Mixed-integer formulation of unit commitment problem for power systems: Focus on start-up cost

Tuffaha, Mutaz; Gravdahl, Jan Tommy

doi:10.1109/iecon.2013.6700498

Cited by 9 publications

(9 citation statements)

References 10 publications

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“…In the UCP variant we consider in this paper, we seek to find a power generation schedule that minimizes the total operational cost subject to typical UCP constraints such as minimum up/down times, generation capacity, demand satisfaction, ramping requirements, and spinning reserve. The typical MIP formulation of this problem is given in (1a)-(1l); see Rajan et al (2005), Ostrowski et al (2011, Tuffaha and Gravdahl (2013), Bendotti et al (2018). In this formulation, binary variables x i j represent whether or not generating unit i ∈ N = {1, .…”

Section: Standard Formulationsmentioning

confidence: 99%

On the Structure of Decision Diagram–Representable Mixed-Integer Programs with Application to Unit Commitment

Salemi

Davarnia

2023

Operations Research

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Despite the successful applications of decision diagrams (DDs) to solve various classes of integer programs in the literature, the question of which mixed-integer structures admit a DD representation remains open. The present work addresses this question by developing both necessary and sufficient conditions for a mixed-integer program to be DD-representable through identification of certain rectangular formations in the underlying sets. This so-called rectangularization framework is applicable to all bounded mixed-integer linear programs, providing a notable extension of the DD domain to continuous problems. As an application, the paper uses the developed methods to solve stochastic unit commitment problems in energy systems. Computational experiments conducted on benchmark instances show that the DD approach uniformly and significantly outperforms the existing solution methods and modern solvers. The proposed methodology opens new pathways to solving challenging mixed-integer programs in energy systems more efficiently.

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Section: Standard Formulationsmentioning

confidence: 99%

On the Structure of Decision Diagram–Representable Mixed-Integer Programs with Application to Unit Commitment

Salemi

Davarnia

2023

Operations Research

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“…Most of the authors in the literature use two steps only (e.g., see [9], and [7]). Thus, building on previous work of the authors of this work [10], let the start-up cost be discretized into two steps only; hc j when x o f f j ≤ ND j /2, and cc j when x o f f j > ND j /2. Then, the start-up cost can be expressed as:…”

Section: Objective Functionmentioning

confidence: 99%

Dynamic formulation of the unit commitment and economic dispatch problems

Tuffaha

Gravdahl

2015

2015 IEEE International Conference on Industrial Technology (ICIT)

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Economic Dispatch (ED) is the problem of scheduling the output power levels of the committed generating units in a power system, over some time horizon to meet the demand (assuming known) at minimum cost. Optimal Control Dynamic Dispatch (OCDD) uses a dynamic model of the power generation based on ramping constraints. In OCDD, the number of committed units in the system is determined in advance by solving the so-called unit commitment (UC) problem. The progress in the mixed-integer programming algorithms has inspired researchers to combine the ED, and UC in one problem, and then solve it as a static problem. In spite of the speed and accuracy, the static optimization solution can not adapt to fast changes in the power systems. In addition, it suffers from the drawback of violating the ramping rates constraints at the beginning of the planning horizon. In this work, we propose a mixed-integer dynamical model for the power generation to solve both ED, and UC by optimal control strategy. We show that the proposed method gives more accurate results than common approaches in literature. The proposed approach is well suited for small or isolated power systems.

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“…The shutdown cost is associated with the gradual reduction of the thermal unit from the nominal minimum power to the actual stop of the unit. Generally, shut-down costs are much smaller than start-up costs; hence several works have neglected them (Tuffaha and Gravdahl, 2013;Wood and Wollenberg, 2012). The decision vector involved in the UC problem comprises the status and the output of each unit (Wood and Wollenberg, 2012).…”

Section: Introductionmentioning

confidence: 99%

A mixed integer programming based approach for unit commitment problem

Alqunun¹

2018

Int. j. adv. appl. sci.

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Unit commitment (UC) problem is a challenging task in power system operation that has attracted much attention in the two last decades. It aims to find the optimum statues of the thermal units and their optimum to the predicted load demands in order to minimize the total production cost. Within this context, this paper presents a piecewise linear approximation method for solving this mixed integer problem (MIP). Power balance, generation capacity, minimum up/down times and spinning reserve constraints are considered in this study. The proposed method is implemented in GAMS 24.2. Simulation results are carried out using the tenunit system.

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Mixed-integer formulation of unit commitment problem for power systems: Focus on start-up cost

Cited by 9 publications

References 10 publications

On the Structure of Decision Diagram–Representable Mixed-Integer Programs with Application to Unit Commitment

On the Structure of Decision Diagram–Representable Mixed-Integer Programs with Application to Unit Commitment

Dynamic formulation of the unit commitment and economic dispatch problems

A mixed integer programming based approach for unit commitment problem

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