.. SPDX-FileCopyrightText: Contributors to GreenBubble .. SPDX-License-Identifier: CC-BY-4.0 .. _tutorial-4-stochastic: Tutorial 4 — Two-Stage Stochastic Optimisation =============================================== The previous tutorials optimise against a **single** year. But the right investment under 2023 prices may be wrong under 2025 prices. **Two-stage stochastic optimisation** finds *one* set of investment decisions (*here-and-now*) that performs best in expectation across several scenarios, while **dispatch adapts per scenario** (*wait-and-see*). We reuse the **brownfield** plant from :ref:`tutorial-2-brownfield` and optimise it across three weather/market scenario years (2022 / 2023 / 2024) at once. .. contents:: On this page :local: :depth: 1 --- 1 · The two-stage idea ---------------------- .. math:: \min_{\text{capacities}}\; \sum_{s} p_s \, \big[\, \text{CAPEX}^{\text{ann}} + \text{OPEX}_s \,\big] Investment variables are **shared** across scenarios :math:`s` (you build one plant); operational variables are **scenario-specific** (each year is dispatched on its own prices and renewable profiles). Scenarios carry a probability :math:`p_s` summing to 1. The objective is the **expected** annual cost. --- 2 · Run it ---------- .. code-block:: bash cp tutorials/4_stochastic/config.yaml config/config.yaml cp tutorials/4_stochastic/n_config.yaml config/n_config.yaml snakemake --cores 4 # downloads/preprocesses all scenario years first .. code-block:: yaml stochastic: stochastic: true EVPI: false # scenarios 2022/2023/2024 and their weights are set in config.default.yaml .. admonition:: Stochastic needs a pure LP — two required changes :class: caution The ``tutorials/4_stochastic/n_config.yaml`` already applies these; they are the reason it differs from the Tutorial 2 brownfield n_config: #. **No unit commitment** — ``committable: false`` everywhere (stochastic cannot use binary variables). #. **No ramp limits** — set ``ramp limit up`` / ``ramp limit down`` to ``null`` for electrolysis, methanolisation and biomethanation. PyPSA (≤ 1.2.2) cannot build ramp-limit constraints on a scenario network, and a value such as ``1`` still builds them — only ``null`` disables them. See :ref:`guide-stochastic` → *Limitations*. The output folder uses the ``STC`` token instead of ``DET``. Temporal resolution is set to ``3h`` to keep solve time manageable. --- 3 · Interpret the results ------------------------- The three scenarios span very different market conditions (2022 = energy-crisis year; 2023/2024 = post-crisis normalization), with weights 10 % / 40 % / 50 %: .. figure:: /_static/tutorials/tut4_inputs_LDC_by_scenario.png :width: 95% Input duration curves for all three scenarios. **2022** was the European energy-crisis year — elevated NG and biomethane prices made this by far the most profitable scenario (€30.0 M/y net). **2023** and **2024** show post-crisis normalization (€5.4 M/y and €3.5 M/y). The 90 % combined weight on 2023/2024 governs the final design. The optimizer finds **one** investment that is robust across all three years: .. figure:: /_static/tutorials/tut4_Opt_capacities_SP_vs_WS.png :width: 95% Stochastic-programme (SP) optimal investments: **electrolyser 4.7 MW**, **biogas upgrading 27.9 MW**, **biomethanation 1.8 MW**, battery 0.9 MWh. Existing brownfield assets (52 MW wind, 30 MW solar, 62.85 t/h DM biogas digester) carry over from Tutorial 2. The expected cost breakdown reveals which revenue streams justify the design: .. figure:: /_static/tutorials/tut4_TSC_by_carrier.png :width: 95% Expected total system cost (probability-weighted) by carrier/agent. **Biomethane export (bioCH4)** dominates revenues at ≈ €18.1 M/y, followed by district heating (€5.1 M/y) and methanol (€1.8 M/y). Fixed CAPEX (€16.0 M/y, identical across scenarios) is largely the brownfield wind, solar and biogas-digester assets. **Expected net profit: €6.9 M/y.** Shadow prices show the internal marginal value of each carrier: .. figure:: /_static/tutorials/tut4_shd_prices_mean_bar.png :width: 95% Energy-weighted mean shadow prices and annual throughput. Biomethane collection (€14.3/MWh) is the marginal cost of routing additional biogas to upgrading. The negative H₂ delivery price (−€12.1/MWh) reflects hydrogen's role as a consumed intermediate in biomethanation rather than a delivered product. The same fixed-capacity plant dispatches differently in each scenario: .. figure:: /_static/tutorials/tut4_CF_operation_by_scenario.png :width: 95% Per-scenario utilization duration curves. Biogas upgrading runs near full capacity year-round in all three scenarios. The small electrolyser (4.7 MW) operates more intensively in 2022 (cheap/negative electricity hours) and more selectively in 2023–2024. .. admonition:: Key results :class: important - **Expected net profit: €6.9 M/y** (0.10 × €30.0 M + 0.40 × €5.4 M + 0.50 × €3.5 M). The 2022 energy-crisis scenario is far more profitable but carries only 10 % weight; the design is governed by 2023–2024 conditions. - The stochastic design is a **hedge**: biogas upgrading (27.9 MW) is built fully because it earns robust revenue in all three years. The electricity-sensitive electrolyser (4.7 MW) is small — sized to exploit cheap-electricity hours without over-betting on any single price environment. Biomethanation is minimal (1.8 MW) for the same reason. - The **same capacity** runs very differently across years: the electrolyser is used more aggressively in 2022, more selectively in 2023–2024. This wait-and-see dispatch flexibility is what makes the stochastic design viable. - Here ``EVPI: false``. Set ``EVPI: true`` to also solve each year with perfect foresight and quantify the **Expected Value of Perfect Information** — the annual value of knowing next year's market in advance. --- What you learned ---------------- - The **here-and-now vs wait-and-see** two-stage structure and expected-cost objective. - How to enable stochastic mode and the **pure-LP requirements** (no committable, null ramp limits). - Reading a stochastic design as a **robust hedge** across scenarios, and interpreting scenario-level profitability spreads. This is the final tutorial in the core sequence. For exploring *near-optimal* alternatives to a single design, see the near-optimal (MGA) guide. .. seealso:: :ref:`guide-stochastic` · :ref:`guide-outputs` · :ref:`config-stochastic` · :ref:`tutorial-2-brownfield`