This study describes a model for optimal scheduling of hydro thermal systems with multiple reservoirs. Inflow to hydropower reservoirs, wind power and exogenously given prices are treated as stochastic variables. Power flow constraints included through linearised model. A representation start‐up costs generating units pumps is provided. The well suited medium‐ long‐term generation has the capability capturing detailed system by using fine time resolution. presented tested on realistic...

Hydropower producers rely on stochastic optimization when scheduling their resources over long periods of time. Due to its computational complexity, the problem is normally cast as a linear program. In future power market with more volatile prices, it becomes increasingly important capture parts hydropower operational characteristics that are not easily linearized, e.g., unit commitment and nonconvex generation curves. Stochastic dual dynamic programming (SDDP) state-of-the-art algorithm for...

This paper describes a method for optimal scheduling of hydropower systems profit maximizing, price-taking, and risk neutral producer selling energy, capacity to separate sequentially cleared markets. The is based on combination stochastic dynamic programming (SDP) dual (SDDP), treats inflow reservoirs prices energy as variables. proposed applied in case study Norwegian watercourse, quantifying the expected changes schedules, water values when going from an energy-only market joint treatment reserve

The authors describe a method for long-term hydro-thermal scheduling allowing treatment of detailed large-scale hydro systems. Decisions each week are determined by solving two-stage stochastic linear programming problem considering uncertainty in weather and exogenous market prices. overall is solved embedding such problems rolling horizon simulator. verified on data the Nordic power system, studying incremental changes expected socio-economic surplus expansions both transmission generation...

Maintenance scheduling is an important and complex task in hydropower systems. In a liberalized market, the generation company will schedule maintenance periods to maximize expected profit. This paper describes method for suitable profit maximizing, price-taking, risk neutral producer selling energy reserve capacity separate markets. The uses Benders decomposition principle coordinate timing of power plant with medium-term system, treating inflow reservoirs prices as stochastic variables....

It is essential to have accurate and reliable daily-inflow forecasting improve short-term hydropower scheduling. This paper proposes a Causal multivariate Empirical mode Decomposition (CED) framework as complementary pre-processing step for day-ahead inflow problem. The idea behind CED combining physics-based causal inference with signal processing-based decomposition get the most relevant features among multiple time-series values. validated two areas in Norway different meteorological...

We present a medium-term hydropower scheduling model that includes inflow- and volume-dependent environmental constraints on maximum discharge. A stochastic dynamic programming algorithm (SDP) is formulated to enable an accurate representation of nonconvex relationships in the problem formulation smaller systems. The used assess impact including state-dependent calculated water values. applied case study Norwegian system with multiple reservoirs. find discharge constraint significantly...

Balancing technical details and computational complexity is an important trade-off in long-term hydropower scheduling (LTHS) models. Rapidly increasing shares of variable renewable energy sources (VRES) challenges historical assumptions regarding the appropriate level representation uncertainties LTHS This work expands on previous research formulates efficient solution strategy to accommodate short-term variability uncertainty into models, through gradually approximating shortterm dispatch...

We test the stochastic dual dynamic programming (SDDP) approach on a system an order of magnitude larger than previously published studies. The analysis shows that SDDP-approach can be applied to very large sizes solve hydropower scheduling problem through formal optimisation and obtain individual decision variables for every reservoir. However, this time-consuming compared other existing models based principles. results from our SDDP-based model compare favorably aggregation-disaggregation...

While hydropower scheduling is a well-defined problem, there are institutional differences that need to be identified promote constructive and synergistic research. We study how established toolchains of computer models organized assist operational in Brazil, Norway, the United States' Colorado River System (CRS). These three systems have vast resources, with numerous, geographically widespread, complex reservoir systems. Although underlying objective essentially same, operated different...

The authors analyse the operational profitability of a hydropower system selling both energy and reserve capacity in competitive market setting. A mathematical model based on stochastic dynamic programming is used to compute water values for considering different power plant configurations. uncertainties inflow prices are considered through discrete Markov chain. Subsequently, operation simulated obtained assess performance expected revenues from two markets. applied case study Norwegian...

Due to the introduction of alternative energy carriers, such as district heating and natural gas, Norwegian system is becoming more complex. Assessing reliability electrical distribution systems a mature field research, but limited work has been carried out concerning for carriers. This paper proposes methodology assessing gas based on experiences drawn from similar analysis power systems. A simple test case presented illustrative purposes basic load-point indices average interruption rate,...

This paper presents a method for accurately treating active power losses in linear (DC) optimal flow models. Quadratic nodal are approximated by iteratively adding constraints. In each iteration programming problem is solved, and constraints on the loss functions built as linearizations around current system operating state. The performance of proposed model - terms computational time convergence properties demonstrated IEEE 118 bus test system.

We present a stochastic mixed-integer model for the optimization of joint trade in day-ahead and balancing markets. The takes perspective risk-neutral price-taking hydropower producer one-day planning horizon. is used to study value trading both markets as opposed trades only. In particular we how this affected by flexibility production system. results indicates small added from market participation which increasing increases.

This paper presents a method for treating transmission network bottlenecks in stochastic hydro-thermal scheduling model. The model is designed long- and medium-term of power system operation, where decisions are made aggregated regional subsystems or areas. aggregate area representation allows simulation large hydro systems with relatively high degree detail, thus making the well suited comprehensive studies on national international scale.

Stochastic dual dynamic programming (SDDP) has become a popular algorithm used in practical long-term scheduling of hydropower systems. The SDDP is computationally demanding, but can be designed to take advantage parallel processing. This paper presents novel scheme for the algorithm, where stage-wise synchronization point traditionally backward iteration partially relaxed. proposed was tested on realistic model Norwegian water course, proving that relaxation significantly improves efficiency.

This paper concerns the assessment of two methods for convex relaxation short-term hydrothermal scheduling problem. The problem is originally formulated as a mixed integer programming problem, and then approximated using both Lagrangian Linear relaxation. are quantitatively compared realistic data description Northern European power system, considering set representative days. We find that approximates system operational costs in range 55-81% closer to solution than show how these cost gaps...

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. aggregation complex hydropower systems into equivalent energy representations (EER) a commonly used technique reduce dimensionality computation time models. This work presents method for coordinating the EERs with their system within model based on stochastic dual dynamic programming (SDDP). SDDP an...

This paper presents a method for treating transmission network bottlenecks in stochastic market model, through flow-based clearing process. The model is designed long-term and medium-term scheduling of hydrothermal power system operation, where generators loads are allocated into regional subsystems or price areas. In addition to detailed hydropower, the allows use wind data start-up costs on thermal generators. A description model's overall simulation logic presented, emphasizing...

Continuous-time optimization models have successfully been used to capture the impact of ramping limitations in power systems. In this paper, continuous-time framework is adapted model flexible hydropower resources interacting with slow-ramping thermal generators minimize hydrothermal system cost operation. To accurately represent non-linear production function forbidden zones, binary variables must be when linearizing discharge and continuity constraints on individual units relaxed....