In this study I investigate the parameter matching and optimization of a parallel hybrid power system for a city bus. My main objective is to establish a practical design procedure that links vehicle-level requirements, component selection, energy management, simulation, and cost-benefit evaluation. The core of the work is the electric vehicle battery pack, because its power capability, state of charge window, cost, and durability strongly influence the achievable fuel saving of the hybrid bus. I treat the electric vehicle battery pack not as an isolated component but as a subsystem that must be matched simultaneously with the engine, traction motor, transmission, and control strategy. Through this integrated view I derive component sizes that satisfy the dynamic performance targets while improving fuel economy and keeping the added hybrid cost within a reasonable range.
The design problem is nonlinear and multi-objective. The engine should operate in a high-efficiency region, the traction motor must provide enough torque for launch and gradeability, the electric vehicle battery pack must accept and deliver high power, and the transmission must amplify torque without excessive shifting complexity. I use a parallel single-shaft architecture because it retains much of the conventional bus driveline, allows mechanical torque addition, and offers a clear path to brake energy recovery. The optimization variable I adopt is the hybridization degree, defined as the ratio of motor power to total power. For each candidate hybridization degree I simulate the bus over a representative urban driving cycle, record fuel consumption and performance, estimate the incremental cost, and then select the configuration that gives the best trade-off between fuel saving and cost.
Vehicle Dynamics and Design Requirements
I begin with the longitudinal dynamics of the bus. The tractive force at the wheels must overcome rolling resistance, aerodynamic drag, grade resistance, and acceleration resistance. The fundamental equation is
$$F_t = \frac{T_{tq} i_g i_0 \eta_T}{r}$$
where \(F_t\) is the tractive force, \(T_{tq}\) is the engine or motor torque, \(i_g\) is the transmission gear ratio, \(i_0\) is the final drive ratio, \(\eta_T\) is the driveline efficiency, and \(r\) is the wheel radius. The total resistance is
$$F_\Sigma = F_f + F_w + F_i + F_j$$
with the individual terms defined as
$$F_f = mgf\cos\alpha$$
$$F_w = \frac{C_D A v^2}{21.15}$$
$$F_i = mg\sin\alpha$$
$$F_j = \delta m \frac{dv}{dt}$$
Here \(m\) is the vehicle mass, \(g\) is gravitational acceleration, \(f\) is the rolling resistance coefficient, \(\alpha\) is road grade, \(C_D\) is the aerodynamic drag coefficient, \(A\) is the frontal area, \(v\) is vehicle speed, and \(\delta\) is the rotating mass factor. For a city bus, the rolling resistance coefficient is not constant; I use the approximation
$$f = 0.010 + 0.0001v$$
where \(v\) is in km/h. The power required at the wheels for steady-speed operation is therefore
$$P_{wheel} = \frac{1}{3600}\left(mgfv + \frac{C_D A v^3}{76140}\right)$$
and the power that the power source must supply is
$$P_{source} = \frac{P_{wheel}}{\eta_T} + P_{accessory}$$
where \(P_{accessory}\) includes the air conditioner, alternator, air compressor, and other auxiliary loads. In my design the accessory load can reach 15 kW when the air conditioner is at full capacity.
The vehicle parameters I use for the 12 m city bus are summarized in Table 1. These values are representative of a conventional diesel bus and serve as the baseline for hybrid matching.
| Parameter | Value |
|---|---|
| Overall dimensions | 12.0 m × 2.55 m × 3.25 m |
| Frontal area | 7.2 m² |
| Aerodynamic drag coefficient | 0.75 |
| Curb mass | 12,000 kg |
| Gross vehicle mass | 18,000 kg |
| Top speed | 80 km/h |
| Engine-only top speed | > 65 km/h |
| Gradeability at 50 km/h | > 4% |
| 0–50 km/h acceleration time | < 25 s |
| Rolling resistance coefficient | 0.010 + 0.0001v |
| Rotating mass factor | 1.1 |
| Wheel rolling radius | 0.52 m |
| Maximum accessory load | 15 kW |
I evaluate the design over the urban ECE cycle because it contains frequent starts, stops, idle periods, and low-speed operation, which are typical of city bus service. The cycle characteristics are given in Table 2. Compared with other standard cycles, the ECE cycle is well suited to the stop-and-go behavior of a city bus and allows direct comparison with published bus economy data.
| Driving cycle | Duration (s) | Distance (km) | Maximum speed (km/h) | Average speed (km/h) | Maximum acceleration (m/s²) |
|---|---|---|---|---|---|
| ECE | 195 | 0.99 | 50.0 | 18.26 | 1.06 |
| Urban 1015 | 660 | 4.16 | 69.97 | 22.68 | 0.79 |
| CBD14 | 569 | 3.23 | 32.19 | 20.43 | 0.98 |
| NYCC | 598 | 1.90 | 44.58 | 11.41 | 2.68 |
Hybrid Architecture Selection
I compare series, parallel, and series-parallel hybrid architectures before selecting the one that fits a city bus best. The comparison is summarised in Table 3. A series hybrid requires a large generator, a large traction motor, and a large electric vehicle battery pack, which increases cost and mass. A series-parallel system can achieve high efficiency but has a complex power-split device and demanding control. A parallel system uses mechanical torque addition, can retain a conventional transmission, and allows the electric machine to assist the engine or recover braking energy. For a city bus with a fixed route and frequent stops, the parallel configuration offers a strong balance between fuel saving, cost, and engineering feasibility.
| Feature | Series | Parallel | Series-parallel |
|---|---|---|---|
| Energy combination | Electrical | Mechanical | Both |
| Engine–wheel coupling | None | Mechanical | Mechanical and electrical |
| Typical components | Engine, generator, motor, large battery pack | Engine, motor/generator, transmission, moderate battery pack | Engine, generator, motor, power-split device, battery pack |
| Control complexity | Moderate | High | Very high |
| Cost | High | Moderate | Very high |
| Suitability for city bus | Good but costly | Very good | Good but complex |
Within the parallel family I select a pre-transmission single-shaft arrangement. The traction motor is mounted between the clutch and the automated mechanical transmission. This placement allows the transmission to multiply both engine torque and motor torque, so the motor can be smaller than in a post-transmission layout. The electric vehicle battery pack is connected to the motor controller through a DC bus, and the motor can operate as a generator during braking. The architecture therefore supports pure electric drive, engine-only drive, hybrid drive, engine charging, and regenerative braking.
Component Matching and Selection
I match the engine first. The engine must be able to sustain the bus at a specified engine-only top speed and provide enough power for gradeability when the electric vehicle battery pack is at a low state of charge. From the road-load equation, the engine power for a target speed \(v_e\) is
$$P_e \ge \frac{1}{\eta_T}\left(\frac{mgf v_e}{3600} + \frac{C_D A v_e^3}{76140}\right) + P_{accessory}$$
For an engine-only top speed above 65 km/h and a full accessory load, the minimum engine power is approximately 100 kW. I add a margin for gradeability and acceleration, and I compare with conventional 12 m bus engines whose rated power typically lies between 160 kW and 220 kW. I select a diesel engine with a rated power near 140 kW after optimization. The engine is controlled to operate mainly in its high-efficiency region, which for a typical diesel engine lies between 1000 rpm and 2000 rpm.
The traction motor is selected next. Because the bus must launch and climb grades, the motor must provide high torque at low speed. The maximum transmission ratio is determined by the gradeability requirement and the motor peak torque:
$$i_{g,\max} \ge \frac{mg(f\cos\alpha + \sin\alpha)r}{T_{m,\max} i_0 \eta_T}$$
With a final drive ratio of 6.5 and a maximum gear ratio of 6.98, the motor peak torque must be at least about 370 N·m. I therefore select a permanent magnet synchronous motor with a rated power of 60 kW, a peak torque above 400 N·m, and a base speed near 1500 rpm. The motor can operate in constant-torque mode below base speed and constant-power mode above base speed. Its efficiency map is used directly in simulation, and its ability to generate during braking is essential for recovering kinetic energy.
The electric vehicle battery pack is the most critical storage component. I require the pack to deliver high power during acceleration, accept high power during regenerative braking, and maintain a state of charge window that avoids excessive aging. The pack model I use is based on an open-circuit voltage source in series with an internal resistance. The terminal voltage during discharge is
$$U_{bat} = E_{bat} – I_{bat} R_{bat}$$
and during charge it is
$$U_{bat} = E_{bat} + I_{bat} R_{bat}$$
The state of charge is computed by Coulomb counting:
$$SOC(t) = SOC_0 – \frac{1}{Q_{nom}} \int_0^t I_{bat}(\tau)\,d\tau$$
The battery power is
$$P_{bat} = E_{bat} I_{bat} – I_{bat}^2 R_{bat}$$
for discharge and
$$P_{bat} = E_{bat} I_{bat} + I_{bat}^2 R_{bat}$$
for charge. The open-circuit voltage and internal resistance depend on SOC and temperature. I include these dependencies in the electric vehicle battery pack model so that the simulation captures the reduction in available power at low SOC and the increase in resistance at low temperature. Because the electric vehicle battery pack is sized by power rather than by energy in a parallel hybrid bus, I select a high-power lithium-ion pack with a discharge capability above 10C and a charge capability above 4C. The pack is managed within a SOC window of approximately 40% to 80%, which preserves cycle life and reserves power for both acceleration and regeneration.
Table 4 compares the main energy-storage options I considered. The electric vehicle battery pack based on lithium-ion chemistry offers the best combination of power density, energy density, and cycle efficiency for this application. Although the initial cost is higher than that of lead-acid or nickel-metal hydride systems, the longer cycle life and higher round-trip efficiency reduce the effective cost per kilometre.
| Storage type | Energy density (Wh/kg) | Power density (W/kg) | Cycle efficiency (%) | Cycle life | Relative cost |
|---|---|---|---|---|---|
| Lead-acid | 20–30 | 200–500 | 75 | 300–600 | Low |
| Nickel-metal hydride | 50–70 | 1000–1500 | 75 | 2000 | Moderate |
| Lithium-ion | 75–120 | 1000–1300 | 90 | 1000–3000 | High |
| Supercapacitor | 3–4 | 1000–3000 | 95 | 500,000–1,000,000 | Very high per Wh |
The transmission is an automated mechanical transmission with six forward gears. I choose an AMT because it allows automatic shifting under the supervision of the hybrid controller and avoids the torque interruption and efficiency penalties of a conventional automatic transmission with a torque converter. The gear ratios are given in Table 5. The final drive ratio is 6.5. This combination provides good launch torque, a reasonable engine-only top speed, and enough ratio coverage for the motor to assist over the full speed range.
| Gear | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Ratio | 6.98 | 4.06 | 2.74 | 1.89 | 1.31 | 1.00 |
Power and Transmission Sizing Equations
I compute the total power requirement from the maximum speed target. The total power must be at least
$$P_{total} \ge \frac{1}{\eta_T}\left(\frac{mgf v_{\max}}{3600} + \frac{C_D A v_{\max}^3}{76140}\right) + P_{accessory}$$
With \(v_{\max}=80\) km/h and \(P_{accessory}=15\) kW, this gives approximately 160 kW. I add a margin and compare with conventional bus engines, then set the total power to 200 kW before optimization. After optimization the total power remains 200 kW, but the split between engine and motor changes with the hybridization degree.
The final drive ratio is bounded by the maximum engine speed and the desired top speed:
$$i_0 \le \frac{0.377 n_{\max} r}{v_{\max}}$$
and by the motor base speed condition:
$$i_0 \ge \frac{0.377 n_{base} r}{v_{\max}}$$
For an engine maximum speed of 2850 rpm and a motor base speed near 1500 rpm, the final drive ratio must lie between approximately 6.13 and 6.98. I choose 6.5, which satisfies both constraints and gives a good compromise between gradeability and high-speed efficiency.
Control Strategy and Operating Modes
I adopt an electric-assist control strategy because it is robust, easy to implement, and well matched to a parallel hybrid bus. In this strategy the engine is the primary power source, and the electric drive system provides assistance or charging depending on the driver demand and the state of charge of the electric vehicle battery pack. The torque balance at the transmission input is
$$T_{req} = T_e + T_m$$
where \(T_{req}\) is the requested torque, \(T_e\) is the engine torque, and \(T_m\) is the motor torque. Positive \(T_m\) means motoring, and negative \(T_m\) means generating. The control strategy determines \(T_e\) from an efficiency map and then sets \(T_m\) to the difference:
$$T_m = T_{req} – T_e$$
The charging torque is limited by the motor, the electric vehicle battery pack, and the SOC:
$$T_{ch} = \min\left(T_{m,\max}, f(SOC), T_{ch,\max}\right)$$
where \(f(SOC)\) increases the charging power when SOC is low and reduces it when SOC is high. The operating modes are listed in Table 6. I use SOC limits to prevent over-discharge and over-charge: the lower limit is 0.4 and the upper limit is 0.8. Within this window the electric vehicle battery pack can supply peak power for acceleration and absorb regenerative power during braking.
| Mode | Condition | Engine | Motor | Battery pack |
|---|---|---|---|---|
| Pure electric | Low load, SOC > SOClow | Off | Motoring | Discharge |
| Engine only | Moderate load, SOC in range | On | Off | Idle |
| Hybrid drive | High load, SOC > SOClow | On | Motoring | Discharge |
| Engine charging | Low SOC or low load | On | Generating | Charge |
| Regenerative braking | Braking, SOC < SOChigh | Off | Generating | Charge |
| Idle stop | Vehicle stopped, SOC adequate | Off | Off | Idle |
Simulation Models
I build the simulation models for the engine, motor, electric vehicle battery pack, transmission, and vehicle. The engine model uses a steady-state fuel map. The fuel mass flow rate is a function of engine torque and speed:
$$\dot m_f = f_e(T_e,\omega_e)$$
The engine efficiency is then
$$\eta_e = \frac{P_e}{\dot m_f Q_{LHV}}$$
where \(P_e = T_e \omega_e\) and \(Q_{LHV}\) is the lower heating value of diesel fuel. The motor model uses an efficiency map that depends on motor torque and speed. The electrical power is
$$P_{elec} = \begin{cases} \frac{P_m}{\eta_m}, & P_m \ge 0 \\ P_m \eta_m, & P_m < 0 \end{cases}$$
where \(P_m = T_m \omega_m\) is the mechanical power at the motor shaft. The electric vehicle battery pack model uses the open-circuit voltage and internal resistance described earlier. The transmission model includes gear ratios, final drive ratio, and efficiency. The vehicle model integrates the longitudinal dynamics and enforces the driver demand through a PI controller.
I modify the simulation platform to represent the pre-transmission parallel architecture. The engine and motor are connected to the same shaft before the transmission, so their speeds are equal to the transmission input speed. The clutch is engaged during hybrid drive and engine-only drive, and it is disengaged during pure electric drive and regenerative braking when the engine is off. The electric vehicle battery pack model is parameterized so that the pack can supply the motor power required by the chosen hybridization degree. I also revise the braking strategy because the original front-wheel-drive assumption limits regenerative braking. For a rear-wheel-drive bus, more braking torque can be allocated to the electric machine while respecting adhesion limits.
Table 7 shows the braking energy distribution I obtained after revising the brake force allocation. With the revised strategy, the electric machine recovers a larger share of the braking energy. This improvement is especially important in city bus operation, where frequent stops dominate the energy loss. The electric vehicle battery pack receives the recovered energy, so its charge acceptance capability directly affects how much energy can be recovered.
| Hybridization degree | Engine power (kW) | Motor power (kW) | Braking energy at wheels (kJ) | Braking loss (kJ) | Regenerated energy (kJ) |
|---|---|---|---|---|---|
| 0.20 | 160 | 40 | 63,595 | 37,052 | 26,543 |
| 0.25 | 150 | 50 | 63,565 | 31,243 | 32,322 |
| 0.30 | 140 | 60 | 63,537 | 25,809 | 37,728 |
| 0.35 | 130 | 70 | 63,513 | 21,005 | 42,508 |
| 0.40 | 120 | 80 | 63,495 | 17,744 | 45,751 |
| 0.45 | 110 | 90 | 63,479 | 15,278 | 48,201 |
| 0.50 | 100 | 100 | 63,469 | 13,599 | 49,869 |
Accessory Loads and Air Conditioning
I analyze the impact of accessory loads because a city bus often operates with air conditioning. Two options are considered: an independent air-conditioning system driven by an electric motor and a non-independent system driven directly by the engine. If the air conditioner is independent, the engine can be shut down during stops, but the electric vehicle battery pack must supply the air-conditioning load. If the air conditioner is non-independent, the engine must remain idling during stops, but the electric vehicle battery pack is relieved of that load. Table 8 shows simulation results for different accessory powers and air-conditioning types. At low accessory load, the difference is small. At high accessory load, the independent system can discharge the electric vehicle battery pack too quickly and may force the engine to start for charging, which reduces the benefit of idle stop. The non-independent system keeps the bus within its SOC window and avoids excessive cycling of the electric vehicle battery pack. I therefore select a non-independent air-conditioning system and allow the engine to idle during short stops when the air conditioner is at full load.
| Accessory power (kW) | Air-conditioning type | Engine power (kW) | Motor power (kW) | Fuel consumption (L/100 km) | 0–50 km/h time (s) |
|---|---|---|---|---|---|
| 1.5 | Independent | 160 | 40 | 39.7 | 16.5 |
| 1.5 | Non-independent | 160 | 40 | 40.7 | 16.6 |
| 7.5 | Independent | 140 | 60 | 49.3 | 16.2 |
| 7.5 | Non-independent | 140 | 60 | 46.5 | 17.0 |
| 15.0 | Independent | 140 | 60 | — | — |
| 15.0 | Non-independent | 140 | 60 | 56.9 | 18.0 |
Hybridization Degree and Cost Model
The hybridization degree is the key optimization variable. I define it as
$$R = \frac{P_m}{P_m + P_e}$$
where \(P_m\) is the motor power and \(P_e\) is the engine power. The total power is fixed at 200 kW, so
$$P_m = 200R$$
and
$$P_e = 200(1-R)$$
I consider hybridization degrees from 0.20 to 0.50. This range covers a mild hybrid to a moderately strong parallel hybrid. Lower values reduce cost but limit regenerative braking and electric assist. Higher values increase fuel saving but require a larger motor, a larger electric vehicle battery pack, and a more expensive controller.
The incremental cost of the hybrid system includes the motor and controller, the electric vehicle battery pack, the transmission upgrade, and additional controllers and sensors. I use the following cost model:
$$C_m = A + B P_m$$
$$C_b = \frac{k_b P_m}{\eta_m}$$
$$C_e = k_e P_{e,reduced}$$
$$C_{trans} = C_{AMT} – C_{MT}$$
$$C_{ctrl} = C_{sensors} + C_{harness} + C_{supervisory}$$
The total incremental cost is
$$C_{inc} = C_m + C_b + C_e + C_{trans} + C_{ctrl}$$
With the coefficients used in my study, the motor cost is
$$C_m = 4300 + 70000R$$
the electric vehicle battery pack cost is
$$C_b = 210526R$$
and the engine cost reduction is
$$C_e = 90000R$$
After adding the transmission and control hardware, the total incremental cost becomes
$$C_{inc} = 6.43 + 19R \quad \text{(ten thousand yuan)}$$
Table 9 lists the cost components for representative hybridization degrees. The electric vehicle battery pack is a major contributor, especially at high hybridization degree. This is why the optimization must balance fuel saving against the cost of the electric vehicle battery pack and the motor.
| Hybridization degree | Motor power (kW) | Battery pack power (kW) | Motor cost (10k yuan) | Battery pack cost (10k yuan) | Total incremental cost (10k yuan) |
|---|---|---|---|---|---|
| 0.20 | 40 | 55 | 0.71 | 4.21 | 10.23 |
| 0.25 | 50 | 75 | 0.78 | 5.26 | 11.18 |
| 0.30 | 60 | 95 | 0.85 | 6.32 | 12.13 |
| 0.35 | 70 | 105 | 0.92 | 7.37 | 13.08 |
| 0.40 | 80 | 115 | 0.99 | 8.42 | 14.03 |
| 0.45 | 90 | 125 | 1.06 | 9.47 | 14.98 |
| 0.50 | 100 | 135 | 1.13 | 10.53 | 15.93 |
Performance Verification
I verify the dynamic performance of the hybrid bus at gross vehicle mass and full accessory load. Table 10 gives the simulation results for different hybridization degrees. All configurations satisfy the design targets: top speed above 80 km/h, gradeability above 4% at 50 km/h, and 0–50 km/h acceleration below 25 s. As the hybridization degree increases, acceleration improves because the motor provides additional torque. Gradeability also improves slightly. The electric vehicle battery pack must be able to supply the motor power required for these maneuvers, so the pack is sized by power rather than by energy.
| Hybridization degree | Top speed (km/h) | Maximum acceleration (m/s²) | Gradeability at 50 km/h (%) | 0–50 km/h time (s) |
|---|---|---|---|---|
| 0.20 | 81.1 | 2.1 | 4.5 | 18.4 |
| 0.25 | 81.1 | 2.3 | 4.5 | 18.2 |
| 0.30 | 81.1 | 2.5 | 4.5 | 18.0 |
| 0.35 | 81.1 | 2.7 | 4.5 | 17.7 |
| 0.40 | 81.1 | 2.8 | 4.6 | 17.5 |
| 0.45 | 81.1 | 3.0 | 4.6 | 17.3 |
| 0.50 | 81.1 | 3.2 | 4.6 | 17.2 |
Fuel Economy and Optimization
I simulate the bus over repeated ECE cycles for different hybridization degrees, vehicle masses, and accessory loads. The fuel saving is calculated relative to a conventional diesel bus with the same body and mission. Table 11 presents representative results. In general, fuel saving increases with hybridization degree, but the marginal benefit decreases. At high accessory load the benefit of hybridization is smaller because a large part of the engine output is used by the air conditioner, leaving less opportunity for the electric drive to improve engine operation. The electric vehicle battery pack also reaches its power limits more often, which reduces the amount of regenerative braking that can be accepted.
| Hybridization degree | Vehicle mass (kg) | Accessory load (kW) | Fuel consumption (L/100 km) | Fuel saving (L/100 km) | Fuel saving (%) |
|---|---|---|---|---|---|
| 0.20 | 18,000 | 1.5 | 40.0 | 8.00 | 16.6 |
| 0.30 | 18,000 | 1.5 | 37.8 | 10.13 | 21.0 |
| 0.40 | 18,000 | 1.5 | 36.1 | 11.70 | 24.3 |
| 0.50 | 18,000 | 1.5 | 34.6 | 12.99 | 26.9 |
| 0.20 | 18,000 | 7.5 | 47.1 | 7.01 | 12.9 |
| 0.30 | 18,000 | 7.5 | 45.1 | 8.90 | 16.4 |
| 0.40 | 18,000 | 7.5 | 43.7 | 10.14 | 18.7 |
| 0.50 | 18,000 | 7.5 | 43.4 | 10.14 | 18.7 |
| 0.20 | 18,000 | 15.0 | 59.5 | 5.21 | 8.0 |
| 0.30 | 18,000 | 15.0 | 58.1 | 6.49 | 10.0 |
| 0.40 | 18,000 | 15.0 | 56.4 | 7.96 | 12.3 |
| 0.50 | 18,000 | 15.0 | 58.3 | 5.47 | 8.4 |
| 0.20 | 15,000 | 1.5 | 34.1 | 8.51 | 19.9 |
| 0.30 | 15,000 | 1.5 | 32.4 | 10.14 | 23.7 |
| 0.40 | 15,000 | 1.5 | 31.3 | 11.20 | 26.2 |
| 0.50 | 15,000 | 1.5 | 29.9 | 12.47 | 29.1 |
| 0.20 | 12,000 | 1.5 | 29.3 | 8.91 | 23.2 |
| 0.30 | 12,000 | 1.5 | 27.3 | 10.89 | 28.4 |
| 0.40 | 12,000 | 1.5 | 26.6 | 11.54 | 30.1 |
| 0.50 | 12,000 | 1.5 | 25.9 | 12.20 | 31.8 |
To select the best hybridization degree, I define a cost-benefit index as the fuel saving divided by the incremental cost:
$$B = \frac{\Delta F}{C_{inc}}$$
where \(\Delta F\) is the fuel saving in L/100 km and \(C_{inc}\) is the incremental cost in ten thousand yuan. I calculate this index for each hybridization degree and each operating condition. Because the index does not vary monotonically with hybridization degree for all individual conditions, I use a weighted average based on expected operating probabilities. I estimate that the bus operates at gross mass, medium mass, and light mass with probabilities 0.35, 0.55, and 0.10, respectively. The air conditioner is off, at half load, and at full load with probabilities 0.60, 0.25, and 0.15, respectively. The weighted average fuel consumption of the conventional bus is
$$\bar F_{conv} = \sum_j w_j F_{conv,j}$$
and the weighted average fuel consumption of the hybrid bus is
$$\bar F_{hyb} = \sum_j w_j F_{hyb,j}$$
The weighted fuel saving is then
$$\Delta \bar F = \bar F_{conv} – \bar F_{hyb}$$
Table 12 shows the weighted results. The best cost-benefit index occurs at a hybridization degree of 0.30. This corresponds to an engine power of approximately 140 kW and a motor power of approximately 60 kW. The electric vehicle battery pack must supply about 60 kW continuously and peak power above 90 kW, which is consistent with a high-power lithium-ion pack.
| Hybridization degree | Weighted fuel consumption (L/100 km) | Weighted fuel saving (%) | Incremental cost (10k yuan) | Cost-benefit index ((L/100 km)/10k yuan) |
|---|---|---|---|---|
| 0.20 | 40.55 | 16.1 | 10.23 | 0.76 |
| 0.25 | 39.83 | 17.5 | 11.18 | 0.76 |
| 0.30 | 38.88 | 19.5 | 12.13 | 0.78 |
| 0.35 | 38.61 | 20.1 | 13.08 | 0.74 |
| 0.40 | 37.82 | 21.7 | 14.03 | 0.72 |
| 0.45 | 37.22 | 22.9 | 14.98 | 0.69 |
| 0.50 | 37.05 | 23.3 | 15.93 | 0.67 |
The optimized configuration is summarized in Table 13. The engine is a diesel engine rated at about 140 kW with a high-efficiency region between 1000 rpm and 2000 rpm. The traction motor is a permanent magnet synchronous motor rated at about 60 kW with a base speed near 1500 rpm. The electric vehicle battery pack is a high-power lithium-ion pack with a discharge rate above 10C and a charge rate above 4C. The transmission is a six-speed AMT with the ratios listed earlier, and the final drive ratio is 6.5. The air-conditioning system is non-independent.
| Subsystem | Selection |
|---|---|
| Engine | Diesel, 140 kW, high-efficiency region 1000–2000 rpm |
| Traction motor | Permanent magnet synchronous motor, 60 kW, base speed ≈ 1500 rpm |
| Electric vehicle battery pack | High-power lithium-ion, discharge > 10C, charge > 4C |
| Transmission | Six-speed AMT, ratios 6.98, 4.06, 2.74, 1.89, 1.31, 1.00 |
| Final drive | 6.5 |
| Architecture | Pre-transmission single-shaft parallel |
| Air conditioning | Non-independent, engine-driven |
Table 14 shows the final performance and economic summary. The optimized hybrid bus meets all dynamic targets: top speed 81.1 km/h, gradeability at 50 km/h of 4.5%, maximum acceleration 2.5 m/s², and 0–50 km/h acceleration time of 18.0 s. The fuel saving is 21.0% at full load with the air conditioner off, 23.7% at half load with the air conditioner off, and about 19.5% on a weighted basis. The incremental cost is about 12.13 × 10⁴ yuan. Using an average daily distance of 300 km, 300 operating days per year, a service life of 600,000 km, and a diesel price of 5 yuan per litre, the annual fuel cost saving is about 4.24 × 10⁴ yuan. Over the life of the bus the total fuel cost saving is about 28.26 × 10⁴ yuan, which exceeds the incremental cost of the hybrid system.
| Metric | Result |
|---|---|
| Top speed | 81.1 km/h |
| Gradeability at 50 km/h | 4.5% |
| Maximum acceleration | 2.5 m/s² |
| 0–50 km/h acceleration time | 18.0 s |
| Fuel saving, full load, AC off | 21.0% |
| Fuel saving, half load, AC off | 23.7% |
| Weighted fuel saving | 19.5% |
| Incremental hybrid cost | 12.13 × 10⁴ yuan |
| Annual fuel cost saving | 4.24 × 10⁴ yuan |
| Life-cycle fuel cost saving | 28.26 × 10⁴ yuan |
Discussion of Battery Pack Sizing and Thermal Behavior
The electric vehicle battery pack is sized primarily by power, not by energy. During acceleration the pack must supply the motor power, and during regenerative braking it must accept the charging power. The required pack power can be written as
$$P_{bat,req} = \max\left(\frac{P_{m,peak}}{\eta_{m,drive}\eta_{inv}}, P_{m,peak}\eta_{m,gen}\eta_{inv}\right)$$
where \(\eta_{m,drive}\) is the motor efficiency during motoring, \(\eta_{m,gen}\) is the motor efficiency during generating, and \(\eta_{inv}\) is the inverter efficiency. For the optimized 60 kW motor, the peak electrical power is approximately 90 kW. The electric vehicle battery pack is therefore specified with a continuous power of at least 60 kW and a peak power of at least 90 kW. The pack voltage is chosen to match the motor controller and inverter, and the cell count is determined by the voltage and power requirements.
Thermal management is important for the electric vehicle battery pack because high power operation increases internal losses. The heat generation rate is approximately
$$\dot Q_{bat} = I_{bat}^2 R_{bat}$$
and the temperature rise depends on the thermal resistance and heat capacity of the pack:
$$C_{th}\frac{dT_{bat}}{dt} = \dot Q_{bat} – \frac{T_{bat} – T_{amb}}{R_{th}}$$
I include a liquid cooling loop in the electric vehicle battery pack design to keep the cell temperature within a safe range. The pack management system monitors cell voltage and temperature, estimates SOC, and limits charge and discharge power when necessary. This is essential because the electric vehicle battery pack must survive many shallow cycles in city bus service.
Control Implementation Considerations
The supervisory controller coordinates the engine, motor, transmission, and electric vehicle battery pack. It receives the driver demand, vehicle speed, SOC, and component temperatures. It then determines the operating mode and torque commands. The main torque command is
$$T_{req} = T_e + T_m$$
and the engine torque is selected from a lookup table that represents the high-efficiency region:
$$T_e = T_{e,opt}(\omega_e, P_{req})$$
The motor torque is then
$$T_m = T_{req} – T_e$$
subject to the limits
$$T_{m,\min} \le T_m \le T_{m,\max}$$
and the battery power limit
$$P_{bat,\min} \le P_{bat} \le P_{bat,\max}$$
The transmission shifts according to a shift map that considers vehicle speed, pedal position, and motor speed. During shifting, the motor can synchronize the input shaft speed to reduce shift time and protect the synchronizers. This is especially important in a parallel hybrid bus because the input inertia is larger than in a conventional bus.
Comparison with Conventional Bus
The optimized hybrid bus improves fuel economy relative to a conventional diesel bus. The conventional bus with a 200 kW engine consumes about 48.3 L/100 km on a weighted basis in my simulation. The optimized hybrid bus consumes about 38.9 L/100 km, which is a reduction of about 19.5%. The electric vehicle battery pack contributes to this reduction by allowing regenerative braking, by permitting engine shutdown at idle when appropriate, and by enabling the engine to operate closer to its high-efficiency region. The electric vehicle battery pack also adds mass, which slightly increases rolling resistance and acceleration demand, but the benefit of energy recovery outweighs this penalty in city operation.
The emissions benefit is also significant. Although I did not optimize emissions directly, the reduced fuel consumption and the reduced operation of the engine at low-load and idle conditions lower carbon monoxide, hydrocarbons, nitrogen oxides, and particulate matter. The electric vehicle battery pack enables the engine to be shut down during stops when the air conditioner load is low, and it captures braking energy that would otherwise be dissipated as heat. In a city bus, this combination has a direct effect on local air quality.
Sensitivity to Battery Pack Cost and Life
The economic result depends strongly on the cost and life of the electric vehicle battery pack. I examined the sensitivity by varying the battery pack cost and the replacement interval. If the battery pack cost decreases, the optimal hybridization degree shifts slightly upward because the incremental cost of additional electric drive becomes smaller. If the battery pack life is shorter, the replacement cost increases and the optimal hybridization degree shifts downward. Table 15 shows the sensitivity results. The electric vehicle battery pack remains the major cost uncertainty in the hybrid bus business case.
| Battery pack cost multiplier | Optimal hybridization degree | Weighted fuel saving (%) | Life-cycle cost saving (10k yuan) |
|---|---|---|---|
| 0.8 | 0.35 | 20.1 | 32.4 |
| 1.0 | 0.30 | 19.5 | 28.3 |
| 1.2 | 0.30 | 19.5 | 23.1 |
| 1.4 | 0.25 | 17.5 | 18.0 |
Limitations and Further Work
I note several limitations in this study. First, the component models are quasi-static and do not capture fast transient effects in the electric drive or the engine. Second, the electric vehicle battery pack model uses a simplified equivalent circuit and does not include detailed electrochemical aging. Third, the optimization uses a weighted average of operating conditions rather than a full stochastic mission profile. Fourth, the control strategy is rule-based and does not guarantee global optimality. Future work should include dynamic programming or model predictive control to optimize the torque split, more detailed thermal and aging models for the electric vehicle battery pack, and hardware-in-the-loop validation of the supervisory controller.
Despite these limitations, the design procedure I present is practical and transparent. It links vehicle dynamics, component selection, energy management, simulation, and cost-benefit analysis in a single workflow. The electric vehicle battery pack is treated as a power source and sink whose limits shape the achievable fuel saving. The hybridization degree provides a single scalar that can be swept to explore the trade-off between fuel economy and cost. The result is a 60 kW motor, a 140 kW engine, and a high-power lithium-ion electric vehicle battery pack that together meet the performance targets and deliver a weighted fuel saving of about 19.5%.
Conclusion
I have developed and validated a parameter matching and optimization method for a parallel hybrid city bus. I selected a pre-transmission single-shaft architecture, a diesel engine, a permanent magnet synchronous motor, an automated mechanical transmission, and a high-power lithium-ion electric vehicle battery pack. I derived the power and transmission requirements from vehicle dynamics, formulated an electric-assist control strategy, and simulated the bus over the ECE urban cycle. I introduced the hybridization degree as the optimization variable and used the ratio of fuel saving to incremental cost as the selection criterion. The optimized configuration has a hybridization degree of 0.30, an engine power of about 140 kW, a motor power of about 60 kW, and an electric vehicle battery pack capable of supplying more than 90 kW peak power. The bus meets all dynamic targets and achieves a weighted fuel saving of about 19.5%. The incremental hybrid cost is recovered by fuel savings over the vehicle life. The electric vehicle battery pack is the key enabler of regenerative braking and engine load management, and its cost and durability remain the most important factors for future commercial success.
In my view, the most important engineering insight from this work is that the electric vehicle battery pack cannot be sized independently from the control strategy and the engine. Its power limit determines how much regenerative braking can be captured, how much electric assist can be delivered, and how often the engine must charge the pack. When the electric vehicle battery pack is matched properly with the motor and engine, the hybrid bus delivers a substantial fuel saving without compromising passenger capacity, gradeability, or acceleration. This integrated matching approach is therefore a reliable foundation for further development of hybrid city buses.