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Batteries are integral to our modern world, powering a wide range of devices and systems. In previous articles we discussed how batteries work, and various technologies used such as lead-acid and lithium-ion. But whenever discussing batteries, two crucial concepts often arise: capacity and output power. Understanding these terms is essential for selecting the right battery for your needs and ensuring optimal performance. In this article, we will delve into the intricacies of electrical terminology, clarifying the definitions of capacity and output power, exploring their relationship, and discussing the factors that influence them.

Battery Capacity

Battery capacity or C, at its simplest, refers to the amount of electrical energy a battery can store and then later release. It is typically measured in ampere-hours (Ah). Capacity represents the total electrical charge the battery can deliver over a specific period of time. For example, a 100Ah battery can theoretically provide a current of 100 amps (A) for one hour before reaching its fully discharged state. Many factors influence this, of course, and there are two types of capacity rating numbers that may be provided by a manufacturer: Nominal or Rated and Effective or Usable.

1. Nominal/Rated Capacity: The advertised capacity most often specified by manufacturers. It represents the idealized capacity under specific conditions, standardized to ensure comparability among battery models. For example, a 100Ah lithium-ion battery can deliver 100 amps of current for one hour (1C). While a similar lead-acid battery can provide 100 amps of power, but it is only rated to do so over 20 hours at a rate of 5 amps per hour, or 5% of its capacity (.05 C).

2. Effective/Usable Capacity: The usable portion of the stated nominal capacity that is actually and practically available for a specific application. Various factors such as discharge rate, temperature, battery chemistry, and age affect the effective capacity. As mentioned above, a lithium-ion battery can deliver nearly all its 100 amps in one hour (1C), but a lead-acid battery will lose over half of that energy if discharged at a rate faster than 15 amps an hour, or 15% of capacity (.15 C), with exponentially more losses at higher discharge rates.

Peukert’s Law: Describes the relationship between discharge rate, capacity, and runtime. It states that at higher discharge rates, the effective capacity of a battery decreases exponentially due to internal battery resistance losses. Therefore, high-current applications will reduce battery runtime compared to low-current applications.

This relationship is distilled into an exponent value and assigned to a battery based on its performance characteristics. The value ranges up from 1, with lower numbers indicating a more efficient (better) discharge capability. For example, a Peukert rating of 1 means that the battery is 100% efficient at charge/discharge, suffering no loss— which is improbable under non-laboratory conditions.

Many lithium-ion batteries (Lithium Iron Phosphate) have a Peukert exponent of 1.05. That means a 100Ah battery at a humble discharge rate of 40 amps per hour (~500W or .4C) will be 83% efficient at delivering its stated capacity. The best lead-acid batteries, on the other hand, have an exponent value around 1.25, which means only 39% of its rated power is actually usable at that same discharge rate.

Real world testing shows this value can be as high as 1.75, which is not remotely usable, even at moderate discharge rates. Note that a lead-acid battery should recover if the discharge rate is again reduced below .05C, and as it does, some of that “lost” capacity will be available for low discharge rates. It is also worth noting that reputable lithium-ion battery vendors often “overbuild” the actual capacity vs the stated capacity. This allows for access to more usable power that better matches the stated capacity.

The graph below demonstrates real world testing (Adventurous Way Charging Analysis) of discharging 200Ah, popular, brand-name batteries of both lead-acid and lithium technologies, and it shows considerably worse performance from lead-acid (AGM – absorbent glass mat) than even the theoretical calculations above do.

Battery Output Power

A battery’s output power refers to the rate at which a battery can deliver electrical energy. It is measured in watts (W) and determines the battery’s ability to supply a load with the required power. Output power is influenced by the battery’s voltage and its internal resistance and is another important factor in a battery’s ability to perform a required task.

1. Voltage: Battery voltage represents the electrical potential difference between the positive and negative terminals and is expressed in volts (V). The voltage level of a battery impacts the potential power it can deliver to a connected device or system. For example, a battery with a higher voltage can deliver more power to a load compared to a battery with a lower voltage, using the same current.

2. Internal Resistance: All batteries have internal resistance, which restricts the flow of current. As a result, the actual output power delivered from a battery to a load may be lower than the theoretical value calculated based just on the voltage and load resistance. Internal resistance can lead to energy losses and voltage drops within the battery, impacting the available output power. This internal resistance has a considerable impact on a battery’s performance while under load. As stated, a lead-acid battery under a heavy load will lose substantial amounts of its potential energy capacity (mostly as resistance heat), when discharged at a rate faster than 5% of its rated capacity.

Ohm’s law – V, I, and R, and sometimes W

At this point, it is worth spending a bit of time with yet another law. This important equation (V = I x R) and its various parts define the measurement of electrical power and its application. The law is named after the German physicist Georg Ohm, who in 1827 described the measurements of applied voltage and current through simple electrical circuits using various lengths of wire. It states that the current (I) through a conductor between two points is proportional to the voltage (V) across the two points and a specified resistance (R). While the physics of why that is the case is beyond the scope of this article, the key takeaway is that these components are proportional to each other, and altering one, by definition, affects the others.

V -Voltage: As briefly described above, this is the potential amount of “push” a circuit, battery, or power source can apply toward a load. A 12-volt car battery can apply 12 volts of this potential as a constant one-way direct-current (DC). It is best thought of as the pressure, if compared to water in a hose.

I -Current: This represents the actual amount of energy moving across a circuit or a battery’s output. It is measured in amps, yet its symbol is I, which originates from the French phrase intensité du courant (current intensity). It can best be thought of as the volume, as compared to water flow.

R -Resistance: This represents “constriction” to the free-flow of energy in a circuit and is measured in ohms (Ω). It dictates how much total power the overall circuit can physically consume/provide. While resistance exists throughout any circuit, including inside the power source, this can best be thought of as the thickness of the water hose combined with any constrictions and attachments leading to the sprinkler-head at the end.

W -Watts: While not specifically a part of Ohms law, this value represents the actual power being produced/consumed in a circuit and is useful to understand overall power usage. It is a measure of the real work being done and can be thought of as the amount of water actually leaving the sprinkler-head to land on your garden.

The simplest and most often used form of this formula/law is W = V x I. This states that the total watts (W) used is equal to the voltage (V) of a circuit multiplied by the current (I) flowing across it, measured in amps (A), and restricted by the overall resistance (R) of the circuit. For example, a 12-volt power source, pushing 10 amps of current, consumes 120 watts of power (120W = 12V x 10A). This circuit has a resistance of 1.2 ohms (Ω) because Ohm’s law also states that R = V / I or 1.2Ω = 12V / 10A. But at 24V, that same 120 watts of power output can be achieved with only 5 amps (120W = 24V x 5A) with a circuit resistance of 4.8 ohms (Ω). Notice how the circuit resistance went up 4x, to constrict/control the flow of power, keeping the formula consistent with 4.8Ω = 24V / 5A.

Note: For this reason, some opt to use higher voltage when designing a power storage system. Equipment rated for higher voltage allows the movement of more power over smaller wiring by using less current. All power cords –along with any part of a circuit— are rated for a maximum amount of current they can safely handle. That’s why the power cord to a 1500-watt kettle is so much smaller than the battery cables used for a car’s starter. Both utilize the same 1500 watts of power (W), but at US household voltage of 120V only 12.5 amps are needed for the kettle to provide that power (1500W = 120V x 12.5A), while a car’s starter easily needs 125 amps to do its job at 12V (1500W = 12V x 125A), necessitating much thicker wiring to carry that many amps. Remember, more current requires more conducting material (thicker wiring) to accommodate it much like a higher volume of water requires a thicker hose to carry it.

Power over time –the eternal struggle? The values and measurements above are all relative to time. This is important to note when understanding terms like amps (A) vs Amp-hours (Ah). The first is a measurement of the active current within a circuit (measured over 1 second), while the other is a value of usage/capacity for a number of said amps over one hour –thus AmpHour. The same applies to Watts. The 1500-watt kettle above would consume the full 1500 watts (or 1.5 Kilowatt-hours), if running for an entire hour –that’s a lot of tea! But it uses 1/6^th of that power (250 watts), if run for a more reasonable 10 minutes (1/6^th of an hour).

Increasing battery capacity vs voltage

As discussed in this previous article, a battery is made up of individual cells. A string of these cells is connected in series (positive of one to negative of the next) to achieve a desired higher voltage. The various battery chemistries used dictate the actual nominal base of each cell’s voltage.

For example, at the simplest, an alkaline battery is a single chemical cell capable of producing 1.5V, while a nickel-metal hydride battery is a single 1.2V cell. But when installed in a device, like a TV remote control, notice how the batteries are installed in series (positive of one to negative of the next) to create the higher voltage needed by the device.

Similarly, in a lead-acid battery, several 2.1V cells (3x and 6x, respectively) are linked together internally to create the familiar 6V and 12V batteries used today (6.3V and 12.6V, actual). In the same way, a typical lithium-ion battery (lithium iron phosphate) is built of several 3.2V cells (4x), in series, to achieve the desired 12.8V of popular “drop-in” replacement batteries used to match the established standard of “12V”.

When comparing a battery system’s capacity in relation to its voltage, two key concepts are important to understand: Series vs Parallel connections.

Series: Just as with individual cells inside a single battery, entire batteries can be connected to each other in series to raise the overall voltage of the circuit. This creates a larger battery made up of individual batteries now acting as single cells. For example, a very popular lead-acid form-factor is the 6V “golf cart” battery. But this type of battery is rarely used at 6V and is instead typically connected with another equal 6V battery, in series, to raise the overall terminal voltage to 12V. That process involves connecting the negative terminal of one battery to the positive terminal of the next battery in the series.
Adding more cells onto the end of the chain in this manner raises the overall voltage of the circuit by the voltage of each added battery, but the total capacity of all the batteries together remains the same at the higher voltage. For example, 4 x 100Ah 6V batteries connected in series would result in a battery that can deliver 100Ah at a voltage of 24V.

Parallel: Another way to connect batteries to each other is in parallel. As the term implies, doing so connects all battery positive terminals together and all negative terminals together, in parallel. This keeps the overall circuit voltage the same, but it increases the capacity (Ah) available at that voltage. For example, using the 4 x 100Ah 6V batteries mentioned earlier, if they were instead connected in parallel (positive to positive, negative to negative), the resulting combination would be one large 6V battery, but with a capacity of 400Ah.
That same number of batteries can be mixed together into a series/parallel combination by using 2 x 6V batteries in series, to achieve 12V, and then linking the resulting 2 sets of 12V series to each other in parallel. This would yield a battery at 12V, but with a total capacity of 200Ah.

Note that with all of these options, the overall potential power output (W) remains the same (24V x 100A or 6V x 400A or 12V x 200A all equal 2400W), but these varied combinations allow for custom-building power storage systems that match the equipment requirements.  

Factors Influencing Capacity and Output Power

Several factors affect both battery capacity and output power. Understanding these factors is crucial for optimizing battery performance and making informed decisions when selecting batteries for specific applications.

1. Battery Chemistry: Different battery chemistries, such as lead-acid, lithium-ion, nickel-metal hydride, and others, exhibit varying capacities and power capabilities. Each chemistry has its strengths and limitations (see a comparison of lead-acid vs lithium-ion), making it important to choose a battery chemistry that aligns with the requirements of the application.

2. Temperature: Temperature plays a critical role in battery performance. Extreme temperatures, either hot or cold, can impact both capacity and output power. High temperatures can accelerate chemical reactions, leading to capacity loss, while low temperatures can increase internal resistance, reducing power delivery. With lithium, for example, low enough temperatures (at freezing) while charging can lead to a loss of capacity and permanent battery damage.

3. Discharge Rate: The rate at which a battery is discharged influences its effective capacity and output power. High discharge rates can cause voltage drops, reducing available power, while necessitating even more current to achieve the same usable power output. Some batteries are better suited for high-discharge applications, while others are only suited for low-discharge scenarios.

4. Battery Age and Cycle Life:  As batteries age, their capacity and power output will degrade. Rechargeable batteries have a limited number of charge-discharge cycles before their performance starts to decline. Monitoring the battery’s health and replacing it when necessary is vital to maintaining optimal performance.

5. Battery Management Systems: Advanced battery management systems (BMS) are employed in many battery applications. A BMS helps monitor and control various parameters, including capacity, power output, and temperature, to maximize battery performance, protect against overcharging or over-discharging, and enhance overall safety and reliability.

Conclusion

Understanding the terminology associated with battery capacity and output power is essential for selecting the right battery for specific applications. Capacity determines how much energy a battery can store, while output power indicates the rate at which the battery can deliver that energy. Factors such as battery chemistry, temperature, discharge rate, battery age, and management systems influence capacity and power output. By considering these factors, you can make informed decisions when selecting batteries, ensuring optimal performance and reliability for devices and systems. It is crucial to match battery specifications to the requirements of the application and to consult manufacturers’ guidelines for accurate information regarding capacity, output power, and other performance characteristics.