Combining Lagrangian relaxation, benders decomposition, and the level bundle method in the stochastic hydrothermal unit‐commitment problem

Colonetti, Bruno; Finardi, Erlon Cristian

doi:10.1002/2050-7038.12514

Cited by 10 publications

(8 citation statements)

References 29 publications

(40 reference statements)

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“…The model is first projected onto the subspace defined by the set of complicating variables. The resulting formulation is then dualized, and the associated extreme rays and points respectively define the feasibility requirements (feasibility cuts) and the projected costs (optimality cuts) of the complicating variables [34,35].…”

Section: Benders Decompositionmentioning

confidence: 99%

Decompositions for MPC of Linear Dynamic Systems with Activation Constraints

et al. 2020

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The interconnection of dynamic subsystems that share limited resources are found in many applications, and the control of such systems of subsystems has fueled significant attention from scientists and engineers. For the operation of such systems, model predictive control (MPC) has become a popular technique, arguably for its ability to deal with complex dynamics and system constraints. The MPC algorithms found in the literature are mostly centralized, with a single controller receiving the signals and performing the computations of output signals. However, the distributed structure of such interconnected subsystems is not necessarily explored by standard MPC. To this end, this work proposes hierarchical decomposition to split the computations between a master problem (centralized component) and a set of decoupled subproblems (distributed components) with activation constraints, which brings about organizational flexibility and distributed computation. Two general methods are considered for hierarchical control and optimization, namely Benders decomposition and outer approximation. Results are reported from a numerical analysis of the decompositions and a simulated application to energy management, in which a limited source of energy is distributed among batteries of electric vehicles.

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Section: Benders Decompositionmentioning

confidence: 99%

Decompositions for MPC of Linear Dynamic Systems with Activation Constraints

et al. 2020

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“…The generated Benders cut is defined as follows:

\begin{matrix} right leftthickmathspace.5em \\ W_{y b}^{r} & + \sum_{g \in \{EG\}} ζ_{y b g}^{r} \cdot {normalPCCS}_{g}^{truemax} \cdot (SCC {normalS}_{y g} - {\hat{normalSCCS}}_{y g}) \\ \leq TE {normalM}_{y b} \end{matrix}

Generated Benders cuts in this subproblem are the coupling constraints between the pollutant generation units and the CCS retrofitting in the planning problem. They are relaxed into the CCS planning of the individual generators by applying the Lagrangian relaxation [32–34]. The inequality (25) is recast as (27) by transferring the constant values (parameters and given variables) in (25) to the right‐hand side of the inequality to simplify the formulation.…”

Section: Problem Formulationmentioning

confidence: 99%

Coordinated G&TEP and carbon capture and storage expansion planning model for emission constrained power systems

Asgharian

Abdelaziz

Kamwa

2020

IET gener. transm. distrib.

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Fossil fuel-fired power plants are still the principal power producers in most power systems. Retrofitting these pollutant generators with carbon capture and storage (CCS) technology can be a key solution to decarbonisation, especially for power systems with low expansion potential for renewable and hydroelectric energy resources. This study presents a coordinated generation and transmission expansion planning (G&TEP) and CCS expansion planning model for carbon emission constrained power systems. The proposed model determines the optimal order and time of retrofitting carbon emitter generators with CCS technology coordinated with the G&TEP. The limits on renewable resources capacity expansion potential and the yearly emission reduction targets are considered. Additionally, the proposed model allows for determining the incentives that are to be offered by the central planning authority to the pollutant generators to incentivise their participation in emission reduction through CCS retrofitting. The problem is formulated as a mixed-integer linear programming model and is decomposed into a master and three subproblems to tackle the large-scale nature of the developed optimisation problem. Numerical results demonstrate that a coordinated G&TEP and CCS expansion planning is a least-cost planning solution for emission constrained power systems with low expansion capacity potential for renewable and hydroelectric resources.

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“…Moreover, the generation scheduling problems are commonly solved by two separate procedures which are the unit commitment (UC) solution followed by the economic dispatch (ELD) solution. Previous works based on the Lagrange relaxation and Benders decomposition method employed a MILP technique in solving the optimal UC-ELD problem [7][8][9]. However, the iterative Benders cut-based method does not necessarily obtain the global optimal solution for nonconvex objective functions.…”

Section: Introductionmentioning

confidence: 99%

Optimal coordinated generation scheduling considering day‐ahead PV and wind power forecast uncertainty

Admasie

Song

Kim

2023

IET Generation Trans & Dist

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Economic operation and reliable supply-demand balance are problems of paramount importance in power grids with a massive share of intermittent renewable energy sources (RESs) of great interest. This paper sought an optimal coordinated generation scheduling for day-ahead power system operation considering RESs and energy storage units. Renewable power generation, particularly, wind and photovoltaic are uncontrollable, whereas can be predicted using forecasting models. Within the proposed framework, a hyperparameteroptimized long short-term memory (LSTM) regression model is employed to forecast the day-ahead weather from the historical time-series weather data. Eventually, an empirical formula is used to estimate the power conversion from the day-ahead weather forecasts for a selected PV module and wind turbine. The objective of the scheduling framework is to keep a delicate supply-demand balance at the lowest possible cost of generation while maintaining the prevailing generation and system constraints. A variance measure uncertainty handling-based grey wolf optimizer (GWO) technique is used to find the optimal day-ahead generation schedules and dispatches under RESs forecast uncertainty. The proposed generation scheduling framework is examined on the IEEE 6 and 30-bus systems. In the studied scenarios, the coordinated operation of generators can decrease the total dayahead operating cost for the modified IEEE 6-bus system by 2.57% compared to supplying electricity generation with conventional generators alone. Likewise, the total operating cost from the coordinated operation of all generation portfolios was reduced by 6.93% from the operating cost of generation during base case simulation (supply only from dispatchable thermal units) on the modified IEEE 30-bus system. Moreover, the case studies show that coordinated generation scheduling can mitigate the RESs power variability problem, provide secure supply-demand operation, and minimize the operating cost of electricity generation.

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Combining Lagrangian relaxation, benders decomposition, and the level bundle method in the stochastic hydrothermal unit‐commitment problem

Cited by 10 publications

References 29 publications

Decompositions for MPC of Linear Dynamic Systems with Activation Constraints

Decompositions for MPC of Linear Dynamic Systems with Activation Constraints

Coordinated G&TEP and carbon capture and storage expansion planning model for emission constrained power systems

Optimal coordinated generation scheduling considering day‐ahead PV and wind power forecast uncertainty

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