Optimal Power Flow Module¶

This module provides functions for AC/DC hybrid optimal power flow analysis [1].

functions are found in pyflow_acdc.ACDC_OPF and pyflow_acdc.ACDC_OPF_model

AC/DC Hybrid Optimal Power Flow¶

Running the OPF¶

This function runs the AC/DC hybrid optimal power flow calculation. It creates the model, chooses an objective function, and solves the model.

Optimal_PF(grid, ObjRule=None, PV_set=False, OnlyGen=True, Price_Zones=False)¶

Performs AC/DC hybrid optimal power flow calculation.

Parameter	Type	Description	Default
`grid`	Grid	Grid to optimize	Required
`ObjRule`	dict	Objective function weights	None
`PV_set`	bool	Sets PV and Slack voltage as fixed variables	False
`OnlyGen`	bool	Only generators are considered in the cost function	True
`Price_Zones`	bool	Enable price zone constraints	False

Example

model, model_res , timing_info, solver_stats =pyf.Optimal_PF(grid, ObjRule=None, PV_set=False, OnlyGen=True, Price_Zones=False)

Creating the OPF model¶

OPF_createModel_ACDC(model, grid, PV_set, Price_Zones)¶

Creates the OPF model.

Parameter	Type	Description
`model`	Model	Model to create
`grid`	Grid	Grid to optimize
`PV_set`	bool	Sets PV and Slack voltage as fixed variables
`Price_Zones`	bool	Enable price zone constraints

Variables

The optimization model includes variables for:

AC node voltages and angles
DC node voltages
Generator active/reactive power
Renewable generation and curtailment
Line flows
Converter power flows
Price zone variables

Constraints

The model enforces constraints for:

For more details on the constraints, please refer to the System Modelling page.

Example

model = pyf.OPF_createModel_ACDC(model,grid,PV_set,Price_Zones)

Objective Functions¶

The user can define the objective by setting the weight of each sub objective. The objective function is defined as:

OPF_obj(model, grid, ObjRule, OnlyGen, OnlyAC=False)¶

This function creates a weighted sum of the different sub objectives.

\[\min \frac{\sum_{i \in O} \left( w_i \cdot f_i \right)}{\sum_{i \in O} w_i}\]

where \(f_i\) is the sub objective and \(w_i\) is the weight.

The following table shows the pre-built objective functions as defined in [1] :

Weight	Description	Formula
`Ext_Gen`	External generation minimization or maximum export	\(\sum_{g \in G} \cdot P_{g}\)
`Energy_cost`	Energy cost	\(\sum_{g \in \mathcal{G}_{ac}} \left(P_{g}^2 \cdot \alpha_g + P_{g} \cdot \beta_g \right)\)
`Curtailment_Red`	Renewable curtailment reduction	\(\sum_{rg \in \mathcal{RG}_{ac}}\left((1-\gamma_rg)P_{rg}\cdot \rho_{rg} \sigma_{rg}\right)\)
`AC_losses`	AC transmission losses	\(\sum_{j \in \mathcal{B}_{ac}} \left( P_{j,\text{from}} +P_{j,\text{to}} \right)\)
`DC_losses`	DC transmission losses	\(\sum_{e \in \mathcal{B}_{dc}} \left( P_{e,\text{from}} +P_{e,\text{to}} \right)\)
`Converter_Losses`	Converter losses	\(\sum_{cn \in \mathcal{C}_{n}} \left( P_{loss_{cn}} + \|\left(P_{c_{cn}}-P_{s_{cn}}\right)\| \right)\)
`General_Losses`	Generation minus demand	\(\left(\sum_{g \in \mathcal{G}} P_{g}+\sum_{rg \in \mathcal{RG}} P_{rg}*\gamma_{rg}- \sum_{l \in \mathcal{L}} P_{L} \right)\)

The following table shows the pre-built objective functions as defined in [2]:

Weight	Description	Formula
`PZ_cost_of_generation`	Price zone generation cost	\(\sum_{m \in \mathcal{M}} CG(P_N)_m\)

The following table shows the pre-built objective functions in development:

Weight	Description	Formula
`Renewable_profit`	Renewable generation profit	\(- \left(\sum_{rg \in \mathcal{RG}} P_{rg}*\gamma_{rg} + \sum_{cn \in \mathcal{C}} \left(P_{loss,cn} + P_{AC,loss,cn}\right)\right)\)
`Gen_set_dev`	Generator setpoint deviation	\(\sum_{g \in G} \left(P_g -P_{g,set}\right)^2\)

Example

weights_def = {
'Ext_Gen': {'w': 0},
'Energy_cost': {'w': 0},
'Curtailment_Red': {'w': 0},
'AC_losses': {'w': 0},
'DC_losses': {'w': 0},
'Converter_Losses': {'w': 0},
'PZ_cost_of_generation': {'w': 0},
'Renewable_profit': {'w': 0},
'Gen_set_dev': {'w': 0}
}

Solvers¶

The OPF module supports pyomo solvers.

To see the available solvers, use the following command:

pyomo help --solvers

Tested with:

IPOPT
Bonmin

OPF_solve(model, grid, solver='ipopt')¶

Solves the OPF model using the specified solver.

Parameters:

model – The optimization model
grid – The grid to optimize
solver – The solver to use

Example

results, solver_stats =pyf.OPF_solve(model,grid)

References