**1. Basic principles of power matching for hybrid electric buses**The principle of determining the total power requirements of a hybrid vehicle is similar to that of a traditional vehicle, which is determined according to the power requirements of the vehicle (maximum speed, acceleration performance, and climbing requirements), as shown in Figure 1. Usually, the maximum power of the power source is determined by the acceleration performance index, that is, as long as the acceleration index is satisfied, other power index will generally be satisfied. The more common design method is to directly deduce the total power of the power source from the acceleration index, that is, to use the vehicle dynamic balance theory to obtain the limit acceleration process of the vehicle, and to process the curve fitting equation to evaluate the power required by the power source.

The dynamic indicators of hybrid vehicles include maximum speed v_{max} (km/h), v_{o}-v_{t} (km/h) acceleration time T (s)And the maximum climbing requirement i_{max} (%).

First, determine the maximum power according to the maximum vehicle speed v_{max}:

In the formula, η_{t} is the powertrain efficiency of the vehicle, η_{t}=η_{cl}·η_{tc}·η_{gb}·η_{fd}. Among them, η_{cl} is the clutch efficiency, η_{tc} is the torque combiner efficiency, η_{gb} is the transmission efficiency, η_{fd} is the rear axle efficiency; f is the rolling resistance coefficient; C_{D} is the air resistance coefficient; A is the windward area.

Secondly, determine the maximum power according to the climbing performance:

In the formula, a_{max}=arctan(i_{max}/100); v_{i }is the climbing speed of the vehicle.

Finally, the total power of the power source is determined according to the acceleration performance. The starting acceleration process of the car can be expressed according to the formula, that is,

In the formula, x is the fitting coefficient, generally about 0.5; t_{m} (s) is the starting acceleration process time; v_{m} (km/h) is the final vehicle speed. Assuming that the whole vehicle is accelerated on a flat road, according to the dynamic equation of the whole vehicle acceleration process, the total power in the transient process is

In the formula, P_{all }(kW) is the total power in the acceleration process; P_{j} is the acceleration power; P_{f} is the rolling resistance power; P_{w} is the air resistance power; δ is the mass conversion factor.

At the end of the acceleration process of the whole vehicle, the power source outputs the maximum power, so the maximum power requirement during the acceleration process is P_{all_max}:

In the formula, dt(s) is the iterative step size of the design process, usually 0.1s can meet the accuracy requirements.

According to the maximum power of each working condition calculated by the above three dynamic indicators, the total power P_{total} of the power source must meet all the above design requirements, so:

**2. Total power matching of hybrid vehicles**For a hybrid vehicle, the vehicle mass, windward area, wind resistance coefficient and some parameters of the drive train can be determined by the parameters of the traditional vehicle, and the driving force of the vehicle can be obtained according to the following design requirements of the hybrid vehicle (taking a certain model as an example) The relationship between power requirements and dynamic performance indicators is shown in Figures 2 to 4.

(1) Maximum speed ≥ 70km/h.

(2) Maximum gradeability ≥ 30%

(3) The continuous speed is 40km/h (4% gradient).

(4) The acceleration time of 0~50km/h is less than or equal to 25s (full load)

(5) The acceleration time of 0~60km/h is less than or equal to 30s (to meet the national typical urban cycle conditions).

From the maximum speed v_{max}=70km/h, substitute into formula (1) to get P_{max1}=68kW, the climbing performance is v_{i}=40km/h, i=4% into formula (2) to get 105kw, and the required power for climbing is P_{max2}=105kw.

Figures 5 and 6 show the relationship between the driving power of a hybrid vehicle and the acceleration time and final vehicle speed. When using the above method to calculate the total power demand of the vehicle power source, it is also necessary to consider the actual shift delay time of the vehicle. Generally, the shift time of AMT transmission is 1.5 (expected value) ~ 2s.

Substitute the acceleration performance required by the index into Equation (5), and consider a certain acceleration reserve (about 20%) requirements, and calculate the total driving power of the hybrid vehicle P_{max3}=200kw. Therefore, comprehensively considering the above dynamic indicators ( Maximum speed, climbing and acceleration) requirements and the power reserve of the vehicle accessory system, the total power demand of the hybrid vehicle power source is determined as P_{total}=220kW≥max (P_{max1}, P_{max2}, P_{max3}).

**3. Matching of engine parameters for hybrid vehicles**1) Basic principles of engine parameter matching

According to the large moment of inertia of the engine itself, the torque response is relatively slow to be affected by fuel injection and combustion, and the response of the motor is relatively fast, so the engine should be allowed to provide steady-state power that changes slowly, and the motor should be allowed to provide the peak value of transient changes. power. The steady-state power includes the power requirement P

_{e1}for driving at the cruising speed, the power requirement P

_{e2}for climbing, the average power requirement P

_{e3}for the cycle condition, and the average power requirement P

_{e4}for the limit acceleration process.

Steady-state power is provided by the engine, that is, to overcome the air resistance, rolling resistance and hill resistance related to vehicle speed; transient power is provided by the motor, that is, to overcome the acceleration resistance of the vehicle, so. The vehicle dynamics equation can be divided into two terms, namely

In the formula, P_{v }(kW) is the steady-state power related to vehicle speed; P_{dv} (kW) is the transient power.

related to acceleration. Substitute the cruising speed v_{cruise} into Equation (7) to calculate P_{e1}. Reference pointed out that it is reasonable to take vcruise as the maximum speed v_{max} of the vehicle, while reference pointed out that v_{cruise} should be taken as the rated speed of the vehicle, that is, the average speed v_{aver} when the vehicle is often driven. That is to say, the value of v_{cruise} should satisfy

When the whole vehicle needs to climb a slope, especially for a long slope, in order to maintain the battery power, under normal circumstances, the motor assistance is not required. Therefore, the climbing power requirement P_{e2} can be calculated by substituting its climbing speed v_{i }and the climbing index i_{max} into formula (7).

The engine power selection also considers the average power P_{e3} of the working conditions. In order to meet the normal driving ability of the working condition, the power of the engine must be at least greater than the average power P_{e3} of the cycle condition:

In the formula, T_{cyc} is the time of the cycle condition.

P_{e1} and P_{e2} are the power required for hybrid vehicles in some special cases (long-time cruising and long-slope climbing require the engine to be driven alone), while P_{e3} is the average power required for driving based on design conditions. At the same time, the final determination of engine power also takes into account another situation – the limit acceleration process of the entire vehicle (such as overtaking, or when the driver presses the accelerator pedal to the maximum position to accelerate when the traffic conditions are good), which is a common process for vehicle acceleration. In this case, the engine is required to provide its average power, and the peak power is provided by the motor. Because this acceleration process is relatively short, the characteristics of the two power sources should be fully utilized. The engine provides the average power P_{e4} of the process, which is calculated as

In the formula, t_{max} (s) is the acceleration time from zero to the maximum speed v_{max} in the limit acceleration process: F_{t} is the driving force of the vehicle.

To sum up, in general, the engine power must at least meet the power requirements determined above, namely

2) Matching engine parameters

According to formula (7) and design requirements, the cruising speed of the vehicle (here, the maximum speed is taken) and the climbing index, the steady-state power is calculated as: P_{e1}=68kw, P_{e2}=105kw.

According to formula (12), the minimum engine power must be selected as 105kw, and a certain margin (about 20%) must be considered, and the engine power should be selected as 120kw.

**4. Main parameter matching of motor system**Compared with AC motors, permanent magnet (PM) motors have better overall performance, so the motor type is selected as PM motors. After the basic type of motor is selected, the key work of motor parameter matching is concentrated on the peak power of the motor, the maximum speed, and the base speed. The following mainly discusses the determination of motor peak power and the basic principles of high-efficiency area matching.

First, the motor needs to start and stop the engine. This requires the motor to have the ability to start the engine instantly, that is, the peak power of the motor is not less than the power P_{m1} (kW) of the engine to start the engine instantly.

In the formula, Je is the moment of inertia of the engine (kg·m²): t_{start} (s) is the time for the motor to start the engine: ω_{e} (rad/s) is the engine speed, ω_{idle} (rad/s) is the idle speed: T_{d} (Nm) is the engine friction torque. Secondly, on a good level road, when the vehicle starts running, the vehicle speed and load are low. To save fuel consumption, the engine is turned off, and the main motor drives the vehicle to achieve pure electric function. From formula (3) and formula (5), the step length is 0.1s, and the minimum power required in the pure electric drive mode of the motor can be calculated by formula (14):

Finally, when the driving resistance increases or the whole vehicle needs to accelerate quickly, the engine and the motor are jointly driven, and the motor assists at this time. According to the previous analysis, in the combined driving mode, the engine provides the power in the steady state during the acceleration process, and the motor provides the dynamic peak power. The peak power when the motor is assisted can be calculated by formula (8):

Based on the above requirements for the peak power of the motor in each working mode, the peak power of each motor can be calculated:

After the peak power and maximum speed of the motor are determined, the rated power and rated speed need to be determined. Since the rated power and rated speed of the motor directly affect the high-efficiency area of the motor, the distribution of the high-efficiency area of the motor has a great influence on the fuel economy of the hybrid vehicle. Therefore, determine the rated power and rated speed of the motor, so that the motor can work in the high-efficiency area to the maximum extent. The maximum efficiency point of the general motor occurs in the range of 0.7 to 1.0 times the rated power, as shown in Figure 7.

The maximum value of efficiency and power factor both occur near the rated load. The motor should match the load, and the motor should not work under light load for a long time. Generally, when the motor is under no load or light load, the efficiency is very low, and the efficiency increases with the load. Increase, near the rated load, the efficiency reaches the maximum, generally up to 75%~92% at full load.

Therefore, the main task of motor matching is to try to distribute the working points of the motor in the high-efficiency area to reduce the power loss of the motor. The high-efficiency area of the motor is determined by the rated speed and rated power of the motor. The maximum efficiency area of the motor is generally in the intersection area of the rated speed and rated power of the motor. When the peak power and maximum speed of the motor are determined, the rated speed and rated power of the motor are determined by the base ratio and overload coefficient of the motor. Adjust the base ratio of the motor and the overload coefficient of the motor. The high-efficiency area of the motor body can be adjusted up and down and left and right. , as shown in Figure 8.

In motor design and parameter matching, it is necessary to correctly match the peak power and maximum speed of the motor according to the actual working conditions and design requirements of the vehicle, and then determine the motor overload coefficient and base ratio based on the common operating conditions of the vehicle and the design and manufacturing conditions of the motor to obtain This determines the rated power and rated speed of the motor, and ensures that the common operating points of the motor are concentrated in the high-efficiency area to improve the efficiency of the motor in use

In the matching design of motor base speed and power parameters, the relationship formula between vehicle speed, motor power and base speed in literature can also be used:

although the functional formula cannot be directly solved, it can also be calculated by interpolation and other methods. Approximate range of results,

**5. In-depth hybrid electric bus battery parameter matching**1) Basic principles of battery parameter matching

The battery parameter matching generally needs to meet the system voltage level, power requirements, maximum charge and discharge current limitations and other factors. For vehicle batteries with pure electric driving function, it is also necessary to calculate the energy requirements of the battery.

2) The principle of battery parameter matching

Assuming a deep hybrid electric bus, the voltage level used is 336V nominal voltage level.

The power level of the battery is related to the motor, that is, the output power of the battery is greater than the sum of the power of the selected motor, and the battery has a certain limit on its charge and discharge current. Otherwise, excessive charge and discharge current will cause the battery temperature to rise and reduce the battery. service life. The charging and discharging current of the battery is related to the capacity, and the maximum current is generally limited to 3~5C (C is the capacity of the battery).

The battery power should match the motor power, and should satisfy the formula (18):

In the formula, P_{b} (kW) is the battery power: η_{m}, η_{c} (%) are the motor and inverter efficiencies, respectively. That is to say, the battery must ensure that it meets the power requirements of the motor to start the engine and the power requirements of the motor for rapid acceleration. Since the voltage level has been determined, the power of the battery is in turn related to the maximum charge and discharge current of the battery.

Substituting the voltage level and the power requirement of the motor to start the engine into equation (18), the maximum current of the battery can be calculated:

In the formula, I_{max} (A) is the maximum discharge current of the battery; V (V) is the maximum discharge voltage of the battery.

The capacity of the battery is related to its maximum charge and discharge capacity. The larger the battery capacity, the greater the charge and discharge power. When the voltage level is determined, its capacity is proportional to its maximum charge and discharge current, that is, the larger the capacity, the greater the allowable maximum charge and discharge current. Therefore, first determine its maximum charge and discharge current according to the above formula, and then determine the relationship between the battery capacity and the maximum charge and discharge current:

In the formula, C_{ci} is the battery capacity and its maximum charge-discharge coefficient. Generally, the value of nickel-metal hydride (NiMH) battery is 1/5~1/3, and the value of lithium-ion (Lion) battery varies greatly due to the different types of positive and negative materials. , but generally can take 1/8~1/5.

Substitute the total power and voltage level of the dual motors and the efficiency parameters of the motors and inverters, and the capacity of the battery can be determined to be 70-90Ah. Considering the minimum cost, the minimum value of 70Ah should be taken. Considering the pure electric function of the whole vehicle, it is necessary to To meet the 20km driving requirement, the determination of the battery capacity needs to be re-matched according to the working conditions.

When pure electric driving is required for 20km (at a constant speed of 20km/h), the required driving power is 7kW, plus the average power of electric accessories during pure electric driving is 3~5kW, the energy demand is 12kW·h, and at least the required battery capacity It is 40Ah. Judging from the selected battery parameters, it fully meets the requirements of pure electric driving range.