## 1. Introduction

Due to the growing concerns of the fuel crisis and increasing environmental degradation, hybrid vehicles are being intensively researched. All-electric powertrains with a fuel cell-battery-supercapacitor combination have been considered in [

1,

2,

3,

4,

5]. In the presence of multiple sources, the distribution of power while ensuring various objectives, such as fuel efficiency, battery aging,

etc., can be considered as a vital aspect in hybrid vehicles. Multiple sources can imply both primary and secondary sources or storage elements. The design and application of different power management optimizations are available in the literature. Of these methods, the extent of rule-based methods and multi-objective optimization is given in [

6] and briefly summarized in this contribution. This contribution contains parts of the text from [

6,

7].

Rule-based strategies are generally designed based on heuristics, human expertise or mathematical models and do not require prior knowledge of the drive cycle [

8]. These strategies are less complex than other types and can be implemented online and in real time. Their major drawback is that they are not optimal with respect to desired vehicle performance, such as fuel consumption minimization,

etc. Several alternatives are available as detailed in [

9]. Considering the advantages of rule-based methods and optimal solutions offered by the alternatives, a combination of rule-based power management to optimization-based methods can be considered: in [

10], dynamic programming (DP) is used to understand the deficiency of rules; in [

11], parameter optimization using genetic algorithms (GA) is considered to determine the optimal control variables for fixed parameters; using this as the baseline, equivalent consumption management strategy (ECMS) and route-based strategies are developed; in [

12], both GA and DP are used; in [

13], ECMS and DP are used, whereas in [

14], a combination of rule-based power management with the sophisticated Non-Dominated Sorting Genetic Algorithm II (NSGA II) is considered. The use of multi-objective genetic algorithms, such as NSGA II, is advantageous due to the conflicting nature of optimization goals often encountered in HEVs. In [

14], for instance, the two conflicting objectives of fuel consumption minimization and sizing are considered, whereas in [

15], the minimization of fuel consumption, as well as battery aging is an issue. Multi-objective algorithms are generally offline implementable, and hence, their integration with online rule-based power management requires decoupling of the offline and online parts. A simple technique described in [

9] as a time-invariant feedback controller consists of storing control algorithms in look-up tables (LUTs). The control variable/variables are functions of current driving conditions (like power demand, velocity) and state variables (like SoCs of storage elements). Thus, the advantages of rule-based strategies, namely relatively simpler structure and low computational effort required, can be utilized along with the multi-objective optimization property of offline algorithms. They can also be combined with prediction and real-time control strategies to provide solutions where no pre-defined drive cycle is given. From the concept of embedded-online optimization by using offline algorithms [

16], it can be concluded that the embedding of optimization results from a decoupled offline process to an online power management controller is possible. Embedding of offline calculated parameters in the context of rule-based power management has been discussed in [

17,

18].

Under real driving conditions for which no pre-defined drive cycle can be used, an adaption of the power management strategy is important. Adaptive power management strategies without using car navigation data are discussed in [

19]. Two options are mentioned: driving condition recognition based on the history of motion and driving condition prediction based on the history of motion. For both options, the procedure is to prepare optimal databases offline and to match the present ones to previously optimized past ones. The difference between the two options is that, in the first option, optimization of the entire drive pattern is considered, whereas in the second option, segment-wise optimization is carried out. Recognition of the present based on the past is considered in the first option, whereas the present is matched to the past in the second option. Moreover, in the first option, updating of rules to integrate new driving patterns is required at regular intervals. In [

20], an adaptive power management based on driving pattern recognition is presented. Here, two separate offline processes are considered. In one process, given drive cycles are used to generate driving patterns. These patterns are classified according to power, such as low, medium and high power demand, and the resulting patterns are stored in look-up tables (LUTs) for online implementation. In the other process, the same drive cycles are analyzed for determining the optimal parameters that minimize fuel consumption. Next, control rules are formulated for a sub-optimal rule-based controller. This controller can be implemented online. In the online process, the classification of the driver velocity into patterns is carried out based on the LUT values from one offline process. The corresponding control rule is determined based on the data from the other offline process, which is optimized before.

Thus, rule-based strategies are online-implementable, real-time control schemes applicable for hybrid electric vehicles. A combination with global optimization methods, such as dynamic programming, multi-objective genetic algorithms,

etc., to optimize various objectives is possible. Individually optimizing the power management rules offline, such that the results from the optimization are stored in look-up tables, can be used to tune controller parameters online. The decoupling of the optimization process ensures the use of offline-applicable multi-objective optimization techniques in online power management. Moreover, decoupling leads to a possibility of adapting the rule-based controller to real driving scenarios. This can be considered by integrating more LUTs for different driving patterns. Thus, by evaluating the potentials and application prospects of rule-based power management, the foundations for the development of an appropriate optimal power management controller that takes into account multiple optimization objectives can be laid. From the detailed literature review presented in [

6] and briefly summarized in this contribution, it can be noted that one generalized power management strategy is required that can deal with multiple objectives online and in real time. The remaining open issue is to realize real-time optimization of power flows such that desired powertrain operations can be achieved. Minimization of fuel consumption and lifetime management of components are the main objectives to be considered. Moreover, the design of a suitable structure to accommodate varying driving patterns is also a necessity. With respect to the above-mentioned concerns, a suitable concept is developed in this contribution.

The HEV powertrain considered in this work is an all-electric powertrain. The configuration comprises a fuel cell as the primary energy source and a battery-supercapacitor combination as the storage unit. According to [

1], the efficiency of all-electric hybrid vehicles depends on the capability of the energy storage unit. The concept of hybrid storage systems (HESS) was previously proposed in [

21,

22,

23] and later elaborated in [

24]. This concept can be used to overcome the problems faced by batteries, that is low charge/discharge efficiency and short cycle life, by utilizing the properties of a supercapacitor. This is possible due to the better power density of supercapacitors and the better energy density of batteries. By combining the two, an improvement in overall performance can be achieved, as the supercapacitor acts as a support to the batteries and is much more robust in handling surge current. A combination of battery-supercapacitor leads to a significant improvement in fuel economy [

25]. The advantages of HESS are detailed in [

1,

2,

24]. Based on the advantages of the fuel cell-battery-supercapacitor hybrid powertrain as stated in [

1,

3] and utilizing the benefits of the battery-supercapacitor combination, a three-source HEV is considered in this contribution. The optimal utilization of each of these sources is a task of power management. The DC/DC converter plays a central role in power management, and it serves two important purposes: to maintain a constant bus voltage and to send desired current requests to the three sources as defined by the power management. In spite of the benefits offered by multiple input DC/DC converters, such as reduced overall size, weight, losses and cost, three single input DC/DC converters are considered in this contribution for the sake of modeling simplicity. This is because the main objective is to develop an appropriate power management concept that determines the optimal distribution of power between the sources.

Mathematical models of hybrid vehicle components are often required for detailed analysis of powertrain performance and power management strategies. Simulation of these models is the first step for realizing their behavior in experimental setups and real driving scenarios. For a given drive cycle, the vehicle energy losses and its performance can be calculated backwards, as mentioned in [

9]. For an unknown velocity pattern, forward modeling becomes necessary, as introduced in [

26]. It is possible to combine a backward model with a forward model to measure the drivability error or to model an entire vehicle in a forward manner to investigate real-time systems where the drive cycle is not given. Depending on whether the HEV powertrain is forward or backward modeled, the individual components have to be modeled accordingly. In [

27], both quasi-static and dynamic models are considered, where the reason for considering a dynamic model of the battery is stated. Therefore, it is possible to consider quasi-static models of the inverter, motor and vehicle. Components like batteries and supercapacitors, where the state-of-charge is an unknown result of power management and optimization algorithms, need to be modeled dynamically. A fuel cell, on the other hand, can be modeled based on experimentally-determined parameters, as detailed in [

28]. Thus, instead of a complex dynamical model as developed in [

28], a quasi-static model can be used based on look-up table values of experimentally-determined parameters in [

28]. A DC/DC converter, which is an essential component in pure-electric powertrains, can be dynamically modeled like the battery and supercapacitor.

The paper is organized as follows: the topologies with HESS are briefly introduced followed by the configuration chosen for this contribution; next, the modeling and sizing of powertrain components is detailed followed by a verification of their dynamics based on the literature; next, the concept of emulation is described followed by a possibility to realize powertrain dynamics with controllable sources and sinks; in the next section, the developed power management optimization concept is explained in detail. The operation of the different blocks and the interactions between them is described. Finally, the simulation and emulation results are presented followed by a summary and conclusions.

## 5. Powertrain Configuration with Emulated Components

Although modeling and simulation are useful for gaining detailed understanding of system dynamics and behavior, experiments are important for investigating the applicability by the validation of these models. According to [

45], validation refers to the precision at which the model represents the physical world, whereas validation experiments are performed to produce data for model validation. For instance, in [

41], experiments are performed with the help of a 1:1 scale laboratory-based dynamic setup; in [

46], first, experiments are conducted on individual units in stationary conditions to evaluate their behavior at constant electric parameters, then their performance under dynamic operations with real driving cycles is evaluated. Instead of performing experiments with real powertrain components, in this contribution, a comparison with experimentally-determined parameters from real components is considered along with a brief introduction of a concept known as emulation. To carry out the power management and control of an analog subsystem integrated with a digital subsystem [

47], the emulation of component dynamics has already been discussed in the literature. According to [

16], emulation is based on controllable powertrain components, which can be used as a replacement for real components. This solves the problems posed by classical setups, namely high cost, deterioration/damage risks, large energy and fuel consumption,

etc.

Emulation of fuel cell dynamics using a programmable power source [

48,

49] and a power electronic converter [

50,

51,

52] has been discussed. Similarly, emulation of a supercapacitor [

48] and a battery [

47,

53] using a programmable power source-sink combination has been discussed. In [

53], an automotive power net test-bench is mentioned. Here, emulation is based on the fact that physical models can be run on a real-time system and the current calculated from the model set by electronic loads. The test-bench proposed in [

53] can be used not only for batteries and supercapacitors, but also systems that behave as controllable source-sink combinations, such as bi-directional DC/DC converters. Load emulation using a dynamically-controllable source-sink [

54] to ensure bi-directional power exchange can also be considered. A fuel cell-supercapacitor-based hardware-in-the-loop (HiL) test rig was built [

28] at the Chair of Dynamics and Control (University of Duisburg-Essen). It was modified and generalized for the emulation of different powertrains, for example hybrid hydraulic powertrains and wind energy conversion systems [

55,

56], along with hybrid electric powertrains. In this work, a further generalization is considered by replacing all of the real powertrain components by emulated components. The experimental setup is shown in

Figure 2. On the left side is the model layer comprising the powertrain configuration. This simulation model of an HEV along with the supervisory controller are compiled into a real-time interface that enables communication with the emulation layer. On the right side is the emulation layer comprising the real hardware components. Here, the simulated models of the fuel cell and DC/DC converter can be considered as a single unit, and the corresponding hardware component- controllable power source

$q1$ can be used. Similarly, for the battery and supercapacitor, source-sink combination

$q2-s2$ and source-sink combination

$q3-s3$ can be used, respectively. Corresponding to the backward simulated part, the power demand or load can be emulated by another source-sink combination

$q4-s4$. The charging dynamics of the battery and supercapacitor are in accordance with the results given in [

16].

For testing the capability of the source-sink combinations in replicating powertrain dynamics, an example for emulating only the backward part of the HEV model can be considered. The simulated behavior and emulated power demand are compared. The performed test results are explained in

Figure 14. The source-sink combination

$q4-s4$ is checked for the emulation of both positive and negative power demand. Here, as demand, the load current from the backward part of the powertrain is used. Its value is positive when the HEV is accelerating or driving at constant velocity and negative when the HEV is braking. During the positive half, the power source

q is expected to supply the demand to the power sink

$s4$. A constant current value is set at

q, and the simulated demand is realized by

$s4$ as motor action. During the negative half, the generator action is realized by

$q4$ as it recuperates energy back to the sink. Here, a constant current is set at the sink.

The result of this test is shown in

Figure 15. It can be noted from the figure that the

$q4-s4$ combination is capable of emulating the motor/generator dynamics. During the positive half of the load cycle, current is drawn by the sink

${s}_{4}$ (motor mode), and in the negative half of the load cycle, power is supplied by the source

${q}_{4}$ (generator mode).

This initial test is important to check the ability of power source-sink combinations in emulating not just the motor/generator dynamics, but also the battery and supercapacitor. The constant current supplied by q in the positive half will be replaced by supply from each/either of the sources, as defined by power management. The constant current demanded by the sink in the negative half will be replaced by the demand from each/either of the storage components.

## 7. Simulated and Emulated Results

In this subsection the effect of the developed power management control concept is discussed. From

Figure 20a, the basic working principles of the power management strategy become clear using an NEDC drive cycle as the example. The battery current is limited, and the more dynamic fluctuations are taken over by the supercapacitor. The fuel cell is operated close to its efficient operating point as calculated in [

28]. To evaluate the feasibility of the emulation hardware in realizing the dynamics of the powertrain, the simulated results are compared to emulation results. In

Figure 20b, the charging of the battery and supercapacitor is shown. This is in accordance with the simulated battery and supercapacitor current, as shown in

Figure 20a. The curves in

Figure 20b demonstrate an inversion of the values shown in

Figure 20a. The negative parts of load represent charging or an increase in sink

$s2$ and

$s3$ currents and positive parts, discharging or an increase in source

$q2$ and

$q3$ currents. Here, only the emulation of charging current is shown. Similarly, the emulation of supply and regeneration dynamics using

s and

q is explained with

Figure 15.

Here, the emulation of both positive and negative parts of the load demand by

$q4-s4$ is given. During the positive half of the load cycle, current is drawn by the sink

$s4$ (motor mode), and in the negative half of the load cycle, power is supplied by the source

$q4$ (generator mode). Therefore, the emulated

$q4$ current, which is an absolute value, can be seen as an inversion of simulated value. From

Figure 15 and

Figure 20, a good coincidence between model behavior and emulation can be noted. Thus, the dynamics of the simulated models of components together with the supervisory controller can be realized using the emulated experimental setup. Corresponding to the three sources, the DC/DC converter current outputs as defined by the power management controller are sent to

$q1$,

$q2-s2$ and

$q3-s3$. The simulated load current from the backward modeled part is sent to

$q4-s4$.

Next, the effect of the optimized controller parameters on the HEV dynamics is analyzed. For the two chosen objectives, namely minimization of fuel consumption and SoC deviation of both the battery and supercapacitor, the results are analyzed in the following manner:

To demonstrate (and to learn about) the principal behaviors, four supercapacitor sizes are chosen for comparison: the reference, double the reference, half the reference and one-fourth the reference. The optimization runs for all of the supercapacitor sizes can be seen in

Figure 21. As shown in

Figure 21b, with the double-sized supercapacitor, a slight improvement in fuel consumption values is noted (

Figure 21b2) at the cost of the deterioration of

$\Delta SoC$ values (

Figure 21b1). However, this does not provide an optimal solution for the total objective function, and further iteration steps of the optimization algorithm are required. As shown in

Figure 21c, with the half-sized supercapacitor, a prominent improvement in

$\Delta SoC$ is noted (

Figure 21c1). The fuel consumption is not minimized within the shown iteration steps. Finally, in

Figure 21d, with one-fourth the supercapacitor, dynamic and fluctuating behavior is noted in

Figure 21d1,d2. Within the shown iteration steps, minimization, particularly of fuel consumption values, is not possible. Thus, with such small supercapacitor sizes, the control task is difficult, and the overall system might become unstable.

In

Figure 22, conflicting solutions for the two objective functions for the reference supercapacitor can be seen. This results from the principle contradictions in the task of fuel consumption minimization and SoC sustenance. However, a convergence of the total objective function can be obtained. From

Figure 22, it can be noted that although minimum values for

$\Delta SoC$ are obtained, the values chosen for fuel consumption are not necessarily the minimum values. Lower fuel consumption values that did not satisfy the minimum

$\Delta SoC$ are rejected, so a compromising solution for both objectives can be obtained.

In the next step, the parameters corresponding to the optimized values obtained from NSGA II are integrated in the online power management control strategy. Three supercapacitor sizes, double (denoted in green), half (denoted in blue) and one-fourth (denoted in black), are compared to the reference size (denoted in red) to analyze the influence on SoC and on fuel consumption. In

Figure 23, the SoCs of the battery and supercapacitor are shown along with the corresponding fuel cell output power and distinguished for small and large supercapacitors.

Smaller supercapacitors: From the battery SoC, it can be seen that the battery is gradually charged in the beginning, so as to gain reserves for following the high demanding part of the drive cycle, due to the insufficient storage capacity of the supercapacitor. Then, the battery is discharged till its lowest SoC value. From the supercapacitor SoC, it can be seen that smaller sizes cause more fluctuations. With the one-fourth size, the response is very dynamic. From the fuel cell output power, it can be seen that power supplied by the fuel cell is more for smaller supercapacitors than larger ones. Transient behavior is noted with the smallest supercapacitor.

Larger supercapacitors: When the supercapacitor is doubled, the battery SoC is constant, meaning that the battery is not required. In this case, the large supercapacitor has sufficient storage capacity. The supercapacitor SoC curve is flatter and less fluctuating in comparison with smaller supercapacitor SoCs. From the fuel cell output power, it becomes clear that the power supplied by fuel cell is also least here.

Thus, with the double-sized supercapacitor, the most desirable performance can be achieved, whereas by using a one-fourth-sized supercapacitor, undesirable effects may result. These undesirable effects need to be avoided, keeping the size and cost of the powertrain in mind. The reference size can be considered as a suitable option.

Next, the priority between the two objectives is varied for the reference supercapacitor. For the realization of different requirements, the priorities are assigned as given in the following three cases: Case 1: priority distribution decided by NSGA II (denoted in green); Case 2: high priority on fuel consumption and less priority on

$\Delta SoC$ (denoted in blue); Case 3: high priority on fuel consumption with least priority on

$\Delta SoC$ (denoted in red). These three cases can be obtained by analyzing the effects of parameter changes during different stages of optimization. In the first case, the parameters correspond to those obtained at the end of optimization. In the second and third cases, the parameters correspond to those obtained in the intermediate stages. In

Figure 24, the SoC variations of the battery and supercapacitor can be seen along with the corresponding fuel cell power.

Case 1 is the standard case and can be used as a reference for the comparison of Cases 2 and 3. Case 2 (blue curve): From the battery SoC, it can be seen that the battery SoC is mostly sustained and discharged only towards the end. The supercapacitor is charged from the fuel cell. By comparing battery $\Delta SoC$ to Case 1 (green curve), it is observed that $\Delta SoC$ in Case 1 is lower than in Case 2. This is because in Case 2, the optimization objective-fuel economy is taken into account, but the second objective-battery $\Delta SoC$ is sacrificed.

Case 3 (red curve): From the battery SoC, it can be seen that the battery is more depleted than in Cases 1 and 2. The supercapacitor is charged from the battery. By comparing battery $\Delta SoC$ with Cases 1 and 2, it is observed that $\Delta SoC$ in both Cases 1 and 2 is lower than in Case 3.

Thus, when priority is assigned in the order fuel consumption followed by supercapacitor $\Delta SoC$ followed by battery $\Delta SoC$, the battery is more often discharged, as shown in the above results. By changing the priority between the objectives, further possibilities can be investigated. However, as the objectives are conflicting in nature, a compromise has to be made.

In

Figure 25, the total energy consumption corresponding to non-optimal power management, optimal power management and optimal power management as a function of different supercapacitor sizes is shown. Total energy consumption denotes the energy of the fuel cell plus the energy of the battery and supercapacitor, which can be added or subtracted from the total energy depending on the charge/discharge. When the supercapacitor size is increased, energy consumption will be reduced. This results directly from the ability of exchanging dynamic load peaks. With smaller supercapacitors, the energy consumption is distinctively higher.