Domain

• electrical storage

Intended application (including scale and resolution)

Intended to be used for testing of process simulations. The time resolution may range from seconds to hours. When the object is the battery itself, the resolution should be in the seconds range. When considering the integration of other components in the system, the resolution can be up to hours. 

Modelling of spatial aspects

• lumped (single device)

The battery is considered as a single lumped component, which provides a certain power or stores a defined amount of energy according to supply and demand. 

Model dynamics

• dynamic

The model is considered as dynamic equivalent circuit model in a relatively short time resolution. 

Model of computation

• time-continuous
• discrete-event

Equations describing the state of the battery are time-continuous, while the sensors measuring the real-time status are discrete event-based. 

Functional representation

• implicit

The model is an equivalent circuit model including lookup tables. 

Input variables (name, type, unit, description)

• Real P_batt: Battery power setpoint, given by controller [kW]

Output variables (name, type, unit, description)

• Real SOC_batt: State of Charge of the battery [%]
• Real U_batt: Output voltage of the battery [V]

Parameters (name, type, unit, description)

• Real N_batt: Number of batteries in the pack [-]
• Real C_rated: Nominal capacity of the battery [Ah]
• Real η_charge: Battery charge efficiency [%]
• Real η_discharge: Battery discharge efficiency [%]
• Real C₁: Battery impedance Capacitor C1 [F]
• Real C₂: Battery impedance Capacitor C2 [F]
• Real C₃: Battery impedance Capacitor C3 [F]
• Real R₀: Battery impedance Resistor R0 [mΩ]
• Real R₁: Battery impedance Resistor R1 [mΩ]
• Real R₂: Battery impedance Resistor R2 [mΩ]
• Real R₃: Battery impedance Resistor R3 [mΩ]
• Array SOC-OCV lookup table: OCV_LT(SOC) [V]

Internal variables (name, type, unit, description)

• Real I_batt: Battery current [A]
• Real U_batt: Battery voltage [V]
• Real U_OCV: Battery open circuit voltage [V]
• Real U_R0: Battery impedance R0 voltage [V]
• Real U_R1: Battery impedance R1 voltage [V]
• Real U_R2: Battery impedance R2 voltage [V]
• Real U_R3: Battery impedance R3 voltage [V]
• Real U_C1: Battery impedance C1 voltage [V]
• Real U_C2: Battery impedance C2 voltage [V]
• Real U_C3: Battery impedance C3 voltage [V]
• Real I_R0: Battery impedance R0 current [A]
• Real I_R1: Battery impedance R1 current [A]
• Real I_R2: Battery impedance R2 current [A]
• Real I_R3: Battery impedance R3 current [A]
• Real I_C1: Battery impedance C1 current [A]
• Real I_C2: Battery impedance C2 current [A]
• Real I_C3: Battery impedance C3 current [A]
• Real C_batt: Real usable capacity of the battery [Ah]
• Real η_cap: Coefficient of the real capacity to nominal capacity [-]
• Real η_charge/dis: Coefficient of charge and discharge [-]

Internal constants (name, type, unit, description)

Model equations

Governing equations

Constitutive equations

-

Boundary conditions

• state of charge: SOC_batt should be between 0% - 100%
• Power setpoint limit: -4KW ≤ P_batt ≤ 4KW

Optional: graphical representation (schematic diagram, state transition diagram, etc.)

Model Validation

Narrative

The system is simulated with a given power setpoint profile, to test the charging and discharging process. In reality, the battery is connected with a battery controller to set this setpoint.

Test system configuration

• Total simulation time: 100000 seconds
• The model is connected to a battery controller. The controller signal is provided as time series, see attached dataset (see Batter_power.csv in data file KIT_Battery_data.zip).

Inputs and parameters

• P_batt is the power set by the battery controller. It is given as attached in the datasets. The unit is kW.
• Number of batteries in series N_batt = 25. For each battery in the series, ther power is: 
• C_rated = 25Ah
• η_charge = 100%
• η_discharge = 95%
• C₁ = 3000 F
• C₂ = 15000 F
• C₃ = 100000 F
• R₀ = 1.5 mω
• R₁ = 0.4 mω
• R₂ = 0.7 mω
• R₃ = 0.5 mω
• SOC-OCV lookup table:
  • OCV = [3.3,3.5,3.55,3.6,3.8]
  • SOC = [0,0.1,0.5,0.9,1.0]

Control function

Initial system state

• initial state of charge: SOC₀ = 4%
• capacity coefficient: η_cap = 100%

Temporal resolution

The time resolution of the measurement of the power demand and other components, which will be simulated together with the battery model, is 5 seconds. Therefore, the time resolution of the test is 5 seconds. 

Evolution of system state

First, the battery is charged and discharged between SOC of 4% and 96% with 3 different patterns (P_batt =±0.4kW, P_batt=±2kW, P_batt=±4kW). Then a dynamic test is performed by alternating power.

Results

The numerical data is provided in the attached dataset (see Battery_result.csv in date file KIT_Battery_data.zip).

Model harmonization

Narrative

This model harmonization uses the same test setup as the one used for model validation. The focus here is on the total energy which is used to charge or is consumed in discharging and the total energy loss due to the impedance. The test is separated into 6 parts: 1) t = [0,24000]
1) t = [24000,44000]
3) t = [44000,51000]
4) t = [51000,58000]
5) t = [58000,63000]
6) t = [63000,69000]
For each part, the following KPIs are evaluated:

• Total energy in each step:
• Loss:
• Impedance energy loss:

Test system configuration

Inputs and parameters

Control function (optional)

Initial system state

Temporal resolution

Evolution of system state

Results

The resulting KPIs for the 6 parts are: