Mathematical Problems in Engineering

Research Article

A New Hybrid Model Based on Data Preprocessing and an Intelligent Optimization Algorithm for Electrical Power System Forecasting

The actual and forecasted value and APE obtained from MFA-BP, E-BP, and E-MFA-BP and the value of evaluation criteria.


Time	Actual	MFA-BP		E-BP		E-MFA-BP
		Forecasted	APE (%)	Forecasted	APE (%)	Forecasted	APE (%)

Short-term wind speed time series

0:00	7.8	8.5	8.97%	7.9	*1.28%*	8.1	3.85%
4:00	9.6	8.8	8.33%	9.4	*2.08%*	9.3	3.12%
8:00	7.7	7	9.09%	7.3	5.19%	7.4	*3.90%*
12:00	9.5	10.2	7.37%	9.9	4.21%	9.3	*2.11%*
16:00	11.3	10.3	8.85%	12	6.19%	11.8	*4.42%*
20:00	11.9	10.9	8.40%	11.4	4.20%	11.5	*3.36%*

MAPE (%)		6.62%		4.31%		*3.86%*
MAE		0.520		0.497		*0.468*
MSE		0.472		0.392		*0.389*
MPE		11.03%		6.20%		*4.51%*

Electrical load time series

0:00	9185.1	9441.2	2.79%	9315.2	1.42%	9289.7	*1.14%*
4:00	7144.9	7338.2	2.71%	7280.6	1.90%	7253.0	*1.51%*
8:00	10356.9	10579.2	2.15%	10488.6	*1.27%*	10502.5	1.41%
12:00	9950.7	10273.2	3.24%	10215.3	2.66%	10111.4	*1.61%*
16:00	9708.8	9962.4	2.61%	9871.5	1.67%	9797.5	*0.91%*
20:00	11073.1	10724.1	3.15%	10835.6	*2.15%*	10801.1	2.46%

MAPE (%)		2.97%		1.48%		*1.23%*
MAE		103.090		100.401		*95.919*
MSE (10⁴)		2.014		1.651		*1.488*
MPE		3.56%		2.93%		*2.51%*

Electricity price time series

0:00	26.6	29.28	9.91%	28.25	6.04%	27.98	*5.03%*
4:00	18.8	20.68	10.00%	19.95	6.12%	19.83	*5.48%*
8:00	33.7	30.82	8.60%	31.73	5.90%	32.01	*5.07%*
12:00	28.9	31.33	8.22%	30.96	6.94%	30.45	*5.18%*
16:00	29.9	32.47	8.49%	31.63	*5.68%*	31.63	*5.68%*
20:00	34.4	31.84	7.55%	33.06	*4.01%*	32.65	5.20%

MAPE (%)		8.75%		*5.92%*		5.96%
MAE		3.894		2.512		*2.505*
MSE		57.025		30.133		*11.788*
MPE		11.31%		7.07%		*5.98%*