varying efficiency in MILP approach
Awaiting user input
Hello,
I'm using gurobi in an python enviroment and would like to Model a varying efficiency for a Battery charge/discharge without the Model losing it's MIPL characteristics.
Example Code:
eta_Batt = 0.9 # Battery Efficiency
E_Batt_StandBy = 0 # Constant Dischsarge in [W]
m = Model()
m.setParam("MIPGap", 0.1)
x_E_Batt_discharge = m.addVars(
Horizont,
name="x_E_Batt_discharge",
vtype=GRB.CONTINUOUS,
lb=0,
ub=E_Batt_discharge_max,
)
x_E_Batt_charge = m.addVars(
Horizont, name="x_E_Batt_charge", vtype=GRB.CONTINUOUS, lb=0, ub=E_Batt_charge_max
)
m.addConstrs(
x_SoC_Batt[t]
== x_SoC_Batt[t - 1]
+ (
x_E_Batt_charge[t] * eta_Batt
- x_E_Batt_discharge[t] / eta_Batt
- E_Batt_StandBy
)
* (100 * (delta_t / 60) / Cap_Batt)
for t in T1
)
m.addConstrs(
x_SoC_Batt[t]
== SoC_Batt_start
+ (
x_E_Batt_charge[t] * eta_Batt
- x_E_Batt_discharge[t] / eta_Batt
- E_Batt_StandBy
)
* (100 * (delta_t / 60) / Cap_Batt)
for t in range(1)
)
I'm searching for a way so that eta_Batt is not a constant but decreases with x_E_Batt_charge or x_E_Batt_discharge without having it directly dependent on these variables and therefore making the contrstaints quadratic.
Thank you in advance
Johanna
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Gurobi Staff
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Hi Johanna,
Could you please write the quadratic mathematical expression defining the relationship between the variables \(\texttt{eta_Batt}\) and \(\texttt{x_E_Batt_charge}\)/\(\texttt{x_E_Batt_discharge}\)?
The Gurobi optimizer can handle non-convex quadratic constraints directly. Have you tried modelling the problem in the quadratic form to evaluate the Gurobi performance?
Best regards,
Maliheh
0 -
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