scholarly journals Unit commitment using complementarity

2021 ◽  
Author(s):  
Steven V. Craig
Keyword(s):  
Unit Commitment ◽  
Discontinuous Solution ◽  
Solution Space ◽  
Mixed Integer ◽  
Nonlinear Constraints ◽  
Mixed Integer Linear Program ◽  
Integer Variables ◽  
Complementarity Theory ◽  
Speed And Accuracy ◽  
Linear Nature

A need exists to optimally dispatch power generation to meet per-hour requirements on the power grid. This is a well documented and established problem called Unit Commitment (UC). It is commonly formulated as a Mixed Integer Linear Program (MILP), which utilizes intelligent solvers to produce a solution with speed and accuracy. The linear nature of MILP requires linear approximations of nonlinear constraints. This work introduces the Theory of Complementarity in order to remove integer variables, resulting in a continuous rather than a discontinuous solution space. This permits use of classical solution techniques, as well as nonlinear constraints, thereby increasing accuracy. A formulation is developed to demonstrate a proof of concept of the complementarity theory as used in UC. A subset of constraints will be used and the results will be compared against an MILP optimization, for 10-and 26-generator configurations. Similar trends in generator status and total cost are noted.

scholarly journals Unit commitment using complementarity

2021 ◽  
Author(s):  
Steven V. Craig
Keyword(s):  
Unit Commitment ◽  
Discontinuous Solution ◽  
Solution Space ◽  
Mixed Integer ◽  
Nonlinear Constraints ◽  
Mixed Integer Linear Program ◽  
Integer Variables ◽  
Complementarity Theory ◽  
Speed And Accuracy ◽  
Linear Nature

A need exists to optimally dispatch power generation to meet per-hour requirements on the power grid. This is a well documented and established problem called Unit Commitment (UC). It is commonly formulated as a Mixed Integer Linear Program (MILP), which utilizes intelligent solvers to produce a solution with speed and accuracy. The linear nature of MILP requires linear approximations of nonlinear constraints. This work introduces the Theory of Complementarity in order to remove integer variables, resulting in a continuous rather than a discontinuous solution space. This permits use of classical solution techniques, as well as nonlinear constraints, thereby increasing accuracy. A formulation is developed to demonstrate a proof of concept of the complementarity theory as used in UC. A subset of constraints will be used and the results will be compared against an MILP optimization, for 10-and 26-generator configurations. Similar trends in generator status and total cost are noted.

Efficient airplane arrival scheduling using a set partitioning-based branch-and-price method

2017 ◽  
Vol 232 (16) ◽  
pp. 2939-2951
Author(s):  
Jae-Hoon Song ◽  
Han-Lim Choi
Keyword(s):  
Large Scale ◽  
Time Window ◽  
Heuristic Method ◽  
Solution Space ◽  
Exact Algorithm ◽  
Set Partitioning ◽  
Mixed Integer ◽  
Branch And Price ◽  
Mixed Integer Linear Program ◽  
Public Data

This article presents an exact algorithm that is combined with a heuristic method to find the optimal solution for an airplane landing problem. For a given set of airplanes and runways, the objective is to minimize the accumulated deviations from the target landing time of the airplanes. A cost associated with landing either earlier or later than the target landing time is incurred for each airplane within its predetermined time window. In order to manage this type of large-scale optimization problem, a set partitioning formulation that results in a mixed integer linear program is proposed. One key contribution of this article is the development of a branch-and-price methodology, in which the column generation method is integrated with the branch-and-bound method in order to find the optimal integer solution. In addition to the exact algorithm, a simple heuristic method is also presented to tighten the solution space. Numerical experiments are undertaken for the proposed algorithm in order to confirm its effectiveness using public data from the OR-Library. As an application in the real-world situation of airplane landing, air traffic data from Incheon International Airport is employed to assure the efficiency of the proposed algorithm.

scholarly journals A Mixed-Integer and Asynchronous Level Decomposition with Application to the Stochastic Hydrothermal Unit-Commitment Problem

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 235 ◽  
Author(s):  
Bruno Colonetti ◽  
Erlon Cristian Finardi ◽  
Welington de Oliveira
Keyword(s):  
Unit Commitment ◽  
Computing Time ◽  
Decomposition Methods ◽  
Mixed Integer ◽  
Unit Commitment Problem ◽  
Integer Variables ◽  
Computational Performance ◽  
Current State ◽  
Commitment Problem ◽  
Time Savings

Independent System Operators (ISOs) worldwide face the ever-increasing challenge of coping with uncertainties, which requires sophisticated algorithms for solving unit-commitment (UC) problems of increasing complexity in less-and-less time. Hence, decomposition methods are appealing options to produce easier-to-handle problems that can hopefully return good solutions at reasonable times. When applied to two-stage stochastic models, decomposition often yields subproblems that are embarrassingly parallel. Synchronous parallel-computing techniques are applied to the decomposable subproblem and frequently result in considerable time savings. However, due to the inherent run-time differences amongst the subproblem’s optimization models, unequal equipment, and communication overheads, synchronous approaches may underuse the computing resources. Consequently, asynchronous computing constitutes a natural enhancement to existing methods. In this work, we propose a novel extension of the asynchronous level decomposition to solve stochastic hydrothermal UC problems with mixed-integer variables in the first stage. In addition, we combine this novel method with an efficient task allocation to yield an innovative algorithm that far outperforms the current state-of-the-art. We provide convergence analysis of our proposal and assess its computational performance on a testbed consisting of 54 problems from a 46-bus system. Results show that our asynchronous algorithm outperforms its synchronous counterpart in terms of wall-clock computing time in 40% of the problems, providing time savings averaging about 45%, while also reducing the standard deviation of running times over the testbed in the order of 25%.

scholarly journals Computing Team-Maxmin Equilibria in Zero-Sum Multiplayer Extensive-Form Games

2020 ◽  
Vol 34 (02) ◽  
pp. 2318-2325
Author(s):  
Youzhi Zhang ◽  
Bo An
Keyword(s):  
Solution Space ◽  
Optimal Strategies ◽  
Mixed Integer ◽  
Multiplayer Games ◽  
Extensive Form ◽  
Mixed Integer Linear Program ◽  
Extensive Form Games ◽  
Security Games ◽  
Zero Sum ◽  
Constraint Method

The study of finding the equilibrium for multiplayer games is challenging. This paper focuses on computing Team-Maxmin Equilibria (TMEs) in zero-sum multiplayer Extensive-Form Games (EFGs), which describes the optimal strategies for a team of players who share the same goal but they take actions independently against an adversary. TMEs can capture many realistic scenarios, including: 1) a team of players play against a target player in poker games; and 2) defense resources schedule and patrol independently in security games. However, the study of efficiently finding TMEs within any given accuracy in EFGs is almost completely unexplored. To fill this gap, we first study the inefficiency caused by computing the equilibrium where team players correlate their strategies and then transforming it into the mixed strategy profile of the team and show that this inefficiency can be arbitrarily large. Second, to efficiently solve the non-convex program for finding TMEs directly, we develop the Associated Recursive Asynchronous Multiparametric Disaggregation Technique (ARAMDT) to approximate multilinear terms in the program with two novel techniques: 1) an asynchronous precision method to reduce the number of constraints and variables for approximation by using different precision levels to approximate these terms; and 2) an associated constraint method to reduce the feasible solution space of the mixed-integer linear program resulting from ARAMDT by exploiting the relation between these terms. Third, we develop a novel iterative algorithm to efficiently compute TMEs within any given accuracy based on ARAMDT. Our algorithm is orders of magnitude faster than baselines in the experimental evaluation.

scholarly journals Profit-Based Unit Commitment for a GENCO Equipped with Compressed Air Energy Storage and Concentrating Solar Power Units

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 576
Author(s):  
Mostafa Nasouri Gilvaei ◽  
Mahmood Hosseini Imani ◽  
Mojtaba Jabbari Ghadi ◽  
Li Li ◽  
Anahita Golrang
Keyword(s):  
Energy Storage ◽  
Solar Power ◽  
Unit Commitment ◽  
Thermal Power ◽  
System Structure ◽  
Compressed Air ◽  
Mixed Integer ◽  
Compressed Air Energy Storage ◽  
Concentrating Solar Power ◽  
Unit Commitment Problem

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.

scholarly journals Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA

2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Solution Vector ◽  
The Impact

The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.

scholarly journals Investment Incentives in Competitive Electricity Markets

2018 ◽  
Vol 8 (10) ◽  
pp. 1978 ◽  
Author(s):  
Jaber Valinejad ◽  
Taghi Barforoshi ◽  
Mousa Marzband ◽  
Edris Pouresmaeil ◽  
Radu Godina ◽  
...  
Keyword(s):  
Electricity Markets ◽  
Electricity Market ◽  
Planning Horizon ◽  
Optimization Method ◽  
Design Criterion ◽  
Mixed Integer ◽  
Investment Incentives ◽  
Mixed Integer Linear Program ◽  
Interconnected Power System ◽  
The Impact

This paper presents the analysis of a novel framework of study and the impact of different market design criterion for the generation expansion planning (GEP) in competitive electricity market incentives, under variable uncertainties in a single year horizon. As investment incentives conventionally consist of firm contracts and capacity payments, in this study, the electricity generation investment problem is considered from a strategic generation company (GENCO) ′ s perspective, modelled as a bi-level optimization method. The first-level includes decision steps related to investment incentives to maximize the total profit in the planning horizon. The second-level includes optimization steps focusing on maximizing social welfare when the electricity market is regulated for the current horizon. In addition, variable uncertainties, on offering and investment, are modelled using set of different scenarios. The bi-level optimization problem is then converted to a single-level problem and then represented as a mixed integer linear program (MILP) after linearization. The efficiency of the proposed framework is assessed on the MAZANDARAN regional electric company (MREC) transmission network, integral to IRAN interconnected power system for both elastic and inelastic demands. Simulations show the significance of optimizing the firm contract and the capacity payment that encourages the generation investment for peak technology and improves long-term stability of electricity markets.

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