# Development of a Hybrid Electric Vehicle Simulation Tool with a Rule-Based Topology
## 2 Materials and Methods  
### Overview of the Simulation Tool  
In this paper, a simulation tool developed on MATLAB(r) and Simulink(r) is introduced to address HEV technologies. This tool offers increased flexibility to choose different control and energy management strategies, enabling the user to explore a wide range of hybrid topologies. The tool enables the user to modify any sub-system according to their requirements. In the simulation, vehicle speed data are needed, e.g., new European driving cycle (NEDC), WLTC, real driving emissions (RDE), etc., and based on the speed profile, the tool calculates the rotational speed of the wheels, the acceleration, and the total forces using the vehicle dynamics equations. Forces that are taken into consideration are aerodynamic resistance force, rolling friction losses, driving force, and uphill driving force. The rolling resistance depends more on the weight of the vehicle, while the aerodynamic ones depend on the speed. When starting the vehicle, only the resistant forces will act, and then, with the increase in speed, the aerodynamic forces will have a greater impact. In addition to the above-mentioned losses, it is also important to calculate inertia losses in a vehicle, as acceleration or deceleration of rotating components causes significant change in equivalent mass of a car due to inertia. The total force of the given vehicle is calculated using the formula provided from the following equations:  
\[\text{Total Force}=\text{F}_{\text{Aerodynamic}}+\text{F}_{\text{Rolling}}+ \text{F}_{\text{Acceleration}}+\text{F}_{\text{Gradient}} \tag{1}\]  
\[\text{F}_{\text{Aerodynamic}}=0.5\rho C_{D}V^{2}A \tag{2}\]  
\[\text{F}_{\text{rolling}}=C_{R}m_{S}\mu\cos\theta \tag{3}\]  
\[\text{F}_{\text{Acceleration}}=m_{v}a \tag{4}\]  
\[\text{F}_{\text{Gradient}}=mg\sin\theta \tag{5}\]  
where \(V\) is the vehicle speed [m/s], \(a\) is the vehicle acceleration [m/s2], \(\rho\) is the density of the air (\(\approx\)1.2 kg/m3), \(A\) is the frontal surface area of the vehicle [m2], \(C_{R}\), \(C_{D}\) is the drag coefficient, \(m_{v}\) is the mass of vehicle + load [kg], \(g\) is the gravity acceleration [9.81 m/s2], \(\mu\) is the friction coefficient [\(\approx\)0.01], \(\alpha\) is the slope [rad]. The calculated total forces are given as input to the ICE model in case of conventional vehicle model. In hybrid vehicle model, additional blocks like EMs and supervisor are also implemented. The supervisor will direct the power demands to ICE or EMs depending on the operating points and the strategy. The control strategy of the supervisor is the most important thing in any model, and system acts/behaves according to the strategy defined by the user. This is nothing but the supervisor in the hybrid powertrain, also known as the brain of the system. The rules of the supervisor are:  
* Continuously meet the driver's power request based on the accelerator and brake pedal positions and available power in the power sources. * Minimize global fuel consumption. * Maintain the state of charge (SOC) of the battery between the bounds of the defined SOC. * Make sure the battery SOC at the end of the driving cycle reaches the user's request. For the control system to switch from one transition to another, certain conditions have to be defined, from which transitions from different states are possible. They include logic functions, and based on these, switching takes place; this is performed for all possible cases in the control system. Once the conditions are defined, they are integrated with the other inputs, where the conditions work by integrating all these the control systems. Figure 1 shows the overview of the HEV simulation tool. The transmission is a set of elements including gears, shaft, and bearings, which are used to transmit the required power from ICE to wheels of vehicle or EMs. In hybrid vehicles, the transmission can be either a stepped one with a reduced number of gears or a full gear set like a conventional ICE vehicle, depending on the HEV architecture.