Secure power management strategy for direct torque controlled fuel cell/ supercapacitor electric vehicles

High reliability is recommended in hybrid electric vehicle applications. In this study, a secure power management strategy has been developed for a fuel cell—supercapacitor hybrid electric vehicle. In addition to its ability to detect the occurrence of failures in vehicle power sources, the proposed power management strategy isolates the faulty source and reconfigures the control scheme to always guarantee bus voltage stability and vehicle traction even in faulty situations. The developed power management strategy enhances vehicle comfort and prevents exhausting one source over another by allowing the fuel cell and the supercapacitor to operate at different power levels. The multiloop control scheme associated with the power sources is highly reliable since both sources can run the vehicle alone and regulate the bus voltage. Vehicle speed and torque controllers are simultaneously tuned using a particle swarm optimization algorithm. Torque and speed ripples are automatically minimized via the use of a new proposed cost function. This approach made the controller design easier and gave the designer the possibility to tradeoff between the variables to be minimized.

1 Introduction

In the last decade, several studies were carried out to investigate alternative nonpolluting energy sources to solve the persisting problem of carbon emission. Vehicle electrification was among the proposed solutions for the elimination or at least the reduction of gas emission. This solution has attracted many researchers and different research axes have been born out of the increasing interest given to this idea, such as vehicle safety and security (Sabaliauskaite et al., 2019), energy management (Zhang et al., 2017a; Yadav and Maurya, 2021a; Yadav and Maurya, 2021b; Yadav and Maurya, 2022), power sources protections (Oubelaid et al., 2022a), power train architecture (Wu et al., 2015), intelligent transportation (Oubelaid et al., 2022b; Oubelaid et al., 2022c), and vehicle control (Max and Lantos, 2014; Vajsz et al., 2017; Oubelaid et al., 2022d).

Hybrid electric vehicles can be thought of as mobile embedded systems that are subjected to unpredictable driving conditions. Knowing that environmental driving conditions are harsh and random, hybrid electric vehicles are permanently subjected to failure risk, which may be due to a fault in one of their components. Several research studies discussing the enhancement of hybrid electric vehicle security are available in the literature. To ensure continuous vehicle operation, researchers use different fault tolerant strategies which are applied to different hybrid electric vehicle components. Yu et al. (2017), Kersten et al. (2019), and Moosavi et al. (2019) have discussed possible open circuit faults occurring in inverters used in electrified vehicles. Faults taking place in traction machines and ensuring electric vehicle traction are also extensively studied in the literature. Mellor et al. (2003), Tashakori and Ektesabi (2013), Kaplan et al. (2021), Liu et al. (2021), and Wu et al. (2022) have proposed fault tolerant control strategies to handle possible faults in vehicle traction machine and ensure continuous and secure operation. Faults which may occur in the different sensors on vehicle boards are also extensively studied in the literature (Kommuri et al., 2016; Peñate et al., 2018; Yu et al., 2021; Zhang et al., 2021). To summarize, although inverters, traction machines, and sensors are more robust compared to fuel cells and supercapacitors, few research works have dealt with possible faults at the vehicle power sources level, except for some works which have mainly discussed power sources degradation (Shchurov et al., 2021; Song et al., 2021; Yi et al., 2022).

As mentioned earlier, vehicle power sources such as fuel cells are too sensitive. In addition, hybrid electric vehicles are always subjected to fast and abrupt load variations which could result in significant damage at both the source and motor sides. For the aforementioned reason, scientists have increased their efforts in developing novel control techniques which protect sensitive power sources such as fuel cells from possible damage due to sudden load variations. Ou et al. (2017) proposed a novel control technique that protects FC from overheating and air starvation that may be caused by rapid load variation. Koprivsek (2018) developed an over-current protection strategy to protect the battery electric vehicles from high currents resulting from rapid load variations. Liu et al. (2017) and Zhang et al. (2020) presented filter based control technique to protect both fuel cells and batteries from transient current ripples arising during abrupt power reference variation caused by abrupt load variations using rate limiters and a first-order transfer function to restrict fuel cell and battery output power and to produce a time delay necessary for the electrochemical reactions that occur within the FC. To conclude, vehicle power sources are so sensitive, and their failure possibility has to be taken into account when elaborating on control techniques or power management strategies.

Recently developed power management strategies for hybrid electric vehicles take into account the sensitivity and slowness of some vehicle power sources, such as fuel cells, but do not consider their possible failure. Ou et al. (2019) proposed a novel energy management technique based on fuzzy logic and state machine control techniques to enhance FC lifespan. He et al. (2020), Tao et al. (2020), and Trinh and Ahn (2021) developed energy management strategies that take into account only FC slow dynamics but do not consider its possible failure, and this reduces driving security. In many research works (Thounthong et al., 2009; Hwang et al., 2012; Zhang et al., 2017b; Wieczorek and Lewandowski, 2017; Meyer et al., 2018; Xie et al., 2018; Zhang et al., 2018; Raghavaiah and Srinivasarao, 2019; Kakouche et al., 2022), one power source always performs DC bus regulation, and the second source intervenes either during regenerative braking or to help the primary source during accelerations and high power demands. In case of failure of the sources fixing the DC bus voltage, the vehicle will lose its main powering source, and this may lead to serious vehicle damages and even total vehicle failure.

In this study, a novel power management strategy that takes into account possible failures in vehicle power sources is presented in this work. Unlike the previously mentioned power sharing techniques, the proposed management strategy offers the following advantages:

• Precise power flow control since, at any driving instant, the fuel cell can deliver any desired fraction of the total power required for traction

• Power sources are operated at known and defined operating points, and this reduces the stress applied on them during high power demands and, hence, increases their lifespan.

• Secure vehicle operation: a fault detection algorithm will detect possible failures in vehicle power sources and correct them via control loop reconfiguration.

Hybrid electric vehicle traction is ensured using direct torque control–based space vector modulation. All vehicle regulators are concurrently tuned using a particle swarm optimization algorithm. This aforementioned intelligent technique permits simultaneous tuning through the use of newly proposed cost functions that allows the designer to tradeoff and prioritize between the design variables to be minimized.

2 Vehicle dynamics

The motion of the vehicle shown in Figure 1 is governed by the following equation:

${\overrightarrow{F}}_{traction}-{\overrightarrow{F}}_r=m\overrightarrow{a},(1)$

where ${\overrightarrow{F}}_{traction}$is the net external force acting on the vehicle body, ${\overrightarrow{F}}_r$ is the net resistive force, m is the vehicle mass, and $\overrightarrow{a}$ is the vehicle acceleration vector.

FIGURE 1

FIGURE 1. HEV in inclined surface.

The net resistive force is defined as given below:

${\overrightarrow{F}}_r={\overrightarrow{F}}_{aero+}{\overrightarrow{F}}_g+{\overrightarrow{F}}_{tire}+{\overrightarrow{F}}_{acc},(2)$

where F_aero is the aerodynamic force, F_g is the force due to gravity, F_tire is the friction force which exists between the vehicle’s tire and ground surface, and F_acc is the acceleration force required by the vehicle to reach maximum speed from rest. Details about the mathematical modeling of each force are provided in the study by Shchurov et al. (2021). Vehicle parameters which are used in this study are shown in Table1.

TABLE 1

TABLE 1. HEV parameters.

3 Power sources modeling

3.1 FC modeling

The output voltage of one fuel cell (FC) is given by Eq. 3, which is approximately equal to 0.7 V. From this equation, one can notice the existence of several voltage drops, such as activation, ohm, and conduction voltage drops. More information about FC dynamics is given in the study by Song et al. (2021). From Eq. 4, the voltage of one FC stack is formed by serial grouping of N_s = 68, which makes the stack nominal voltage approximately 48 V.

$V_{FC,cell}=E_{nernst}-V_{act}-V_{ohm}-V_{cond,}(3)$

$V_{FC}=N_S{V}_{FC,cell}.(4)$

The voltage-current characteristic and power-current characteristics of one fuel cell stack are highlighted in Figure 2. The green points on the curves represent the nominal current, voltage, and power of the used FC.

FIGURE 2

FIGURE 2. Fuel cell characteristic curves.

3.2 SC modeling

The supercapacitor (SC) is used along with the fuel cell to make up for the FC’s slow dynamics and also to increase vehicle performance. In addition to their fast dynamics, SCs are known for their robustness and their high number of charge and discharge cycles. Figure 3 shows the SC characteristic curve where one can notice that it gets charged very fast and sustains very high charge currents.

FIGURE 3

FIGURE 3. Supercapacitor characteristic curve.

The electrical SC equivalent circuit is shown in Figure 4. It is modeled as a controlled voltage source in series with an equivalent series resistance, as shown next.

FIGURE 4

FIGURE 4. Electrical supercapacitor equivalent model.

SC cell voltage V_SC is calculated by Eq. 5 using the Stern equation. Details about this last-mentioned equation are provided in the study by Yi et al. (2022). The SC state of charge (SOC_SC) is calculated by Eq. 6 using the initial and the total SC charges, Q_init and Q_T, respectively.

$V_{SC}={V_T-r}_{sc}{i}_{sc},(5)$

${SOC}_{SC}=100\ast \frac{Q_{init}-{{\displaystyle \int }}_{\mathit{0}}^{t}i\left(\tau \right)d\tau }{Q_T}.(6)$

The total SC stack voltage is given by Eq. 7:

$V_{SC,tot}=N_{SC}{V}_{SC},(7)$

where V_{sc, tot} is the total SC voltage, V_sc is the SC cell voltage, and N_sc is number of series supercapacitors.

4 HEV traction and control

4.1 HEV traction

Permanent magnet synchronous machine (PMSM) is used to ensure HEV traction. It is chosen among other types of machines because of its robustness and its high torque to mass ratio, which means that it can deliver high torque and occupy small place in the space at the same time.

Stator flux and currents of PMSM motor in the dq rotating frame are, respectively, given by Eq. 8 and Eq. 9:

$\{\begin{array}{c}{\lambda }_d=L{i}_d+\varphi \\ {\lambda }_q=L{i}_q,\end{array}(8)$

$\{\begin{array}{c}\frac{d{i}_d}{dt}=-\frac{{\mathrm{r}}_s}{L}{i}_d+\frac{V_d}{L}+p{w}_r{i}_q\\ \frac{d{i}_q}{dt}=-\frac{{\mathrm{r}}_s}{L}{i}_q+\frac{V_q}{L}-p{w}_r{i}_d-\frac{\varphi w_r}{L},\end{array}(9)$

where r_S and L are the stator resistance and inductance, respectively.$\varphi$ is the flux of the permanent magnet. More information about PMSM is provided in the study by Jnayah and Khedher (2019). The parameters of the PMSM motor used in this work are shown in Table 2.

TABLE 2

TABLE 2. HEV and environment parameters.

4.2 HEV control

The HEV discussed in this study is shown in Figure 5. It can be seen that the traction machine is controlled using direct torque control–based space vector modulation This control technique was chosen on purpose because of the fast torque response it provides.

FIGURE 5

FIGURE 5. Top view of SC-FC HEV.

At each sampling time Ts, the flux on the αβ frame and flux magnitude are estimated using Eq. 10 and Eq. 11. It is worth noticing that the PMSM stator resistance was neglected during flux estimation. Eq. 12 and Eq. 13 are used to estimate PMSM torque and rotor angle, respectively.

$\{\begin{array}{c}{\varphi }_{\alpha }\left[k+\mathit{1}\right]={{\varphi }_{\alpha }\left[k\right]+T}_s{*V}_{\alpha }\left[k\right]\\ {\varphi }_{\beta }\left[k+\mathit{1}\right]={\varphi }_{\beta }\left[k\right]+T_s{V}_{\beta }\left[k\right]\end{array},(10)$

${\varphi }_{es}\left[k+\mathit{1}\right]=\sqrt{{\varphi }_{\alpha }^{\mathit{2}}\left[k+\mathit{1}\right]+{\varphi }_{\beta }^{\mathit{2}}\left[k+\mathit{1}\right]},(11)$

$T_{es}=\mathrm{1.5}p\left({\varnothing }_{\alpha }{i}_{\beta }-{\varnothing }_{\beta }{i}_{\alpha }\right),(12)$

${\theta }_s\left[k+\mathit{1}\right]={\mathit{tan}}^{-\mathit{1}}\left(\frac{{\varphi }_{\beta }\left[k+\mathit{1}\right]}{{\varphi }_{\alpha }\left[k+\mathit{1}\right]}\right).(13)$

Figure 6 presents the steps followed for the integration of particle swarm optimization (PSO) along with the DTC control technique. PSO is used offline to provide a self-tuning for HEV regulators: PI1, PI2, and PI3.

FIGURE 6

FIGURE 6. Integration of PSO to the HEV control system.

The steps for the integration of this optimization technique into the HEV control system are as follows:

• Initialize the swarm in a six-dimension search space.

• For each population particle, run the HEV system for a complete speed profile and evaluate the particle’s performance using the following cost function:

$J=\left(\overline{AASE}+\overline{AATE}\right).(14)$

$\overline{\mathrm{A}\mathrm{A}\mathrm{S}\mathrm{E}}$ is the average absolute speed error and $\overline{\mathrm{A}\mathrm{A}\mathrm{T}\mathrm{E}}$ is the average absolute torque error, which are, respectively, calculated by Eqs 15 and 16, where Ω_i and T_i are the reference speed and torque at each sampling time T_s. $\widehat{{\Omega }_i}$ and $\widehat{{\mathrm{T}}_i}$ represent the measured HEV speed and torque, respectively. N is the length of the torque and speed vectors, and it is given by Eq. 7. T_d is the duration of the speed profile

$\overline{AASE}=\frac{\mathit{1}}{N}{\displaystyle \sum }_{k=\mathit{1}}^N\left|{\Omega }_i-\widehat{{\Omega }_i}\right|,(15)$

$\overline{AATE}=\frac{\mathit{1}}{N}{\displaystyle \sum }_{k=\mathit{1}}^N\left|T_i-\widehat{T_i}\right|,(16)$

$N={T_{s}T}_d.(17)$

• Apply penalty function to exclude unstable PI combinations that result in infinite cost values. Infinite or large cost values mean that the actual PMSM speed or torque values are too far from their references.

• Update the particle’s speed and position using Eq. 18 and Eq. 19, respectively

$v_i^{t+\mathit{1}}={w_{t}v}_i^t+c_{\mathit{1}}{r}_{\mathit{1}}\left[P_{best}^t-x_i^t\right]+c_{\mathit{2}}{r}_{\mathit{2}}\left[G_{best}^t-x_i^t\right],(18)$

$x_i^{t+1}=x_i^t+v_i^{t+1}.(19)$

• Evaluate the cost of the particle at its new location. If it is smaller than the previous cost value, then update it

• Keep iterating until the decision signal D (Figure 6) is 1. This last-mentioned signal is equal to 1 when the maximum number of iterations is elapsed or the minimum cost is reached.

• Extract the best position resulting in the smallest cost value.

The used PSO parameters in this study are highlighted in Table 3.

TABLE 3

TABLE 3. Particle swarm optimization parameters.

5 Secure power management strategy

The connection of the SC and FC to the inverter DC bus is made, respectively, through bidirectional and unidirectional DC/DC converters, as shown in Figure 7.

FIGURE 7

FIGURE 7. Connection of power sources to DC bus.

As mentioned earlier, SC and FC have complementary characteristics. This is why their use has to be managed to ensure driving comfort and good vehicle performance. Figure 8 highlights a top-level view of the proposed fault-tolerant power management strategy developed in this study. This bloc takes as inputs the power required by the HEV P_HEV, supercapacitor current i_SC and its SOC and FC current. It outputs three gate signals that control the operation of the power sources through the control of DC/DC converters gate signals.

FIGURE 8

FIGURE 8. Proposed secure power management strategy.

The blue highlighted area in Figure 8 is used for the detection of faults that may occur in HEV power sources. If the SC or FC is in a failure state, this bloc will detect the fault and isolate it. After that, it will reconfigure the control loops associated with the power sources to ensure HEV traction and DC bus regulation. Details about this bloc are discussed in the coming sections. The signals N_FC and N_SC are called initial control signals, and A and B are considered final control signals.

5.1 Power management algorithm

In this work, the required HEV power is divided into three sets: low-power P_L, average-power P_A and high-power P_H. The supercapacitor SOC is divided into four levels, as given by Eq. 20:

${SOC}_{SC}=\{\begin{array}{c}{SOC}_{H}if{\mathrm{80}\le SOC}_{SC}\le \mathrm{90}\\ {SOC}_{N}if{\mathrm{65}\le SOC}_{SC}<\mathrm{80}\\ {SOC}_{A}if{\mathrm{50}\le SOC}_{SC}<\mathrm{65}\\ {SOC}_{L}if{\mathrm{0}\le SOC}_{SC}<\mathrm{50}\end{array}.(20)$

The power management algorithm sub bloc highlighted in Figure 8 takes as input the required HEV power and the supercapacitor SOC and outputs two initial control signals N_FC and N_SC which are integers ranging from 1 to 4. These two last mentioned signals will be used to control the flow of power in FC and SC during normal HEV operation (absence of failures in HEV power sources). The table below presents different rules that are used by the power the management algorithm unit shown in Figure 8.

From the Table 4 the following subsections, one can notice that the proposed energy management not only switches ON and OFF the power sources but also controls the percentage of power delivered by each source, as shown in the following sub-sections:

TABLE 4

TABLE 4. Different driving rules.

5.2 Fuel cell control

The flow of power in the FC is controlled using the control scheme shown in Figure 9. Four loops are connected to a multiport switch, whose output depends on the final control signal $C_{FC}^F$, which is an integer variable ranging from 1 to 4. The control signal G_FC will trigger ON and OFF the gate of the DC/DC converter associated with the FC to control the flow of power on it.

FIGURE 9

FIGURE 9. FC control scheme. If $C_{FC}^F$ equals 1, $i_{fc,ref}=i_{fc,ref\mathit{1}}$, and the FC will ensure DC bus regulation.

If $C_{FC}^F$ equals 2, $i_{fc,ref}=i_{fc,ref\mathit{2}}$, and the FC will provide 70% of the required power.

If $C_{FC}^F$ equals 3, $i_{fc,ref}=i_{fc,ref\mathit{3}}$, and the FC will be turned OFF or isolated (disconnected).

If $C_{FC}^F$ equals 4, $i_{fc,ref}=i_{fc,ref\mathit{4}}$, and the FC will deliver 50% of the required power.

5.3 Supercapacitor control

The SC control scheme is shown in Figure 10. Multiple SC reference currents are connected to a multiport switch, whose output depends on the final control signal $C_{SC}^F$, which is an integer variable ranging from 1 to 4.

FIGURE 10

FIGURE 10. SC control scheme.

If $C_{SC}^F$ equals 1, $i_{sc,ref}=i_{sc,ref\mathit{1}}$, and the SC will ensure DC bus regulation.

If $C_{SC}^F$ equals 2, $i_{sc,ref}=i_{sc,ref\mathit{2}}$, and the SC will be charge under different modes.

If $C_{SC}^F$ equals 3, $i_{sc,ref}=i_{sc,ref\mathit{3}}$, and the SC will be turned OFF or isolated (disconnected).

If $C_{SC}^F$ equals 4, $i_{sc,ref}=i_{sc,ref\mathit{4}}$, and the SC will deliver its maximum power.

5.3.1 Supercapacitor charging

The dashed red lines of Figure 10 show the SC charging bloc, which takes as input the SC voltage and its SOC. Eq. 21 presents the two SC charging modes depending on the SOC. These two formulas limit the charging currents and prevent the SC from damage caused by current abrupt peaks.

$i_{SC,ref}=\{\begin{array}{c}\frac{\mathrm{0.45}{P}_{SC,\mathit{max}}}{V_{SC}}{{ifSOC}_L\le SOC}_{SC}<{SOC}_H\\ \frac{\mathrm{0.7}{P}_{SC,\mathit{max}}}{V_{SC}}{ifSOC}_{SC}<{SOC}_L\end{array}.(21)$

5.3 Fault detection and correction

While FC or SC is operating alone (mode 1, 2, 5, and 13), the initial control signal of the other nonoperating source ($C_{FC}$ or $C_{SC}$) will be set to 3 for it to be off, as can be deduced from Table 4. So, a given source is in a failure state if its current is null and its initial control signal generated by the power management algorithm is different from 3.

The used function for the detection of any possible fault in the FC is given by the following equation:

$F_{FC}=\{\begin{array}{c}\mathrm{1};if{C}_{FC}\ne \mathrm{3}and{i}_{FC}=\mathrm{0})\\ 0otherwise\end{array}.(22)$

In order to detect faults on SC, the following equation is used:

$F_{SC}=\{\begin{array}{c}\mathrm{1};if\left(C_{SC}\ne \mathrm{3}\&and{i}_{SC}=\mathrm{0}\right)\\ \mathrm{0}otherwise\end{array}.(23)$

Once a fault is detected, the faulty source will be isolated, and the HEV must keep running by relying only on one source. When a fault occurs, the fault correction bloc, shown in Figure 8, uses the following truth table to reconfigure the control scheme and to isolate the faulty source. The correction bloc outputs two control signals $C_{FC}^F$ and $C_{SC}^F$, which will control the state of SW1 and SW2 and the power flow in SC and FC.

From the Table 4 the following subsections, it can be seen that, in the absence of faults (F_SC = F_FC = 0), the isolation bloc outputs directly the initial control signals generated by the management algorithm bloc and behaves as IN-OUT bloc. When a fault occurs, the final control signal of the non-faulty source ($C_{FC}^F$ or$C_{SC}^F$) will be set to 1 to guarantee DC bus voltage stability, and the faulty source control signal ($C_{FC}^F$ or$C_{SC}^F$) will be set to 3 to isolate it, as shown in Table 5.

TABLE 5

TABLE 5. Fault correction truth table.

6 Simulation and results

To evaluate the effectiveness of the developed fault-tolerant power management algorithm, we cause, on purpose, two temporary faults, F1 and F2, and one permanent fault, F3, as listed below:

F1: Temporary fault occurs in FC at 84s and lasts 5s.

F2: Temporary fault occurs in SC at 300s and lasts 5s.

F3: Permanent fault occurs in FC and persists till the end of the ride.

Figure 11 shows the HEV speed along with the reference speed applied for the HEV during the 660s. It is clear that the HEV speed tracks well its reference. Figure 12 shows the HEV torque response. The vehicle torque matches its reference, and the torque ripples are minimized in a narrow hysteresis band.

FIGURE 11

FIGURE 11. HEV speed response.

FIGURE 12

FIGURE 12. HEV torque response.

Initial control signals, final control signals, and fault signals generated are shown in Figure 13. One can notice that during normal operation, the final control signals A and B are the initial control signals image of N_SC and N_FC, respectively,

FIGURE 13

FIGURE 13. Fault and control signals during HEV ride.

generated by the power management algorithm. When a failure occurs in either SC or FC, the fault detection bloc detects the fault, and the isolation bloc uses the truth table in Table 5 to determine whether to isolate the faulty source and to keep the DC bus voltage at its reference.

• At F1: “$C_{SC}^F$’’ stays at 1 to let the SC fix the DC bus voltage, and “$C_{FC}^F$’’ toggles from 4 to 3 to disconnect the faulty FC. At the end of the temporary fault, the signal $C_{SC}^F$ returns to its previous state, which is 4.

• At F2: “$C_{SC}^F$’’ goes from 1 to 3 to disconnect the SC, and “$C_{FC}^F$’’ toggles from 4 to 1 to enable the FC to fix the DC bus voltage. After the end of fault at 305s, $C_{FC}^F$ and $C_{SC}^F$ recover their previous values, 4 and 1, respectively.

• At F3: “$C_{SC}^F$’’ goes from 3 to 1 to enable the SC to regulate the DC bus voltage because the FC is in a failure state. The correction bloc also toggles “$C_{FC}^F$’’ from 1 to 3 to disconnect the faulty FC. In this case, the control signals are kept in this position till the end of the ride since the fault is assumed to be permanent.

One can also remark on the effectiveness of the fault detection bloc, which did not emit any false threshold signal and responded immediately to the different faults.

Figure 14 shows the HEV, SC power, and FC power. It can be seen that the HEV power, at each instant, is obtained as the sum of SC and FC powers. It can be seen that during fault situations (F1, F2, and F3), the non-faulty source ensures HEV traction and the faulty source is isolated.

FIGURE 14

FIGURE 14. SC, FC, and HEV powers.

To provide a closer look at the behavior of power sources during vehicle ride, Figure 15 shows the SC and FC power along with the driving mode number during the period [75.5s and 92.5s].

• During [75.5, t₁]: During this time period, SOC_SC = SOC_N and HEV power demand is low. Following Table 4, FC will ensure HEV traction while fixing DC bus voltage $\left(C_{FC}^F=\mathit{1}\right)$, and the SC will be turned OFF ${(C}_{SC}^F=\mathit{3})$.

• During [t_1, t₂]: In this time interval, HEV power demand is average, and SOC_SC belongs to SOC_N. In this case, both FC and SC will provide 50% of the total power required for traction, as shown in Figure 15, where both sources deliver half of the load power applied on the HEV

• During [t₂, t₃] U [t₄, t₅]: During this time period, HEV power demand is high, and the SC state of charge belongs to SOC_N. Hence, FC and SC deliver 50% of the required traction power for traction, as highlighted in Figure 15, where both sources deliver 4 kW.

• During [t₃, t₄]: In this time interval, a fault occurs at the FC level, while HEV power demand is high and SOC_SC belongs to SOC_N. The fault detection and correction block, shown in Figure 8, overwrite the decision of the power management algorithm to ensure continuous HEV operation and DC bus regulation. This is achieved through the reconfiguration of the SC control scheme to position 1 ($C_{SC}^F=\mathit{1}$) and the FC control loop to position 3 ($C_{FC}^F=\mathit{1}$).

FIGURE 15

FIGURE 15. SC, FC, and HEV powers.

Figure 16 shows the SC SOC. It dropped from 82 to 70% during [210s, 350s], which corresponds to an average- and high-power demand. During the regenerative braking period [350,450], SOC_SC increased from 70 to 86%. Globally, the SOC_SC stayed within safe limits during the ride.

FIGURE 16

FIGURE 16. SC state of charge.

Figure 17 highlights the inverter DC bus voltage. One can notice that it follows its reference set to 560 V. The presence of some voltage ripples due to connection and disconnection of power sources can be remarked. These ripples are within an allowed band of 10 V. The zooms in Figure 17 present the voltage fluctuations during the occurrence of faults. These fluctuations are always within safe limits.

FIGURE 17

FIGURE 17. DC bus voltage.

The minimum cost after each iteration is shown at 18. It can be seen that cost decreases over iterations, which means that the solutions produced after each generation are better than the previous ones in term of torque and speed ripple minimization. Starting from 30, the cost value is constant, which means that the PSO algorithm converges to an optimum solution.

7 Real-time validation

The effectiveness of the proposed energy management strategy is assessed by implementing it in real-time using the OPAL-RT LAB simulator. Figure 18 describes in detail how the HEV model is adapted for simulation on the aforementioned simulation platform. The first step toward RT simulation is model separation. It should be divided into computation and console blocks, which are highlighted with blue and dark dashed lines, respectively, in Figure 18. The console block contains user interface blocks such as scopes, displays, manual switches, and constants. It is worth noticing that the console block runs asynchronously only on the host PC from the computation subsystems. The computational subsystem contains all the computational elements of the model, mathematical operations, I/O blocks, signal generators, and physical models. Data between the computation subsystem and console are exchanged asynchronously through the TCP/IP link, but data exchange between two computation subsystems, namely, master (SM) and slave (SS), is performed synchronously through shared memory. Data from the RT simulator are displayed on the digital oscilloscope using Bayonet Neill–Concelman connector (BNC) to BNC cable.

FIGURE 18

FIGURE 18. Real-time simulation using RT LAB.

After building and loading the HEV program to the OP 57000 simulator, constant power of 5 kW is applied as a load power to the vehicle. This requested power will be ensured by FC and SC following the proposed energy management strategy. Figure 19 shows the obtained results using the RT LAB simulator, where fuel cell and supercapacitor powers are highlighted with magenta and blue colors, respectively. The aforementioned figure confirms the facts stated in section 5 where it has been said that the fuel cell can be operated safely at different predefined operating points. In zone 1 (Z1), the supercapacitor delivers all the necessary power for traction while the fuel cell is turned off by setting its control loop to position 3, as shown in Figure 9. In zone 2 (Z2), FC and SC control loops were set to positions 4 and 1, respectively. This last-mentioned control loop configuration has made both FC and SC deliver 50% of the required power for traction. It is worth noticing that SC in Z2 delivers 50% of the required power for traction while ensuring DC bus regulation. At Z3, a temporary fault took place at the FC level. As soon as the fault occurs at the fuel cell level, as pointed out with white dashed lines, the fault detection and correction block, already shown in Figure 20, will intervene to isolate the FC and overwrite the power management algorithm by forcing FC power to zero. This is performed by the reconfiguration of the FC control loop from position 4 to position 3, as shown in Figure 9. This will make the supercapacitor deliver, alone, all the power required for traction while ensuring DC bus regulation. From zone 4 to 8, one can see that the fuel cell delivers a percentage of total power that is equal to the power contribution factor C_FC. For example, in zones 4, 5, and 6, the fuel cell delivers respectively 50, 100, and 30% of the required power for traction. One of the advantages of such a power management technique is the precise control of power flow in power sources. In addition to that, this power management strategy reduces the stress applied on power sources by preventing their operation above their maximum power. In zone 9, a fault occurred at the SC level, which is responsible for DC bus regulation. The fault detection and correction block shown in Figure 20 has isolated SC by reconfiguring its control loop shown in Figure 9 from position 1 to position 3. Furthermore, the FC control loop was set to position 1 to ensure DC bus regulation and deliver all the necessary power for traction.

FIGURE 19

FIGURE 19. Real-time simulation using RT LAB.

FIGURE 20

FIGURE 20. Evolution of cost over iterations.

8 Conclusion

The developed power management strategy has improved HEV security since failures in vehicle power sources are detected and isolated. HEV reliability and comfort are also enhanced because both SC and FC are able to regulate the DC bus voltage, power the HEV alone, and operate at different power levels. The offline use of PSO in the design of HEV controllers has made the controller design task easy and automatic via the use of a proposed cost function that trades between design variables to be minimized.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.

Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

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Nomenclature

Abbreviations

$\mathit{A}\mathit{A}\mathit{S}\mathit{E}$ Average absolute speed error

$\mathit{A}\mathit{A}\mathit{T}\mathit{E}$ Average absolute torque error

Ang Angle

DC Direct current

D Decision signal

DTC Direct torque control

FC Fuel cell

HEV Hybrid electric vehicle

PMSM Permanent magnet synchronous machine

PSO Particle swarm optimization

RT Real-time

SC Supercapacitor

SVM Space vector modulation

S_ABC Inverter gate signals

Symbols

a Vehicle acceleration [m/s²]

E_nernst Nernst voltage [V]

F_traction External force [N]

F_r Resistive force [N]

F_aero Aerodynamic force [N]

F_g Gravitational force [N]

F_tire Tire force [N]

F_acc Acceleration force [N]

i_SC Supercapacitor current [A]

m Vehicle mass [kg]

i_d Direct axis current [A]

i_q Quadratic axis current [A]

$i_{\alpha }$ Alpha axis current [A]

$i_{\beta }$ Beta axis current [A]

L Stator inductance [H]

N_s Number of series fuel cells

N_sc Number of series supercapacitors

P_FC Fuel cell power [kW]

Q_init Initial supercapacitor charge [C]

Q_T Total supercapacitor charge [C]

P_SC Supercapacitor power [kW]

r_sc Supercapacitor series resistance [Ω]

SOC_SC Supercapacitor state of charge

V_{FC, cell} Fuel cell voltage [V]

V_FC Fuel cell stack voltage [V]

V_act Activation voltage drop [V]

V_ohm Ohmic voltage drop [V]

V_cond Conduction voltage drop [V]

V_SC Supercapacitor voltage [V]

V_SC,tot Supercapacitor total voltage [V]

V_T Terminal voltage [V]

$\varphi$ Permanent magnet flux [Wb]

${\lambda }_d$ Direct axis flux linkage [V]

${\lambda }_q$ Quadratic axis flux linkage [V]

V_d Direct axis voltage [V]

V_q Quadratic axis voltage [V]

$p$ Number of poles

$w_r$ Motor angular frequency [rad/s]

P Motor power [kW]

T_n Motor nominal torque [N]

r_s Motor stator resistance [Ω]

J Rotor inertia [kg.m²]

B Rotor viscous friction [N.m.s]

${\varphi }_{\alpha }$ Alpha axis flux [Wb]

${\varphi }_{\beta }$ Beta axis flux [Wb]

T_S Sampling time [s]

$V_{\alpha }$ Alpha axis voltage [V]

$V_{\beta }$ Beta axis voltage [V]

${\varphi }_{es}$ Estimated flux [Wb]

$T_{es}$ Estimated torque [N.m]

${\theta }_s$ Estimated flux angle [°]

V_DC DC bus voltage [V]

C_bus Bus capacitor [F]

Ω_i Reference speed at ith iteration [rad/s]

T_i Reference torque at ith iteration [N.m]

N Torque and speed vectors length

$T_d$ Speed profile duration [s]

$e_T$ Torque error [N.m]

$e_s$ Speed error [rad/s]

$v_i^t$ Particle’s velocity

$w_t$ Inertia factor

$c_1$,$c_2$ Cognitive and swarm influence

$r_1$,$r_2$ Random numbers

$P_{best}^t$ Personal best

$G_{best}^t$ Global best

$x_i^t$ Particle’s position in the swarm

$C_{\mathrm{F}\mathrm{C}}$ Initial fuel cell control signal

$C_{\mathrm{S}\mathrm{C}}$ Initial supercapacitor control signal

$C_{FC}^F$ Final fuel cell control signal

$C_{SC}^F$ Final supercapacitor control signal