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Near-term output forecast of wind electric generators (WEG) has uncertainties. Optimal power flow (OPF) schedules that consider forecasted output of WEGs carry risk due to these uncertainties. This risk can be quantified as expected energy not served (EENS). Traditional methods such as Monte Carlo simulation (MCS) with OPF can capture the stochastic nature of WEG output while considering ac transmission system constraints to simultaneously minimize risks from EENS and total operating costs, analyze influence of wind variability on total costs, correlate reserves and wind variability, etc. However, the MCS technique is extremely time consuming and computationally burdensome. This paper proposes a new triangular approximate distribution (TAD) model that very closely represents the normal probabilistic distribution function of forecasted wind speed to capture stochastic information of WEG output forecast and quantify EENS. This TAD model is used to formulate the proposed OPF method considering ac transmission systems to: 1) simultaneously minimize risk due to EENS and total operating costs and 2) analyze the impact of wind variability on system parameters such as EENS, operating costs, location marginal prices, and reserve costs. Tests on IEEE test systems reveal that the proposed method is accurate, fast, and suitable for real-time use.
Date of Publication: Nov. 2012