Using semidefinite relaxation to solve the day-ahead hydro unit commitment problem

Paredes, Miguel; Martins, L. S. A.; Soares, S.

doi:10.1109/pesgm.2015.7285717

Cited by 8 publications

(18 citation statements)

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“…Note that when the first-stage decisions are feasible, the equality in (8a) holds due to the strong duality of linear programs (see, e.g., [41]). Then we obtain a reformulation of the worst-case operating cost as (9a) (9b) Third, we substitute the dual formulation (9) into formulation (1) to obtain a reformulation as follows: (10a) where represents the value of , and constraints (10a) follows from formulation (9). For any given pair of , we call inequality (10a) a Benders' cut pertaining to .…”

Section: Solution Methodologymentioning

confidence: 99%

“…In practice, bilinear heuristic (see, e.g., [42] and [22]) has been very helpful to find local optima of problem (9) in a short time, which can then be used in Step (b) above to generate a Benders' cut. In this paper, we apply the alternating direction method in [42] for solving problem (9) and summarize this approach as follows.…”

Section: Solution Methodologymentioning

confidence: 99%

“…1 (9) as a linear program, record optimal solution , return and output as a locally optimal solution to problem (9). Otherwise, update to be and go to Step 1.…”

Section: Solution Methodologymentioning

confidence: 99%

“…Indeed, as reported in [7], a deterministic generation scheduling model with a single turbine can incorporate more than 2,000 additional binary variables, and can take up to 2 hours to obtain an optimal solution. Similarly, nonlinear approximation of the hill charts (see, e.g., [8], [9], and [17]) results in nonlinear recourse in the proposed model (1)- (2), which can also be computationally challenging. In this paper, we focus on modeling the uncertain natural water inflow and obtaining good UC solutions (i.e., good first-stage solutions) in the two-stage robust generation scheduling model, for which we might accept reasonable approximations of the second-stage problem to better balance the modeling fidelity and the resulting computational burdens.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In contrast to [6] and [7], [8] approximates the hill charts by using quadratic functions and solves the hydro-thermal coordination problem to global optimality by considering tight semidefinite programming (SDP) relaxations. Later, [9] further extends the study of the SDP relaxations by accounting for the ac power flow constraints. Taking the Itaipú hydroelectric plant as a case study, [10] employs a dynamic programming approach to optimize the commitment and dispatch of the turbines.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Weekly Two-Stage Robust Generation Scheduling for Hydrothermal Power Systems

Dashti

Conejo

Jiang

et al. 2016

IEEE Trans. Power Syst.

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Abstract-As compared to short-term forecasting (e.g., 1 day), it is often challenging to accurately forecast the volume of precipitation in a medium-term horizon (e.g., 1 week). As a result, fluctuations in water inflow can trigger generation shortage and electricity price spikes in a power system with major or predominant hydro resources. In this paper, we study a two-stage robust scheduling approach for a hydrothermal power system. We consider water inflow uncertainty and employ a vector autoregressive (VAR) model to represent its seasonality and accordingly construct an uncertainty set in the robust optimization approach. We design a Benders' decomposition algorithm to solve this problem. Results are presented for the proposed approach on a real-world case study.

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Section: Solution Methodologymentioning

confidence: 99%

Section: Solution Methodologymentioning

confidence: 99%

“…1 (9) as a linear program, record optimal solution , return and output as a locally optimal solution to problem (9). Otherwise, update to be and go to Step 1.…”

Section: Solution Methodologymentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Weekly Two-Stage Robust Generation Scheduling for Hydrothermal Power Systems

Dashti

Conejo

Jiang

et al. 2016

IEEE Trans. Power Syst.

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Semidefinite relaxation and generalised benders decomposition to solve the transmission expansion network and reactive power planning

Alvarez

Paredes

Rider

2020

IET Generation, Transmission & Distribution

Self Cite

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Real-Time Dispatch for Multi-Unit Hydroelectric Plants With AC Optimal Power Flow: The Case of the Santo Antonio System

2021

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The growing demand for green energy has driven the building of large-capacity hydroelectric plants away from the load centers. In this setting, one key aspect is constructing electrical networks for efficient power transmission to the primary grid, which is sometimes combined with high-voltage direct current systems. However, in-site applications based on real-time dispatch problems often do not model the AC power flow (ACPF) constraints, partly due to a lack of appealing methods to simultaneously include the dispatch and ACPF operating characteristics. Furthermore, a precise hydropower production function, a priority in this kind of problem, can introduce additional complexity, and practical applications commonly sacrifice the grid-connection modeling. This paper proposes a technique for incorporating ACPF constraints in real-time hydro dispatch, promoting widespread methods and optimization tools. The presented strategy is based on mixed-integer quadratic programming that yields convergent electrical variables compatible with exact ACPF to minimize a compromise between transmission losses and turbined outflow. The testbed is the Santo Antônio system, composite by 50 generating units, 13 power transformers, and 41 buses. Simulations based on real-life data demonstrate the impact of ACPF modeling, achieving losses reduction consistently above 5%, at the cost of a higher processing time.

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Using semidefinite relaxation to solve the day-ahead hydro unit commitment problem

Cited by 8 publications

References 0 publications

Weekly Two-Stage Robust Generation Scheduling for Hydrothermal Power Systems

Weekly Two-Stage Robust Generation Scheduling for Hydrothermal Power Systems

Semidefinite relaxation and generalised benders decomposition to solve the transmission expansion network and reactive power planning

Real-Time Dispatch for Multi-Unit Hydroelectric Plants With AC Optimal Power Flow: The Case of the Santo Antonio System

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