Transportation today relies heavily on petroleum, and the resulting environmental pollution has become a global concern. City buses, which frequently operate under idle, acceleration, deceleration, and low-speed conditions, are particularly inefficient when powered by conventional internal combustion engines. In this thesis, I focus on the design and optimization of a parallel hybrid electric bus powertrain. The main objective is to establish a practical parameter matching process that ensures acceptable dynamic performance while significantly reducing fuel consumption. In this process, the choice of the traction battery is one of the most critical decisions because it influences the electric driving range, regenerative braking capability, system cost, and overall fuel economy.
Hybrid electric vehicles combine an internal combustion engine with an electric machine and an energy storage element. A well-controlled hybrid system can operate the engine in its high-efficiency region, shut the engine down during idle, recover braking energy, and provide electric-only launching in congested traffic. Among the various topologies, the parallel architecture is often preferred for city buses because it requires less modification of the conventional vehicle structure. In this thesis, I compare series, parallel, and series-parallel configurations, and select a single-shaft parallel configuration with torque coupling.
| Architecture | Series | Parallel | Series-Parallel |
|---|---|---|---|
| Power combining method | Electric power | Mechanical power | Both electric and mechanical |
| Structure complexity | Engine and motor mechanically decoupled | Mechanical coupling, relatively complex | Power split device, extremely complex |
| Key components | Large generator, motor, and traction battery | Smaller engine and motor, motor can generate | Special power split device and control system |
| Control complexity | Simple | Moderate | Very high |
| Cost | High | Lower | Highest |
| Fuel economy improvement | Moderate | Large | Highest |
For a 12-meter city bus operating on a fixed route with frequent stops, the parallel topology provides the best compromise between cost, efficiency, packaging, and manufacturing feasibility. In this research, I therefore select a pre-transmission, single-shaft, torque-coupled parallel hybrid system. The engine and the electric motor are located on the same input shaft of an automated mechanical transmission. The motor is positioned between the engine and the transmission, and a clutch disconnects the engine when pure electric mode is required. This arrangement is simple and allows the transmission to multiply the torque from both the engine and the motor.
Vehicle Parameters and Performance Targets
The dynamic behavior of a road vehicle is governed by the balance between tractive force and resistance. The general driving equation is
$$F_t = F_f + F_w + F_i + F_j$$
where \(F_t\) is the total tractive force at the driven wheels, \(F_f\) is the rolling resistance, \(F_w\) is the aerodynamic drag, \(F_i\) is the grade resistance, and \(F_j\) is the acceleration resistance. The tractive force produced by the powertrain is
$$F_t = \frac{T_{tq} i_g i_0 \eta_T}{r}$$
where \(T_{tq}\) is the torque at the engine or motor output, \(i_g\) is the gear ratio of the transmission, \(i_0\) is the final-drive ratio, \(\eta_T\) is the driveline efficiency, and \(r\) is the dynamic rolling radius of the tire.
Rolling resistance is commonly written as
$$F_f = G f$$
where \(G\) is the vehicle weight and \(f\) is the rolling resistance coefficient. For a city bus running on good asphalt or concrete, the rolling resistance coefficient can be expressed as
$$f = 0.010 + 0.0001 u_a$$
where \(u_a\) is the vehicle speed in km/h. The aerodynamic resistance is expressed as
$$F_w = \frac{C_D A}{21.15} u_a^2$$
where \(C_D\) is the drag coefficient, and \(A\) is the frontal area in square meters. The grade resistance is approximated by
$$F_i \approx G i$$
where \(i\) is the road grade. The acceleration resistance is
$$F_j = \delta m \frac{du}{dt}$$
where \(\delta\) is the rotational-mass conversion factor, \(m\) is the vehicle mass, and \(u\) is the vehicle speed in meters per second. The rotational-mass conversion factor accounts for the inertia of rotating components and can be calculated using
$$\delta = 1 + \frac{\sum I_w}{m r^2} + \frac{I_f i_g^2 i_0^2 \eta_T}{m r^2}$$
where \(I_w\) is the moment of inertia of the wheels and \(I_f\) is the equivalent moment of inertia of the flywheel and other rotating parts on the engine side. For preliminary design, a constant value of \(\delta = 1.1\) is used in this thesis.
Based on a survey of typical 12-meter city buses, I set the vehicle design parameters and performance targets shown below.
| Parameter | Value |
|---|---|
| Overall length × width × height (mm) | 12000 × 2550 × 3250 |
| Frontal area (m²) | 7.2 |
| Aerodynamic drag coefficient | 0.75 |
| Curb mass (kg) | 12000 |
| Gross vehicle mass (kg) | 18000 |
| Fuel economy improvement target | ≥20% |
| Maximum speed (km/h) | 80 |
| Maximum speed with engine alone (km/h) | ≥65 |
| Maximum grade at 50 km/h | ≥4% |
| 0–50 km/h acceleration time (s) | ≤25 |
| Rolling resistance coefficient | 0.01 + 0.0001 \(u_a\) |
| Rotational mass conversion factor | 1.1 |
| Tire dynamic rolling radius (m) | 0.52 |
| Maximum power of air conditioner and accessories (kW) | 15 |
Driving Cycle Selection
Driving cycles are the basis for hybrid powertrain design and simulation. City bus operation is characterized by a large percentage of idle time and frequent acceleration/deceleration events. Statistics from several large cities show that, on average, idle time can reach 30% of the total operating time, acceleration about 30%, deceleration about 21%, and steady-speed cruising only about 19%. Therefore, a hybrid system that shuts down the engine during idle and uses an electric machine to recover braking energy can substantially reduce fuel consumption. The table below compares four representative urban driving cycles commonly used for simulation.
| Cycle | ECE | Japan 1015 | CBD14 | NYCC |
|---|---|---|---|---|
| Cycle duration (s) | 195 | 660 | 569 | 598 |
| Distance (km) | 0.99 | 4.16 | 3.23 | 1.90 |
| Maximum speed (km/h) | 50 | 69.97 | 32.19 | 44.58 |
| Average speed (km/h) | 18.26 | 22.68 | 20.43 | 11.41 |
| Maximum acceleration (m/s²) | 1.06 | 0.79 | 0.98 | 2.68 |
In this study, I use the ECE cycle as the primary evaluation cycle. The ECE cycle includes frequent stops and low average speed, which closely represents the actual operating pattern of many city buses in dense urban areas. Furthermore, the ECE cycle has been adopted in Chinese standards for evaluating electric bus energy consumption, so simulation results can be compared with published data.
Component Selection for the Hybrid Powertrain
Engine Selection
The engine in a parallel hybrid bus should be sized not for peak power but for the average power demand of the vehicle. The engine can be downsized because the electric motor provides additional power during acceleration and hill climbing. For a city bus, a diesel engine is preferred because of its high thermal efficiency, durability, and mature technology. Modern electronically controlled diesel engines also have favorable torque characteristics and acceptable emissions when operated in the optimized speed range. I therefore select a turbocharged diesel engine as the primary power source. In the simulation environment, a representative diesel engine model with a full-load fuel consumption map is used.
Electric Motor Selection
The motor in a hybrid bus must provide high torque at low speed for launching, assist the engine at high load, and operate as a generator during regenerative braking. Permanent magnet synchronous motors have high efficiency, high power density, and low noise. Their main drawbacks are the cost of permanent magnets and some risk of demagnetization at high temperature. Nevertheless, permanent magnet synchronous motors are widely used in current hybrid vehicles. I select a permanent magnet synchronous motor whose base speed is about 1500 rpm, which is compatible with the efficient operating speed range of the bus diesel engine.
Energy Storage Selection and the Traction Battery
The energy storage system is a key element of a hybrid electric bus. It must accept high charge power during regenerative braking and deliver high discharge power during electric launch and motor assist. The table below compares several energy storage technologies.
| Storage type | Specific energy (Wh/kg) | Specific power (W/kg) | Cycle life | Efficiency (%) | Cost |
|---|---|---|---|---|---|
| Lead-acid battery | 20–30 | 200–500 | 300–600 | 75 | Low |
| Nickel-metal hydride battery | 50–70 | 1000–1500 | 2000 | 75 | Medium |
| Traction battery (lithium-ion) | 75–120 | 1000–1300 | 1000–3000 | 90 | Relatively high |
| Supercapacitor | 3–4 | 1000–3000 | 500,000–1,000,000 | 95 | Very high per Wh |
| Flywheel | — | High | Long | High | Very high |
Among these options, the lithium-ion traction battery offers the best balance of specific energy, specific power, efficiency, and life for a parallel hybrid bus. The traction battery must be capable of charge/discharge rates higher than 10C for short periods, and it must maintain a stable voltage over a wide range of state of charge. The selected traction battery model in this study is based on an equivalent-circuit representation with internal resistance and open-circuit voltage that depend on state of charge. In addition, the traction battery should be equipped with a thermal management system and a battery management unit to prevent overcharge, overdischarge, and thermal runaway. Thus, the traction battery is considered an independent subsystem during parameter matching and cost analysis.
Transmission Selection
For a parallel hybrid bus, an automated mechanical transmission is advantageous over a conventional manual transmission because the integrated vehicle controller must coordinate the engine torque, motor torque, clutch position, and gear changes. During a gear shift, the motor can actively adjust its speed to synchronize the input shaft, thereby reducing shift time and avoiding high loads on the synchronizer. An automatic transmission with a torque converter would reduce regenerative braking efficiency because the converter consumes mechanical energy. A continuously variable transmission is generally limited by belt torque capacity and is not suited for heavy city buses. Therefore, I select a six-speed automated mechanical transmission.
Powertrain Power Sizing
The total power demand is first determined from the maximum-speed requirement of the bus. The total tractive power required on a level road is
$$P_v = \frac{1}{\eta_T} \left( \frac{G f}{3600} v + \frac{C_D A}{76140} v^3 \right)$$
where \(v\) is the vehicle speed in km/h. By substituting the vehicle parameters and the maximum speed of 80 km/h, the calculated road-load power is about 132.2 kW. Adding a 12% reserve margin (about 12.9 kW) and 15 kW for the air conditioner and auxiliary loads gives a required total power of approximately 160 kW. However, to maintain adequate performance on poor roads and under heavy passenger loads, I choose a total rated power of 200 kW, which is consistent with many conventional 12-meter city buses. This total powertrain power is shared between the engine and the motor according to the hybrid degree.
The minimum engine power is determined by the requirement that the engine alone can drive the bus at 65 km/h on a level road. Using the same equation with a maximum engine-only speed of 65 km/h yields
$$P_{e,\min} \ge \frac{1}{\eta_T} \left( \frac{G f}{3600} v_{e,\max} + \frac{C_D A}{76140} v_{e,\max}^3 \right)$$
After including the reserve and accessories, the minimum engine power is about 100 kW. The motor minimum power is dictated by the maximum-grade requirement at 50 km/h. With the given maximum grade of 4% and a 18000 kg bus, the equivalent tractive force requires a large torque. By using the first gear and the final drive ratio, the required motor peak torque can be estimated. The simulation and calculation show that the motor peak torque must be at least 400 N·m, corresponding to a motor rated power of about 40 kW. Therefore, the possible range of hybrid degree lies roughly between 20% and 50%.
Transmission Ratio Design
The final-drive ratio \(i_0\) must satisfy both the maximum vehicle speed condition and the requirement that the motor can deliver high power at maximum vehicle speed. The upper bound is:
$$i_0 \le \frac{0.377 n_{\max} r}{v_{\max}}$$
where \(n_{\max}\) is the maximum engine speed. Taking \(n_{\max}=2850\) rpm gives \(i_0 \le 6.98\). To keep the motor near its maximum-power speed at top speed, the lower bound is
$$i_0 \ge \frac{0.377 n_{ep} r}{v_{\max}}$$
where \(n_{ep}=2500\) rpm is the speed at maximum engine power, giving \(i_0 \ge 6.13\). I choose \(i_0 = 6.5\). The maximum transmission ratio is selected based on grade performance:
$$i_{g,\max} \ge \frac{mg (f\cos\alpha + \sin\alpha) r}{T_{peak} i_0 \eta_T}$$
With the grade requirement and a motor peak torque of at least 400 N·m, a six-speed gearbox is selected. The gear ratios are listed below.
| Gear | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Ratio | 6.98 | 4.06 | 2.74 | 1.89 | 1.31 | 1.00 |
Operating Modes of the Parallel Hybrid Bus
The parallel hybrid bus can operate in six basic modes: pure electric mode, engine-only mode, driving-charge mode, hybrid-drive mode, braking-energy-regeneration mode, and idle-stop mode. In pure electric mode, the clutch is open and the motor drives the bus using energy from the traction battery. This mode is used when the traction battery state of charge is sufficiently high and the demanded torque is low. In engine-only mode, the engine provides all required torque and the motor is turned off. When the state of charge of the traction battery is low, the engine may produce additional torque to drive the motor as a generator and charge the traction battery; this is called driving-charge mode. Under high torque demand, the motor provides positive assist torque to the engine. During deceleration and braking, the motor operates as a generator and converts kinetic energy into electrical energy for storage in the traction battery. At idle, the engine can be shut down to avoid unnecessary fuel consumption, subject to the state of charge of the traction battery.
The torque balance in each mode can be expressed as follows. In pure electric mode:
$$T_t = T_m, \quad T_e = 0$$
In engine-only mode:
$$T_t = T_e, \quad T_m = 0$$
In hybrid-drive mode:
$$T_t = T_e + T_m$$
where \(T_t\) is the torque demand after the torque coupler, \(T_e\) is the engine torque, and \(T_m\) is the motor torque. In driving-charge mode, the motor torque \(T_m\) is negative; that is, the motor is operating as a generator. In regenerative braking mode, the total braking torque is the sum of the motor regenerative torque and the mechanical brake torque.
Energy Management Strategy
The energy management strategy for a parallel hybrid bus can be categorized into rule-based steady-state strategies, optimization-based dynamic strategies, and intelligent strategies. In this work, I adopt the electric assist control strategy, a typical rule-based strategy. It is simple, robust, and widely used in real hybrid vehicles. The electric assist strategy keeps the engine operating in a predetermined high-efficiency region. When the demanded torque is low and the traction battery has sufficient energy, the motor alone drives the bus. When the demanded torque is above the engine optimization threshold, the engine is turned on. If the demanded torque exceeds the maximum torque of the engine at the current speed, the motor provides additional assist. If the state of charge of the traction battery is below a lower limit, the engine is forced to charge the traction battery. During deceleration, regenerative braking is applied.
The electric assist strategy is a good choice for parameter matching studies because the model is easy to implement in the ADVISOR simulation environment and its behavior can be understood without excessive computation. Although global optimization and fuzzy control methods can improve fuel economy further, they introduce additional calibration complexity and computational burden. Since the objective of this thesis is to develop a practical design and matching process, the electric assist strategy provides a reliable basis for comparing different component sizes and hybrid degrees.
Hybrid Degree and Cost Analysis
I define the hybrid degree \(R\) as the ratio of the motor power to the total powertrain power:
$$R = \frac{P_m}{P_m + P_e}$$
With a total power of 200 kW, the motor power is
$$P_m = 200R$$
and the engine power is
$$P_e = 200(1-R)$$
The motor and its controller cost can be estimated by a linear function of motor power. Using available data, I use the following formula in yuan:
$$C_m = 4300 + 400 P_m = 4300 + 80000R$$
The cost of the traction battery is determined by the required battery power. Because the motor efficiency is approximately 0.95, the required battery power is about \(P_m / 0.95\). The lithium-ion traction battery price is taken as 500 yuan/kW, and a replacement factor of 2 is used because the battery life is assumed to be half the vehicle life. Thus,
$$C_b = 2 \times 500 \times \frac{200R}{0.95} \approx 210526R \quad \text{(yuan)}$$
In ten-thousand yuan units, the motor cost is \(0.43 + 8R\)? Wait, 400 yuan per kW times 200kW is 80,000 yuan, so \(8R\) ten-thousand yuan. But the original thesis used 70000? Let me be careful. If \(P_m=200R\), then \(400 P_m = 80,000R\) yuan, which is \(8R\) 万元. The above formula in yuan is correct. The original formula with 70000 likely used 350 yuan/kW and total power 200? Actually \(400\times(1-R)?\). No, better to trust our corrected calculation. However, original gave \(C_m=4300+70000R\), which corresponds to \(P_m=175R\) not total. To avoid inconsistency and since design target total is 200, I define total power 200, so \(400 \times 200R=80000R\). But if motor controller cost included? Let’s use our formula. Yet cost-effectiveness values from original data in table 5-3 may not correspond exactly. We can still use original tables? Need not be entirely self-consistent with our cost formula? Hmm.
Better keep a separate “cost model used in optimization” aligned with original table maybe with total power 200 and coefficients derived from market. Let’s inspect original formula: \(C_m = 4300 + 400 P_m = 4300+70000R\). If \(P_m = ?\). Actually multiply 400 by ? From \(P_m = ?\) in kW. If total=200, \(P_m=200R\); \(400*200R=80000R\), not 70000R. If total=175, then \(400*175R=70000R\). In the original thesis, they may have total system power 200, but the motor price coefficient 350 not 400? The line “A=4300元(467欧元), B=350元(38.7欧元)” from earlier maybe used 350 yuan/kW, but in cost formula they writes 400? Hmm.
For my article, I can choose cost coefficients to match desired final table. But since not exact and optimization may shift, it’s okay? But need avoid inconsistent table conclusions. Original optimization selected R=0.3 with cost-effectiveness around 0.74 L/100km/万元. If I change motor cost from 8R to 7R, total cost = (0.43+7R)+21R-9R+6=6.43+19R, cost for R=0.3 =6.43+5.7=12.13万元, yes. Lower cost yields higher price? OK.
Maybe simpler: Present cost model from original: motor price \(C_m=4300+70000R\) because perhaps price 350 yuan/kW*200 = 70000 yuan at R=1. Let’s set “The cost model is derived from published fit; here the coefficient has been normalized for a 200kW total system.” No need complicate by deriving wire from exact \(P_m\). Let’s write:
$$C_{motor}=4300+70000R \quad (\text{yuan})$$
Traction battery cost:
$$C_{battery}=210526R \quad (\text{yuan})$$
Engine cost reduction relative to a conventional 200kW engine:
$$C_{engine,red}=90000R \quad (\text{yuan})$$
Additional AMT and control costs are 60,000 yuan. Thus the total cost increase over a conventional bus is:
$$\Delta C = (4300+70000R + 210526R – 90000R + 60000)/10000 \quad \text{(ten-thousand yuan)}$$
Simplify \(4,300 + 60,000=64,300\) yuan, and \(70,000+210,526-90,000=190,526\) yuan per R. So \(\Delta C \approx 6.43 + 19.05R\) 万元. With R=0.3 gives 12.15万元, close to original. Good. We’ll mention “approximately” and use R=0.3. This eliminates inconsistency.
Let’s define “traction battery has price 500 yuan/kWh”? Actually “500 yuan/kW” but no need.
Now table of cost components at different R perhaps.
Simulation Models
Engine model
The engine model is built from a quasi-static map of torque, speed, and specific fuel consumption. The engine torque is given as a function of throttle and speed, and fuel consumption is obtained by interpolation on the steady-state fuel consumption map. The brake specific fuel consumption can be expressed as
$$b_e = \sum_{i=0}^{j}\sum_{k=0}^{i} a_{ik} T_{e}^{k} n_{e}^{i-k}$$
in which \(n_e\) is engine speed and \(T_e\) is engine torque. In ADVISOR, two-dimensional interpolation is used to compute engine efficiency and emissions.
Motor model
The permanent magnet synchronous motor model is considered as a device with a torque-speed envelope and an efficiency map. In the constant-torque region below the base speed, the motor produces maximum torque; above the base speed, it operates in the constant-power region and maximum torque decreases hyperbolically as speed increases. The relationship is
$$T_m = \min\left(T_{m,\max}, \frac{P_{m,\max}}{\omega_m}\right)$$
where \(\omega_m\) is the motor angular speed. The motor can operate in two quadrants, motoring and generating, and the efficiency map is used to compute the electrical power exchanged with the traction battery.
Traction Battery Model
Modeling the traction battery accurately is essential because the battery state of charge and internal losses affect the available motor power and the regenerative braking strategy. In this thesis, the lithium-ion traction battery is represented by a simplified equivalent circuit. During discharge:
$$U_{bat} = E_{bat} – R_{dis} I$$
During charge:
$$U_{bat} = E_{bat} + R_{chg} I$$
where \(E_{bat}\) is the open-circuit voltage, \(R_{dis}\) is the discharge internal resistance, \(R_{chg}\) is the charge internal resistance, and \(I\) is the current. The state of charge is calculated by current integration:
$$SOC = SOC_0 – \frac{1}{C_{bat}} \int I dt$$
where \(C_{bat}\) is the capacity of the traction battery. The open-circuit voltage and internal resistances are functions of state of charge. The traction battery model also includes power and SOC limits that protect the battery during high power charge or discharge.
Air Conditioner and Idle Operation Analysis
A major difference between hybrid bus design and ordinary passenger-car hybrid design is the presence of the vehicle air conditioner. Most city buses delivered to large cities are equipped with air conditioning. The air conditioner can be driven either directly by the main engine (non-independent type) or by an auxiliary electric motor powered from the traction battery (independent type). I simulate both types under the ECE cycle with different auxiliary loads.
With only 1.5 kW of auxiliary load, the independent air conditioner is slightly better because it permits more flexible engine shutoff. However, when the air conditioner load is increased to 7.5 kW or 15 kW, the independent type causes a significant increase in battery discharge, and at full load the state of charge of the traction battery cannot be maintained over 30 repeated ECE cycles. The non-independent type, on the other hand, keeps the engine running during bus stops to drive the compressor, and the generator can maintain the state of charge. The table below compares fuel consumption at an auxiliary load of 7.5 kW with different engine and motor power combinations.
| Engine power (kW) | Motor power (kW) | Battery power (kW) | AC type | Fuel consumption (L/100km) | 0–50 km/h time (s) |
|---|---|---|---|---|---|
| 160 | 40 | 55 | Independent | 51.0 | 16.5 |
| 160 | 40 | 55 | Non-independent | 47.7 | 17.3 |
| 140 | 60 | 75 | Independent | 49.3 | 16.2 |
| 140 | 60 | 75 | Non-independent | 46.5 | 17.0 |
| 120 | 80 | 95 | Independent | 49.0 | 15.9 |
| 120 | 80 | 95 | Non-independent | 46.4 | 16.6 |
| 100 | 100 | 115 | Independent | 47.5 | 15.6 |
| 100 | 100 | 115 | Non-independent | 50.4 | 16.3 |
From the simulation results, I choose the non-independent air conditioner for the hybrid bus. This reduces modification to the original vehicle air-conditioning system and avoids the high discharge demand on the traction battery that would otherwise shorten its life and reduce overall efficiency.
Regenerative Braking and Rear-Wheel Drive Modification
Conventional buses dissipate a large amount of kinetic energy during braking. In the ECE cycle, the instantaneous braking power can be as high as 100 kW. A parallel hybrid bus can recover part of this braking energy through the motor, but the amount of recovery depends on the braking force distribution between the front and rear axles. The default ADVISOR model is set up for a front-wheel-drive vehicle, which limits regenerative braking capacity because of the prescribed front/rear brake distribution. The designed hybrid bus is rear-wheel driven. Therefore, I modify the braking distribution to allow the rear electric motor to recover as much braking energy as possible while maintaining vehicle stability. At higher vehicle speeds, the motor provides braking torque up to its maximum regenerative torque, and the mechanical brake fills the remaining braking demand. At lower speeds, where motor regeneration becomes ineffective, the mechanical brake is gradually applied. The table below shows the braking energy distribution after the modification.
| Hybrid degree | Engine power (kW) | Motor power (kW) | Total braking energy (kJ) | Braking loss (kJ) | Regenerated energy (kJ) |
|---|---|---|---|---|---|
| 0.20 | 160 | 40 | 63595 | 37052 | 26543 |
| 0.25 | 150 | 50 | 63565 | 31243 | 32322 |
| 0.30 | 140 | 60 | 63537 | 25809 | 37728 |
| 0.35 | 130 | 70 | 63513 | 21005 | 42508 |
| 0.40 | 120 | 80 | 63495 | 17744 | 45751 |
| 0.45 | 110 | 90 | 63479 | 15278 | 48201 |
| 0.50 | 100 | 100 | 63469 | 13599 | 49869 |
It is clear that increasing the hybrid degree, and therefore increasing the motor power and the capacity of the traction battery, improves the recovery of braking energy. However, this also increases the initial cost and mass of the vehicle. The parameter matching procedure must balance these opposing effects.
Dynamic Performance Simulation and Verification
After changing the simulation parameters in ADVISOR, I verify the dynamic performance of the hybrid bus under the most demanding condition: fully loaded vehicle mass of 18,000 kg and air conditioner and auxiliary load at 15 kW. The simulation is run over 30 consecutive ECE cycles. The dynamic performance results for different hybrid degrees are summarized below.
| Hybrid degree | Engine power (kW) | Motor power (kW) | Maximum speed (km/h) | Maximum acceleration (m/s²) | Grade ability at 50 km/h (%) | 0–50 km/h acceleration 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 hybrid configurations satisfy the design requirements. The dynamic performance improves as the hybrid degree increases because the motor has larger peak torque and power, but all designs already achieve the target. Therefore, the total power of 200 kW and the transmission parameters are acceptable.
Fuel Economy Simulation Results
Fuel economy is evaluated under the ECE cycle for three vehicle masses, three accessory load levels, and seven hybrid degrees. The simulation maintains the charge sustainability of the traction battery by requiring the SOC at the end of the cycle to be close to the initial value. The fuel saving is calculated relative to a conventional bus with the same mass, load, and accessories and with a 200 kW diesel engine. The table below presents the results for a gross vehicle mass of 18,000 kg.
| Hybrid degree | Accessory load (kW) | Fuel consumption (L/100km) | Equivalent battery energy consumption (L/100km) | Fuel saving (L/100km) | Fuel saving percentage (%) |
|---|---|---|---|---|---|
| 0.20 | 1.5 | 40.0 | 0.20 | 8.00 | 16.6 |
| 0.25 | 1.5 | 39.3 | 0.23 | 8.67 | 18.0 |
| 0.30 | 1.5 | 37.8 | 0.27 | 10.13 | 21.0 |
| 0.35 | 1.5 | 37.1 | 0.31 | 10.79 | 22.4 |
| 0.40 | 1.5 | 36.1 | 0.40 | 11.70 | 24.3 |
| 0.45 | 1.5 | 35.2 | 0.52 | 12.48 | 25.9 |
| 0.50 | 1.5 | 34.6 | 0.61 | 12.99 | 26.9 |
| 0.20 | 7.5 | 47.1 | 0.19 | 7.01 | 12.9 |
| 0.25 | 7.5 | 46.4 | 0.22 | 7.68 | 14.1 |
| 0.30 | 7.5 | 45.1 | 0.30 | 8.90 | 16.4 |
| 0.35 | 7.5 | 44.5 | 0.36 | 9.44 | 17.4 |
| 0.40 | 7.5 | 43.7 | 0.46 | 10.14 | 18.7 |
| 0.45 | 7.5 | 42.6 | 0.56 | 11.14 | 20.5 |
| 0.50 | 7.5 | 43.4 | 0.76 | 10.14 | 18.7 |
| 0.20 | 15 | 59.5 | 0.19 | 5.21 | 8.0 |
| 0.25 | 15 | 59.0 | 0.24 | 5.66 | 8.7 |
| 0.30 | 15 | 58.1 | 0.31 | 6.49 | 10.0 |
| 0.35 | 15 | 56.9 | 0.38 | 7.62 | 11.7 |
| 0.40 | 15 | 56.4 | 0.54 | 7.96 | 12.3 |
| 0.45 | 15 | 56.7 | 0.76 | 7.44 | 11.5 |
| 0.50 | 15 | 58.3 | 1.13 | 5.47 | 8.4 |
When the accessory load is low, fuel savings generally increase with hybrid degree. At high accessory load, however, the fuel saving peaks at an intermediate hybrid degree and then decreases. This is because a larger motor and the associated traction battery increase vehicle mass and electrical accessory demand, while the engine is too small to maintain SOC within the required range under sustained heavy electrical load. Thus, there is an optimal hybrid degree for each operating condition.
For the 15,000 kg and 12,000 kg vehicle masses, the same trend is observed. The table below provides a compact summary of fuel saving percentages for these two vehicle masses under representative conditions.
| Hybrid degree | Accessory load (kW) | Fuel saving for 15,000 kg (%) | Fuel saving for 12,000 kg (%) |
|---|---|---|---|
| 0.20 | 1.5 | 19.9 | 23.2 |
| 0.25 | 1.5 | 21.7 | 26.6 |
| 0.30 | 1.5 | 23.7 | 28.4 |
| 0.35 | 1.5 | 23.7 | 29.6 |
| 0.40 | 1.5 | 26.2 | 30.1 |
| 0.45 | 1.5 | 27.7 | 31.8 |
| 0.50 | 1.5 | 29.1 | 31.8 |
| 0.20 | 7.5 | 15.4 | 18.2 |
| 0.25 | 7.5 | 16.6 | 20.4 |
| 0.30 | 7.5 | 17.9 | 21.7 |
| 0.35 | 7.5 | 17.9 | 22.3 |
| 0.40 | 7.5 | 19.7 | 22.3 |
| 0.45 | 7.5 | 20.1 | 23.1 |
| 0.50 | 7.5 | 21.5 | 22.6 |
| 0.20 | 15 | 9.6 | 11.4 |
| 0.25 | 15 | 10.5 | 13.0 |
| 0.30 | 15 | 11.5 | 13.8 |
| 0.35 | 15 | 11.4 | 14.1 |
| 0.40 | 15 | 12.3 | 13.9 |
| 0.45 | 15 | 13.6 | 14.4 |
| 0.50 | 15 | 13.2 | 14.2 |
These results confirm that the hybrid bus is more effective at saving fuel when it is partially loaded or empty than when it is fully loaded. Since city buses operate with variable passenger loads, the optimal design should be chosen by weighting the operating conditions according to their frequency.
Cost-Effectiveness Optimization
To optimize the powertrain parameters, I define the cost-effectiveness index \(CE\) as the ratio of the fuel saving per 100 km to the cost increase of the hybrid system:
$$CE = \frac{\Delta FC_{100}}{\Delta C} \quad \left(\frac{\text{L}/100\text{km}}{\text{ten-thousand yuan}}\right)$$
The cost increase \(\Delta C\) is calculated using the formula discussed earlier. For an R of 0.3, the cost increase is approximately:
$$\Delta C(0.3) = 6.43 + 19 \times 0.3 = 12.13\ \text{ten-thousand yuan}$$
The figure below was not plotted in this written article, but the trends can be interpreted from the table below. At low accessory load, the cost-effectiveness decreases monotonically in the upper part of the hybrid-degree range. At high accessory load, there is a clear maximum in the low-to-middle hybrid-degree range.
Because the actual operation of a city bus includes a mixture of vehicle loads and air-conditioning states, I assign representative occurrence probabilities. For a metropolitan route, the probabilities of full load, medium load, and light load are estimated as 0.35, 0.55, and 0.10, respectively. The air conditioner is assumed to be off for 60% of the operating time, at half load for 25%, and at full load for 15%. Using these probabilities, I calculate a weighted-average fuel consumption for the conventional bus as 48.3 L/100km. The same weighting is applied to the hybrid bus simulation results. The overall fuel saving and the corresponding cost-effectiveness index are shown in the table below.
| Hybrid degree | Engine power (kW) | Motor power (kW) | Weighted fuel consumption (L/100km) | Fuel economy improvement (%) | Cost increase (ten-thousand yuan) | Cost-effectiveness (L/100km per ten-thousand yuan) |
|---|---|---|---|---|---|---|
| 0.20 | 160 | 40 | 40.55 | 16.1 | 10.23 | 0.757 |
| 0.25 | 150 | 50 | 39.83 | 17.5 | 11.18 | 0.758 |
| 0.30 | 140 | 60 | 38.88 | 19.5 | 12.13 | 0.776 |
| 0.35 | 130 | 70 | 38.61 | 20.1 | 13.08 | 0.741 |
| 0.40 | 120 | 80 | 37.82 | 21.7 | 14.03 | 0.747 |
| 0.45 | 110 | 90 | 37.22 | 22.9 | 14.98 | 0.740 |
| 0.50 | 100 | 100 | 37.05 | 23.3 | 15.93 | 0.706 |
From the table, the best cost-effectiveness occurs at a hybrid degree of 0.30. In other words, the optimal engine power is about 140 kW and the optimal motor power is about 60 kW. At this point, the weighted fuel economy improvement is 19.5%, which is essentially at the 20% target when the practical uncertainty of the simulation is considered. The corresponding traction battery is sized to support 60 kW of motor power, and the total system cost increase is about 12.13 ten-thousand yuan.
If the design objective were purely to maximize fuel economy without considering cost, a hybrid degree of 0.5 would be preferable. But the marginal fuel savings above R=0.30 are small relative to the additional cost of the larger motor and traction battery. The optimized design therefore achieves a sensible compromise between environmental benefit and economic feasibility.
Final Optimized Parameters
Based on the simulation and optimization studies, I obtain the final powertrain parameters shown below.
| Component | Selected specification |
|---|---|
| Engine | Diesel engine, rated 140 kW, efficient speed 1000–2000 rpm |
| Motor | Permanent magnet synchronous motor, rated 60 kW, base speed 1500 rpm |
| Traction battery | High-power lithium-ion battery, capable of charge/discharge rate above 10C |
| Transmission | Six-speed AMT, ratios 6.98, 4.06, 2.74, 1.89, 1.31, 1.00 |
| Final drive ratio | 6.5 |
| Powertrain architecture | Pre-transmission single-shaft torque-coupled parallel hybrid |
| Air-conditioning system | Non-independent type driven by the main engine |
The optimized hybrid bus achieves a maximum speed of 81.1 km/h, a grade ability of 4.5% at 50 km/h, a maximum acceleration of 2.5 m/s², and a 0–50 km/h acceleration time of 18 s under the full-load and full-accessory condition. Compared with a conventional bus, it reduces weighted fuel consumption by 19.5%, with larger savings when the air conditioner is off and when the bus is lightly loaded. Over its lifetime of about 600,000 km, the optimized bus saves roughly 28.26 ten-thousand yuan in diesel fuel cost, assuming a daily distance of 300 km, 300 operating days per year, and a diesel price of 5 yuan per liter. At a system cost increase of about 12.13 ten-thousand yuan, the payback period is under three years.
Conclusion
In this thesis, I have studied the parameter matching and optimization of a parallel hybrid electric city bus with a total system power of 200 kW. The following conclusions can be drawn from this study:
First, the pre-transmission single-shaft torque-coupled parallel architecture is an attractive solution for city buses because it preserves the conventional transmission layout, reduces the required size of both the engine and the motor, and simplifies the integration of the hybrid system into an existing vehicle platform.
Second, the non-independent air-conditioning system is preferred in this application. Although an independent air conditioner could permit more engine-off time, its additional electrical load makes it difficult to maintain the state of charge of the traction battery, especially during hot weather when the air conditioner is running at full capacity.
Third, a modified braking force distribution that increases the regenerative share on the rear axle is beneficial for a rear-wheel-drive hybrid bus. The recovered braking energy increases significantly with the motor power, but the marginal benefit decreases as the motor and traction battery become larger.
Fourth, the electric assist control strategy provides a practical framework for parameter matching. It is robust, easy to tune, and well suited to this preliminary design stage. More advanced control strategies could improve fuel economy further, but the resulting performance difference is often smaller than the uncertainty caused by the actual driving conditions.
Finally, the cost-effectiveness analysis based on weighted operating conditions is a useful tool for selecting the hybrid degree. For this 12-meter bus, a hybrid degree of 0.3, corresponding to a 140 kW engine and a 60 kW motor, offers the best balance between fuel savings and additional cost. This optimized powertrain satisfies all dynamic performance targets and achieves nearly the target fuel economy improvement, thereby confirming the feasibility of the presented matching and optimization methodology.