**1. Introduction**

Since the industrial era, the demand for fossil fuels has increased and the burning of fossil fuels has led to an increase in global carbon dioxide emissions, which has also increased global warming. The National Oceanic and Atmospheric Administration (NOAA) conducted a network sampling of carbon dioxide concentration based on 40 regions around the world. The survey found that since 1979, the global atmospheric carbon dioxide concentration has risen sharply. With a carbon dioxide concentration of 336 ppm in 1979, the global atmospheric carbon dioxide concentration has reached 414 ppm in March 2020. According to Taiwan's CO2 emissions survey by the Environmental Protection Agency of the Ministry of Administration, the energy sector's CO2 emissions accounted for approximately 10.5% of total fuel combustion emissions, industry accounted for 47.8%, transportation accounted for 14.6%, services accounted for 13.4%, residential emissions accounted for 12.6%, and agriculture accounted for 1.1% [1]. It is clear that transportation emissions are the second-largest source, after industrial emissions.

Due to carbon dioxide emissions, major car manufacturers currently commit to the development of new energy to replace gasoline, including electric energy, solar energy, biomass energy, etc. Many automobile manufacturers are optimistic about electric energy since it can be practically used in mass production. With low fuel consumption and exhaust emissions, hybrid electric vehicles (HEVs) have been attracting widespread public attention in recent years. Hendrickson et al. [2] presented the GM two-mode, front-wheel-drive hybrid powertrain, detailing the mechanical structure and operating

mode of this powertrain system. Meisel et al. [3] presented the power distribution of the hybrid transmission in different modes and four fixed-gear ratios in detail. They also compared the differences between the Toyota THS-II gearbox and the GM two-mode gearbox, aiming at energy loss and engine fuel consumption. The advantages of the GM two-mode power system were clearly explained. For the hybrid electric vehicle architecture, the control strategy of the vehicle is critical and is mainly to allocate energy and improve energy efficiency. Many energy management strategies for hybrid electric vehicles have been proposed. They can be divided into two main types: those with 1 a rule-based strategy, and those with 2 an optimization strategy. Torres et al. [4] focused on rule-based controls. The benefits of these controls were rapid rule design and easy implementation. Schouten et al. [5] applied fuzzy logic in HEV control strategies. The rules were judged based on the accelerator and brake pedal signals, battery state of charge (SOC), and motor speed. This optimization method heavily relied on the experience and intuition of the engineers.

The optimization strategy for vehicle fuel economy simulation can be categorized into two areas, global optimization and real-time local optimization. The global optimization algorithm requires completing the whole driving cycle in order to obtain the best fuel economy. This makes it difficult to apply on real road scenarios. Genetic algorithms (GAs) are one of the global optimization algorithms. Montazeri et al. [6] applied GA optimization in parallel HEVs, where the engine torque and battery SOC were design variables with the objective of minimizing fuel consumption and emissions. Dynamic programming (DP) is another typical global optimization algorithm. Wu et al. [7] presented the application of DP on electric buses and used DP to explore energy management strategies for range-extended electric buses (REEBs). Zheng et al. [8] applied stochastic DP in plug-in hybrid vehicles to achieve a global optimization. Wang et al. [9] implemented the DP algorithm in a plug-in HEV (PHEV) and showed a 20% improvement in fuel consumption. DP analyzes the whole driving cycle, searching for minimum fuel consumption to get the global optimum. It provides an improvement for fuel economy; however, it takes a lot of time for the whole simulation and process. An alternative way is to utilize the optimum patterns obtained from pre-calculated DP, such as rule-based (RB) control. RB can be adapted for real-time applications; however, the fuel economy of RB might not be as good as DP's due to the instant change in actual scenarios.

For real-time applications, optimized fuel consumption needs to be carried out quickly for each time step. Local optimization can be suitable for the applications. The equivalent consumption minimization strategy (ECMS) does not require long calculation and is one control algorithm fitting for real-time fuel consumption optimization. Paganelli et al. [10] presented the application of the equivalent consumption minimization strategy (ECMS) in parallel HEVs. They managed the power distribution to minimize fuel consumption, which includes the actual fuel consumed by the engine and an equivalent fuel converted from the electrical energy consumed by motors. Their simulation maintained the battery SOC in a reasonable range by applying a penalty function to ensure battery life. Particle swarm optimization (PSO) is another real-time control algorithm for vehicle fuel consumption. Chen et al. [11] discussed the application of particle swarm optimization (PSO) on HEVs. They optimized the engine output power as an energy management strategy. Wu et al. [12] applied PSO to plug-in HEVs. The main goal of their study was to optimize the control strategy to achieve the best fuel economy. For charge depleting (CD) mode, restrictions were imposed to optimize the PSO. Abido et al. [13] applied PSO to the energy flow control problem of buses. The main goal was to minimize fuel consumption and improve voltage stability. Wang et al. [14] applied a particle-swarm-optimization-based nonlinear model predictive control strategy on a series-parallel hybrid electric bus to optimize the fuel consumption. Chen et al. [15] discussed the application of PSO on plug-in HEVs (PHEVs). In terms of vehicle speed, fuzzy logic judgments were added. Then, the PSO determined the upper and lower limits of the required engine power to obtain the optimal result. Chen et al. [16] implemented improved particle swarm optimization (IPSO) in HEVs. The difference from the original PSO was mainly to add the value of a poor function. This function would cause the PSO particles to speed-up to find the best solution. Beside ECMS and PSO, there are other control

algorithms to achieve better fuel economy. Zheng et al. [17] applied Pontryagin's minimum principle to optimize a parallel plug-in hybrid electric bus. Feng et al. [18] combined an artificial neural network model and a fuzzy-logic controller to optimize the fuel consumption of a hybrid electric mining truck. Comparing the differences between PSO and genetic algorithms (GAs), GAs remove the worst position at one time, and PSO keeps the worst particles, judging the best solution according to the position of each particle [18]. In addition, GAs mainly process the replication, mating, and mutation, which requires a large amount of calculation [19]. Relatively speaking, since the information transmission between PSO particles and the interaction mechanism between particles is relatively simple in PSO, the amount of calculation is lower and the delivery time can be shortened. With the advantages of quick convergence, the PSO algorithm is suitable for real-time control applications for vehicle fuel consumption optimization. This research applied PSO for real-time optimization control.

In 2018, global battery electric vehicle (BEV) and HEV sales exceeded 5.1 million, a significant increase of 63% from the previous year. BEVs and HEVs will become the first choice for the public in the future. The two-mode hybrid (TMH) system was the power system applied in this research. A basic rule-based control was implemented as the base model with an initial energy management strategy, and the simulation result was compared to the manufacturer data. Then, the PSO control strategy was added to optimize fuel consumption and explore the reasons for improvement. This paper investigated a TMH system that had power-split hybrid functionality.
