Load Forecasting using Multivariable Regression

In layman's terms, Load forecasting is basically a technique which is used by energy providing companies to predict the energy needed to meet the demand and maintain an equilibrium. The forecasting helps the companies in the operation and management of the supply to their customers and is a mandatory tool for the proper functioning of the electrical industry.

The objective of load forecasting is to enhance the utility of the energy that is being produced. It is a rather difficult and uncertain task as the load series is complex and dependent on a lot of variables, like changes in the supply demand curve, fluctuation of energy prices during peak seasons, and very high variability of weather conditions. Because of the high dependence on weather conditions, the output can not be guaranteed at any particular point.

Depending on the time zones of planning strategies, Load forecasting can broadly be classified into three categories namely:

1. Short term load forecasting: It usually has a period ranging from one hour to one week. This helps provide information about daily operations while preventing overloading.
2. Medium term load forecasting: Its period ranges from a week to an year. It is important to schedule supplies and the management of the unit.
3. Long term load forecasting: It has a period of more than a year and helps predict the future need of expansion and equipment purchase.

Our main objective is to minimize the Load forecast error. ie, The difference between the actual load and the Load forecast.

The accuracy of the forecast can be improved by studying statistical models and develop a mathematical theory that explains the convergence of these algorithms. Statistical approaches like Multiple linear regression are usually preferred over the black box approaches like that of Artificial neural networks. Regression is one of the most widely used techniques as it is helpful in establishing a relationship between load consumption and other factors such as weather, day type, season, holidays etc.

Multiple Regression

Multivariable Regression is used in load forecasting when the predictor variable Y is set to be a function of more than one variable. A linear regression model is given as:

where,

Ŷ(k) is the estimated load for the next year, Xᵢ(k) are the multiple variables, aᵢ are the model parameters to be computed and λ is the number of years span considered in the forecasting process.

It is also possible to have a non-linear relationship between the load estimate and the variables. An mᵗʰ order polynomial has the form:

where, aᵢⱼ are the unknown parameters which are to be computed.

Some examples of the multiple variables Xᵢ(k) can be temperature, humidity, wind speed and cloud density.

Since no forecast is absolutely correct, there are ways we can improve our forecast. Some of the ways which can be adopted to understand the errors we obtain are as follows:

• Due to uncertainty in long term weather and economy forecasts in long term load forecasting, the load forecasting may incur some significant errors. It is very important to understand how much error is contributed by modelling error, weather forecast error and other sources. Breaking down the error improves interpretability and also increases the utility of forecasts.
• One of the best practices is to combine various forecasting models and try to create a hybrid which offers more accurate results.

Sources

1. N. Amral, C. S. Ozveren and D. King, "Short term load forecasting using Multiple Linear Regression," 2007 42nd International Universities Power Engineering Conference, Brighton, 2007, pp. 1192-1198.
2. Anwar, Tahreem & Sharma, Bhaskar & Chakraborty, Koushik & Sirohia, Himanshu. (2018). Introduction to Load Forecasting. International Journal of Pure and Applied Mathematics. 119. 1527-1538. 
3. T. Haida and S. Muto, "Regression based peak load forecasting using a transformation technique," in IEEE Transactions on Power Systems, vol. 9, no. 4, pp. 1788-1794, Nov. 1994.