# How to Interpret Battery Discharge Curves?

Batteries are complex electrochemical and thermodynamic systems, with multiple factors affecting battery performance.

While battery chemistry is certainly the most critical factor, when determining which battery is best suited for a specific application, other factors such as charge and discharge rates, operating temperature, storage conditions, physical structural details, and more also need to be considered.

First, we need to define several terms:

Open Circuit Voltage (Voc) is the voltage between the battery terminals when the battery is not under load.

Terminal Voltage (Vt) is the voltage between the battery terminals when a load is applied to the battery; typically, lower than Voc.

Cutoff Voltage (Vco) is the voltage specified by the battery for a complete discharge. Although there may still be some residual charge, operating the battery below Vco voltage may damage it.

Capacity measures the total ampere-hour (AH) that a battery can provide at full charge until Vt reaches Vco.

★ Charge-Discharge Rate (C-Rate) is the rate at which a battery is charged or discharged relative to its rated capacity.

For example, a 1C rate will charge or discharge the battery completely within 1 hour. At a discharge rate of 0.5C, the battery will be fully discharged in 2 hours. Using higher C-Rates often reduces the available battery capacity and can potentially damage the battery.

★ State of Charge (SoC) quantifies the remaining battery capacity as a percentage of its maximum capacity. When SoC reaches zero and Vt reaches Vco, there may still be some remaining charge in the battery, but the battery cannot be further discharged without damaging it and impacting future capacity.

★ Depth of Discharge (DoD) is the complement of SoC, measuring the percentage of battery capacity that has been discharged; DoD = 100 – SoC.

• Cycle life is the number of available cycles a battery can undergo before reaching the end of its operational life.

★ End of Life (EoL) for a battery refers to when the battery can no longer perform according to its designated minimum specifications. EoL can be quantified in various ways: l

• Capacity degradationis based on a given percentage drop in battery capacity compared to the rated capacity under specified conditions.
• Power degradationis based on a given percentage drop in maximum battery power compared to the rated power under specified conditions.
• Energy throughput quantifies the total amount of energy the battery is expected to handle during its lifetime, such as 30MWh, based on specific operating conditions.

★ State of Health (SoH) measures the percentage of remaining useful life a battery has before reaching EoL.

## Polarization Curve

The battery discharge curve is formed based on the polarization effects that occur during the discharge process.

The amount of energy a battery can provide under different operating conditions, such as C-rate and working temperature, is closely related to the area under the discharge curve.

During the discharge process, the battery’s Vt (terminal voltage) decreases. The decrease in Vt is related to several main factors:

### ✔ IR Drop

The voltage drops in the battery caused by the current passing through the internal resistance of the battery.

This factor increases at a basically linear rate at higher discharge rates, with constant temperature.

### ✔ Activation Polarization

This refers to various deceleration factors related to the kinetics of electrochemical reactions, such as the work functions that ions must overcome at the interface between the electrode and electrolyte.

### ✔ Concentration Polarization

This factor considers the resistance ions face as they transfer from one electrode to another during mass transfer (diffusion) processes. This factor dominates when a lithium-ion battery is completely discharged, and the slope of the curve becomes very steep.

The battery’s polarization curve (discharge curve) illustrates the cumulative impact of IR drop, activation polarization, and concentration polarization on Vt (battery potential). (Image: BioLogic)

## The factors considered in the discharge curve

Batteries have been designed for a wide range of applications, offering various performance characteristics.

For instance, there are at least six basic lithium-ion (Li-ion) chemical systems, each with its unique feature set.

Discharge curves are typically plotted with Vt on the Y-axis and SoC (or DoD) on the X-axis. Since battery performance is related to various parameters like C-rate and operating temperature, each battery chemistry system has a series of discharge curves based on specific sets of operating parameters.

For example, the graph below compares the discharge behavior of two common lithium-ion chemical systems and lead-acid batteries at room temperature and a discharge rate of 0.2C.

The shape of the discharge curve holds significant importance for designers.

Discharge curves for lithium-ion and lead-acid batteries using a discharge rate of 0.2C. (Image: Off Grid Ham)

A flat discharge curve can simplify certain application designs because the battery voltage remains relatively stable throughout the entire discharge cycle.

On the other hand, a sloping curve can simplify estimating the remaining charge, as the battery voltage is closely correlated with the remaining charge in the battery.

However, for lithium-ion batteries with flat discharge curves, estimating the remaining charge requires more complex methods, such as Coulomb counting, which measures the battery’s discharge current and integrates the current over time to estimate the remaining charge.

Furthermore, batteries with a downward-sloping discharge curve experience a decrease in power throughout the discharge cycle. It may be necessary to oversize the battery to support high-power applications towards the end of the discharge cycle. Boost converters are often required to power sensitive devices and systems using batteries with steep discharge curves.

Here is the discharge curve for lithium-ion batteries, showing that if the battery is discharged at a very high rate (or conversely, at a low rate), the effective capacity will decrease (or increase). This is known as capacity fade, and this effect is common in most battery chemistry systems.

The voltage and capacity of lithium-ion batteries decrease as the C-rate increases. (Image: Richtek)

Operating temperature is a crucial parameter affecting battery performance.

• At extremely low temperatures, batteries with aqueous electrolytes may freeze, limiting the lower end of their operating temperature range.

Lithium-ion batteries(https://dlnenergy.com/21700-battery/) can experience lithium deposition on the negative electrode at low temperatures, permanently reducing their capacity.

• At high temperatures, chemical substances may decompose, causing the battery to cease functioning.

Between freezing and chemical breakdown, battery performance typically varies significantly with temperature changes.

The chart below illustrates the impact of temperature on the performance of lithium-ion batteries at different temperatures.

Performance can be significantly degraded at very low temperatures.

However, the battery discharge curve is just one aspect of battery performance. For example, the further a battery’s operating temperature deviates from room temperature (whether high or low), the lower the cycle life.

A comprehensive analysis of all factors affecting the applicability of various battery chemistry systems for specific applications goes beyond the scope of this article on battery discharge curves. Other examples of methods for analyzing different battery performance are Ragone plots.

Battery voltage and capacity depend on temperature. (Image: Richtek)

## Ragone plots

Ragone plots compare the specific power to specific energy of different energy storage technologies.

For instance, when considering electric vehicle batteries, specific energy is related to range, while specific power corresponds to acceleration performance.

Comparison of the relationship between specific energy and specific power for various technologies in a Ragone chart. (Image: Researchgate)

A Ragone chart is based on mass energy density and power density and does not include any information related to volume parameters.

Although metallurgist David V. Ragone developed these charts to compare the performance of various battery chemistries, Ragone charts are also applicable for comparing any set of energy storage and power devices, such as engines, gas turbines, and fuel cells.

The ratio between specific energy on the Y-axis and specific power on the X-axis represents the hours of operation of the device at its rated power. The size of the device does not affect this relationship because larger devices will have proportionally larger power and energy capacity. The isochronal curves on the Ragone chart that represent constant run-time are straight lines.

### Conclusion

Understanding the discharge curves of batteries and various parameters that constitute the family of discharge curves related to specific battery chemistries is crucial.

Due to the complexity of electrochemical and thermodynamic systems, battery discharge curves are also complex, but they are just one way to comprehend the performance trade-offs between different battery chemistries and structures.