Second load forecasting scenario Brasilia 2001-2003

Brasilia is the federal capital of Brazil. Located at coordinates 15.78S - 47.83W, it was founded in 1960, purpose built to serve as the new national capital closer to Brazil’s geographic center. Currently, Brasilia and its metro area are estimated to be the 4th most populous city in Brazil, and it has the highest GDP per capita among major Latin American cities. The evolution of both population and GDP is shown in Figure 5.32.

Figure 5.32: Evolution of Brasilia’s population and GDP between 1999 and 2014. Credits: CODEPLAN

Besides being the political center, Brasilia is an important economic center, represen- ting 3.76% of the total Brazilian GDP. The main economic activity of the federal capital results from its administrative function, with services accounting for more than 90% of the city’s GDP. The public sector is the largest employer, providing around 40% of the city jobs. Besides the government, the city also hosts the headquarters of important companies, such as the two biggest public banks, the Brazilian postal service and a large telecommunications company.

Located in the middle of the Brazilian highlands, Brasilia has a tropical savanna climate with two distinct seasons. The rainy season occurs from October to April, while the dry season spans from May to September. September is also the hottest month, averaging 21.7 Celsius and maximas of 28.3 Celsius. The coldest month is July, averaging 18.3 Celsius and 12.9 Celsius minima. Relative Humidity oftenly drops below 50% between July and September. Average insolation hours vary from 138 in December to 266 in July, mainly determined by the presence of clouds in the sky.

Figure 5.33: Location of Juscelino Kubistchek International Airport relative to Brasilia and the Federal District. Credits: Google Maps

The historical weather data has been collected from the Juscelino Kubistchek Inter- national Airport METeorological Aerodrome Reports (METAR), located in a central position relative to the larger load centers as shown in Fig. 5.33. Similarly to what occurred in Leipzig weather measurements, METAR data regarding January 2004 is unavailable. As such, the forecasting of Brasilia electric load has been divided in two scenarios: from July 1st 2001 to December 2003 and from February 2004 to June 2010. Coincidently, the first period is concurrent with an electricity supply crysis, while the second coincides with a strong economic growth cycle. The first period is analised in this Subsection, while the second period is the third forecasting scenario analised in Subsection 5.1.3. Peak, average and base load in the first period are illustrated in Figure 5.34.

Figure 5.34: Evolution of electric load in Brasilia, from July 2001 to December 2003. Base load is plotted in black, Average load in blue and Peak load in red.

The proposed and the benchmark forecasting methods are used to predict the total load supplied by Brasilia’s distribution company. This scenario uses a shorter training period of 182 days, between July 1st 2001 to December 31st 2001, while the prediction period comprises 729 days between January 2002 and December 2003. Error metrics are calculated exclusively for the prediction period.

In order to validate the proposed PCA-Kalman load forecasting system (PKF) per- formance, similarly to the Leipzig scenario, the load time series have been forecast by concurrent methods of linear and nonlinear natures. A classical Kalman Filter (KF) without PCA and variance estimation represent the linear approaches, while a classical BP double layer Artificial Neural Network (BP) and a PCA enhanced BP ANN (PBP) are employed to showcase the performance of these nonlinear methods. The Kalman filter methods employ an model order estimation in the initialization phase, in this scenario eight is selected as the size of the state vector, as shown in Figure 5.35.

Figure 5.35: Total Squared Error for the second scenario, as a function of Model Order. The minimum is achieved when the Order is set to 8.

The above described benchmark models are used to forecast base, average and peak demand. For each prediction the four error metrics are calculated. Nine input sets are tested, each designated by a capital letter. The input sets have been described in Chapter 4, Table 4.1. Over the results presented in [87], this work expands the scope by adding the input set H, which includes solar resource and natural illumination inputs.

The forecasting period starts at January 1st 2002 and comprises 729 days. Tables 5.37, 5.38 and 5.39, respectively, summarize results for base, average and peak load forescasting.

Table 5.37: Error metrics for Base load, Brasilia first period Metric Method A B C D E F G H Z MSE PKF 162,8 91,4 114,9 76,4 234,3 189,3 92,1 40,5 39,7 KF 155,1 92,3 137,3 88,1 251,4 218,7 92,1 322,5 322,5 PBP 177,8 336,4 517,0 474,0 130,6 110,5 321,4 392,1 354,8 BP 137,4 348,6 353,4 500,4 165,3 94,3 252,6 388,8 397,7 MAPE PKF 3,05 2,33 2,63 2,12 3,47 3,29 2,26 1,45 1,45 KF 2,99 2,30 2,86 2,24 3,53 3,07 2,26 4,45 4,45 PBP 3,32 4,49 5,64 5,14 2,90 2,69 4,23 4,90 4,55 BP 2,92 4,57 4,47 5,55 3,31 2,39 3,65 4,74 4,80 MPE PKF 20,8 11,8 13,1 11,1 24,6 19,6 15,1 10,7 9,8 KF 20,3 14,5 16,6 14,3 30,4 35,9 15,1 21,5 21,5 PBP 19,3 18,4 21,6 37,4 13,2 13,2 18,9 20,6 18,5 BP 11,8 18,8 20,7 23,0 13,0 11,4 17,7 22,7 22,0

The predictions provided by the PCA-Kalman are compared to the real values in figure 5.36:

Figure 5.36: Prediction (red line) plotted against the measured base load in Brasilia (2001- 2003 period) over 360 days of observation.

Note that all input sets provide reasonable forecasting performance. For the state space approaches, set C slightly outperforms input set A, as D also outperforms B, giving evidence that the performed preprocessing is beneficial to linear predicting algorithms. The ANN methods, however, are negatively affected. Input set F works well with the neural networks. Input set Z combined with the PCA-Kalman load forecasting system provide the best performance.

Table 5.38: Error metrics for Average load, Brasilia first period

Metric Method A B C D E F G H Z MSE PKF 579,0 339,2 454,4 302,2 1403 631,6 204,2 77,4 73,6 KF 554,2 343,4 484,8 338,7 851,8 640,2 204,2 991,7 991,7 PBP 1247 1780 1306 1999 1544 1152 1945 1343 1435 BP 1567 2597 1685 1988 1170 1220 1648 1522 1449 MAPE PKF 3,62 2,90 3,26 2,59 4,71 3,87 2,14 1,06 1,02 KF 3,51 2,89 3,37 2,81 4,16 3,57 2,14 3,90 3,90 PBP 5,79 7,48 6,23 7,72 6,71 5,91 7,33 4,52 4,62 BP 6,69 9,13 7,09 7,54 6,06 6,02 6,75 4,97 4,64 MPE PKF 40,8 18,3 23,4 22,8 54,9 37,0 22,1 6,4 6,9 KF 40,4 18,4 33,6 19,3 39,9 37,0 22,1 38,7 38,7 PBP 28,2 28,8 21,3 33,7 35,2 29,9 30,0 21,1 31,4 BP 36,1 26,4 31,0 40,5 30,9 30,8 25,2 27,0 24,2

Overall, the prediction of average load displays the largest error metrics, probably due to the larger quantity of outliers in this particular time series. The only exception is the PCA- Kalman system, as it shows smaller relative errors at the cost of increased maximum error, as compared with the base load prediction problem. ANN do not seem to perform well in this scenario, displaying large error metrics. The forecasts obtained from the PCA-Kalman are compared to the real values in figure 5.37:

Figure 5.37: Prediction (red line) plotted against the measured average load (blue line) in Brasilia (2001-2003 period) over 360 days of observation.

Table 5.39: Error metrics for Peak load, Brasilia first period

Metric Method A B C D E F G H Z MSE PKF 501,8 294,2 389,2 263,3 1046,3 529,3 189,9 77,4 73,6 KF 491,0 289,5 413,4 275,4 786,4 494,4 189,9 991,7 991,7 PBP 646,0 1365 1079 1476 813,3 550,0 1627 1343 1435 BP 666,1 1988 808,2 1630 587,2 561,5 1205 1522 1449 MAPE PKF 2,63 2,06 2,30 1,88 3,11 2,72 1,69 1,06 1,02 KF 2,60 2,06 2,38 1,98 2,98 2,43 1,69 3,90 3,90 PBP 3,22 4,68 4,20 4,75 3,50 2,99 5,20 4,52 4,62 BP 3,15 5,74 3,63 5,15 3,06 2,79 4,13 4,97 4,64 MPE PKF 27,0 15,4 18,3 14,2 39,4 28,0 8,8 6,4 6,9 KF 27,0 14,8 22,5 14,3 31,5 28,0 8,8 38,7 38,7 PBP 22,4 25,5 16,5 23,5 19,5 15,2 21,6 21,1 31,4 BP 24,5 23,0 17,0 26,7 15,2 25,2 25,6 27,0 24,2

The proposed PCA-Kalman based approach vastly outperforms the other methods for peak load prediction. The KF achieves a MSE almost three times larger, yet forecasting

with good accuracy. ANN methods produce better results when employing input set F.

Overall, the proposed system displays good forecasting performance, being capable of daily predicting demands with MAPE lower than 2 % in all scenarios. In comparison, the linear and nonlinear predictors employed as benchmark could only achieve MAPE lower than 2.5%, at best. The peak load predictions provided by the PCA-Kalman are compared to the real values in figure 5.38:

Figure 5.38: Prediction (red line) plotted against the measured peak load (blue line) in Brasilia (2001-2003 period) over 360 days of observation.