Information on lead acid batteries
Stress factors
Stress factors are all conditions that either directly or indirectly contribute
to ageing (irreversible degradation) of the battery but are not in themselves
an ageing mechanism. The operation of a battery can be described by its time
series of temperature, voltage, current and SoC (state of charge), the latter
being a parameter calculated from the time series of the first three values.
Stress factors are statistical parameters derived from these time series. The
stress factors make it easier to characterise the operating conditions and to
link them to ageing conditions. In lead acid batteries stress factors are for
instance total Ah throughput , charge factor and time between subsequent full
charges.
Stress factors have a relation to ageing mechanisms. This does not mean that a
specific stress factor causes the ageing process and the removal of that stress
factor would stop the process. A schematic overview of the interrelations
between stress factors and ageing mechanisms is given
here.
All renewable energy systems can be sorted into a number of categories of
"similar use" based on how the batteries are used (stressed) in the energy
system. These categories are thus subjected to a similar combination of stress
factors. It is possible that different applications (e.g. wind or solar) result
in the same category. Also similar applications (e.g. two solar home systems)
can be sorted in different categories as a result of differences between the
user's behaviour. Batteries can belong to the same category irrespective of
other physical parameters such as size, capacity or voltage.
The categorisation of battery use in an application can be performed using
measured or simulated time series of the battery's operating conditions. The
categorisation process is described in detail in reference[1].
A summary is provided below.
The number of selected stress factors was kept low to maintain independent
stress factors with relatively clear effects of the factors on the ageing
mechanisms and to maintain a good overview of the categorisation. The
individual stress factors determined during the categorisation process are:
charge factor; time between full charge; Ah throughput; time at low SoC;
highest discharge rate; and partial cycling. Additionally two
temperature-related stress factors were defined. Each of these stress factors
is described in the following sections.
The individual stress factors are calculated by a simple statistic analysis of
data for the time period concerned, which is typically a year or more.
The intensity of each individual stress factor must be evaluated in order to
quantify the influence of the stress factors on ageing. A five level intensity
index was used (1: Very low intensity; 2: Low intensity; 3: Medium intensity;
4: High intensity; and 5: Very high intensity). In most, but not all, cases a
low intensity level is associated with a small effect of the stress factor on
the ageing mechanisms. An exception is the Charge Factor: both low and high
intensity level of the CF provokes (different) ageing mechanisms.
A single stress factor intensity level does not simply indicate the
significance of that stress factor for an ageing mechanism. Depending on the
ageing mechanism the combination of certain stress factors can have a
counterbalancing effect or an amplifying effect. Only the combination of all
stress factor intensities indicates the impact of a particular ageing
mechanism. The performance fading and life limitation in a real RES system by a
particular ageing mechanism depends on the battery technology, design and
quality. The ageing mechanisms are benchmarked by the combination of the stress
factors intensities.
-
Charge factor
The charge factor is defined as the Ah charged divided by the Ah discharged
over the period of analysis. It represents to Ah-losses associated with battery
usage.
Indexation of the charge factor:
| 5: |
very high intensity |
> 130 (%) |
| 4: |
high intensity |
[115; 130) |
| 3: |
medium |
[108; 115) |
| 2: |
low |
[102; 108) |
| 1: |
very low |
<= 102 |
-
Ah throughput
This factor is defined as the cumulative Ah discharge in a one-year period
normalised in units of the battery nominal capacity.
Indexation of the Ah throughput:
| 5: |
very high intensity |
> 100 (C10) |
| 4: |
high intensity |
[70; 100) |
| 3: |
medium |
[40; 70) |
| 2: |
low |
[10; 40) |
| 1: |
very low |
<= 10 |
-
Highest discharge rate
This factor is defined by the highest current at which at least 1% of the Ah
throughput was discharged. The current is expressed in the units of the nominal
current (I10 = C10 / 10h).
Indexation of the highest discharge rate:
| 5: |
very high intensity |
> 1.7 (I10) |
| 4: |
high intensity |
[1.4; 1.7) |
| 3: |
medium |
[0.5; 1.4) |
| 2: |
low |
[0.1; 0.5) |
| 1: |
very low |
<= 0.1 |
-
Time between full charge
This factor is the average time between recharges above 90% SoC.
Indexation of the time between full charge:
| 5: |
very high intensity |
> 8 (days) |
| 4: |
high intensity |
[2.5; 8) |
| 3: |
medium |
[1.2; 2.5) |
| 2: |
low |
[0.7; 1.2) |
| 1: |
very low |
<= 0.7 |
-
Time at low SoC
This factor is the percentage of a year during which the battery remained below
35% SoC.
Indexation of the time at low SoC:
| 5: |
very high intensity |
> 25 (%) |
| 4: |
high intensity |
[15.5; 25) |
| 3: |
medium |
[4.5; 15.5) |
| 2: |
low |
[1; 4.5) |
| 1: |
very low |
<= 1 |
-
Partial cycling factor
Cumulative Ah throughput (in units of C10) sorted in the
following SoC ranges:
A (100 – 85%), B (85 – 70%), C (70 – 55%), D (55 – 40%), E (40 – 0%)
The partial cycling factor is calculated by the weighting function:
PC=(A*1 + B*2 + C*3 + D*4 + E*5)/5
Partial cycling at a low SoC results in a higher "Partial cycling factor".
Indexation of the partial cycling factor:
| 5: |
very high intensity |
> 70 (C10) |
| 4: |
high intensity |
[50; 70) |
| 3: |
medium |
[40; 50) |
| 2: |
low |
[30; 40) |
| 1: |
very low |
<= 30 |
-
Temperature acceleration factor
The effect of elevated battery temperature is expressed in the temperature
acceleration factor.
Tac = ∫a*ek(T-T0)dt/∫dt
T = battery temperature; T0 = 20°C
10°C increase double the factor (a=1, k=ln2/10)
Indexation of the temperature acceleration factor:
| 5: |
very high intensity |
> 1.6
|
| 4: |
high intensity |
[1.15; 1.6) |
| 3: |
medium |
[0.85; 1.15) |
| 2: |
low |
[0.4; 0.85) |
| 1: |
very low |
<= 0.4 |
-
Low battery environmental temperature
The lowest operating battery temperature maintained for at least 12 hours
(average over a 12 hour period).
Indexation of the low battery temperature:
| 5: |
very high intensity |
< -9 (°C) |
| 4: |
high intensity |
[-9; -5) |
| 3: |
medium |
[-5; 0) |
| 2: |
low |
[0; 5) |
| 1: |
very low |
>= 5 |