A Distributionally Robust Optimization Model for Unit Commitment Considering Uncertain Wind Power Generation

Xiong, Peng; Jirutitijaroen, Panida; Singh, Chanan

doi:10.1109/tpwrs.2016.2544795

Cited by 295 publications

(128 citation statements)

References 29 publications

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“…Although Beta distribution cannot model the fat tail of the forecast errors perfectly [38], due to its variable kurtosis [38], it is still more suitable than the Gaussian distribution and gives reasonably accurate results [38,39]. Beta PDF has been used in many recent studies [40][41][42][43] and therefore is chosen in this paper to represent wind power forecast errors. The PDF of the Beta distribution is defined as [36]:…”

Section: Scenario Generationmentioning

confidence: 99%

A Framework for Real-Time Optimal Power Flow under Wind Energy Penetration

Mohagheghi

Gabash

2017

Energies

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Developing a suitable framework for real-time optimal power flow (RT-OPF) is of utmost importance for ensuring both optimality and feasibility in the operation of energy distribution networks (DNs) under intermittent wind energy penetration. The most challenging issue thereby is that a large-scale complex optimization problem has to be solved in real-time. Online simultaneous optimization of the wind power curtailments of wind stations and the discrete reference values of the slack bus voltage which leads to a mixed-integer nonlinear programming (MINLP) problem, in addition to considering variable reverse power flow, make the optimization problem even much more complicated. To address these difficulties, a two-phase solution approach to RT-OPF is proposed in this paper. In the prediction phase, a number of MINLP OPF problems corresponding to the most probable scenarios of the wind energy penetration in the prediction horizon, by taking its forecasted value and stochastic distribution into account, are solved in parallel. The solution provides a lookup table for optional control strategies for the current prediction horizon which is further divided into a certain number of short time intervals. In the realization phase, one of the control strategies is selected from the lookup table based on the actual wind power and realized to the grid in the current time interval, which will proceed from one interval to the next, till the end of the current prediction horizon. Then, the prediction phase for the next prediction horizon will be activated. A 41-bus medium-voltage DN is taken as a case study to demonstrate the proposed RT-OPF approach.

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Section: Scenario Generationmentioning

confidence: 99%

A Framework for Real-Time Optimal Power Flow under Wind Energy Penetration

Mohagheghi

Gabash

2017

Energies

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“…This type of model needs to set a large capacity of spinning reserve to ensure the safety of the system operation, which is too conservative and not economical. The second type is the uncertain model, such as probabilistic model [14][15][16][17], fuzzy set theory [18,19], scenario analysis [6,20], stochastic programming theory [21][22][23][24], etc. For example, the authors in Reference [14] regard the forecast error of load demand and wind power as normal distribution, and propose a probabilistic model to estimate the reserve capacity demand.…”

Section: Introductionmentioning

confidence: 99%

Multi-Time Scale Rolling Economic Dispatch for Wind/Storage Power System Based on Forecast Error Feature Extraction

et al. 2018

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This paper looks at the ability to cope with the uncertainty of wind power and reduce the impact of wind power forecast error (WPFE) on the operation and dispatch of power system. Therefore, several factors which are related to WPFE will be studied. By statistical analysis of the historical data, an indicator of real-time error based on these factors is obtained to estimate WPFE. Based on the real-time estimation of WPFE, a multi-time scale rolling dispatch model for wind/storage power system is established. In the real-time error compensation section of this model, the previous dispatch plan of thermal power unit is revised according to the estimation of WPFE. As the regulating capacity of thermal power unit within a short time period is limited, the estimation of WPFE is further compensated by using battery energy storage system. This can not only decrease the risk caused by the wind power uncertainty and lessen wind spillage, but also reduce the total cost. Thereby providing a new method to describe and model wind power uncertainty, and providing economic, safe and energy-saving dispatch plan for power system. The analysis in case study verifies the effectiveness of the proposed model.

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“…Mathematical methodologies introduced above provide some motivation for solving ED problems with ambiguous distribution information of random variables in power system analysis, see recent references . Papers proposed DRO‐based unit commitment (UC) via 2‐stage optimization.…”

Section: Introductionmentioning

confidence: 99%

“…In paper, two types of ambiguous distribution are addressed: a moment model with just known mean values of the random supply variables, and a mixture distribution type with a convex hull of finite known distribution forms. Paper studied UC problem under an ambiguous distribution set of first‐order moment uncertainty (ie, mean condition). In a previous study by Summers et al, a stochastic multiperiod optimal power flow problem is solved on the basis of conditional value and risk, and distributional robustness where the ambiguous distribution is set on equality conditions of mean and variance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A distributionally robust optimization-based risk-limiting dispatch in power system under moment uncertainty

Tong¹,

Luo

Yang

et al. 2017

Int. Trans. Electr. Energ. Syst.

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Summary In this paper, we study the risk‐limiting dispatch (RLD) of power system in the case that the distribution information of random variable is ambiguous. Under an ellipsoidal moment uncertainty of the mean and the covariance matrix, we develop the distributionally robust optimization approach to set up a new RLD model, named robust RLD (RRLD for short). The RRLD considers simultaneously the risk of unsafe operation limit by conditional Value‐at‐Risk management. We further convert the RRLD model into a solvable convex optimization for a special case that the operation constraint is addressed on the overloading transmission current. The new RRLD model is a development and generalization of the traditionary economic dispatch and the RLD approach. Meanwhile, our research extends the distributionally robust optimization application in portfolio problems to a security economic operation of power system. The IEEE‐14 and IEEE‐30 bus system are chosen as numerical test systems. Preliminary numerical examples show the validity of the model and its reformulation.

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A Distributionally Robust Optimization Model for Unit Commitment Considering Uncertain Wind Power Generation

Cited by 295 publications

References 29 publications

A Framework for Real-Time Optimal Power Flow under Wind Energy Penetration

A Framework for Real-Time Optimal Power Flow under Wind Energy Penetration

Multi-Time Scale Rolling Economic Dispatch for Wind/Storage Power System Based on Forecast Error Feature Extraction

A distributionally robust optimization-based risk-limiting dispatch in power system under moment uncertainty

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