A probabilistic approach to solve the economic dispatch problem with intermittent renewable energy sources

In this paper, a methodology for solving the ED (economic dispatch) problem considering the uncertainty of wind power generation and generators reliability is presented. The corresponding PDF (probability distribution function) of available wind power generation is discretized and introduced in the optimization problem in order to probabilistically describe the power generation of each thermal unit, wind power curtailment, ENS (energy not supplied), excess of power generation, and total generation cost. The reliability of each unit is incorporated by estimating the joint PDF of power generation and failure events, while the PDF of ENS is incorporated by convoluting the PDF of ENS due to the forecasting error and any failure event. The performance of the proposed approach is analyzed by studying two power systems of 5 and 10 units. The proposed method is compared to MCS (Monte Carlo Simulation) approach, being able to reproduce the PDF in a reasonable manner, specifically when system reliability is not taken into account.

[1]  David R. Cocker,et al.  Emissions of regulated pollutants from in-use diesel back-up generators , 2006 .

[2]  Patrick A. Narbel,et al.  Global wind power development: Economics and policies , 2013 .

[3]  Wei-Jen Lee,et al.  Studies on stochastic unit commitment formulation with flexible generating units , 2010 .

[4]  Jin Lin,et al.  A Versatile Probability Distribution Model for Wind Power Forecast Errors and Its Application in Economic Dispatch , 2013, IEEE Transactions on Power Systems.

[5]  S. Tewari,et al.  A Statistical Model for Wind Power Forecast Error and its Application to the Estimation of Penalties in Liberalized Markets , 2011, IEEE Transactions on Power Systems.

[6]  Maria Grazia De Giorgi,et al.  Error analysis of short term wind power prediction models , 2011 .

[7]  Kenneth Bruninx,et al.  A Statistical Description of the Error on Wind Power Forecasts for Probabilistic Reserve Sizing , 2014, IEEE Transactions on Sustainable Energy.

[8]  Neil Strachan,et al.  The uncertain but critical role of demand reduction in meeting long-term energy decarbonisation targets , 2014 .

[9]  David Pozo-Vázquez,et al.  A methodology for evaluating the spatial variability of wind energy resources: Application to assess the potential contribution of wind energy to baseload power , 2014 .

[10]  Wilsun Xu,et al.  Economic Load Dispatch Constrained by Wind Power Availability: A Here-and-Now Approach , 2010, IEEE Transactions on Sustainable Energy.

[11]  Jizhong Zhu,et al.  Optimization of Power System Operation , 2009 .

[12]  A. Llombart,et al.  Statistical Analysis of Wind Power Forecast Error , 2008, IEEE Transactions on Power Systems.

[13]  Sangmin Lee,et al.  A Computational Framework for Uncertainty Quantification and Stochastic Optimization in Unit Commitment With Wind Power Generation , 2011, IEEE Transactions on Power Systems.

[14]  Peter B. Luh,et al.  Grid Integration of Intermittent Wind Generation: A Markovian Approach , 2014, IEEE Transactions on Smart Grid.

[15]  Yongpei Guan,et al.  Unified Stochastic and Robust Unit Commitment , 2013, IEEE Transactions on Power Systems.

[16]  Jamshid Aghaei,et al.  Multi-objective self-scheduling of CHP (combined heat and power)-based microgrids considering demand response programs and ESSs (energy storage systems) , 2013 .

[17]  Chongqing Kang,et al.  Modeling Conditional Forecast Error for Wind Power in Generation Scheduling , 2014, IEEE Transactions on Power Systems.

[18]  Hongbin Sun,et al.  A New Real-Time Smart-Charging Method Considering Expected Electric Vehicle Fleet Connections , 2014, IEEE Transactions on Power Systems.

[19]  Qianfan Wang,et al.  A chance-constrained two-stage stochastic program for unit commitment with uncertain wind power output , 2012, 2012 IEEE Power and Energy Society General Meeting.

[20]  B. F. Hobbs,et al.  Commitment and Dispatch With Uncertain Wind Generation by Dynamic Programming , 2012, IEEE Transactions on Sustainable Energy.

[21]  Kumudhini Ravindra,et al.  Decentralized demand–supply matching using community microgrids and consumer demand response: A scenario analysis , 2014 .

[22]  Roy Billinton,et al.  Reliability evaluation of power systems , 1984 .

[23]  Tomonobu Senjyu,et al.  A technique for unit commitment with energy storage system , 2007 .

[24]  R. Chedid,et al.  Probabilistic performance assessment of wind energy conversion systems , 1999 .

[25]  Antonio Punzo,et al.  Discrete approximations of continuous and mixed measures on a compact interval , 2012 .

[26]  Ebrahim Farjah,et al.  An efficient scenario-based and fuzzy self-adaptive learning particle swarm optimization approach for dynamic economic emission dispatch considering load and wind power uncertainties , 2013 .

[27]  David C. Yu,et al.  An Economic Dispatch Model Incorporating Wind Power , 2008, IEEE Transactions on Energy Conversion.

[28]  Peter J. G. Pearson,et al.  The role of large scale storage in a GB low carbon energy future: Issues and policy challenges , 2011 .

[29]  Wilsun Xu,et al.  Minimum Emission Dispatch Constrained by Stochastic Wind Power Availability and Cost , 2010, IEEE Transactions on Power Systems.

[30]  M. O'Malley,et al.  Unit Commitment for Systems With Significant Wind Penetration , 2009, IEEE Transactions on Power Systems.

[31]  Xian Liu,et al.  Economic Load Dispatch Constrained by Wind Power Availability: A Wait-and-See Approach , 2010, IEEE Transactions on Smart Grid.

[32]  Bri-Mathias Hodge,et al.  Wind power forecasting error distributions over multiple timescales , 2011, 2011 IEEE Power and Energy Society General Meeting.

[33]  P. Sauer,et al.  Uncertainty Management in the Unit Commitment Problem , 2009, IEEE Transactions on Power Systems.