scholarly journals Outer Approximation Method for the Unit Commitment Problem with Wind Curtailment and Pollutant Emission

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2686
Author(s):  
Xiali Pang ◽  
Haiyan Zheng ◽  
Liying Huang ◽  
Yumei Liang

This paper considers the fast and effective solving method for the unit commitment (UC) problem with wind curtailment and pollutant emission in power systems. Firstly, a suitable mixed-integer quadratic programming (MIQP) model of the corresponding UC problem is presented by some linearization techniques, which is difficult to solve directly. Then, the MIQP model is solved by the outer approximation method (OAM), which decomposes the MIQP into a mixed-integer linear programming (MILP) master problem and a nonlinear programming (NLP) subproblem for alternate iterative solving. Finally, simulation results for six systems with up to 100 thermal units and one wind unit in 24 periods are presented, which show the practicality of MIQP model and the effectiveness of OAM.

2020 ◽  
Vol 12 (23) ◽  
pp. 10100
Author(s):  
Khalid Alqunun ◽  
Tawfik Guesmi ◽  
Abdullah F. Albaker ◽  
Mansoor T. Alturki

This paper presents a modified formulation for the wind-battery-thermal unit commitment problem that combines battery energy storage systems with thermal units to compensate for the power dispatch gap caused by the intermittency of wind power generation. The uncertainty of wind power is described by a chance constraint to escape the probabilistic infeasibility generated by classical approximations of wind power. Furthermore, a mixed-integer linear programming algorithm was applied to solve the unit commitment problem. The uncertainty of wind power was classified as a sub-problem and separately computed from the master problem of the mixed-integer linear programming. The master problem tracked and minimized the overall operation cost of the entire model. To ensure a feasible and efficient solution, the formulation of the wind-battery-thermal unit commitment problem was designed to gather all system operating constraints. The solution to the optimization problem was procured on a personal computer using a general algebraic modeling system. To assess the performance of the proposed model, a simulation study based on the ten-unit power system test was applied. The effects of battery energy storage and wind power were deeply explored and investigated throughout various case studies.


2020 ◽  
Vol 7 (5) ◽  
pp. 668-683
Author(s):  
Ashutosh Bhadoria ◽  
Sanjay Marwaha

Abstract This paper proposes a new approach based on the moth flame optimizer algorithm. Moth flame optimizer simulates the natural fervent navigation technique adopted by moths looking for a source of light. The proposed method is further improved by priority list-based ordering; the unit commitment problem (UCP) is a non-linear, non-convex, and combinatorial complex optimization problem. It contains both continuous and discrete variables. This further increases its complexity. Moth flame optimizer is very good at obtaining a commitment pattern: allocation of power on the committed units obtained by mixed-integer quadratic programming method. Heuristic search strategies are used to adopt for the repair of minimum up and downtime, and spinning reserve constraints. MFO effectiveness is tested on the standard UCP reference IEEE model buses 14 and 30, and 10 and 20 units. The efficiency of the projected algorithms is compared to classical PSO, PSOLR, HPSO, PSOSQP, hybrid MPSO, IBPSO, LCA-PSO, NPSO, PSO-GWO, and various other evolutionary algorithms. The comparison result shows that MFO can lead to all methods reported earlier in literature.


2013 ◽  
Vol 7 (11) ◽  
pp. 1210-1218 ◽  
Author(s):  
Juan P. Ruiz ◽  
Cong Liu ◽  
Gengyang Sun ◽  
Jianhui Wang

2014 ◽  
Vol 952 ◽  
pp. 319-322
Author(s):  
Lin Feng Yang ◽  
Jie Li ◽  
Zhi Hui Ge

A continue method based on relaxation is applied to solve the unit commitment problem (UCP). At first, the primal UCP is reformulated as a simple mixed integer quadratic programming (MIQP), and then the MIQP is solved by interior point method (IPM) and commercial software CPLEX. The first continues problem, UCP without integer constraints, can be solved by IPM to get the no integer solution. The second continues problem, an equivalent continues problem of UCP, can be solved starting from the solution obtained in first problem.


Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 576
Author(s):  
Mostafa Nasouri Gilvaei ◽  
Mahmood Hosseini Imani ◽  
Mojtaba Jabbari Ghadi ◽  
Li Li ◽  
Anahita Golrang

With the advent of restructuring in the power industry, the conventional unit commitment problem in power systems, involving the minimization of operation costs in a traditional vertically integrated system structure, has been transformed to the profit-based unit commitment (PBUC) approach, whereby generation companies (GENCOs) perform scheduling of the available production units with the aim of profit maximization. Generally, a GENCO solves the PBUC problem for participation in the day-ahead market (DAM) through determining the commitment and scheduling of fossil-fuel-based units to maximize their own profit according to a set of forecasted price and load data. This study presents a methodology to achieve optimal offering curves for a price-taker GENCO owning compressed air energy storage (CAES) and concentrating solar power (CSP) units, in addition to conventional thermal power plants. Various technical and physical constraints regarding the generation units are considered in the provided model. The proposed framework is mathematically described as a mixed-integer linear programming (MILP) problem, which is solved by using commercial software packages. Meanwhile, several cases are analyzed to evaluate the impacts of CAES and CSP units on the optimal solution of the PBUC problem. The achieved results demonstrate that incorporating the CAES and CSP units into the self-scheduling problem faced by the GENCO would increase its profitability in the DAM to a great extent.


Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.


Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3017
Author(s):  
Elias Dörre ◽  
Sebastian Pfaffel ◽  
Alexander Dreher ◽  
Pedro Girón ◽  
Svenja Heising ◽  
...  

Energy generation and consumption in the power grid must be balanced at every single moment. Within the synchronous area of continental Europe, flexible generators and loads can provide Frequency Containment Reserve and Frequency Restoration Reserve marketed through the balancing markets. The Transmission System Operators use these flexibilities to maintain or restore the grid frequency when there are deviations. This paper shows the future flexibility potential of Germany’s household sector, in particular for single-family and twin homes in 2025 and 2030 with the assumption that households primarily optimize their self-consumption. The primary focus is directed to the flexibility potential of Electric Vehicles, Heat Pumps, Photovoltaics and Battery Storage Systems. A total of 10 different household system configurations were considered and combined in a weighted average based on the scenario framework of the German Grid Development Plan. The household generation, consumption and storage units were simulated in a mixed-integer linear programming model to create the time series for the self-consumption optimized households. This solved the unit commitment problem for each of the decentralized households in their individual configurations. Finally, the individual household flexibilities were evaluated and then aggregated to a Germany-wide flexibility profile for single-family and twin homes. The results indicate that the household sector can contribute significantly to system stabilization with an average potential of 30 negative and 3 positive flexibility in 2025. In 2030, the corresponding flexibilities potentially increase to 90 and 30 , respectively. This underlines that considerable flexibility reserves could be provided by single-family and twin homes in the future.


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