With the rapid growth of vehicle ownership and the strengthening of environmental regulations worldwide, hybrid electric vehicles have drawn increasing attention. Among various configurations, the parallel hybrid electric bus is widely regarded as a practical solution for urban transit due to its balanced efficiency, driving performance, and cost. This article presents a systematic study on the parameter matching and optimization of the power system for a parallel hybrid electric city bus. The work covers system architecture selection, component sizing, energy management strategy, simulation validation, and cost-effectiveness optimization. Special emphasis is placed on the role of the EV battery pack in energy storage and power delivery. The design methodology follows a first-principles approach and is verified through simulation using ADVISOR. The results demonstrate that the proposed parameter optimization method can achieve a fuel consumption reduction of about 20% while maintaining acceptable vehicle performance.
1. Introduction and Background
The automobile industry has long relied on petroleum, leading to severe environmental pollution and energy crises. Urban buses, which operate in congested traffic with frequent start-stop cycles, are particularly inefficient in fuel consumption and produce high emissions. Hybrid electric vehicles combine an internal combustion engine with one or more electric machines, offering an effective way to reduce both fuel usage and pollution without sacrificing driving range. In the context of city buses, the parallel hybrid configuration provides a favorable compromise between system complexity and fuel economy improvement.
This investigation focuses on a 12-meter city bus equipped with a parallel hybrid powertrain. The primary goal is to find a rational and cost-effective combination of engine power, motor power, battery capacity, and transmission ratios. The study is based on the development project of a hybrid electric city bus, aiming to achieve fuel savings of at least 20% compared with a conventional diesel bus while maintaining comparable driving performance. The work includes dynamic analysis, component selection, control strategy formulation, simulation modeling, and parameter optimization.
In the following sections, I first present the fundamental vehicle dynamics and design constraints. Then, I analyze the basic structural configurations of hybrid powertrains and select the most suitable architecture for city buses. Subsequently, I perform a detailed design of the power unit and drivetrain parameters. After that, I describe the simulation models and the energy management strategy. Finally, I evaluate the fuel economy and cost-effectiveness under different hybrid degrees and propose an optimal matching scheme.
2. Vehicle Parameters and Dynamic Requirements
The vehicle under consideration is a 12-meter city bus. The key parameters are summarized in Table 2.1.
| Parameter | Value |
|---|---|
| Length × Width × Height (mm) | 12000 × 2550 × 3250 |
| Frontal area (m²) | 7.2 |
| Aerodynamic drag coefficient | 0.75 |
| Curb mass (kg) | 12000 |
| Maximum total mass (kg) | 18000 |
| Rolling resistance coefficient | 0.01 + 0.0001·v |
| Rotational mass conversion factor | 1.1 |
| Wheel rolling radius (m) | 0.52 |
| Maximum speed (km/h) | 80 |
| 0–50 km/h acceleration time (s) | <25 |
| Maximum grade at 50 km/h | >4% |
The engine alone must be able to drive the bus at a speed of at least 65 km/h. The air conditioning and auxiliary accessories have a maximum power demand of 15 kW. These targets define the design space for the hybrid powertrain.
2.1 Vehicle Dynamics Equations
The longitudinal dynamics of the vehicle are described by the tractive force balance:
$$ F_t = F_f + F_w + F_i + F_j $$
where \(F_f\) is the rolling resistance, \(F_w\) the aerodynamic drag, \(F_i\) the grade resistance, and \(F_j\) the acceleration resistance. The rolling resistance is given by
$$ F_f = m g f \cos\alpha $$
with \(f = 0.01 + 0.0001 v\). The aerodynamic drag is
$$ F_w = \frac{C_D A v^2}{21.15} $$
where \(v\) is the vehicle speed in km/h. The grade resistance is \(F_i = m g \sin\alpha\), and the acceleration resistance is \(F_j = \delta m \frac{dv}{dt}\).
The engine power required to maintain a constant speed \(v\) on a level road is
$$ P = \frac{v}{3600 \eta_t} \left( m g f + \frac{C_D A v^2}{21.15} \right) $$
where \(\eta_t\) is the drivetrain efficiency. Based on the maximum speed requirement of 80 km/h and taking into account a power margin of 12% and the auxiliary load of 15 kW, the total power demand is calculated as approximately 160 kW. By comparing with existing 12-m buses, a total power rating of 200 kW is selected as the base for the hybrid system.
3. Configuration Selection and Component Sizing
Three main hybrid architectures were compared: series, parallel, and series-parallel. For a city bus, the parallel configuration offers the best balance between cost and efficiency. The engine and motor are mechanically coupled to deliver torque through a common shaft. This arrangement minimizes energy conversion losses and allows the use of smaller electrical components. In this study, a front-mounted single-shaft torque-coupling parallel system is adopted. A clutch is placed between the engine and the motor, and an automated manual transmission (AMT) is used to provide multiple gear ratios.
3.1 Engine Selection
The engine must satisfy the average power demand of the driving cycle. In conventional buses, the engine is oversized for peak torque requirements. In a hybrid bus, the motor assists during peak loads, allowing the engine to be downsized to operate more efficiently. The minimum engine power is calculated from the requirement that the engine alone can propel the bus at 65 km/h:
$$ P_{e,\min} \ge \frac{v_{e,\max}}{3600 \eta_t} \left( m g f + \frac{C_D A v_{e,\max}^2}{21.15} \right) $$
With \(v_{e,\max} = 65\) km/h and the same vehicle parameters, the calculation gives \(P_e \ge 89.3\) kW. Adding the 12% margin and auxiliary load results in a minimum engine power of about 100 kW. The final engine power is linked to the hybrid degree and will be optimized later.
3.2 Motor Selection
The electric motor must provide torque during engine-off launches, assist during acceleration, and recover energy during braking. A permanent magnet synchronous motor (PMSM) is chosen due to its high efficiency, high power density, and mature control technology. The motor is required to deliver a peak torque of at least 400 Nm to meet the maximum grade requirement. The relationship between the required motor torque and the transmission ratio is derived from the gradeability equation:
$$ T_{m,\max} \ge \frac{m g r_w (f \cos\alpha + \sin\alpha)}{i_{g,\max} i_0 \eta_t} $$
Using the maximum grade of 4% at 50 km/h and the first gear ratio of 6.98, the motor peak torque must be at least 370.7 Nm; therefore, a motor with a peak torque of 400 Nm and a rated power of 40 kW is initially considered. The motor rated power can be increased according to the hybrid degree, and this trade-off is the focus of the optimization study.
3.3 Energy Storage and the EV Battery Pack
The energy storage system is a critical component of any hybrid powertrain. It must provide high instantaneous power for assisting acceleration and absorb energy during regenerative braking. Among various options, the EV battery pack based on lithium-ion technology is selected for its high specific energy, high specific power, and long cycle life. The EV battery pack is designed to operate within a state-of-charge (SOC) window of 50% to 85% to maintain high round-trip efficiency and extend battery life. The battery voltage and capacity are chosen to match the motor and the electric motor controller. The internal resistance and open-circuit voltage characteristics of the EV battery pack are modeled as functions of SOC and temperature.
The EV battery pack is modeled as a voltage source in series with an internal resistance. The discharge equation is:
$$ U_{bat} = E_{bat} – R_{dis} I_{dis} $$
where \(E_{bat}\) is the open-circuit voltage, \(R_{dis}\) is the discharge resistance, and \(I_{dis}\) is the discharge current. The charging equation is:
$$ U_{bat} = E_{bat} – R_{chg} I_{chg} $$
The state of charge is given by:
$$ SOC = SOC_{init} – \frac{1}{C_{cap}} \int I_{bat} dt $$
where \(C_{cap}\) is the effective capacity of the EV battery pack. This model is embedded in the ADVISOR simulation environment.
3.4 Transmission and Drivetrain
The drivetrain includes a six-speed AMT and a rear axle with final drive ratio \(i_0\). The final drive ratio is chosen based on the maximum vehicle speed and the engine’s maximum power speed. The relationship is:
$$ i_0 \le \frac{0.377 r_w n_{e,\max}}{v_{\max}} $$
With \(n_{e,\max} = 2850\) rpm and \(v_{\max} = 80\) km/h, \(i_0 \le 6.98\). Additionally, to ensure the motor can operate at peak power at maximum speed, the ratio must satisfy
$$ i_0 \ge \frac{0.377 r_w n_{e,P}}{v_{\max}} = 6.13 $$
Therefore, \(i_0 = 6.5\) is selected. The gear ratios are listed in Table 3.1.
| Gear | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Ratio | 6.98 | 4.06 | 2.74 | 1.89 | 1.31 | 1.00 |
This gearset provides a wide overall ratio range, enabling the electric motor to launch the vehicle smoothly and the engine to operate efficiently at highway speeds.
4. Operating Modes and Energy Management Strategy
The parallel hybrid bus operates in several distinct modes:
- Pure electric mode: when SOC is high and the demanded torque is low, the engine is off and the motor alone drives the vehicle.
- Engine-only mode: when the demanded torque is within the engine’s efficient range, the motor is not activated.
- Hybrid drive mode: when the demanded torque exceeds the engine’s capability, the motor provides additional torque.
- Charge-sustaining mode: when SOC is low, the engine produces more torque than required and the motor operates as a generator to charge the EV battery pack.
- Regenerative braking mode: the motor acts as a generator to recover braking energy and store it in the EV battery pack.
- Idle/stop mode: both engine and motor are shut off during stops, unless air conditioning requires engine idle.
The energy management strategy used in this study is the electric assist control strategy. This rule-based strategy keeps the engine operating in a high-efficiency zone while using the motor to “shave the peaks” and “fill the valleys” of the power demand. The control logic is illustrated in Figure 4.2 (not shown here). The key variables are the demanded torque, the engine torque limits, and the SOC of the EV battery pack.
The electric assist strategy can be described mathematically as follows. The demanded torque \(T_{dmd}\) is the driver’s torque request at the transmission input. The engine command torque \(T_e\) is determined by:
$$ T_e = \begin{cases} 0 & \text{if } T_{dmd} < T_{e,\min} \text{ and } SOC \ge SOC_{low} \\ T_{e,opt} & \text{if } T_{e,\min} \le T_{dmd} \le T_{e,\max} \\ T_{e,\max} & \text{if } T_{dmd} > T_{e,\max} \end{cases} $$
The motor torque \(T_m\) is then:
$$ T_m = T_{dmd} – T_e $$
If SOC falls below \(SOC_{low}\), the engine is forced to run at a higher torque to charge the battery. Conversely, if SOC is above \(SOC_{high}\), the motor is used more aggressively to discharge the battery.
The electric assist strategy is simple, robust, and easy to implement in real-time controllers. It does not require knowledge of the future driving cycle, making it suitable for practical city bus operation. Although more advanced strategies such as global optimization or fuzzy logic can achieve better fuel economy, the electric assist strategy provides a fair basis for comparing different power system parameters.
5. Hybrid Degree and Cost Analysis
The hybrid degree \(R\) is defined as the ratio of the motor power to the total power:
$$ R = \frac{P_m}{P_m + P_e} $$
Since the total power is fixed at 200 kW, \(P_m = 200R\) and \(P_e = 200(1-R)\). The hybrid degree influences vehicle performance, fuel economy, and system cost. This study considers \(R\) values from 0.2 to 0.5 in steps of 0.05. The following relationships are used for cost estimation.
5.1 Motor Cost
The cost of the motor and its controller is approximated as:
$$ C_m = A + B P_m = 4300 + 70000 R \quad \text{(CNY)} $$
where \(A = 4300\) CNY and \(B = 350\) CNY/kW, giving \(C_m = 4300 + 70000R\).
5.2 Battery Cost
The cost of the EV battery pack is related to the power rating. Assuming a specific cost of 500 CNY/kWh and a replacement factor of 2 (because battery life is about half that of the bus), the battery cost is:
$$ C_b = \frac{500 \cdot 2 \cdot P_m}{\eta_m} = 210526 R $$
where \(\eta_m\) is the motor efficiency (taken as 0.95).
5.3 Engine Cost Saving
Because the hybrid engine is smaller than the conventional 200 kW engine, the cost saving is:
$$ C_e = 450 \cdot 200 R = 90000 R $$
5.4 Additional Costs
The AMT adds 40,000 CNY compared with a manual transmission, and additional controllers/sensors add 20,000 CNY. Thus, the total additional cost of the hybrid system relative to a conventional bus is:
$$ C_{total} = 6.43 + 19R \quad \text{(10,000 CNY)} $$
This cost model is used to evaluate the cost-effectiveness of different hybrid degrees.
6. Simulation Models and Setup
ADVISOR (Advanced Vehicle Simulator) is used to evaluate the design. The simulation environment includes component models for the engine, motor, battery, transmission, and vehicle. I modified the default models to match the designed parameters. The engine map is represented as a lookup table of fuel consumption rate versus speed and torque. The motor is modeled with a dynamic efficiency map. The EV battery pack is modeled with the equivalent circuit described earlier. The driving cycle used for evaluation is the ECE cycle, which represents urban driving with frequent stops and starts.
6.1 Engine Model
The engine output torque is limited by the full-load curve, which is a function of engine speed:
$$ T_{e,\max}(n) = \sum_{i=0}^{k} a_i n^i $$
The fuel consumption rate \(g_e(kW \cdot h)\) is obtained from a two-dimensional interpolation of the fuel map. The engine’s thermal efficiency is calculated as:
$$ \eta_e = \frac{3600}{g_e \cdot H_u} $$
where \(H_u\) is the lower heating value of diesel fuel.
6.2 Motor Model
The motor model includes both motoring and generating modes. The maximum torque is constant below the base speed and decreases with speed in the constant-power region. The electrical power consumption is:
$$ P_{elec} = \frac{T_m \omega}{\eta_m} \quad \text{(motoring)} $$
or
$$ P_{elec} = T_m \omega \eta_m \quad \text{(generating)} $$
where \(\eta_m\) is the motor efficiency, interpolated from a map.
6.3 Energy Storage Model
The EV battery pack model calculates the terminal voltage and SOC based on the current. The battery resistance is a function of SOC and sign of current. The power loss inside the battery is \(I^2 R\). The overall system efficiency depends strongly on the battery operating window. To protect the battery, the SOC is maintained between 0.3 and 0.8 in the control strategy.
7. Results and Discussion
7.1 Power Performance Verification
All hybrid configurations were simulated under full load (18000 kg) with air conditioning running at maximum power (15 kW). The results are shown in Table 7.1.
| Hybrid degree R | Engine power (kW) | Motor power (kW) | Max speed (km/h) | Max acceleration (m/s²) | Grade at 50 km/h (%) | 0–50 km/h time (s) |
|---|---|---|---|---|---|---|
| 0.20 | 160 | 40 | 81.1 | 2.1 | 4.5 | 18.4 |
| 0.25 | 150 | 50 | 81.1 | 2.3 | 4.5 | 18.2 |
| 0.30 | 140 | 60 | 81.1 | 2.5 | 4.5 | 18.0 |
| 0.35 | 130 | 70 | 81.1 | 2.7 | 4.5 | 17.7 |
| 0.40 | 120 | 80 | 81.1 | 2.8 | 4.6 | 17.5 |
| 0.45 | 110 | 90 | 81.1 | 3.0 | 4.6 | 17.3 |
| 0.50 | 100 | 100 | 81.1 | 3.2 | 4.6 | 17.2 |
All configurations meet the design targets. Increasing the motor power improves the acceleration time and gradeability, but the differences become smaller as the motor grows larger.
7.2 Fuel Economy Results
Fuel economy was simulated for three vehicle masses (18000 kg, 15000 kg, 12000 kg) and three accessory power levels (1.5 kW, 7.5 kW, 15 kW). The results are summarized in Table 7.2 for the full-load condition with 1.5 kW accessory load.
| R | Fuel consumption (L/100km) | Battery energy equivalent (L/100km) | Savings (L/100km) | Improvement (%) |
|---|---|---|---|---|
| 0.20 | 40.0 | 0.20 | 8.00 | 16.6 |
| 0.25 | 39.3 | 0.23 | 8.67 | 18.0 |
| 0.30 | 37.8 | 0.27 | 10.13 | 21.0 |
| 0.35 | 37.1 | 0.31 | 10.79 | 22.4 |
| 0.40 | 36.1 | 0.40 | 11.70 | 24.3 |
| 0.45 | 35.2 | 0.52 | 12.48 | 25.9 |
| 0.50 | 34.6 | 0.61 | 12.99 | 26.9 |
The fuel saving generally increases with hybrid degree, but the incremental benefit diminishes at high \(R\) values. When the accessory load is high (15 kW), the trend can become non-monotonic because the engine must idle to drive the air conditioning compressor, and the smaller engine may consume more fuel during extended idle periods.
Table 7.3 shows the results for 7.5 kW accessory load and 18000 kg.
| R | Fuel consumption (L/100km) | Savings (L/100km) | Improvement (%) |
|---|---|---|---|
| 0.20 | 47.1 | 7.01 | 12.9 |
| 0.25 | 46.4 | 7.68 | 14.1 |
| 0.30 | 45.1 | 8.90 | 16.4 |
| 0.35 | 44.5 | 9.44 | 17.4 |
| 0.40 | 43.7 | 10.14 | 18.7 |
| 0.45 | 42.6 | 11.14 | 20.5 |
| 0.50 | 43.4 | 10.14 | 18.7 |
At 15 kW accessory load, the optimum occurs around \(R = 0.4\), because a very small engine must compensate for the high auxiliary load with less efficient operation. This observation highlights the importance of considering real-world auxiliary loads when matching hybrid system parameters.
7.3 Cost-Effectiveness Evaluation
The cost-effectiveness is defined as the ratio of the fuel saving per 100 km to the total additional cost of the hybrid system:
$$ \lambda = \frac{\Delta Q_{100}}{C_{total}} \quad \text{(L/100km per 10,000 CNY)} $$
Figure 7.1 (conceptually) shows \(\lambda\) versus \(R\) for various conditions. The curves are not monotonic in the range 0.2 to 0.4. To obtain a single optimal hybrid degree, I used a weighted average based on the estimated probability of each operating condition. The probabilities for vehicle mass are 0.35 for full load, 0.55 for medium load, and 0.10 for light load. The probabilities for accessory power are 0.60 for 1.5 kW, 0.25 for 7.5 kW, and 0.15 for 15 kW. The weighted average fuel consumption for the conventional bus is 48.3 L/100km. Table 7.4 gives the weighted results.
| R | Weighted consumption (L/100km) | Improvement (%) | Total cost C_total (10,000 CNY) | λ (L/100km per 10,000 CNY) |
|---|---|---|---|---|
| 0.20 | 40.55 | 16.1 | 10.23 | 0.757 |
| 0.25 | 39.83 | 17.5 | 11.18 | 0.758 |
| 0.30 | 38.88 | 19.5 | 12.13 | 0.776 |
| 0.35 | 38.61 | 20.1 | 13.08 | 0.741 |
| 0.40 | 37.82 | 21.7 | 14.03 | 0.714 |
| 0.45 | 37.22 | 22.9 | 14.98 | 0.674 |
| 0.50 | 37.05 | 23.3 | 15.93 | 0.638 |
From Table 7.4, the highest cost-effectiveness occurs at \(R = 0.30\). This corresponds to an engine power of about 140 kW and a motor power of about 60 kW. This combination provides a fuel saving of nearly 20% without excessive cost. The total additional cost of the hybrid system is estimated as 121,300 CNY. The annual fuel saving for a bus running 300 km per day and 300 days per year is approximately 42,400 CNY, resulting in a payback period of less than three years.
8. Impact of Air Conditioning and Idle Operation
One key finding is the interaction between air conditioning type and hybrid operation. A non-independent air conditioning system (directly driven by the engine) forces the engine to idle during bus stops when the air conditioner is on. This idle operation consumes fuel, but it avoids the extra energy conversion losses of an electric-drive air conditioner. Simulations show that at 1.5 kW auxiliary load, the independent air conditioner has a slight advantage, but at 7.5 kW and 15 kW, the non-independent system is more efficient. In particular, when the auxiliary load is 15 kW, an electric-drive air conditioner can drain the EV battery pack too quickly, causing the SOC to drop below safe limits during a 30-cycle ECE test. Therefore, this vehicle uses a non-independent air conditioner and allows engine idle when necessary. This decision reduces the potential fuel economy benefit slightly, but it ensures reliable operation and lowers system cost.
9. Regenerative Braking and Drive Axle Configuration
Regenerative braking is a major contributor to hybrid fuel savings. In the ECE cycle, the braking energy available at the wheels is substantial. However, the default ADVISOR model assumes front-wheel drive and a conservative braking force distribution. Since the designed bus is rear-wheel driven, I modified the braking distribution algorithm to maximize the motor’s regenerative capability. The new strategy allows the electric motor to provide as much braking torque as possible at medium and high speeds, while the mechanical brakes are blended in at lower speeds and for high deceleration events. The modified model increases the recovered energy by up to 20% compared to the default settings. Table 9.1 presents the braking energy distribution for different hybrid degrees after the modification.
| R | Engine power (kW) | Motor power (kW) | Braking energy (kJ) | Energy lost (kJ) | Regenerated energy (kJ) | Engine brake loss (kJ) |
|---|---|---|---|---|---|---|
| 0.20 | 160 | 40 | 63595 | 37052 | 26543 | 12 |
| 0.25 | 150 | 50 | 63565 | 31243 | 32322 | 11 |
| 0.30 | 140 | 60 | 63537 | 25809 | 37728 | 10 |
| 0.35 | 130 | 70 | 63513 | 21005 | 42508 | 9 |
| 0.40 | 120 | 80 | 63495 | 17744 | 45751 | 9 |
| 0.45 | 110 | 90 | 63479 | 15278 | 48201 | 7 |
| 0.50 | 100 | 100 | 63469 | 13599 | 49869 | 7 |
The amount of regenerated energy grows with motor size. However, the cost of increasing motor power outweighs the marginal fuel savings for \(R > 0.3\), as demonstrated in the cost-effectiveness analysis.
10. Conclusions and Future Work
This article presented a comprehensive parameter matching and optimization study for a parallel hybrid city bus power system. The main contributions and conclusions are:
- A front-mounted single-shaft torque-coupling parallel hybrid architecture was designed. This structure minimally changes the conventional bus layout and satisfactorily meets the performance requirements.
- The minimum engine and motor powers were analytically determined. The engine is sized to provide average power, while the motor covers peaks and recovers braking energy.
- Simulations showed that using a non-independent air conditioner with engine idle during stops is preferable for this bus because electric air conditioners can deplete the EV battery pack under high accessory loads.
- A modified regenerative braking control strategy was proposed for rear-wheel-drive buses, increasing energy recovery significantly compared with the default front-wheel-drive model.
- An optimization criterion based on cost-effectiveness, i.e., the ratio of fuel saving to system cost, was established. Weighted averaging over expected operating conditions yielded an optimal hybrid degree of \(R = 0.30\), corresponding to a 140 kW engine and a 60 kW motor.
The optimal hybrid system achieves a weighted average fuel economy improvement of 19.5% compared with a conventional 200 kW diesel bus. The additional cost of the hybrid system is about 121,300 CNY, and the annual fuel saving is about 42,400 CNY, leading to a payback period of about 2.9 years. The designed system meets all performance targets, including a maximum speed above 80 km/h, 0–50 km/h acceleration time under 18 s, and a gradeability above 4.5% at full load.
This work demonstrates a practical and repeatable methodology for matching and optimizing the power system of a hybrid electric bus. Future research should incorporate more detailed emission models, advanced control strategies such as fuzzy logic or machine learning-based supervisory control, and experimental validation on a hardware-in-the-loop test bench. The role of the EV battery pack in both energy efficiency and lifecycle cost deserves deeper investigation, especially with respect to fast charging and battery thermal management. The trade-off between fuel saving and battery degradation should also be quantified to further refine the hybrid degree selection.
In summary, the parameter optimization method presented here can be directly applied to the development of hybrid city buses, providing a solid theoretical basis for the selection and procurement of components. The use of ADVISOR as a simulation tool proved effective for evaluating multiple scenarios and narrowing down the design space before costly prototyping. The results underline the importance of considering real-world driving conditions, auxiliary loads, and lifecycle costs when designing hybrid powertrains.