PhD Thesis - Cranfield University

Chapter 3
3.12 Battery State of Charge (SoC)
The battery state of charge is a dimensionless parameter that represents the present capacity
in relation to the nominal capacity of the battery. As the battery is discharged and charged,
the SoC indicates the relative amount of energy that has been removed or added into the
battery Expressed in a normalised ratio, the SoC of a battery system is stated as,
actual battery charge
SoC batt =
( 3-24)
total battery charge
The accuracy in determining this parameter is important for successful implementation of
any power and energy management scheme as well as for providing information regarding
the amount of usable energy in the battery system. Various techniques have been used to
estimate battery SoC such as fuzzy logic modelling [96] , analytical methods using Peukert’s
equation [97] and a combined approach using empirically obtained look-up table [2].
In most SoC determination methods, the battery current is integrated over time and related
to battery nominal capacity. Current integration methods however are prone to integration
errors caused by long-term drift in the calculation. A periodic resetting of the SoC is
therefore required.
Discharging a battery system rated at Cn from t0 to t1 at discharge current I b brings the
battery state of charge at t1 to,
SoC
batt
∫
t1
I b ( t)
to
( t1)
= SoCbatt
( t0)
+
( 3-25)
C 3600
n
in real time control applications, the battery SoC can be calculated in discrete time steps as,
⎛ I b∆T
⎞
SoC ( + 1)
= ( ) + ⎜
⎟
batt k SoCbatt
k
( 3-26)
⎝ Cn
3600 ⎠
with ∆T being the sampling period between k and k+1 and the sampling time is sufficiency
small to assume that the battery current remains constant during the time step.
69