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 3

Results of CPSO-BD-BPANN.

Hour	Actual demand	Forecasting demand (CPSO-BPANN)	MAPE (demand)	Actual DV	Forecasting DV (CPSO-BPANN)	MAPE (DV)	Actual price	Forecasting price (CPSO-BPANN)	MAPE (price, CPSO-BPANN)	Forecasting price (CPSO-BD-BPANN)	MAPE (price, CPSO-BD-BPANN)	Improvement
0:00	5414.8	5492.2153	1.43%	240.8	219.57536	8.80%	22.49	26.880519	19.52%	25.01289458	11.22%	8.30%	*
0:30	5253.18	5306.663	1.02%	265.4	243.41062	8.30%	19.79	23.418112	18.33%	21.8012801	10.16%	8.17%
1:00	5606.09	5350.7844	4.55%	261.4	267.36513	2.30%	21.45	20.436447	4.73%	20.01302299	6.70%	−1.97%	†
1:30	5419.17	5549.2508	2.40%	276.5	246.72087	10.77%	19.6	23.108165	17.90%	22.49201997	14.76%	3.14%	*
2:00	5239.77	5139.7849	1.91%	307.1	259.74285	15.43%	17.06	21.551401	26.33%	19.78797409	15.99%	10.34%
2:30	5070.66	5082.3405	0.23%	386.2	270.54802	29.94%	13.13	18.729147	42.64%	18.7853548	43.07%	−0.43%	†
3:00	4911.51	4955.8072	0.90%	373.2	336.4826	9.84%	13.16	14.119062	7.29%	14.72827195	11.92%	−4.63%
3:30	4797.44	4789.1308	0.17%	355.9	297.47988	16.41%	13.48	14.636359	8.58%	16.09900721	19.43%	−10.85%
4:00	4715.03	4778.4144	1.34%	393.9	285.25176	27.58%	11.97	15.798302	31.98%	16.75156848	39.95%	−7.96%
4:30	4668.43	4700.7516	0.69%	396.6	298.37235	24.77%	11.77	14.555668	23.67%	15.75464871	33.85%	−10.19%
5:00	4692.85	4720.5633	0.59%	384	289.67213	24.57%	12.22	14.408606	17.91%	16.29622854	33.36%	−15.45%
5:30	4758.21	4764.3251	0.13%	347.6	319.21548	8.16%	13.69	15.334222	12.01%	14.92510684	9.02%	2.99%	*
6:00	4912.88	4884.1285	0.59%	326.4	313.75764	3.88%	15.05	17.408772	15.67%	15.56656418	3.43%	12.24%
6:30	5003.4	5199.2274	3.91%	357.9	311.08704	13.08%	13.98	19.288571	37.97%	16.71309538	19.55%	18.42%
7:00	4960.1	5168.1909	4.20%	331.3	334.2254	0.87%	14.97	17.91098	19.65%	15.46319001	3.29%	16.35%
7:30	5117.18	4922.7543	3.80%	311.6	296.53318	4.85%	16.42	18.762677	14.27%	16.60102342	1.10%	13.16%
8:00	5318.34	5297.6919	0.39%	257.9	290.00561	12.44%	20.62	20.57195	0.23%	18.26754984	11.41%	−11.18%	†
8:30	5495.88	5547.3933	0.94%	212.9	302.2374	41.94%	25.81	25.67494	0.52%	18.35442365	28.89%	−28.36%
9:00	5642.2	5674.7367	0.58%	188.2	218.76175	16.24%	29.98	31.919947	6.47%	25.94025953	13.47%	−7.00%
9:30	5710.65	5767.462	0.99%	177.6	203.63688	14.68%	32.16	36.591638	13.78%	28.32228561	11.93%	1.85%	*
10:00	5768.91	5795.6082	0.46%	169.3	169.44063	0.10%	34.08	38.313277	12.42%	34.20435895	0.36%	12.06%
10:30	5824.49	5821.0626	0.06%	173.7	164.75679	5.15%	33.53	39.638414	18.22%	35.33124535	5.37%	12.85%
11:00	5875.85	5838.2803	0.64%	175	167.62649	4.23%	33.57	38.044351	13.33%	34.82910358	3.75%	9.58%
11:30	5921.07	5908.7385	0.21%	179.8	185.71187	3.28%	32.93	37.171662	12.88%	31.81669919	3.38%	9.50%
12:00	5913.02	5935.1334	0.37%	181.7	176.38607	2.93%	32.54	35.834762	10.13%	33.64853796	3.41%	6.72%
12:30	5895.12	5890.3105	0.08%	188.2	174.95423	7.05%	31.32	35.028453	11.84%	33.66772215	7.50%	4.34%
13:00	5946.73	5896.7971	0.84%	181.7	183.04082	0.74%	32.73	33.400088	2.05%	32.21574978	1.57%	0.48%
13:30	5914.24	6031.6281	1.98%	170.5	175.40448	2.88%	34.69	35.102752	1.19%	34.38696758	0.87%	0.32%
14:00	5856.43	5921.8544	1.12%	187.9	155.72492	17.14%	31.16	37.676124	20.91%	38.02765926	22.04%	−1.13%	†
14:30	5849.54	5825.7947	0.41%	191.9	179.74411	6.31%	30.49	33.492881	9.85%	32.41160238	6.30%	3.55%	*
15:00	5887.96	5880.9772	0.12%	183.1	193.4568	5.63%	32.15	32.229431	0.25%	30.39943415	5.44%	−5.20%	†
15:30	5890.44	5957.7337	1.14%	168.5	173.90229	3.18%	34.95	34.471827	1.37%	34.25908615	1.98%	−0.61%
16:00	5979.28	5922.67	0.95%	146.3	152.40082	4.20%	40.88	38.232693	6.48%	38.86245512	4.94%	1.54%	*
16:30	6233.19	6108.8388	1.99%	138.9	127.597	8.15%	44.87	45.338569	1.04%	47.87603855	6.70%	−5.66%	†
17:00	6581.07	6619.2217	0.58%	103.9	119.09502	14.57%	63.31	49.906215	21.17%	55.5793317	12.21%	8.96%	*
17:30	6822.35	6799.2178	0.34%	77.35	92.64065	19.77%	88.2	69.094306	21.66%	73.39345962	16.79%	4.87%	†
18:00	6742.56	6848.7633	1.58%	84.82	88.597835	4.45%	79.49	90.229561	13.51%	77.30170033	2.75%	10.76%	*
18:30	6595.51	6704.684	1.66%	107.9	79.521754	26.30%	61.13	81.428552	33.21%	84.3125764	37.92%	−4.72%	†
19:00	6362.9	6425.7627	0.99%	138.1	115.19771	16.61%	46.06	60.10706	30.50%	55.78029774	21.10%	9.39%	*
19:30	6299.54	6270.3806	0.46%	141.5	148.37372	4.86%	44.52	41.978859	5.71%	42.26072192	5.07%	0.63%
20:00	6203.49	6217.1247	0.22%	142.7	152.30635	6.70%	43.46	40.572231	6.64%	40.81986587	6.07%	0.57%
20:30	6085.82	6108.2877	0.37%	149.5	154.24126	3.20%	40.72	40.786703	0.16%	39.60216314	2.75%	−2.58%	†
21:00	5937.52	5882.9523	0.92%	166.5	160.28586	3.73%	35.66	39.121866	9.71%	36.70287807	2.92%	6.78%	*
21:30	5772.1	5914.9629	2.48%	189.4	168.41194	11.10%	30.47	34.602221	13.56%	35.12199356	15.27%	−1.71%	†
22:00	5584.53	5668.5092	1.50%	178.4	178.40287	9.31𝐸−05	31.3	28.618536	8.57%	31.7736434	1.51%	7.05%	*
22:30	5421.07	5528.3863	1.98%	209.9	177.88209	15.24%	25.83	30.635709	18.61%	31.07893729	20.32%	−1.72%	†
23:00	5605	5365.2112	4.28%	189.4	214.68836	13.38%	29.6	25.656578	13.32%	24.99069397	15.57%	−2.25%
23:30	5484.05	5522.2096	0.70%	220.2	193.76899	11.99%	24.91	30.594098	22.82%	28.49893352	14.41%	8.41%	*
Average	5645.03	5660.4733	1.23%	222.7	208.90924	10.79%	30.9	33.091943	14.18%	31.80895055	12.31%	1.87%	‡
Variance	555.278	558.35349	1.18%	88.95	70.212986	8.96%	16.48	16.238851	10.18%	16.02614904	11.05%	8.87%