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Today’s battery powered electric vehicles still face many issues: (1) Ways of improving the regenerative braking energy; (2) how to maximally extend the driving-range of electric vehicles (EVs) and prolong the service life of batteries; (3) how to satisfy the energy requirements of the EVs both in steady and dynamic state. The electrochemical double-layer capacitors, also called ultra-capacitors (UCs), have the merits of high energy density and instantaneous power output capability, and are usually combined with power battery packs to form a hybrid power supply system (HPSS). The power circuit topology of the HPSS has been illustrated in this paper. In the proposed HPSS, all the UCs are in series, which may cause an imbalanced voltage distribution of each unit, moreover, the energy allocation between the batteries and UCs should also be considered. An energy-management scheme to solve this problem has been presented. Moreover, due to the parameter variations caused by temperature changes and produced errors, the modelling procedure of the HPSS becomes very difficult, so an H_{∞} current controller is presented. The proposed hybrid power source circuit is implemented on a laboratory hardware setup using a digital signal processor (DSP). Simulation and experimental results have been put forward to demonstrate the feasibility and validity of the approach.

_{∞}control

With the emergence of the energy crisis, electric vehicles (EVs) are attached with great importance because of their high efficiency and environmentally friendly features. Hybrid electric vehicles (HEV), plug-in electric vehicles (PEV) and fuel-cell electric vehicles (FEV) have been getting more attention in recent years. Many famous enterprises have launched their feature EVs. PEVs still face several challenges: (1) How to recover the braking energy more efficiently with minimum harm to the batteries; (2) How to provide instantaneous and maximum power output when the EVs are in accelerating or climbing operations; (3) How to maximally extend the mileage of PEVs.

Aiming at resolving the aforementioned challenges, a lot of work has been done so far in the last decade. A hybrid power source system (HPSS), which was based on an ultra-capacitor-battery combination is put forward to solve this problem. The ultra-capacitor, or electrochemical double-layer capacitor, has great advantages compared to the standard electrolytic capacitor in high energy and power density, high efficiency and cycling capability, and long endurance [^{2}/g [

The state-of-art on HPSS can be summarized as follows: In [

From the aforementioned previous works, we may know that much of the research work related to HPSS has been done [_{∞} for HPSS is designed, weighing functions selection criteria for H_{∞} are elaborated in

_{b}, which serves as the main energy system, is directly connected to the load through a DC-bus. The UCs are connected to the DC-bus via a bi-directional buck-boost DC/DC converter which contains two power transistors (T11, T12) and an inductance _{bat} and ultracapacitor current _{uc}. The proposed scheme can satisfy both the steady and dynamic power requirements for the PEV. Therefore, how to manage the energy between the two power sources is the key of this paper.

From

Similarly, for braking operation, the possible modes are: (

In the following parts, Since (

Proposed hybrid power source for EVs. (

Operation in regenerative braking happens when the EVs are in deceleration or running downhill, regenerative braking can provide an electric braking torque for the motor, the direction of the braking current _{brake} from the mains will change from the positive to negative direction. If the EVs are running at high speed, the instantaneous braking power for the motor would be very big. In a conventional PEV system, the batteries are controlled to absorb this energy, instantaneous and large charging current might occur for braking control, and without being properly controlled, this charging current _{bat} might be harmful to the batteries, such as causing fast internal temperature rise, which will shorten the life-time of batteries, and sometimes, even cause serious explosions. The ultra-capacitor, by its nature, has the capability of absorbing large currents and is suitable for this application.

_{uc} can be large enough to keep the DC-link voltage at its reference value.

The charging current of the batteries in

The charging current of the batteries in

Operation principles of the HPSS in regenerative braking operation. (

From the aforementioned description of the charging current direction in regenerative braking operation, we can know that the bidirectional DC-DC converter is assigned as an interface between the batteries and the ultracapacitors. The combination of batteries and ultracapacitors has the merits of high power density and specific energy. Hence, how to dynamically allocate the charging current between the batteries and the ultracapacitors is the key issue.

In [

From the above analysis, we can conclude that the best way for energy allocation of HPSS is to certify the needed power of EVs in use, which is decided according to the state of charge (SOC) of the batteries and ultra-capacitors, then, the energy allocation scheme can be realized by fuzzy control theory. Another solution is to put forward an objective optimization function which is composed of minimum battery energy consumption, the real maximum power output of EVs, the SOC of batteries and ultra-capacitors, the maximum output current of the batteries, and the variations of the acceleration pedal.

An optimal way to improve the energy recovery efficiency of HPSS is to detach the instantaneous charging current _{ac} and the consistent charging current _{dc} from the total braking power P_{Brake}, to realize this purpose, a current filter is needed. _{h} can be derived by the difference between the total braking current _{brake} and dc-current component _{dc}. Since the ultra-capacitors are series together, state of charge (SOC) on ultra-capacitors should be considered, the current allocation for each UCs are different.

Current allocation scheme for ultrapacitors and batteries in regenerative braking operation.

From _{dc} and the DC-component of the DC-link current _{bat}.

In the proposed scheme, either in driving or regenerative braking operation the bidirectional DC-DC converter is the key issue. The DC-DC converter contains power transistor T11 and T12, filter inductance _{bat} and the motor, and the driving motor. Since the structure of the two energy sources are similar, hence, the same equivalent circuit can be used for modeling, in the following parts, we will conclude the mathematical model of the hybrid power source system in regenerative braking operations.

In regenerative braking operation, the back electromotive force (BEMF) of the motor, the DC-DC converter, the UCs and batteries form a closed circuit, The Kirchhoff’s Voltage Law (KVL) equation of the power circuit can be derived in continuous conduction mode (CCM):

In _{s}), _{s} is the modulation period of the power transistor. The regenerative braking energy is temporarily stored in the filter inductance. The voltage drop on the inductance would be:

In Equation (1), _{m} is the filter inductance, _{m} denotes the BEMF of the motor, _{m} is the motor current, _{m} and _{d} denote as the internal resistance of the motor and equivalent of the diode in on-state.

When T12 is _{s} ≤ _{s}):

According to the electromagnetic torque equation:

Assuming that the state variable _{m} ω]^{T}, output current is _{b}, back electromotive force (BEMF) expression of the driving motor is _{m} = _{e}ω.

When T12 is _{1}, control matrix _{1} and output control matrix C_{1} under regenerative braking can be derived as:

Similarly, When T12 is _{2}, control matrix _{2} and output control matrix _{2} under regenerative braking operation can be derived as:

After being processed by perturbation, and steady state variable separation and instantaneous variable, the linear small signal model of the system can be written as:

Nowadays, the H_{∞} control issues has been standardized, and block diagram of H_{∞} design can be represented as shown in

H_{∞} design.

In

In Equation (5), _{1}, _{11}, _{21} are the coefficient matrices for noise input signal _{2}_{12}_{1} and _{2} are the state variable coefficient matrix, respectively. Equation (5) can also be written as the system matrix expressed as:

Then, the transfer-function of G(s) from noise signal input _{zw}_{11} + _{12}_{22}^{-1}_{21}

In Equation (7), LFT is the Linear Fraction Transformation function (LFT), _{11}, _{12}, _{21}, _{22} in Equation (7) are defined as:

In the design procedure of a feedback control system, performance requirements of the closed-loop system include: robust stability, sensitivity to the disturbances, dynamic performance, and speed response error both in steady state and steady-state. Among them, robust stability and sensitivity to disturbance are especially important in a closed-loop system, and they are also the basic conditions for normal operation of a system. In order to reduce the sensitivity to perturbation and improve the robustness-stability of the system, special requirements are needed for the sensitivity-function in finite-frequency range. Compound sensitivity optimization has particular merits; by selecting a proper weighing function, it can force the system’s sensitivity function to be changeable within the expected rule, thus satisfying as a result, the requirements of the closed-loop system.

In this paper, based on the H_{∞} compound sensitivity control theory, aiming at the HPSS system, a robust regenerative braking H_{∞} is designed to guarantee the robust stability of the system under parameter variations and un-modelled component of the batteries and UCs, this method can minimize and disturbance caused by disturbances. The multiplicative uncertain feed-back control system is shown in

Multiplicative uncertain feed-back control system.

In ^{-1} is defined as the complementary sensitivity function. If the variations of the system △^{-1}(^{-1}

Hence, the tracking error of the system for the reference ^{-1}(^{-1}

Since the H_{∞} design problem can be realized by solving two Riccati equations [_{∞} control problem, _{∞} control of a mixed-sensitivity design problems.

The mixed-sensitivity design methodology diagram being transformed to a H_{∞} standard controller.

In

The closed-loop transfer-function _{zw}(s) of the system from _{zw}_{l}_{11} + _{12}_{22}^{-1}_{21}
_{l}_{zw}_{∞} ＜ 1

In _{1}(_{2}(_{2}(_{2}(s) should be large enough at high-frequency section, in addition, frequency of _{1}(_{2}(_{2}(_{3}(_{3}(_{∞} is equal to the sum of the controlled object and weighing function, in order to get a low exponent H_{∞}, it is better to choose a low exponent weighing function under the guarantee of the system’s design requirements.

After being regulated many times using Matlab/robust toolbox, the frequency weighing function of the H_{∞} of the EVs in regenerative braking operation can be written as:
_{1}(_{2}(_{3}(

According to the mathematical model described in Equation (4), and the suggested weighing function in Equations (14)–(16), The frequency weighing composite sensitivity H_{∞} can be derived as:

Assuming that the sampling time

In order to validate the proposed scheme, an HPSS system hardware platform using a digital signal processor (DSP)-TMS320F28335 (Texas Instruments, Dallas, TX, USA) has been set up in the laboratory (see _{d} coefficient) in experiments are chosen by simulation verifications using Matlab/SimPowersystem. Specifications of the HPSS used in the hardware platform are listed in _{p} = 1.5, _{i} = 0.002, _{d} = 0, sample time _{s}

In motoring operation, when the PEV needs an instantaneous and peak power output, and meanwhile, the ultra-capacitors are fully charged and have stored enough energy, the HPSS is controlled as a boost DC-DC converter which works in parallel driving mode. The additional energy is provided by the ultra-capacitors and batteries.

Since the ultra-capacitor has the merits of high energy and power density, and high efficiency of charging and discharging current. In deceleration or braking operation, the ultra-capacitors have priority to be charged. A constant power charging control strategy is implemented in this paper, which means position of the pedal determines the braking power command. The maximum braking power reference is limited to 10 kW.

Hardware setup for experiments. (

_{b} stands for the batteries’ discharging current, _{c} stands for discharging current of the ultra-capacitors. In motoring operation, the DC-DC converter acts when the discharging current of the batteries _{b} is greater than 140 A; the additional current needs are supplied by the ultra-capacitors, in this way, the batteries can be protected from over-discharging.

Discharging current of the batteries and ultra-capacitors under motoring operation. (_{∞}.

Also seen from _{∞} can perform very well, the total discharging current _{dc} is well constrained to 140 A, yet, the performance indicates that the steady state error and time response of H_{∞} are superior than that of conventional PID controller. The steady state error _{ss} and time response of PID controller are: _{ss_pid} ≈ 5 A, _{pid}_{∞}, they are: _{ss_H∞} ≈ 2 A, _{∞} = 11 s. Hence, the H_{∞} has much faster time response (2 s) than the PID controller, which is caused by a large integral variable existing in the PID controller. The larger the integral coefficient is, the slower the time response would be. On the contrary, Equation (18) is discrete, which does not have any integral component, so it is easier for fast implementation. It should also be noted that the smaller the upper limit of batteries’ discharging current is, the larger its available capacitance would be, but this upper limit is constrained by the maximum energy stored in the ultra-capacitors. If the energy stored in the ultra-capacitor is large enough, it would be better if the batteries’ reference discharging current is restrained to be a relatively smaller value. This would be beneficial for improving the available capacitance of the batteries. In our experiment, the energy stored in the ultra-capacitors is relatively smaller, that is why the batteries’ discharging current is set to 140 A.

_{∞}, respectively, under regenerative braking. The terminal voltage of the ultra-capacitors V_{C} and their charging current _{c} are also provided. It can be clearly seen that the regenerative braking operation starts at 1 s, the charging current of the ultra-capacitors increases from 0 to 60 A (peak value). This procedure lasts about 0.25 s. After that, the EVs slow down, and the charging current starts to decrease, at 4.5 s, the charging current, again, is reduced to 0 A. The ultra-capacitors’ terminal voltage increases from 100 to 200 V during the braking procedure. _{c}, since the reference charging power of the ultra-capacitors is constrained to 10 kW, the experimental shows that the charging power is well controlled to the reference value, and this procedure lasts about 3.5 s.

Charging current of the ultra-capacitors using PID controller in regenerative braking operation. (_{c} and charging current _{c}; (_{c}).

Compared to a conventional PID controller, H_{∞} is also adopted in our implementation. _{∞} under regenerative braking. As compared to _{∞} and 9.5 kW for PID controller, which means that the H_{∞} could acquire more energy (about 5.3%) than the PID controller under the same conditions.

Charging current of the ultra-capacitor pack using H_{∞} under regenerative braking. (_{c}) and charging current _{c}; (_{c}).

In this paper, we have analyzed a hybrid power supply system composed by UCs and batteries for extending the one time charging driving mileage and energy recovery efficiency of EVs. The main objective of this paper is to provide a practical DC-DC converter and an optimal energy management control scheme. Based on that, stability, dynamic response, and a design procedure for H_{∞} are put forward. The experimental results demonstrate that when using the proposed energy-management scheme and the proposed H_{∞}, a vehicle can acquire more braking energy (about 5.3%) than with a conventional PID controller under the same conditions.

Future work includes the calculation of the energy allocation scheme for two or more energy saving components, where parameter variations of the buck-boost inductance and capacitance of the ultra-capacitor pack should also be taken into account and this is left for future investigation.

This work was simultaneously supported by the Fundamental Research Funds for the Central Universities of China (NO. ZYGX2012J095), China Postdoctoral Science Foundation Funded Project (2013M542266), Natural Science Foundation of China (NSFC) (No. 61106107), and supported by the National Research Foundation of Korea (NRF) funded by the Government of South Korea (MEST) (No. 2013009458) and (No.2013068127). The authors would like to thank all the reviewers for their advices and suggestions on improving this paper.

Bo Long and Zhi Feng Bai conceived and developed the idea behind the present research and proposed the Hinf controller for HPSS under regenerative braking. Bo Long, Shin Teak Lim and Ji Hyoung Ryu have carried out the hardware setup of HPSS, literature review and manuscript preparation. Final review, including final manuscript corrections, was done by Kil to Chong and Bo Long.

Parameters of the hybrid power source system used in experiments.

Elements | Parameters | Values |
---|---|---|

Battery pack | Rated capacity _{e} |
245 Ah |

Battery type | Lead-acid | |

Recommended charging and discharging current | 20A/800 A | |

Quality of each unit | 55 kg | |

Batteries used in series | 10 | |

Battery manufacture factory | Panasonic | |

Ultra-capacitor pack | Rated energy saving | 43 kJ |

Capacitance _{UC} |
0.7 F | |

Number of ultra-capacitors in series | 2 | |

Rated voltage | 350 V | |

Rated charging and discharging current | <400 A | |

Parameters of EVs | Mass of the EV | 1500 kg |

Rated power output | 20 kW | |

Radios of the tire | 0.287 m | |

Transmission ratio of the gear | 4.7 |

The authors declare no conflict of interest.