# Dynamic Simulation and Control of a New Parallel Hybrid Power System
## 1 Introduction
### Hybrid Power Control Module  
This module uses the relation among vehicle electric position, vehicle speed, and SOC as the basis for power distribution, allowing the power from the internal combustion engine, electric motor, and generator to be properly distributed. The electric position of the electric motor is analogized to the throttle position of the internal combustion engine. It controls the power output of the motor. First, the input conditions are converted, via the fuzzy controller, into linguistic variables expressed by a fuzzy set. This step is called fuzzification, and its input conditions are shown in Figure 3a-c. The vehicle speed for the electric position is divided into 12 attribution functions--including those in the low-speed range (Z, TL, T-L1, T-L2, T-L3), with the attribution functions set to 0-35 km/h; those in the medium-speed range (T-M), with the attribution functions set to 36-65 km/h; and those in the high-speed range (T-H, T-H1, T-H2, T-H3, T-H4, T-H5, T-H6), with the attribution functions set to 66-130 km/h. The division of the vehicle-speed input attribution functions is roughly the same as that of the attribution functions of the electric position. The attribution function of SOC is divided into two. The first is when the SOC is low (LOW), in the range 0-30, and the second is when the SOC is normal (HIGH), in the range 30-100.  
The control rule base is formulated according to the characteristics of the control target and the state to be controlled. Figure 4a-d show a 3D diagram representing the relative relations of the rule base. The rules established in the fuzzy logic control rule base adjust the output power percentage of the internal combustion engine and the electric motor according to conditions such as the electric position, vehicle speed, and SOC. As for the attribution function of the output power, this study uses middle of maxima defuzzification as its output condition, as shown in Figure 5a-c. There are 11 throttle positions, of which \"off\" means the throttle is closed. The optimal range of throttle positions for the internal combustion engine is set to 80%. This setting is based on the test torque data of the internal combustion engine in this system. The optimal operating range of this system is achieved when the throttle position is \(\sim\)80%, at a speed of 5700 rpm and a torque of 13.1 Nm. The specification of combustion engine is showed in Supplementary Figure S3. According to the control rules of this system, the electric motor position is determined to range from 0% to 100%, and there are 11 output attribution functions, where Zm indicates that the electric motor is turned off. There are three attribution functions for the generator to control the position output, which are mainly divided into low, medium, and high regions.  
Figure 3: _Cont._Figure 4: Three-dimensional maps of the rule base for (**a**) electric position and vehicle speed vs. motor position, (**b**) electric position and vehicle speed vs. throttle position, (**c**) electric position and SOC vs. motor position, and (**d**) electric position and throttle position vs. SOC.  
Figure 3: Input attribution functions of (**a**) electric position, (**b**) vehicle speed, and (**c**) state of charge (SOC).