Non-anticipativity¶

Some decisions can't wait. Take the day-ahead market: you send your bids the day before delivery, and you only see tomorrow's prices once the market clears. So how much should you bid, without knowing the price?

The simple answer is a point forecast: take the price you expect, and bid what would be best at that price. That works as long as the forecast is right, and the bid is only as good as that one guess.

You can do better with a probabilistic forecast. It gives you several possible price paths, each with a probability: the scenarios. Instead of betting on one of them, you look for the single bid that does best across all of them, weighed by how likely each one is.

This page shows how odys finds that bid.

Decisions that can't wait¶

The Scenarios page gave every decision one copy per scenario, and each copy knows its own future. That's fine for a battery reacting to prices as they come. It doesn't work for a bid: each copy would bid what is best for its prices, and you'd end up with a different bid per scenario. But you can only send one, and you have to send it before you know which prices will happen.

So a decision taken before the uncertainty resolves must take the same value in every scenario. That rule is called non-anticipativity: the decision doesn't anticipate the future. It's what turns "the best bid in each future" into one concrete bid you can actually send.

Two stages¶

With non-anticipativity, the model becomes a two-stage problem. First, you commit to the decisions that can't wait. Then one of the futures happens, and everything else adapts to it:

flowchart LR
    Now(["Now: commit the trades<br/>on stage-fixed markets<br/>(one plan for every future)"])
    Now --> S1(["Scenario 1 happens:<br/>dispatch adapts"])
    Now --> S2(["Scenario 2 happens:<br/>dispatch adapts"])
    Now --> S3(["Scenario 3 happens:<br/>dispatch adapts"])

In odys, you choose the first stage per market, with EnergyMarket(stage_fixed=True). Today, market trades are the only decisions that can be stage-fixed.

The second stage sees its scenario's whole future at once: intraday trades, for instance, are planned knowing every price and every wind value of the day. Real intraday trading happens while forecasts keep improving, so the second stage is optimistic. Two stages are the simplest model of "commit now, adapt later"; a model with more stages would add a decision point for each update.

NA-1 · Stage-fixed trades are the same in every scenario¶

Every trade on a stage-fixed market takes the same value in all scenarios.

Here \(s_0\) is the first scenario, in the order you passed them to the EnergySystem.

Read aloud: on a stage-fixed market, whatever you buy or sell at a step in one future, you buy or sell in all of them.

Why it looks like this. Without it, the optimizer would place a different day-ahead bid in each future, as if it already knew tomorrow's prices when bidding. That is free clairvoyance, and the plan would look far better than anything you could actually do. Tying every scenario to the first one rules it out.

You could write the same thing with a single variable shared by all scenarios. odys keeps one copy per scenario and ties the copies together instead. That way every market variable has the same shape (asset, scenario, time) as every other variable in the model, and the rest of the formulation never has to treat stage-fixed markets differently.

Good to know.

• odys also writes the row for \(s_0\) itself, where it simply reads \(x = x\). These rows do nothing (#154).
• The trade mode \(y^{trade}\) is tied too, so a stage-fixed market also picks "buy" or "sell" once for all futures. The trade mode only removes plans that are worth the same profit; see #140.
• A stage-fixed trade is a price-independent bid: one volume per step, accepted whatever price the market clears at. Real day-ahead bids are price-quantity curves, whose accepted volume depends on the clearing price. odys doesn't model them, so in a scenario with a low price the plan still buys or sells the same volume as in one with a high price.
• Generator commitment is second-stage: a unit can be on in one scenario and off in another at the same step. If a unit has to be scheduled in advance, model that commitment through a stage-fixed market position. First-stage commitment is proposed in #153.

Added: always (empty without a stage-fixed market) · Binds: on markets with stage_fixed=True · Names: non_anticipativity_market_buy_volume_constraint, non_anticipativity_market_sell_volume_constraint, non_anticipativity_market_trade_mode_constraint

What it changes in the plan¶

Without non-anticipativity, each scenario would get its own ideal bid. With it, there is one bid, and it has to work in every future. If prices come in high, you may wish you had sold more, and a battery or a generator makes up some of it; if they come in low, you may be left with energy to store or sell back on another market. The second-stage decisions make up the difference in each future, and the bid lands where the probability-weighted outcome is best.

That's also what makes the scenarios interact: the first-stage trades are shared, so a choice that helps one future affects all the others. The risk term CV-1 is the only other link between them.

Where to find each symbol in odys¶

Decisions are made for something. What is odys chasing? See the Objective.

Implemented in odys.optimization.formulations.energy_market.