| 0 | <a href="https://scholar.google.no/citations?user=1b7OBl0AAAAJ&hl=no&oi=ao" target="_blank">Michael Martin Belsnes</a>, Jarand Roynstrand, and <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a> | Handling state dependent nonlinear tunnel flows in short-term hydropower scheduling | NaN | 2004 | <a href="http://ieeexplore.ieee.org/document/1460223/" target="_blank">Url</a> | <a href="https://doi.org/10.1109/ICPST.2004.1460223" target="_blank">Doi</a> | NaN |
| 1 | <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a>, and <a href="https://scholar.google.no/citations?user=1b7OBl0AAAAJ&hl=no&oi=ao" target="_blank">Michael Martin Belsnes</a> | Short-term hydro scheduling in a liberalized power system | 2004 International Conference on Power System Technology – PowerCon 2004 | 2004 | | <a href="https://doi.org/10.1109/ICPST.2004.1460206" target="_blank">Doi</a> | The paper addresses the challenges of short-term hydropower scheduling in a liberalized power system. Hydropower systems may have quite complex topologies with many cascaded reservoirs/power plants in the same river system. The reservoirs may have very different storage capacity with significant water travel time that makes the decisions coupled between several time steps. In other words, the decisions in one time interval have strong impact on what's possible to do in later time steps. In systems where some of the reservoirs have significant storage capacity, the use of the hydropower resources short-term will be coupled with the long-term strategic decisions. It is not feasible to have the short-term decisions within the same model as the long-term decisions because modeling of uncertainty is important. The problem is decomposed into a planning hierarchy where the long/mid-term models provide boundary conditions for the short-term models. The major items of this paper are: challenges and possible solutions in hydro system modeling, a flexible coupling principle between short-term and mid-term scheduling, strategies for bidding in a spot market. |
| 2 | <a href="https://scholar.google.no/citations?user=hCTulYcAAAAJ&hl=no&oi=ao" target="_blank">Per Aaslid</a>, <a href="https://scholar.google.no/citations?user=1b7OBl0AAAAJ&hl=no&oi=ao" target="_blank">Michael Martin Belsnes</a>, and <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a> | Optimal microgrid operation considering battery degradation using stochastic dual dynamic programming | SEST 2019 - 2nd International Conference on Smart Energy Systems and Technologies | 2019 | | <a href="https://doi.org/10.1109/SEST.2019.8849150" target="_blank">Doi</a> | Intermittent energy sources demand temporal storages to balance generation and load, and batteries stand out as an alternative. However, the lifetime is limited, and cycling depth affects the battery degradation rate. Current stochastic multi-stage methods lack proper representation of battery degradation. This paper proposes a stochastic multi-stage model for optimizing battery operation in a microgrid considering battery degradation with a piece-wise linear cost function with uncertain wind power production and load. The model is solved using Stochastic Dual Dynamic Programming (SDDP) and is demonstrated on a 4-bus test case with limited import and export capacity to illustrate the battery degradation cost's impacts on the battery cycling strategy. The results show that the importance of a stochastic method is more pronounced when battery degradation is modelled. |
| 3 | <a href="https://scholar.google.no/citations?user=hCTulYcAAAAJ&hl=no&oi=ao" target="_blank">Per Aaslid</a>, Frederik Geth, <a href="https://scholar.google.no/citations?user=k7TrwpEAAAAJ&hl=no&oi=ao" target="_blank">Magnus Korpås</a>, <a href="https://scholar.google.no/citations?user=1b7OBl0AAAAJ&hl=no&oi=ao" target="_blank">Michael Martin Belsnes</a>, and <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a> | Non-linear charge-based battery storage optimization model with bi-variate cubic spline constraints | Journal of Energy Storage | 2020 | | <a href="https://doi.org/10.1016/j.est.2020.101979" target="_blank">Doi</a> | Variable renewable generation demands increasing amount of flexible resources to balance the electric power system, and batteries stand out as a promising alternative. Battery models for optimization typically represent the battery with power and energy variables, while the voltage, current, charge variable space is used for simulation models. This paper proposes a non-linear battery storage optimization model in the voltage, current, charge variable space. The battery voltage is conceived as an empirical function of both state-of-charge and charge current and represented through bi-variate cubic splines. The voltage source converter losses are also approximated with a cubic spline function. Compared to energy-based storage models, the results show that this approach enables safe operation closer to the battery voltage and current limits. Furthermore, it prefers operating around high state-of-charge due to the higher efficiency in that region. |
| 4 | <a href="https://scholar.google.no/citations?user=hCTulYcAAAAJ&hl=no&oi=ao" target="_blank">Per Aaslid</a>, <a href="https://scholar.google.no/citations?user=k7TrwpEAAAAJ&hl=no&oi=ao" target="_blank">Magnus Korpås</a>, <a href="https://scholar.google.no/citations?user=1b7OBl0AAAAJ&hl=no&oi=ao" target="_blank">Michael Martin Belsnes</a>, and <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a> | Pricing electricity in constrained networks dominated by stochastic renewable generation and electric energy storage | Electric Power Systems Research | 2021 | | <a href="https://doi.org/10.1016/j.epsr.2021.107169" target="_blank">Doi</a> | NaN |
| 5 | <a href="https://scholar.google.no/citations?user=OLSf0mAAAAAJ&hl=no&oi=ao" target="_blank">Jiehong Kong</a>, <a href="https://scholar.google.no/citations?user=LHinTOkAAAAJ&hl=no&oi=ao" target="_blank">Hans Ivar Skjelbred</a>, and <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a> | An overview on formulations and optimization methods for the unit-based short-term hydro scheduling problem | Electric Power Systems Research | 2020 | | <a href="https://doi.org/10.1016/J.EPSR.2019.106027" target="_blank">Doi</a> | The short-term hydro scheduling (STHS) problem aims at determining the optimal power generation schedules for either a single hydropower plant or an integrated system of cascaded watercourses during a time horizon from a single day to one week. Traditionally, an aggregated plant concept is usually adopted in the formulation of the STHS problem. The hydro-turbine generator units in a plant are aggregated as one equivalent unit. Nowadays, more and more hydro producers participate in both energy and capacity markets. It highlights the need for the precise calculation for energy conversion and available capacity of each unit. Formulating the STHS problem on individual units can accurately capture the physical and the operational characteristics of the unit. In this overview, a detailed classification of mathematical programming approaches to model and solve the unit-based STHS problem is presented. The various modeling techniques proposed in the publications since 2000 are categorized by their objectives and constraints. This provides a comprehensive comparison and discussion for each specific issue in the formulation of STHS. We anticipate this overview to be a starting point for finding more computationally solvable and effective methods to handle the challenges in the unit-based STHS problem. |
| 6 | <a href="https://scholar.google.no/citations?user=hCTulYcAAAAJ&hl=no&oi=ao" target="_blank">Per Aaslid</a>, <a href="https://scholar.google.no/citations?user=k7TrwpEAAAAJ&hl=no&oi=ao" target="_blank">Magnus Korpås</a>, <a href="https://scholar.google.no/citations?user=1b7OBl0AAAAJ&hl=no&oi=ao" target="_blank">Michael Martin Belsnes</a>, and <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a> | Stochastic Optimization of Microgrid Operation With Renewable Generation and Energy Storages | IEEE Transactions on Sustainable Energy | 2022 | <a href="https://hdl.handle.net/11250/2984166" target="_blank">Url</a> | <a href="https://doi.org/10.1109/TSTE.2022.3156069" target="_blank">Doi</a> | NaN |
| 7 | Chiara Bordin, <a href="https://scholar.google.no/citations?user=LHinTOkAAAAJ&hl=no&oi=ao" target="_blank">Hans Ivar Skjelbred</a>, <a href="https://scholar.google.no/citations?user=OLSf0mAAAAAJ&hl=no&oi=ao" target="_blank">Jiehong Kong</a>, and Zhirong Yang | Machine Learning for Hydropower Scheduling: State of the Art and Future Research Directions | Procedia Computer Science | 2020 | | <a href="https://doi.org/10.1016/J.PROCS.2020.09.190" target="_blank">Doi</a> | This paper investigates and discusses the current and future role of machine learning (ML) within the hydropower sector. An overview of the main applications of ML in the field of hydropower operations is presented to show the most common topics that have been addressed in the scientific literature in the last years. The objective is to provide recommendations for novel research directions that can be taken in the near future to cover those areas that have not been studied so far. The key contribution of this paper lies in a critical investigation of the state of the art of ML applications in hydropower scheduling. In light of the established literature available in the last years, this study identifies and discusses new roles that can be covered by ML, coupled with cyber-physical systems (CPSs), with a particular focus on short-term hydropower scheduling (STHS) challenges. |
| 8 | <a href="https://scholar.google.no/citations?user=1b7OBl0AAAAJ&hl=no&oi=ao" target="_blank">Michael Martin Belsnes</a>, O. Wolfgang, T. Follestad, and <a href="https://scholar.google.no/citations?user=-Bc-M9oAAAAJ&hl=no&oi=ao" target="_blank">Ellen Krohn Aasgård</a> | Applying successive linear programming for stochastic short-term hydropower optimization | Electric Power Systems Research | 2016 | | <a href="https://doi.org/10.1016/J.EPSR.2015.08.020" target="_blank">Doi</a> | We present a model for operational stochastic short-term hydropower scheduling, taking into account the uncertainty in future prices and inflow, and illustrate how the benefits of using a stochastic rather than a deterministic model can be quantified. The solution method is based on stochastic successive linear programming. The proposed method is tested against the solution of the true non-linear problem in a principal setting. We demonstrate that the applied methodology is a first-order approximation to a formal correct head-of-water optimization and achieve good results in tests. How the concept of stochastic successive linear programming has been implemented in a prototype software for operational short-term hydropower scheduling is also presented, and the model's ability is demonstrated through case studies from Norwegian power industry. From these studies, improvements occurred in terms of the objective function value and decreased risk of spill from reservoirs. |
| 9 | <a href="https://scholar.google.no/citations?user=LHinTOkAAAAJ&hl=no&oi=ao" target="_blank">Hans Ivar Skjelbred</a>, <a href="https://scholar.google.no/citations?user=OLSf0mAAAAAJ&hl=no&oi=ao" target="_blank">Jiehong Kong</a>, and <a href="https://scholar.google.no/citations?user=qvcFfpIAAAAJ&hl=no&oi=ao" target="_blank">Olav Bjarte Fosso</a> | Dynamic incorporation of nonlinearity into MILP formulation for short-term hydro scheduling | International Journal of Electrical Power & Energy Systems | 2020 | | <a href="https://doi.org/10.1016/J.IJEPES.2019.105530" target="_blank">Doi</a> | Optimization tools are widely used for solving the short-term hydro scheduling (STHS) problem in a cascaded hydro system. In a mixed integer linear programming (MILP)-based formulation, the nonlinear and non-convex hydropower production function (HPF) is represented by piecewise linear approximation. However, instead of using a set of predefined curves with static breakpoints or a preprocessing phase to define the complete relationship between the power output, the net head, and the water discharge, this paper proposes a novel method in which the breakpoints in the linearization are determined dynamically, taking into account the time-varying head effect, intake loss, penstock loss, tailrace loss, and head-dependent turbine efficiency. Only one binary variable is needed to indicate the on/off status and power generation of a unit per period. Furthermore, there are few studies available on how to represent the HPF precisely for the hydraulic system where penstocks are shared by multiple generating units. In this paper, we investigate three heuristics to explicitly incorporate the nonlinear and state-dependent power loss in shared penstocks into the STHS problem. The method and heuristics have been implemented in an operational STHS tool used by many hydropower producers in Nordic countries. We use a simple hydro system to illustrate the method and heuristics and a real hydro system in Northern Norway to study calculation efficiency and solution quality. The numerical results indicate that the proposed method can precisely represent the head-dependent and nonlinear operating characteristics of the generating units. The accurate modeling of a system with multi-level shared penstock configurations is crucial for obtaining the optimal unit commitment. The heuristics can effectively handle the power loss in shared penstock in various operating conditions. |
