A refresher on how to size batteries sans software

Sizing battery banks for switchgear and control applications is commonly performed using software designed specifically for that purpose. Just input the required load profile, and the program selects the optimum battery configuration. Although this is quite simple, an engineer should be capable of performing a straightforward hand calculation — either to confirm the results of a software-generated solution or to serve as an accurate design for a simple battery system.

Do you know how to perform these calculations by hand? If not, then read on. This article will help you understand the basic premise of sizing switchgear battery systems and provide an example calculation for clarification of the concept. IEEE Standard 485-1997, “Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications,” also provides detailed guidelines for battery sizing.

### Number of cells

Battery banks for switchgear and control applications are made up of many cells. These cells are typically wired in series to achieve a desired voltage and may also be wired in parallel to achieve additional ampere capacity. Sizing of these battery banks, therefore, includes selecting the number and type of cells to be used.

The terminal voltage per cell varies with the battery's chemical composition. The required number of series wired cells to achieve the more common DC control voltages for switchgear control is shown in **Table 1.** Selection of the type of cell is based on the required peak ampere output and total Ampere-hour (Ah) output capacity for the load and duration.

### Load type

IEEE Standard 485-1997 classifies individual DC loads as continuous, non-continuous, and momentary. Typical continuous loads include lighting, continuously energized coils, and power to protective relay and communications systems. Non-continuous loads are less common and include critical ventilation system motors and valve actuators with operating times exceeding 1 minute. Momentary loads do not exceed 1 minute in duration and include inrush currents and circuit breaker operations.

The duty cycle imposed on switchgear batteries usually consists of momentary high ampere loading during charging of the respective tripping or closing springs, in addition to the small continuous load of powering protective relays and lights.

While both motors for charging the tripping or closing springs can be DC, the more common switchgear design uses an AC closing motor and a DC tripping motor. Such a design reduces the total DC load because tripping is of the utmost importance — particularly when a fault occurs. However, this only allows one full operational cycle following a power failure because there is no AC to charge the closing spring.

### Sizing guidelines

Since the momentary load on a switchgear battery bank is much higher than the continuous load, the required 1-minute (peak) *ampere* rate typically determines the battery cell type. However the *Ampere-hour* rate should also be checked. The battery cell type that meets the worst-case condition between the two should be selected.

These rates are tabulated in the manufacturer's standard literature at several final voltages. Use the rates published at a final voltage of 1.75 volts-per-cell for lead acid cells or 1.14 volts-per-cell for nickel cadmium cells. As an example, the data in **Table 2** on page 43 is excerpted from a manufacturer's Web site. (The model designations are fictitious.)

To calculate the required 1-minute ampere rate, assume the peak rate to be equal to the sum of the loads (i.e. in-rush current for all breaker charging motors, load currents for all relays and other loads, and ignore pilot lights).

Although momentary loads usually exist for much less than a minute — perhaps only a fraction of a second — it is common practice to use the full ampere value for an entire minute. Assign a required 1-minute rate equal to this peak rate divided by the ambient temperature derating factor, the battery aging factor, and a design margin as listed in **Table 3** on page 43.

To calculate the required Ampere-hour rate, compute the average continuous load and divide by the ambient temperature-derating factor and battery-aging factor, as listed in Table 3. Use the manufacturer's data to select the battery cell type that meets both the ampere and Ampere-hour requirements.

### Sample calculation

To use a hypothetical real-world example, calculate the battery size for the 69kV substation loads listed in **Table 4.** The battery type shall be lead acid, operate the given loads for 8 hours at 125VDC, and be housed in a climate-controlled building.

*Step 1*: Calculate the required 1-minute discharge rate.

As can be seen in Table 4, the peak discharge rate is 96.2A. Divide this number by an ambient temperature factor of one for a 77°F room, by a 0.8 battery-aging factor, and by 0.85 for the design margin.

Required 1-minute discharge rate = 96.2 A ÷ 0.8 ÷ 0.85 = 141.5A

*Step 2*: Calculate the required Ampere-hour (Ah) rate.

As can be seen in **Table 5**, the total Ampere-hour rate is 27.1 Ah. Divide by an ambient temperature factor of one for a 77°F room, and by a 0.8 battery-aging factor.

Required total Ah rate = 27.1 Ah ÷ 0.8 = 33.9 Ah

*Step 3*: Select the appropriate cell from the manufacturer's literature.

Referring back to Table 2, a Model A battery has a 1-minute discharge rate of 177A and an 8-hour Ah rate of 180 Ah, down to 1.75V. This type of battery is, therefore, more than sufficient for this particular load. The 125VDC, 180 Ah battery bank would be composed of 60 Model A cells.

### Back to basics

So whether you're one of those people that refuses to trust a computer farther than you can throw it — or you simply feel more comfortable double checking calculations by hand — possessing the knowledge to size battery banks for switchgear the old-fashioned way is a good skill for any engineer to master. Not only will you impress your peers, but you'll also feel more confident about recommending a rock solid switchgear solution.

*Hall is an electrical engineer based in the Las Vegas office of CH2M HILL, Inc.*

Control Voltage | Battery Type | |
---|---|---|

Ni-Cad | Lead acid | |

48VDC | 37 cells | 24 cells |

125VDC | 92 cells | 60 cells |

250VDC | 184 cells | 120 cells |

Final Volts | Models | Nominal Rates at 77°F (25°C) | |||||||
---|---|---|---|---|---|---|---|---|---|

Ampere-Hours (Ah) | Amperes (A) | ||||||||

8-hr | 4-hr | 3-hr | 1.5-hr | 1-hr | 30 min | 15 min | 1 min | ||

1.75V | A | 180 | 142 | 132 | 65 | 81 | 109 | 134 | 177 |

B | 250 | 210 | 195 | 98 | 126 | 172 | 219 | 303 | |

C | 330 | 280 | 260 | 130 | 168 | 230 | 292 | 404 | |

D | 410 | 350 | 326 | 163 | 204 | 285 | 362 | 500 |

Derating Function | Battery Type | |
---|---|---|

Ni-Cad | Lead-Calcium | |

Ambient temperature | ||

77°F | 1.0* | 1.0* |

32°F | 0.7 | 0.67 |

0°F | 0.5 | 0.8 |

Battery aging factor | 0.8* | 0.8* |

Design margin | 0.85* | 0.85* |

*Per IEEE Std. 485 recommended practice |

125VDC Load Description | Quantity | Current (A) | Subtotal (A) |
---|---|---|---|

69kV circuit switchers | 2 | 15.0 | 30.0 |

69kV substation relays | 8 | 0.2 | 1.6 |

5kV vacuum breakers | 9 | 7.0 | 63.0 |

5kV switchgear relays | 8 | 0.2 | 1.6 |

5kV switchgear indicating lights | Ignore | 0.0 | 0.0 |

Total | 96.2A |

125VDC Load Description | Quantity | Current (A) | Hours (h) | Subtotal (Ah) |
---|---|---|---|---|

69kV circuit switchers | 2 | 15.0 | 0.016* | 0.5 |

69kV substation relays | 8 | 0.2 | 8.0 | 12.8 |

5kV vacuum breakers | 9 | 7.0 | 0.016* | 1.0 |

5kV switchgear relays | 8 | 0.2 | 8.0 | 12.8 |

5kV switchgear indicating lights | Ignore | 0.0 | 8.0 | 0.0 |

Total | 27.1 Ah | |||

*0.016 hours = 1 minute |