for the ECMS causes more battery usage, which leads to more battery capacity loss compared with other strategies. Figure 8 shows that the modern simple power prediction index strategy and SB strategy approximately have similar SC behavior until the first 100 seconds of load profile A. However, the curves are different afterwards. At around time instant 100 second, the SOP limitations of SC are activated, and the modern simple power prediction index strategy limits the SC power. This predictive decision helps SC deplete later and helps the battery save its capacity. Therefore, at the end of the cycle test, SC voltage and SOC are higher than the other strategies.Figure 8
Comparison of supercapacitor. (a) Voltage. (b) Current and (c) SOC for different energy management systems for load profile A.
(a)(b)(c)Fuel cell current and voltage profile (Figure9) indicate that the modern simple power prediction index strategic energy management of the SOP strategy performance is slightly improved compared with the ECMS method, that is, higher fuel cell voltage and lower fuel cell current in the last 50 seconds of the load profile. The supercapacitor-based strategy engages the fuel cell more in the last 100 s of load profile, which leads to more fuel consumption, compared with other methods.Figure 9
Comparison of fuel cell. (a) Voltage and (b) current for different energy management systems for load profile A.
(a)(b)Table2 lists the battery life and fuel cell consumption for different energy management systems, and the SOP strategy improvements percentages are shown. The lower fuel consumption indicates more mileage of the FCHES. As can be seen in Table 2, supercapacitor-based strategy improves battery life of ECMS. However, fuel cell consumption of the supercapacitor-based is higher than that of ECMS. The modern simple power prediction index strategic energy management of the SOP strategy has the highest battery life, while fuel cell consumption is the lowest. This significant achievement of the modern simple power prediction index strategy is related to the better ability of SC charge management to reduce battery and fuel cell stresses.Table 2
Battery life and fuel consumption for different energy management systems.
Battery life (year)Fuel consumption (gram)ECMSSBSOPSBECMSSOP7.1513.5717.635.9740.3435.03SOP improvement (%)SOP improvement (%)ECMSSBSOPSBECMSSOP146.189.8—2.715.1—In order to further investigate the effectiveness of the proposed method, load profile B is employed for SC power comparison by repeating the scenario of load profile A for 30 minutes. Figure10(a) illustrates the performance comparison for different energy management systems for load profile B. As it is shown, ECMS and SOP strategies provide similar power, in order to respond to the demand power. Supercapacitor-based strategy cannot supply the demand power at some periods, for instance, at about time instant 350 s. This is related to its inability of SC state of power prediction. In other words, the priority of SC charging and providing the demand power is not applied properly and the power is dedicated to charge SC, instead of answering the demand power (Figure 10(b)).Figure 10
(a) SC power comparison for different energy management systems in load profile B. (b) Supercapacitor-based power performance.
(a)(b)


## 5. Conclusion

In order to achieve the best fuel cell hybrid electric system (FCHES) performance, this study uses SOP algorithm’s prediction to prevent supercapacitor depletion in the battery/supercapacitor hybrid system. ECMS manages the power-sharing between battery and FC without considering the supercapacitor state in order to reduce fuel consumption. Therefore, ECMS works as a battery-based power distribution system for a hybrid energy storage system. Different energy management systems are investigated to be applied to the FCHES for comparison with the proposed method, that is, modern simple power prediction index strategy. A supercapacitor-based power distribution system is chosen for replacing the power distributor of the battery and SC in the ECMS strategy. The results show that the supercapacitor-based strategy improves the battery life compared with the conventional ECMS because of the more battery usage in the SC-based strategy than the battery-based one. In supercapacitor-based method, fuel cell consumption increases. However, prediction of the future low SOC for the supercapacitor is not possible, which limits its performance. Therefore, when supercapacitor is fully discharged, battery provides the demand power, as well as the fuel cell.A simple yet effective predictive supercapacitor charge algorithm is proposed in this article in order to prevent early draining of the SC charge during the power demand peaks. The proposed algorithm works based on the SC SOP. The SOP calculates the power limits of the SC based on its voltage and SOC prediction for a certain future time period. This is a popular method for the battery behavior prediction and in some applications for the SC states. In this article, the SOP of the SC is deployed in the FCHES. The results show that the proposed modern simple power prediction index strategy engages SC more efficiently, compared with the conventional ECMS and supercapacitor-based strategies. Therefore, contributions of this research are summarized as follows:(i)
Battery life and fuel consumption of a fuel cell hybrid electric system are investigated.(ii)
The basic energy management of the FCHES is an equivalent consumption minimization strategy for calculating fuel cell power.(iii)
The modern simple power prediction index strategic energy management uses SOP method to improve battery life and fuel consumption, simultaneously.(iv)
The maximum improvement of the new energy management system is 146.1 percent for the battery life.(v)
Improvement of the minimum fuel consumption for the new power distribution system is 15.1 percent.(vi)
For implementing the proposed method, no new hardware or extra cost is needed.



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*Source: 8028874-2022-09-17.xml*