## 1 Introduction  
Countries worldwide have begun to impose stringent environmental regulations to mitigate global warming due to greenhouse gases (GHG) such as CO\({}_{2}\). In the industrial sector, emissions of pollutants due to road traffic are significant contributors to global warming [1]. Therefore, reducing the fossil fuels consumed by cars is a fundamental solution to overcome the problem of air pollution. According to a comprehensive assessment report by the Intergovernmental Panel on Climate Change (IPCC), the rate of climate change is expected to accelerate. Studies have indicated that the complete stoppage of fossil-fuel consumption by 2100 is necessary to ensure that the rise in global temperature does not exceed 2 \({}^{\circ}\)C [2]. However, despite the imposition of stricter environmental regulations, the control of air pollution in large cities (e.g., Seoul, Beijing, Shanghai, Delhi, Paris, and London) has been inadequate, and governments worldwide have proposed several countermeasures to address this challenge [3]. After the 2015 Paris Agreement, several countries established regulations for average vehicle fuel consumption and CO\({}_{2}\) emissions, which are expected to be stringently applied by 2021. Several nationsare expected to expand their electric-vehicle (EV) market to strengthen the fuel economy, comply with CO\({}_{2}\) regulations, and utilize mandatory new energy vehicle credits [4]. According to IHS Markit, the share of internal combustion engine (ICE) vehicles equipped with pure ICEs or idle stop-and-go (ISG) systems is expected to be less than 50% of the vehicle market by 2031 [5]. In South Korea, the Ministry of Environment has set the goal of having 1 million green vehicles on the road by 2020, including hybrid cars (800,000), electric cars (200,000), and hydrogen-fuel cell vehicles (500) [6]. Therefore, it has become imperative to develop eco-friendly vehicles that meet the consumer demand for increased power and fuel efficiency; such vehicles include hybrid, electric, solar, and hydrogen-fuel cell vehicles, and vehicles that satisfy the emission standards specified by the Ministry of Trade, Industry and Energy (MOTIE) of Korea [7]. Hybrid electric vehicles (HEVs) provide driving power by combining the output of an engine and a motor. The HEV operates under motor power only during starts and low-speed driving. During wheel braking, a secondary-cell battery is charged by regenerative braking, where the motor is transformed into a generator that generates a decelerating load to recover electrical energy. Using a regenerative braking system, the fuel economy can be 40% or more relative to conventional ICE vehicles, and emissions are reduced. At high loads (e.g., during climbing), the engine and motor can operate together to generate high power, achieve high acceleration, and facilitate smooth driving. The vehicle used in this study is a transmission mounted electric device (TMED)-type parallel HEV in which an electric motor for driving and generating power is installed in front of an automatic transmission without a torque converter. A clutch controls the power between the engine and motor, and the HEV operates in one of the following modes, depending on driving conditions. The \"engine-only mode\" operates when the state of charge (SOC) of the battery is low or during high-speed driving. In this mode, the energy for vehicle driving is supplied by engine output completely. The \"mixed mode\" operates during rapid acceleration or with maximum load. In this mode, the internal combustion engine and the electric motor supply driving power to the vehicle simultaneously. The \"fixed charging mode\" operates when the SOC of the battery is low. In this mode, the engine is used to charge the battery and maintain a constant charge. The \"regenerative braking mode\" is activated when the vehicle is braking. A portion of the braking force is recovered as electrical energy using the magnetic resistance of the electric motor.