Battery

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Description

A battery is an energy storage device that stores electrical energy in chemical form and releases it as needed. It is commonly used in power networks to supply power when generation is insufficient or to store excess energy when available. This simulation component models a battery within a power network, tracking its charge state, charge and discharge rates, time to recharge and state of health (SoH) over time.

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Example Use Cases

• Energy Storage: Used to balance supply and demand by storing excess energy and discharging when needed.
• Satellite Power Management: Simulates battery usage in space applications where solar power is intermittent.

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Module Implementation

The battery class is a Physical Object that can be added to any spacecraft, ground station or entity within the simulation framework. By default, it has a Capacity of 1 Amp-hour and a Voltage of 12.0 Volts.

The power data regarding the current and voltage coming in and out of the terminals are computed by the power bus based on the network available. Batteries can be added to a power network in both series and parallel. More information on the network configuration can be found in the Power Bus technical manuals.

Updating Charge

The charge of the battery is calculated based on the capacity and the Charge Fraction, which is the fraction between 0 and 1 that the battery currently is at. Calculating the charge is dependent on the power model’s current into the battery and the current going out of the battery, which is computed by the power bus.

If the current into the battery is greater than the current out of the battery, the charge is calculated using the following:

$$\Delta C=\frac{(I_{\text{in}}-I_{\text{out}})\Delta t}{3600}$$ $$f=\frac{C+\Delta C}{\mathrm{Capacity}}$$

where $C$ is the charge, $I$ is the current, $\Delta t$ is the step size and $f$ is the charge-fraction of the battery. Additionally, if $(I_{\text{in}}-I_{\text{out}})$ exceeds the Max Charge Current, this value will be locked to the maximum current if it is set. This assumes excess current is dissipated as heat, but is not strictly calculated by the battery model.

If the current into the battery is less than the current going out of the battery, the charge is calculated using the following:

$$\Delta C=\frac{(I_{\text{out}}-I_{\text{in}})\Delta t}{3600}$$

Similarly, the Max Discharge Current can cap the maximum current in the battery causing the discharge of the battery to be limited by this current.

Time To Recharge

The time to recharge (TTR) of the battery is a auto calculated value in seconds determined from the Current In and Out of the battery, it’s Capacity and Charge Fraction $f$ using:

$$TTR=\frac{({\mathrm{Capacity}}_{\mathrm{real}}(1.0-f)}{3600(I_{\text{in}}-I_{\text{out}})}$$

The real Capacity of the battery is used, so that Sate of Health Modelling influences the time to recharge. If the Current In and Out of the Battery are within 1 nA of each other, the TTR is set to Positive Infinity as the battery is deemed to not be charging or discharging. Additionally if the Charge Fraction $f$ is 100%, the TTR is 0 seconds.

State of Health

The state of health ($\mathrm{SoH}$) is determined by considering multiple degradation factors, including depth of discharge, charge rate, temperature, and calendar life. These parameters can be configured for the state of health calculation but are not required and is disabled by default. The $\mathrm{SoH}$ will affect the overall Capacity of the battery.

$${\mathrm{Capacity}}_{\mathrm{real}}={\mathrm{Capacity}}_{\mathrm{nominal}}\mathrm{SoH}$$

The Depth of Discharge, $\mathrm{DoD}$, and charge rate, $\dot{C}$, parameters are calculated using the following formulae:

$$\mathrm{DoD}=1.0-f$$ $$\dot{C}-\frac{|I_{\mathrm{in}}-I_{\mathrm{out}}|}{{\mathrm{Capacity}}_{\mathrm{nominal}}}$$

Then, assuming a temperature difference of $\Delta T$ from the Nominal Temperature, if it exists and the Thermal Model as been added, the State of Health can be computed using the following formula:

$$\mathrm{SoH}=1-W_{\mathrm{DoD}}\mathrm{DoD}+W_{\dot{C}}\dot{C}+W_T\Delta T+W_{\mathrm{CL}}\mathrm{CL}$$

where $W_{\mathrm{DoD}}$ is the weight for the depth-of-discharge, $W_{\dot{C}}$ is the weight for the charge rate, $W_T$ is the weight for the temperature change and $W_{\mathrm{CL}}$ is the weight for the calendar life, $\mathrm{CL}$ defined by the age of the battery in years. This approach ensures degradation effects are modelled realistically to reflect battery aging.

Internal Components

The battery functionality, when connected to the power bus, contains an internal resistor and an internal voltage source. The resistance is a fixed value, usually defaulted to 1 Ohm of power. The battery voltage is calculated as the following equation:

$$V=V_{\mathrm{nominal}}f$$

which is the Nominal Voltage multiplied by the charge fraction $f$.

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Assumptions/Limitations

• The thermal model is optional; if absent, temperature effects are ignored in the State of Health calculation.
• Calendar life degradation is modelled linearly.
• Any difference in current when using the maximum charge or discharge rates is assumed to be perfectly dissipated, without affecting the rest of the circuit.