Abstract and Applied Analysis

Research Article

A Hybrid Forecasting Model Based on Bivariate Division and a Backpropagation Artificial Neural Network Optimized by Chaos Particle Swarm Optimization for Day-Ahead Electricity Price

Table 5

Results of case 2 study (CPSO-BPANN and BD-BPANN).
HourMarch 10thMarch 11thMarch 12thMarch 13thMarch 14thMarch 15thMarch 16th
CPSO-BPANNBD-BPANNCPSO-BPANNBD-BPANNCPSO-BPANNBD-BPANNCPSO-BPANNBD-BPANNCPSO-BPANNBD-BPANNCPSO-BPANNBD-BPANNCPSO-BPANNBD-BPANN
0:0024.84%7.68%11.00%10.90%1.19%0.20%13.93%9.23%6.57%5.93%9.85%4.47%11.20%5.79%
0:303.97%6.62%11.81%8.95%5.67%0.14%1.60%2.32%18.90%8.18%6.47%10.29%4.84%5.44%
1:0010.89%12.39%9.81%11.63%11.43%3.46%4.46%3.15%30.53%9.04%9.75%10.12%10.15%3.53%
1:3043.24%29.28%14.46%8.34%16.35%17.88%17.41%14.99%18.26%11.95%18.06%5.55%10.02%10.60%
2:008.82%11.14%5.26%6.67%16.49%13.42%8.60%1.41%24.53%10.87%17.65%4.76%13.13%10.52%
2:3024.27%25.43%2.12%4.11%16.42%15.51%4.84%1.22%37.32%4.88%14.36%1.02%1.68%2.19%
3:0010.35%14.93%13.20%9.72%11.65%4.03%0.58%4.57%41.35%3.10%3.31E-051.89%0.38%0.85%
3:301.24%3.19%1.64%10.06%20.59%18.19%0.08%6.57%48.48%11.47%2.08%4.17%1.28%2.74%
4:004.07%11.62%1.63%8.41%13.82%12.88%1.42%3.05%50.32%12.51%2.94%3.19%0.18%1.38%
4:301.73%10.50%2.59%5.66%15.30%18.45%16.66%14.25%58.04%11.31%5.51%5.95%0.74%0.06%
5:003.82%9.62%26.84%29.81%21.57%21.21%21.31%19.48%55.06%20.70%8.89%8.59%0.24%1.05%
5:300.18%6.04%16.35%9.77%6.18%4.89%4.43%8.77%29.33%3.08%10.77%14.16%1.04%0.92%
6:008.54%4.65%1.36%10.10%5.62%11.51%8.07%5.32%10.05%23.27%0.67%0.36%1.89%0.08%
6:307.65%2.86%19.30%20.07%17.10%14.21%6.47%9.54%44.25%29.30%7.99%8.26%2.81%0.76%
7:007.80%2.31%43.34%42.89%35.03%39.22%23.57%19.97%10.96%6.97%15.49%20.04%2.03%0.43%
7:306.89%10.37%5.12%1.42%6.19%2.99%0.90%1.45%25.48%11.00%8.35%10.67%9.00%10.59%
8:002.66%3.66%20.24%15.58%9.43%8.69%11.98%13.45%23.35%24.39%22.27%21.40%13.98%14.70%
8:303.05%2.89%2.03%4.01%6.92%10.64%8.17%5.79%19.30%6.85%21.01%17.20%12.23%12.43%
9:002.26%1.16%7.45%19.91%0.04%2.09%15.56%15.37%31.05%24.43%15.61%8.50%9.17%9.22%
9:3010.48%7.50%20.38%6.20%27.06%28.82%3.63%8.60%31.39%18.20%21.27%26.97%4.76%4.46%
10:005.32%4.34%14.48%13.36%21.69%17.97%10.87%1.38%26.45%18.38%11.12%9.89%15.55%14.01%
10:3010.36%11.26%13.92%12.93%1.87%5.03%18.15%28.11%38.69%18.89%20.57%0.68%4.74%7.05%
11:0011.33%6.91%14.35%19.48%6.16%3.50%8.11%14.30%30.56%19.16%5.19%18.60%16.05%17.81%
11:3011.92%10.42%11.68%6.03%5.05%0.02%14.52%12.38%20.98%9.67%12.05%16.89%8.33%12.70%
12:0039.24%36.91%6.74%25.63%0.17%3.34%9.86%12.17%2.97%13.19%8.54%15.92%6.15%11.48%
12:3010.27%14.18%0.02%11.06%26.01%27.82%10.20%14.66%15.52%5.54%2.37%12.21%1.90%3.77%
13:0026.71%10.66%3.41%0.18%3.61%12.88%6.51%10.00%20.31%33.87%0.20%14.10%0.95%6.47%
13:3034.96%26.82%3.12%13.24%6.51%15.07%6.38%6.90%73.27%5.40%0.83%14.00%4.27%8.93%
14:0016.67%13.80%6.39%9.31%1.39%8.02%21.17%16.98%87.29%7.33%2.27%12.63%31.34%30.79%
14:3043.77%56.10%7.96%6.63%8.46%16.93%41.29%40.22%19.65%17.94%12.88%22.76%62.99%67.56%
15:0074.23%16.29%1.32%14.35%1.49%8.73%54.92%62.31%59.84%71.38%9.31%23.32%47.70%9.33%
15:303.02%35.42%7.13%8.44%6.71%4.47%68.29%53.43%39.37%59.22%1.79%15.50%46.12%23.08%
16:0037.97%21.15%9.01%5.52%17.96%3.56%24.37%6.58%22.17%18.36%4.90%9.69%35.95%10.88%
16:3025.87%20.25%15.63%0.49%11.67%10.57%68.22%20.05%8.35%20.36%3.02%11.14%28.08%17.43%
17:00103.16%52.47%45.55%29.45%30.19%43.40%42.99%0.34%66.01%7.56%1.77%13.53%2.77%45.72%
17:3011.22%47.06%2.21%3.42%3.64%2.06%52.72%2.37%77.97%14.63%13.21%1.97%32.22%14.49%
18:0045.89%10.40%3.31%5.82%7.45%8.69%6.44%24.83%128.32%12.45%22.66%4.74%5.06%5.22%
18:3041.12%10.72%1.37%6.49%15.47%19.01%2.22%17.09%8.10%23.79%4.50%12.66%62.57%5.01%
19:009.13%16.77%5.28%2.60%10.51%11.20%38.34%25.85%13.67%15.43%2.23%9.20%19.47%5.37%
19:3018.20%8.45%27.32%24.56%1.96%2.24%74.99%25.86%178.85%28.94%37.95%23.21%27.88%0.87%
20:0021.36%21.35%0.21%3.48%13.16%4.95%10.94%10.84%29.96%18.78%34.45%16.74%29.54%8.69%
20:3025.51%6.41%2.24%10.55%10.49%10.06%13.27%18.69%25.38%13.01%5.99%10.33%17.64%26.62%
21:003.24%2.77%5.90%8.65%5.09%3.23%6.94%1.58%38.73%11.07%7.83%2.41%5.65%1.85%
21:3026.63%11.13%18.37%15.87%21.87%19.18%15.63%19.67%1.59%5.79%52.19%43.13%35.43%29.07%
22:009.78%16.58%1.89%0.09%9.34%16.09%11.35%10.64%10.45%5.76%6.34%19.69%5.55%2.55%
22:303.26%3.58%7.81%0.94%20.26%18.16%15.32%25.75%7.81%13.00%13.31%3.44%9.06%2.83%
23:001.58%7.07%16.49%11.25%16.71%16.87%2.52%4.65%22.99%12.57%2.40%6.08%2.19%5.73%
23:302.11%2.18%9.49%8.29%3.64%0.52%2.12%1.18%8.88%11.43%8.01%1.11%3.67%0.90%
Mean17.93%14.28% 10.39% 10.88%11.51% 11.71%17.34%13.69% 35.39%16.05% 10.98% 11.52%14.16%10.29%
Std.20.16%12.93%10.02%8.59%8.40%9.62%18.95%12.85%32.41%12.73%10.40%8.35%16.17%12.57%