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Short-term hydropower optimization in the day-ahead market using a nonlinear stochastic programming model

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Abstract

Hydropower producers participate in electricity markets by providing bids in market auctions, typically day-ahead. Making good bids that obey all market rules and consider uncertain prices for large, interconnected hydropower watercourses is challenging. This investigation aims to find bidding strategies that attend to the market aspects and all constraints relevant to short-term hydropower production. We present a stochastic mixed-integer nonlinear model and a nonlinear heuristic method for the bidding optimization problem and show a comparison of the model’s performance in two case studies. The comparison of the two models shows that their results are close and that the heuristic method can reach the optimal solution after a few iterations. The numerical experiments are also compared with results from the Short-term Hydro Optimization Program (SHOP), which is a piece of software used for operational planning in the Nordic electricity market.

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Data availability

The dataset generated during the current study is not publicly available as it contains proprietary information that the authors acquired through a license. Information on how to obtain it and reproduce the analysis is available from the corresponding author on request.

Abbreviations

T :

Set of periods

C :

Set of hydropower plants

S :

Set of scenarios

I :

Set of bid points

\(J_t^c\) :

Set of the number of active turbines (surfaces) in plant \(c \in C\) at period \(t \in T\)

\(r^c\) :

Set of hydropower plants upstream of plant \(c \in C\)

\(w_{t}\) :

Duration of period \(t \in T\) (h)

\(\zeta\) :

Conversion factor from (m\(^{3}\)/s) to (Mm\(^{3}\)/h)

\(q_{min}^{c}\) :

Minimum water discharge at plant \(c \in C\) (m\(^{3}\)/s)

\(q_{max}^{c}\) :

Maximum water discharge at plant \(c \in C\)(m\(^{3}\)/s)

\(v_{min}^{c}\) :

Minimal volume of plant \(c \in C\) reservoir (Mm\(^{3}\))

\(v_{max}^{c}\) :

Maximum volume of plant \(c \in C\) reservoir (Mm\(^{3}\))

\(v_{Initial}^c\) :

Initial volume of reservoir \(c \in C\) (Mm\(^{3}\))

\(v_{final}^c\) :

Final volume of reservoir \(c \in C\) (Mm\(^{3}\))

\(P_i\) :

Fixed prices in bid point \(i \in I\) for the day-ahead market

\(\pi ^{s}\) :

Probability of scenario \(s \in S\)

\(\rho _{t}\) :

Day-ahead market price at period \(t \in T\)

\(\alpha _{t}\) :

Reward factor for excess supply in period \(t \in T\)

\(\beta _{t}\) :

Penalty factor for the lack of supply at period \(t \in T\)

\(q^{c}_t\) :

Water discharge at plant \(c \in C\) and period \(t \in T\) (m\(^3\)/s)

\(v^{c}_t\) :

Reservoir volume of plant \(c \in C\) at period \(t \in T\) (Mm\(^{3}\)/h)

\(g^{c}_t\) :

Water spillage at plant \(c \in C\) and period \(t \in T\)(m\(^{3}\)/s)

\(z^{c}_{j,t}\) :

\(\left\{ \begin{array}{ll}1&{}\quad \text {if surface j is chosen at period }t \in T\text { for plant }c \in C\\ 0&{}\quad \text {otherwise}\end{array}\right.\)

\(\chi ^{c} _{j,t}\) :

Power production for surface \(j \in J_t^c\) at period \(t \in T\) and plant \(c \in C\) (MW)

\(yd_{t}\) :

Committed hourly volume in the day-ahead market at period \(t \in T\)

\(xd_{i,t}\) :

Bid volume for the day-ahead market at period \(t \in T\) and bid point \(i \in I\)

\(H^{s} _t\) :

Produced volumes of scenario \(s \in S\) at period \(t \in T\) for hourly bids

\(zd^{s} _t\) :

Supply shortage for scenario \(s \in S\) at period \(t \in T\)

\(zu^{s} _t\) :

Oversupply for scenario \(s \in S\) at period \(t \in T\)

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Acknowledgements

This research was funded by a Discovery grant provided by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, Université du Québec à Chicoutimi, Saguenay, QC, G7H 2B1, Canada

    S. Séguin

  2. Department of Applied Sciences, Université du Québec à Chicoutimi, Saguenay, QC, G7H 2B1, Canada

    M. Jafari Aminabadi & I. Fofana

  3. Group for Research in Decision Analysis (GERAD), Montréal, QC, H3T 2A7, Canada

    M. Jafari Aminabadi, S. Séguin & I. Fofana

  4. Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    S.-E. Fleten

  5. Aneo AS, 7031, Trondheim, Norway

    E. K. Aasgård

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  1. M. Jafari Aminabadi
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Jafari Aminabadi, M., Séguin, S., Fofana, I. et al. Short-term hydropower optimization in the day-ahead market using a nonlinear stochastic programming model. Energy Syst (2023). https://doi.org/10.1007/s12667-023-00618-8

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