EFFECT OF WEATHER ON PREDICTION OF ELECTRICITY DEMAND
Pawan Lingras
Department of Mathematics and Computing Science
Saint Mary's University, Halifax, Nova Scotia, Canada, B3H 3C3
and
Roberto Mannella
Manitoulin Transport, Manitoulin Island, Ontario, Canada

ABSTRACT

Weather changes affect the demand for electricity. Typically, weather variables are used in the prediction of demand for electricity. This paper reports the effect of weather variables on the prediction of hourly electricity demand. The predictions are based on neural network and statistical modeling. The results indicate that, in some cases, the effect of weather is indirectly taken into account by other variables, and explicit use of weather variables may not be necessary. However, the decision to include or exclude weather variables should be analyzed for each individual situation.

INTRODUCTION

Forecasting the demand for electricity is an important issue for a power company. An accurate forecast can result in significant savings for a power company [7]. These forecasts are used for scheduling functions such as hydro-thermal coordination and transaction evaluation as well as for short-term analysis such as dispatcher power flow and optimal power flow [5].

Great Lakes Power (GLP) Limited, located in Sault Ste. Marie, Ontario, Canada, supplies power to approximately 5000 square miles area. The peak power demand is 360MW. GLP’s peak generating capacity is 340MW. Thus, at peak demand and generation, there is a deficit of 20MW of electricity in the customer area. Purchasing additional power from Ontario Hydro makes up this difference. Billing by Ontario Hydro is based on hourly peak consumption. In other words, for an hour, GLP is billed based on the highest consumption reached during that hour. Since factors including preventative maintenance and weather conditions inhibit generating stations from operating at peak capacity, GLP is often making supplemental purchases of power. If the amount of purchased supplemental power can be reduced, there will be significant savings for the electrical utility company. Therefore, having the ability to predict fluctuations in demand is important, allowing the operators of dam telemetry to maximize available output and minimize supplemental purchases.

This paper reports the results of experiments for predicting hourly demand using the power consumption data available until the previous hour. Time delay neural networks and autoregression models are used for the predictions. Both the techniques were employed with historical information of the electricity demand along with the weather data. In order to test the impact of the weather data on prediction accuracy, two different types of models were developed. The first set of models used only the historical electricity demand for previous 168 hours (one week). The second set of models used the corresponding temperatures in addition to the historical demand for previous 168 hours. The results were mixed and different from the experience of some of the previous researchers [1]-[7]. In the past, researchers have used shorter historical data and weather forecast as input. The use of longer historical data is now feasible because of the availability of more powerful computing facilities. The predicted weather data introduces additional complexity in the model, and can introduce weather prediction errors in the computations. The results obtained from the different inputs used in the present study are comparable to (if not better than) previous studies. The data collection for the model recommended by this study is less complicated than the previous studies.

STUDY DATA AND EXPERIMENTAL DESIGN

This section describes the study data and models used to predict hourly power consumption values. 

Consumption and Weather Data

The models were trained using hourly consumption data for the city of Sault Ste. Marie. The weather data consisted of hourly temperature, wind speed, wind direction, cloud cover and air pressure for Sault Ste. Marie, Ontario. Data were available for the entire years of 1992, 1993, 1994, and 1995. Data for the months of January through July were available for 1996. 

Models 
It is assumed that the reader is familiar with basic neural network and autoregression terminology.

The neural network model for the prediction of hourly demand for electricity consists of 168 inputs and one output. The input is historical data from previous 168 hours. The output is the demand for the next hour. General format of the model is:

,	(1)	

where   is the demand for hour j, with n being the next hour. The time delay neural network (TDNN) used in this study had 168 input nodes corresponding to the previous 168 hourly power consumption values and one output for the power consumption to be predicted. The nature of the input nodes is shown in FIG. 1. There was one input to the network, which was the power consumption of the previous hour, and 167 delays of the input.

Eighty-five hidden layer nodes were used based on the general rule of thumb that the number of hidden nodes should be the average of the number of input nodes and the number of output nodes. The TDNN design used in this study did not have delays in the hidden layer. The second neural network had twice as many neurons in the input and hidden layer. The additional input neurons corresponded to the temperatures for previous 168 hours. The structure of these 168 new input neurons was similar as before, i.e. one input of hourly temperature through first input neuron was delayed 167 times through the remaining 167 input neurons. The mathematical form of the second neural network model can be written as:
,	
(2)	

where  is the demand for hour j, and  is the temperature for hour j, with n being the next hour.

The inputs for the autoregression models were similar to the two TDNN models. The first autoregression model used previous 168 hours of power consumption as:
,	
(3)	

where  is the demand for hour j, with n being the next hour.

The input for the second autoregression model included additional 168 variables corresponding to the hourly temperatures as:
,	
(4)	

where  is the demand for hour j and  is the temperature for hour j, with n being the next hour.

The models used in this study are different from the previous studies in two aspects. Unlike previous studies, the present study does not use the predicted weather information. Secondly, the extent of historical demand used as input is longer than the previous studies. If weather forecasts were used, the accuracy of demand predictions would depend on the accuracy of weather predictions. Moreover, weather forecasting will introduce additional complexity to the models. The extended history used in these experiments is based on the fact that newer computers can handle the larger number of input variables.

RESULTS AND DISCUSSION

Table 1 shows the average percentage errors obtained from the neural network and autoregression models for two different sets of inputs. The column Hourly refers to the models that use only the historical electricity demand as input. The column Weather+Hourly refers to the models that use weather information in addition to the historical demand as input. 

Hour	Errors Expressed as Percentages	
	Hourly	Weather+Hourly	
	ANN	Reg.	ANN	Reg.	
Min	3.0	0.4	3.6	0.4	
Max	5.4	1.4	5.6	1.3	

Table 1.	Average Percentage Errors

As can be seen from Table 1, the errors for the first neural network model are in the range 3.0% - 5.4%. This range is similar to the other studies that used neural networks for forecasting the demand for electricity [2][3]. The errors were slightly higher (ranging from 3.6% to 5.6%) for the second neural network model. This may be due to the fact the network had to process a larger amount of information, when weather data was added. The autoregression models, on the other hand, didn't show this anomaly. For autoregression models, the range of average errors were slightly decreased from 0.4%-1.4% to 0.4%-1.3%, when the weather data was added to the analysis. However, these changes in errors due to the addition of weather data are relatively small for either of the techniques. The forecasting errors from these autoregression models are similar to the ones obtained by other researchers for similar statistical models [5]. The errors for autoregression models are significantly lower than the corresponding errors for the neural network models. This seems to indicate that the autoregression model should be used for forecasting demand for electricity in Sault Ste. Marie. The best model in this study is the one that used the historical weather data in addition to the historical demand. However, the small increase in accuracy may not justify additional complexity in the model.

Hour	Errors Expressed as Percentages	
	Hourly	Weather+Hourly	
	ANN	Reg.	ANN	Reg.	
Min.	7.3	1.1	8.7	<1.0	
Max.	13.0	3.7	14.0	3.1	

Table 2. 	95th Percentile Errors

Table 2 shows the 95th percentile errors obtained from the neural network and autoregression models for the two different sets of inputs. The difference between errors for the four models is more pronounced. However, the conclusions are similar to the ones that can be drawn from the average errors reported in Table 1. That is, the autoregression models faired significantly better than the neural network models. The effect of using the weather data is positive for autoregression models, and negative for neural network models. The 95th percentile errors for the first autoregression model tell us that forecasts will be accurate within ±1% to ±3.7% for approximately 350 days in a year. This level of accuracy may not warrant further refinement of the model using the weather data.

CONCLUSIONS

The weather plays an important role in the determination of electricity demand. However, the historical demand is already affected by weather variables. This paper reports the effect of weather variables on the prediction accuracy of electricity demand. The effect of inclusion of weather variables was studied for autoregression and neural network models. The results obtained from the study favor the use of autoregression model for the City of Sault Ste. Marie. However, such a conclusion may not be applicable to other regions. The inclusion of weather data resulted in a small reduction of errors for autoregression models. The errors for neural network models increased slightly with the inclusion of weather data. However, the changes in errors with the addition of weather data were relatively small. Moreover, the forecasting errors for the preferred autoregression model were very small. Therefore, a refined version of the model using the weather data may not be necessary.

ACKNOWLEDGEMENTS

Authors wish to thank the NSERC, Canada and Great Lakes Power Limited, Sault Ste. Marie, Ontario, Canada for the funding of this project.

REFERENCES

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