Approximating hydropower systems by feasibility spaces in stochastic dual dynamic programming

This work investigates and improves methodology for approximating hydropower systems by feasibility spaces, which can be embedded in the stochastic dual dynamic programming algorithm and applied in the context long-term hydrothermal scheduling. The feasibility spaces are derived from optimization of the detailed hydropower system and are expressed in few dimensions to facilitate efficient computations. Test results from a case study for the Norwegian power system demonstrate how feasibility spaces serve to realistically constrain the hydropower system.publishedVersio

Hydropower Aggregation by Spatial Decomposition – an SDDP Approach

The balance between detailed technical description, representation of uncertainty and computational complexity is central in long-term scheduling models applied to hydro-dominated power system. The aggregation of complex hydropower systems into equivalent energy representations (EER) is a commonly used technique to reduce dimensionality and computation time in scheduling models. This work presents a method for coordinating the EERs with their detailed hydropower system representation within a model based on stochastic dual dynamic programming (SDDP). SDDP is applied to an EER representation of the hydropower system, where feasibility cuts derived from optimization of the detailed hydropower are used to constrain the flexibility of the EERs. These cuts can be computed either before or during the execution of the SDDP algorithm and allow system details to be captured within the SDDP strategies without compromising the convergence rate and state-space dimensionality. Results in terms of computational performance and system operation are reported from a test system comprising realistic hydropower watercourses.Hydropower Aggregation by Spatial Decomposition – an SDDP ApproachacceptedVersio

Detailed long-term hydro-thermal scheduling for expansion planning in the Nordic power system

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Approximating Ramping Constraints in Hydropower Scheduling

This work concerns the modeling of ramping constraints on discharge in medium-term hydropower scheduling models applied in a liberalized market context. Such models often apply a coarse time discretization to ensure reasonable computation times. Consequently, ramping constraints at a fine time-resolution are challenging to represent. To address this challenge, we derive a quadratic transition-cost term capturing the power production shifted to time periods with less favorable prices due to ramping constraints. We approximate the quadratic term by linearization so that it can be embedded in an existing hydropower scheduling tool based on stochastic linear programming. A prototype hydropower scheduling model, including the approximated transition-cost term, was tested on a realistic hydropower system in Norway. We demonstrate that the improved modeling of ramping constraints significantly impacts discharge patterns and comes at a significant, but not prohibitive, increase in computation time.Approximating Ramping Constraints in Hydropower SchedulingacceptedVersio

Modelling uncertainty in gas and CO2 prices – consequences for electricity price

A hydro-thermal market model is applied to a description of the north-European electricity system. The paper describes how modelling uncertain gas and CO 2 prices affects uncertainty in calculated electricity prices. Gas and CO 2 price uncertainty are modelled using historic price variations. With this new uncertainty modelling, the resulting electricity price uncertainty increases significantly compared to the deterministic modelling of thermal marginal costs that is standard in these types of models. Changes in electricity price uncertainty are shown using visual and quantitative measures for some representative price areas in the modelled system. Price forecasts from hydro-thermal models are among others used for hydro investment analysis. An underestimation of the future price uncertainty leads to less investment in flexibility which is much needed in the future electricity system with large shares of new renewables.Modelling uncertainty in gas and CO2 prices – consequences for electricity priceacceptedVersio

Continuous Hydrothermal Flexibility Coordination Under Wind Power Uncertainty

This paper develops a stochastic continuous-time optimization model for coordinating the operation of flexibility in a hybrid hydro-thermal-wind power system. The developed model gives insight for investigating the short-term interactions between the different generation technologies. The continuous-time model captures the sub-hourly variations of wind power and load, and can accurately model the ramping capability of the system. A simplified Northern European system is studied over a 30 hour period to examine the potential of using hydropower as a comprehensive flexibility provider. Norwegian hydropower is shown to be a significant source of flexibility used to mitigate wind power variations, especially during ramping constrained periods. The hydropower provides 73.5% of the balancing energy in the base case, which includes smoothing out longer wind power deviations as well as rapid ramping relief. The short-term implications of increasing the offshore wind power in the North Sea by 50% compared to 2020 was also studied in the Northern European test system. The increased wind power causes steeper ramping in the net load, which drives the hydropower to its full balancing potential to allow thermal units to operate within their ramping limits.Continuous Hydrothermal Flexibility Coordination Under Wind Power UncertaintyacceptedVersio

A Comprehensive Simulator for Hydropower Investment Decisions

Due to a higher share of power production from renewable sources with high short-term variation, hydro systems must more often operate closer to their components' physical limits. To simulate system behaviour, a hydropower system simulator must therefore include most physical details. We present a simulator for hydropower investment analysis that combines a medium-term production planning model based on stochastic dual dynamic programming principles with a detailed and deterministic short-term hydro scheduling model. To reduce computation times, the system description for the short-term model may include only a snipped subset of the plants and reservoirs without deteriorating the results. The simulator is verified in a case study where an investment decision has been analysed for a Norwegian hydropower producer. The combination of medium-term optimization and short-term, detailed simulation is a useful decision support tool and provides both economic results and detailed physical information about the system behaviour.A Comprehensive Simulator for Hydropower Investment DecisionsacceptedVersio

Hydropower Scheduling with State-Dependent Discharge Constraints: An SDDP Approach

Environmental constraints in hydropower systems serve to ensure sustainable use of water resources. Through accurate treatment in hydropower scheduling, one seeks to respect such constraints in the planning phase while optimizing the utilization of hydropower. However, many environmental constraints introduce state-dependencies and even nonconvexities to the scheduling problem, making them challenging to represent in stochastic hydropower scheduling models. This paper describes how the state-dependent maximum discharge constraint, which is widely enforced in the Norwegian hydropower system, can be embedded within the stochastic dual dynamic programming (SDDP) algorithm for hydropower scheduling without compromising computational time. In this work, a combination of constraint relaxation and time-dependent auxiliary lower reservoir volume bounds is applied, and the modeling is verified through computational experiments on two different systems. The results demonstrate that the addition of an auxiliary lower bound on reservoir volume has significant potential for improved system operation, and that a bound based on the minimum accumulated inflow in the constraint period is the most efficient.Hydropower Scheduling with State-Dependent Discharge Constraints: An SDDP ApproachpublishedVersio