# What is a global optimization-based energy management strategy for hybrid electric vehicles?

The global optimization method is an optimization method that seeks optimization in the entire operating range. It applies the optimization method and optimal control theory, and uses the global optimization method for a given driving cycle to optimize the torque distribution at each moment to achieve the optimum of the entire working condition. The global optimization algorithm can realize the optimization in a real sense. However, this algorithm needs to know the actual driving information and traffic information of the vehicle in advance, which is difficult to realize under the current conditions. Moreover, the global optimization algorithm is complex and requires a large amount of calculation, so it is difficult to be applied in real vehicles at this stage, but its optimization results can provide reference and comparison targets for other control strategies.

The dynamic programming algorithm is a method to solve the multi-stage decision-making problem, and the fuel economy optimization problem of the hybrid electric vehicle can also be established as a multi-stage decision-making problem. First, the cycle conditions are divided into N stages (i.e. discretization) by time. These stages are interconnected, and a decision is made on the energy distribution in each stage. This decision not only affects the cost function value of this stage, but also determines The initial state of the next stage is obtained, and a decision sequence is obtained after decisions are made in each stage. Finally, the optimal decision-making scheme under this working condition is obtained through the forward optimization method. It can be seen that the accuracy of the results of the dynamic programming algorithm depends on the degree of discrete variables. The more discrete points, the closer the results are to the ideal and optimal, but the amount of computation is also greatly increased.

The specific process of applying the dynamic programming algorithm program to optimize the energy management strategy is shown in Figure 1. It is worth noting that the cost function in this article refers only to fuel consumption. Since the dynamic programming adopts the numerical solution method, the time and system state are firstly discretized, and the calculation grid of the battery SOC is divided along the time direction of the driving cycle. According to the known driving cycle, the whole vehicle model is used to calculate the power and rotational speed of the power source along the time direction of the driving cycle. According to the constraints of the motor, battery and engine, starting from the initial state and final state of the system, respectively, the reachable boundary of the system for the entire driving cycle is obtained. Afterwards, within the reachable boundary range, under the condition that the system constraints are satisfied, the reachable state matrix R and the fuel consumption matrix F of the entire driving cycle are obtained by forward calculation according to the designed cost function. Finally, by means of recursive calls, reverse from the terminal state to the initial state, complete the traversal optimization process, obtain the energy distribution trajectory (control trajectory) that minimizes fuel consumption, and output the calculation result.

According to Bellman’s principle, the main idea of the dynamic programming method is to solve the optimal performance index piece by piece according to the reasoning relationship provided by the basic equation. Determined by the control variable u(k), the functional equation of the performance index of the whole process of the system is expressed as

J*[x(k)]=min{L_{k}[x(k),u(k)]+ f_{k+1}[x(k),u(k)]} k=N-1, N-2,..,0 J[x(N), N]=0

In the formula, J*[x(k)] represents the state value reachable at the kth time: x(k) represents the initial time, until the optimal index value after the optimization is completed, x(k) should satisfy the following constraints:

0≤T_{em}(t) ≤T_{em_max}[ω_{em}(t)]

T_{ice_min}[ω_{ice}(t)]≤T_{ice}(t)≤T_{ice_max}[ω_{ice}(t)]

0≤ω_{em}(t)≤ω_{em_max}

ω_{ice_min}≤ω_{ice}≤ω_{ice_max}

SOC_{k_min}≤SOC_{k}≤ SOC_{k_max}

In the formula, T_{ice} (N·m) is the engine torque: T_{em} (N·m) is the motor torque; T _{ice_min} (N·m) represents the minimum torque of the engine: T_{ice_max} (N·m) is the maximum torque of the engine; T_{em_max} (N m) represents the maximum torque of the motor: ωice (rad/s) is the engine speed: ω_{ice_max} is the maximum engine speed: ω_{ice_min} is the minimum engine speed: ω_{em }(rad/s) is the motor speed: SOC_{k_min} is the kth stage Minimum value of SOC: SOC_{k_max} is the maximum value of the SOC in the kth stage. Among them, SOC_{k_min} and SOC_{k_max} are both functions of the initial SOC, and the control process needs to maintain the SOC of the kth stage within a specific range [SOC_{k_min}, SOC_{k_max}].

Some scholars have applied the dynamic programming global optimization algorithm to conduct a global optimization study on the energy management strategy of parallel plug-in hybrid electric vehicles under different driving distances. The research results show that different driving mileage has a great impact on the fuel economy of plug-in hybrid electric vehicles. When the driving mileage of the vehicle is less than 55km, an energy management strategy based on electric motors should be used. use an engine-based energy management strategy).

There is also an energy management control strategy based on historical traffic information, which uses a dynamic programming algorithm to strengthen the power control in the power consumption mode, and reduces the battery SOC to a specific value at the end of the vehicle operating condition. It is compared with the traditional CD-CS mode energy management strategy, and the results show that the fuel economy of plug-in hybrid electric vehicles can be significantly improved.