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CN108509734B - A Boundary Calculation Method for Realizing Electricity Balance of Hybrid Power System - Google Patents

A Boundary Calculation Method for Realizing Electricity Balance of Hybrid Power System Download PDF

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CN108509734B
CN108509734B CN201810304880.XA CN201810304880A CN108509734B CN 108509734 B CN108509734 B CN 108509734B CN 201810304880 A CN201810304880 A CN 201810304880A CN 108509734 B CN108509734 B CN 108509734B
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曾小华
王越
杨南南
宋大凤
朱丽燕
张学义
崔皓勇
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Jilin University
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Abstract

The invention provides a boundary calculation method capable of realizing electric quantity balance of a hybrid power system, which belongs to the technical field of new energy automobiles. By solving the boundary constraint, a penalty function is not needed any more, and the robustness of the algorithm is not influenced by model parameters and operation conditions any more.

Description

Boundary calculation method capable of realizing electric quantity balance of hybrid power system
Technical Field
The invention provides a boundary calculation method capable of realizing electric quantity balance of a hybrid power system, and belongs to the technical field of new energy automobiles.
Background
Hybrid power has the requirement of electric quantity balance, and the current method for realizing the electric quantity balance of the hybrid power system mainly adopts a penalty function to carry out a large amount of debugging and realization. Energy management policy optimizations such as those based on DP typically employ penalty functions to satisfy the conditions for system power balance. However, the penalty function in most of researches needs a researcher to debug for many times through experience, the debugging workload is huge, and the automatic implementation of the algorithm is not facilitated. In addition, since the model parameters for optimization will change with the passage of time or the change of the vehicle state, and the target working condition of global optimization will also change with the change of historical operating data, these factors will cause researchers to show that the calibrated penalty function has no good robustness, and further reduce the application value of the penalty function method.
Disclosure of Invention
The invention aims to provide a boundary calculation method which can overcome the defects, avoid a large amount of debugging work of penalty functions and effectively realize the electric quantity balance of a hybrid power system, and the technical content is as follows:
firstly, establishing a relation between the battery capacity and the current of the hybrid power system: the equivalent internal resistance model is used as a battery model, and the relation between the battery current and the battery power can be obtained:
Figure GDA0003136327010000011
in the formula (1), the open-circuit voltage E ═ f of the batteryU(SOC), which is a function of SOC, based on the relationship of SOC to battery capacity and current:
Figure GDA0003136327010000012
in the formula (2), E is the open-circuit voltage of the battery, IbatIs a current of rintTo equivalent internal resistance, QbatTo the true capacity, Q, of the capacitormaxThe maximum capacity of the battery and the SOC are the state of charge of the battery, and the relation between the capacity and the current of the hybrid power system can be obtained by the following formula (2):
Qbat(k+1)＝Qbat(k)+IbatΔt (3)
secondly, determining the relation between the system state variable and the control variable: the relationship of the system state variables to the control variables can be obtained according to equation (3) as follows:
Figure GDA0003136327010000021
the relationship between the system state variables and the control variables can be expressed by equation (4):
xk+1＝fk(xk,uk)+xk (5)
thirdly, a method for solving the lower boundary of the system state comprises the following steps: defining the minimum state variable value at which the time k can allow the system to reach the lower boundary of the end state as the lower boundary constraint x at that timek,lowThe range of the system end state is a known quantity for the control target according to the charge balance requirement of the hybrid system, that is: x is the number ofN,low＝xf,min，xf,minFor the lower boundary value of the termination state, the lower boundary of the system state at the time when k-N-1 to k-0 can be solved by backward iterative calculation as follows:
Figure GDA0003136327010000022
considering that the state variable of the present system is SOC, which is a positive number between [0,1], equation (6) can be further rewritten as:
Figure GDA0003136327010000023
in backward iterative computation, xk+1,lowIs a known quantity with an initial value of xf,minOnly xk,lowAnd ukFor unknown variables, the solution x can be carried out by using a fixed point iteration methodk,lowThe lower boundary solving process at the time k is as follows:
firstly, initializing:
Figure GDA0003136327010000024
j is an iteration index of a lower boundary of the calculated state quantity at the moment k;
starting iterative calculation until a specific tolerance is reached:
Figure GDA0003136327010000025
the following were used:
Figure GDA0003136327010000026
taking into account the order of magnitude of the state variable SOC, take the tolerance ξ ═ 10-5After the lower boundary at the time k is solved, repeating the first step and the second step, and continuously solving to obtain the lower boundary at the time k-1 until k is equal to 0;
fourthly, a system state upper boundary calculation method comprises the following steps: the upper boundary of the system state is calculated in the same way as the lower boundary of the system state is solved in the third step.
Compared with the prior art, the invention has the following beneficial effects:
according to the method, before DP backward optimization, system boundary calculation is firstly carried out, boundary constraint of a state variable at each moment is obtained, and then the boundary constraint is considered in the backward iterative optimization process, so that the electric quantity balance of the system is realized. By solving the boundary constraint, a penalty function is not needed any more, and the robustness of the algorithm is not influenced by model parameters and operation conditions any more.
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FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 shows the system boundary calculation result and the system state under the typical working condition of the Chinese city.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
the boundary calculation method for realizing the electric quantity balance of the hybrid power system is shown in fig. 1: firstly, establishing a relation between the battery capacity and the current of the hybrid power system: the equivalent internal resistance model is used as a battery model, and the relation between the battery current and the battery power can be obtained:
Figure GDA0003136327010000031
in the formula (1), the open-circuit voltage E ═ f of the batteryU(SOC), which is a function of SOC, based on the relationship of SOC to battery capacity and current:
Figure GDA0003136327010000032
in the formula (2), E is the open-circuit voltage of the battery, IbatIs a current of rintTo equivalent internal resistance, QbatTo the true capacity, Q, of the capacitormaxThe maximum capacity of the battery and the SOC are the state of charge of the battery, and the relation between the capacity and the current of the hybrid power system can be obtained by the following formula (2):
Qbat(k+1)＝Qbat(k)+IbatΔt (3)
secondly, determining the relation between the system state variable and the control variable: the relationship of the system state variables to the control variables can be obtained according to equation (3) as follows:
Figure GDA0003136327010000033
the relationship between the system state variables and the control variables can be expressed by equation (4):
xk+1＝fk(xk,uk)+xk (5)
thirdly, a method for solving the lower boundary of the system state comprises the following steps: defining the minimum state variable value at which the time k can allow the system to reach the lower boundary of the end state as the lower boundary constraint x at that timek,lowThe range of the system end state is a known quantity for the control target according to the charge balance requirement of the hybrid system, that is: x is the number ofN,low＝xf,min，xf,minFor the lower boundary value of the termination state, the lower boundary of the system state at the time when k-N-1 to k-0 can be solved by backward iterative calculation as follows:
Figure GDA0003136327010000041
considering that the state variable of the present system is SOC, which is a positive number between [0,1], equation (6) can be further rewritten as:
Figure GDA0003136327010000042
in the backward directionIn iterative calculation, xk+1,lowIs a known quantity with an initial value of xf,minOnly xk,lowAnd ukFor unknown variables, the solution x can be carried out by using a fixed point iteration methodk,lowThe lower boundary solving process at the time k is as follows:
firstly, initializing:
Figure GDA0003136327010000043
j is an iteration index of a lower boundary of the calculated state quantity at the moment k;
starting iterative calculation until a specific tolerance is reached:
Figure GDA0003136327010000044
the following were used:
Figure GDA0003136327010000045
taking into account the order of magnitude of the state variable SOC, take the tolerance ξ ═ 10-5After the lower boundary at the time k is solved, repeating the first step and the second step, and continuously solving to obtain the lower boundary at the time k-1 until k is equal to 0;
fourthly, a system state upper boundary calculation method comprises the following steps: the upper boundary of the system state is calculated in the same way as the lower boundary of the system state is solved in the third step.
Based on the method, a system boundary constraint solving result and an optimized system state are obtained under the typical city working conditions in China, as shown in figure 2. Considering the efficient working interval of the battery, the method limits the change range of the SOC of the battery to 40% -60%, and simultaneously sets boundary constraint [ x ] of the termination state for realizing the battery power balancef,min,xf,max]Is [ 50%, 51%]. As can be seen from fig. 2, the adopted boundary solving method can effectively ensure the terminating state value, so as to achieve the electric quantity balance, and the SOC of the battery at the terminating time reaches 50%.

Claims (1)

1.一种可实现混合动力系统电量平衡的边界计算方法，其特征在于：1. A boundary calculation method that can realize the power balance of a hybrid power system is characterized in that: 第一步，建立混合动力系统电池容量与电流的关系：采用等效内阻模型作为电池模型，可以得到电池电流和电池功率之间的关系：The first step is to establish the relationship between the battery capacity and current of the hybrid power system: using the equivalent internal resistance model as the battery model, the relationship between battery current and battery power can be obtained:
Figure FDA0003136317000000011
Figure FDA0003136317000000011
 式(1)中，电池开路电压E＝fU(SOC)，是关于SOC的函数，根据SOC与电池容量、电流的关系：In formula (1), the battery open circuit voltage E=f U (SOC) is a function of SOC, according to the relationship between SOC and battery capacity and current:
Figure FDA0003136317000000012
Figure FDA0003136317000000012
 式(2)中，E为电池开路电压，Ibat为电流，rint为等效内阻，Qbat为电容真实容量，Qmax为电池最大容量，SOC为电池荷电状态，由式(2)可以得到混合动力系统容量与电流的关系：In formula (2), E is the open circuit voltage of the battery, I bat is the current, r int is the equivalent internal resistance, Q bat is the real capacity of the capacitor, Q max is the maximum capacity of the battery, and SOC is the state of charge of the battery. ) can obtain the relationship between the capacity of the hybrid system and the current: Qbat(k+1)＝Qbat(k)+IbatΔt (3)Q bat (k+1)=Q bat (k)+I bat Δt (3) 第二步，确定系统状态变量与控制变量的关系：根据式(3)可以得到系统状态变量与控制变量的关系，如下：The second step is to determine the relationship between the system state variable and the control variable: According to formula (3), the relationship between the system state variable and the control variable can be obtained, as follows:
Figure FDA0003136317000000013
Figure FDA0003136317000000013
 由式(4)系统状态变量与控制变量之间的关系可以表示为：The relationship between system state variables and control variables can be expressed as: xk+1＝fk(xk,uk)+xk (5)x k+1 = f k (x k , u k )+x k (5) 第三步，系统状态下边界求解方法：定义k时刻能够允许系统达到终止状态下边界的最小状态变量值为该时刻的下边界约束xk,low，根据混合动力系统的电量平衡要求，系统终止状态的范围为控制目标是已知量，即：xN,low＝xf,min，xf,min为终止状态的下边界值，k＝N-1到k＝0时刻的系统状态下边界可以用后向迭代计算进行求解，如下：The third step, the method of solving the lower boundary of the system state: define the minimum state variable value that allows the system to reach the lower boundary of the terminal state at time k is the lower boundary constraint x k,low at this moment, according to the power balance requirements of the hybrid system, the system terminates The range of the state is that the control target is a known quantity, namely: x N,low =x f,min , x f,min is the lower boundary value of the termination state, and the lower boundary of the system state from k=N-1 to k=0 It can be solved by backward iterative calculation, as follows:
Figure FDA0003136317000000014
Figure FDA0003136317000000014
 考虑系统的状态变量为SOC，为[0,1]之间的正数，式(6)可以进一步改写为：Considering that the state variable of the system is SOC, which is a positive number between [0, 1], equation (6) can be further rewritten as:
Figure FDA0003136317000000015
Figure FDA0003136317000000015
 在后向迭代计算中，xk+1,low为已知量，初始值为xf,min，仅xk,low和uk为未知变量，可以利用不动点迭代方法进行求解xk,low，k时刻的下边界求解流程如下：In the backward iterative calculation, x k+1,low are known variables, the initial value is x f,min , only x k, low and uk are unknown variables, and the fixed point iteration method can be used to solve x k, low , the lower boundary solution process at time k is as follows: ①初始化：
Figure FDA0003136317000000021
其中j为k时刻计算状态量下边界的迭代次数索引；①Initialization:
Figure FDA0003136317000000021
where j is the iteration index for calculating the lower boundary of the state quantity at time k; ②开始迭代计算，直到达到特定的容差：
Figure FDA0003136317000000022
如下：②Start iterative calculation until a specific tolerance is reached:
Figure FDA0003136317000000022
as follows:
Figure FDA0003136317000000023
Figure FDA0003136317000000023
 考虑状态变量SOC的数量级，取容差ξ＝10-5，在完成k时刻的下边界求解后，重复上述①②，继续求解得到k-1时刻的下边界，直到k＝0；Considering the magnitude of the state variable SOC, take the tolerance ξ=10 -5 , after completing the solution of the lower boundary at time k, repeat the above ① and ②, and continue to solve to obtain the lower boundary at time k-1 until k=0; 第四步，系统状态上边界计算方法：用第三步求解系统状态下边界的相同方法计算系统状态上边界。The fourth step, the calculation method of the upper boundary of the system state: calculate the upper boundary of the system state with the same method as the third step to solve the lower boundary of the system state.
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