CN113978478B - Fuel cell automobile energy-saving driving method based on layering convex optimization - Google Patents
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Abstract
The invention discloses a fuel cell automobile energy-saving driving method based on layering convex optimization, which comprises the following steps: s1, establishing a fuel cell automobile power transmission system model and a traffic signal lamp model; s2, decoupling the energy-saving driving problem of the fuel cell automobile into a layered optimization problem, wherein the layered optimization problem comprises an upper-layer automobile speed planning problem and a lower-layer energy management problem; s3, the upper vehicle speed planning problem is bulged, wherein the bulge is performed on the constraint of the signal lamp and the cost function; s4, solving the vehicle speed planning problem after the convexity by using a convexity optimization solver to obtain an optimal vehicle speed; s5, the problem of lower-layer energy management is raised, including the power battery model and the fuel battery system model; s6, solving the raised energy management problem by using an alternate direction multiplier method according to the optimal vehicle speed output by the upper layer, and obtaining an optimal control variable. The invention can realize great improvement of calculation speed while maintaining similar energy consumption economy.
Description
Technical Field
The invention relates to the field of fuel cell automobile speed planning and energy management, in particular to a fuel cell automobile energy-saving driving method based on layering convex optimization.
Background
Through vehicle-to-infrastructure V2I communication, the network-connected automobile can acquire real-time signal lamp information on a road, and energy-saving driving is realized by optimizing a vehicle speed track. Energy efficient driving of fuel cell automobiles is a coupling problem involving vehicle speed planning and energy management. One solution to this problem is to perform joint optimization of vehicle speed and energy with the goal of minimizing the total energy consumption of the driveline, but the ultra-high computational burden results in joint optimization that is difficult to implement for real-time applications. Another solution is to completely decouple the vehicle motion planning and driveline control, and reduce the computational effort with hierarchical optimization, i.e. vehicle speed planning is first aimed at minimizing the power demand at the wheels, and then energy management is based on the vehicle speed.
In the prior art, energy-saving driving methods of fuel cell automobiles in signal lamp scenes are few, and it is difficult to achieve a balance between optimality and real-time.
Disclosure of Invention
The invention aims to make up the defects of the prior art and provides a fuel cell automobile energy-saving driving method based on layered convex optimization.
In order to achieve the above purpose, the present invention adopts the following technical scheme: a fuel cell automobile energy-saving driving method based on layering convex optimization comprises the following steps:
s1, establishing a fuel cell automobile power transmission system model and a traffic signal lamp model;
further, the fuel cell vehicle powertrain model described in step S1 includes a vehicle longitudinal dynamics model, a motor model, a fuel cell system model, a power cell model, and a system power balance model;
the traffic signal model comprises a signal position and signal phase timing model.
S2, decoupling the energy-saving driving problem of the fuel cell automobile into a layered optimization problem, wherein the layered optimization problem comprises an upper-layer automobile speed planning problem and a lower-layer energy management problem;
s3, the upper vehicle speed planning problem is bulged, wherein the bulge is performed on the constraint of the signal lamp and the cost function;
s4, solving the vehicle speed planning problem after the convexity by using a convexity optimization solver to obtain an optimal vehicle speed;
s5, the problem of lower-layer energy management is raised, including the power battery model and the fuel battery system model;
s6, solving the raised energy management problem by using an alternate direction multiplier method according to the optimal vehicle speed output by the upper layer, and obtaining an optimal control variable.
Further, the upper vehicle speed planning problem and the lower energy management problem described in step S2 are specifically as follows:
the state variables of the upper vehicle speed planning problem are vehicle position and speed, the control variables are vehicle acceleration, the optimization target is that the total wheel end required power is minimum, and the constraint conditions comprise state variable constraint, control variable constraint and signal lamp constraint;
the state variable of the lower-layer energy management problem is the state of charge of the power battery, the control variable is the chemical power of the power battery, the optimization target is the minimum total hydrogen consumption, and the constraint conditions comprise state variable constraint, control variable constraint and net power constraint of the fuel cell system.
Further, the signal constraint and cost function are raised in step S3, which is specifically as follows:
obtaining an upper limit of a vehicle position track by using an intelligent driver model, determining a green light window through which the vehicle passes, wherein a lower limit of the vehicle position track needs to pass through a terminal point of the selected green light window and is ensured not to exceed the upper limit of the position track, and the actual arrival time of the vehicle is the average value of terminal time of the upper limit and the lower limit of the position track, so that the non-convex signal lamp constraint can be converted into a linear time-varying vehicle position track constraint;
and converting a cost function which is originally a cubic function of the vehicle speed into a quadratic function of the vehicle speed by utilizing the average vehicle speed to approximate the real-time vehicle speed.
Further, the convex optimization solver described in step S4 may be one of Gurobi, mosek, SDPT and SeDuMi in the CVX toolkit.
Further, the power battery model and the fuel battery system model are embossed as described in step S5, specifically as follows:
taking the internal resistance and the open-circuit voltage of the power battery model as constants, so that the output power of the power battery is converted into a quadratic function of the control variable; fitting the hydrogen consumption rate of the fuel cell system to a quadratic function of the power required by the input end of the motor; thereby representing the objective function as a convex function of the control variable.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the invention, the upper vehicle speed planning problem including signal lamp constraint is raised, so that quick solution is realized;
(2) Compared with a layered dynamic planning method, the energy-saving driving method based on layered convex optimization can achieve great improvement of calculation speed while maintaining similar energy consumption economy.
Drawings
FIG. 1 is a flow chart of a fuel cell vehicle energy saving driving optimization method according to the present invention;
fig. 2 is a schematic diagram of signal lamp constraint convexity in the present invention.
Detailed Description
The following detailed description of the embodiments of the invention refers to the accompanying drawings, which are not intended to limit the scope of the invention.
As shown in fig. 1, a fuel cell automobile energy-saving driving method based on layering convex optimization comprises the following steps:
s1, establishing a fuel cell automobile power transmission system model and a traffic signal lamp model
The fuel cell automobile power transmission system model comprises a vehicle longitudinal dynamics model, a motor model, a fuel cell system model, a power cell model and a system power balance model, and the traffic signal lamp model comprises a signal lamp position and signal phase timing model.
S11, building a longitudinal dynamics model of the vehicle
Vehicle longitudinal dynamics, as shown in equation (1):
wherein s, v, M, f r And A represents the position, speed, mass, rolling resistance coefficient and frontal area of the vehicle, respectively; acceleration of vehicleF drv And F brk Respectively representing the mechanical force of a motor and the braking force of a brake pad at the wheel; g represents gravitational acceleration; θ represents the road gradient; ρ and C D Respectively, the air density and the air resistance coefficient.
Demand power P at the wheels dmd As shown in formula (2):
P dmd ＝(F drv +F brk )v (2)
s12, building a motor model
Motor speed omega mot And torque T mot As shown in formulas (3) and (4):
wherein r is whl Is the tire rolling radius, i FD And eta FD The gear ratio and efficiency of the final drive, respectively.
Mechanical power P of motor mot,m And electric power P mot,e As shown in formulas (5) and (6):
wherein eta mot Representation and ω mot And T mot Regarding motor efficiency, sgn is a sign function.
S13, establishing a fuel cell system model
Hydrogen consumption rateCan be expressed as the net power P of the fuel cell system fcs As shown in equation (7):
fuel cell system efficiency eta fcs As shown in formula (8):
wherein LHV represents the lower heating value of hydrogen.
S14, building a power battery model
The equivalent circuit model of the power battery is shown as a formula (9):
wherein V is bat ，V OC ，I bat ，R 0 ，P bat And P OC Respectively representing power cell voltage, open circuit voltage, current, internal resistance, output power and chemical power. V (V) OC And R is 0 Are a function of the state of charge SOC of the power battery.
Power battery current I bat As shown in formula (10):
battery system dynamics, as shown in equation (11):
wherein Q is bat Representing the battery capacity.
S15, establishing a system power balance model
A power balance model, as shown in equation (12):
wherein eta DC/AC And eta DC/DC Representing the efficiency of the DC/AC inverter and the DC/DC converter, respectively.
S16, building a traffic signal lamp model
At the total length s f N traffic signal lamp intersections are distributed on the road, and the position of the ith signal lamp is S i ∈[0,s f ]I.epsilon. {1,2,3 …, N }. For the ith signal lamp, the red and green durations thereof are respectivelyAnd->The time in the signal period is a function of the travel time t, as shown in equation (13):
wherein the method comprises the steps ofIs a signal lamp period>Is->Is the initial value of (a). />Is defined at the start of the red light.
The running time of the vehicle passing through the signal lamp is recorded asTo avoid running red light, the vehicle needs to meet the signal light constraint as shown in equation (14):
s2, decoupling the energy-saving driving problem of the fuel cell automobile into a layered optimization problem, wherein the layered optimization problem comprises an upper-layer automobile speed planning problem and a lower-layer energy management problem
S21, constructing an upper vehicle speed planning problem
The state variables of the upper vehicle speed planning problem are vehicle position and speed, the control variables are vehicle acceleration, the optimization target is that the total wheel end required power is minimum, and the constraint conditions comprise state variable constraint, control variable constraint and signal lamp constraint, as shown in a formula (15):
wherein t is f Is the desired arrival time.
S22, construction of lower energy management problem
The state variable of the lower-layer energy management problem is the state of charge of the power battery, the control variable is the chemical power of the power battery, the optimization target is the minimum total hydrogen consumption, and the constraint conditions comprise state variable constraint, control variable constraint and net power constraint of the fuel cell system, and the upper-layer vehicle speed planning problem is as shown in a formula (16):
s3, the upper vehicle speed planning problem is highlighted, including the signal lamp constraint and the cost function are highlighted
As shown in fig. 2, the upper limit of the vehicle position track is obtained by using the intelligent driver model, a green light window through which the vehicle passes is determined, the lower limit of the vehicle position track needs to pass through the end point of the selected green light window and is ensured not to exceed the upper limit of the position track, and the actual arrival time of the vehicle is the average value of the terminal time of the upper limit and the lower limit of the position track, so that the non-convex signal lamp constraint can be converted into the linear time-varying vehicle position track constraint. An intelligent driver model, as shown in equation (17):
wherein a is IDM Acceleration of the intelligent driver model, deltav is the speed difference with the front vehicle, deltax is the distance difference with the front vehicle, S HD For the visual range of the intelligent driver model, P tss Indicating the state of the signal lamp, P tss =0 represents green light or no signal light visible, P tss =1 represents red light, s * (v, deltav) is the desired distance to the lead vehicle as shown in equation (18)
Wherein s is 0 T is the distance from the head to the tail of the front car hw For a desired time interval.
Vehicle position railTrace upper limit s upper As shown in formula (19):
wherein t is f,upper The arrival time at the upper limit of the position trajectory.
Lower limit s of vehicle position track lower The end points of the selected green light windows can be sequentially connected in the distance-time diagram.
Finally, linear time-varying vehicle position track constraints are obtained, as shown in formula (20):
s lower (t)≤s(t)≤s upper (t) (20)
the desired arrival time is shown in equation (21):
wherein t is f,lower The arrival time at the lower limit of the position trajectory.
The average vehicle speed is utilized to approximate the real-time vehicle speed, and the cost function which is originally a cubic function of the vehicle speed is converted into a quadratic function of the vehicle speed, as shown in a formula (22):
wherein,
s4, solving the vehicle speed planning problem after the convexity by utilizing a convexity optimization solver to obtain the optimal vehicle speed
The convex optimization solver may be one of Gurobi, mosek, SDPT and SeDuMi in the CVX toolkit. The Mosek solver is adopted to solve the raised vehicle speed planning problem, and an optimal vehicle speed track is obtained and is used as the input of the lower energy management problem.
S5, the problem of lower energy management is raised, including the power battery model and the fuel battery system model
Regarding the internal resistance and the open-circuit voltage of the power battery model as constants, thereby converting the power battery output power into a quadratic function of the control variables, as shown in formula (23):
fitting the hydrogen consumption rate of the fuel cell system to a quadratic function of the power demand at the motor input as shown in equation (24):
thereby representing the objective function as a convex function of the control variable as shown in equation (25):
s6, solving the raised energy management problem by using an alternate direction multiplier method according to the optimal vehicle speed output by the upper layer to obtain an optimal control variable
Introducing a dual variable ζ, reconstructing and discretizing the energy management problem, as shown in equation (26):
wherein, phi is the 1 vector of N-1 columns, and psi is the lower triangle 1 matrix of (N-1) x (N-1).
Solving according to the iteration flow of the alternating direction multiplier method to obtain the optimal control variableAnd state variable SOC * Then the optimal fuel is obtainedBattery system net power->
While the foregoing is directed to the preferred embodiments of the present invention, it is to be understood that the scope of the invention is not limited to such specific statements and examples. Modifications and variations within the spirit of the invention will be apparent to those of ordinary skill in the art from the teachings herein and are intended to be within the scope of the appended claims.
Claims (5)
1. The fuel cell automobile energy-saving driving method based on layering convex optimization is characterized by comprising the following steps of:
s1, establishing a fuel cell automobile power transmission system model and a traffic signal lamp model;
s2, decoupling the energy-saving driving problem of the fuel cell automobile into a layered optimization problem, wherein the layered optimization problem comprises an upper-layer automobile speed planning problem and a lower-layer energy management problem;
s3, the upper vehicle speed planning problem is bulged, wherein the bulge is performed on the constraint of the signal lamp and the cost function;
obtaining an upper limit of a vehicle position track by using an intelligent driver model, determining a green light window through which the vehicle passes, wherein a lower limit of the vehicle position track needs to pass through a terminal point of the selected green light window and is ensured not to exceed the upper limit of the position track, and the actual arrival time of the vehicle is the average value of terminal time of the upper limit and the lower limit of the position track, so that the non-convex signal lamp constraint can be converted into a linear time-varying vehicle position track constraint; an intelligent driver model, as shown in equation (17):
wherein a is IDM Acceleration of the intelligent driver model, deltav is the speed difference with the front vehicle, deltax is the distance difference with the front vehicle, S HD For the visual range of the intelligent driver model, P tss Indicating the state of the signal lamp, P tss =0 represents green light or no signal light visible，P tss =1 represents red light, s * (v, deltav) is the desired distance to the lead vehicle as shown in equation (18)
Wherein s is 0 T is the distance from the head to the tail of the front car hw For a desired time interval;
vehicle position track upper limit s upper As shown in formula (19):
wherein t is f,upper The arrival time at the upper limit of the location trajectory;
lower limit s of vehicle position track lower The end points of the selected green light windows can be sequentially connected in the distance-time diagram;
finally, linear time-varying vehicle position track constraints are obtained, as shown in formula (20):
s lower (t)≤s(t)≤s upper (t)(20)
the desired arrival time is shown in equation (21):
wherein t is f,lower The arrival time for the lower limit of the position track;
the average vehicle speed is utilized to approximate the real-time vehicle speed, and the cost function which is originally a cubic function of the vehicle speed is converted into a quadratic function of the vehicle speed, as shown in a formula (22):
wherein,
s4, solving the vehicle speed planning problem after the convexity by using a convexity optimization solver to obtain an optimal vehicle speed;
s5, the problem of lower-layer energy management is raised, wherein the problem comprises the raising of a power battery model and a fuel battery system model in a fuel battery automobile power transmission system model;
s6, solving the raised energy management problem by using an alternate direction multiplier method according to the optimal vehicle speed output by the upper layer, and obtaining an optimal control variable.
2. The fuel cell vehicle energy saving driving method based on layering convex optimization as claimed in claim 1, wherein: the fuel cell automobile power transmission system model in the step S1 also comprises a vehicle longitudinal dynamics model, a motor model and a system power balance model; the traffic signal model comprises a signal position and signal phase timing model.
3. The fuel cell vehicle energy saving driving method based on layering convex optimization as claimed in claim 1, wherein: the upper vehicle speed planning problem and the lower energy management problem described in step S2 are specifically as follows:
the state variables of the upper vehicle speed planning problem are vehicle position and speed, the control variables are vehicle acceleration, the optimization target is that the total wheel end required power is minimum, and the constraint conditions comprise state variable constraint, control variable constraint and signal lamp constraint;
the state variable of the lower-layer energy management problem is the state of charge of the power battery, the control variable is the chemical power of the power battery, the optimization target is the minimum total hydrogen consumption, and the constraint conditions comprise state variable constraint, control variable constraint and net power constraint of the fuel cell system.
4. The fuel cell vehicle energy saving driving method based on layering convex optimization as claimed in claim 1, wherein: the convex optimization solver described in step S4 is one of Gurobi, mosek, SDPT and SeDuMi in the CVX toolkit.
5. The fuel cell vehicle energy saving driving method based on layering convex optimization as claimed in claim 1, wherein: the power cell model and the fuel cell system model in the fuel cell automobile power train model are subjected to the convexity in step S5, specifically as follows:
taking the internal resistance and the open-circuit voltage of the power battery model as constants, so that the output power of the power battery is converted into a quadratic function of the control variable; fitting the hydrogen consumption rate of the fuel cell system to a quadratic function of the power required by the input end of the motor; thereby representing the objective function as a convex function of the control variable.
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