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Reliability constraint stochastic UC by considering the correlation of random variables with Copula theory

IET RENEWABLE POWER GENERATION 2019年第14期13卷 2587-2593页

作者： Yu, Dongmin Ghadimi, Noradin Northeast Elect Power Univ Dept Elect Engn Jilin 132012 Jilin Peoples R China Islamic Azad Univ Ardabil Branch Young Researchers & Elite Club Ardebil Iran

This essay performs a reliability constraint stochastic model for unit commitment problem by considering generation and transmission constraints with high wind penetration and volatility of load demands. This query is expressed as a MILP that is based on the linear direct current model. The proposed approach models uncertainty of wind generators output power, load demand fluctuations and stochastic elements outage of the system like generators and transmission lines. In this paper, stochastic interdependence between random variables like wind speed and load demand is recognized. To establish the probability distribution of these correlated random variables, Copula theory is applied. Correlation structure between wind speed of different locations and a group of loads existing in the same area is investigated and studied based on historical data. For representing these uncertainties in the stochastic unit commitment problem, possible scenarios are generated with Monte Carlo simulation method. The reliability constraints are utilized in each scenario to evaluate the feasibility of solutions from a reliability point. The introduced stochastic UC is executed on the RTS 96-bus test system. Numerical results demonstrate the advantages of implementing stochastic programming on the UC problem by taking into account the intermittent behavior of wind energy and load inconstancy.

关键词： power generation economics Monte Carlo methods stochastic programming linear programming power markets stochastic processes wind power plants power generation dispatch probability integer programming power system reliability power generation scheduling stochastic elements outage transmission lines stochastic interdependence wind speed correlated random variables Copula theory correlation structure stochastic UC problem reliability constraints reliability point introduced stochastic UC RTS-96-bus test system stochastic programming wind energy load inconstancy reliability constraint stochastic UC reliability constraint stochastic model unit commitment problem transmission constraints high wind penetration volatility mixed-integer linear programme linear direct current model approach models uncertainty wind generators output power load demand fluctuations

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Enhanced Lagrange relaxation for the optimal unit commitment of identical generating units

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第18期14卷 3920-3928页

作者： Nikolaidis, Pavlos Poullikkas, Andreas Cyprus Univ Technol Dept Elect Engn POB 50329 CY-3603 Limassol Cyprus Cyprus Energy Regulatory Author POB 24936 CY-1305 Nicosia Cyprus

Intelligent generation scheduling for seamless integration of uncertain and volatile renewable sources constitutes a crucial solution in delivering future low carbon energy. System operators need to devise effective flexibility adequacy plans for their power systems so as to guarantee power balance and ensure feasible and economical operation over different time horizons and under different generational, environmental and technical constraints. In this work, the authors propose a novel approach for addressing the unit commitment problem of identical generating units, based on Lagrange relaxation framework. The proposed method is characterised by a double decomposition formulation to determine the optimal path for the commitment of identical heat-rate units. This approach is tested and compared to conventional Lagrange relaxation on systems with a number of generating units in the range of 20-100. The proposed approach completely outperforms the conventional alternative in terms of total fuel cost savings, as well as the number of required iterations. In addition, the required iterations are found to increase linearly with system size, which is favourable for large-scale implementations.

关键词： power system planning power generation dispatch power generation economics renewable energy sources power generation scheduling optimisation power generation planning enhanced Lagrange relaxation optimal unit commitment identical generating units intelligent generation scheduling seamless integration uncertain sources volatile renewable sources future low carbon energy system operators effective flexibility adequacy plans power systems power balance feasible operation economical operation different time horizons different generational constraints environmental constraints technical constraints unit commitment problem Lagrange relaxation framework optimal path identical heat-rate units conventional Lagrange relaxation system size

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A mid-term, market-based power systems planning model

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APPLIED ENERGY 2016年第0期179卷 17-35页

作者： Koltsaklis, Nikolaos E. Dagoumas, Athanasios S. Georgiadis, Michael C. Papaioannou, George Dikaiakos, Christos Univ Piraeus Sch Econ Business & Int Studies Dept Int & European Studies Piraeus 18532 Greece Aristotle Univ Thessaloniki Dept Chem Engn Thessaloniki 54124 Greece Independent Power Transmiss Syst Operator SA ADMI Dept Res Technol & Dev Athens 10443 Greece

This paper presents a generic Mixed Integer Linear Programming (MILP) model that integrates a Midterm Energy Planning (MEP) model, which implements generation and transmission system planning at a yearly level, with a unit commitment (UC) model, which performs the simulation of the Day Ahead Electricity Market. The applicability of the proposed model is illustrated in a case study of the Greek interconnected power system. The aim is to evaluate a critical project in the Ten Year Network Development Plan (TYNDP) of the Independent Power Transmission System Operator S.A. (ADMIE), namely the electric interconnection of the Crete Island with the mainland electric system. The proposed modeling framework identifies the implementation (or not) of the interconnection of the Crete Island with the mainland electric system, as well as the optimum interconnection capacity. It also quantifies the effects on the Day-Ahead electricity market and on the energy mix. The paper demonstrates that the model can provide useful insights into the strategic and challenging decisions to be determined by investors and/or policy makers at a national and/or regional level, by providing the optimal energy road map and management, as well as clear price signals on critical energy projects under real operating and design constraints. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Mixed integer linear programming unit commitment problem Mid-term energy planning Electric interconnections Power markets

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Comparative Analysis of Economic Viability with Distributed Energy Resources on unit commitment

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2016年第14期44卷 1588-1607页

作者： Govardhan, Manisha Roy, Ranjit Sardar Vallabhbhai Natl Inst Technol Dept Elect Engn Surat 395007 Gujarat India

Classic unit commitment is the important and challenging task of allocating generating units subject to basic constraints over a scheduled time horizon to obtain the least generation cost. Penetration of distributed energy resources in modern power systems makes generation planning more complex. This article presents the individual and combined effect of three distributed energy resources, namely wind power generator as a renewable energy source, plug-in electric vehicles, and emergency demand response program on unit commitment. The inconsistent nature of wind speed and wind power is characterized by the Weibull probability distribution function considering overestimation and underestimation costs of stochastic wind power. The comprehensive comparative analysis of the economic viability on unit commitment is carried out to minimize the total cost of the entire system. To obtain the optimum solution, a modified teaching-learning-based optimization algorithm is used. The IEEE standard ten-unit test system is used for this study. To validate the efficacy of the modified teaching-learning-based optimization algorithm, a 26-unit reliability test system is also considered. It is found that the collective effect of wind power generator, plug-in electric vehicles, and emergency demand response program on unit commitment provides significant reduction in the total cost.

关键词： distributed energy resources emergency demand response program modified teaching-learning-based optimization algorithm plug-in electric vehicles teaching-learning based optimization algorithm unit commitment problem Weibull probability distribution function

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An integrated model for risk management in electricity trade

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ENERGY 2017年 124卷 350-363页

作者： Dagoumas, Athanasios S. Koltsaklis, Nikolasos E. Panapakidis, Loannis P. Univ Piraeus Sch Econ Business & Int Studies Energy & Environm Policy Lab 126 Gr Lambraki StrRoom 501 Piraeus 18532 PC Greece Aristotle Univ Thessaloniki Dept Chem Engn Thessaloniki 54124 Greece Technol Educ Inst Thessaly Dept Elect Engn Larisa 41110 Greece

This paper presents an integrated model for risk management of electricity traders. It integrates the unit commitment (UC) problem, which provides the power generation units' dispatch and the electricity price forecasting of a power system, with artificial neural network (ANN) models, which provide electricity price forecasting of a neighbouring power system by incorporating a clustering algorithm. The integrated model is further extended to estimate the traders' profitability and risk, incorporating risk provisions. The integrated model is applied in bi-directional trading between the Italian and Greek day-ahead electricity markets. The UC and neural network models provide forecasts of the wholesale electricity price in Greece and Italy respectively. The model attributes a confidence level of the price forecasts, depending on the data clustering and the forecasting performance of each model. The integrated model identifies periods with high price margins for trading for each power flow, aligned with a forecasting confidence and a risk level. The integrated model can provide price signals on the profitability of traders and useful insights into the risk of traders. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Electricity trade Electricity price forecasting Risk unit commitment problem Artificial neural networks Day-ahead market

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Improved tight and effective two-binary-variable formulations for UC problems

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第9期14卷 1663-1672页

作者： Yang, Linfeng Fang, Beihua Zhang, Chen Li, Wei Guangxi Univ Sch Comp Elect & Informat Guangxi Key Lab Multimedia Commun & Network Techn Nanning 530004 Peoples R China Guangxi Univ Sch Elect Engn Nanning 530004 Peoples R China

This study presents two mixed-integer programmings formulations for the unit commitment (UC) problem. First, the authors proposed a variable upper bound-based UC formulation, which is simultaneously tight and compact. Moreover, the tighter and relatively compact multi-period formulation is also presented. Both formulations ('Multi_New' and 'Mult') are tighter than the previous 2-bin (Base) and the tighter characteristic largely reduces the computational time of the formulations. Compared to the 'Base' formulation, the proposed formulations reduced by at least 6.6%, even 42.1% in the average time of calculation. The proposed models were tested on 73 instances over a scheduling period of 24 and 48 h. Compared to the 'Base' formulation, the initial Gap of 'New' formulation is improved by at least 8.4%. Moreover, compared to 'Multi' formulation, the compactness of 'Multi_New' formulation is improved by at least 33%. In addition, the numeric experiments show dramatic improvements in computational time for their proposed models. They provide evidence that the proposed models have better performance than the previous models.

关键词： integer programming power generation dispatch linear programming power generation scheduling Multi_New formulation computational time two-binary-variable formulations mixed-integer programmings formulations unit commitment problem variable upper bound-based UC formulation Base formulation multiformulation compact multi-period formulation time 24 0 hour time 48 0 hour

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Robust unit commitment with security criteria

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2016年第3期83卷 373-408页

作者： Gourtani, Arash Xu, Huifu Pozo, David Tri-Dung Nguyen Univ Southampton Sch Math Southampton SO17 1BJ Hants England Univ Southampton Sch Math Sci Southampton SO17 1BJ Hants England Pontificia Univ Catolica Chile Ind & Syst Engn Dept Santiago Chile

The short-term unit commitment and reserve scheduling decisions are made in the face of increasing supply-side uncertainty in power systems. This has mainly been caused by a higher penetration of renewable energy generation that is encouraged and enforced by the market and policy makers. In this paper, we propose a two-stage stochastic and distributionally robust modeling framework for the unit commitment problem with supply uncertainty. Based on the availability of the information on the distribution of the random supply, we consider two specific models: (a) a moment model where the mean values of the random supply variables are known, and (b) a mixture distribution model where the true probability distribution lies within the convex hull of a finite set of known distributions. In each case, we reformulate these models through Lagrange dualization as a semi-infinite program in the former case and a one-stage stochastic program in the latter case. We solve the reformulated models using sampling method and sample average approximation, respectively. We also establish exponential rate of convergence of the optimal value when the randomization scheme is applied to discretize the semi-infinite constraints. The proposed robust unit commitment models are applied to an illustrative case study, and numerical test results are reported in comparison with the two-stage non-robust stochastic programming model.

关键词： unit commitment problem Distributionally robust optimization Mixture distribution Sample average approximation Convergence analysis

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Fuzzy based fast dynamic programming solution of unit commitment with ramp constraints

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EXPERT SYSTEMS 2009年第4期26卷 307-319页

作者： Patra, S. Goswami, S. K. Goswami, B. Assam Engn Coll Dept Elect Engn Gauhati Assam India Jadavpur Univ Dept Elect Engn Kolkata W Bengal India

A fast dynamic programming technique based on a fuzzy based unit selection procedure is proposed in this paper for the solution of the unit commitment problem with ramp constraints. The curse of dimensionality of the dynamic programming technique is eliminated by minimizing the number of prospective solution paths to be stored at each stage of the search procedure. Heuristics like priority ordering of the units, unit grouping, fast economic dispatch based on priority ordering, and avoidance of repeated economic dispatch through memory action have been employed to make the algorithm fast. The proposed method produced comparable results with the best performing methods found in the literature.

关键词： dynamic programming unit commitment problem heuristic procedures fuzzy based unit selection

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Linear daily UC model to improve the transient stability of power system

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第13期13卷 2877-2888页

作者： Naghdalian, Salar Amraee, Turaj Kamali, Sadegh KN Toosi Univ Technol Fac Elect Engn Tehran Iran

As coherency of generators decreases, the risk of rotor angle instability increases, especially under severe contingencies. The slow coherency as a network characteristic may be controlled by the locations of committed generators. unit commitment (UC) problem is conventionally carried out regarding operational and network constraints. In this study, a two-step strategy is developed to promote the slow coherency via the network constrained UC (NCUC) model on a daily horizon. First, conventional NCUC is executed. The most important generators with both economic and coherency merits are then determined as representative generators. In the second step, the Slow Coherency Based unit commitment (SCBUC) is re-optimisedaccording to the results obtained from the first step, using a multi-objective function. The first part of the multi-objective function is devoted to the cost of generation, start-up, and shutdown of generators. The goal of the second part of the multi-objective function is to maximise the coherency between the committed generators to reach a transient stability margin. The proposed model is converted to a mixed integer linear programming model. The performance of the proposed method of promoting transient stability is investigated using the dynamic IEEE 118-bus test system.

关键词： linear programming power generation dispatch IEEE standards power generation economics power generation scheduling integer programming power system transient stability load flow power system security linear daily UC model power system generators decreases rotor angle instability increases severe contingencies slow coherency network characteristic committed generators unit commitment problem two-step strategy daily horizon conventional NCUC important generators representative generators multiobjective function transient stability margin mixed integer linear programming model

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Frequency stability improvement in wind-thermal dominated power grids

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第4期14卷 619-627页

作者： Zadeh, Alireza Ashouri Toulabi, Mohammadreza Dobakhshari, Ahmad Salehi Ranjbar, Ali Mohammad Sharif Univ Technol Ctr Excellence Power Syst Management & Control Tehran Iran KN Toosi Univ Technol Dept Elect Engn Tehran Iran Univ Guilan Fac Engn Dept Elect Engn Rasht Iran

With the proliferation of intermittent renewable energy sources, power systems need to withstand an increasing number of disturbances that may affect system frequency. In this paper, we focus on the effects of high penetration level of wind turbine-generators (WTG) on the power system operational planning from the frequency point of view. Specifically, an exact formulation for the minimum frequency calculation is presented to increase accuracy and speed of analyses. Then, the effect of WTG's frequency response on the power system frequency stability is investigated to compute the maximum acceptable generation outage as a function of penetration level. Finally, as an application to power system operational planning, the obtained frequency dynamics of the power system and the wind turbine frequency response are integrated into the unit commitment problem. Simulations are performed on the IEEE 39-bus test system to study the effects of the WTGs on the frequency stability of the system. Results illustrate a more secure and reliable operation of the power system when the wind turbines participate in the frequency regulation task. Moreover, including the frequency response of the wind turbines in the unit commitment problem can reduce the ancillary cost, meanwhile increase the frequency stability of the system.

关键词： frequency response wind turbines power generation scheduling power generation control power grids wind power plants frequency control turbogenerators power generation dispatch power generation planning power distribution control thermal power stations power system stability intermittent renewable energy sources wind turbine generators power system operational planning power system frequency stability frequency dynamics wind turbine frequency response IEEE 39-bus test system frequency regulation task frequency stability improvement wind-thermal dominated power grids WTG frequency response unit commitment problem

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