Sector Coupling

The sector coupling model extends the power system optimization to include interactions with other energy sectors through storage and conversion processes. This formulation allows modeling sector coupling with various energy carriers (e.g., heat, hydrogen, etc.) while maintaining the temporal and operational constraints of the power system.

Model Structure

Sets

Additional sets for the sector coupling model include:

Name	Description
nx	Boundary sector nodes
nx_CC	Boundary sector nodes without the EndCascade node
lx	Boundary sector lines
slx	Boundary sector spillage lines
xu(au)	Boundary sector only units

Parameters

Key parameters specific to the sector coupling model:

Name	Units	Description
SectorXDemand(nx,h)	MWh	Demand profile in boundary sectors
X2PowerConversionMultiplier(nx,au,h)	%	Discharge efficiency for boundary sector
Power2XConversionMultiplier(nx,au,h)	%	Charging efficiency for boundary sector
SectorXStorageCapacity(nx)	MWh	Storage capacity of the boundary sector
SectorXStorageSelfDischarge(nx)	%	Boundary sector storage self discharge rate
SectorXStorageMinimum(nx)	MWh	Boundary sector storage minimum level
SectorXStorageProfile(nx,h)	%	Required storage level profile
SectorXAlertLevel(nx,h)	MWh	Storage alert level - violated only to avoid rationing
SectorXFloodControl(nx,h)	MWh	Storage flood control level

Variables

Additional variables specific to the boundary sector model:

Sector Coupling Units

Sector coupling units are specific units that enable the conversion between the power sector and boundary sectors. These units can operate in two modes:

Power-to-X: Converting electrical power to another energy carrier (e.g., power-to-heat, power-to-hydrogen)
X-to-Power: Converting energy from a boundary sector back to electrical power (e.g., fuel cells)

The conversion process is governed by efficiency parameters:

\[\begin{split}\begin{split} \mathit{SectorXStorageInput}_{nx,i} = & \sum_{au} \mathit{Power2XConversionMultiplier}_{nx,au,i} \cdot \mathit{PowerConsumption}_{au,i} \cdot \mathit{LocationX}_{au,nx} \\ & - \sum_{au} \mathit{X2PowerConversionMultiplier}_{nx,au,i} \cdot \mathit{Power}_{au,i} \cdot \mathit{LocationX}_{au,nx} \end{split}\end{split}\]

This equation represents the net storage input as the difference between: - Charging: Power consumption multiplied by the Power-to-X conversion efficiency - Discharging: Power generation multiplied by the X-to-Power conversion efficiency

Boundary Sector Storage

Each boundary sector can include storage capabilities, subject to the following constraints:

Storage Level Minimum:

\[\mathit{SectorXStorageMinimum}_{nx} \leq \mathit{SectorXStorageLevel}_{nx,i}\]

Storage Level Maximum:

\[\mathit{SectorXStorageLevel}_{nx,i} \leq \mathit{SectorXStorageCapacity}_{nx}\]

Storage Balance:

\[\begin{split}\begin{split} \mathit{SectorXStorageLevel}_{nx,i} = & \mathit{SectorXStorageInitial}_{nx} \cdot \delta_{i=1} + \mathit{SectorXStorageLevel}_{nx,i-1} \cdot (1-\delta_{i=1}) \\ & + \mathit{SectorXStorageInput}_{nx,i} \cdot \mathit{TimeStep} \\ & - \mathit{SectorXStorageSelfDischarge}_{nx} \cdot \mathit{SectorXStorageLevel}_{nx,i} \cdot \mathit{TimeStep} \end{split}\end{split}\]

where \(\delta_{i=1}\) is 1 for the first time step and 0 otherwise.

Storage Final Level:

\[\mathit{SectorXStorageFinalMin}_{nx} \leq \mathit{SectorXStorageLevel}_{nx,i} + \mathit{SectorXStorageLevelViolation}_{nx}\]

for the final time step i.

Boundary Sector Demand

The demand in boundary sectors can be categorized into two types:

Non-Flexible Demand

Non-flexible demand (\(\mathit{SectorXDemand}_{nx,h}\)) represents the fixed energy requirements that must be met at each time step. This demand is typically defined through input time series and must be satisfied either through: - Direct conversion from power using sector coupling units - Discharge from boundary sector storage - Alternative supply options (at a high cost penalty)

Flexible Demand

Flexible demand (\(\mathit{SectorXFlexDemand}_{nx,h}\)) represents demand that can be shifted in time, subject to constraints:

\[\sum_{h} \mathit{SectorXFlexDemand}_{nx,h} = \mathit{SectorXFlexDemandInput}_{nx}\]

This ensures that the total flexible demand over the optimization horizon matches the required input while allowing temporal flexibility in when it is met.

Additional constraints limit the maximum flexible demand at each time step:

\[\mathit{SectorXFlexDemand}_{nx,h} \leq \mathit{SectorXFlexMaxCapacity}_{nx}\]

Cost Terms

The sector coupling model introduces additional cost terms to the objective function:

\[\begin{split}\begin{split} & + \sum_{nx,i} \mathit{CostXSpillage}_{slx,i} \cdot \mathit{SectorXSpillage}_{slx,i} \cdot \mathit{TimeStep} \\ & + \sum_{nx,i} \mathit{CostXStorageAlert}_{nx,i} \cdot \mathit{SectorXStorageLevelViolation\_H}_{nx,i} \cdot \mathit{TimeStep} \\ & + \sum_{nx,i} \mathit{CostXFloodControl}_{nx,i} \cdot \mathit{SectorXStorageLevelViolation}_{nx} \cdot \mathit{TimeStep} \\ & + \sum_{nx,i} \mathit{CostXNotServed}_{nx,i} \cdot (\mathit{LL\_SectorXFlexDemand}_{nx} + \mathit{LL\_SectorXFlexSupply}_{nx}) \cdot \mathit{TimeStep} \end{split}\end{split}\]

These terms account for: - Spillage between boundary sector nodes - Violations of storage alert levels and flood control levels - Deficits in meeting flexible demand or supply requirements - Energy not served in boundary sectors