**3. Modeling of the vehicle subsystems**

Three main approaches exist for modeling and simulation of electric vehicles topologies:


**Figure 2.** *Schematic of a parallel HEV topology.*

The backward-facing and forward-facing approaches are also known as "effectcause" and "cause-effect", respectively. Since a backward methodology carries out significant advantages such as simplicity and low computational cost in model-in- the-loop applications it is the most ideal testbed for integration into optimization algorithms requiring iterative operations [9]. Therefore, the backward-facing method is used for drivetrain modeling and simulation phase of this study. In principle, the backward facing calculation starts from the driving cycle velocity inputs to calculate the required tractive force at the wheel for propulsion. The required power, the translated torque and rotational speed will be calculated in a backward direction distributed through the components considering the powersplit control block defined in an EMS subsystem. In this regard, **Figure 3** illustrates the calculation direction of a backward-facing model in a simplified way. The detailed modeling process of the subsystems are provided as follows.

The driving cycles are velocity time series representing a driving pattern; bring the road to a computer simulation and provide the profile that a vehicle requires to follow. The use of driving cycles assists modeling the drivetrain and the required performance to be considered for an appropriate design [8]. The standard New European Driving Cycle (NEDC), as represented in **Figure 4**, as the timedependent dynamic input of simulation process is used in this chapter.

A vehicle simulation model is required to be linked into the optimization algorithm for optimized integrated design and evaluation of the vehicle performance over the considered driving cycle. Hence, an energetic vehicle model based on the longitudinal dynamic motion laws is developed in MATLAB/Simulink® in this study. The vehicle longitudinal dynamic model uses speed and acceleration timeseries of a driving cycle to calculate the required tractive forces considering the

**Figure 3.** *Calculations direction in a generic backward-looking modeling.*

**Figure 4.** *Standard NEDC driving cycle, velocity profile [10].*

*Application of Ant Colony Optimization for Co-Design of Hybrid Electric Vehicles DOI: http://dx.doi.org/10.5772/intechopen.97559*

drag resistance force, the rolling resistance force, the gradient resistance force, and the inertia force:

$$F\_T = \frac{1}{2}\rho v^2 \mathbf{C}\_D A + \mathbf{C}\_r m \mathbf{g} \cos a + m \mathbf{g} \sin a + m \mathbf{C}\_\emptyset \frac{dv}{dt} \tag{1}$$

where its constant values are described and given in **Table 1**.

Consequently, the torque *Tw* and the rotational speed *ω<sup>w</sup>* required to be supplied can be modeled. Along this line, by knowing the wheels radius *Rw* one can readily have the output of vehicle dynamic model to be fed into transmission subsystem model:

$$T\_w = F\_T R\_w \tag{2}$$

$$
\rho\_w = \frac{v}{R\_w} \tag{3}
$$

In general, the vehicle components can be modeled using physical equations, analytical models (i.e. equivalent circuit) or considering related efficiency maps, which relate torque-speed or voltage–current pairs to their corresponding efficiency [11]. Using the obtained input torque and rotational speed values, the efficiency map defined in a look-up-table (LUT), power flow through the Electric Motor (EM) can mathematically be expressed as:

$$T\_G = T\_w G\_r \eta^\beta \tag{4}$$

$$
\rho\_G = \rho\_w G\_r \tag{5}
$$

It is notable that the efficiency term in Eqs. (4) and (5) must be treated contrarily for motoring and regenerating braking modes having positive and negative power flows, respectively. To this end, the efficiency operators β = �1 for the motoring mode (P > 0), and β = 1 for the braking mode (P < 0) are considered in the modeling process.

**Figure 5** represents the efficiency map of the 75kw EM considered for the present study stored in EM LUT which can be scaled by torque and consequently power as an EM sizing decision variable in the optimization procedure.

$$P = T\_{\text{EMOEM}} \eta^{\beta}(T\_{\text{EM}}, a\_{\text{EM}}) \tag{6}$$


**Table 1.** *Constants of vehicle dynamic calculation.*

**Figure 5.** *75 kW EM efficiency map [12].*

Similarly, the core functionality of the ICE subsystem used in this study is based on an input–output approach using torque-speeds pairs corresponded to the efficiency and fuel rate map stored into LUTs in the vehicle model. Having the output fuel consumption rates data and the fuel density, the consumed fuel in liter can be modeled in fuel tank subsystem as given in Eq. (7), where *m*\_ represents the fuel consumption rate and *ρ <sup>f</sup>* is the fuel density [13]. **Figure 6** represents the efficiency map of the 41 kW engine considered for the present study which can be scaled by torque and consequently power as a sizing variable in the optimization procedure.

$$Fuel = \int\_0^t \frac{\dot{m}}{\rho\_f} dt \tag{7}$$

A lithium-ion battery pack based on a semi-empirical first order Thevenin equivalent circuit is modeled in the battery subsystem. The elements of the battery model can be identified by using the experimental data [14] for open circuit voltage (Voc), the internal resistance (Rint), the polarization capacitance (Cp), and the polarization resistance (Rp), which are stored in the LUTs of the corresponding subsystem. The terminal voltage of the pack Vbatt and SoC can be expressed as:

*Ibatt* <sup>¼</sup> *Iload NBatt* (8)

**Figure 6.** *41 kW ICE efficiency map [12].*

*Application of Ant Colony Optimization for Co-Design of Hybrid Electric Vehicles DOI: http://dx.doi.org/10.5772/intechopen.97559*

$$\frac{dV\_{cp}}{dt} = \frac{-V\_{cp}}{C\_p R\_p} + \frac{I\_{Batt}}{C\_p} \tag{9}$$

$$\mathbf{V}\_{\rm Ratt} = \mathbf{N}\_{\rm Batter} \left( \mathbf{V}\_{oc} - I\_{\rm Batt} \mathbf{R}\_{\rm int} - \mathbf{V}\_{cp} \right) \tag{10}$$

$$\text{SoC} = \text{SoC}\_0 + \frac{1}{\text{3600}} \left[ \frac{I\_{\text{Batt}}}{C\_b} dt \right] \tag{11}$$

**Table 2** provides the specification of LiFePO4 (LFP) battery cells used for modeling while number of cells are considered as the battery power sizing decision variable in the optimization procedure.

The output of power converters is modeled considering the power flow calculation direction and the components efficiency are used in their corresponding LUTs. The operators β = �1, and β = 1 are considered for the motoring mode (while P > 0), and the braking mode (while P < 0), respectively.

$$P\_{out} = P\_{in} \eta^{\beta} \tag{12}$$

The main role of the energy management strategy (EMS) subsystem in HEVs is to define power sharing control principles satisfying set of required control objectives. The control strategies are mainly categorized into rule-based (RB) and optimization-based (OB) ones. The RB strategies as they are structurally working under If-Then rules, may handle trivial control objectives (e.g. HEV battery chargesustaining), however, they are highly fragile in leading to optimal results when it comes to fuel consumption minimization. Hence, there is a need for coupling RB strategies into OB strategies to form a robust control framework as considered in the context of the present chapter. To this end, a RB strategy considering different vehicle operation modes is linked to a Low Pass Filter (LPF) OB strategy in the EMS block of the modeled vehicle to satisfy control optimization constraints and objectives. The RB control part updates the operating modes through the simulation considering the requested load, speed, accessible power from energy sources, battery state-of-charge (SoC) and power split control variables. The operating modes considering these objectives can be categorized as follows:



**Table 2.** *LiFePO4 battery cell parameters.*


However, the fuel consumption is significantly depended not only on the defined operating rules, but also on the OB power-split method used, specifically for the hybrid operating modes for improving efficiency and control robustness. Hence, an optimized Low Pass Filter (LPF) strategy will be introduced to the optimization algorithm to optimize the power-split control part by finding the best sharing control variable of LPF strategy satisfying power sharing objectives and constraints. In this regard, the considered OB-LPF strategy optimizes power sharing between the supplying components (i.e. battery and ICE) to provide required driving power while minimizing fuel consumption. Through using a filter-based transfer function, the filtered component of the required power passes to be supplied by the ICE while its difference with the total demand will be supplied by the battery subsystem [15]. The standard transfer function defined in the energy management subsystem and optimization process is considered as below. Here the LPF denominator (τ) is the control variable to be searched through optimization routine toward having the control objectives and constraints satisfied:

$$f\_{LPF} = \frac{\mathbf{1}}{\mathbf{r}\,\mathbf{s} + \mathbf{1}} \tag{13}$$

The elaborated subsystems are integrated in the Simulink® environment to form the whole vehicle model to work in tandem with a MATLAB-based ANT Colony (ACOR) algorithm for component sizing and control optimization.
