Determination of the lithium-ion battery thermal parameters

Standard methods for the determination of the material thermal parameters can be used for lithium-ion batteries. These methods allow determination of a single thermal parameter such as thermal conductivity or specific heat capacity. The density of the lithium-ion battery is usually calculated by measuring the volume and mass of the cell.

The heat capacity is a measurable physical quantity of a substance that characterizes the amount of heat needed to change the temperature of the substance by one degree. In other words, it is the ratio between the amount of heat Q (J) transferred to the sample and the resulting increase in the temperature T (K) by the absorbed heat. The heat capacity can be specified in different terms; molar heat capacity, which is per mole of a pure substance, and specific heat capacity, which is per unit mass of a material (Wilhelm and Letcher, 2009).

The result of the heat capacity determination process depends on the quantity of heat absorbed, which in turn depends on the ambient conditions of the process. In thermodynamics, two processes are usually considered: a constant volume or a constant pressure. The heat capacity at a constant volume can be defined as in (Wilhelm and heat added to the system (J).

The definition of the heat capacity at a constant pressure is derived from the first law of thermodynamics and the enthalpy H (J) of the system (Wilhelm and Letcher, 2009)

P calculated as in (Wilhelm and Letcher, 2009)

T

where a is the coefficient of linear thermal expansion (1/K), V is the volume (m³), and βT

is the isothermal compressibility (1/Pa).

As the heat capacity of the sample depends on its mass, the specific heat capacity is usually used. The value of the specific heat capacity is defined as the value of the sample heat capacity divided by its mass.

The most common way to measure the specific heat capacity of a solid or a liquid is to heat the substance in a calorimeter. The heat capacity of the whole system is defined according to Eq. (1.25), and the heat capacity of the substance under study is calculated by taking into account the heat capacity of the calorimeter. When measuring the liquid heat capacity, the liquid should be stirred to ensure an even distribution of the heat energy throughout its volume.

A similar method for the determination of the specific heat capacity of a lithium-ion battery was used in (Pesaran and Keyser, 2001, Maleki et al., 1999). The presented measurement process requires that a deeply discharged cell is heated in a liquid bath in a Dewar vessel. The specific heat capacity of the cell is calculated by taking into account the Dewar vessel heat capacity and the relation between the required energy and the temperature rise of the liquid.

A cylindrical cell can be heated by using a heating band, which is uniformly distributed on the cell surface as it was done for example in (Barsoukov et al., 2002). The thermally insulated cylindrical cell is heated and the temperature of the cell surface is measured during the heating process. The heat capacity of the cell is determined by Eq. (1.25).

The methods for the determination of the thermal conductivity can roughly be divided into state and transient methods (Yoon et al., 2014). The most common steady-state method is a guarded hot plate, which is more suitable for dry homogeneous samples that can be formed on the plate. The material under study is placed between a heat source and a heat sink. The thermal conductivity of the sample can be determined in the steady state from the information about the heat flux, the temperature difference across the sample and the sample thickness (Czichos et al., 2006)

T h k q



  . (1.27)

where k is the thermal conductivity (W/(m²∙K)), q is the heat flux (W/m²), h is the sample thickness (m), and ∆T is the temperature difference across the sample (K).

The heat-flow meter method is similar to the guarded hot plate method. However, the heat flux is determined by one or two installed heat flux sensors. The heat flux sensors should be calibrated by using one or more reference materials (Czichos et al., 2006). Another method that is more suitable for powdered or granular materials is the radial heat flow method. The powdered or granular material is filled into a cylindrical tube with a large length to diameter ratio, and there is a cylindrical heat source in the middle of the tube.

The thermal conductivity is measured in the steady state by taking into account the length

of the cylinder, the heating power, the temperature differential between two internally located sensors and their radial position.

The steady-state methods need quite a long measurement time, as a steady state is required before starting the measuring process. In transient methods, the measurements can be performed before the steady state has been established. However, these methods require information about the density and heat capacity of the sample. Based on information obtained, the thermal conductivity can be calculated from the thermal diffusivity, which can be directly measured or calculated from an experiment. The measurement of the thermal diffusivity requires accurate recording of the temperature throughout the test.

There are many different transient methods to measure the thermal conductivity. One of the most common transient methods is the transient hot wire. The theory of the method is based on a linear heat source of infinite length and infinitesimal diameter. A line heat source is embedded in the material. The material under study is heated by a linear heat source, and the temperature is measured at a known distance from this heat source (Czichos et al., 2006). A method similar to the transient hot wire method was used to determine the heat transfer resistance of a cylindrical cell in (Forgez et al., 2010). The cell was heated by internal losses during its operation. The temperatures inside the cell and on the cell surface were measured by temperature sensors.

Thermal Impedance Spectroscopy (TIS) can be used for the determination of the battery specific heat capacity and thermal conductivity at the same time. The technical procedure of the TIS has several analogies to the electrochemical impedance spectroscopy (EIS). It addresses the thermal behaviour of a battery in the frequency domain in a similar way to EIS where the electrochemical transfer behaviour is considered. TIS determines the thermal impedance G(jω) that is the transfer function of the temperature response T(jω) with respect to the heat generation Q(jω)

   

 

 

 

 _Re j _Im

j

j j G G

Q

G  T    . (1.28)

where GRe(ω) and GIm(ω) are the real and imaginary parts of the thermal impedance (Ω), respectively. The T(jω) and Q(jω) can be obtained from the Fourier transform of the time signals such as the temperature T(t) and the heat generation Q(t). The temporal signal T(t) can be measured from the surface of the battery, from which the heat is dissipated, and Q(t) can be calculated by Eq. (1.17).

TIS was used for the determination of the cell parameters in (Barsoukov et al., 2002, Schmidt et al., 2011, Fleckenstein et al., 2013). The sinusoidal heat losses were produced by using an external heat source in (Barsoukov et al., 2002) and by using internal heat losses of the battery in (Schmidt et al., 2011, Fleckenstein et al., 2013).