Heat sector

7. Heat sector#

el1xr_opt models a behind-the-meter heat sector alongside electricity and hydrogen. It is built by oM_HeatSector.create_heat_sector and is a no-op for cases that carry no heat data, so electricity/hydrogen-only cases are unchanged.

7.1. Scope#

The heat sector is nodal (one heat balance per node) and behind-the-meter – there is no heat network with pipe flows or losses yet (that is the next setting). A node’s heat is supplied by:

  • a heat pump (htp): electricity to heat, heat = COP x electricity. This is the cross-sector coupling – the heat-pump electricity draw is a load on the electricity balance.

  • a boiler (a heat generator that burns fuel),

  • a thermal store (hts): shifts heat in time, with a charge/discharge efficiency and an inventory balance,

  • heat-to-power (htw, an ORC / CHP turbine): heat back to electricity. Adding it closes the power-heat loop (heat pump alone is power-to-heat only).

  • heat-not-served (vHeatNotServed): an expensive slack so the balance is always feasible, priced at pHeatNSCost.

7.2. Sets#

htd heat demands, htg heat generators (heat pumps and boilers), htp heat pumps (a subset of htg), htw heat-to-power units, hts thermal stores, with the node maps n2htd / n2htg / n2hts / n2htw.

7.3. Variables#

vHeatOutput (generator heat output), vHeatPumpElec (heat-pump electricity draw), vHeatCharge / vHeatDischarge / vHeatInventory (thermal store), vHeatConsumed and vHeatToEle (heat-to-power), and vHeatNotServed.

7.4. Constraints#

eHeatBalance – nodal heat balance, supply == demand at each node. The supply side is the sum of vHeatOutput over all heat generators htg (which already include the heat pumps, so heat-pump output is not a separate term), plus the net store flow vHeatDischarge - vHeatCharge over thermal stores, plus vHeatNotServed (a + supply slack). The demand side is the fixed pHeatDemand plus vHeatConsumed, the heat drawn by the heat-to-power units:

\[\sum_{\genindex \in htg_{\busindex}} \vheatoutput_{\periodindex,\scenarioindex,\timeindex,\genindex} + \sum_{\storageindex \in hts_{\busindex}} \left( \vheatdischarge_{\periodindex,\scenarioindex,\timeindex,\storageindex} - \vheatcharge_{\periodindex,\scenarioindex,\timeindex,\storageindex} \right) + \sum_{\demandindex \in htd_{\busindex}} \vheatnotserved_{\periodindex,\scenarioindex,\timeindex,\demandindex} = \sum_{\demandindex \in htd_{\busindex}} \pheatdemand_{\periodindex,\scenarioindex,\timeindex,\demandindex} + \sum_{\genindex \in htw_{\busindex}} \vheatconsumed_{\periodindex,\scenarioindex,\timeindex,\genindex} \quad \forall \periodindex,\scenarioindex,\timeindex,\busindex\]

eHeatPumpCOP – heat-pump coupling, heat out = COP x electricity in (the electricity draw is what couples the heat sector to the electricity balance):

\[\vheatoutput_{\periodindex,\scenarioindex,\timeindex,\genindex} = \pheatpumpcop_{\genindex} \, \vheatpumpelec_{\periodindex,\scenarioindex,\timeindex,\genindex} \quad \forall \periodindex,\scenarioindex,\timeindex,\genindex \in htp\]

eHeatToEle – heat-to-power, electricity out = efficiency x heat in:

\[\vheattoele_{\periodindex,\scenarioindex,\timeindex,\genindex} = \pheattoeleeff_{\genindex} \, \vheatconsumed_{\periodindex,\scenarioindex,\timeindex,\genindex} \quad \forall \periodindex,\scenarioindex,\timeindex,\genindex \in htw\]

eHeatInventory – thermal-store inventory dynamics. The charge and discharge are powers, so they are weighted by the load-level duration to accumulate energy, matching the electricity and hydrogen inventory balances (the heat balance above stays a power balance, with no duration, like eEleBalance):

\[\vheatinventory_{\periodindex,\scenarioindex,\timeindex,\storageindex} = \vheatinventory_{\periodindex,\scenarioindex,\timeindex-\ptimestep,\storageindex} + \ptimestepduration_{\periodindex,\scenarioindex,\timeindex} \left( \pheatstoeff_{\storageindex} \, \vheatcharge_{\periodindex,\scenarioindex,\timeindex,\storageindex} - \vheatdischarge_{\periodindex,\scenarioindex,\timeindex,\storageindex} \right) \quad \forall \periodindex,\scenarioindex,\timeindex,\storageindex \in hts\]

with the first load level starting from the initial inventory pHeatStoInitial.

A thermal store is now coupled across temporal-Benders windows by a boundary inventory variable (St, the heat analogue of Se / Sh); see Decomposition (Benders).

The electricity balance eEleBalance is coupled to the heat sector: it subtracts the heat-pump electricity load and adds the heat-to-power injection at each node.

7.5. Cost#

The heat operating cost (heat-not-served penalty plus generator running cost) is added to the objective, discounted by period and weighted by the load-level duration like the electricity and hydrogen operating costs. The heat-pump electricity is already priced on the electricity side, so it is not charged again here.

7.6. Loop topology#

  • Power to heat is an open loop by default (heat pump / boiler; heat is a terminal demand). Adding a heat-to-power unit (htw) closes the power-heat loop.

  • Hydrogen is already closed-loop when a case includes both the electrolyser (e2h) and the fuel cell (h2e).

Which loops are active is selected by the conversion units a case includes.

7.7. Input tables#

A heat-bearing case adds oM_Data_HeatGeneration (with a Type column – HeatPump / Boiler / Heat2Ele / Storage), oM_Data_HeatDemand and oM_Data_VarMaxHeatDemand. See Data & I/O.