TECHNICAL_DOC.md

Technical Documentation

Load shifting can be viewed as virtual storage, and the code uses this terminology. In practice, load shifting is implemented via a Transfer Matrix T[i,j] representing the amount of energy originally demanded at time i but purchased at time j. Optimizing load shifts thus corresponds to finding values for T[i,j] that minimize the cost of procured electricity while satisfying all flexibility constraints.

Key transfer matrix properties:

• Row sum Σⱼ T[i,j]: Represents energy removed from time i
• Column sum Σᵢ T[i,j]: Represents energy added to time j

Typical flexibility constraints include:

1. Temporal flexibility: How many time units a load can be shifted earlier or later, defined by which elements in T[i,j] can be non-zero. For example, in the visualization above, loads can be shifted 2 hours earlier or 3 hours later.
2. Maximum power: The sum of original demand and added energy must not exceed the maximum allowed power at any time.
3. Energy conservation: Energy removed from any time period cannot exceed the original demand at that time.

Moving Horizon Control Strategy

The optimizer provides a moving horizon control strategy that facilitates daily optimization runs, mimicking real-world scenarios in which price information becomes available incrementally. For example, day-ahead spot prices for the next day are revealed in the afternoon, enabling day-by-day load optimization. In practice, this iteratively solves small portions of a larger transfer matrix, as shown in the animation below.

Key Time Periods:

• Lookahead Period: The whole horizon optimized (the period with available price information).
• Control Period: The period that is implemented in practice (typically 24 hours for day by day).
• History: Historical decisions from previous optimizations (constraints)
• Spillover: Potential Energy transfer to/from the next control period (spillover).

However, this iterative process risks adding/removing consumption to/from the next period if the horizon with known prices is longer than the control horizon (24 hours for day-by-day optimization). Extra bookkeeping is needed to account for this when solving optimization problems over successive days. This bookkeeping is illustrated in the animation above, where spillover from period n becomes a historical constraint when optimizing loads for period n+1.