Molly Ayala
The term battery was first used by Benjamin Franklin in 1749 during his experiments with electricity using sets of linked Leyden jar capacitors. Today, batteries are a source of electric power consisting of one or more electrochemical cells with external connections for powering electrical devices. The energy supplied by a battery can be calculated using the equation $E=VIt$, where $I$ is the current through the battery. This energy is related to the voltage, which is the potential difference between the positive and negative terminals of the battery. To find the equivalent electricity of a battery, one can use an Equivalent Circuit Model (ECM) or a Physics-Based Model (PBM). These models are used to optimise the performance and safety of batteries, especially in electric vehicles.
| Characteristics | Values |
|---|---|
| Definition of Electric Battery | A source of electric power consisting of one or more electrochemical cells with external connections for powering electrical devices |
| Types of Electric Battery | Primary (single-use or "disposable") and Secondary (rechargeable) |
| Examples of Primary Battery | Alkaline battery used for flashlights and portable electronic devices |
| Examples of Secondary Battery | Lead-acid batteries used in vehicles and lithium-ion batteries used for portable electronics such as laptops and mobile phones |
| How to Calculate the Energy Supplied by a Battery | E=VIt, where I is the current through the battery |
| How to Measure Power Over Time | Watt-hours or Killowatt-hours |
| How to Measure Current | Using a calibrated "shunt" with a max of 10 Amps and an Arduno Uno processor with its built-in ADC |
| How to Model Li-ion Batteries | Equivalent Circuit Model (ECM) and Physics-Based Model (PBM) |
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What You'll Learn
Calculating the energy supplied by a battery
The energy supplied by a battery is sometimes referred to as its battery capacity. This can be measured in ampere-hours (Ah), which indicates how much current can be drawn over a given length of time. For example, a 12Ah capacity battery could supply 1A for 12 hours or 0.1A for 120 hours.
Battery energy capacity, or the amount of energy supplied by a battery, is measured in joules (J), watt-hours (Wh), or kilowatt-hours (kWh). To calculate the energy supplied by a battery in time t, the formula E=VIt can be used, where I is the current through the battery. If the internal resistance is r, the formula becomes E=V^2/rt.
For example, let's calculate the energy supplied by a Ni-MH battery cell with a cell voltage of 1.2 V and a current capacity of 2200 mAh. First, we convert the current capacity from mAh to Ah by dividing by 1000, giving us 2.2 Ah. Next, we can calculate the energy supplied using the formula E=VIt, where V is the voltage (1.2 V), I is the current (2.2 A), and t is the time in hours. Assuming we want to find the total energy supplied by the battery, we can set t = 1 to find the energy supplied in joules. Plugging these values into the formula, we get E = 1.2 V * 2.2 A * 1 hour = 2.64 J.
It's important to note that these formulas assume a constant battery voltage and that the internal resistance is the only resistance in the circuit. If the battery voltage is not constant or there is additional load resistance, the calculation becomes more complex and may involve integrals.
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The history of the electric battery
Before the invention of batteries, experimenters in the mid-18th century used Leyden jars to store electrical charge. These jars, unlike electrochemical cells, stored their charge physically and would release it all at once. One of these experimenters was colonial American inventor Benjamin Franklin, who is believed to have first used the term "battery" in 1749 when he hooked several Leyden jars together to create a stronger charge.
In 1780, Italian biologist Luigi Galvani discovered that when two different types of metal came into contact with a dead frog's leg, an electrical current ran between them, causing the leg to twitch. This marked the first discovery of the principle behind batteries. Alessandro Volta, a friend and fellow scientist of Galvani, believed that the observed electrical phenomena were caused by two different metals joined by a moist intermediary. He verified this hypothesis through experiments and, in 1800 (or 1801, according to some sources), invented the first true battery, known as the voltaic pile. This battery stored and released a charge through a chemical reaction instead of physical means and produced a continuous and stable current.
However, Volta's original models had some technical flaws, including electrolyte leakage and short battery life. These issues were addressed by Scotsman William Cruickshank, who invented the trough battery, and by Volta himself, who invented the Crown of Cups, a more efficient but less popular model.
In the late 19th and early 20th centuries, several important advancements were made in battery technology. In 1868, Georges Leclanché invented the Leclanché cell, the origin of today's dry batteries. However, it was inconvenient to use due to its spilling issues. This problem was solved by German inventor Carl Gassner in 1888, who created a "dry cell" or "dry battery" that did not spill, even though it contained liquid. In 1899, Swedish engineer Waldemar Jungner invented the nickel-cadmium battery, a precursor to today's storage batteries. The following year, Thomas Edison invented the nickel-iron storage battery.
In the 20th century, the development of "secondary" or "rechargeable" batteries extended the life of cells. The introduction of nickel and lithium-based batteries in the latter half of the century enabled the creation of innumerable portable electronic devices, from powerful flashlights to mobile phones. More recently, in 1979, researchers John B. Goodenough and Koichi Mizushima developed a rechargeable lithium-ion battery, which has become the basic prerequisite for battery-powered e-mobility.
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The internal resistance of a single battery
The internal resistance of a battery is a key parameter that affects its performance and longevity. It is influenced by several factors, including the size of the battery, its state of charge, chemical properties, age, temperature, and the discharge current.
In simple terms, internal resistance refers to the battery's natural hindrance of current flow. This resistance is always present and is caused by the battery's internal configuration and the materials used. A battery with low internal resistance can carry a significant amount of current, while a battery with high internal resistance can only carry a small amount. Ideally, a battery's internal resistance should be zero to allow for maximum current flow without energy loss.
The internal resistance of a battery can be calculated using the formula:
> R_int = ((V_NL / V_FL) - 1) * R_L
Where:
- R_int is the internal resistance
- V_NL is the open-circuit voltage
- V_FL is the load voltage
- R_L is the load resistance
It's important to measure the internal resistance of a battery for quality control and maintenance. A higher internal resistance results in greater energy loss, which is converted into heat. This not only wastes energy but also contributes to the degradation of the battery over time. By regularly measuring the internal resistance, one can identify degraded batteries and ensure consistent battery quality during production.
Additionally, internal resistance plays a role in battery safety. As the internal resistance hinders the passage of current, it generates thermal heating, which, if not controlled, can lead to a thermal runaway event, causing harm to the system and its surroundings. Therefore, understanding and managing internal resistance is crucial in optimising battery performance and safety.
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Equivalent Circuit and Physics-Based Models for lithium-ion batteries
Lithium-ion batteries are widely used in various applications, from portable electronic devices to electric vehicles and grid storage systems, due to their high energy and power density, lightweight design, and wide working temperature range. However, they are not without their drawbacks, as they can suffer from safety issues such as internal short circuits and thermal runaway. To ensure safe and reliable operation, a Battery Management System (BMS) is employed to monitor the battery's status in real time and provide essential functionalities like battery state, health, and power estimation.
The BMS relies on accurate battery modelling to make these estimations, and there are two primary modelling methodologies: the Equivalent Circuit Model (ECM) and the Physics-Based Model (PBM). The ECM is a well-established and widely used technique that employs electrical circuits to define behavioural voltage approximations in response to different input currents. It offers advantages in computational speed, ease of calibration, and accuracy within its calibration range, making it suitable for applications in controls, diagnosis, and state estimation of lithium-ion battery packs. However, the calibration process can be extensive, requiring a wide range of operating conditions to be tested.
On the other hand, the PBM provides accuracy beyond the calibration dataset, making it predictive for high-rate operations. While it offers valuable insights, the PBM also necessitates the estimation of numerous physical parameters, a time-consuming calibration process, and longer computational times for variable current scenarios. The ECM and PBM complement each other, and by understanding their strengths and limitations, we can optimise battery performance and safety.
In an attempt to bridge the gap between these two modelling approaches, researchers have developed a Physics-Based Equivalent Circuit Model for Lithium-Ion Cells. This model combines the advantages of both methods by analytically defining the ECM parameters using a calibrated Extended Single-Particle Model (ESPM). By doing so, the complexity of the electrochemical model is reduced, making it more accessible and efficient while still providing valuable insights into the underlying physics of the battery.
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How to measure the current in a circuit
Measuring current is a fundamental task in electrical engineering and electronics, playing a crucial role in troubleshooting, designing, and maintaining circuits. There are various tools available for measuring current, each offering unique advantages and suitability for specific use cases.
One of the most commonly used tools for measuring current is a multimeter, which can measure voltage, resistance, and current (both AC and DC). To measure current using a multimeter, it must be connected in series with the circuit, allowing the current to flow through it. Before connecting the multimeter, ensure it is set to the current measurement mode and rated for the expected current. Power off the circuit to prevent potential damage or injury, then open the circuit and connect the multimeter probes across the two open points. After securing the connections, power on the circuit and read the measurement from the multimeter's display. If your multimeter is not auto-ranging, start with the highest range and decrease gradually to obtain an accurate reading without overloading the device.
Another tool for measuring current is the clamp meter, which offers the advantage of measuring current without physically contacting the conductor or interrupting the circuit. Clamp meters work by clamping around a single wire and measuring the magnetic field to calculate the current flow, making them ideal for quick diagnostics in live circuits, especially in high-current scenarios like industrial applications.
Ammeters are specifically designed to measure electric current with high precision and are also connected in series with the circuit. Oscilloscopes, while primarily used for waveform analysis, can also measure current with the help of a current probe, allowing for the observation of current changes over time, making them valuable for device analysis, debugging, and research.
When measuring current, it is important to understand the characteristics of the circuit. In a parallel circuit, current is additive between each line, while in a series circuit, the current remains constant. This knowledge helps determine the most beneficial and accessible location for taking measurements.
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Frequently asked questions
The easiest way to measure the capacity of a battery is in Ah (Ampere-hours). This unit indicates how much current can be drawn from a battery over a given length of time.
The energy supplied by a battery over time t can be calculated using the formula E=VIt, where I is the current through the battery.
If the internal resistance is r, the energy supplied by the battery can be calculated using the formula E=(V^2)/rt.
