**4. Analysis of Load-Diversity**

Since load centres in diverse regions experience different weather conditions throughout a day, the electrical demands of these load centres, which are dependent on weather, also vary. Hence, the electricity demand of the load centres cannot be analyzed with a single ag‐ gregate model. Instead, the aggregate demand for electricity is best explained using multiregion modelling. This section presents an analysis of the twelve conforming load centres and weather data of the control region.

#### **4.1. Aggregate and Multi-Region Load Modelling**

The two approaches for developing load forecasting models include building aggregate models and multi-region models. An aggregate model does not differentiate between load sectors or physical locations. The strength of this approach is that it provides better analysis for load growth trends and is easier to use. An aggregate model performs well for a small geographic area which can include dense and undifferentiated load categories, such as in a suburb. This model type does not support assessing where and when electrical demand will occur throughout the system. As a consequence, aggregate models do not provide adequate inputs for analysis of grid integrity, and statistical modifiers are often applied on the model outputs so as to provide an average assessment of system response [7].

A multi-region model offers a more discrete analysis for distinct loads or load clusters. This model type is useful for large geographic areas where regionalized load profile trends differ considerably, which often results from economic or weather diversity within the forecast area. The benefit of these models is their ability to provide higher resolution prediction re‐ sults within the grid, contributing to analysis of grid integrity. However multi-region mod‐ els are more difficult to construct and operate, as the number of inputs grows with each additional region to the model. Irrespective of whether the aggregate or multi-region ap‐ proach is adopted, constructing a load forecasting model involves considerations of four as‐ pects: trend, cyclicality, seasonality, and a random white noise error [8].

To illustrate the load diversity among the regions, the region code, average load, and peak load for the twelve load centres from the period of January 2005 to December 2011 are listed in Table 3.

It can be observed from the dataset that the regions experience different weather conditions at different times such that the temperature distributions and the variances in temperature are not the same. Table 2 lists the seasonal average daily variation of wind chill temperatures expe‐ rienced by each of the twelve load centres during the period of investigation from January 2005 to December 2011. Significant temperature variation exists among the twelve regions and indi‐

Thus, it can be seen from Tables 1 and 2 that the weather experienced in each of the twelve re‐ gions vary considerably. Weather diversity was evidenced by the seasonal differences, daily wind chill ranges, and distribution of wind chill temperatures among the regions. The evidence for weather diversity supports our proposal for the development of a multi-region model.

Since load centres in diverse regions experience different weather conditions throughout a day, the electrical demands of these load centres, which are dependent on weather, also vary. Hence, the electricity demand of the load centres cannot be analyzed with a single ag‐ gregate model. Instead, the aggregate demand for electricity is best explained using multiregion modelling. This section presents an analysis of the twelve conforming load centres

The two approaches for developing load forecasting models include building aggregate models and multi-region models. An aggregate model does not differentiate between load sectors or physical locations. The strength of this approach is that it provides better analysis for load growth trends and is easier to use. An aggregate model performs well for a small geographic area which can include dense and undifferentiated load categories, such as in a suburb. This model type does not support assessing where and when electrical demand will occur throughout the system. As a consequence, aggregate models do not provide adequate inputs for analysis of grid integrity, and statistical modifiers are often applied on the model

A multi-region model offers a more discrete analysis for distinct loads or load clusters. This model type is useful for large geographic areas where regionalized load profile trends differ considerably, which often results from economic or weather diversity within the forecast area. The benefit of these models is their ability to provide higher resolution prediction re‐ sults within the grid, contributing to analysis of grid integrity. However multi-region mod‐ els are more difficult to construct and operate, as the number of inputs grows with each additional region to the model. Irrespective of whether the aggregate or multi-region ap‐ proach is adopted, constructing a load forecasting model involves considerations of four as‐

outputs so as to provide an average assessment of system response [7].

pects: trend, cyclicality, seasonality, and a random white noise error [8].

vidual load centres experience a considerable range of temperatures in an average day.

**4. Analysis of Load-Diversity**

254 Decision Support Systems

and weather data of the control region.

**4.1. Aggregate and Multi-Region Load Modelling**


**Table 3.** Region Code, Average Load, and Peak Load (January 2005 to December 2011).

It can be seen from Table 3 that the peak load for most load centres tends to be twice the average load, which indicates that considerable load swings are possible within each load centre. The aggregate load model approach would not be able to represent the possible load swings within each centre.

To demonstrate the seasonal trends in electricity demand of the load centres, the hourly aggregate electricity demands of the load centres over four years are shown in Figure 2. In this figure, it can be seen that these seasonal patterns correspond to periodic daily, weekly, and monthly variations. Peaks are found in the winter and summer months, while troughs are found in the spring and autumn months. Limited load growth is found during this period, but a considerable variance is possible within each season, which usu‐ ally results from significant weather diversity.

The dark black line in Figure 2 indicates the seasonal trends of the system. Peaks are found in the winter and summer months and troughs in spring and autumn. These seasonal pat‐ terns correspond to periodic daily, weekly, and monthly variation. Limited load growth is found during this period, but a considerable variance is possible within each season, which usually results from considerable weather diversity.

**Figure 2.** Hourly Aggregate Electricity Demands of Load Centres from January 1, 2005 to December 31, 2008.

#### **4.2. Regional Peaking Responses Versus System Peaking Response**

Demand for electricity is not static and varies according to a multitude of variables. Load centres will peak at certain periods during the day, usually conforming to business cycle and weather-related influences. The system peak response is the aggregate peak of the val‐ ues of all the load centres within a control area, which may occur at a different time from the peak response of an individual load centre. A significant difference in peak response be‐ tween regions and the system constitutes evidence for a diverse load environment. This evi‐ dence can provide motivation for the development of multi-region models.

To determine whether the observed load swings of the studied load centres occurred within the same time frame of the aggregate system response, the coincidence factor C [7, 9] is adopted, which is defined as,

$$C = \frac{\sum P\_i}{P\_A} \tag{1}$$

The load diversity among the twelve load centres was calculated by comparing the peak load of each load centre to the system peak load across an increasing time interval: begin‐ ning with a daily peak to a thirty-one day peak for the period of January 1, 2011 to January

Towards Developing a Decision Support System for Electricity Load Forecast

http://dx.doi.org/10.5772/51306

257

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 **Time Interval (Day)**

**Figure 3.** Average Load Diversity Factor Applied to an Increasing Time Interval (January 1, 2011 to January 31, 2011).

It can be seen from Figure 3 that the results of the diversity factor calculation are greater than 1 and its value increases over greater calculation time intervals. Both facts provide evidence for the existence of load diversity amongst the load centres examined. Considering the data pre‐ sented in Table 3 and Figure 3, it is reasonable to conclude significant load diversity exists throughout the control region. Therefore, both the weather and load diversity observed within the control area provide justification for the development of multi-region forecasting models. The performance of both aggregate and multi-region models will be statistically benchmarked

Three load forecasting models were developed: (1) Similar Day Aggregate Load Model, (2) ANN Aggregate Load Model, and (3) ANN Multi-Region Load Model. The similar day ag‐ gregate load model provides the industry benchmark. The ANN aggregate load model serves as the baseline to show the performance enhancement achieved by the ANN ap‐ proach. The ANN multi-region load model demonstrates the performance enhancement achieved by the multi-region approach. All models were evaluated according to the same performance evaluation methods, which will be described in section 6. The models were tested with the same case study, which will be presented in section 7. A comparison of the characteristics of the models is presented in Table 4 and a comparison of the input variables to the models is presented in Table 5. The research methodology and modelling process for

to identify the best model type and structure for STLF in Saskatchewan.

each of the three models will be described in this section.

31, 2011. The results of this calculation are shown in Figure 3.

1

1.005 1.01 1.015 1.02 1.025 1.03

**Average Diversity Factor**

**5. Load Forecasting Models**

Where, *Pi* is the peak load of a single load centre, and *PA* is the system peak load.

The coincidence factor describes the degree of discrepancy between regional peaking re‐ sponses versus system peaking response. If C is greater than 1 and continues to appreciate across an increasing timeline, the load centres peak at different times than the aggregate sys‐ tem load, which provides evidence for the existence of load diversity among the regions. If C is greater than 1 but remains consistent, an aggregate model can be used to accurately pre‐ dict load swings. In a somewhat consistent or non-diverse system, C will oscillate about 0 and a multi-region model is likely to be of little value in predicting load swings.

The load diversity among the twelve load centres was calculated by comparing the peak load of each load centre to the system peak load across an increasing time interval: begin‐ ning with a daily peak to a thirty-one day peak for the period of January 1, 2011 to January 31, 2011. The results of this calculation are shown in Figure 3.

**Figure 3.** Average Load Diversity Factor Applied to an Increasing Time Interval (January 1, 2011 to January 31, 2011).

It can be seen from Figure 3 that the results of the diversity factor calculation are greater than 1 and its value increases over greater calculation time intervals. Both facts provide evidence for the existence of load diversity amongst the load centres examined. Considering the data pre‐ sented in Table 3 and Figure 3, it is reasonable to conclude significant load diversity exists throughout the control region. Therefore, both the weather and load diversity observed within the control area provide justification for the development of multi-region forecasting models. The performance of both aggregate and multi-region models will be statistically benchmarked to identify the best model type and structure for STLF in Saskatchewan.
