Analysis of the key factors affecting the energy efficiency of batteries in electric vehicle

The energy efficiency for electric vehicle battery is affected by many factors. Through the definition of energy efficiency we find the relationship between energy efficiency, voltage efficiency and coulomb efficiency. The factors such as current, internal resistance, SOC and temperature which affect coulomb efficiency and voltage efficiency, will affect energy efficiency as well. An equation is given to show how internal resistance and current influence the energy efficiency. The relationship between these factors and energy efficiency was analyzed through theory and experimental data. This will show ways to increase battery energy efficiency and improve the battery performance.


Introduction
An electric vehicle's running cost and service life are affected by the battery performance, and the full use of energy of the battery can reduce the operating cost and prolong the service life.The energy efficiency is a significant parameter for electric vehicle battery.So it is necessary to study the key factors affecting the energy efficiency.The purpose is to reduce the charging time reasonably and increase the discharge energy.And then, improve the whole performance of the electric vehicle.There are several ways to express the battery efficiency.We usually use coulomb efficiency and energy efficiency for evaluating battery performance.The battery's coulomb efficiency is defined in USABC (1996) as the ratio of the discharged capacity to the capacity needed to be charged to the initial state before discharge.The coulomb efficiency is shown in [1] as: Where d I is the discharge current, d t is the discharge time, c I is the charge current and c t is the charge time.The experiment indicates that the coulomb efficiency is different with respect to different current rates.At different state-of-charge (SOC) the coulomb efficiency also changes.Only the average coulomb efficiency in the whole charge and discharge processes are obtained from Eq. ( 1).The definition of energy efficiency is similar with the coulomb efficiency.Energy efficiency is defined as the ratio of the discharged energy to the energy needed to be charged to the initial state before discharge.The energy efficiency is shown as: Suppose that the battery is discharged at a constant current d I over a period of time d t in order to restore the initial state before charge.During this time the voltage is expressed by d U .Total capacity and energy According to the definitions of coulomb efficiency and energy efficiency, coulomb efficiency C η and energy efficiency W η can be shown as: From Eq. (7) and Eq.(8) the relationship between coulomb efficiency and energy efficiency is shown as: Where d U is the average voltage of the battery in the whole discharge process and c U is the average voltage of the battery in the whole charge process.And the voltage efficiency V η is defined as the ratio of the discharged average voltage d U to the charged average voltage c U .So the energy efficiency is the product of coulomb efficiency and voltage efficiency: From Eq. ( 10) we find that energy efficiency is affected by voltage efficiency and coulomb efficiency.Decomposing energy efficiency into two parts will make the analysis of the key factors affecting the energy efficiency easier Through the analysis we find that the significant factors that can affect coulomb efficiency C η and voltage efficiency V η are as follows: discharge and charge current , state-of-charge, internal resistance, temperature and the age of battery.The analysis and experiments below eliminate the influence of temperature, SOC and the age of battery and focus on the relationships between current, internal resistance and energy efficiency.

Factors affecting energy efficiency
First, think about the influence on voltage efficiency V η caused by different charging and discharging currents.Charging voltage and discharging voltage are the function of state-of-charge, and they also have to do with internal resistance.Consider the simple Thevenin equivalent in [2] for a battery consisting of an ideal battery of voltage B V in series with an internal resistance, i R (Fig. 1).Voltage Thus the voltage efficiency V η can be shown as From Eq. ( 13), when internal resistance is constant if discharge current d I is greater, the voltage efficiency V η will decrease.With the same discharge current d I , if internal resistance increases, it will also leads to the drop of voltage efficiency V η .During those charge and discharge times, there are i I R power losses in the internal resistance.Since those losses go as the square of current, faster charge or discharge times result in much higher losses.Coulomb efficiency is influenced mainly by three key factors: temperature, current and state-of-charge.Since when the battery is used in an electric vehicle SOC should be limited from 0.2~0.8 in which the coulomb efficiency approximates 1.The relationship between coulomb efficiency and charge or discharge currents can be deduced by the Peukert equation.The Peukert equation in [3] gives a relationship between immediately available capacity deliverable as a function of current.It is commonly modeled as Where Q , capacity, is measured in Ampere-hours, K and n are the Peukert constant and exponent (characteristic battery constant and the battery discharge rate sensitivity exponent), respectively, and I the current in Amperes.In words, it states that as the discharge current increases, the total capacity of the battery (in Ampere-hours), or the total energy delivered by the battery, decreases disproportionately.So coulomb efficiency can be shown as Where d I is discharge current, N I is base current, d Q is the capacity discharged by d I and N Q is the capacity discharged by base current N I .From Eq. (13) and Eq. ( 15) the relationship between energy efficiency and discharge current and internal resistance can be given as So eliminating temperature factor and SOC factor, the energy efficiency can be described in Eq. ( 16).From Eq. ( 16), the internal resistance and discharge current are two important factors that decrease the energy efficiency, so during the use of the battery small internal resistance and appropriate charge and discharge current will help to increase the energy efficiency.

Experimental analysis
Ni-MH batteries from three different companies are tested for analyzing the relationship between energy efficiency; coulomb efficiency and voltage efficiency described in Eq. ( 10).Three companies are shown as A, B and C. In the tables below, experiment result of energy efficiency is the quotient of energy discharged and energy charged; calculation result of energy efficiency is the product of voltage efficiency and coulomb efficiency.For further analysis the relationship between voltage efficiency and internal resistance, the internal resistances are tested.The internal resistance of there three companies are respectively 21.86m Ω , 17.15m Ω and 16.8m Ω as shown in Figure 3.In order to show voltage efficiency better, voltage efficiency of A, B and C companies is given again in Table 4 and compared in Figure 4 below.From the comparison between Figure 3 and Figure 4, it is easy to see that the experimental results correspond to the Eq. ( 13).With the increasing of internal resistance, voltage efficiency of the battery will decrease.From the comparison between Figure 2 and Figure 3, we can also see the relationship between internal resistance and energy efficiency: when the internal resistance increases, energy efficiency decreases as a result.

Conclusion
Through the analysis, energy efficiency can be separated into two parts: voltage efficiency and coulomb efficiency.The key factors such as charge and discharge current, internal resistance, SOC and temperature affecting coulomb efficiency and voltage efficiency will influence the energy efficiency as well.
The relationship between current, internal resistance and energy efficiency is given.Reducing internal resistance and control charge and discharge current appropriately will help to increase the energy efficiency.

BV
can be considered to be the open circuit "rest" voltage of the battery as measured some hours after either charging or discharging has occurred.

Figure 1 :
Figure 1: Thevenin equivalent circuit for a battery According to Thevenin equivalent, internal resistance and current can affect battery voltage during charging and discharging processes.Assuming that during a

Figure 2 :
Figure 2: Comparison between experiment result of energy efficiency and calculation result of energy efficiency

Figure 3
Figure 3 Internal resistances of three companies

1 AFigure 4
Figure 4 Voltage efficiency of three companies

Table 1 :
Experimental data of battery A

Table 2 :
Experimental data of battery B

Table 3 :
Experimental data of battery C

Table 4 :
Voltage efficiency of three companies