Battery#

The block implements a basic non-stationary model of a lithium-ion battery.

For lead-acid battery type, the model uses the following equations:

Discharge model \((i^* {\: > \:} 0)\) (1) :

(1)#\[ U_{батраз}=E_0 - R \cdot i - K \cdot \frac{Q}{Q-it} \cdot i^* - K \cdot \frac{Q}{Q-it}\cdot\ +{Laplace}^{-1}(\frac{Exp(s)}{Sel(s)}\cdot0) \]

Charge model \((i^* {\: < \:} 0)\) (2) :

(2)#\[ U_{батзар}=E_0 - R\cdot i - K\cdot\:\frac{Q}{it + 0.1 \cdot Q}\cdot i^*- K\cdot\:\frac{Q}{Q-\:it}\cdot\:it\:+{Laplace}^{-1}(\frac{Exp(s)}{Sel(s)}\cdot \frac{1}{s}) \]

For lithium-ion battery type, the model uses the following equations:

Discharge model \((i^* {\: > \:} 0) \) (3) :

(3)#\[ U_{батраз}=\:E_0\:- R\cdot\:i-\:K\cdot\:\frac{Q}{Q-\:it}\cdot\:i\:*\:- K\cdot\:\frac{Q}{Q-\:it}\cdot\:it\:+ A\cdot exp(\!- \!B\cdot it) \]

Charge model \((i^* {\: < \:} 0)\) (4) :

(4)#\[ U_{батзар}=\:E_0\:- R\cdot\:i-\:K\cdot\:\frac{Q}{it + 0.1 \cdot Q}\cdot\:i\:*\:- K\cdot\:\frac{Q}{Q-\:it}\cdot\:it\:+ A\cdot exp(\!- \!B\cdot it) \]

For nickel-cadmium and nickel-metal-hybrid battery type, the modeluses the following equations:

Discharge model \((i^* {\: > \:} 0)\) (5) :

(5)#\[ U_{батраз}=E_0 - R\cdot i-\:K\cdot \frac{Q}{Q-it}\cdot i^* - K\cdot\frac{Q}{Q-it}\cdot it + {Laplace}^{-1}(\frac{Exp(s)}{Sel(s)}\cdot0) \]

Charge model \((i^* {\: < \:} 0)\) (6) :

(6)#\[ U_{батзар}=E_0 - R\cdot\:i-\:K\cdot\:\frac{Q}{\left| it \right| + 0.1 \cdot Q}\cdot\:i^*\:- K\cdot\:\frac{Q}{Q-\:it}\cdot\:it\:+ {Laplace}^{-1}(\frac{Exp(s)}{Sel(s)}\cdot \frac{1}{s}) \]

where:

\(E_0\) - battery voltage constant, [V];

\(R\) - Battery resistance, [Ohm];

\(K\) - polarization constant, [\(\frac{V}{A \cdot h}\)];

\(Q\) - battery capacity, [A \(\cdot\) h];

\(it\) - actual battery charge, [A\( \cdot\) h];

\(A\) - amplitude of the exponential form, [V];

\(B\) - inverse time constant of exponential form, [\(\frac{1}{A \cdot h}\)];

\(i\) - battery current, [A];

\(i^*\) - filtered battery current, [A].

1. Properties#

Property	Default value	Description	Units of measurement
Battery type: Li-ion; Lead-acid; NiCd; NiMH	Li-ion	–	–
No-load voltage	3.366	–	V
Battery capacity	2.3	–	А\(\cdot\)h
Polarization constant	0.0076	–	\(\frac{V}{А\cdot h}\)
Battery resistance	0.01	–	Ohm
Exponential area amplitude	0.26422	–	V
Exponential area time constant	26.5487	–	\(\frac{1}{А\cdot h}\)

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Discharging current	Input	–	A	Automation
Electrical port. Voltage	Output	–	V	Voltage
State of charge	Output	–	dimensionless value	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports