A Pontryagin Minimum Principle-Based Adaptive Equivalent Consumption Minimum Strategy for a Plug-in Hybrid Electric Bus on a Fixed Route

Abstract

When developing a real-time energy management strategy for a plug-in hybrid electric vehicle, it is still a challenge for the Equivalent Consumption Minimum Strategy to achieve near-optimal energy consumption, because the optimal equivalence factor is not readily available without the trip information. With the help of realistic speeding profiles sampled from a plug-in hybrid electric bus running on a fixed commuting line, this paper proposes a convenient and effective approach of determining the equivalence factor for an adaptive Equivalent Consumption Minimum Strategy. Firstly, with the adaptive law based on the feedback of battery SOC, the equivalence factor is described as a combination of the major component and tuning component. In particular, the major part defined as a constant is applied to the inherent consistency of regular speeding profiles, while the second part including a proportional and integral term can slightly tune the equivalence factor to satisfy the disparity of daily running cycles. Moreover, Pontryagin's Minimum Principle is employed and solved by using the shooting method to capture the co-state dynamics, in which the Secant method is introduced to adjust the initial co-state value. And then the initial co-state value in last shooting is taken as the optimal stable constant of equivalence factor. Finally, altogether ten successive driving profiles are selected with different initial SOC levels to evaluate the proposed method, and the results demonstrate the excellent fuel economy compared with the dynamic programming and PMP method.

Intelligent Energy Management Control for Extended Range Electric Vehicles Based on Dynamic Programming and Neural Network

“…The trained NN controller can control battery SOC variations along the target curve, and thus, the current battery SOC, SOC cur (k), can be replaced by the target battery SOC, SOC des (k). Combined with Equation (7), Equation (12) can be modified as follows: (13) In this study, the EREV leaves the charging station with full battery energy; when it arrives at the charging station the next time, the battery energy is used up. Thus, the initial and final battery SOC are constant values in Equation (13), and E per is only related to the driving distance for an EREV.…”

“…In the first stage, the battery SOC changed slowly and decreased to 60.6% when the EREV was driven for approximately 114 km. According to Equation (13), the E per consumed in this stage was very close to E per_200 ; therefore, the NN C2 controller was applied during this stage. Then, the battery SOC decreased quickly and reached a low threshold as the EREV completed the trip.…”

“…They were the charging deplete/charging sustain (CD/CS) strategy and the blended control strategy [11][12][13]. According to the former strategy, vehicles work in a pure electric mode within the all-electric range (AER), and this stage is called the CD stage [14] Beyond the AER, the extender is turned on as the main energy source to satisfy the average power demand from the traction motor (TM).…”

Integrated Component Optimization and Energy Management for Plug-In Hybrid Electric Buses

“…Moreover, many real-time control strategies have also been given more attention, such as adaptive Pontryagin's minimum principle (A-PMP) [25], adaptive equivalent consumption minimization strategy (A-ECMS) [26], model predictive control (MPC) [27,28], stochastic dynamic programming (SDP) [29], and reinforcement learning-based real-time energy management [30]. Since the PMP can transform the global energy management problem into an instantaneous optimization problem by minimizing the Hamilton function, the PMP-based EMS has been one of the most promising methods for a real-time energy management application, where the determination of the co-state (or the equivalence factor) is one of the key issues [31][32][33].Currently, various methodologies have been proposed to determine the optimal co-state (or the equivalence factor), aiming at implementing the PMP-based EMS online while decreasing fuel consumption. In Reference [34], the optimal co-state was considered as a constant value, under the assumption that battery characteristics are almost unchangeable with respect to the changing state-of-charge (SOC).…”

“…To overcome this deficiency, the shooting method was employed in iterative computations to identify the optimal co-state trajectory. However, the acceptable initial co-state value should be provided in advance [31]. In Reference [35], an approach based on preformulated look-up tables was proposed to search for the optimal initial co-state value using the shooting method.…”