On the Influence of Weather Forecast Errors in Short-Term Load

Forecasting Models

Damien Fay,John V. Ringwood

IEEE POWER SYSTEMS, 2010

Outline

Introduction Data sets Weather forecast errors modeling Fusion model

Preliminary AR linear model Sub-models Fusion algorithm

Results Conclusion

Introduction Short-term load forecasting(STLF) refers to forecast

electricity demand on an hour basis from one to several days ahead.

STLF reduce the amount of excess electricity production by underestimate the load accurately.

In many electricity grid systems, “weather” is an important factor to estimate the load and has been proved that it will improve the prediction accuracy. However, weather forecasts often come with forecasting errors, and cause about 17% to 60% load forecasting errors.

Introduction Main idea in this paper is to combine several

models(called sub-models), or model fusion, as a technique for minimizing the effect of weather forecast errors in load forecasting models.

Model fusion has been widely used in general field forecasting, but this is the first use to deal with forecast errors. The sub-models in fusion algorithm may be trained by actual weather data and the effect of weather forecasting error taken into account when combining models.

Data sets

Weather forecast errors modeling

Previous approach in STLF simply model the weather forecast errors as a IID Gaussian random variable

Weather in Ireland is dominated by Atlantic weather systems. When a weather front reaches Ireland, there is a shift in the level of temperature and other variables. This shift is also an important factor and must be detected.

Turning points represent the arrival of the weather front. And the turning points were found using peak detection algorithm.

Weather forecast errors modeling

Weather forecast errors modeling

In order to generate pseudo-weather forecast errors, the turning points are first identified. Then a multivariate Gaussian pseudo-random number generator is used to generate random errors for each weather variables.

Fusion Model-Preliminary AR linear model

Previously the authors found decomposing load data into 24 parallel series, one for each hour of the day, is advantageous due to these parallel series are independent.

The parallel series for hour on day , , has a trend, , which is first removed using Basic Structural Model(BSM), via an integrated random walk, leaving a residual , which composed of weather, nonlinear auto-regression and white noise components

Fusion Model-Sub-Models

Three sub-models were chosen with different inputs. These are chosen so that forecast errors can be attributed to particular inputs.

A fourth sub-model is included using all the available inputs to capture any nonlinear relationships between the inputs and the residual.

Fusion Model-Sub-Models

The fusion technique combines the forecasts of sub-models to give a fused forecast, of the residual for series on day

Three sub-models all use feed forward neural networks. And all of them are trained using actual data.

𝑥 ( 𝑗 ,𝑘−1 )𝑥 ( 𝑗 ,𝑘−2 )

Fusion Model-Fusion Algorithm

The data fusion algorithm seeks to minimize the variance of the fused forecast based on the covariance matrix of sub-model forecasts.

A combined forecast, of the load is created using weighted average of individual forecasts, ,…, :

where is the weight applied to the forecast from sub-modelfor hour

Fusion Model-Fusion Algorithm

is derived from error covariance matrices of ,…, as

is the sample error covariance of sub-model with sub-model for hour , and M is the number of samples used

Fusion Model-Fusion Algorithm

where=

and the final weight is determined using the constraint that is unbiased:

Fusion Model-Fusion Algorithm

Finally the fused load forecast, , is estimated by reintroducing the trend:

Results-Cases

The results are analyzed for three cases.

Sub-model parameters

estimate

Error covariance matrices estimate

Models evaluate

Case I actual actual actual

Case II actual pseudo pseudo

Case III actual actual pseudo

Results-cross-covariance

The cross-covariance matrix of sub-models forecast errors

Covariance of sub-models 2 to 4 increases when pseudo-weather forecast are used, indicates the degradation of the models due to weather forecast errors.

Results-weights

Corresponding values of , ,

Results-MAPE of cases

Mean absolute percentage error(MAPE)

Case I: Actual weather Case II: pseudo weather forecast

Results-model performance

Conclusion This paper examined the effect of weather

forecast errors in load forecasting models, and found Gaussian distribution was not appropriate in this case.

The proposed method utilizes a combination of forecasts from several load forecasting models(sub-models) to minimizing the effect of weather forecast errors. And finally, the fusion model was shown successfully separate the tasks of model training and rejecting weather forecast errors.