CN113492727B - Fuel cell hybrid power system control method based on EMPC - Google Patents

Fuel cell hybrid power system control method based on EMPC Download PDF

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CN113492727B
CN113492727B CN202110959160.9A CN202110959160A CN113492727B CN 113492727 B CN113492727 B CN 113492727B CN 202110959160 A CN202110959160 A CN 202110959160A CN 113492727 B CN113492727 B CN 113492727B
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empc
fuel cell
predictive control
lithium battery
control system
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CN113492727A (en
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李�昊
宾洋
金庭安
岳肖
胡杰
徐泽俊
周春荣
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Chongqing Jinhuanghou New Energy Automobile Manufacturing Co ltd
Daojian Youxing Chongqing Technology Co ltd
Chongqing Vocational College of Transportation
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Daojian Youxing Chongqing Technology Co ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L58/00—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles
    • B60L58/40—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for controlling a combination of batteries and fuel cells
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
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    • B60L2210/10—DC to DC converters
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    • Y02T10/60—Other road transportation technologies with climate change mitigation effect
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Abstract

The invention discloses a fuel cell hybrid power system control method based on EMPC, which comprises the steps of establishing a fuel cell hybrid power system based on a PEMFC system and a lithium battery, and modeling a fuel cell hybrid power system model; constructing an EMPC (empirical mode Power controller) predictive control system and setting an objective function and constraint conditions of the EMPC predictive control system based on the fuel cell hybrid power system model; according to the EMPC predictive control system, the objective function and the constraint conditions thereof, a multi-parameter secondary planning problem is constructed, the multi-parameter secondary planning problem is solved, the optimal input variable of the EMPC predictive control system is obtained, the power distribution of the PEMFC system and the lithium battery is optimized, the control of the fuel cell hybrid power system is realized, the calculation time consumption of a control strategy can be obviously improved, and the requirements of the work and the control of the fuel cell in a laboratory simulation real scene can be well met.

Description

Fuel cell hybrid power system control method based on EMPC
Technical Field
The invention relates to the technical field of fuel cell hybrid power system control, and particularly discloses a fuel cell hybrid power system control method based on EMPC.
Background
In order to reduce the dependence on fossil fuels, hybrid technologies and electric vehicles in the transportation field have received a high degree of attention in recent years. The low efficiency and high environmental pollution of internal combustion engines have led automobile manufacturers to become increasingly concerned with electric powertrains.
Due to insufficient output characteristics of the fuel cell, when the load demand changes sharply, if the power demand is provided only by the fuel cell, the performance and life of the fuel cell will be adversely affected. To avoid this, a multi-power hybrid system may be employed, and spikes may be eliminated so that the system can obtain a smooth output voltage. At present, a hybrid power mode composed of a fuel cell and an auxiliary energy storage system has a dual energy source structure composed of a fuel cell and a power cell or a super capacitor, and a triple energy source structure composed of a fuel cell, a power cell and a super capacitor. Due to the diversity and complexity of their structures, the design of control strategies becomes especially important.
As the name suggests, a fuel cell hybrid power system has a plurality of energy sources, so how to reasonably realize power distribution during the operation of the system is a key problem, and because the fuel cell hybrid power system has the problems of complex structure, slow response and the like, the existing control method cannot well enable each energy source to exert respective advantages, so that the problems of unreasonable power distribution, low efficiency, high energy loss and the like of the system are caused.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a control method for a fuel cell hybrid system based on an EMPC, so as to solve the problems of unreasonable power distribution, low efficiency, high energy loss, etc. in the fuel cell hybrid system in the prior art, because each energy source cannot exert its own advantages.
In order to achieve the purpose, the invention provides the following technical scheme:
an EMPC-based fuel cell hybrid power system control method comprises the following steps:
s1: establishing a fuel cell hybrid power system based on a PEMFC system and a lithium battery, and modeling a fuel cell hybrid power system model;
s2: constructing an EMPC predictive control system based on the fuel cell hybrid power system model and setting an objective function and constraint conditions of the EMPC predictive control system;
s3: and constructing a multi-parameter secondary planning problem according to the EMPC predictive control system, the objective function and the constraint condition thereof, solving the multi-parameter secondary planning problem to obtain the optimal input variable of the EMPC predictive control system, optimizing the power distribution of the PEMFC system and the lithium battery, and realizing the control of the fuel cell hybrid power system.
Further, in step S1, the fuel cell hybrid system includes a PEMFC system, a DC/DC converter, a lithium battery, and a load, the PEMFC system is connected to the power bus via the DC/DC converter and then connected to the load, the PEMFC system is configured to transmit electric energy generated by the electrochemical reaction to the DC/DC converter to drive the load, and the DC/DC converter is configured to adjust an output current of the PEMFC system to implement power distribution between the PEMFC system and the lithium battery; the lithium battery is connected with the load after being connected to the power bus, and the lithium battery is used as an auxiliary power source and provides power for the load.
Further, in step S1, when modeling the fuel cell hybrid system, modeling is performed for the PEMFC system, the DC/DC converter, and the lithium battery, respectively, which specifically includes:
setting basic parameters of the DC/DC converter, modeling the DC/DC converter to obtain a static model of the DC/DC converter:
ηdc＝AdcPfc 5-BdcPfc 4+CdcPfc 3-DdcPfc 2+EdcPfc+Fdc；
wherein: etadcIs the output efficiency of the DC/DC converter; a. thedc,Bdc,Cdc,Ddc,Edc,FdcModel coefficients of a static model of the DC/DC converter are respectively; pfcIs the output power of the PEMFC system;
setting basic parameters of the PEMFC system, and modeling the PEMFC system:
Figure GDA0003683805020000021
wherein:
Figure GDA0003683805020000022
the molar mass of hydrogen consumed for the reactor reaction in the PEMFC system;
Figure GDA0003683805020000023
the low heating value of hydrogen of a galvanic pile in the PEMFC system; etafcIs the stack efficiency in the PEMFC system;
setting basic parameters of the lithium battery, and establishing a charge/discharge model of the lithium battery according to the change condition of the state of charge of the lithium battery:
Figure GDA0003683805020000024
wherein: SOC is the state of charge of the lithium battery; v0Is the open circuit voltage of the lithium battery; rbtThe internal resistance of the lithium battery for charging/discharging; ploadDemand power for the load; pdcAs output of a DC/DC converterOutputting power; qbtThe battery capacity of a lithium battery.
Further, the specific step of step S2 is:
s201: setting state variables and input variables of the fuel cell hybrid power system, constructing an EMPC (empirical mode Power controller) predictive control model, setting load required power as a measurable disturbance item, and amplifying the load required power serving as the state variables into the EMPC predictive control model;
s202: discretizing the augmented EMPC predictive control model to obtain a final EMPC predictive control system;
s203: and constructing an objective function and a constraint condition of the EMPC predictive control system.
Further, in step S202, the EMPC predictive control system is a linear time-invariant discrete-time system, and the expression thereof is:
x(t+1)＝Ax(t)+Bu(t)；
wherein: x (t) is the state variable of the EMPC predictive control system at the current moment, including the molar mass of hydrogen consumed by the reactor in the PEMFC system
Figure GDA0003683805020000031
Nuclear power state SOC and load demand power P of lithium batteryload(ii) a x (t +1) is a state variable of the next moment of the EMPC predictive control system; u (t) is the input variable of the EMPC predictive control system at the current moment, including the output power P of the PEMFC systemfc(ii) a A and B are coefficient matrixes corresponding to state variables and input variables of the EMPC predictive control system respectively.
Further, in step S203, the objective function is expressed as:
Figure GDA0003683805020000032
wherein: u is an input variable sequence of prediction output; k is the sampling time, k is 0,1, …, N; Δ xkState increment at time k; Δ ukInputting increment for k time; q, S are state increment and input respectivelyA weight coefficient of the increment;
the constraint conditions include:
xmin≤xk≤xmax；k＝0,1,…,N；
Δumin≤Δuk≤Δumax；k＝0,1,…,N；
umin≤uk≤umax；k＝0,1,…,N。
further, the specific step of step S3 is:
s301: constructing a multi-parameter quadratic programming problem based on the EMPC predictive control system and a target function thereof according to the linear time invariant characteristic of the EMPC predictive control system;
s302: simplifying the multi-parameter quadratic programming problem to obtain a standard form of the multi-parameter quadratic programming problem;
s303: solving the standard form of the multi-parameter quadratic programming problem offline by using a KKT condition to obtain a state partition and a corresponding control law of the EMPC predictive control system so as to obtain an explicit control model of the EMPC predictive control system;
s304: and searching a state partition corresponding to the state variable on line, calculating by using the explicit control model to obtain an optimal input variable sequence, acting the optimal input variable sequence in the fuel cell hybrid power system, and adjusting power distribution between the PEMFC system and the lithium battery to realize control of the fuel cell hybrid power system.
Further, the specific process of constructing the multi-parameter quadratic programming problem in step S301 is as follows:
according to the linear time invariant characteristic of the EMPC predictive control system, calculating to obtain a state variable x of the EMPC predictive control system at the t moment based on a multi-parameter quadratic programming probleme(t) and input variables u assumed by the EMPC predictive control system from time t to time t + k-1 in the future based on the multi-parameter quadratic programming problemeAccording to assumed input variables ueObtaining input variables of the EMPC predictive control system from t moment to t + k moment based on the multi-parameter quadratic programming problemxe(t+k)：
Figure GDA0003683805020000041
Wherein: x is a radical of a fluorine atomeState variables at time t in a multi-parameter quadratic programming problem, including the increase in molar mass of hydrogen consumed by reactor reactions in a PEMFC system
Figure GDA0003683805020000042
Nuclear power state SOC and load demand power P of lithium batteryloadAnd delta P of PEMFC system output powerfc；ueInput variables in the problem for multiparameter quadratic programming, including the output power P of the PEMFC systemfc(ii) a (t + k | t) represents the prediction of time t + k at time t; j is the predicted time from the future time t to the time t + k-1, and j is 0,1, …, k-1; a. thee,BeConstraint matrices which are all corresponding variables;
the input variable xeSubstituting (t + k) into an objective function of the EMPC predictive control system to obtain an expression of the multi-parameter quadratic programming problem:
Figure GDA0003683805020000043
s.t.Geue≤We+Sexe(t)；
wherein: heIs a Hessian matrix, He>0；Ye,Ge,Fe,We,SeConstraint matrices which are all corresponding variables; the subscript e represents the constraint.
Further, the specific process of simplifying the multi-parameter quadratic programming problem in step S302 is as follows:
definition of
Figure GDA0003683805020000044
Simplifying the expression of the multi-parameter quadratic programming problem into a standard form as shown in the following:
Figure GDA0003683805020000051
s.t.Gez≤We+Sexe；
wherein: z is a state variable xeThe affine function of (1) is solved by using a first-order karo-kun-tach condition, and an explicit expression of the affine function z is as follows:
Figure GDA0003683805020000052
wherein:
Figure GDA0003683805020000053
are respectively equivalent to the constraint matrix Ge,We,Se。
Further, the specific process of obtaining the explicit controller of the EMPC predictive control system in step S303 is as follows:
calculating a first critical domain corresponding to the initial state variable of the EMPC predictive control system according to the KKT condition, and then using the formula in the step S302
Figure GDA0003683805020000054
Substituting the optimal input variable sequence into an explicit expression of an affine function z to obtain an explicit expression of the optimal input variable sequence in the first critical domain about state variables, and applying a first term of the optimal input variable sequence to the fuel cell hybrid power system to obtain a state partition corresponding to the first critical domain and a corresponding control law:
ue＝fexe+ge,xe∈CR0；
wherein: f. ofe,geParameters, CR, of local affine functions in the sequence of open-loop optimal input variables, respectively, corresponding to the first critical domain0Is a first critical domain;
repeating the above process to obtain the rest state partitions and the corresponding control laws:
Figure GDA0003683805020000055
wherein:
Figure GDA0003683805020000056
parameters, CR, of local affine functions in the sequence of open-loop optimal input variables corresponding to the ith critical domainiFor the ith critical domain, i belongs to {1, 2., n }, and n is the number of state partitions;
and (3) sorting the state partitions and the corresponding control laws of the critical domains to obtain an explicit control model of the EMPC predictive control system:
ue(k)＝fx(xe)；
wherein: f. ofx(xe) Represents a state variable xeAbout the optimal input variable ue(k) The control function of (2).
According to the scheme, the dynamic change process of the key state in the fuel cell hybrid power system is described, the fatigue output characteristic of the fuel cell is comprehensively considered, and the lithium battery can play a role of 'peak clipping and valley filling' by setting the constraint and the weight, so that the power distribution between the PEMFC system and the lithium battery is realized, and the system is ensured to operate in a safe working condition range; an EMPC predictive control system is designed based on an MPC control theory and an MPQP control theory, the online solved quadratic programming problem is converted into an offline obtained polyhedral piecewise function, the control performance is guaranteed, the real-time performance of a control strategy is obviously improved, and the calculation time consumption of the whole control process is obviously saved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims thereof.
Drawings
Fig. 1 is a flowchart of a control method of a fuel cell hybrid power system based on an EMPC according to the present invention.
Fig. 2 is a block diagram of a fuel cell hybrid system.
Fig. 3 is a circuit schematic of the DC/DC converter.
Fig. 4 is a graph of the output efficiency of the DC/DC converter.
Fig. 5 is a polarization plot of a stack in a PEMFC system.
Fig. 6 is a flowchart of step S2.
Fig. 7 is a flowchart of step S3.
FIG. 8 is a drawing showing
Figure GDA0003683805020000061
State partitioning diagram on subspace.
FIG. 9 is a graph comparing the control effect of the EPMC predictive control system with that of the conventional MPC control system.
FIG. 10 is a graph comparing the time taken for the EMPC predictive control system to solve for a single step with a conventional MPC control system.
Detailed Description
The following is further detailed by way of specific embodiments:
examples
As shown in fig. 1, a flowchart of a control method of a fuel cell hybrid system based on an EMPC according to the present invention specifically includes the following steps:
s1: and establishing a fuel cell hybrid power system model.
And establishing a fuel cell hybrid power system based on the PEMFC system and the lithium battery, and modeling the fuel cell hybrid power system model.
In the present embodiment, a motorcycle is considered as a research object, and the main parameters of the fuel cell hybrid motorcycle are shown in table 1 below:
parameter name Numerical value
Vehicle mass 175kg
Size of the whole vehicle 2190×770×1140mm
Rated power of motor 3200W
Peak power 8000W
Maximum vehicle speed 100km/h
Maximum climbing angle 11°
Diameter of tyre 466mm
TABLE 1
The fuel cell hybrid system can be divided into four configurations, which require less power according to the main parameters of the fuel cell hybrid motorcycle, and the fuel cell system (i.e., PEMFC system) in the fuel cell hybrid system is considered as the main power source and the lithium battery is considered as the auxiliary power source, and thus, in the present embodiment, the fuel cell hybrid system as shown in fig. 2 is established.
As shown in fig. 2, the fuel cell hybrid system includes a PEMFC system connected to a power bus and then connected to a load through a DC/DC converter, a lithium battery, and a load, and the PEMFC system is used to transmit electric energy generated by an electrochemical reaction to the DC/DC converter to drive the load. The DC/DC converter is used for adjusting the output current of the PEMFC system to realize power distribution between the PEMFC system and the lithium battery so as to ensure that the fuel cell hybrid power system operates in a safe working condition range. The lithium battery is connected with a load after being connected to the power bus, and the lithium battery is used as an auxiliary power source to provide power for the load.
Then, modeling is performed for the PEMFC system, the DC/DC converter, and the lithium battery in the fuel cell hybrid system, respectively.
(1) The DC/DC converter is modeled.
As shown in fig. 3, the DC/DC converter adopts a bidirectional buck-boost dual-quadrant converter, and includes an inductor L, two filter capacitors C1 and C2, two fully-controlled IGBT or MOSFET transistors Q1 and Q2, and two freewheeling diodes D1 and D2.
In this embodiment, the basic parameters of the DC/DC converter are shown in table 2 below:
mode of operation Voltage, current, buck-boost
Input voltage range 24～80V
Output voltage range 0～79V
Rated output current 36A
Maximum output current 48A
Rated output power 2160W
TABLE 2
According to the basic parameters shown in the table 2, the open loop experiment test is carried out on the DC/DC converter, and the output power P of the PEMFC system is adjustedfcTo obtain the output power P of different PEMFC systemsfcAnd fitting the discrete data by using a fifth-order polynomial to obtain an output efficiency curve of the DC/DC converter, wherein the output efficiency curve of the DC/DC converter is shown in FIG. 4, and further a static model of the DC/DC converter is obtained:
ηdc＝AdcPfc 5-BdcPfc 4+CdcPfc 3-DdcPfc 2+EdcPfc+Fdc (1)
wherein: etadcIs the output efficiency of the DC/DC converter; a. thedc,Bdc,Cdc,Ddc,Edc,FdcModel coefficients of a static model of the DC/DC converter are respectively; pfcIs the output power of the PEMFC system.
(2) The PEMFC system was modeled.
In this example, the basic parameters of the PEMFC system are shown in table 3 below:
parameter name Numerical value
Size of 249×213×210mm
Operating temperature (according to the output current I of the pile)fcCalculating) 0.233×Ifc+35.1℃
Rated power 2000W
Pressure of hydrogen gas 0.5bar
Efficiency of electricity generation ≥50％
Purity of hydrogen ≥99.95％
Number of tablets 59
Quality of 6.5kg
Operating temperature -5～40℃
Working humidity
10～90％
TABLE 3
The PEMFC system is modeled according to the basic parameters shown in table 3, and in this embodiment, since the change of hydrogen consumption by the reactor in the PEMFC system is described, the modeling of the PEMFC system is expressed as:
Figure GDA0003683805020000091
wherein:
Figure GDA0003683805020000092
the molar mass of hydrogen consumed for the reactor reaction in the PEMFC system; pfcIs the output power of the PEMFC system;
Figure GDA0003683805020000093
the low heating value of hydrogen of a galvanic pile in the PEMFC system; etafcIs the stack efficiency in the PEMFC system.
The PEMFC system model was simulated to obtain its polarization curve, which is shown in fig. 5.
(3) And modeling the lithium battery.
The lithium battery is used as an auxiliary power source in the fuel cell hybrid power system, and needs to meet both voltage class and capacity, and in the embodiment, the rated voltage of the load is 72V, so the lithium battery with the rated voltage of 72V is correspondingly selected. The basic parameters of the lithium battery are shown in the following table 4:
parameter name Numerical value
Nominal voltage 72V
Cut-off voltage 48V
Standard capacity 48Ah
Maximum discharge current 144A
Size of 560×210×150mm
TABLE 4
According to the basic parameters shown in table 4, a lithium battery model is established, and since the lithium battery model describes the change of the state of charge of the lithium battery, the charge/discharge model of the lithium battery is expressed as:
Figure GDA0003683805020000094
wherein: SOC is the state of charge of the lithium battery; v0Is the open circuit voltage of the lithium battery; r isbtThe internal resistance of the lithium battery for charging/discharging; p isloadDemand power for the load; pdcIs the output power of the DC/DC converter, which is composed of PfcIs represented by, i.e. Pdc＝ηdcPfc；QbtThe battery capacity of a lithium battery.
The lithium battery model can be divided into a charging model and a discharging model, and the internal resistances of the lithium batteries corresponding to the charging model and the discharging model are different. Therefore, when modeling the charging and discharging states of the lithium battery, respectively, the internal resistance in the corresponding state needs to be measured.
Specifically, the internal charging resistance measuring method of the lithium battery measures the open-circuit voltage V of the lithium battery under the SOC value of each charge state0Then, againConnected to a power supply and with a constant current IbCharging the lithium battery and measuring the supply voltage V at that timepThereby obtaining the charging internal resistance R of the lithium batterycha：
Figure GDA0003683805020000101
Through measurement, the internal resistance of the lithium battery is basically 0.042 omega in the charging process, in the embodiment, the internal resistance of the lithium battery in charging is simplified, and R is uniformly selectedcha＝0.042Ω。
Similarly, the method for measuring the internal discharge resistance of the lithium battery firstly measures the open-circuit voltage V of the lithium battery under the SOC value of each charge state0Then connected to a load with a constant current IbFor discharging, and measuring the supply voltage V at that timelThereby obtaining the charging internal resistance R of the lithium batterydis：
Figure GDA0003683805020000102
According to the method for calculating the internal discharge resistance of the lithium battery, actual measurement is carried out, data are collected, then the functional relation between the internal discharge resistance of the lithium battery and the SOC of the lithium battery is calculated, and finally the linear control model of the lithium battery is obtained, wherein the linear control model of the lithium battery is as follows:
Figure GDA0003683805020000103
wherein: a. thebt,Bbt,CbtModel coefficients of a linear control model of discharge of a lithium battery, respectively, in the present embodiment, abt＝-1.3446×10-15，Bbt＝2.7537×10-4,Cbt＝-2.732×10-4。
The charging linear control model of the lithium battery is as follows:
Figure GDA0003683805020000104
wherein: dbt,Ebt,FbtModel coefficients of a linear control model for charging of lithium batteries, respectively, in the present embodiment, Dbt＝3.5527×10-15，Ebt＝2.7537×10-4,Fbt＝-2.732×10-4。
S2: and constructing an EMPC control system and setting an objective function and constraint conditions.
To achieve power distribution between the PEMFC system and the lithium battery and complete the entire driving process with minimum fuel consumption and minimum exhaust emissions, an EMPC predictive control system is constructed and set the EMPC predictive control system objective function and constraints based on the fuel cell hybrid system model.
As shown in fig. 6, the step S2 includes the following steps:
s201: and constructing an EMPC (empirical mode Power controller) predictive control model and amplifying the EMPC predictive control model.
Specifically, state variables and input variables of the fuel cell hybrid power system are set, an EMPC predictive control model is constructed, load demand power is set as a measurable disturbance item, and then the load demand power is used as the state variables to be amplified into the EMPC predictive control model.
The augmented EMPC predictive control model is expressed as:
x+＝Ax+Bu (8)
wherein: x is the state variable after the current time is expanded,
Figure GDA0003683805020000111
Figure GDA0003683805020000112
the molar mass of hydrogen consumed by a reactor reaction in a PEMFC system, SOC is the nuclear power state of a lithium battery, PloadFor load demand power, T represents the transpose of the matrix; x is a radical of a fluorine atom+The state variable after the augmentation of the next moment; u is an input variable at the present time,
Figure GDA0003683805020000113
Pfcis the output power of the PEMFC system; a and B are coefficient matrixes corresponding to the state variable and the input variable respectively.
S202: and (4) performing discretization processing on the EMPC control prediction model to obtain an EMPC prediction control system.
Specifically, discretization processing is performed on the augmented EMPC predictive control model obtained in step S201, and sampling time is set to obtain a final EMPC predictive control system, where the EMPC predictive control system is a linear time invariant discrete time system and has an expression:
x(t+1)＝Ax(t)+Bu(t) (9)
wherein: x (t) is the state variable of the EMPC predictive control system at the current moment, including the molar mass of hydrogen consumed by the reactor in the PEMFC system
Figure GDA0003683805020000114
Nuclear power state SOC and load demand power P of lithium batteryload(ii) a x (t +1) is a state variable of the next moment of the EMPC predictive control system; u (t) is the input variable of the EMPC predictive control system at the current moment, including the output power P of the PEMFC systemfc(ii) a A and B are coefficient matrixes corresponding to state variables and input variables of the EMPC predictive control system respectively.
In this embodiment, the coefficient matrices a and B are respectively:
Figure GDA0003683805020000115
Figure GDA0003683805020000116
wherein: t issFor sampling time, in this embodiment, Ts＝0.01s。
S203: and constructing an objective function and a constraint condition of the EMPC predictive control system.
In order to ensure that the overall fuel consumption of the fuel cell hybrid power system is minimum, the efficiency (a PEMFC system, a DC/DC converter and a lithium battery) of the whole fuel cell hybrid power system is comprehensively considered through modeling, and the optimal input variable at the current time, namely the optimal input variable corresponding to the minimum fuel consumption at the current moment, is solved through setting weights, so that the objective function of the EMPC predictive control system is designed as follows:
Figure GDA0003683805020000121
the constraint conditions are as follows:
xmin≤xk≤xmax；k＝0,1,…,N (13)
Δumin≤Δuk≤Δumax；k＝0,1,…,N (14)
umin≤uk≤umax；k＝0,1,…,N (15)
wherein: u is an input variable sequence of prediction output; k is the sampling time, k is 0,1, …, N; Δ xkIs the state increment at time k; Δ ukInputting an increment for the k moment; q and S are weight coefficients of the state increment and the input increment respectively.
In the present embodiment, xmin＝[0 -0.2 -5]T，xmax＝[10 0.2 5]T，umin＝200W，umax＝1400W，Δumin＝-150W，Δumax＝150W。
To ensure that power P is demanded at loadloadThe output power P of the PEMFC system is changed greatlyfcStill slowly, in this embodiment, the weight coefficient Q of the state increment is:
Figure GDA0003683805020000122
in order to prevent the PEMFC system from being damaged by a large increment of output power, in this embodiment, the weighting coefficient S of the input increment is:
S＝1×10-4 (17)
s3: and solving the multi-parameter quadratic programming problem off line, optimizing power distribution and realizing the control of the fuel cell hybrid power system.
Specifically, a multi-parameter secondary planning problem (MPQP problem) is constructed according to the EMPC predictive control system, a target function and constraint conditions of the EMPC predictive control system, the multi-parameter secondary planning problem is solved, the optimal input variable of the EMPC predictive control system is obtained, the power distribution of the PEMFC system and the lithium battery is optimized, and the control of the fuel cell hybrid power system is realized.
As shown in fig. 7, the step S3 includes the following steps:
s301: and constructing a multi-parameter quadratic programming problem.
And constructing a multi-parameter quadratic programming problem based on the EMPC predictive control system and the objective function thereof. The solving process of the multi-parameter quadratic programming problem can be an offline process, and during online control, power distribution between the PEMFC system and the lithium battery can be realized only by selecting and implementing a corresponding state feedback control law according to the current state of the fuel cell hybrid power system.
Specifically, the EMPC predictive control system is a linear time-invariant discrete time system, and the state variable x of the EMPC predictive control system at the time t based on the multi-parameter quadratic programming problem is known according to the linear time-invariant characteristice(t) and input variables u assumed by the EMPC predictive control system from time t to time t + k-1 in the future based on the multi-parameter quadratic programming problemeAccording to assumed input variables ueThe input variable x of the EMPC predictive control system from the time t to the time t + k based on the multi-parameter quadratic programming problem can be obtainede(t+k)：
Figure GDA0003683805020000131
Wherein: x is the number ofeState variables for time t in a multi-parameter quadratic programming problem, including the increase in molar mass of hydrogen consumed by a reactor reaction in a PEMFC system
Figure GDA0003683805020000132
Nuclear power state SOC and load demand power P of lithium batteryloadAnd delta P of PEMFC system output powerfcI.e. by
Figure GDA0003683805020000133
ueInput variables in the problem for multiparameter quadratic programming, including the output power P of the PEMFC systemfc(ii) a (t + k | t) represents a prediction of time t + k at time t; j is the predicted time from t to t + k-1 in the future, j is 0,1, …, k-1; a. thee,BeAre constraint matrices for the corresponding variables.
The input variable x of the above formula (18)eSubstituting (t + k) into the objective function of the EMPC predictive control system in the formula (10) to obtain an expression of the multi-parameter quadratic programming problem:
Figure GDA0003683805020000134
s.t.Geue≤We+Sexe(t) (20)
wherein: heIs a Hessian matrix, He>0；Ye,Ge,Fe,We,SeConstraint matrices which are all corresponding variables; the subscript e represents the constraint.
S302: and simplifying the multi-parameter quadratic programming problem to obtain a standard form of the multi-parameter quadratic programming problem.
Definition of
Figure GDA0003683805020000135
Simplifying the expression of the multi-parameter quadratic programming problem into a standard as shown belowForm (a):
Figure GDA0003683805020000136
s.t.Ge z≤We+Sexe (22)
wherein: z is a state variable xeAn affine function of (1) solved using a first order karo-cusn-tower condition (KKT), the explicit expression of affine function z being:
Figure GDA0003683805020000141
wherein:
Figure GDA0003683805020000142
are respectively equivalent to the constraint matrix Ge,We,Se。
S303: and solving the MPQP problem off line to obtain a state partition, a corresponding control law and an explicit control model.
Solving the standard form of the multi-parameter quadratic programming problem off-line using a first order Carlo-Cohen-Tak condition (KKT condition) due to He>And 0, obtaining the unique solution, then obtaining the state partition and the corresponding control law of the EMPC predictive control system, and further obtaining the explicit control model of the EMPC predictive control system.
Specifically, the initial state variable x of the EMPC predictive control system is calculated according to a first-order Carolingo-Kuen-Tak condition (KKT condition)eCorresponding first critical region CR0Then, the formula defined in step S302 is applied
Figure GDA0003683805020000143
Said first critical domain CR being obtained by substitution in an explicit expression of an affine function z of formula (23)0Internally optimal input variable sequence ueWith respect to the state variable xeAnd the optimal input variable is inputSequence ueThe first term of (a) is applied to the fuel cell hybrid system to obtain the first critical region CR0The corresponding state partition and the corresponding control law:
ue＝fexe+ge,xe∈CR0 (24)
wherein: f. ofe,geParameters, CR, of local affine functions in the sequence of open-loop optimal input variables, respectively, corresponding to the first critical domain0Is the first critical domain.
Repeating the above process to obtain the rest state partitions and the corresponding control laws:
Figure GDA0003683805020000144
wherein:
Figure GDA0003683805020000145
parameters, CR, of local affine functions in the sequence of open-loop optimal input variables corresponding to the ith critical domainiFor the ith critical domain, i ∈ {1, 2.., n } which is the number of state partitions.
Through calculation, the present embodiment finally obtains 37 partitions, since the explicit control model includes four relevant parameters, that is, the control model includes four relevant parameters
Figure GDA0003683805020000146
Therefore, by organizing the state partitions and the corresponding control laws of the critical domains, the explicit control model of the EMPC predictive control system can be expressed as:
ue(k)＝fx(xe) (26)
wherein: f. ofx(xe) Represents a state variable xeAbout the optimal input variable ue(k) The control function of (2).
When Δ PfcWhen 300W, one can draw
Figure GDA0003683805020000147
The state partition on the subspace is schematically shown in fig. 8.
S304: and solving the most input variable on line to realize the control of the fuel cell hybrid power system.
When the fuel cell hybrid power system is controlled on line, the state partition corresponding to the state of the fuel cell hybrid power system at the current moment is searched on line, the optimal input variable sequence is obtained by utilizing the explicit control model through calculation, the optimal input variable sequence is acted in the fuel cell hybrid power system, and the power distribution between the PEMFC system and the lithium battery is adjusted, so that the control of the fuel cell hybrid power system can be realized.
Finally, in order to verify the control effect of the scheme, the power P is required based on the loadloadIn a variation, the EPMC predictive control system of the present solution is compared with a conventional MPC control system.
As shown in FIG. 9, comparing the control effect of the EPMC predictive control system with that of the conventional MPC control system, it can be seen that the power P is demanded by the loadloadWhen the battery is changed violently, the characteristic of battery fatigue is considered, the EMPC prediction control system and the traditional MPC control system can both control the output power of the fuel battery to change slowly, and meanwhile, the lithium battery can play a role of 'peak clipping and valley filling' in time. However, the online solving capability of the EMPC predictive control system is far higher than that of the MPC control system, so that the EMPC predictive control system can enable the system to tend to be stable more quickly, and the real-time performance of the control strategy is obviously improved.
The difference in the control effect is largely due to the time consumption of the two algorithms. To quantitatively analyze this difference, simulation time-consuming comparative analysis of the two control systems using the above simulation environment was performed.
As shown in fig. 10, a comparison graph of the time consumed by the single-step solution of the EMPC predictive control system of the present embodiment and the conventional MPC control system is shown. It is obvious that the single-step solving of the EMPC predictive control system is less time-consuming in most cases than the MPC control system, and is more time-consuming in few cases than the MPC control system, and for quantitative analysis of the difference between the two, the comparison data of the time-consuming control of the EMPC predictive control system and the MPC control system are shown in table 5:
control system Maximum time of single step Single step with minimal time consumption Total time consumption Average single step time consumption
MPC control system 108.5ms 7.4ms 27165.5ms 10ms
EMPC predictive control system 9.6ms 1.1ms 4599.2ms 1.7ms
TABLE 5
As can be seen from Table 5, the single-step maximum time consumption of the MPC control system is 108.5ms, while the single-step maximum time consumption of the EMPC predictive control system is only 9.6ms, and the EMPC predictive control system is reduced by 98.9ms compared with the MPC control system; the minimum time consumption of the MPC control system is 7.4ms, the minimum time consumption of the EMPC prediction control system is 1.1ms, the EMPC prediction control system is reduced by 6.3ms compared with the MPC control system, the EMPC prediction control system saves the online control time compared with the MPC control system, and the average single-step running speed is increased by 8.3 ms.
The method is based on the EMPC control theory, considers the diversity and complexity of the structure of the fuel cell hybrid power system, and describes the dynamic change process of the key state in the system; meanwhile, the output characteristic of the fuel cell which is weak is also considered, and the lithium battery plays a role of 'peak clipping and valley filling' by setting the restriction and the weight, so that the high-efficiency and stable operation of the system is ensured; the method has the advantages that the EMPC is designed by using the MPQP theory, the problem of long on-line calculation period of the existing MPC predictive control system can be solved, the solving process of the optimal problem of the traditional MPC predictive control system is changed from on-line to off-line, the power distribution between the PEMFC system and the lithium battery is realized only according to the current state of the system during on-line control, the calculation time consumption of a control strategy is obviously improved, the control strategy of the fuel cell hybrid power system control method provided by the invention is accurate, and the requirements of the fuel cell on working and control in a laboratory simulation real scene can be well met.
The above description is only an example of the present invention, and the common general knowledge of the known specific structures and characteristics in the schemes is not described herein. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several variations and modifications can be made, which should also be regarded as the scope of the present invention, and these do not affect the effect of the implementation of the present invention and the practicability of the present invention.

Claims (6)

1. The control method of the fuel cell hybrid power system based on the EMPC is characterized by comprising the following steps:
s1: establishing a fuel cell hybrid power system based on a PEMFC system and a lithium battery, and modeling a fuel cell hybrid power system model;
in step S1, the fuel cell hybrid system includes a PEMFC system, a DC/DC converter, a lithium battery, and a load, the PEMFC system is connected to a power bus via the DC/DC converter and then connected to the load, the PEMFC system is configured to transmit electric energy generated by an electrochemical reaction to the DC/DC converter to drive the load, and the DC/DC converter is configured to adjust an output current of the PEMFC system to implement power distribution between the PEMFC system and the lithium battery; the lithium battery is connected with a load after being connected to the power bus, and the lithium battery is used as an auxiliary power source to provide power for the load;
when modeling the fuel cell hybrid power system, modeling the PEMFC system, the DC/DC converter, and the lithium battery respectively, which specifically includes:
setting basic parameters of the DC/DC converter, modeling the DC/DC converter to obtain a static model of the DC/DC converter:
ηdc＝AdcPfc 5-BdcPfc 4+CdcPfc 3-DdcPfc 2+EdcPfc+Fdc；
wherein: etadcIs the output efficiency of the DC/DC converter; a. thedc,Bdc,Cdc,Ddc,Edc,FdcModel coefficients of a static model of the DC/DC converter are respectively; pfcIs the output power of the PEMFC system;
setting basic parameters of the PEMFC system, and modeling the PEMFC system:
Figure FDA0003683805010000011
wherein:
Figure FDA0003683805010000012
the molar mass of hydrogen consumed for the reactor reaction in the PEMFC system;
Figure FDA0003683805010000013
the low heating value of hydrogen of a galvanic pile in the PEMFC system; etafcIs the stack efficiency in the PEMFC system;
setting basic parameters of the lithium battery, and establishing a charge/discharge model of the lithium battery according to the change condition of the state of charge of the lithium battery:
Figure FDA0003683805010000014
wherein: SOC is the state of charge of the lithium battery; v0Is the open circuit voltage of the lithium battery; rbtThe internal resistance of the lithium battery for charging/discharging; ploadDemand power for the load; p isdcIs the output power of the DC/DC converter; qbtThe battery capacity of the lithium battery;
s2: constructing an EMPC (empirical mode Power controller) predictive control system and setting an objective function and constraint conditions of the EMPC predictive control system based on the fuel cell hybrid power system model;
the specific steps of step S2 are:
s201: setting state variables and input variables of the fuel cell hybrid power system, constructing an EMPC predictive control model, setting load required power as a measurable disturbance item, and amplifying the load required power serving as the state variables into the EMPC predictive control model;
s202: discretizing the augmented EMPC predictive control model to obtain a final EMPC predictive control system;
in step S202, the EMPC predictive control system is a linear time-invariant discrete-time system, and its expression is:
x(t+1)＝Ax(t)+Bu(t)；
wherein: x (t) is the state variable of the EMPC predictive control system at the current moment, including the molar mass of hydrogen consumed by the reactor in the PEMFC system
Figure FDA0003683805010000021
Nuclear power state SOC and load demand power P of lithium batteryload(ii) a x (t +1) is a state variable of the next moment of the EMPC predictive control system; u (t) is the input variable of the EMPC predictive control system at the current moment, including the output power P of the PEMFC systemfc(ii) a A and B are respectively state changes of the EMPC predictive control systemA coefficient matrix corresponding to the quantity and the input variable;
s203: constructing an objective function and a constraint condition of the EMPC predictive control system;
s3: and constructing a multi-parameter secondary planning problem according to the EMPC predictive control system, the objective function and the constraint condition thereof, solving the multi-parameter secondary planning problem to obtain the optimal input variable of the EMPC predictive control system, optimizing the power distribution of the PEMFC system and the lithium battery, and realizing the control of the fuel cell hybrid power system.
2. The EMPC-based fuel cell hybrid system control method of claim 1, wherein in step S203, the objective function is expressed as:
Figure FDA0003683805010000022
wherein: u is an input variable sequence of prediction output; k is the sampling time, k is 0,1, …, N; Δ xkState increment at time k; Δ ukInputting increment for k time; q and S are weight coefficients of the state increment and the input increment respectively;
the constraint conditions include:
xmin≤xk≤xmax；k＝0,1,…,N；
Δumin≤Δuk≤Δumax；k＝0,1,…,N；
umin≤uk≤umax；k＝0,1,…,N。
3. the EMPC-based fuel cell hybrid power system control method of claim 2, wherein the specific steps of step S3 are as follows:
s301: constructing a multi-parameter quadratic programming problem based on the EMPC predictive control system and a target function thereof according to the linear time invariant characteristic of the EMPC predictive control system;
s302: simplifying the multi-parameter quadratic programming problem to obtain a standard form of the multi-parameter quadratic programming problem;
s303: solving the standard form of the multi-parameter quadratic programming problem offline by using a KKT condition to obtain a state partition and a corresponding control law of the EMPC predictive control system so as to obtain an explicit control model of the EMPC predictive control system;
s304: and searching a state partition corresponding to the state variable on line, calculating by using the explicit control model to obtain an optimal input variable sequence, acting the optimal input variable sequence in the fuel cell hybrid power system, and adjusting power distribution between the PEMFC system and the lithium battery to realize control of the fuel cell hybrid power system.
4. The EMPC-based fuel cell hybrid power system control method of claim 3, wherein the specific process of constructing the multi-parameter quadratic programming problem in the step S301 is as follows:
according to the linear time invariant characteristic of the EMPC predictive control system, calculating to obtain a state variable x of the EMPC predictive control system at the t moment based on a multi-parameter quadratic programming probleme(t) and input variables u assumed by the EMPC predictive control system from time t to time t + k-1 in the future based on the multi-parameter quadratic programming problemeAccording to assumed input variables ueObtaining an input variable x of the EMPC predictive control system from the time t to the time t + k based on the multi-parameter quadratic programming probleme(t+k)：
Figure FDA0003683805010000031
Wherein: x is the number ofeState variables at time t in a multi-parameter quadratic programming problem, including the increase in molar mass of hydrogen consumed by reactor reactions in a PEMFC system
Figure FDA0003683805010000032
Nuclear power state SOC and load demand of lithium batteryPower PloadAnd delta P of PEMFC system output powerfc；ueInput variables in the problem for multiparameter quadratic programming, including the output power P of the PEMFC systemfc(ii) a (t + k | t) represents a prediction of time t + k at time t; j is the predicted time from t to t + k-1 in the future, j is 0,1, …, k-1; a. thee,BeConstraint matrices which are all corresponding variables;
inputting the variable xeSubstituting (t + k) into an objective function of the EMPC predictive control system to obtain an expression of the multi-parameter quadratic programming problem:
Figure FDA0003683805010000033
s.t.Geue≤We+Sexe(t)；
wherein: heIs a Hessian matrix, He＞0；Ye,Ge,Fe,We,SeAll are constraint matrices of corresponding variables; the subscript e represents the constraint.
5. The EMPC-based fuel cell hybrid power system control method of claim 4, wherein the specific process of simplifying the multi-parameter quadratic programming problem in step S302 is as follows:
definition of
Figure FDA0003683805010000041
Simplifying the expression of the multi-parameter quadratic programming problem into a standard form as shown in the following:
Figure FDA0003683805010000042
s.t.Gez≤We+Sexe；
wherein: z is a state variable xeAn affine function ofSolving by using a first-order Carlo-Couin-Tack condition, wherein the explicit expression of the affine function z is as follows:
Figure FDA0003683805010000043
wherein:
Figure FDA0003683805010000044
are respectively equivalent to the constraint matrix Ge,We,Se。
6. The EMPC-based fuel cell hybrid power system control method of claim 5, wherein the specific process of finding the explicit controller of the EMPC predictive control system in step S303 is as follows:
calculating a first critical domain corresponding to the initial state variable of the EMPC predictive control system according to the KKT condition, and then using the formula in the step S302
Figure FDA0003683805010000045
Substituting the optimal input variable sequence into an explicit expression of an affine function z to obtain an explicit expression of the optimal input variable sequence in the first critical domain about state variables, and applying a first term of the optimal input variable sequence to the fuel cell hybrid power system to obtain a state partition corresponding to the first critical domain and a corresponding control law:
ue＝fexe+ge,xe∈CR0；
wherein: f. ofe,geRespectively as the parameters, CR, of local affine functions in the open-loop optimal input variable sequence corresponding to the first critical domain0Is a first critical domain;
repeating the above process to obtain the rest state partitions and the corresponding control laws:
Figure FDA0003683805010000046
wherein:
Figure FDA0003683805010000047
parameters, CR, of local affine functions in the sequence of open-loop optimal input variables corresponding to the ith critical domainiFor the ith critical domain, i belongs to {1, 2., n }, and n is the number of state partitions;
and (3) sorting the state partitions and the corresponding control laws of the critical domains to obtain an explicit control model of the EMPC predictive control system:
ue(k)＝fx(xe)；
wherein: f. ofx(xe) Represents a state variable xeAbout the optimal input variable ue(k) The control function of (2).
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