User’s Manual
43
These are the definitions of the variables we will use in the following equations:
𝐶
𝑒𝑜𝑙
- Capacitance at end of life
𝐶
𝑡𝑜𝑡
- Total capacitance of the entire cap bank
𝐸𝑠𝑟
𝑡𝑜𝑡
- Total equivalent ESR for the entire cap bank
𝐸𝑠𝑟
- Internal resistance at end of life
𝐼
𝑝𝑒𝑎𝑘
- Peak current into the M3534 during the discharge cycle
𝐽
𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒
- Total energy in charged capacitor bank prior to discharge
𝐽
𝐿𝑜𝑠𝑠𝑇𝑜𝑡
- Total losses during discharge
𝐽
𝑜𝑢𝑡
- Energy required to hold up the system during the outage
𝑛
𝑠𝑒𝑟𝑖𝑒𝑠
- Number of capacitors in each series string
𝑃
𝑠𝑦𝑠
- System power in kilowatts
𝑇
𝑜𝑢𝑡
- Time outage in seconds
𝑉
𝐶ℎ𝑎𝑟𝑔𝑒
- Charge voltage at beginning of discharge
𝑉
𝐶𝑎𝑝𝐸𝑛𝑑
- The capacitor string voltage at the end of the discharge
𝑉
𝐶𝑎𝑝𝑀𝑎𝑥
- Maximum charge voltage for the capacitor
𝑉
𝑒𝑛𝑑
- Lowest voltage the capacitor bank can reach
𝑉
𝑇𝑒𝑟𝑚𝐸𝑛𝑑
- Terminal voltage of an individual capacitor during discharge
7.4.1.
E
NERGY
R
EQUIRED FOR
O
UTAGE
The total energy required for the event must be calculated first.
Using the following equation, the total number of joules required for the
outage can be calculated:
J
Out
= P
sys
∗ T
out
We will use a specification of 100 hp. for a 2 second outage for this example.
For instance, a 100 hp drive outage for 2 seconds would be
P
sys
= 100hp ∗ .746 kwatts horsepower
⁄
= 75kW
The total number of joules required is:
J
Out
= 75kW ∗ 2s = 150kJ
7.4.2.
M
INIMUM
C
APACITOR
B
ANK
V
OLTAGE
There is a minimum voltage level that must be maintained at the end of the
discharge during backup. An M3534R for a 460VAC nominal system has a
minimum input voltage of 320VDC. Therefore, the final discharge voltage of
the capacitor bank (
𝑉
𝑒𝑛𝑑
) should be 320 VDC.
These data are available in the specifications for the specific M3534R by
nominal system voltage.
