IEEE

NICKEL-CADMIUM BATTERIES FOR STATIONARY APPLICATIONS Std 1115-2000

6.2 Additional considerations

Before proceeding to calculate the cell size required for a particular installation, the designer should
consider the following factors that will influence cell size.

6.2.1 Temperature derating factor (Tt)

The available capacity of a cell is affected by its operating temperature. The standard temperature for stating
cell capacity is 25 °C. If the lowest expected electrolyte temperature is below standard, select a cell large
enough to have the required capacity available at the lowest expected temperature. The battery manufacturer
should be consulted for capacity derating factors for various discharge times and temperatures. If the lowest
expected electrolyte temperature is above 25 °C, generally there is no noticeable increase in the available
capacity.

6.2.2 Design margin

It is prudent design practice to provide a capacity margin to allow for unforeseen additions to the dc system,
and less-than-optimum operating conditions of the battery due to improper maintenance, recent discharge,
ambient temperatures lower than anticipated, or a combination of these factors. A method of providing this
design margin is to add a percentage factor to the cell size determined by calculations. If the various loads
are expected to grow at different rates, it may be more accurate to apply the expected growth rate to each
load for a given time and to develop a duty cycle from the results.

Note that the “margins” required by 6.3.1.5 and 6.3.3 of IEEE Std 323-1983 are to be applied during “quali-
fication” and are not related to “design margin.”

The cell size calculated for a specific application will seldom match a commercially available cell exactly,
and it is normal procedure to select the next higher cell size. The additional capacity obtained can be consid-
ered part of the design margin.

6.2.3 Aging factor

Capacity decreases gradually during the life of the battery, with no sudden capacity loss being encountered
under normal operating conditions. Since the rate of capacity loss is dependent upon such factors as operat-
ing temperature, electrolyte-specific gravity, and depth and frequency of discharge, an aging factor should be
chosen based on the required service life (see IEEE Std 1106-1995). The choice of aging factor is, therefore,
essentially an economic consideration. In the sizing calculation shown in Figure A.1, an aging factor of 1.25
is used, meaning that the battery is sized to carry the loads until its capacity has decreased to 80% of its rated
capacity. For an application involving continuous high temperatures and/or frequent deep discharges, it may
be desirable to use a factor of, say, 1.43, and replace the battery when its capacity falls to 70% of rated
capacity. For applications involving short, high-rate discharges such as engine starting, the rate of fall-off in
short-rate performance is slower and a lower aging factor may be used. For example, in an uninterruptible
power supply (UPS) application with a 15 min discharge time and a 15 year desired service life, it may be
appropriate to use a 1.11 aging factor, so that the battery would be replaced when its performance falls to
90% of the published value. The battery manufacturer should be consulted for additional information on
aging factors.

6.3 Effects of constant potential charging

Prolonged float charging of a nickel-cadmium battery will cause a lowering of the average voltage on
discharge. Depending on the discharge rate and minimum battery voltage, the available capacity may be
affected.

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Std 1115-2000 IEEE RECOMMENDED PRACTICE FOR SIZING

The designer should make sure that capacity rating factors, Kt (see 6.4.3) obtained from the manufacturer are
based on constant potential operation.

CAUTION
Hermetically-sealed nickel-cadmium batteries should not be used in constant potential charging applications
(see 5.1).

6.4 Cell size

This section describes and explains a proven method of calculating the cell capacity necessary for satisfac-
tory performance on a given duty cycle. Annex A demonstrates the use of this method for a specific duty
cycle in a stationary float application. An optional preprinted worksheet (Figure 3) is used to simplify the
calculations. Instructions for the proper use of the worksheet are given in 6.5.

6.4.1 Initial cell size

Equation (1) (see 6.4.2) requires the use of a capacity rating factor Kt (see 6.4.3) that is based on the dis-
charge characteristics of a particular range of cell types. Thus, the initial calculation must be based on a trial
selection of cell range. Depending on the results of this initial calculation, it may be desirable to repeat the
calculation for other cell ranges to obtain the optimum cell type and size for the particular application. Use
the capacity from the first calculation as a guide for selecting additional ranges to size.

6.4.2 Sizing methodology

The cell selected for a specific duty cycle must have enough capacity to carry the combined loads during the
duty cycle. To determine the required cell size, it is necessary to calculate, from an analysis of each section
of the duty cycle (see Figure 2), the maximum capacity required by the combined load demands (current
versus time) of the various sections. The first section analyzed is the first period of the duty cycle.

AN
A2 AN–A(N–1) {
A1
A2–A1 { A3–A2
{ A(N–1)
A3

P1 P2 P3 P(N–1) PN
S1
CURRENT

S2
S3
S(N–1)
SN
TIME

Figure 2—Generalized duty cycle diagram

Using the capacity rating factor (see 6.4.3) for the given cell range and the applicable temperature derating
factor Tt, a cell size is calculated that will supply the required current for the duration of the first period. For
the second section, the capacity is calculated assuming that the current A1 required for the first period is
continued through the second period; this capacity is then adjusted for the change in current (A2 - A1) during
the second period. In the same manner, the capacity is calculated for each subsequent section of the duty

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 IEEE
NICKEL-CADMIUM BATTERIES FOR STATIONARY APPLICATIONS Std 1115-2000

cycle. This iterative process is continued until all sections of the duty cycle have been considered. The calcu-
lation of the capacity FS required by each section S, where S can be any integer from 1 to N, can be
expressed mathematically as follows:

P=S
FS = ∑ [ A P – A ( P – 1 ) ]K t T t (1)
P=1

The maximum capacity (max FS) calculated determines the cell size that can be expressed by the following
general equation:

S=N
cell size = max FS (2)
S=1

where

S is the section of the duty cycle being analyzed. Section S contains the first S periods of the duty
cycle (for example, section S5 contains periods 1 through 5). See Figure 2 for a graphical represen-
tation of “section.”
N is the number of periods in the duty cycle
P is the period being analyzed
AP is the amperes required for period P
t is the time in minutes from the beginning of period P through the end of section S
Kt is the capacity rating factor (see 6.4.3) for a given cell type, at the t minute discharge rate, at 25 °C,
to a definite end-of-discharge voltage
Tt is the temperature derating factor at t minutes, based on electrolyte temperature at the start of the
duty cycle
FS is the capacity required by each section S

If the current for period P + 1 is greater than the current for period P, then section S = P + 1 will require a
larger cell than section S = P. Consequently, the calculations for section S = P can be omitted.

6.4.3 Capacity rating factor, Kt

The capacity rating factor, Kt, is the ratio of rated ampere-hour capacity (at a standard time rate, at 25 °C,
and to a standard end-of-discharge voltage) of a cell, to the amperes that can be supplied by that cell for t
minutes at 25 °C and to a given end-of-discharge voltage. Kt factors are available from the battery manufac-
turer, or may be calculated from other published data (see Annex C). Equation (1) and Equation (2) can be
combined as follows:

S=N S=N P=S

cell size = max FS = max ∑ [ A P – A ( P – 1 ) ]K t T t
P=1
S=1 S =1

6.4.4 Random load calculations

When equipment loads that occur at random are included as part of the battery duty cycle, it is necessary to
calculate the cell size required for the duty cycle without the random load(s) and then add this to the cell size
required for the random load(s) only.

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IEEE
Std 1115-2000 IEEE RECOMMENDED PRACTICE FOR SIZING

6.5 Cell sizing worksheet

A worksheet, Figure 3, has been designed, and may be used to simplify the manual application of the proce-
dure described in 6.4. Examples of its use will be found in Annex A, specifically in Figure A.3. Instructions
for proper use of the worksheet areas are as follows:

a) Fill in necessary information in the heading of the worksheet. The temperature and voltage recorded
are those used in the calculations. The voltage used is the minimum battery voltage divided by the
number of cells in the battery.
b) Fill in the amperes and the minutes in columns (2) and (4) as indicated by the section heading nota-
tions. See Annex B for the method of converting power loads to current loads.
c) Calculate and record the changes in amperes as indicated in column (3). Record whether the changes
are positive or negative.
d) Calculate and record the amount of time in minutes from the start of each period to the end of the
section as indicated in column (5).
e) Record in column (6) the capacity rating factors Kt, and in column (7) the temperature derating
factors Tt, for each discharge time calculated in column (5).
f) Calculate and record the cell size for each period as indicated in column (8). Note the separate sub-
columns for positive and negative values.
g) Calculate and record in column (8) the subtotals and totals for each section as indicated.
h) Record the maximum section size [the largest total from column (8)] in item (9), the random section
size in item (10), and the uncorrected size (US) in items (11) and (12).
i) Enter the design margin (≥1.0) in item (13) and the aging factor (≥1.0) in item (14). Combine items
(12), (13), and (14) as indicated and record the result in item (15).
j) When item (15) does not match the capacity of a commercially available cell, the next larger cell is
required. Show the result in item (16).
k) From the value in item (16) and the manufacturer’s literature, determine the commercial designation
of the required cell and record it in item (17).

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NICKEL-CADMIUM BATTERIES FOR STATIONARY APPLICATIONS Std 1115-2000

Project: Date: Page:

Lowest Expected Minimum
Electrolyte Temp: °F/°C Cell Voltage: Cell Mfg: Cell Type: Sized By:
(1) (2) (3) (4) (5) (6) (7) (8)
Temperature Required Section Size
Change in Duration Time to End Capacity Rating Derating (3) x (6) x (7)
Load Load or Period of Section Factor at Factor for = Rated Amp Hrs
Period (amperes) (amperes) (minutes) (minutes) (Ktt ) )
t Min Rate (K (Ttt ))
t Min (T Pos. Values Neg. Values
Section 1 - First Period Only - if A2 is greater than A1, go to Section 2
1 A1= A1-0= M1= t=M1= ***
Sec 1 Total ***
Section 2 - First Two Periods Only - if A3 is greater than A2, go to Section 3
1 A1= A1-0= M1= t=M1+M2=
2 A2= A2-A1= M2= t=M2=
Sec Sub Total
2 Total ***
Section 3 - First Three Periods Only - if A4 is greater than A3, go to Section 4
1 A1= A1-0= M1= t=M1+M2+M3=
2 A2= A2-A1= M2= t=M2+M3=
3 A3= A3-A2= M3= t=M3=
Sec Sub Total
3 Total ***
Section 4 - First Four Periods Only - if A5 is greater than A4, go to Section 5
1 A1= A1-0= M1= t=M1+...M4=
2 A2= A2-A1= M2= t=M2+M3+M4=
3 A3= A3-A2= M3= t=M3+M4=
4 A4= A4-A3= M4= t=M4=
Sec Sub Total
4 Total ***
Section 5 - First Five Periods Only - if A6 is greater than A5, go to Section 6
1 A1= A1-0= M1= t=M1+...M5=
2 A2= A2-A1= M2= t=M2+...M5=
3 A3= A3-A2= M3= t=M3+M4+M5=
4 A4= A4-A3= M4= t=M4+M5=
5 A5= A5-A4= M5= t=M5=
Sec Sub Total
5 Total ***
Section 6 - First Six Periods Only - if A7 is greater than A6, go to Section 7
1 A1= A1-0= M1= t=M1+...M6=
2 A2= A2-A1= M2= t=M2+...M6=
3 A3= A3-A2= M3= t=M3+...M6=
4 A4= A4-A3= M4= t=M4+M5+M6=
5 A5= A5-A4= M5= t=M5+M6=
6 A6= A6-A5= M6= t=M6=
Sec Sub Total
6 Total ***
Section 7 - First Seven Periods Only - if A8 is greater than A7, go to Section 8
1 A1= A1-0= M1= t=M1+...M7=
2 A2= A2-A1= M2= t=M2+...M7=
3 A3= A3-A2= M3= t=M3+...M7=
4 A4= A4-A3= M4= t=M4+...M7=
5 A5= A5-A4= M5= t=M5+M6+M7=
6 A6= A6-A5= M6= t=M6+M7=
7 A7= A7-A6= M7= t=M7=
Sec Sub Total
7 Total ***
Random Equipment Load Only (if needed)
R AR= AR-0= MR= t=MR= ***

Maximum Section Size (9) ________ + Random Section Size (10) ________ = Uncorrected Size (US) (11) ________
US (12) ________ x Design Margin (13) 1. x Aging Factor (14) 1. = (15) ________
When the cell size (15) is greater than a standard cell size, the next larger cell is required.
Required cell size (16) ________ Ampere Hours. Therefore cell (17) ________ is required.

Figure 3—Cell sizing worksheet

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Std 1115-2000 IEEE RECOMMENDED PRACTICE FOR SIZING

Annex A
(informative)

Duty cycle
In the following example, the duty cycle used is that of Figure A.1 and the lowest expected electrolyte
temperature is 0 °C. Subclause A.1 provides an example of a calculation selecting the number of cells to be
used in the battery. Subclause A.2 shows how the cell sizing worksheet can be used to calculate the required
cell size.

A.1 Required number of cells

Example: The dc system voltage limits are from 105 V to 140 V; for the particular cell type being considered
(see subclause A.2), the manufacturer recommends a cell voltage of 1.47 V for satisfactory charging. The
battery and charger must remain directly connected to the dc system at all times.

Number of cells = 140 V / 1.47 V per cell = 95.2, therefore 95 cells

End-of-discharge voltage = 105 V / 95 cells = 1.10 V per cell

A.2 Required cell capacity

From the battery duty cycle diagram, Figure A.1, we can construct Table A.1, which will be of value in fill-
ing in the cell sizing worksheet. The last column of Table A.1 shows the capacity removed for each period.
The total ampere-hour capacity removed may be used to determine the initial cell size (see 6.4.1) for the cal-
culation. Table A.2 shows hypothetical tabular discharge data for the KM medium performance cell range
manufactured by the ABC Company. The table gives current values for discharges started at 25 °C and
terminated when the average cell voltage reaches 1.10 V. In this example, the total capacity removed is 433
Ah and the next larger cell size is KM438P. Therefore, the capacity rating factors (Kt) for the initial
calculation are derived from the data for this cell type. These factors are shown in Table A.3.

Figure A.2 shows hypothetical temperature derating factors (Tt) for KM cells over a wide range of
temperatures.

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