Battery Power Estimator

Calculate maximum charging and discharging power of battery pack over time horizon

Since R2024b

Libraries:
Simscape / Battery / BMS / Estimators

Description

The Battery Power Estimator block calculates the maximum charging and discharging power capabilities of a battery pack across a specified time horizon. This block adheres to the sign convention where the current and power are positive values during the battery charging process.

Equations

To estimate the maximum charging and discharging power capabilities of a battery pack, the Battery Power Estimator block uses the hybrid pulse power characterization (HPPC) method [1].

Diagram of pulse test voltage, on the Y axis, versus time, on the X axis

To calculate the discharging and charging currents, the block uses these equations,

$\begin{array}{l} i_{dischg,volt,n} = - \frac{V_{0} (S O C, T) - v_{\min}}{R_{dischgDt}} \\ i_{chg,volt,n} = - \frac{V_{0} (S O C, T) - v_{\max}}{R_{chgDt}} \end{array}$

where:

V₀(SOC,T) is the open-circuit voltage.
v_min and v_max are the minimum and maximum cell voltages.
R_dischgDt and R_chgDt are the discharging and charging resistances over a pulse of Δt seconds.
i_{dischg,volt,n} and i_chg,volt,n are the discharging and charging currents for the nth cell based on the voltage constraints.

For a constant current i_n, the state-of-charge (SOC) relationship is

$S O C_{n} (t + Δ t) = S O C_{n} (t) - \frac{η Δ t i_{n}}{3600 Q},$

where:

Q is the capacity in ampere-hour.
SOC_n is the state of charge of the nth cell.
η is the efficiency factor, with η = 1 for discharging and η ≤ 1 for charging.

Minimum and a maximum permissible values limit the state of charge for all cells in the pack such that

$S O C_{\min} \leq S O C_{n} (t) \leq S O C_{\max} .$

The block then computes the current limits based on the SOC:

$\begin{array}{l} i_{dischg,SOC,n} = - \frac{3600 \cdot Q \cdot (S O C_{n} - S O C_{\min})}{Δ t} \\ i_{chg,SOC,n} = - \frac{3600 \cdot Q \cdot (S O C_{n} - S O C_{\max})}{η Δ t} \end{array}$

To calculate the discharging and charging currents of the entire battery pack, the block uses these equations:

$\begin{array}{l} i_{dischg} = \max (i_{\min}, \max_{n} i_{dischg,SOC,n}, \max_{n} i_{dischg,volt,n}) \\ i_{chg} = \min (i_{\max}, \min_{n} i_{chg,SOC,n}, \min_{n} i_{chg,volt,n}) \end{array}$

Finally, the block calculates the charging and discharging power limits for a prediction horizon Δt:

$\begin{array}{l} P_{\max, dischg} = N_{p} \max (N_{s} P_{\min}, \sum_{n = 1}^{N_{s}} i_{dischg} (V_{0} (S O C_{n} (t) - i_{dischg} \frac{Δ t}{3600 Q}, T) - i_{dischg} R_{dischgDt})) \\ P_{\min, chg} = N_{p} \min (N_{s} P_{\max}, \sum_{n = 1}^{N_{s}} i_{chg} (V_{0} (S O C_{n} (t) - i_{chg} \frac{η Δ t}{3600 Q}, T) - i_{chg} R_{chgDt})) \end{array}$

where N_p is the number of parallel modules and N_s is the number of series modules.

Assumptions and Limitations

During the battery charging process, the current and power are positive values.

Ports

Input

expand all

CellSOC — Cell state of charge, unitless
scalar | vector

State of charge of one or multiple cells, specified as a scalar or vector of entries in the range [0, 1]. The size of this input port must be equal to the size of the CellTemperature input port.

CellTemperature — Cell temperature, K
scalar | vector

Cell temperature, specified as a scalar for a single cell or a vector for multiple cells. The size of this input port must be equal to the size of the CellSOC input port.

Output

expand all

MaxPowerDischarging — Maximum power for discharging battery
scalar

Maximum power for discharging the battery over the prediction horizon.

MaxPowerCharging — Maximum power for charging battery
scalar

Maximum power for charging the battery over the prediction horizon.

Parameters

expand all

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Battery

Vector of state-of-charge values, SOC (-) — SOC breakpoints
`[0, .1, .25, .5, .75, .9, 1]` (default) | vector of scalars in the range [0, 1]

Vector of the state-of-charge breakpoints that defines the points at which you specify lookup data. The entries of this vector must be in strictly ascending order. The block calculates the state-of-charge value with respect to the nominal battery capacity specified in the Cell capacity, AH (A*Hr) parameter. The SOC is the ratio of the available battery charge q_battery and the nominal battery capacity q_nom(T,n). Make sure that, for each temperature value, an SOC of 1 represents the battery charge capacity for the corresponding element of the Cell capacity, AH (A*Hr) parameter when you model a fresh battery with a number of cycles N equal to 1 and δ_AH(n = 1, T_fade) equal to 0:

$S O C = \frac{q_{battery}}{q_{nom} (T, n)} for N = 1 and δ_{A H} (n, T_{fade}) = 0, q_{nom} (T, n) = A H .$

Vector of temperatures, T — Temperature breakpoints
`[278, 293, 313]` (default) | vector of positive scalars

Vector of temperature breakpoints that defines the points at which you specify lookup data. This vector must be strictly ascending and greater than 0 K. The physical unit of this parameter must be the same as the physical unit of the CellTemperature input port.

No-load voltage, V0(SOC,T), (V) — V₀ lookup table
`[3.49, 3.5, 3.51; 3.55, 3.57, 3.56; 3.62, 3.63, 3.64; 3.71, 3.71, 3.72; 3.91, 3.93, 3.94; 4.07, 4.08, 4.08; 4.19, 4.19, 4.19]` (default) | matrix of nonnegative entries

Lookup data, in volt, for open-circuit voltages across the fundamental battery model at the specified SOC. The number of rows of this matrix is equal to the size of the Vector of state-of-charge values, SOC (-) parameter. The number of columns of this matrix is equal to the size of the Vector of temperatures, T parameter.

Charging pulse test resistance, R0Dt(SOC,T), (ohm) — Charging resistances over pulse of `Δt` seconds
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` (default) | matrix of nonnegative entries

Charging resistances over a pulse of Δt seconds. The number of rows of this matrix is equal to the size of the Vector of state-of-charge values, SOC (-) parameter. The number of columns of this matrix is equal to the size of the Vector of temperatures, T parameter.

Discharging pulse test resistance, R0Dt(SOC,T), (ohm) — Discharging resistances over pulse of `Δt` seconds
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` (default) | matrix of nonnegative entries

Discharging resistances over a pulse of Δt seconds. The number of rows of this matrix is equal to the size of the Vector of state-of-charge values, SOC (-) parameter. The number of columns of this matrix is equal to the size of the Vector of temperatures, T parameter.

**Cell capacity, AH (A*Hr)** — Battery capacity when fully charged
`27` (default) | nonnegative scalar

Cell capacity of the battery, in ampere-hour. The block calculates the state of charge by dividing the accumulated charge by this value. The block calculates the accumulated charge by integrating the battery current.

Number of series modules, Ns — Number of modules in series
`10` (default) | positive scalar

Number of series-connected modules inside the battery pack.

Number of parallel modules, Np — Number of modules in parallel
`1` (default) | positive scalar

Number of parallel-connected modules inside the battery pack.

Charging efficiency ratio — Ratio of charging efficiency
`1` (default) | nonnegative scalar in the range (0,1]

Ratio of the charging efficiency.

Limits

Minimum cell voltage (V) — Minimum voltage of cell
`2.5` (default) | positive scalar

Minimum voltage of the battery cell, in volt. The value of this parameter must be less than the value of the Maximum cell voltage (V) parameter.

Maximum cell voltage (V) — Maximum voltage of cell
`4.5` (default) | positive scalar

Maximum voltage of the battery cell, in volt. The value of this parameter must be greater than the value of the Minimum cell voltage (V) parameter.

Minimum state of charge, SOCmin(-) — Minimum state of charge
`0.1` (default) | nonnegative scalar in the range [0,1]

Minimum state of charge of the battery cell. The value of this parameter must be less than the value of the Maximum state of charge, SOCmin(-) parameter.

Maximum state of charge, SOCmax(-) — Maximum state of charge
`0.9` (default) | nonnegative scalar in the range [0,1]

Maximum state of charge of the battery cell. The value of this parameter must be greater than the value of the Minimum state of charge, SOCmax(-) parameter.

Minimum pack current (A) — Minimum current of pack
`-200` (default) | negative scalar

Minimum current of the battery pack, in ampere. The value of this parameter must be less than the value of the Maximum pack current (A) parameter. If you set this value to -inf, the block ignores this parameter.

Maximum pack current (A) — Maximum current of pack
`200` (default) | positive scalar

Maximum current of the battery pack, in ampere. The value of this parameter must be greater than the value of the Minimum pack current (A) parameter. If you set this value to inf, the block ignores this parameter.

Minimum cell power (W) — Minimum power of battery cell
`-inf` (default) | negative scalar

Minimum power of the battery cell, in watt. The value of this parameter must be less than the value of the Maximum cell power (W) parameter. If you set this value to -inf, the block ignores this parameter.

Maximum cell power (W) — Maximum power of battery cell
`inf` (default) | positive scalar

Maximum power of the battery cell, in watt. The value of this parameter must be greater than the value of the Minimum cell power (W) parameter. If you set this value to inf, the block ignores this parameter.

Time horizon (s) — Time horizon
`10` (default) | positive scalar

Time, in seconds, over which the block calculates the maximum charging and discharging power capabilities of the battery pack.

References

[1] Plett, Gregory L. Battery Management Systems. Volume II, Equivalent-Circuit Methods. Norwood, MA: Artech House, 2015.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024b

Battery Power Estimator

Description

Equations

Assumptions and Limitations

Ports

Input

CellSOC — Cell state of charge, unitless scalar | vector

CellTemperature — Cell temperature, K scalar | vector

Output

MaxPowerDischarging — Maximum power for discharging battery scalar

MaxPowerCharging — Maximum power for charging battery scalar

Parameters

Battery

Vector of state-of-charge values, SOC (-) — SOC breakpoints [0, .1, .25, .5, .75, .9, 1] (default) | vector of scalars in the range [0, 1]

Vector of temperatures, T — Temperature breakpoints [278, 293, 313] (default) | vector of positive scalars

No-load voltage, V0(SOC,T), (V) — V0 lookup table [3.49, 3.5, 3.51; 3.55, 3.57, 3.56; 3.62, 3.63, 3.64; 3.71, 3.71, 3.72; 3.91, 3.93, 3.94; 4.07, 4.08, 4.08; 4.19, 4.19, 4.19] (default) | matrix of nonnegative entries

Charging pulse test resistance, R0Dt(SOC,T), (ohm) — Charging resistances over pulse of Δt seconds [.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089] (default) | matrix of nonnegative entries

Discharging pulse test resistance, R0Dt(SOC,T), (ohm) — Discharging resistances over pulse of Δt seconds [.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089] (default) | matrix of nonnegative entries

Cell capacity, AH (A*Hr) — Battery capacity when fully charged 27 (default) | nonnegative scalar

Number of series modules, Ns — Number of modules in series 10 (default) | positive scalar

Number of parallel modules, Np — Number of modules in parallel 1 (default) | positive scalar

Charging efficiency ratio — Ratio of charging efficiency 1 (default) | nonnegative scalar in the range (0,1]

Limits

Minimum cell voltage (V) — Minimum voltage of cell 2.5 (default) | positive scalar

Maximum cell voltage (V) — Maximum voltage of cell 4.5 (default) | positive scalar

Minimum state of charge, SOCmin(-) — Minimum state of charge 0.1 (default) | nonnegative scalar in the range [0,1]

Maximum state of charge, SOCmax(-) — Maximum state of charge 0.9 (default) | nonnegative scalar in the range [0,1]

Minimum pack current (A) — Minimum current of pack -200 (default) | negative scalar

Maximum pack current (A) — Maximum current of pack 200 (default) | positive scalar

Minimum cell power (W) — Minimum power of battery cell -inf (default) | negative scalar

Maximum cell power (W) — Maximum power of battery cell inf (default) | positive scalar

Time horizon (s) — Time horizon 10 (default) | positive scalar

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

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CellSOC — Cell state of charge, unitless
scalar | vector

CellTemperature — Cell temperature, K
scalar | vector

MaxPowerDischarging — Maximum power for discharging battery
scalar

MaxPowerCharging — Maximum power for charging battery
scalar

Vector of state-of-charge values, SOC (-) — SOC breakpoints
`[0, .1, .25, .5, .75, .9, 1]` (default) | vector of scalars in the range [0, 1]

Vector of temperatures, T — Temperature breakpoints
`[278, 293, 313]` (default) | vector of positive scalars

No-load voltage, V0(SOC,T), (V) — V₀ lookup table
`[3.49, 3.5, 3.51; 3.55, 3.57, 3.56; 3.62, 3.63, 3.64; 3.71, 3.71, 3.72; 3.91, 3.93, 3.94; 4.07, 4.08, 4.08; 4.19, 4.19, 4.19]` (default) | matrix of nonnegative entries

Charging pulse test resistance, R0Dt(SOC,T), (ohm) — Charging resistances over pulse of `Δt` seconds
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` (default) | matrix of nonnegative entries

Discharging pulse test resistance, R0Dt(SOC,T), (ohm) — Discharging resistances over pulse of `Δt` seconds
`[.0117, .0085, .009; .011, .0085, .009; .0114, .0087, .0092; .0107, .0082, .0088; .0107, .0083, .0091; .0113, .0085, .0089; .0116, .0085, .0089]` (default) | matrix of nonnegative entries

**Cell capacity, AH (A*Hr)** — Battery capacity when fully charged
`27` (default) | nonnegative scalar

Number of series modules, Ns — Number of modules in series
`10` (default) | positive scalar

Number of parallel modules, Np — Number of modules in parallel
`1` (default) | positive scalar

Charging efficiency ratio — Ratio of charging efficiency
`1` (default) | nonnegative scalar in the range (0,1]

Minimum cell voltage (V) — Minimum voltage of cell
`2.5` (default) | positive scalar

Maximum cell voltage (V) — Maximum voltage of cell
`4.5` (default) | positive scalar

Minimum state of charge, SOCmin(-) — Minimum state of charge
`0.1` (default) | nonnegative scalar in the range [0,1]

Maximum state of charge, SOCmax(-) — Maximum state of charge
`0.9` (default) | nonnegative scalar in the range [0,1]

Minimum pack current (A) — Minimum current of pack
`-200` (default) | negative scalar

Maximum pack current (A) — Maximum current of pack
`200` (default) | positive scalar

Minimum cell power (W) — Minimum power of battery cell
`-inf` (default) | negative scalar

Maximum cell power (W) — Maximum power of battery cell
`inf` (default) | positive scalar

Time horizon (s) — Time horizon
`10` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.