Substation Battery Sizing Calculation Made Easy

Batteries are the lifeline to substations, providing backup power. I’m going to go over a typical substation battery sizing calculation.

I’ll show you step by step how to do the calculation. Also, the considerations you need to make for your different substation loads.

Before we go over the calculation, let’s discuss batteries in substations. You can then better appreciate the importance of this calculation.

The lifeline of substations are batteries

Substations are a part of every power grid. They convert voltage from high to low, and vice versa.

Without substations, power grids around the world couldn’t operate.

Now, why do substations need batteries? Batteries ensure all critical substation loads will operate at all times.

To better understand, in a substation, the primary source of power comes from your AC power supply. But, you can’t completely rely on your AC power supply.

If a substation’s transmission line or generation source goes offline, you’ll lose power. Without your AC power supply, how will critical equipment remain operable?

To answer this question, take a look at the schematic diagram below.

21kv switchgear dc schematic

You can see the 120V AC supply feeds the 21kV switchgear protection loads. The protection loads are all powered by 48V DC though.

For this reason, we use a battery charger. The battery charger converts the 120V AC supply to 48V DC. Also, in parallel, a 48V DC battery floats.

What is float charging?

It’s also called standby use. We use a battery as an alternate power source in case we lose the 120V AC power source.

So, the battery must remain fully charged ready to use at all times.

How does the battery system work?

The battery always remains online. And with the AC power supply connected, the following two things will happen:

  1. The battery charger will trickle charge the battery as needed.
  2. The AC power supply will power the loads through the battery charger.

If you need more power, the battery will supply it. But, if you lose your AC power supply, the battery will supply power without interruption.

This way, if there’s a power outage, all devices will continue to have power. This is the benefit of independent power sources like batteries in your system.

Low voltage power schematic with a DC panel

The next schematic is similar to the previous. But now, the battery charger feeds a 125V DC panel.

The 125V DC panel then feeds all the critical DC loads. Again, we have a floating battery in case we lose AC power.

125v dc schematic

Reviewing these schematics, it’s clear how batteries are a backup to the AC power supply. They also do the following:

  • Power microprocessor relays, control circuits, emergency lighting, and communication equipment.
  • Provide uninterruptible power.
  • Actuate power circuit breaker trip and close coils.
  • Operate motor-operated air breaks, motor-operated valves, pumps, and fans.

Without DC backup power, you can damage substation and downstream equipment. It can also become a safety concern.

Substation battery sizing calculation

batteries in substation control room

We’ll calculate the size of a flooded cell, lead-acid battery for a substation. The battery will have a rating of 125V DC nominal. Also, the battery will have an amp-hour capacity rated for an 8-hour rate of discharge.

The 8-hour rate of discharge is typical for substations. This gives operators 8-hours to fix any AC power supply issues.

Important Note: the substation battery sizing calculation is per IEEE Standard 485. This standard is a method for defining DC loads and sizing lead-acid batteries. 

Before we start, the following are the two different load types in a substation:

  • Continuous loads: loads that normally operate continuously. Operating for 8 hour periods.
  • Momentary loads: loads that operate for less than 1 minute.

Now, we’ll go over the loads for our substation battery sizing calculation.

Continuous load list

  • Auxiliary relays & timers: (10) x 5VA = 50VA
  • Indicating lights (LED): (20) x 5.5VA = 110VA
  • Multifunction relays: (18) x 5VA = 90VA
  • Power meter: (16) x 10VA = 160VA
  • SCADA allowance: 1000VA

Total: 50VA + 110VA + 90VA + 160VA + 1000VA = 1,410VA

\Rightarrow \dfrac{1410VA}{125VDC} = 11.28A\: at\: 125VDC

Important Note: the “Multifunction relays” consist of all your regular protection relays. For example, 86L, 86B, 86T, 151T/151N, 87A, 51AT, and so on.

They’re grouped together in our calculation for simplicity. Typically, each relay has a load no greater than 5VA. But, you should individually check each relay’s load to verify.

Momentary load list

  • Auxiliary relays: (5) x 5VA = 25VA at 1 second
  • Breaker close coil: (20) x 150VA = 3,000VA at 0.05 seconds
  • Breaker spring winding motor: (20) x 500VA = 10,000VA at 5 seconds
  • Lockout relays: (6) x 325VA = 1,950VA at 0.01 seconds
  • Main breaker trip coil: (20) x 150VA = 3,000VA at 0.03 seconds

Total summed design load

Peak load (S_{p}) = Continuous load + Coincident intermittent load
= 1,410VA + (25 + 3,000 + 10,000 + 1,950) VA
= 1,410VA + 14,975VA = 16,385VA

Important Note: don’t include both the “main breaker trip coil” and “breaker close coil”. You can only activate one at a time. Thus, we include only one in our peak load calculation. 

Design load (S_{d}) = S_{p}(1 + K_{g})(1 + K_{c}), where:

  • K_{g} = contingency for future load growth (assume 10% = 0.1)
  • K_{c} = design contingency margin (assume 10% = 0.1)

(S_{d}) = S_{p}(1 + K_{g})(1 + K_{c})
= 16,385VA (1 + 0.1)(1 + 0.1)
= 19,825.85VA

\Rightarrow \dfrac{19825.85VA}{125VDC} = 158.61A\: at\: 125VDC

Design energy demand calculation

E_{d} = E_{t}(1 + K_{g})(1 + K_{c}), where:

  • K_{g} = contingency for future load growth (assume 10% = 0.1)
  • K_{c} = design contingency margin (assume 10% = 0.1)

E_{t} = (1,410VA \times 8 \: hours) + (25VA \times 1 \: min \times \dfrac{1 \: hour}{60 \: min}) +  (3,000VA \times 1 \: min \times \dfrac{1 \: hour}{60 \: min}) + (10,000VA \times 1 \: min \times \dfrac{1 \: hour}{60 \: min}) +  (1,950VA \times 1 \: min \times \dfrac{1 \: hour}{60 \: min})

E_{t} = 11,280VAh + 0.42VAh + 50VAh + 166.67VAh + 32.5VAh
= 11,529.59VAh

E_{d} = E_{t}(1 + K_{g})(1 + K_{c})
= 11,529.59VAh (1+.1)(1+.1)
= 13,950.8VAh

C_{min} = Minimum battery capcaity in Ah

C_{min} = E_{d}\dfrac{(K_{a} \times K_{t} \times K_{c})}{V_{dc}}\times K_{dod} \times K_{e}, where:

  • E_{d} = design energy demand (VAh)
  • V_{dc} = nominal battery bank voltage (Vdc)
  • K_{a} = battery ageing factor (%). This value captures a battery’s decrease in performance due to age.
  • K_{t} = temperature correction factor (%). This value captures the ambient installation temperature. Use the temperature correction factor table from IEEE-485.
  • K_{c} = capacity rating factor (%). This value captures the voltage depressions from battery discharge.
  • K_{e} = system efficiency (%). Allowance for losses in the battery.
  • K_{dod} = maximum depth of discharge (%)

Below, we’ll assign values to our above listed variables:

  • E_{d} = 13,950.8VAh
  • V_{dc} = 125VDC
  • K_{a} = 1.25 aging factor
  • K_{t} = 1.19 (50°F ambient)
  • K_{c} = 1.1
  • K_{e} = 0.97
  • K_{dod} = 0.8 (80%)

C_{min} = 13,950.8VAh \times 1.25 \times \dfrac{1.19 \times 1.1}{125VDC} \times 0.8 \times 0.97=141.71Ah

Next, we increase the calculated battery capacity by 125%. This ensures the battery meets our design requirements throughout its entire life.

125% of 141.71 Ah = 177.14Ah

Important Note: select a battery amp-hour capacity that’s greater than the minimum capacity we calculated. 

Also, specify the battery discharge rate, C rating. For example, for 24 hours of discharge, use C24 in your battery call out. 

Our battery will have a minimum rating of 200Ah at an 8-hour rate (or C8).

Sizing the substation battery charger

batteries in substation control room connected to dc panel

Required charger rating: A = \dfrac{kC}{H} + L_{c}, where:

  • A = required charger output rating
  • k = efficiency factor (1.1 for lead acid batteries)
  • C = calculated Ah discharge from the battery based on the duty cycle
  • H = recharge time (8 hours)
  • L_{c} = continuous load in amps

A = \dfrac{1.1\times141.71Ah}{8} + 11.3  = 30.79 Amps

125% x 30.79 amps = 38.49 Amps. So, the battery charger will have a minimum output rating of 40 amps.

Important Note: all batteries have an internal resistance. This causes the cell voltage to decreases as it depletes. The 125% multiplier accounts for this drop in voltage to ensure the battery isn’t undersized. 

Important battery notes

1) Heavy discharge: lead-acid batteries prefer intermittent loads over continuous loads. Intermittent loads give batteries a rest period to recompose their chemical reaction.

2) Battery room ventilation: lead-acid batteries release hydrogen gas when recharging. Without proper ventilation, hydrogen gas builds up and increases explosion risks.

3) Battery room temperature: optimum temperature is normally between 68-77° Fahrenheit. Battery life will shorten if the temperature goes too much higher.

4) Slow charging: lead-acid batteries charge slow. The typical charging time is 14 to 16 hours.

5) Full state of charge: lead-acid batteries need to always remain fully charged. A low charge causes sulfation. In other words, the battery performance will drop.

6) Charging voltage: maintain the correct voltage limits in charging. A low voltage limit will lead to poor battery performance. Also, it’ll cause sulfation buildup on the negative battery plate.

A high voltage limit will improve performance. But, it’ll cause grid corrosion to form on the positive battery plate.

So, it’s critical the battery charger applies the right voltage to a fully charged battery. This way, the battery will not overcharge or see any damage.

Substation battery sizing calculation wrap up

Substation battery sizing calculations are very straightforward.

All you need is your load information. I find collecting load information to be the most tedious part of the process.

Now requirements aside, every critical component in a machine needs redundancy. And a power substation is essentially a very big machine.

So, always include properly sized batteries and chargers in your substation. This will ensure you never face downtimes, which could cost you millions of dollars.

Do you have any substation battery sizing tips?  In what other systems have you seen batteries provide backup to the main power source?

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8 thoughts on “Substation Battery Sizing Calculation Made Easy”

  1. Hello Sir, I find your article very useful and relevant to my work as a maintenance personnel in a distribution Utilities. I have a query sir. 1) In our 20 MVA Substation, we are going to replace our 48 VDC Batteries (4-12 VDC batteries, 100AH into 2Volts, 200AH batteries (24pcs.). This is to have a longer years for the batteries to operate. My question is: a) Is there a need to upgrade the charger since we will upgrade the battery’s AH? the charger is rated at 25A, 48V output, and 240V input. The continuous load is at 3.8 A. thank you.

    Reply
    • Glad you found it helpful!

      As an off-the-cuff reply, you probably would need to replace the charger, but there are other variables you need to consider too. Thus, you need your engineer on record to review the existing charger’s compatibility.

      Reply
  2. Batteries with step loads as you have described will inherently decrease in voltage as they progress further into their 8 hours cycle. While you might float the batteries at 130VDC you typically have an end voltage of somewhere around 105VDC. Your calculations utilize the nominal voltage of 125VDC but battery load profiles will show you that the battery voltage will continuously taper off during the load draw. IEEE recommends you use the lowest voltage of your battery to calculate all your loads and during sizing. Additionally if you use any large battery manufacturer sizing programs, you will find that they as well utilize the end voltage to convert VA(W) to Amps. While I agree using the end voltage is ultra conservative, the method of using the nominal voltage is incorrect and results in undersized batteries for true use. You have masked that by adding all of your % increases but ultimately it will not be sized sufficiently for the full life cycle.

    Reply
    • Michael, thanks for your great comment.

      Yes, all batteries have an internal resistance, and the cell voltage decreases as it depletes.

      The 125% you’re referencing, accounts for the slack with the voltage drop. This percent actually outputs a more conservative value than using 105V. While noting, 105V is another assumption value similar to the 125%. Using the nominal value with a thought-out multiplier is more practical than thinking you have precision with the 105V value.

      To also point out, the VAs are not constant, as each device is based on a range of voltages. While noting, as the voltage drops on a DC system, the current drops as well (assuming a constant resistance). This needs to be considered as well.

      Your comment highlights how the post needs some added clarity with the percentage though. I added a note.

      Reply

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