## 2 Models and Methods  
### Real Driving Emission Tests  
Vehicle pollutant emissions have been widely measured using the driving cycle testing method in a laboratory environment. The driving cycle testing method combines some common vehicle operating conditions and severe polluting emission conditions into a test cycle, and the specific-distance pollutant emissions of the vehicle are measured during this test cycle on a laboratory chassis dynamometer. However, the vehicle's real driving conditions are very diverse. The constructed test cycles (e.g., NEDC, WLTC) cannot adequately characterize the real driving conditions of the vehicles, resulting in the emission test results of the driving cycle test method being often inconsistent with the reality of vehicle emissions [38, 39, 40, 41]. Thus, Europe introduced the real driving emission test procedure in the Euro 6 emission standards, which requires real-time measurement of pollutant emissions under on-road driving conditions using a portable emission measurement system (PEMS). It has become a global consensus to examine vehicle pollutant emissions based on real driving emission test procedures [42]. In this study, the real driving emission test procedure specified in the China 6 emission standard is followed to investigate the real driving emissions of the EREV. The test EREV has a total mass of 1600 kg and a whole load mass of 2125 kg. The extended-range powertrain consists of an engine, generator, drive motor, power battery, and electronic controller. The engine is an upright, 4-cylinder, 1.5 L, naturally aspirated Atkinson gasoline engine with multi-point fuel injection technology; it has a maximum power of 51.6 kW at 4200 r/min and a minimum fuel consumption rate of 215 g/(kW-h). The exhaust after-treatment uses a three-way catalytic, whose front stage is connected to the engine cylinder head, and the rear stage is assembled after the exhaust connecting pipe; the exhaust after-treatment system is not equipped with a gasoline particulate filter (GPF). The drive motor is a permanent magnet synchronous motor with a rated power of 50 kW, a rated torque of 90 Nm, a maximum speed of 16,000 r/min, and a peak efficiency of 96%. The drive motor drives the front axle wheels directly through a two-stage gearbox. The generator is also a permanent magnet synchronous motor with a voltage rating of 350 V, a rated power of 42 kW, a rated torque of 47 Nm, and a maximum speed of 15,000 r/min. The power battery is a lithium iron phosphate battery with a capacity of 75 Ah and a rated voltage of 350 V. The control system has a vehicle control unit responsible for vehicle drive mode management, energy management, and accessory management; it also includes an engine control unit, a battery management unit, and a power control unit responsible for generator and motor control. The portable emission test system used for the tests is the HORIBA OBS-ONE, which consists of a gaseous pollutant analysis module (OBS-ONE-GS), a particle counting module (OBS-ONE-PN), a central control unit, an exhaust flow meter, and a power supply, attaching the peripherals of a weather station and a global positioning system. The OBS-ONE-GS uses a heated non-dispersive infrared (NDIR) analyzer to measure CO and CO\({}_{2}\) emissions and a chemiluminescence detector (CLD) to measure NO\({}_{\mathrm{x}}\) emissions. The OBS-ONE-GS measures these gaseous pollutant concentrations with an accuracy of \(\pm\)2%. The OBS-ONE-PN uses laser scattering condensed ion counting (CPC) to detect the particle number concentration of test vehicle emissions, with a measurement accuracy of \(\pm\)10%. GPS and the weather station measure real-time vehicle driving speed, altitude, latitude and longitude, ambient temperature, humidity, and atmospheric pressure.