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
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