    \begin{algorithmic}
        \State \textbf{\textit{Initialization of the set of time steps}}
        \State $T_{div} \gets {t \in T_{m} \mkern9mu | \mkern9mu bn_{t} > 0}$\\
        
        \State \textbf{\textit{Initialization of the first slice $i = 1$}}
        \State $V_{1} \gets \min(V^{s}, \max\limits_{t \in T_{div}} bn_{t})$\\

        \State \textbf{\textit{Recursion}}
        \For{$i > 1$}
            \While{$\mkern9mu \sum\limits_{1 \leq j < i} (V_{j}) < \max\limits_{t \in T_{div}} bn_{t}$}
                \State $V_{i} \gets \min(V^{s}, \min\limits_{t \in T_{div}} (bn_{t} - \sum\limits_{1 \leq j < i} (V_{j})))$\Comment{Compute the maximum size of $V_{i}$}\\

                \For{$t \in T_{div}$}
                    \State $q_{t,i} \gets |V_{i}|$\Comment{Extract the order quantity for relevant time steps}
                    \State $\sigma_{t,i} \gets -1$\Comment{Set the order direction}
                    \If{$bn_{t} - \sum\limits_{1 \leq j \leq i} (V_{j}) = 0$}\Comment{Remove now "empty" time steps from $T_{div}$}
                        \State $T_{div} \gets T_{div} - \{t\}$
                    \EndIf
                \EndFor
                \State $i \gets i+1$
            \EndWhile
        \EndFor
    \end{algorithmic}

\begin{algorithmic}
\State \textbf{\textit{Initialization of the set of time steps}}
\State $T_{div} \gets {t \in T_{m} \mkern9mu | \mkern9mu bn_{t} > 0}$\\
\State \textbf{\textit{Initialization of the first slice $i = 1$}}
\State $V_{1} \gets \min(V^{s}, \max\limits_{t \in T_{div}} bn_{t})$\\
\State \textbf{\textit{Recursion}}
\For{$i > 1$}
\While{$\mkern9mu \sum\limits_{1 \leq j < i} (V_{j}) < \max\limits_{t \in T_{div}} bn_{t}$}
\State $V_{i} \gets \min(V^{s}, \min\limits_{t \in T_{div}} (bn_{t} - \sum\limits_{1 \leq j < i} (V_{j})))$\Comment{Compute the maximum size of $V_{i}$}\\
\For{$t \in T_{div}$}
\State $q_{t,i} \gets |V_{i}|$\Comment{Extract the order quantity for relevant time steps}
\State $\sigma_{t,i} \gets -1$\Comment{Set the order direction}
\If{$bn_{t} - \sum\limits_{1 \leq j \leq i} (V_{j}) = 0$}\Comment{Remove now "empty" time steps from $T_{div}$}
\State $T_{div} \gets T_{div} - \{t\}$
\EndIf
\EndFor
\State $i \gets i+1$
\EndWhile
\EndFor
\end{algorithmic}
{
    "title": "atlas: a model of short-term european electricity market processes under   uncertainty -- balancing modules",
    "id": "2402.12859",
    "abstract": "the atlas model simulates the various stages of the electricity market chain in europe, including the formulation of offers by different market actors, the coupling of european markets, strategic optimization of production portfolios and, finally, real-time system balancing processes. atlas was designed to simulate the various electricity markets and processes that occur from the day ahead timeframe to real-time with a high level of detail. its main aim is to capture impacts from imperfect actor coordination, evolving forecast errors and a high-level of technical constraints -- both regarding different production units and the different market constraints. this working paper describes the simulated balancing processes in detail and is the second part of the atlas documentation.",
    "categories": "econ.gn math.oc q-fin.ec",
    "doi": "",
    "created": "2024-02-20",
    "updated": "",
    "authors": [
        "florent cogen",
        "emily little",
        "virginie dussartre",
        "quentin bustarret"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2402.12859"
}
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