# Battery Packs

## Energy Density and Power Density in Batteries and Electric Vehicles

Power density is the core measure controlling the speed and range you can get with a given vehicle. Power density controls the quantity of electricity you can store within a given space, and is measured two ways: (For more about these units see http://visforvoltage.org/book/ev-batteries/13232)

volume = the size of the area for batteries
weight = the carrying capacity of the vehicle

These are usually measured as

volume energy density = kilowatt-hours / liter = kwh / l
weight energy density = kilowatt-hours / kilogram = kwh / kg
volume power density = kilowatt-hours / liter = kw / l
weight power density = kilowatt-hours / kilogram = kw / kg

Remember that

1 kilowatt-hour = 1 kilowatt used over 1 hour = kwh
1 kilowatt = 1,000 watts

And remember that, as an electric vehicle moves down the road, it consumes electricity. Say the vehicle has a 120 volt electrical system, and uses 30 amps to cruise, therefore the vehicle cruises at 3.6 kilowatts. If the vehicle is run for an hour, it consumes 3.6 kilowatt hours of electricity.

The main measurement controlling the range capability of a given battery pack in a given vehicle is, how many kilowatt-hours can you carry in the vehicle. Hence, the power density of the chosen battery pack directly determines the kilowatt-hours in the vehicle. Obviously the batteries have to fit within the physical dimensions of the vehicle, hence the "volume power density" measure given above. Another consideration is how much weight the vehicle can carry on its frame, tires, and suspension system, maybe you have lots of room for batteries but you'd overload the car if you filled it to capacity. Hence the "weight power density" measure given above.

## Electrical Basics covering batteries in electric vehicles

The next electrical measurement of interest is "kilowatt-hours".

1 kilowatt-hour = 1 kilowatt used over 1 hour
1 kilowatt = 1,000 watts

To bring this to every day terms, the typical lightbulb is 100 watts, yes? Well, unless you're like me and use compact flourescent lighting, in which case the lightbulb in question uses about 40 watts. In any case, if you have ten 100 watt lightbulbs, that is 1,000 watts. Leave them running for an hour, and that is a kilowatt-hour. By modern electricity rates it will cost you in the neighborhood of ten cents for that electricity. As an electric vehicle moves down the road, it consumes electricity. Say the vehicle has a 120 volt electrical system, and uses 30 amps to cruise, therefore the vehicle cruises at 3.6 kilowatts. If the vehicle is run for an hour, it consumes 3.6 kilowatt hours of electricity.

Batteries are rated in voltage and amp-hour storage capacity. Obviously this is the kilowatt-hours of storage capacity. By the way, these measures also relate to batteries in cell phones and laptop computers, and directly relate to the "talk time" capacity of either one. In actuality the true capacity of a battery pack relates to the usage model.

When a battery company gives an "amp-hour" rating for a battery, they also specify the rate of discharge. Often the rating is given for a "20-hour" discharge, meaning that the rate amps are drawn from the battery is geared towards discharging the battery in a 20-hour period. When batteries are used at a higher rate the actual amp-hours that can be drawn from the battery often is lower than its 20-hour discharge rate implies.

<< Need a chart here showing the typical pattern - also explain C/20 and C/1 nomenclature >>

### Wiring a battery pack for a given voltage and amperage

Since the typical batteries are 12 volts, how do we get a 120 volt (or more) battery pack? It's simply done by wiring the batteries in parallel or serial fashion to get the desired numbers.

In a series-connected battery pack the measurements come out as follows:

voltage = volts-per-cell * number-of-cells
amperage = amps-per-cell

In other words, for a series connected pack the voltages add based on the number of cells. However the amperage does not increase.

There is a big assumption in those formulas. Namely, that your battery pack will only use batteries of the same rating. Such a "matched" battery pack is known to work much better than a mis-matched battery pack. It's even best to measure the actual batteries and ensure that their actual characteristics match the other batteries in a given battery pack.

In a parallel-connected battery pack the measurements are the reverse of the series-connected ones:

voltage = volts-per-cell
amperage = amps-per-cell * number-of-cells

You can also combine techniques if necessary, to create a series-parallel battery pack

You can wire a series-parallel pack as shown (wire the batteries in parallel "strings", and connect each string in series) or the other way around (wire them in series strings, connecting each string in parallel). The effect will be the same, namely:

voltage = volts-per-string * number-of-strings
amps = amps-per-string * number-of-strings

## Battery pack power density and energy density

Energy Density and Power Density are two ways to measure the speed and range you can get with a given vehicle. Each vehicle has a maximum weight it can carry, and a maximum volume or size it can carry. Together those form a budget into which you fit the people, cargo, drive train, electronics, and battery pack.

volume = the size of the area for batteries (in liters)
weight = the carrying capacity of the vehicle (in kilograms)

Energy density is the kilowatt-hours stored by volume or by weight. Power density is the energy (in watts) that can be delivered by volume or by weight.

power-density = max-watts / liter or kilogram
energy-density = kilowatt-hours / liter or kilogram

These are usually measured as

volume energy density = kilowatt-hours / liter = kwh / l
weight energy density = kilowatt-hours / kilogram = kwh / kg

Remember that

1 kilowatt-hour = 1 kilowatt used over 1 hour = kwh
1 kilowatt = 1,000 watts

And remember that, as an electric vehicle moves down the road, it consumes electricity. Say the vehicle has a 120 volt electrical system, and uses 30 amps to cruise, therefore the vehicle cruises at 3.6 kilowatts. If the vehicle is run for an hour, it consumes 3.6 kilowatt hours of electricity.

The main measurement controlling the range capability of a given battery pack in a given vehicle is, how many kilowatt-hours can you carry in the vehicle. Each vehicle has a designed carrying capacity in both volume and weight. Based on the energy density of a given battery pack determines how many kilowatt-hours can be fit into the vehicle. Obviously the batteries have to fit within the physical dimensions and carrying capacity of the vehicle.

Adapted from: Power Density in Batteries and Electric Vehicles

## Basic battery pack wiring to achieve specific voltage and amp-hour capacities

Refer to Electrical basic measurements and values for basic electric vehicle for basic electrical values. More details about batteries are in: EV Batteries

Batteries come with voltage values which depend on the battery chemistry, and on the arrangement of battery cells to form the battery pack. The amp-hour capacity is based on the battery chemistry, and essentially how heavy the battery is because the more material in the battery the more electrical charge it can store.

Typical per-battery-cell voltages are:-

• Lead acid: 12 volts (technically lead acid batteries are delivered as multiple cells packaged as one battery)
• NiMH: 1.2 volts
• Lithium ION: 3.7 volts
• LiFePO4: 3.2 volts

How do we get a 36 volt, 48 volt, 120 volt (or more) battery pack? It's simply done by wiring the batteries in parallel or serial fashion to get the desired numbers.

In a series-connected battery pack the measurements come out as follows:

voltage = volts-per-cell * number-of-cells
amp-hours = amps-hours-per-cell

In other words, for a series connected pack the voltages add based on the number of cells. However the amp-hour capacity does not increase.

A big assumption in this is that each battery in the pack has the same rating. It's best to have matched batteries in a battery pack. It's been observed that in a mismatched pack cells with less capacity will cause the rest of the pack to work harder, and the pack becomes damaged more quickly.

In a parallel-connected battery pack the measurements are the reverse of the series-connected ones:

voltage = volts-per-cell
amp-hours = amp-hours-per-cell * number-of-cells

You can also combine techniques if necessary, to create a series-parallel battery pack

You can wire a series-parallel pack as shown (wire the batteries in parallel "strings", and connect each string in series) or the other way around (wire them in series strings, connecting each string in parallel). The effect will be the same, namely:

voltage = volts-per-string * number-of-strings
amp-hours = amp-hours-per-string * number-of-strings

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# Battery Packs

## Energy Density and Power Density in Batteries and Electric Vehicles

Power density is the core measure controlling the speed and range you can get with a given vehicle. Power density controls the quantity of electricity you can store within a given space, and is measured two ways: (For more about these units see http://visforvoltage.org/book/ev-batteries/13232)

volume = the size of the area for batteries
weight = the carrying capacity of the vehicle

These are usually measured as

volume energy density = kilowatt-hours / liter = kwh / l
weight energy density = kilowatt-hours / kilogram = kwh / kg
volume power density = kilowatt-hours / liter = kw / l
weight power density = kilowatt-hours / kilogram = kw / kg

Remember that

1 kilowatt-hour = 1 kilowatt used over 1 hour = kwh
1 kilowatt = 1,000 watts

And remember that, as an electric vehicle moves down the road, it consumes electricity. Say the vehicle has a 120 volt electrical system, and uses 30 amps to cruise, therefore the vehicle cruises at 3.6 kilowatts. If the vehicle is run for an hour, it consumes 3.6 kilowatt hours of electricity.

The main measurement controlling the range capability of a given battery pack in a given vehicle is, how many kilowatt-hours can you carry in the vehicle. Hence, the power density of the chosen battery pack directly determines the kilowatt-hours in the vehicle. Obviously the batteries have to fit within the physical dimensions of the vehicle, hence the "volume power density" measure given above. Another consideration is how much weight the vehicle can carry on its frame, tires, and suspension system, maybe you have lots of room for batteries but you'd overload the car if you filled it to capacity. Hence the "weight power density" measure given above.

## Electrical Basics covering batteries in electric vehicles

The next electrical measurement of interest is "kilowatt-hours".

1 kilowatt-hour = 1 kilowatt used over 1 hour
1 kilowatt = 1,000 watts

To bring this to every day terms, the typical lightbulb is 100 watts, yes? Well, unless you're like me and use compact flourescent lighting, in which case the lightbulb in question uses about 40 watts. In any case, if you have ten 100 watt lightbulbs, that is 1,000 watts. Leave them running for an hour, and that is a kilowatt-hour. By modern electricity rates it will cost you in the neighborhood of ten cents for that electricity. As an electric vehicle moves down the road, it consumes electricity. Say the vehicle has a 120 volt electrical system, and uses 30 amps to cruise, therefore the vehicle cruises at 3.6 kilowatts. If the vehicle is run for an hour, it consumes 3.6 kilowatt hours of electricity.

Batteries are rated in voltage and amp-hour storage capacity. Obviously this is the kilowatt-hours of storage capacity. By the way, these measures also relate to batteries in cell phones and laptop computers, and directly relate to the "talk time" capacity of either one. In actuality the true capacity of a battery pack relates to the usage model.

When a battery company gives an "amp-hour" rating for a battery, they also specify the rate of discharge. Often the rating is given for a "20-hour" discharge, meaning that the rate amps are drawn from the battery is geared towards discharging the battery in a 20-hour period. When batteries are used at a higher rate the actual amp-hours that can be drawn from the battery often is lower than its 20-hour discharge rate implies.

<< Need a chart here showing the typical pattern - also explain C/20 and C/1 nomenclature >>

### Wiring a battery pack for a given voltage and amperage

Since the typical batteries are 12 volts, how do we get a 120 volt (or more) battery pack? It's simply done by wiring the batteries in parallel or serial fashion to get the desired numbers.

In a series-connected battery pack the measurements come out as follows:

voltage = volts-per-cell * number-of-cells
amperage = amps-per-cell

In other words, for a series connected pack the voltages add based on the number of cells. However the amperage does not increase.

There is a big assumption in those formulas. Namely, that your battery pack will only use batteries of the same rating. Such a "matched" battery pack is known to work much better than a mis-matched battery pack. It's even best to measure the actual batteries and ensure that their actual characteristics match the other batteries in a given battery pack.

In a parallel-connected battery pack the measurements are the reverse of the series-connected ones:

voltage = volts-per-cell
amperage = amps-per-cell * number-of-cells

You can also combine techniques if necessary, to create a series-parallel battery pack

You can wire a series-parallel pack as shown (wire the batteries in parallel "strings", and connect each string in series) or the other way around (wire them in series strings, connecting each string in parallel). The effect will be the same, namely:

voltage = volts-per-string * number-of-strings
amps = amps-per-string * number-of-strings

## Battery pack power density and energy density

Energy Density and Power Density are two ways to measure the speed and range you can get with a given vehicle. Each vehicle has a maximum weight it can carry, and a maximum volume or size it can carry. Together those form a budget into which you fit the people, cargo, drive train, electronics, and battery pack.

volume = the size of the area for batteries (in liters)
weight = the carrying capacity of the vehicle (in kilograms)

Energy density is the kilowatt-hours stored by volume or by weight. Power density is the energy (in watts) that can be delivered by volume or by weight.

power-density = max-watts / liter or kilogram
energy-density = kilowatt-hours / liter or kilogram

These are usually measured as

volume energy density = kilowatt-hours / liter = kwh / l
weight energy density = kilowatt-hours / kilogram = kwh / kg

Remember that

1 kilowatt-hour = 1 kilowatt used over 1 hour = kwh
1 kilowatt = 1,000 watts

And remember that, as an electric vehicle moves down the road, it consumes electricity. Say the vehicle has a 120 volt electrical system, and uses 30 amps to cruise, therefore the vehicle cruises at 3.6 kilowatts. If the vehicle is run for an hour, it consumes 3.6 kilowatt hours of electricity.

The main measurement controlling the range capability of a given battery pack in a given vehicle is, how many kilowatt-hours can you carry in the vehicle. Each vehicle has a designed carrying capacity in both volume and weight. Based on the energy density of a given battery pack determines how many kilowatt-hours can be fit into the vehicle. Obviously the batteries have to fit within the physical dimensions and carrying capacity of the vehicle.

Adapted from: Power Density in Batteries and Electric Vehicles

## Basic battery pack wiring to achieve specific voltage and amp-hour capacities

Refer to Electrical basic measurements and values for basic electric vehicle for basic electrical values. More details about batteries are in: EV Batteries

Batteries come with voltage values which depend on the battery chemistry, and on the arrangement of battery cells to form the battery pack. The amp-hour capacity is based on the battery chemistry, and essentially how heavy the battery is because the more material in the battery the more electrical charge it can store.

Typical per-battery-cell voltages are:-

• Lead acid: 12 volts (technically lead acid batteries are delivered as multiple cells packaged as one battery)
• NiMH: 1.2 volts
• Lithium ION: 3.7 volts
• LiFePO4: 3.2 volts

How do we get a 36 volt, 48 volt, 120 volt (or more) battery pack? It's simply done by wiring the batteries in parallel or serial fashion to get the desired numbers.

In a series-connected battery pack the measurements come out as follows:

voltage = volts-per-cell * number-of-cells
amp-hours = amps-hours-per-cell

In other words, for a series connected pack the voltages add based on the number of cells. However the amp-hour capacity does not increase.

A big assumption in this is that each battery in the pack has the same rating. It's best to have matched batteries in a battery pack. It's been observed that in a mismatched pack cells with less capacity will cause the rest of the pack to work harder, and the pack becomes damaged more quickly.

In a parallel-connected battery pack the measurements are the reverse of the series-connected ones:

voltage = volts-per-cell
amp-hours = amp-hours-per-cell * number-of-cells

You can also combine techniques if necessary, to create a series-parallel battery pack

You can wire a series-parallel pack as shown (wire the batteries in parallel "strings", and connect each string in series) or the other way around (wire them in series strings, connecting each string in parallel). The effect will be the same, namely:

voltage = volts-per-string * number-of-strings
amp-hours = amp-hours-per-string * number-of-strings

## Who's online

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Current Size: 100%

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The text passage provides technical information about battery packs, energy density, power density, and basic battery pack wiring in electric vehicles. It includes several examples and explanations of electrical measurements and concepts, but does not contain any direct mathematical questions or answers.

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