Dynamic Modeling and Simulation on a Hybrid Power System for Electric Vehicle Applications

Hybrid power systems, formed by combining high-energy-density batteries and high-power-density ultracapacitors in appropriate ways, provide high-performance and high-efficiency power systems for electric vehicle applications. This paper first establishes dynamic models for the ultracapacitor, the battery and a passive hybrid power system, and then based on the dynamic models a comparative simulation between a battery only power system and the proposed hybrid power system was done under the UDDS (Urban Dynamometer Driving Schedule). The simulation results showed that the hybrid power system could greatly optimize and improve the efficiency of the batteries and their dynamic current was also decreased due to the participation of the ultracapacitors, which would have a good influence on batteries’ cycle life. Finally, the parameter matching for the passive hybrid power system was studied by simulation and comparisons.


Introduction
With the appearance of 89 kinds of new-energy vehicles in the 2010 Beijing Auto Show, various types of Electric Vehicles (EVs), like pure electric vehicles, hybrid electric vehicles and fuel cell electric vehicles, have begun to appear on the market [1,2].Batteries are usually selected as the electric OPEN ACCESS energy storage system of EVs [3], but when a longer purely electric driving range (i.e., higher energy), higher acceleration rates, and higher power-assisted performance (i.e., higher power) are required simultaneously, as in plug-in hybrid electric vehicles, it is hard for a battery-only power system to meet these demands.One solution is to select more costly larger capacity batteries, which would increase the vehicle weight and decrease the vehicle economy.Another solution is to maintain the original battery capacity and to overcharge or overdischarge the battery, which would decrease its lifespan and make it work at lower efficiency.This dilemma suggests combining together batteries and ultracapacitors to form hybrid power systems as a promising solution to these problems because the ultracapacitor has a higher specific power and much longer lifespan than a battery, despite the fact that its energy density is much smaller than that of a battery [4].The hybrid power system then benefits from the mutual compromise by integrating the advantages and avoiding the disadvantages of batteries and ultracapacitors.Topology and control strategy are key technologies of the hybrid power system, which have a great influence on the energy density, power density, efficiency and ultimate cost of hybrid power systems [5][6][7][8].In comparison, the passive topology, which directly combines ultracapacitors and batteries in parallel, is the simplest one with the least complicated control strategy.This paper mainly discusses the passive hybrid power system to check its advantages and find a reasonable way to match its parameters.

Dynamic Model of the Battery
Compared with other battery models, the Thevenin model is more suitable for modeling lithium-ion batteries [9].Its topology is shown in Figure 1, where U OC represents an ideal voltage source, which describes the battery open-circuit voltage; R b is ohm resistance; Polarization resistance R P and polarization capacitance C P describe the battery's over-voltage U P , used to describe the dynamic characteristics of the battery; i b and U Lb are the load current and load voltage of the battery, respectively.
where SoC 0 is the initial value of SoC; C N is the nominal capacity of battery; η is the coulomb efficiency (including discharging efficiency η dis and charging efficiency η ch ); k ch and k dis are the influence coefficients on the current integration from charging current (i b < 0) and discharging current (i b ≥ 0) respectively, if the battery is charging, The main state equation for the Thevenin battery model is given by Equation ( 2): The Hybrid Pulse Power Characterization (HPPC) test [10] was implemented for a lithium-ion battery module with a nominal voltage of 57.6 V and a nominal capacity of 30 Ah.The model parameter results identified using the robust least squares method are listed in Table 1 [11].

Dynamic Model of the Ultracapacitor
To model the ultracapacitor, a circuit model topology is selected, as shown in Figure 2 [12].Here R uc is ohm resistance; R Puc is self-discharge resistance, which is much larger than R uc ; i uc , U Luc , U c are load current, load voltage and terminal voltage of the ultracapacitor, respectively.Although the manufacturer provides a nominal capacity for the ultracapacitor, the actual capacity must still be verified experimentally, and the main calculated expression is as given by Equation (3): where ΔU Luc is the variation of load voltage during the constant-current experiment.
The load voltage can be calculated using Equation ( 4): In order to indicate the residual electricity of ultracapacitor, State of Voltage (SoV) [13] is used and defined as in Equation ( 5): where U cmax is the nominal voltage of the ultracapacitor.
Based on the experiment data of an ultracapacitor module with nominal voltage of 16.8 V and nominal capacity of 500 F, using the robust least squares method, the model parameters R uc , C uc , which are the function of i uc , and R Puc are identified as in Tables 2-4, respectively.

Dynamic Model of the Hybrid Power System
A passive hybrid power system with the topology as shown in Figure 3 is selected.For use in EVs, the output power from battery pack and ultracapacitor pack must meet the motor's driving power requirements.Since the battery pack and ultracapacitor pack are directly connected in parallel, given a certain power load profile P m , the battery current i b and ultracapacitor current i uc can be found from basic circuit rules like Kirchhoff's voltage and current laws: where τ hps = C uc (R uc + R b ), and  is determined by the initial state of U c , U L , i L .Based on Equations ( 6)-( 9), the iterative calculation process for passive hybrid power system can be accomplished with a discretization algorithm as described in Figure 4.

Simulation Experiments
For the passive hybrid power system, since the terminal voltages of battery pack and ultracapacitor pack are equal at any time, the current division between the battery pack and ultracapacitor pack is determined solely by their internal resistances and open-circuit voltages.
In order to show the different performance of a battery only power system and a hybrid power system, a comparison simulation experiment was carried out under the UDDS (Urban Dynamometer Driving Schedule).What's more, in order to find the influence of different parameter matching on the performance of the passive hybrid power system, several simulation experiments were carried out comparing a fixed ultracapacitor pack and different battery packs with different cells.The basic parameters of the simulated hybrid electric vehicle are shown in Table 5.   Simulation results and comparisons between the batteries only power system and the hybrid power system are shown in Figures 5 and 6.SoC of battery only power system SoV of hybrid power system SoC of hybrid power system From Figure 5, the ultracapacitor pack absorbs the regenerative braking energy quickly and the impact of a big charging current on the battery pack is avoided.Furthermore, the charging current of the battery pack in the hybrid power system is less than 0.5 C, which would be very helpful to increase the cycle life of battery; while in power battery only power system, the charging current is nearly 2 C.However, inevitably, the battery pack charges the ultracapacitor pack for voltage balancing, so the discharging current of battery pack in the hybrid power system sees no significant reduction.
From Figure 6, because the ultracapacitor pack absorbs the braking energy actively and efficiently, and affords the additional peak power to meet the vehicle driving power requirement, the battery pack's output is smoothed, its SoC consumption is decreased by 2% and 7.78% electricity is saved after one UDDS, compared with the battery only drive system, which should be very helpful to extend the vehicle's driving range.
Figure 7 shows a comparison of the current histogram between the battery only power system and the hybrid power system.For the battery only power system, the duration of the charging current at 1 C is more than 100 s and at 2 C it is more than 30 s, while for the hybrid power system, the charging current of battery pack is less than 0.33 C, and the braking energy is absorbed by the ultracapacitor pack, which results in much higher efficiency, furthermore, the battery pack's working condition is greatly optimized.Table 6 lists the simulation results of difference of SoC, difference of SoV and SoC consumption savings and electricity savings percent compared with the battery only power system after one UDDS for different hybrid power systems.It was shown that some reasonable matching of battery pack and ultracapacitor pack parameters is necessary to achieve a higher performance.If the open-circuit voltage of the battery pack is lower than the maximum voltage of the ultracapacitor pack, the ultracapacitor pack would discharge a lot, which leads to low-SoV working of the ultracapacitor pack with a decrease of battery pack life.If the open-circuit voltage of the battery pack is larger than the maximum voltage of the ultracapacitor pack, the ultracapacitor pack's work is limited and the battery pack would discharge a lot, which makes it difficult to make the best of the advantages of the hybrid power system.
order to indicate the residual electricity of the battery, State of Charge (SoC) is traditional used, which is defined by Equation (1): b

Figure 2 .
Figure 2. The circuit topology of ultracapacitor model.

Figure 3 .
Figure 3.The circuit topology of a passive hybrid power system.

Figure 4 .
Figure 4. Iterative algorithm for hybrid power system calculation.

Figure 6 .
Figure 6.Comparison of SoC and SoV curves.

Table 1 .
The list of the identification results of lithium-ion battery model parameters.

Table 2 .
The list of the identification results of R uc .

Table 3 .
The list of the identification results of C uc .

Table 4 .
The list of the identification results of R Puc .

Table 5 .
The basic parameters of the simulated vehicle.