Managing Wind Power Forecast Uncertainty in Electric Grids
Electricity generated from wind power is both variable and uncertain. Wind forecasts provide valuable information for wind farm management, but they are not perfect. Chapter 2 presents a model of a wind farm with compressed air energy storage (CAES) participating freely in the day-ahead electricity market without the benefit of a renewable portfolio standard or production tax credit. CAES is used to reduce the risk of committing uncertain quantities of wind energy and to shift dispatch of wind generation to high price periods. Using wind forecast data and market prices from 2006 – 2009, we find that the annual income for the modeled wind-CAES system would not cover annualized capital costs. We also estimate market prices with a carbon price of $20 and $50 per tonne CO2 and find that the revenue would still not cover the capital costs. The implied cost per tonne of avoided CO2 to make a wind-CAES profitable from trading on the day-ahead market is roughly $100, with large variability due to electric power prices.
Wind power forecast errors for aggregated wind farms are often modeled with Gaussian distributions. However, data from several studies have shown this to be inaccurate. Further, the distribution of wind power forecast errors largely depends on the wind power forecast value. The few papers that account for this dependence bin the wind forecast data and fit parametric distributions to the actual wind power in each bin. A method to model wind power forecast uncertainty as a single closed-form solution using a logit transformation of historical wind power forecast and actual wind power data is presented in Chapter 3. Once transformed, the data become close to jointly normally distributed. We show the process of calculating confidence intervals for wind power forecast errors using the jointly normally distributed logit transformed data. This method has the advantage of fitting the entire dataset with five parameters while also providing the ability to make calculations conditioned on the value of the wind power forecast.
The model present in Chapter 3 is applied in Chapter 4 to calculate increases in net load uncertainty introduced from day-ahead wind power forecasts. Our analyses uses data from two different electric grids in the U.S. having similar levels of installed wind capacity with large differences in wind and load forecast accuracy due to geographic characteristics. A probabilistic method to calculate the dispatchable generation capacity required to balance day-ahead wind and load forecast errors for a given level of reliability is presented. Using empirical data we show that the capacity requirements for 95% day-ahead reliability range from 2100 MW to 5600 MW for ERCOT and 1900 MW to 4500 MW for MISO, depending on the amount of wind and load forecast for the next day. We briefly discuss the additional requirements for higher reliability levels and the effect of correlated wind and load forecast errors. Additionally, we show that each MW of additional wind power capacity in ERCOT must be matched by a 0.30 MW day-ahead dispatchable generation capacity to cover 95% of day-ahead uncertainty. Due to the lower wind forecast uncertainty in MISO, the value drops to 0.13 MW of dispatchable capacity for each MW of additional wind capacity.
Direct load control (DLC) has received a lot of attention lately as an enabler of wind power. One major benefit of DLC is the added flexibility it brings to the grid. Utilities in some parts of the U.S. can bid the load reduction from DLC into energy markets. Forecasts of the resource available for DLC assist in determining load reduction quantities to offer. In Chapter 5, we present a censored regression model to forecast load from residential air conditioners using historical load data, hour of the day, and ambient temperature. We tested the forecast model with hourly data from 467 air conditioners located in three different utilities. We used two months of data to train the model and then ran day-ahead forecasts over a six week period. Mean square errors ranged from 4% to 8% of mean air conditioner load. This method produced accurate forecasts with much lower data requirements than physics based forecast models.