Domain

• electrical storage

Intended application (including scale and resolution)

The model primarily aims at reproducing the operational constraints imposed by the integrated battery management system while the electrochemical processes are simplified and not modelled in detail (“leaky bucket with linear degradation”). Typical time resolutions are in the order of seconds.

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

• quasi-static

Model of computation

• time-continuous

Functional representation

• explicit

The model is an equivalent circuit model including lookup tables. 

Input variables (name, type, unit, description)

• P_set [kW]: Requested discharge rate (negative values=battery is requested to charge) of the entire unit, measured at AC terminals
• Q_set [kVAr]: Requested reactive power production (negative values=requested consumption) of the entire unit, measured at AC terminals

Output variables (name, type, unit, description)

• P_inst [kW]: Instantaneous power production/discharge (negative values=power consumption/charge) of the entire unit, measured at AC terminals
• Q_inst [kVAr]: Instantaneous reactive power production (negative values=power consumption) of the entire unit, measured at AC terminals
• SOC [%]: State of charge of the entire battery unit

Parameters (name, type, unit, description)

• Cap_r [kWh]: Rated (initial) capacity of the unused battery unit
• S_r [kVA]: Rated apparent power of the unit (assumed to correspond to the inverter current limit)
• P_r [kW]: Rated active power of the unit (all quadrants)
• Q_r [kVAr]: Rated reactive power of the unit (all quadrants)
• init_age [cycles]: Initial cycle age of the battery, in full cycle equivalents
• init_SOC [%]: Initial state of charge of the entire battery unit
• eta_chg [p.u.]: Charging efficiency, i.e. energy stored after lumped inverter and electrochemical losses
• eta_dis [p.u.]: Discharging efficiency, i.e. energy available at AC terminals after lumped electrochemical and inverter losses
• k_age [p.u]: Capacity degradation (as a fraction of rated capacity) per full cycle. Degradation is assumed to be linear, i.e every full cycle reduces the available capacity by k_age

Internal variables (name, type, unit, description)

• rem_cap [kWh]: Remaining capacity of the battery unit, i.e. rated capacity minus ageing
• inst_age [cycles]: Instantaneous cycle age of the battery, in full cycle equivalents
• E_st [kWh]: Usable energy stored in the battery. “Usable” refers to the energy stored above SOC=0 (i.e. the safe discharge threshold of the battery) such that SOC=1 corresponds to E_st=rem_cap.
• P_eff [kW]: electrochemical charge/discharge power (effect of P_inst on battery energy content after losses)
• P_max_chg [kW]: Maximum charge rate allowed by BMS at current operating point
• P_max_dis [kW]: Maximum discharge rate allowed by BMS at current operating point

Internal constants (name, type, unit, description)

Model equations

Governing equations

Note:

• Bold variables are taken from the previous time step
• maximum rates obtained from ext. control function

Constitutive equations

-

Initial conditions

• SOC=init_SOC
• inst_age=init_age
• rem_cap=Cap_r*(1-init_age*k_age)
• E_st=rem_cap*init_SOC

Boundary conditions

 -

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

Model Validation

Narrative

This test can be used to validate the stationary battery model by testing for correct response under different active and reactive power limiting conditions, i.e., with the charging or discharging power limited by the maximum inverter current or high SOC derating. The test covers the following elements of the model:

• Charge and discharge efficiency
• Charge derating at high SOC (provided by external control function)
• Current limit of inverter

Test system configuration

Only the simulation model and the BMS controller are required to perform the simulation, i.e. there is no necessity to interact with other models. The test starts at zero POSIX epoch time (=00:00:00 UTC, Jan 1st, 1970) and will run for 24h of simulation time (86400 seconds).

Inputs and parameters

Inputs:

• timeseries of active and reactive power setpoints (NHN_ts_pqset.csv in data file DTU_Battery_data.zip). The two columns map to the P_set and Q_set model inputs.

• Cap_r=400kWh
• S_r=175kVA
• P_r=150kW
• eff = 1
• Q_r=120kVAr
• init_SOC=50%
• init_age=2
• eta_chg=0.95
• eta_dis=0.95
• k_age=0.1 (this is an extremely high value but useful for evaluating the ageing mechanism)

Control function (optional)

Initial system state

• SOC=init_SOC
• inst_age=init_age
• rem_cap=Cap_r*(1-init_age*k_age)
• E_st=Cap_r*init_SOC
• P_inst=0
• Q_inst=0
• P_eff=0

Temporal resolution

Evolution of system state

The plot below shows active and reactive setpoint patterns with different characteristics being applied to the battery. Some of these setpoints exceed the rated capability of the battery. The power drawn at the battery's point of common coupling is a function of power limitations imposed by the battery capability (static), the inverter current limit (dynamic) and limitations imposed by the BMS (dynamic) in certain SOC ranges. The sequence shown below covers the full spectrum of causes for charging power limitations (for a full discussion, see the "Results" section).

Results

• Between t=5000 and t=20000, a discharge setpoint is applied to the battery. For the entire duration, the setpoint (P=200kW) exceeds the power rating of the battery (P=150kW). Until SOC drops to 10% near t=8000, the battery limits discharge to its power rating. After this point, the BMS progressively lowers the discharge limit below the rated power in order to prevent cell undervoltages. This causes the discharge process to gradually slow and eventually reach the steady state of P=0 at SOC=0%. Battery ageing is not affected in this period (ageing is modeled to only happen during the charging process).
• Between t=0 and t=10000, a reactive power setpoint of Q=-125kVAr is applied to the battery. The unit follows this setpoint most of the time, except for a period between t=5000 and t=8000, where the full discharge operation of the battery causes the reactive power output to be reduced by the inverter's current limiter.
• Between t=40000 and t=65000, a charge/ discharge/charge setpoint pattern is applied. All setpoints are below the rated power; therefore, the power at the terminals follows the setpoint, except in the period from around t=58000 where a high SOC causes the BMS to limit the charging power in order to prevent cell overvoltages. This causes the charging process to gradually slow and eventually reach the steady state of P=0 at SOC=100%. The battery ages by 0.42 and 0.87 full cycle equivalents during the two charging cycles.
• Between t=50000 and t=70000, a reactive power setpoint is applied to the battery. For the entire duration, the setpoint (q=150kVAr) exceeds the reactive power rating of the battery (P=120kVAr). For the entire period, the battery inverter limits reactive power output to the reactive power rating. The inverter's current limiter is not reached at any point.

Model harmonization

Narrative

Test system configuration

Inputs and parameters

The dataset used is the same as in Model Validation; however, P and Q setpoints correspond to the mean of all setpoint values since the previous timestamp (boxcar average):

where T is the current timestamp and dt is the timestep length.

Initial system state

Temporal resolution

Evolution of system state

Since the test uses the same testing pattern as the validation test, it exhibits the same phenomena, albeit at less detail. The main focus at this lower time resolution (and potentially even lower resolutions) should be on comparing the medium and long-term indicators of battery performance over a more than one cycle:

Energy content (related to the state of charge) and battery degradation (related to cycle age).

Results

• At a one-hour time resolution, the state of charge (SOC) reaches 100% within the timestep ranging from 57600s to 61200s. When simulated at 10s, the SOC at 61200s is 98.99%, and an (almost) full battery (SOC=99.96%) is reached at t=65000, when the charging setpoint is set to zero. This shows one of the sources of error caused by lower time resolution: At t=57600s, SOC is at 77%, below the threshold at which the battery BMS applies rate limiting due to high SOC. At the next timestep, the battery is already full - i.e. the entire rate limiting mechanism "falls through the cracks" and is masked by available time resolution. In a scenario with frequent setpoint changes, this deviation may accumulate to a large error in final SOC over time.
• The cycle age (corresponding to the integral over all energy moved into the battery) is 3.27 at the end of the 24-hour period at one-hour resolution, compared to 3.29 when simulated at a resolution of ten seconds. This deviation is a good indicator of long-term precision.