La coherencia semántica a nivel global como propiedad textual

The battery model is a quasi-steady state semi-empirical model used to calculate the SoC and voltage of the battery based on the net current flow. The battery current is positive for current flowing into the battery, calculated by subtracting the current drawn by the motor from that supplied by the DC/DC Converter. The SoC estimation is a simple a charge accumulation model based on the nominal capacity of the battery. The voltage estimation uses a combination of the Shepherd equation and Peukert’s Law, see Figure 3.12.

Ibat

SOC Estimation

Voltage Estimation V_bat H

Figure 3.12: Battery Model

The Shepherd equation (Equation 3.4.9) is a semi-empirical model used to predict the voltage of the battery, Vbat, dependent on the current, Ibat, and the SoC, H. The first term, V₀, represents the open-circuit voltage, the second, kf(1 − H), represents the voltage drop due to the battery SoC, the third due to the internal resistance, Ri, and the final term empir-ically represents the sudden voltage drop at low SoC using an experimentally determined over-voltage coefficient, ks, also known as the Shepherd coefficient.

V_bat= V_bat,0− k_f(1 − H) − R_iI_bat− k_s 1

H (3.4.9)

For lead acid batteries, the over-voltage coefficient is highly dependent on the current.

At low current draws, the voltage will not begin to suddenly drop until a very low SoC is reached, whereas at high loading, the effect of this parameter will occur much sooner. This can be accounted for by using Peukert’s Law (Equation 3.4.10). Peukert’s law describes how the capacity of the battery is affected by the current loading. This uses the Peukert expo-nent, np, to calculate the Peukert capacity, Cp, which is constant for all current loadings.

k_p = I_bat^npt (3.4.10)

Peukert’s law can be rearranged to solve for the time to depletion, t, and multiplied by the current in order to calculate the normalised capacity of the battery, see Equation 3.4.11.

C_n= C_pI_bat^1−np (3.4.11)

Combining this with the Shepherd equation gives Equations 3.4.12 and 3.4.13, where F represents the absolute Depth of Discharge (DoD) (measured in Ah) and f(I) represents the relative DoD at that current (expressed as a ratio between 0 and 1). These equations differ slightly depending on whether the cell is charging or discharging, and the empiri-cally derived parameters Cp, ks, np, V0, kf, and Ri are subscripted to differentiate between charging, c, and discharging, d.

f (I) = This model does not include dynamic effects due to internal resistance or mass transport within the cell, and also does not include the effects of temperature. In order to prevent algebraic loops in the model, a low pass filter has been used to simulate some delay in the reaction of the output voltage. This filter roughly replicates the response of the battery during testing, however, it is anticipated that the dynamic effects of the battery should not significantly affect the results due to the fact that the dynamics of the battery are much faster than that of the EMS as a whole.

Temperature, however, may have significant effect on the performance of the battery, but has been neglected in this model because a) it is not the focus of the investigation, b) inclusion would significantly increase testing and validation requirements, and c) the extra state would increase the computational effort required for optimisation. The major advan-tage of this model is that it is relatively simple, but detailed enough to include the main effects of current and SoC over a wide range of values, and that can easily be parameterised using experimental results, and as a result, the reduced model uses an identical battery sub-model.

3.4.3.1 Characterisation

The traction battery pack in the Microcab is made up of four AGM lead acid batteries con-nected in series, giving a total nominal voltage of 48V and a total nominal capacity of 44Ah (2.1 kWh). AGM lead acid batteries were chosen due to their deep discharge capacity and low cost. The specification of the battery pack is shown in Table 3.3.

The battery pack has been characterised using the battery testing rig available at Lough-borough University. A single battery was charged and discharged at various levels of cur-rent and the voltage was measured as the state of charge decreased. The resulting data were compiled and used to optimise the coefficients used in the combined Shepherd-Peukert model. The final optimised coefficients are shown in Table 3.4, and the resultant map of battery voltage against current and state as charge is shown in Figure 3.13. It has been as-sumed that all four batteries will behave identically and therefore the output voltage of the single battery can simply be multiplied by a factor of 4. Although in reality this is a simpli-fication, it represents the ideal case. This model represents a battery pack maintained by a battery management system, although technically the Microcab H4 is not fitted with one.

Battery balancing may have an effect on the results, however, it is difficult to accurately represent typical deviations between batteries and still generate reproducible results.

Quantity Value

Battery Model Enersys PC1200

Chemistry Lead Acid

Battery Type AGM

Nominal Voltage, Vbat,nom 12 V Maximum Voltage, Vbat,max 12.84 V Minimum Voltage, Vbat,min 11.7 V Nominal Capacity, Cnom 44 Ah Short-circuit Current, Ibat,max 2600 A Batteries in Series, Ns 4 Batteries in Parallel, Np 1 Internal Resistance, Ri 4.5 mΩ

Table 3.3: Battery Pack Specification

Parameter Value

Open-Circuit Voltage, V0 12.84 V SoC Voltage Drop Coefficient, kf 1.14 V Shepherd Discharge Coefficient, ks,d 0.2 Shepherd Charge Coefficient, ks,c 0.1 Nominal Capacity, Cnom 44 Ah Peukert Exponent (Discharge), np,d 1.28 Peukert Exponent (Charge), np,c 1.013 Peukert Capacity (Discharge), Cp,d 100 Ah Peukert Capacity (Charge), Cp,c 100 Ah Internal Resistance (Discharge), Ri,d 4.5 mΩ Internal Resistance (Charge), Ri,c 10 mΩ

Table 3.4: Battery Pack Model Coefficients

4

Combined Peukert & Shepherd Equations (MATLAB): 1.28

Voltage /V

The results of the battery model have been compared to test data logged on the vehicle during dynamometer testing. Figure 3.14 shows the comparison between the test data in blue, and the model estimation of battery voltage and power based on the input current and depth of discharge (calculated by coulomb counting). The model estimation is shown as a dashed black line. It can be seen that the model accurately represents the test data during both charging and discharging.

Figure 3.14: Battery Test Data

3.4.4 DC/DC Converter

The role of the main DC/DC converter is to step up the voltage generated by the fuel cell (nominally 24V) to the traction battery pack voltage (48V nominal). The model assumes that the DC/DC converter output power perfectly follows the demand from the EMS controller and any dynamic effects can be safely ignored. As a result, the model DC/DC converter can be extremely simple, see Figure 3.15.

P_dem

VDC,in

VDC,out

Output Power

Efficiency

IDC,out

IDC,in

PDC,out

Figure 3.15: DC/DC Converter Model

The output current, IDC,out, is calculated as the EMS demand, Pdem, divided by the output voltage, VDC,out, see Equation 3.4.14.

I_DC,out= P_dem

VDC,out (3.4.14)

An empirically derived linear equation is used to calculate the power drawn at the input.

The input current, IDC,in, is simply calculated by dividing the input power by the input voltage, VDC,in, see Equation 3.4.15.

I_DC,in= 1

η_DC(P_DC,out)

P_DC,out

V_DC,in (3.4.15)

3.4.4.1 Reduced Model

The reduced model of the DC/DC converter neglects the coupling of voltage and current and is based solely on the flow of power through the DC/DC converter. As a result, there is no feedback between the fuel cell and DC/DC converter, nor between the battery and DC/DC converter and the model is entirely unidirectional in order to maximise the computational efficiency of the model, see Figure 3.16.

Pdem Output Power

Efficiency

P_DC,out

P_DC,in P_DC,out

Figure 3.16: DC/DC Converter Model

3.4.4.2 Characterisation

The specification of the DC/DC converter is shown in Table 3.5. The DC/DC converter is rated to a maximum power of 1.7kW, however, the fuel cell is only rated at 1.2kW and therefore the true output power of the DC/DC converter is actually limited by the supply voltage from the fuel cell. The maximum efficiency of the fuel cell is given as 81% which correlates well with the test data.

Parameter Value

Model Zahn DC6350F-SU

Maximum Power, PDC,max 1.7 kW Input Voltage Range, VDC,in 24-63 V Output Voltage Range, V_DC,out 24-63 V Maximum Input Current, I_DC,in,max 50 A Maximum Output Current, IDC,out,max 46 A

Switching Frequency 125 kHz

Maximum Efficiency, η_DCDC,max 81 %

Table 3.5: DC/DC Converter Specification

Analysis of around 110 hours of data collected at the University of Birmingham by Iain Staffell shows that the DC/DC converter efficiency can be approximated using a linear relationship between output power and input power. In reality, the relationship is likely to be more complicated than this, and the efficiency is likely to vary depending on the input and output voltages as well as the loading. However, the DC/DC converter on the Microcab is used under a relatively limited range of operating points, each of which can be fully described using only a single variable, either the input power or output power. As a result, it is possible to simplify the model significantly with minimal loss of fidelity.

Figure 3.17 shows a selection of the data logged during the Microcab’s usage on the University of Birmingham campus. The linear relationship is used to predict the output power of the DC/DC converter based on its input power. It can be seen that the linear relationship accurately represents the vast majority of the test data. Figure 3.18 shows the relationship of output power to input power for the same test data. The linear relationship is very clear in this plot. There is a very high amount of noise in these data, which is most apparent around 1000W output power. This is because the DC/DC converter spends a substantial proportion of its time in this region.

Figure 3.17: DC/DC Converter Test Data

Figure 3.18: DC/DC Converter Output Power vs. Input Power