EAG §4(2) — Net-Zero Electricity Balance

Legal requirement

EAG §4(2) (Erneuerbaren-Ausbau-Gesetz, Renewable Energy Expansion Act) requires that Austria's total electricity consumption is covered 100% nationally on a net-balance basis ("bilanziell") from renewable energy sources from 2030 onwards.

"Bilanziell" means the balance is assessed annually across the whole country, not hour-by-hour or region-by-region. An hour of deficit can be offset by a surplus in another hour, and electricity imported at one moment can be balanced by exports at another.

Implementation approach

The requirement is enforced through four coupled linear constraints added to the linopy model at the start of each solve_network call for planning horizons ≥ 2030.

Why four constraints?

Gas, hydrogen, and methanol power plants can contribute to the electricity balance under the "bilanziell" interpretation — their electricity output is renewable if and only if their fuel inputs are domestically produced from renewable sources. Three companion constraints (2–4) enforce this fuel-origin condition on each fuel chain independently and propagate green-ness across cross-fuel chains (e.g. H2 used by Sabatier to make green gas must itself be domestically produced green H2).

Constraint 1: green electricity produced  ≥  national electricity demand
Constraint 2: domestic green gas produced ≥  gas consumed by gas-fired power plants (elec. share)
Constraint 3: domestic green H2 produced  ≥  H2 consumed for power (elec. share)
                                             + H2 consumed by other green-fuel synthesis
Constraint 4: domestic green methanol     ≥  methanol consumed by methanol-fired plants (elec. share)

Biomass-to-power plants count as green in constraint 1 without a companion constraint because solid biomass is treated as an inherently renewable carrier in the model.

Mathematical formulation

Electricity balance (Constraint 1):

\[G_c - L_c \geq D_c\]

Left-hand side — net green production

Symbol	Description	Unit
\(G_c\)	Annual green electricity production — renewables, storage dispatch, green fuel-to-power links	MWh/yr
\(L_c\)	Annual electricity withdrawals — P2X, charging, auxiliary loads, grid losses	MWh/yr

Right-hand side — exogenous demand

Symbol	Description	Unit
\(D_c\)	Annual exogenous electricity demand — `Load` `p_set` on AC and low-voltage buses	MWh/yr

Fuel-origin constraints (Constraints 2–4), for each fuel \(f \in \{\text{gas, H}_2\text{, methanol}\}\):

\[P_c^f \geq \phi_c^f \cdot F_c^f + X_c^f\]

Left-hand side — green fuel production

Symbol	Description	Unit
\(P_c^f\)	Domestic green production of fuel \(f\)	MWh/yr

Right-hand side — fuel consumed for electricity

Symbol	Description	Unit
\(F_c^f\)	Fuel \(f\) consumed by power plants	MWh/yr
\(\phi_c^f\)	Electricity fraction (see below): share of fuel input attributed to electricity output	—
\(X_c^f\)	Fuel \(f\) consumed by green-fuel synthesis links (H2 only; see Constraint 3)	MWh/yr

Electricity fraction

For a link \(i\) with output ports \(p\) (each landing on a bus with carrier \(c_{i,p}\) and efficiency \(\eta_{i,p}\)), the electricity fraction is

\[ \phi_i \;=\; \frac{\displaystyle\sum_{p \in \mathcal{E}_i}\eta_{i,p}\,\mathbb{1}\!\left[c_{i,p}\in\{\text{AC},\,\text{low voltage}\}\right]} {\displaystyle\sum_{p \in \mathcal{E}_i}\eta_{i,p}} \]

where \(\mathcal{E}_i\) is the set of output ports landing on energy buses only. Ports landing on accounting-only carriers (co2, co2 stored, process emissions) are excluded from both numerator and denominator — their efficiency is an emission rate (e.g. ≈ 0.198 tCO2/MWh for fossil gas), not an energy output. Negative efficiencies (electricity-input ports such as methanolisation bus2 = AC, efficiency2 < 0) are also excluded.

For a pure power plant (single AC output) this evaluates to 1.0. For a gas CHP with electrical efficiency \(\eta_1\) and heat efficiency \(\eta_2\) it evaluates to \(\eta_1 / (\eta_1 + \eta_2)\): only the electricity-attributable share of fuel input must be green; the heat output share is not required to be covered by green fuel.

Constraint 1 — electricity balance

Right-hand side scalar — exogenous demand

Sum of weighted p_set for all active Austrian Load components on AC and low-voltage buses (base load, industry, agriculture, transport, heat-pump-coupled loads, etc.). Loads on other buses (e.g. hydrogen, gas) are out of scope and are governed by the energy-system optimisation as usual.

Left-hand side positive terms — green production

Renewable generators — generators where carrier ∈ n.meta["renewable"] (including hydro sub-carriers such as run-of-river and PHS, plus solar rooftop) and bus on an Austrian electricity bus.
StorageUnit dispatch — StorageUnit-p_dispatch of hydro reservoir and PHS units in Austria.
Green fuel-to-power links — Link-p × efficiency × weightings for any link whose bus0 is in an Austrian fuel bus (carrier ∈ mods.net_zero_electricity.fuels) and any positive-efficiency output port lands on an Austrian electricity bus. Green-ness of the consumed fuel is enforced by Constraints 2–4.
Storage discharger Links — battery, home-battery, and V2G dischargers, valued at Link-p × efficiency.

Left-hand side withdrawal terms — subtracted from production

All terms are positive Power×time quantities; the constraint subtracts them from the green LHS before comparing against \(D_c\).

PHS pumping — StorageUnit-p_store of PHS units (captures the round-trip loss; PHS dispatch on the supply side and pumping here together carry the energy cycle).
Power-to-X consumption — Link-p × weightings for any link with bus0 on an Austrian electricity bus and no output port landing on any electricity bus (battery and home-battery chargers, H2 electrolysis, heat pumps with p_max_pu > 0, …). AC-to-AC transmission and distribution links are excluded by the "no electricity output port" filter.
Auxiliary electricity at negative-efficiency ports — for any port \(p\) with bus on an electricity bus and efficiency_p < 0 (e.g. methanolisation bus2 = AC, efficiency2 < 0), the consumed power −Link-p × efficiency_p is added back to the RHS.
Reverse-flow links (heat pumps) — PyPSA-Eur models heat pumps with bus0 = heat, bus1 = electricity, p_max_pu ≤ 0. They draw electricity at bus1 even though bus0 is not on an electricity bus, so they are added explicitly via −Link-p × efficiency.
Electricity distribution grid losses — the electricity distribution grid link has bus0 = AC, bus1 = low voltage, efficiency < 1. LV loads are already captured in \(D_c\); only the dissipated fraction Link-p × (1 − efficiency) is added here.
Domestic AC transmission line losses — when transmission_losses > 0 in config, PyPSA creates a Line-loss variable and the constraint subtracts Line-loss × weightings summed over Austrian AC lines (both bus0 and bus1 in Austria).

Cross-border AC transmission and DC interconnectors are excluded from withdrawal: the P2X filter requires no electricity output, and bidirectional transmission links have electricity at both ports.

Constraint 2 — green gas production

Left-hand side — domestic green gas production:

Links where name.startswith(country), bus1 ∈ Austrian gas buses, and bus0 carrier ≠ "gas". This structurally captures biogas to gas, biogas to gas CC, and Sabatier while excluding EU→AT gas imports and pipeline flows (whose bus0 also has carrier "gas").

Sabatier (H2 → gas) is counted as green gas. Its green-ness is propagated to the H2 chain by Constraint 3, which requires the H2 it consumes to come from domestic green producers.

Right-hand side — gas attributed to electricity production:

\[\sum_i \phi_i \cdot F_i^{\text{gas}}\]

summed over all gas-to-power links \(i\) (links with bus0 in Austrian gas buses and a positive-efficiency electricity output port). For a pure gas turbine \(\phi = 1.0\). For a gas CHP \(\phi = \eta_\text{elec} / (\eta_\text{elec} + \eta_\text{heat})\), so the heat output share is not required to be covered by green gas.

Constraint 3 — green H2 production

Left-hand side — domestic green H2 production:

Links where name.startswith(country), bus1 ∈ Austrian H2 buses, and bus0 carrier is in the configurable mods.net_zero_electricity.h2_sources allowlist. The default allowlist is {"AC", "low voltage", "solid biomass"}, admitting H2 Electrolysis and biomass-to-H2 as green producers.

Why an allowlist and not a "bus0 ≠ H2" mirror of the gas/methanol pattern: SMR / SMR CC (bus0 = gas, bus1 = H2) are blue/grey H2. A "bus0 ≠ H2" filter would silently admit fossil-gas H2 onto the green-H2 LHS. The allowlist makes the policy decision explicit.

Right-hand side — two-part demand:

H2 consumed by H2-to-power × electricity_fraction (same pattern as Constraints 2/4).
Full H2 withdrawal by H2-to-other-green-fuel synthesis — for each green fuel \(f' \in \{\text{gas, methanol, solid biomass}\}\), every link with bus0 ∈ Austrian H2 buses and any output port on an Austrian \(f'\) bus contributes its entire H2 input (Link-p × weightings, no electricity-fraction scaling). This captures Sabatier (H2 → gas) and methanolisation (H2 → methanol).

The second term ensures green-fuel chains are not satisfied with grey-H2-derived "green" products: any green gas or green methanol made from H2 is itself backed by domestically produced green H2.

Constraint 4 — green methanol production

Left-hand side — domestic green methanol production:

Links where bus1 ∈ Austrian methanol buses and bus0 carrier ≠ "methanol". Captures biomass-to-methanol, biomass-to-methanol CC, and methanolisation. Excludes EU→AT methanol imports (bus0 carrier "methanol").

Right-hand side — methanol consumed by methanol-to-power links (CCGT methanol, OCGT methanol, CCGT methanol CC) × electricity_fraction. For these pure-electricity-output plants \(\phi = 1.0\).

Configuration

mods:
  net_zero_electricity:
    enable: true
    fuels: ["gas", "H2", "solid biomass", "methanol"]
    # Primary-green source bus_carriers admitted as green-H2 producers.
    # "gas" is intentionally omitted: SMR / SMR CC (bus0=gas → bus1=H2)
    # is blue/grey H2 and the green-gas constraint only enforces green gas
    # for gas-to-power, NOT for gas-to-H2. Admitting "gas" here would let
    # fossil gas reach the green-H2 LHS through SMR.
    h2_sources: ["AC", "low voltage", "solid biomass"]
    # Country keys map to inclusive start years. Constraints activate for
    # planning_horizons >= the listed year.
    AT: "2030"

Key	Purpose
`enable`	Master toggle. If false or absent, all four constraints are skipped.
`fuels`	Carriers treated as green fuels for Constraint 1 LHS (green fuel-to-power links).
`h2_sources`	Bus carriers admitted as green-H2 producers in Constraint 3 LHS.
`<country>: <year>`	Inclusive start year per country prefix (e.g. `AT: "2030"`).

Known limitations

Export overstatement — if a gas, H2, or methanol plant produces electricity that is exported (and therefore not counted toward the Austrian demand in Constraint 1's RHS), its fuel consumption is still included in the RHS of Constraints 2–4. The required domestic green fuel production is slightly overstated in scenarios where Austrian power plants are net exporters. For Austria as a structural electricity importer the practical impact is expected to be small.

CHP heat share — only the electricity-attributable share of fuel consumption (via electricity_fraction) must come from green sources. The heat output share is not required to be backed by green fuel. This reflects the model interpretation that the EAG target covers electricity specifically, not total final energy.

Annual balance only — the constraint is assessed over the full simulation period (weighted snapshot sum), not hour-by-hour. Hourly deficits are permissible as long as the annual total balance is satisfied.

Biogas-fed SMR not admitted as green H2 — extending the green-H2 LHS to admit biogas-fed SMR would require a downstream "share of H2 that ends up as electricity" factor analogous to \(\phi\), propagated across two conversion stages (gas → H2 → power). Today gas is intentionally omitted from h2_sources so the single-stage constraint stack stays consistent.

Implementation reference

The four constraint functions live in mods/constraints/eag.py:

Function	Constraint
`_add_net_zero_electricity_production_constraint`	Constraint 1
`_add_green_gas_production_constraint`	Constraint 2
`_add_hydrogen_production_constraint`	Constraint 3
`_add_methanol_production_constraint`	Constraint 4
`_compute_electricity_fraction`	shared helper computing \(\phi_i\)

The orchestrator constraint_net_zero_electricity calls all four, is exported from mods/__init__.py, and is invoked from scripts/pypsa-at/additional_functionality.py.

Verification

Each constraint is independently verified by a pytest.statistics-based test that mirrors the constraint's LHS/RHS using pypsa.statistics aggregations:

Test	Verifies
`test_net_zero_electricity_constraint_statistics`	Constraint 1
`test_green_gas_constraint_statistics`	Constraint 2
`test_green_h2_constraint_statistics`	Constraint 3
`test_green_methanol_constraint_statistics`	Constraint 4

The tests live in test/test_mods/test_mods.py and require a solved scenario via --result-path. A second per-constraint test reuses the constraint helpers directly to provide an algebraic cross-check; both must pass before a scenario is considered EAG-compliant.