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Robust UC model based on multi-band uncertainty set considering the temporal correlation of wind/load prediction errors

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第2期14卷 180-190页

作者： Chen, Yanbo Zhang, Zhi Chen, Hao Zheng, Huiping North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Sch Elect & Elect Engn Beijing 102206 Peoples R China State Grid Shanxi Elect Power Res Inst Taiyuan 030001 Shanxi Peoples R China

With the increasing proportion of wind power connected to grid, power system dispatching is facing more and more challenges from uncertainty. To cope with this uncertainty, robust optimization has been applied in unit commitment (UC) problem. In this paper, a multi-band uncertainty set considering the temporal correlation (MBUSCTC) of wind/load prediction error is proposed firstly, which has two characteristics: (1) The MBUSCTC rigorously and realistically reflect the distribution characteristics of uncertainties in uncertainty intervals, thereby effectively reducing the conservatism of the traditional singe-band uncertainty set;(2) the temporal correlation constraints of wind power/load prediction errors in MBUSCTC could limit the realization of uncertainties fluctuating frequently in uncertain intervals, thereby eliminating scenarios with lower probability in uncertainty sets. Then the proposed MBUSCTC is applied to UC problem, leading a robust UC model based on MBUSCTC, which is solved by Benders decomposition method and C&CG method. Finally, case studies based on the modified IEEE-118 bus system and an actual power system of China demonstrate that the proposed method can effectively reduce the conservativeness of the robust UC model and ensure the robustness of the unit commitment solution.

关键词： power generation dispatch probability power generation scheduling optimisation load forecasting wind power plants uncertainty sets traditional robust UC models wind power output multiband uncertainty MBUSCTC uncertainty intervals traditional singe-band uncertainty temporal correlation constraints UC problem robust UC model UC solution power system dispatching robust optimisation unit commitment problem

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Three-Stage Robust unit commitment Considering Decreasing Uncertainty in Wind Power Forecasting

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2022年第2期18卷 796-806页

作者： Cho, Youngchae Ishizaki, Takayuki Imura, Jun-Ichi Tokyo Inst Technol Dept Syst & Control Engn Tokyo 1528550 Japan

To ensure powersupply-demand balance under the increasing penetration of wind power, the existing nonanticipative robust unit commitment models (NRUCs) co-optimize the commitment status and the dispatch policy of power sources. Exploiting the fact that the wind power uncertainty reduces over time, this article proposes an NRUC where determining the dispatch policy is delayed until the uncertainty decreases. The proposed NRUC features three decision-making problems sequentially solved under different degrees of uncertainty. The first decision-making problem is formulated as an intractable three-stage robust optimization problem. To solve this problem, a suboptimal approach is developed where a constraint is imposed on the dispatch policy so that the transmission capacity constraint is met regardless of the dispatch level. Results of simulations on a 24-bus and a 300-bus test system show that the proposed NRUC outperforms existing NRUCs regarding feasibility and optimality under currently severe but decreasing wind power uncertainty.

关键词： Uncertainty Wind power generation Generators Forecasting Predictive models Planning Optimization Non-anticipativity power system operations robust optimization unit commitment problem wind power forecasting

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Impact of the penetration of renewables on flexibility needs

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ENERGY POLICY 2017年 109卷 360-369页

作者： Koltsaklis, Nikolaos E. Dagoumas, Athanasios S. Panapakidis, Ioannis P. Univ Piraeus Sch Econ Business & Int Studies Energy & Environm Policy Lab Piraeus 18532 Greece Technol Educ Inst Thessaly Dept Elect Engn Larisa 41110 Greece Aristotle Univ Thessaloniki Dept Chem Engn Thessaloniki 54124 Greece

The paper aims to quantify the impact of the penetration of renewables on the flexibility needs and *** signal. It uses a generic Mixed Integer Linear Programming (MILP) model that integrates long-term power system planning with a unit commitment (UC) model, which performs the simulation of the Day-Ahead Electricity Market (DAEM). The integrated model evaluates the need of flexibility services, under different conditions of renewable penetration. A case study of the Greek interconnected electric system is examined. Results show that the main flexibility needs concern photovoltaics causing the sunset effect, while the needs from stochastic wind are alleviated from the fact that wind output is de-linked from the demand evolution and that wind installations' positions are diversified. The identification of flexibility needs from the Transmission System Operators (TSOs) require detailed data to depict the spatial and technical characteristics of each power system, which can reveal that ramping rates, and not just the magnitude of ramping capacity, can be an important flexibility requirement, due to large single-hour ramp contribution in some months. Such an analysis can also reveal the options for increasing flexibility, which are power system specific.

关键词： Flexibility services Renewable energy resources Power system planning unit commitment problem Ramping capacity

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Exploring the Modeling Capacity of Two-Stage Robust Optimization: Variants of Robust unit commitment Model

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IEEE TRANSACTIONS ON POWER SYSTEMS 2015年第1期30卷 109-122页

作者： An, Yu Zeng, Bo Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA

To handle significant variability in loads, renewable energy generation, as well as various contingencies, (two-stage) robust optimization method has been adopted to construct unit commitment models and to ensure reliable solutions. In this paper, we further explore and extend the modeling capacity of two-stage robust optimization and present two new robust unit commitment variants: the expanded robust unit commitment and the risk constrained robust unit commitment model. We derive structural properties, demonstrate the connection to the popular scenario based stochastic unit commitment models, and present a customized column-and-constraint generation method. Numerical experiments on those models are performed using practical data sets, which illustrate their modeling strength, economic outcomes, and the algorithm performance in solving those models.

关键词： Column-and-constraint generation method robust optimization uncertainty set unit commitment problem

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Hourly optimization and sizing of district heating systems considering building refurbishment - Case study for the city of Zagreb

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ENERGY 2017年 137卷 1264-1276页

作者： Pavicevic, Matija Novosel, Tomislav Puksec, Tomislav Duic, Neven Univ Zagreb Fac Mech Engn & Naval Architecture Dept Energy Power Engn & Environm Ivana Lucica 5 Zagreb 10000 Croatia

District heating plays a crucial role in future energy systems due to its beneficial impacts on the overall flexibility and efficiency of the energy system as a whole. In order to fully utilize its benefits, the sizing and operation of said systems needs to be optimized. This is a computationally difficult task due to a large number of parameters that need to be considered and calculated. Another issue is a need for long optimization horizons of at least one year, in order to capture seasonal, and a small time step of 1 h or less, to capture intraday variations. The goal of this work has been the development and demonstration of an optimization model capable of handling both the sizing and the operation of a district heating system based on a heat only boiler, solar thermal collectors, electric heaters, heat pumps and thermal energy storage units while considering building refurbishment. The model has been implemented on nine scenarios. The results of the analysis have demonstrated the economic and environmental benefits of the utilization of highly efficient and renewable energy sources in the proposed system. (C) 2017 The Authors. Published by Elsevier Ltd.

关键词： District heating MILP optimization Thermal energy storage unit commitment problem Energy planning

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A polyhedral study of the semi-continuous knapsack problem

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MATHEMATICAL PROGRAMMING 2013年第1-2期142卷 169-203页

作者： de Farias, Ismael Regis, Jr. Zhao, Ming Texas Tech Univ Dept Ind Engn Lubbock TX 79409 USA SAS Cary NC USA

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Such structure arises in a wide variety of important problems, e. g. blending and portfolio selection. We show how strong inequalities valid for the semi-continuous knapsack polyhedron can be derived and used in a branch-and-cut scheme for problems with semi-continuous variables. To demonstrate the effectiveness of these inequalities, which we call collectively semi-continuous cuts, we present computational results on real instances of the unit commitment problem, as well as on a number of randomly generated instances of linear programming with semi-continuous variables.

关键词： Semi-continuous variables Mixed-integer programming Disjunctive programming Polyhedral combinatorics Branch-and-cut unit commitment problem

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Optimal generation scheduling and dispatch of thermal generating units considering impact of wind penetration using hGWO-RES algorithm

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APPLIED INTELLIGENCE 2019年第4期49卷 1517-1547页

作者： Bhadoria, Ashutosh Kamboj, Vikram Kumar DAV Univ Dept Elect Engn Jalandhar Punjab India Lovely Profess Univ Sch Elect & Elect Engn Phagwara Punjab India

In order to achieve paramount economy, hybrid renewable energy sources are gaining importance, as renewable sources are costless. Over the past few years wind energy incorporation drew more consideration in the electricity market, as wind power took an affirmative role in energy saving as well as sinking emission pollutants. Recently developed Grey wolf optimizer (GWO) algorithm has conspicuous behavior for verdicting global optima, without getting ensnared in premature convergence. In the proposed research the exploitation phase of the grey wolf optimizer has been further improved using random exploratory search algorithm, which uses perturbed solutions vectors along with previously generated solution vectors. The paper presents a hybrid version of Grey Wolf Optimizer algorithm combined with random exploratory search algorithm (hGWO-RES) for the solution of combinatorial scheduling and dispatch problem of electric power systems. To validate the feasibility of the algorithm, the proposed algorithm has been tested on 23 benchmark problems. To verify the feasibility and efficacy of operation of proposed algorithm on generation scheduling and dispatch of electric power systems, small and medium scale power systems consisting of 7-, 10-, 19-, 20- and 40-generating units systems taken into consideration. commitment and scheduling pattern has been evaluated with and without wind integration and it has been experimentally founded that proposed hybrid algorithm provides superior solution as compared to other recently reported meta-heuristics search algorithms.

关键词： Generation scheduling and dispatch (GSD) Grey wolf optimizer unit commitment problem

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An integrated model for assessing electricity retailer's profitability with demand response

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APPLIED ENERGY 2017年 198卷 49-64页

作者： Dagoumas, Athanasios S. Polemis, Michael L. Univ Piraeus Sch Econ Business & Int Studies Energy & Environm Policy Lab Piraeus 18532 Greece Univ Piraeus Dept Econ Piraeus Greece

This paper introduces a model that integrates a unit commitment (UC) model, which performs the simulation of the day-ahead electricity market, combined with an econometric model that estimates the income and price elasticities of electricity demand. The integrated model is further extended to estimate the retailers' profitability with demand responsive consumers. The applicability of the proposed model is illustrated in the Greek day-ahead electricity market. The model is designed to identify the effects of demand responsiveness to the fluctuations of spot prices, based on their short-term price elasticities. It provides price signals on the profitability of retailers demand aggregators, when forming their tariffs. We argue that the non-linearity between demand response and evolution of wholesale price, inherits risk for retailers. This finding could lead even to losses for some time periods, affecting strongly their viability. The model provides useful insights into the risk of retailers from their price responsive customers and therefore acts as a pivotal study to policy makers and government officials (i.e. regulators, transmission and distribution system operators) active in the electricity market. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Demand response Electricity retailers Day ahead electricity market unit commitment problem Price responsiveness

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Alternative linearisations for the operating cost function of UC problems

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IET GENERATION TRANSMISSION & DISTRIBUTION 2017年第8期11卷 1992-1996页

作者： Geng, Zhaowei Conejo, Antonio J. Xia, Qing Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Ohio State Univ Dept ISE Columbus OH 43210 USA Ohio State Univ Dept ECE Columbus OH 43210 USA

The cost of a generating unit as a function of its power output is generally non-linear and discontinuous. Therefore, the objective function of a unit commitment (UC) problem is generally non-linear and discontinuous as well. The authors describe two efficient piecewise-linear formulations of the objective function of an UC problem that are not found in the power literature. These formulations allow representing non-convexities and discontinuities. They compare these formulations with a common one in the power literature. They show the advantage of the proposed formulations for both deterministic and stochastic UC problems.

关键词： power generation dispatch power generation scheduling alternative linearisations operating cost function unit commitment problem piecewise-linear formulations stochastic UC problem deterministic UC problem

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

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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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