.. _guide-economic-analysis: Economic Analysis of Results ============================= This guide describes the economic interpretation framework built into GreenBubble's post-processing pipeline (``scripts/plots.py``). It covers: - how the network represents markets via buses and shadow prices, - the product topology (collection bus + delivery bus), - the Levelised Cost of Production (LCOP) formula and its components, - the KKT-based LCOP verification (zero-profit condition), - the short-run marginal cost (SRMC) and merit order, - the full KKT revenue and annual profit, and - how to interpret LCOP versus the shadow price at the collection bus. --- Network topology as a market ------------------------------ GreenBubble is a linear PyPSA model. Every **bus** is a commodity market at a specific location and quality level. The **KKT multiplier** at a bus (``n.buses_t.marginal_price``) is the shadow price of the energy balance constraint there — the marginal value of one additional unit of that commodity at that time step. **Links** are technologies that convert commodities. A multilink with ports ``bus0 … busN`` satisfies: .. code-block:: text flow at bus_k = p0 × efficiency_k (k ≥ 1) flow at bus0 = −p0 (convention: bus0 always consumes) Positive ``efficiency_k`` → the link *produces* at bus_k (output or by-product). Negative ``efficiency_k`` → the link *consumes* from bus_k (additional input). --- Product topology ----------------- Every product (bioCH4, H2, Methanol) uses a two-bus structure: .. code-block:: text [technology A] ──┐ [technology B] ──┤──► bioCH4 collection ──► bioCH4 delivery ──► demand / store [technology C] ──┘ ▲ is_product_bus = True ``bioCH4 collection`` The **collection bus**. All technologies producing bioCH4 inject here directly via ``bus1`` of their multilink. Tagged ``is_product_bus=True`` in the network so post-processing can discover it automatically. ``bioCH4 delivery`` The **delivery bus**. The exogenous demand load (demand mode) or the price-setting sale link (price mode) is attached here. - **Demand mode**: a zero-cost ``{product}_collection_to_demand`` link transfers product to the delivery bus, where a ``Load`` sets the time profile and an optional cyclic ``Store`` provides intra-period flexibility. - **Price mode**: a ``{product}_collection_to_delivery`` link carries a time-varying ``marginal_cost`` equal to the exogenous selling price series. A non-cyclic annual ``Store`` (``e_nom_max = total_demand``) caps cumulative annual production. The shadow price at the collection bus (``λ_collection``) is determined at equilibrium by the marginal producer — the highest-cost technology that is still dispatched. Technologies with lower cost earn an *intra-marginal rent*. --- Shared components ------------------ Compressors, HP storage, and other auxiliary equipment often serve multiple technologies and are modelled as a single shared component (separate carrier). They are **not** included in the LCOP computation for the production technologies themselves. Their capital and operational costs appear implicitly via the shadow price at the buses they connect to (e.g. ``H2 distribution``, ``CO2 distribution``). When a production technology draws H2 from ``H2 distribution``, the KKT ``λ_{H2 distribution}`` already reflects the full cost of H2 at that pressure level, including compression. --- LCOP — Levelised Cost of Production ------------------------------------- For a multilink ``lk`` whose ``bus1`` is a collection bus (``is_product_bus=True``), first define the **indirect OPEX**: .. math:: \text{indirect OPEX} = -\sum_{k \neq 1} \eta_k \cdot \overline{(\lambda_{k} \cdot p_0)} where :math:`\eta_0 = -1` for bus0 (primary feedstock, always consumed), and :math:`\overline{(\lambda_k \cdot p_0)} = \sum_t p_{0,t} \cdot \lambda_{k,t} \cdot w_t` with snapshot weights :math:`w_t` from ``snapshot_weightings["objective"]``. The sign convention makes indirect OPEX **positive when input costs dominate** (the typical case) and negative only if by-product credits exceed all feedstock costs. .. list-table:: Port contributions to indirect OPEX :header-rows: 1 :widths: 28 12 60 * - Port - :math:`\eta_k` - Contribution to indirect OPEX * - bus0 — primary feedstock - −1 - :math:`+p_0 \cdot \lambda_{\text{bus0}} \cdot w` — adds feedstock cost * - bus2..N — additional input - < 0 - :math:`+|\eta_k| \cdot p_0 \cdot \lambda_k \cdot w` — adds feedstock cost * - bus2..N — by-product output - > 0 - :math:`-\eta_k \cdot p_0 \cdot \lambda_k \cdot w` — subtracts by-product credit Then: .. math:: \text{LCOP} = \frac{\text{CAPEX} + \text{OPEX} + \text{indirect OPEX}}{Q_\text{main}} where: - :math:`\text{CAPEX}` = ``n.statistics.capex()`` for the link (annualised capital cost) - :math:`\text{OPEX}` = ``n.statistics.opex()`` for the link (explicit ``marginal_cost`` × dispatch — variable O&M such as enzyme or maintenance rates, **not** feedstock costs) - :math:`Q_\text{main} = \sum_t p_{0,t} \cdot \eta_1 \cdot w_t` — annual production at bus1 **No double-counting:** ``OPEX`` is the explicit variable O&M declared in ``tech_costs`` (VOM). Indirect OPEX captures the *market value* of feedstocks consumed and by-products produced via KKT shadow prices. These measure different things and do not overlap. **Existing (EXI\_) assets:** whether CAPEX appears in the LCOP depends on ``remaining_investment_fraction`` (``rif``) in ``n_config.yaml``: - ``rif = 0`` (default — sunk cost): ``capital_cost = 0`` in the network, so ``CAPEX = 0`` from statistics. LCOP reflects short-run cost only (OPEX + indirect OPEX). - ``rif > 0`` (residual obligation outstanding): ``capital_cost = rif × I(construction_year) × annuity(amortization_period, discount_rate)``. CAPEX is non-zero and the LCOP includes this residual capital charge. See :ref:`economics-brownfield` for the full parameter description. --- Revenue, net market value, and annual profit --------------------------------------------- .. math:: \text{revenue main product} = \eta_1 \cdot \sum_t p_{0,t} \cdot \lambda_{\text{bus1},t} \cdot w_t This is the market value of the main product at the collection bus — what the market would pay for everything the technology produces there. .. math:: \text{net market value} = \text{revenue main product} - \text{indirect OPEX} .. math:: \text{annual profit} = \text{net market value} - \text{CAPEX} - \text{OPEX} = \text{revenue main product} - \text{indirect OPEX} - \text{CAPEX} - \text{OPEX} Annual profit is the economic rent: what the market pays the technology for its product, minus every cost it incurs (capital, O&M, feedstocks net of by-products). - **annual profit ≈ 0** — the technology is the marginal (price-setting) producer. - **annual profit > 0** — intra-marginal rent; technology has lower cost than the price-setter. - **annual profit < 0** — technology is loss-making under current market conditions (possible for EXI\_ assets if market prices are low). .. note:: The zero-profit condition holds for optimally expanded technologies in a fully endogenous problem. When exogenous selling prices are set (price mode), the complementary slackness argument breaks down and all dispatched technologies can earn positive profit if the price exceeds the LCOP of the marginal producer. **Intra-marginal rent:** .. code-block:: text rent_per_MWh ≈ λ̄_collection − LCOP where ``λ̄_collection`` is the energy-weighted mean shadow price at the collection bus (from ``shadow_prices_mean.csv``). The technology with ``LCOP ≈ λ̄_collection`` is the price-setter; all others earn rent proportional to the cost gap. --- Output files ------------- The following output files are generated by ``scripts/plots.py``: ``csv/lcop_by_technology.csv`` One row per product link (index column: ``link``). .. list-table:: :header-rows: 1 :widths: 38 62 * - Column - Description * - ``carrier`` - PyPSA carrier name of the link * - ``product`` - Product name (bioCH4, H2, Methanol …) * - ``CAPEX (EUR)`` - Annualised capital cost from ``n.statistics.capex()`` * - ``OPEX (EUR)`` - Variable O&M from ``n.statistics.opex()`` (explicit marginal cost × dispatch) * - ``indirect OPEX (EUR)`` - Feedstock costs minus by-product credits via KKT shadow prices; positive = net cost (typical), negative = by-products exceed feedstock cost * - ``revenue main product (EUR)`` - Market value of annual main-product output at the collection bus * - ``net market value (EUR)`` - ``revenue main product`` − ``indirect OPEX`` * - ``annual production (MWh)`` - Annual energy output at bus1 = :math:`\sum_t p_{0,t} \cdot \eta_1 \cdot w_t` * - ``LCOP (EUR/MWh)`` - ``(CAPEX + OPEX + indirect OPEX) / annual production`` * - ``annual profit (EUR)`` - ``net market value − CAPEX − OPEX``; economic rent earned by the technology ``plots/lcop_by_technology.png`` Two-panel bar chart: LCOP [€/MWh] (top) and annual profit [k€] (bottom). ``csv/lcop_kkt_by_technology.csv`` Verification table produced by ``compute_lcop_kkt_by_technology()``. For each product link, LCOP is independently computed as the production-weighted average KKT shadow price at the collection bus: .. math:: \text{LCOP}_\text{kkt} = \frac{\displaystyle\sum_t w_t \cdot \eta_1 \cdot p_{0,t} \cdot \lambda_{\text{bus1},t}} {\displaystyle\sum_t w_t \cdot \eta_1 \cdot p_{0,t}} At optimum this equals the cost-based LCOP (zero-profit condition). The ``diff cost−kkt`` column confirms agreement to < 0.01 €/MWh. Columns: ``carrier``, ``product``, ``annual_production_MWh``, ``LCOP_cost (EUR/MWh)``, ``LCOP_kkt (EUR/MWh)``, ``diff cost−kkt (EUR/MWh)``, ``π_bus1_mean``, ``π_bus1_std``, ``π_bus1_prod_weighted``. ``csv/srmc_by_technology.csv`` / ``plots/srmc_by_technology.png`` Short-run marginal cost (SRMC) computed by ``compute_srmc_by_technology()``. For each product technology at every snapshot: .. math:: \text{SRMC}_{s,t} = \frac{\lambda_{\text{bus0},t} - \displaystyle\sum_{k \geq 2} \eta_k \cdot \lambda_{\text{bus}_k,t} + \text{VOM}_{s}}{\eta_1} This is the instantaneous cost of producing one more MWh of main product at time *t*, given current input market prices. It is distinct from the model input ``marginal_cost`` on links (which is the VOM, one term in the formula). The long-form CSV has columns: ``snapshot``, ``link``, ``product``, ``SRMC_EUR_per_MWh``, ``dispatch_MW``, ``π_product_bus``, ``in_merit`` (whether SRMC ≤ product shadow price at that hour). The plot shows one subplot per product with SRMC time series per technology and the product bus shadow price as a dashed reference line. --- Shadow price outputs --------------------- ``csv/shadow_prices_mean.csv`` Energy-weighted mean KKT for every bus in ``plots_config.yaml → bus_list_mp``, including collection buses. Computed regardless of whether any technology actively dispatches to the bus. Formula: .. math:: \bar{\lambda}_\text{bus} = \frac{\sum_t \lambda_{t} \cdot q_t \cdot w_t}{\sum_t q_t \cdot w_t} where :math:`q_t` is the net injection at the bus (generators + positive-efficiency link outputs + storage discharge), and :math:`w_t` is the snapshot weight. Falls back to duration-weighted mean when a bus has no measurable injection. Columns: .. list-table:: :header-rows: 1 :widths: 40 60 * - Column - Description * - ``bus`` (index) - Bus name from ``bus_list_mp`` * - ``energy weighted mean (EUR/MWh)`` - Energy-weighted mean shadow price at that bus ``plots/shd_prices_mean_bar.png`` Bar chart of energy-weighted mean shadow prices. Collection buses are excluded — delivery buses are sufficient to read the product market price. Buses with no active injection are also dropped. ``plots/shd_prices_violin.png``, ``plots/shd_prices_ldc.png`` **Snapshot distribution** of shadow prices (one observation per time step), with the scenario-weighted mean marked. These show *when* prices are high or low, not an energy-weighted average. Restricted to the same delivery-bus subset as the bar chart, further filtered to buses with at least one injecting link above the ``LINK_TH`` capacity threshold. --- Comparing LCOP to shadow prices --------------------------------- A practical diagnostic workflow: 1. Look at ``shadow_prices_mean.csv`` — read the ``energy weighted mean (EUR/MWh)`` for the delivery bus of each product (e.g. ``bioCH4 delivery``) — this is ``λ̄_delivery``, which equals ``λ̄_collection`` when the collection-to-delivery link is zero-cost. 2. Look at ``lcop_by_technology.csv`` — compare each technology's ``LCOP (EUR/MWh)`` to ``λ̄_delivery`` of its product. 3. Technologies with ``annual_profit_EUR ≈ 0`` are price-setters. 4. Technologies with ``annual_profit_EUR > 0`` earn intra-marginal rent — check whether they are EXI\_ (legacy) assets or optimally expanded. 5. In price mode, all technologies that run may earn positive profit if the exogenous selling price exceeds the LCOP of the marginal producer. 6. Use ``srmc_by_technology.csv`` to see *when* each technology is in-merit (``in_merit = True``). Hours with SRMC near the shadow price reveal the marginal technology. Large SRMC variance indicates strong sensitivity to electricity or H2 price fluctuations.