# Calculators

We are gradually adding a number of battery calculators to our pages. Here is a centralised list of pages with calculators built into them.

Do please send us ideas or even existing calculations that you make on the back of an envelope and would like to see as an online calculator.

#### Bidirectional Buck and Boost DC-DC

Circuit Diagram, Equations and Calculator for Calculating different aspects like Power, Current and Voltage average, Inductance, Switch On and off time etc in a Bidirectional Buck and Boost DC to DC converter. I will write an article separately explaining the workings of DC to DC converter.

#### Cell Energy Density

The calculations are quite simple as the energy content of the cell [Wh] = Vnom x Ahnom. This value is then just divided by the volume of the cell to calculate volumetric energy density or divided by the mass of the cell to calculated the gravimetric energy density.

There are some cautionary points though.

#### Cylindrical Cell Electrode Estimation

Knowing the outer and inner diameter of the spiral along with it’s thickness we can calculate the length of the material to create it.

D is the inner diameter of the cylindrical can.

The inner diameter is that of the mandrel around which we wind the spiral.

#### Pack Mass Estimation

Battery pack mass estimation is a key parameter required early in the conceptual design. There are a number of key reasons for estimating the mass, one of the main ones being the significant percentage it is of the overall mass of the complete system.

This calculator uses benchmark data to estimate the mass of everything other than the cells.

#### Pack Mass from Cell Density

The key relationship we have is between cell and pack gravimetric energy density.

This graph has been pulled together by scouring the internet for cell and battery data.

The ratio of cell density to pack density is 0.6235 and this is very close to the total cell to pack mass relationship of 1.6034

#### Pack Usable and Total Energy

The usable energy (kWh) of the pack is fundamentally determined by:

• Number of cells in series (S count)
• Number of cells in parallel (P count)
• Capacity of a single cell (Ah)
• Nominal voltage of a single cell (Vnom)
• Usable SoC window (%)

Energy (kWh) = S x P x Ah x Vnom x SoCusable / 1000

Note: this is an approximation as the nominal voltage is dependent on the usable window. Also, the variation in cell capacity will be needed to be understood to establish accurate pack capacity values in production. However, all of this takes time and hence please use this as a first approximation.

#### Pre-Charge Resistor

When the battery pack contactors are closed onto a motor and inverter there will be an inrush of current into the inverter capacitor. This very high current is at a minimum likely to age the contactors, it could permanently damage the contactors.

Therefore, when we closed the contactors on the battery pack we do this in three steps:

1. Close the main negative contactor
2. Close a contactor with a resistor in series
3. Close the main positive contactor