#### Optimization method of energy management system based on dynamic programming

Based on the fuzzy logic energy management system, the use efficiency of the power battery of the pure electric vehicle with a single energy source is effectively improved, and the economic performance and dynamic performance of the whole vehicle are improved on the premise that the total energy of the power battery remains unchanged. On the basis of this control strategy, an optimization unit is added, which is guided by** dynamic programming **theory, extracts valuable control rules, and automatically adjusts the fuzzy controller according to the actual situation of the vehicle, so that the sum of the energy loss of the vehicle reaches minimum. Experiments show that:

Under the same driving conditions, the optimization method can further improve the economic performance of the whole vehicle.

Because the conventional fuzzy controller does not have the self-adjustment ability of rules and parameters, it cannot automatically adjust its parameters to adapt to the change of the object. When the robustness of the system needs to be analyzed, if the method of fuzzy control is adopted, the system cannot complete the analysis faster than using the control theory commonly used in the past. The system can also fluctuate if the quantifiers are poorly chosen, or if the control rules are poorly structured or covered.

Secondly, due to the limitations of the design itself, the fuzzy control designed by using experience is easily affected by subjective influence. Therefore, when applying fuzzy control strategy to solve complex multi-stage control problems, it is often easy to fall into local optimum. The dynamic programming can decompose the more complex problems, and then obtain the optimal solution of the whole problem by solving each problem one by one. For some difficult optimization problems, it can often reflect its superiority, especially for some discrete optimization problems. In this section, from the perspective of modifying and improving the fuzzy control principle, the optimization problem of the energy management system of pure electric vehicles is expressed as a dynamic programming theoretical optimization problem with the goal of minimizing the sum of the energy loss of the whole vehicle. The control effect of dynamic programming theory is verified by calculating the optimal control solution under specific cycle conditions.

- Description of the dynamic programming optimization problem

Let the allocable power of the energy management system at any time be Pe. The power relationship is as follows (1):

Due to the loss of the drive motor and the power devices of the thermal management system, the power provided by the energy management system cannot be used for effective work, that is, the efficiency of the two is not 1, and the relationship is as follows (2):

Among them, is the function of the thermal management system components on the ambient temperature T, and is the function of the motor speed N. The cycle conditions of the whole vehicle are divided into n stages, k∈n, and the following assumptions are made:

(1) State variable xk: represents the power allocated by the energy system to the thermal management system from the kth time period to the nth time period.

(2) Decision variable uk: represents the power allocated by the energy management system to the thermal management system in the kth time period.

Under the action of the decision uk, the state variable xk changes, and the state transition equation is (3)

Indicates the power allocated by the energy management system to the thermal management system from the k+1th time period to the nth time period. When the energy management system distributes according to the decision variable uk, the power flows through the drive motor and the thermal management system respectively, which will generate corresponding incentives for the two, so that the characteristic states of the two will change. Since the efficiency of the drive motor is a function of the motor speed, and the efficiency of the thermal management system is related to the ambient temperature, the energy Jsys lost by the system at time k is a function of the state variable xk and the decision variable uk. Let it be the dynamic optimization stage index function vk(xk, uk), then (4):

represents the system loss caused by the power allocation of decision uk in the kth time period.

In this way, according to the power demand of the whole vehicle, starting from time 0, different control rates U will generate different new states (state variables) x, and at the same time face the problem of selecting a new control rate (decision variable) U until the whole cycle works. situation is over. Since the initial conditions of the vehicle simulation will be given, the power optimization control problem of the pure battery vehicle energy management system can be summarized as: the initial state x(0)=x0 given, the terminal x(n)=0 optimal control The problem is shown in Figure (5):

In the process of vehicle driving, if the distribution of each control rate in all cycles is optimal, the sum of energy losses generated by the system at each moment can be minimized. In the case of the same total amount of energy system, that is It can be understood that the efficiency of the energy system in the cycle is the largest, and the economic performance of the vehicle is the best. From this, the optimization objective shown in Equation (6) can be set:

fk(xk, Wk) represents the sum of the system losses caused by the power allocation of the decision uk from the kth time period to the nth time period. In the process of vehicle cycle conditions, the power of the drive system and thermal management system and the energy of the power battery system must meet the following constraints (7):

In this way, the output of the energy management system can be adjusted by solving the optimal control rate under dynamic programming, and the energy management system can be further optimized. According to the principle of Bellman optimality, to solve the dynamic programming recursive equation with constraints, the steps are as follows:

①Using the boundary condition fN(xN, uN)=0, obtain the optimal control un in the Nth stage when the state is xn.

②According to the values of the formula xk+1=xk-uk and fk(xk, uk), find the optimal control uk-1 and fk-1 (xk-1, uk- 1).

③ Let k=k-1, if 0≤k≤N-1 is satisfied, go back to step ②; if not, go to step ④. ④ Obtain the optimal control u0 and f0 (x0, u0) when the state is x0 at the initial moment, then the sequence {u0, 1…, uN-1} is the optimal control strategy, and f0 (x0, u0) is the optimal control strategy. The optimal performance index corresponding to the optimal control strategy.

- Validation of dynamic programming optimization method

Because the dynamic programming takes the minimum energy loss of the whole vehicle as the optimization goal, the energy consumption rate of the whole cycle process is lower than that of the fuzzy control strategy, and there is no under-power situation in the later cycle of the cycle. The control amount allocated by the optimization algorithm is smaller at the beginning of the cycle, because the initial temperature of the system is lower and the efficiency loss of the thermal management system is larger. As the cycle progresses, the system temperature gradually increases, the efficiency loss of the thermal management system becomes smaller, and the control amount allocated by the algorithm gradually increases. In addition, when the motor speed is low, the system energy loss is relatively large, and the algorithm will appropriately reduce the allocated control amount; when the motor speed increases to the high-efficiency working area, its guiding significance for the real vehicle is as follows:

(1) When the initial temperature is low, appropriately reduce the allocated control amount.

(2) When the temperature in the mid-term is high, increase the allocated control amount appropriately.

(3) When the motor speed is low, reduce the allocated control amount appropriately.

(4) The motor enters the high-efficiency area, and the allocated control amount is appropriately increased.