Implementation of a predictive energy management strategy for battery and supercapacitor hybrid energy storage systems of pure electric vehicles 1

1.1 Literature review

A key point is how to design an efficient energy management control strategy for battery and supercapacitor hybrid energy storage systems. Specifically, energy management control strategies should determine the appropriate amount of power for each energy storage system according to their actual energy states. From the point view of control model, the energy management control strategies have been divided into two categories: optimization-based control strategies and rule-based control strategies respectively [11, 12].

In optimization-based strategies, the cost functions are designed using past data and are minimized based on future variables/inputs. The controllers are usually optimized offline and then implemented on hybrid energy storage systems. A commonly used optimization method is dynamic programming, where a state model for the hybrid energy storage system need to be first built and a control system that would seek the global optimal power sequences for the battery and supercapacitor is subsequently established [13]. Although the dynamic programming algorithm can give the best solutions in theory, it requires the priori information of a driving cycle and thus is time-consuming. The optimized results are often used as benchmarks for optimizing other energy management control strategies. Global search heuristics are also important members of the global optimization family, which find exact or approximate solutions for complex nonlinear controls and the objective functions that will evolve toward their minimum values. They have been adopted for developing controllers of hybrid energy storage systems, including particle swarm optimization [14], genetic algorithm [15], DIRECT global optimization [16]. To seek tradeoffs between control performance and calculation time, the global optimization algorithms have been simplified into instantaneous ones and the optimization horizons are shortened depending on specific application conditions. In [17], the authors used equivalent consumption minimization strategy (ECMS) to online optimize power flow between two power systems. In the ECMS, the battery charge was converted to the equivalent fuel coefficient, and the total fuel consumption (actual and equivalent) was minimized at each sampling interval. In [18], a model predictive controller (MPC) was developed for real-time power flow optimization during operation, considering physical constraint limitations of each power source in the system. In [19], an optimal operation management framework of clean smart islands was proposed based on primal-dual method of multipliers. This method was proved to be effective in dealing with energy communication problem.

From the perspective of practical engineering application, rule-based strategies are the best ideal candidates because they have good real-time performance and robustness. Such features are mainly based on their simple control structures. The deterministic rule-based control systems perform on a set of rules that have been pre-defined and carried out prior to actual operation. In [20], a multimode control system for hybrid energy storage systems of pure electric vehicles was developed for implementing power distribution. The vehicle operation state switching was realized by a set of logic rules depending on the energy states of battery and supercapacitor. The effectiveness of the proposed method was validated by simulation test. In [21], a new topology structure for hybrid energy storage system was designed. In the topology structure, different working modes was switched by deterministic logic rules. In [22], in order to recycle more braking energy and increase the diving distance of an electric vehicle, the discharge of the supercapacitor was controlled by some simple control logics according to the acceleration states of electric vehicle. The determined rule strategy can realize good control performance by tuning rule parameters reasonably. Fuzzy logic-based strategies are perfect for time-varying and nonlinear control systems, as they are adaptable and robust to parameter variations and easily adjustable [23, 24]. An adaptive energy management control system using fuzzy logic was designed in [25]. In this system, fuzzy rules were determined according to specific driving cycle information, namely the control rules were switched depending on the variations of the driving cycles. Such system can further improve the controller performance, but more control logics are also needed. The rule-based strategies can adjust the peak power between the two energy sources, but they fail to deal with rapidly changing power variations. Urban electric vehicles often need obviously shifty and stochastic power demands for responding uncertain traffic conditions, such as frequent acceleration and deceleration operations, up-hill followed by down-hill runs, etc. To match the dynamic response features of the battery and supercapacitor, filtration-based strategy was further proposed for extracting different frequent components. In [26], load power demand was decomposed into high frequent part and low frequent part. The high frequent part was assigned to the supercapacitor because of its quick charge and discharge rates, and the low frequent part was shared by the fuel cell and battery based on their slow response features. In this way, the load power demand can be satisfied effectively and the system energy loss can also be reduced.

In summary, rule-based and filtration-based strategies have their advantages, a combination of the two is expected to achieve a better control performance. In [27], a combination of wavelet and fuzzy logic was proposed for a hybrid energy storage system. In this strategy, wavelet was used to analyze and capture the transients of load power demand. After that, a fuzzy logic controller was further designed for regulating power flow among energy sources depending on the supercapacitor. Energy management systems with ability to predict vehicle conditions can achieve better control performance. At present, the study of vehicle condition prediction has two main ideas. Some researchers use advanced technologies such as geographic information systems (GIS) and global positioning systems (GPS) to obtain future vehicle speed, slope, and other data. For example, in [28], a scenario-based drive mission for a heavy diesel truck was studied. Look-ahead terrain information was used for optimizing the velocity trajectory with respect to a criterion formulation that weighs trip time and fuel consumption. In [29], the potentials of 3-D road terrain maps were quantified to improve the fuel economy of a parallel hybrid vehicle. Some researchers use methodologies to predict future vehicle condition information. For example, support vector machine method was used to predict the current driving cycle based on the classification results. Finally, according to the current operating cycle slope information, a switchable driving controller is established. In [30], specific roadway types and traffic congestion levels were predicted using learning vector quantization (LVQ) neural network algorithm to emulate the optimal solutions generated by DP, and generalized the optimal power settings to real-world vehicle operation based on the predictive driving condition information. In this study, we propose an energy management control strategy based on a combination of filtration and fuzzy logic for battery and supercapacitor hybrid energy storage system of pure electric vehicles. Different from prior research work, Markov chain model is introduced to the proposed strategy for improve the control performance. The effectiveness of the proposed method is validated based on a 72 V battery and supercapacitor hybrid energy test platform. Some stochastic problems of energy management have been discussed, for example, in [31], stochastic scheduling problem of hybrid AC/DC microgrids considering the plugin hybrid electric vehicles charging demands was studied. In this work, a data-driven framework based on point estimate method and support vector machine was developed to model the uncertainty effects. In [32], the power output uncertainty of the renewable resources was modelled using the Unscented Transform (UT) approach owing to its capability of correlation modelling. In [33], A stochastic framework was designed using point estimate method (PEM) to capture the uncertainties of the photovoltaic and wind turbine forecast error, power company price, the operating temperature of the proton exchange membrane fuel cell, the price for natural gas, price for selling hydrogen, and the pressure of the H2 and O2 in the fuel cell stack. In [34], an effective stochastic framework for smart coordinated operation of wind park and energy storage unit was proposed and the problem formulation was constructed as a tri-level max-min-max structure for getting more sensible results. These above proposed methods handle uncertainties in system components. In this work, the basic idea is to model the driving cycle as a stochastic process considering the uncertainty of the traffic condition.

The actual power demand of an electric vehicle is strongly affected by the traffic conditions, especially for urban traffic conditions. Owing to uncertain and random incidents, the power values for energy storage systems are often largely fluctuating. In the conventional sole energy source system, the battery is frequently suffering from the drastically power peak and high frequent variation, which would potentially degrade the battery electrochemical reaction and thus increase internal resistance and energy loss. To overcome this problem, a low-pass filter is employed for decomposing the load power demand into low and high frequent components. The specific filter model is directly adopted in the MATLAB/SIMULINK software module. For convenience, symbol P _LF is used to represent the low frequency power value from the filter, symbol P _HF is used to represent the high frequency power value from the filter, and symbol P _load is used to represent the load power demand. Consequently, the following two relationship expression can be given by P LF = F ( P load )(1) P HF = P load - P LF(2) where F represents a low-pass filter function. This filter operation would stop battery from providing high frequency power demand and extend its lifetime.

In this work, we model vehicle acceleration state in the upcoming time step by the following first order Markov chain. P ijm = Pr ( a k + 1 = i | a k = j , v k = s )(3) where vehicle speed v_k and acceleration a_k are Markov state parameters, P_ijm is the transition probability of vehicle acceleration, transferring from the acceleration state a_k at the current time step to the acceleration state a_k+1 at the next time step while current vehicle speed v _k  = s.

To obtain Markov transition probabilities, the observation data need to be collected from selected driving cycles and then calculate it by the following expression. P i , j = m i , j m i(4) where m_i,j represents the number of occurrences of vehicle acceleration state transition from a_k to a_k+1 at vehicle speed v _k  = s, m _i represents the total transition number of the acceleration a_k.

Fig. 2 shows the acceleration transition probabilities of UDDS, SC03 and NEDC driving cycles. It can be observed that the state transition probabilities of the three driving cycles are obviously different. Based on speed and acceleration information, the power demand at the next moment can be calculated in (5)and (6).

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Fig. 2

The state transition probabilities of UDDS, SC03 and NEDC driving cycles.

v k + 1 = v k + a k · t(5)

P k + 1 = v k + 1 η ( mfgcos ( θ ) + mgcos ( θ ) + C D A 21.15 u k + 1 2 + δ ma k + 1 )(6) where the formula in (6) is a vehicle longitudinal dynamic model, which is used for power demand calculation. In the model, η represents the energy deliver efficiency of the powertrain system, m represents vehicle weight, f represents the rolling resistance coefficient of tires, g represents gravitational acceleration constant, A represents the frontal area of vehicle, C _D represents drag coefficient, δ represents the conversion factor of rotational motion mass in a vehicle, θ represents road slope angle, here it is assumed to be zero, namely flat road surface. The parameter values of the vehicle model adopted in this study is given in Table 1.

In this subsection, a fuzzy logic controller is designed for regulating power flow between the battery and supercapacitor. The input parameters of the fuzzy controller are the low frequency current obtained from the low-pass filter and supercapacitor voltage, and the output parameter is the surplus current distributed to the supercapacitor for voltage regulation. Different types of membership functions are employed for partitioning the possible variation range of input and output parameters into several fuzzy areas. The current input parameter has four fuzzy domains, which are entitled with negative large (NL), negative small (NS), positive small (PS), positive large (PL). The supercapacitor voltage has three fuzzy domains, which are entitled with low (L), medium (M), high (H). The fuzzy domains used for the output parameter are similar with that of the current input parameter.

In order to obtain an improved fuzzy controller so that the battery current can be effectively reduced. The membership function curves of inputs and output are designed according to the possible power demand levels. An electric vehicle has the same driving state at current and next time interval, namely an electric vehicle is currently in driving state, according to Markov prediction, at the next time interval, it will be still in driving state; or an electric vehicle is currently in braking state, according to Markov prediction, at the next time interval, it will be still in braking state. Either driving or barking states, the fuzzy controller should can reasonably control the supercapacitor discharge for satisfying the continuous power supply of an electric vehicle. The membership function curves of input and output parameters are plotted together using Fig. 3. As for the battery current, the triangular membership function is employed for dividing the current variations into four fuzzy areas from 0 to 100 A, as pictured using Fig. 3(a). For the supercapacitor, in this work, the voltage variation is preset from 0.2 to 1. The triangular curves are employed for the low and high voltage areas, as shown using Fig. 3(b). For the surplus current, the layout of the membership function curves is the same with that of the battery current.

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Fig. 3

The membership function curves of the input and output parameters.