scholarly journals Non-convex nested Benders decomposition

2022 ◽  
Author(s):  
Christian Füllner ◽  
Steffen Rebennack
Keyword(s):  
Benders Decomposition ◽  
Unit Commitment ◽  
Piecewise Linear ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Global Optimality ◽  
Value Functions ◽  
State Variables ◽  
Lipschitz Continuous ◽  
Nested Benders Decomposition

AbstractWe propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). We call this algorithm non-convex nested Benders decomposition (NC-NBD). NC-NBD is based on solving dynamically improved mixed-integer linear outer approximations of the MINLP, obtained by piecewise linear relaxations of nonlinear functions. Those MILPs are solved to global optimality using an enhancement of nested Benders decomposition, in which regularization, dynamically refined binary approximations of the state variables and Lagrangian cut techniques are combined to generate Lipschitz continuous non-convex approximations of the value functions. Those approximations are then used to decide whether the approximating MILP has to be dynamically refined and in order to compute feasible solutions for the original MINLP. We prove that NC-NBD converges to an $$\varepsilon $$ ε -optimal solution in a finite number of steps. We provide promising computational results for some unit commitment problems of moderate size.

scholarly journals Security-Constrained Unit Commitment Based on a Realizable Energy Delivery Formulation

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Hongyu Wu ◽  
Qiaozhu Zhai ◽  
Xiaohong Guan ◽  
Feng Gao ◽  
Hongxing Ye
Keyword(s):  
Unit Commitment ◽  
Piecewise Linear ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Comparative Case Study ◽  
Dynamic Programming Method ◽  
Individual Unit ◽  
New Formulation ◽  
Bus System

Security-constrained unit commitment (SCUC) is an important tool for independent system operators in the day-ahead electric power market. A serious issue arises that the energy realizability of the staircase generation schedules obtained in traditional SCUC cannot be guaranteed. This paper focuses on addressing this issue, and the basic idea is to formulate the power output of thermal units as piecewise-linear function. All individual unit constraints and systemwide constraints are then reformulated. The new SCUC formulation is solved within the Lagrangian relaxation (LR) framework, in which a double dynamic programming method is developed to solve individual unit subproblems. Numerical testing is performed for a 6-bus system and an IEEE 118-bus system on Microsoft Visual C# .NET platform. It is shown that the energy realizability of generation schedules obtained from the new formulation is guaranteed. Comparative case study is conducted between LR and mixed integer linear programming (MILP) in solving the new formulation. Numerical results show that the near-optimal solution can be obtained efficiently by the proposed LR-based method.

scholarly journals Security Constrained Unit Commitment in a Power System based on Benders Decomposition and Mixed Integer Non-linear Programming

2018 ◽  
Vol 7 (2.6) ◽  
pp. 283 ◽  
Author(s):  
Pranda Prasanta Gupta ◽  
Prerna Jain ◽  
Suman Sharma ◽  
Rohit Bhakar
Keyword(s):  
Linear Programming ◽  
Network Security ◽  
Power System ◽  
Optimal Power Flow ◽  
Benders Decomposition ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Reserve Requirement ◽  
Non Linear Programming ◽  
Non Linear

In deregulated power markets, Independent System Operators (ISOs) maintains adequate reserve requirement in order to respond to generation and system security constraints. In order to estimate accurate reserve requirement and handling non-linearity and non-convexity of the problem, an efficient computational framework is required. In addition, ISO executes SCUC in order to reach the consistent operation. In this paper, a novel type of application which is Benders decomposition (BD) and Mixed integer non linear programming (MINLP) can be used to assess network security constraints by using AC optimal power flow (ACOPF) in a power system. It performs ACOPF in network security check evaluation with line outage contingency. The process of solving modified system would be close to optimal solution, the gap between the close to optimal and optimal solution is expected to determine whether a close to optimal solutionis accepetable for convenientpurpose. This approach drastically betters the fast computational requirement in practical power system .The numerical case studies are investigated in detail using an IEEE 118-bus system. 

scholarly journals Unit commitment based reliability analysis with contingency constraint

2019 ◽  
Vol 16 (1) ◽  
pp. 74
Author(s):  
Raheema Syed ◽  
P. Srinivasa Varma ◽  
R. B. R Prakash ◽  
Ch. Rami Reddy
Keyword(s):  
Power Plants ◽  
Benders Decomposition ◽  
Unit Commitment ◽  
Reliability Assessment ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Unit Commitment Problem ◽  
Commitment Problem ◽  
Model Reliability ◽  
The Cost

<span lang="EN-IN">Unit commitment state’s the strategic choice to be prepared in order to define which of the accessible power plants should be taken into account to supply power. It permits utilities to reduce generation price of power. In this paper, the unit commitment problem is elucidated by taking N-1-1 contingency as a foremost constraint. The standard N-1-1 contingency takes the loss of sequential two components in the network having intervening interval for network modifications in the middle of two losses. The crucial objective to carry out contingency constrictions is to make certain that the operations of power system are adequately strong to unexpected losses of the components of the network. The optimal scheduling/allocation of the generating units is resolved by taking into account the N-1-1 criterion of contingency. By considering the N-1-1 criterion of contingency, the problem results to give an optimised model which is a linear model of mixed integer form. The linear program of mixed integer is a technique of an operational assessment in which restriction is imposed on few variables to be integers. Primarily benders decomposition was considered but for the improvement of results, the algorithm of branch and cut is presented. IEEE 30 bus system is taken into consideration and widespread analysis is accomplished to associate performance of the system under N-1-1 criterion contingency. The computational outcomes determine the value for taking into concern the intervening interval for the adjustments of the system with respect to the cost and robustness of the system. Later to the above model reliability assessment is proposed to calculate the Loss Of Load Expected (LOLE). This model is solved using MATLAB/MATPOWER software.</span>

Study and Application on Real Time Optimum Operation for Plant Units

2005 ◽  
Author(s):  
Yanfen Liao ◽  
Jiejin Cai ◽  
Xiaoqian Ma
Keyword(s):  
Power Plant ◽  
Large Scale ◽  
Unit Commitment ◽  
Operating Cost ◽  
Target Function ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Coal Consumption ◽  
Allocation Model ◽  
Load Demand

The optimum unit commitment is to determine an optimal scheme which can minimize the system operating cost during a period while the load demand, operation constrains of the individual unit are simultaneously satisfied. Since it is characterized as a nonlinear, large scale, discrete, mixed-integer combinatorial optimization problem with constrains, it is always hard to find out the theoretical optimal solution. In this paper, a method combining the priority-order with dynamic comparison is brought out to obtain an engineering optimal solution, and is validated in a power plant composed of three 200MW and two 300MW units. Through simulating the on-line running datum from the DCS system in the power plant, the operating cost curves are obtained in different units, startup/shut-down mode and load demand. According to these curves, an optimum unit commitment model is established based on equal incremental rate principle principle. Make target function be minimum gross coal consumption, the results show that compared with the duty-chief-mode that allocates the load based on operators’ experience, the units’ mean gross coal consumption rate is reduced about 0.5g/(kW·h) when operating by this unit commitment model, and its economic profit is far more than the load economic allocation model that doesn’t considered the units’ start-up/shut-down.

scholarly journals Minimum Frequency and Voltage Stability Constrained Unit Commitment for AC/DC Transmission Systems

2019 ◽  
Vol 9 (16) ◽  
pp. 3412 ◽  
Author(s):  
Ningyu Zhang ◽  
Qian Zhou ◽  
Haoming Hu
Keyword(s):  
Direct Current ◽  
Voltage Stability ◽  
Benders Decomposition ◽  
Unit Commitment ◽  
Power Grid ◽  
Eastern China ◽  
Normal Operation ◽  
Mixed Integer ◽  
Programming Algorithm ◽  
Frequency Regulation

An increased use of the high-voltage direct current (HVDC) technologies can have important effects on frequency performance and voltage stability of the receiving-end grid during normal operation as well as during blocking failure. The main reasons are the inherent characteristics of the HVDC such as its much larger capacity than thermal plants and lack of voltage supporting ability to the alternating current (AC) grid. These has led to new challenges for AC/direct current (DC) power grid operators in terms of ensuring power system security. To address these challenges, a unit commitment (UC) of the receiving-end in the AC/DC hybrid grid is presented in this paper. In the proposed model, primary frequency modulation constraints are added to provide sufficient capacity for HVDC blocking. Besides, grid security constraint after secondary frequency regulation is also considered because HVDC blocking failure would cause large range power transfer and transmission lines overload. Meanwhile, voltage stability constraints are employed to guarantee enough voltage supporting capacity from thermal plants at the HVDC feed-in area. Based on the characteristics of the model, Benders decomposition and mixed integer programming algorithm are used to get the optimal transmission power of the HVDC and schedule of thermal units. The study is done by considering the IEEE-39 and Jiangsu power grid in eastern China, containing two HVDC transmission projections respectively. The results are also validated by simulation of different HVDC blocking failure scenarios.

scholarly journals On Mixed-Integer Programming Formulations for the Unit Commitment Problem

2020 ◽  
Author(s):  
Bernard Knueven ◽  
James Ostrowski ◽  
Jean-Paul Watson
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Unit Commitment ◽  
Piecewise Linear ◽  
Practical Importance ◽  
Production Costs ◽  
Mixed Integer ◽  
Real World Data ◽  
Unit Commitment Problem ◽  
Comprehensive Overview

We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation.

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