A neural network-based ECMS for optimized energy management of plug-in hybrid electric vehicles

Highlights

• Dual neural networks are constructed to regulate equivalent factor online.

• Dynamic algorithm is exploited to optimize equivalent factor globally.

• A novel equivalent factor correction is designed to satisfy terminal SOC constrains

• Standard and real-world cycles are utilized to prove the control effectiveness.

Abstract

For plug-in hybrid electric vehicles, the equivalent consumption minimum strategy is typically regarded as a battery state of charge reference tracking method. Thus, the corresponding control performance is strongly dependent on the quality of state of charge reference generation. This paper proposes an intelligent equivalent consumption minimum strategy based on dual neural networks and a novel equivalent factor correction, which can adaptively regulate the equivalent factor to achieve the near-optimal fuel economy without the support of the state of charge reference. The Bayesian regularization neural network is constructed to predict the near-optimal equivalent factor online, while the backpropagation neural network is designed to forecast the engine on/off with the aim of improving the quality of equivalent factor prediction. The corresponding neural network training takes advantage of the global optimality of dynamic programming. Besides, the novel equivalent factor correction can guarantee that the electrical energy is gradually consumed along the trip and the terminal battery state of charge satisfies the preset constraints. A series of virtual simulations under a total of nine driving cycles demonstrates that the proposed method can deliver a competitive fuel economy comparing to the optimal solution derived from the dynamic programming, as well as regulating the battery state of charge to reach the desired terminal value at the end of the trip.

Introduction

Widely accepted, the electrified powertrain system is the most promising technology for addressing the air pollution and energy crisis in transportation sector. Thanks to invertible energy storage devices and electric motors, the electrification enables vehicles to recover baking energy and introduces an additional degree of freedom for the power-flow distribution control, potentially enhancing overall powertrain efficiency and fuel economy [1]. Thus, numerous efforts have been devoted to developing electrified powertrain configurations and corresponding control strategies. In particular, the popularity of plug-in hybrid electric vehicles (PHEVs) are increasing in both the automotive industry and academia [2,3]. For PHEVs, the vehicle's energy storage system can be not only charged by the engine-driven generator but the external electric power source. Thus, compared with conventional hybrid electric vehicles (HEVs), a larger capacity battery is normally mounted in PHEVs to store cheaper electrical energy from external sources, which has the great potential of improving the fuel economy [4]. Moreover, the large-capacity battery allows the integration of one or multiple powerful traction motors in the electrified propulsion system, which can restrain the internal combustion engine (ICE) from operating in low-toque and low-efficiency regions. Additionally, PHEVs with the large-capacity battery is able to prolong the endurance mileage, thereby alleviating the range anxiety to a certain extent [5].

Due to the existence of multiple power sources in the electrified powertrain system, the resulting flexibility and complexity of the energy flow require a sophisticated energy management strategy (EMS) to distribute the power demand optimally among all onboard power sources. Generally speaking, EMSs can be categorized as rule-based, optimization-based, and learning-based strategies. Rule-based EMSs are beneficial from the straightforward structure, low computational cost, and ease of implementation, thereby becoming the common choice for commercial hybrid vehicles [6]. Nevertheless, the inherent rigidity of rule-based EMSs is the inevitable defect that causes the low adaptiveness to the dynamic and complex real-world driving conditions. Although numerous studies are dedicated to the adaptiveness and performance improvement of rule-based EMSs [7,8], this type of EMSs consistently have difficulties finding optimal management solutions in practice [9]. On the contrary, optimization-based EMSs intend to pursue optimal energy consumption by minimizing a fuel-related cost function and, therefore, maximize the benefits of powertrain hybridization. Dynamic programming (DP) is the most preferred global optimization algorithm to solve the energy management problem for hybrid vehicles [10], thanks to its distinguished capability to solve constrained and nonlinear optimization problems. Whereas, due to the serve computational burden and strong dependence on the prior knowledge of future driving conditions, the DP method is inapplicable for the real-time energy management system. It is typically regarded as a benchmark to explore the maximum fuel economy improvement, thereby evaluating performance or extracting the optimal control parameters for alternative EMSs [11]. Instantaneous optimization algorithms, compared with global ones, can obtain a trade-off between the computational cost and fuel economy optimality. Essentially, the fuel-related cost function is optimized instantaneously without gathering comprehensive information of entire driving conditions in advance. The resulting local-optimal power flow distribution can offer fuel economy close to that of global optimization methods [12]. Learning-based EMSs have been rapidly developed thanks to the recent advances in machine learning and artificial intelligence techniques for data-based network training approaches [13]. The excellent generalization and prediction capabilities of learning methods enable EMSs to learn from the globally optimized control actions and, afterwards, apply them locally. Reinforcement learning and neural network learning are standard leaning methods in terms of the EMSs’ design.

Among the existing EMSs, the equivalent consumption minimum strategy (ECMS), a representative of instantaneous optimization algorithms, is the most promising online EMSs and has been widely used in practical applications at present [14,15]. This method, derived from the Pontryagin's minimum principle (PMP), was initially proposed for HEVs by Paganelli [16]. The basic concept of ECMSs is to unify the ICE fuel consumption and the battery electrical energy consumption into a single variable representing the fuel economy of vehicles. The single variable is referred to as equivalent fuel consumption. The unification as mentioned above enables the feasibility of the instantaneous optimization of the total energy consumption, including both fuel and electrical energy. The fuel-electricity conversion process is performed by introducing an equivalent factor (EF) that weighs the electrical energy expenditure as an equivalent quantity of fuel consumption. For the sake of pursuing maximum energy saving, the EF should be a volatile value and tunned dynamically on the basis of powertrain operations in real time. Consequently, a variety of EF estimation methods have been proposed to adaptively regulate EF considering the vehicle status and driving conditions. Regarding HEVs' applications, it is expected that the EF is regulated according to the parameters related to the battery state of charge (SOC) at each instant, aiming to suppress the excessive SOC deviation from the desired constant. For example, a tangent-shape function of the SOC deviation was employed to correct the EF, to ensure the vehicle charge-sustaining [17]. Unsimilar to HEVs, PHEVs attempts to fully deplete the battery power at the end of the current trip and recharged before the next trip. Thus, the desired SOC trajectory for PHEVs is no longer a constant. Ideally, SOC should decline gradually along with the travel distance to reach the admissible minimum at the end of the trip. In other words, a SOC reference trajectory is required for PHEVs to guide power flow distribution along the trip, thereby ensuring both optimal energy consumption and the desired value of the terminal SOC. For simplicity, some researchers proposed to define the SOC reference trajectory as a linear function of the remaining trip distance, while only delivering the sub-optimal fuel economy [[18], [19], [20]]. The SOC reference trajectory planning can be improved by introducing the extra variables on top of the trip distance, such as future average speed [21] or predicted power demand [22]. Besides, artificial neural networks (NNs), such as recurrent NN (RNN) [23] and neuro-fuzzy system [24], also can be applied to generate the SOC reference trajectory based on the historical driving data. The NN-enhanced SOC reference generator takes advantage of the outstanding learning ability of NN, which facilitates full use of implicit knowledge from optimal SOC reference trajectories of different driving cycles. Given the existence of the SOC reference trajectory, the EF online regulation can be simplified as the SOC tracking problem. In other words, the tracking methods, such as PID controllers [25,26] and map-based methods [2], have to be employed to adjust the EF with the aim of tracking SOC reference. It should be noted that both the inevitable imperfections of SOC reference generation and SOC tracking errors contribute to control performance degradation. To eliminate the twofold defects causing sub-optimal performance, EF online estimation method should regulate the EF intelligently without the support of the SOC reference trajectory, as well as guaranteeing not only SOC ending at the desired value but the optimal fuel economy. This ideal scenario is achievable by applying the data-driven NN-enhanced ECMS. Xie et al. [5] constructed a common three-layer backpropagation NN to predict the EF online with three accessible input variables, including the current power demand, the battery SOC, and the ratio of the travelled distance to the total distance. The training simples were extracted from the global optimal solutions over 4 real-world bus driving cycles. Without the SOC reference, the network verification over test driving cycle shows that the SOC is able to terminate at the desired value within an accepted toleration. Moreover, merely around 1.5% fuel economy deterioration can be expected when comparing the proposed NN-enhanced ECMS with the global optimized offline controller. However, the weakness of Xie's research is the lack of robustness test for the proposed method, as there is only one driving cycle selected for the network verification. Even worse, only city bus routes, which are quite regular and similar, were selected for both network training and verification. Note that only few researches, to the authors' knowledge, have been conducted to investigate intelligent ECMS for PHEVs' energy management without the SOC reference trajectory.

In conclusion, the SOC reference generator is typically employed in EMSs for PHEVs, thereby ensuring that the electrical energy is gradually and optimally depleted along the trip. Concerning ECMS applications, EF regulation methods are primarily conceived to track the given SOC trajectory. Nevertheless, both SOC reference generation and tracking unavoidably result in the control performance degradation due to their parasitic deficiencies, such as sub-optimal SOC trajectory generation and tracking errors. To remove the aforementioned twofold deficiencies, an NN-enhanced ECMS is herein developed in this research, which consists of ECMS as the core algorithm and two NNs to regulate the EF online. One NN is trained to directly predict the EF, while the other is to recognize the optimal engine on/off status with the aim of correcting the predicted EF. In this manner, the EF is adaptively and optimally regulated by the combined NNs based on the influential driving features. Regarding the NN training, the training dataset with inputs and outputs is extracted from optimized control actions over selected driving cycles. The global optimization is achieved by the DP algorithm with the objective to minimize the total equivalent fuel consumption over the entire driving cycle. Moreover, the SOC-distance factor is proposed to further correct the predicted EF for the purpose of reaching the desired terminal SOC. Last, the proposed NN-based ECMS is validated over two test driving cycles to demonstrate its adaptiveness to different driving conditions and the optimality of power distribution management. The main contributions of this research can be summarized into the following three aspects: (1) the Bayesian regularized NN (BRNN) is, to the authors’ knowledge, first proposed to predict the EF for ECMS online application. Compared with Levenberg–Marquardt training algorithm, the main merit of the Bayesian regularization is the capability of developing considerable generalized quality networks [27]. The resulting accuracy and prediction performance are justified in this research; (2) a classification NN is utilized to predict the engine on/off status, so as to adjust the predicted EF to lessen the side effects of the prediction error; (3) a novel EF correction factor is introduced to ensure that the terminal SOC reaches at the desired value at the end of the trip. Thus, the SOC reference trajectory generation is excluded in the energy management system, thereby eliminating its parasitic deficiencies.

The remainder of this paper is organized as follows. Section Ⅱ describes the PHEV powertrain model for EMS performance evaluation. Section Ⅲ demonstrates the overall structure of the proposed NN-based ECMS firstly. The basic ECMS and DP optimization procedure is then presented, followed by detailing the data processing method for the training data preparation. Afterwards, the novel EF correction method is discussed. The NN quality assessment is presented at the end of this section. Section Ⅵ displays important results in terms of the fuel economy. Finally, the main conclusions are summarized in Section Ⅴ.