Download Intro to IEEE 450 Annex J battery model

Introduction to
IEEE 450 Annex J battery model
Before we can delve into battery impedance, we have to make sure
some key electrical principles are understood.
DC electrical theory (constant voltage, frequency is 0)
The element that limits the flow of electricity is called Resistance.
It can be calculated with Ohms Law.
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 (𝑉)
𝑅=
𝑂ℎ𝑚𝑠 (Ω)
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 (𝐴)
AC electrical theory (changing voltage, frequency is greater than 0)
The property that limits electricity flow is called Impedance.
When an AC voltage is applied there is resistance like DC but there are
2 new electrical elements.
Capacitance
Inductance
Impedance =
Resistance + Capacitance Resistance + Inductance Resistance
The term for Capacitance and Inductance Resistance is Reactance (X).
The resistance of the 2 new elements is more complicated because
they depend on the frequency of the voltage applied.
Capacitance reactance XC =
1
2𝜋𝒇𝐶
Inductance reactance XL= 2𝜋𝒇𝐿
f stands for frequency
Impedance (Z)= Resistance (R) + Reactance (X)
However because of the Reactance, Impedance is more complicated
and can be best represented as vectors. X = XL - XC
𝑍 =
𝑅2 + (𝑋𝐿 − 𝑋𝐶 )2
𝑋𝐿 −𝑋𝐶
−1
𝑡𝑎𝑛 (
)
𝑅
𝐴𝑛𝑔𝑙𝑒 =
Impedance is a complex number it has a
modulus (Z) and an Angle (q).
Impedance can be represented in
the following format.
The inverse of Impedance(Z) is
Admittance(Y), and the inverse of
Resistance(R) is Conductance(G).
Admittance 𝑌 =
1
𝑍
Conductance 𝐺 =
1
𝑅
A battery can be represented by a simplified lumped model so that
Electrical Theory can be utilised to quantify the battery behaviour.
Source IEEE 450-2010 Annex J
The Warburg Impedance Zw can be ignored because it’s effect is at
extremely low frequencies outside the range of the existing technology
in the market for online battery impedance measurements.
=
The battery inductance is very small and the battery capacitance is
large. Therefore it is typical to only use one vertical axis, and the
convention is for the axis to point upwards.
The battery impedance is dependent on frequency therefore if we take
two measurements with different frequencies it can be represented as
follows by points f1 and f2.
The battery impedance decreases as the
frequency increases because the battery’s
capacitance is much greater than its
1
inductance. 𝑋𝐶 = 2𝜋𝑓𝐶
Therefore f1 is a higher frequency than f2,
so Z1 is smaller than Z2.
The above result shows if two battery instruments with different test
frequencies measure the same battery the readings are different.
In the battery/electrochemical industry a graph as per the previous
slide is used when a battery’s impedance has been measured across a
range of frequencies, this is known as a Nyquist plot.
Battery model Nyquist plot.
Battery Nyquist plots are unique, like
human finger prints, batteries have
different plots and the differences are more
significant for different types and sizes of
batteries.
Thank you.