Since a hybrid vehicle is powered by two power sources, the engine and the
battery, its design is much more complex than that of a traditional vehicle
powered by a single power source (engine). At present, the method of experience
and trial calculation is mainly used, referring to the selection mode of
traditional cars, determining the power level of each component and the range of
related parameters through some empirical formulas, then selecting parts that
meet the conditions, and then verifying the selected parameters. Or adjustment,
the parts selected in this way have many limitations. Although they can meet the
performance of the car, the matching between the parts and each other is not
optimal, and the process requires repeated verification and adjustment many
times.
Foreign research mainly focuses on energy management and distribution
strategies, and there are few documents specifically discussing matching
optimization. Among them, the ADV IOR software has a matching function. This
software mainly adjusts and calculates existing component parameters, and is
targeted at specific operating conditions and vehicle types. This paper takes
the series fuel cell hybrid vehicle as the research object. Through the analysis
and transformation of the research object, the power source selection and
matching problem of the series hybrid vehicle is transformed into a mathematical
optimization problem, and different energy management strategies are used to
solve the problem. Considering the performance of parts and components, use
optimization algorithms to solve them, and conduct analysis and research based
on the results obtained.
1 Introduction to optimized configuration
The configuration of a series fuel cell hybrid vehicle is shown in Figure
1. The entire vehicle solution consists of a fuel cell engine, DC/DC, power
battery, motor and transmission. The solid lines in Figure 1 are mechanical
connections and the dotted lines are electrical connections. The fuel cell
engine generates electricity, and after DC/DC conversion, it is electrically
coupled with the battery to provide energy to the motor, which drives the
transmission to drive the entire vehicle.
Figure 2 is a schematic diagram of the energy input and output of
components. In order to reduce optimization parameters and processing needs, the
fuel cell engine and DC/DC are considered as a whole, represented by PS in the
figure. The control unit is responsible for the energy management strategy,
determining the working status and output power of the PS and battery stack, and
the working status of the motor.
For the fuel cell vehicle studied, its vehicle parameters are shown in
Table 1, and its power performance indicators are shown in Table 2.
2 Transformation and processing of optimization problems
The above optimization problem can be described as: for the specified
vehicle structural parameters, dynamic indicators and selected working
conditions, select powertrain components with different power levels and
characteristics so that the vehicle can fuel the vehicle while meeting the
dynamic indicators. The best economy. That is, under the constraints of dynamic
indicators, find the optimal components and their performance parameters to
achieve the best fuel economy of the vehicle.
2.1 Determination of optimization function
The objective function is cycle fuel economy, which consists of two parts:
hydrogen consumption of the fuel cell engine and hydrogen consumption converted
from changes in battery SOC, namely
In the formula, b is the engine fuel consumption rate, U and I are the
voltage and current of the battery respectively, Peng is the output power of the
fuel cell engine, Qfuel is the low calorific value of the fuel, Xeng, Xbat and
Xmot are the power levels of the engine, battery and motor respectively. T is
the total time of cycle conditions.
Since all the mechanical energy of the series hybrid vehicle is output by
the motor, the selection of the motor is based on the premise that it satisfies
the dynamic index of the entire vehicle. Based on this, the maximum power of the
motor is obtained, and the distribution of the operating point in the
high-efficiency area of the motor is determined by the corresponding The cyclic
working conditions are converted, and finally the motor power that meets the
requirements, as well as performance indicators such as efficiency maps are
obtained. In this way, the parameters of the optimization problem can be
reduced, and the above optimization objective function can be transformed into a
selection problem of battery and fuel cell power levels. The total power demand
can be determined by equation (2)
In the formula, Pneed is the total power demand of the vehicle, m is the
mass of the vehicle, CD and A are the air resistance coefficient and windward
area of the vehicle respectively, v is the vehicle speed, and D is the rotation
mass conversion coefficient.
At this time, the engine power demand and battery power demand are
In the formula, V (SOC, Pneed) is the power distribution coefficient, which
is determined by the control strategy.
2.2 Transformation of constraints
The constraints are power indicators, that is, the power components can
meet the requirements of the maximum vehicle speed, maximum climbing angle and
acceleration time, as shown in Table 2, which are converted into corresponding
constraints on the power of the fuel cell engine and battery, that is,
In the formula, Pneed (vmax) is the power demand at the highest speed, Pi
(v) is the power demand at vehicle speed v and slope i, Geff and Gmot are the
mechanical transmission efficiency and motor efficiency respectively, Tmot is
the output torque of the motor, i0 , ig are the main reducer and transmission
speed ratios respectively, r is the wheel radius, Pfc_max and Pbat_max are the
maximum output power of the fuel cell and battery respectively.
For the maximum vehicle speed, the power required to reach the maximum
vehicle speed is obtained from equation (2), that is
The power requirement of the vehicle can be obtained from the maximum
gradeability requirement as
The constraint of the acceleration time is the acceleration phase. The
motor torque Tmot(t) and the corresponding vehicle speed v(t) at each moment
should satisfy
In the formula, fw and ff are the wind resistance and rolling resistance
respectively at the current vehicle speed, and vset is the terminal speed given
in the acceleration time indicator.
2.3 Control strategy
For different control strategies, it means that the vehicle has different
performance and requirements for the corresponding parts. The article gives two
typical energy management strategies used by series hybrid vehicles, namely
switching control strategy and power following control strategy. Control
Strategy. By comparing and analyzing the optimization results of different
control strategies and control parameters, the results of component selection
and optimization suitable for different design requirements are obtained through
comprehensive consideration and analysis.
(1) Switching control strategy The engine switch is determined by the upper
and lower limits of the battery SOC. When the engine is working, it works at the
optimal fuel economy point. This control strategy mainly relies on the battery
to follow and respond to the power demand of the vehicle.
(2) Power following control strategy The engine starts and stops based on
power demand and battery SOC. The engine works on the optimal fuel economy curve
and tries to maintain the battery SOC at the set value to ensure driving
range.
The control strategy is mainly used to allocate power according to working
conditions, but it is difficult to express it in mathematical expressions. This
paper uses model modeling to implement the control strategy.
2.4 Introduction to optimization algorithms
For the above optimization problems, engineering optimization algorithms
can be used to deal with them, and engineering methods can be used to deal with
the convergence and boundary conditions in the optimization problems, and
finally obtain better optimization results.
For the optimization problem described above, two optimization algorithms,
sequential quadratic programming and partition matrix method, are used in this
paper to optimize and solve the problem. The mathematical model obtained by
converting the above engineering problem and the control strategy represented by
the modeling are substituted into the two optimization algorithms, the cut-off
conditions are set, and then the following results are obtained through
iterative calculations. The two optimization algorithms are as follows.
(1) Sequential quadratic optimization algorithm (SQP)
For a given initial value, a quadratic programming sub-problem is
constructed. By solving the quadratic programming sub-problem, the search
direction and step size are obtained, and the solution is iteratively optimized.
The advantage of this algorithm is that it is mature and very effective for
smoothing problems, but it requires the optimization function to be
differentiable, and at the same time it obtains a local optimal solution.
(2) Division matrix method (DIRECT)
For the optimization interval, first normalize and calculate the function
value of the center point, set the number of iterations, determine the optimal
matrix set, select a rectangle in the set to divide and calculate its center
point value, until the number of iterations is reached or the optimization
interval iteration is completed. This algorithm does not require the
optimization function to be differentiable, can obtain global optimization, does
not require the selection of initial values, and does not require control
parameters during the optimization process. However, this algorithm does not
have a convergence criterion to judge whether the optimization has converged, so
it can only optimize a small number of variables.
3 Optimization result analysis
Based on typical bus urban working conditions, the average output power
based on the working conditions can be obtained. Converted to the fuel cell
engine, the power is 42kW. That is, the optimal operating point of the fuel cell
engine is located near 42kW. From this comparison, the power of the fuel cell
can be obtained The level is around 52kW. In order to meet the requirements of
working conditions, the instantaneous power the battery needs to provide reaches
150kW. For a large-capacity battery of 80A#h, the voltage level required for 3C
discharge reaches 625V, which requires 52 cells and 10 cells. Only a battery
module composed of batteries can meet the requirements, and the results obtained
cannot be used.
In view of the above optimization problem, a model of the complete vehicle,
components and control strategy was established, and two optimization algorithms
were used for optimization simulation. The final results are shown in Table
3.
3.1 Comparative analysis of control strategies
The switch-type control strategy is generally used in vehicles with poor
dynamic response of fuel cell engines, batteries as the main power source, and
large hybrids. Therefore, relatively large batteries are generally used. For
this control strategy, when the battery SOC is between 013 and 018, it means
that the battery needs to provide power in a wide range. Under this control
method, the fuel cell rarely participates in the work, and the battery provides
power under most working conditions.
When the battery SOC is between 014 and 016, due to the small SOC control
range, that is, the battery's working range is relatively small, the number of
battery modules finally optimized is smaller than the control strategy for the
battery SOC between 013 and 018. When the battery SOC is between 013 and 018, it
is mainly powered by the battery. The battery capacity is large, the charge and
discharge current is small, the efficiency is high, and the power consumption is
replenished at the highest efficiency point of the fuel cell, so the economy is
good; while the battery SOC is Between 014 and 016, the battery capacity is
small, the charge and discharge current is large, and the efficiency is low.
When the engine starts and stops, due to the limitation of the power change
rate, more fuel is consumed, so the economy is better than the battery SOC
between 013 and 018. difference between.
The power following control strategy is suitable for vehicles where the
fuel cell engine has good dynamic response, uses the fuel cell engine as the
main power source, and is a moderate or mild hybrid vehicle. This control
strategy requires the fuel cell to provide most of the driving energy. As can be
seen from Figures 3 and 4, the fuel cell provides most of the energy. The
battery is used to make up for the insufficient power demand of the fuel cell.
Its power output is basically 20kW. below, and the battery SOC is basically
maintained around 015.
Due to the dynamic changes of the fuel cell engine, its operating point is
not the optimal economic point. However, because the fuel cell has high
efficiency in a wide range, the fuel economy obtained by the power following
control strategy is better than that of the switching control strategy. Battery
SOC between 014 and 016 has better economic efficiency, but it is worse than
battery SOC between 013 and 018.
Since the average power demand under working conditions is about 50kW, in
order to meet the requirements of dynamic indicators, the required power is
about 200kW. Although the two different control strategies lead to different
main power output components based on working conditions, due to the limitations
of dynamic indicators , the final result is that the power level of the
components is higher.
3.2 Comparative analysis of different optimization algorithms
Comparing the two optimization algorithms, we can see that for the
switching control strategy, in the battery SOC range of 013~018, since most of
the working conditions are mainly operated by the battery, the optimization
results obtained are the same, while when the battery SOC is In the interval of
014~016, the optimization results obtained by the two algorithms are quite
different, but the fuel economy indicators are basically the same. This is
mainly because the end conditions used by the two optimization algorithms are
different, resulting in different final optimal results. See Figure 5. ,Figure
6.
It can be seen from Figures 5 and 6 that during the entire cycle, the fuel
cell engine is initially turned off, and most of the driving energy is provided
by the battery. When using a smaller battery (see Figure 5), the fuel cell
engine mainly starts when the battery SOC is lower than the set value or the
power demand is large in the last period of the working condition. The fuel cell
works for a long time. At this stage, the fuel cell is used to provide power and
Charging the battery is beneficial to improving system efficiency, but the
discharge current of the battery is large, which is detrimental to the life of
the battery, and the efficiency of the battery is low. When a larger battery is
used (see Figure 6), the discharge current of the battery is reduced, which is
beneficial to the life of the battery and the efficiency of charging and
discharging. The fuel cell is mainly used to maintain the SOC value of the
battery.
4 Conclusion
(1) Different energy management strategies correspond to different
selection requirements for power components. When selecting, the impact of
energy management strategies on component performance needs to be fully
considered.
(2) For the same control strategy, there may be multiple sets of
optimization solutions, so it is necessary to consider which combination of
components to use based on the actual component performance.
(3) The SQP algorithm requires a suitable initial value to be given in
advance, but the DIRECT algorithm does not. However, since the DIRECT algorithm
does not have a convergence criterion, the optimization solution time is longer
than that of the SQP algorithm, but both algorithms can solve the problem.
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