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 2

Results of BD-BPANN.

Hour	Actual demand	Forecasting demand (BPANN)	MAPE (demand)	Actual DV	Forecasting DV (BPANN)	MAPE (DV)	Actual price	Forecasting price (BPANN)	MAPE (price, BPANN)	Forecasting price (BD-BPANN)	MAPE (price, BD-BPANN)	Improvement
0:00	5414.8	5442.3104	0.51%	240.8	215.49331	10.50%	22.49	27.594881	22.70%	25.25512481	12.29%	10.40%	*
0:30	5253.18	5284.0131	0.59%	265.4	232.03984	12.58%	19.79	22.490634	13.65%	22.77200803	15.07%	−1.42%	†
1:00	5606.09	5266.4948	6.06%	261.4	248.91589	4.76%	21.45	21.258555	0.89%	21.15772899	1.36%	−0.47%
1:30	5419.17	5339.1006	1.48%	276.5	247.95654	10.32%	19.6	22.055641	12.53%	21.53240496	9.86%	2.67%	*
2:00	5239.77	5235.039	0.09%	307.1	261.63496	14.82%	17.06	21.746225	27.47%	20.00894253	17.29%	10.18%
2:30	5070.66	5112.8046	0.83%	386.2	280.15216	27.46%	13.13	18.772312	42.97%	18.25009901	39.00%	3.98%
3:00	4911.51	5134.0262	4.53%	373.2	291.94975	21.77%	13.16	15.194394	15.46%	17.5853074	33.63%	−18.17%	†
3:30	4797.44	4829.5796	0.67%	355.9	288.04488	19.06%	13.48	14.110274	4.68%	16.76676069	24.38%	−19.71%
4:00	4715.03	4753.9841	0.83%	393.9	290.25239	26.31%	11.97	15.899535	32.83%	16.3787943	36.83%	−4.00%
4:30	4668.43	4646.7215	0.47%	396.6	293.38185	26.03%	11.77	15.2975	29.97%	15.83847612	34.57%	−4.60%
5:00	4692.85	4754.847	1.32%	384	293.45887	23.58%	12.22	14.34174	17.36%	16.2027717	32.59%	−15.23%
5:30	4758.21	4832.7262	1.57%	347.6	292.35656	15.89%	13.69	15.517764	13.35%	16.53024745	20.75%	−7.40%
6:00	4912.88	4924.456	0.24%	326.4	284.52861	12.84%	15.05	16.922151	12.44%	17.3074197	15.00%	−2.56%
6:30	5003.4	5140.7882	2.75%	357.9	280.17246	21.72%	13.98	19.766599	41.39%	18.34865658	31.25%	10.14%	*
7:00	4960.1	5143.8833	3.71%	331.3	288.59885	12.90%	14.97	19.594035	30.89%	17.8236444	19.06%	11.83%
7:30	5117.18	4938.0315	3.50%	311.6	282.69038	9.29%	16.42	19.072568	16.15%	17.46798557	6.38%	9.77%
8:00	5318.34	5357.6693	0.74%	257.9	278.11501	7.83%	20.62	21.63026	4.90%	19.26422207	6.58%	−1.68%	†
8:30	5495.88	5525.5037	0.54%	212.9	245.17048	15.14%	25.81	24.911201	3.48%	22.53739351	12.68%	−9.20%
9:00	5642.2	5629.6762	0.22%	188.2	203.71598	8.25%	29.98	31.321237	4.47%	27.63492669	7.82%	−3.35%
9:30	5710.65	5771.7986	1.07%	177.6	177.64214	0.04%	32.16	35.888593	11.59%	32.49115641	1.03%	10.56%	*
10:00	5768.91	5738.3228	0.53%	169.3	161.25699	4.74%	34.08	37.976947	11.43%	35.58495464	4.42%	7.02%
10:30	5824.49	5827.4595	0.05%	173.7	159.3596	8.26%	33.53	39.714597	18.44%	36.56798612	9.06%	9.38%
11:00	5875.85	5875.5412	0.01%	175	168.03384	4.00%	33.57	39.576878	17.89%	34.96641707	4.16%	13.73%
11:30	5921.07	5914.5372	0.11%	179.8	177.5588	1.25%	32.93	38.320271	16.37%	33.31030251	1.15%	15.21%
12:00	5913.02	5965.4175	0.89%	181.7	184.585	1.58%	32.54	37.36692	14.83%	32.3179965	0.68%	14.15%
12:30	5895.12	5903.9873	0.15%	188.2	180.62093	4.04%	31.32	35.282581	12.65%	32.68717122	4.37%	8.29%
13:00	5946.73	5898.7832	0.81%	181.7	186.44404	2.62%	32.73	33.633542	2.76%	31.63835756	3.34%	−0.57%	†
13:30	5914.24	6046.6289	2.24%	170.5	178.24	4.55%	34.69	34.40681	0.82%	33.92408544	2.21%	−1.39%
14:00	5856.43	5895.5677	0.67%	187.9	162.70022	13.43%	31.16	37.333873	19.81%	36.23576938	16.29%	3.52%	*
14:30	5849.54	5824.1822	0.43%	191.9	182.44249	4.90%	30.49	33.800372	10.86%	31.92338672	4.70%	6.16%
15:00	5887.96	5915.1964	0.46%	183.1	187.82561	2.56%	32.15	31.37679	2.41%	31.49302427	2.04%	0.36%
15:30	5890.44	5984.3436	1.59%	168.5	179.66382	6.60%	34.95	34.276918	1.93%	33.30856348	4.70%	−2.77%	†
16:00	5979.28	5932.6459	0.78%	146.3	159.13812	8.80%	40.88	37.643712	7.92%	37.27985404	8.81%	−0.89%
16:30	6233.19	6118.3096	1.84%	138.9	134.84939	2.93%	44.87	45.104528	0.52%	45.37143043	1.12%	−0.59%
17:00	6581.07	6525.8842	0.84%	103.9	129.07518	24.17%	63.31	49.75938	21.40%	50.55878385	20.14%	1.26%	*
17:30	6822.35	6874.8221	0.77%	77.35	95.021935	22.85%	88.2	73.377177	16.81%	72.34984345	17.97%	−1.16%	†
18:00	6742.56	6946.8078	3.03%	84.82	83.750475	1.26%	79.49	94.148773	18.44%	82.94648873	4.35%	14.09%	*
18:30	6595.51	6653.9664	0.89%	107.9	87.440297	18.96%	61.13	74.163976	21.32%	76.09725325	24.48%	−3.16%	†
19:00	6362.9	6441.8524	1.24%	138.1	108.96495	21.12%	46.06	60.105859	30.49%	59.11857523	28.35%	2.14%	*
19:30	6299.54	6159.9071	2.22%	141.5	147.50474	4.24%	44.52	51.411757	15.48%	41.76073974	6.20%	9.28%
20:00	6203.49	6230.2734	0.43%	142.7	150.18509	5.22%	43.46	40.316111	7.23%	41.48396847	4.55%	2.69%
20:30	6085.82	6113.2257	0.45%	149.5	150.97197	1.01%	40.72	41.213382	1.21%	40.49245619	0.56%	0.65%
21:00	5937.52	5988.264	0.85%	166.5	153.18458	8.00%	35.66	39.223883	9.99%	39.09181919	9.62%	0.37%
21:30	5772.1	5910.8892	2.40%	189.4	168.13084	11.25%	30.47	38.878744	27.60%	35.15648301	15.38%	12.22%
22:00	5584.53	5727.8769	2.57%	178.4	192.49561	7.89%	31.3	32.765402	4.68%	29.755883	4.93%	−0.25%	†
22:30	5421.07	5546.936	2.32%	209.9	177.50303	15.42%	25.83	33.122254	28.23%	31.24980994	20.98%	7.25%	*
23:00	5605	5380.5298	4.00%	189.4	210.78249	11.31%	29.6	26.070365	11.92%	25.52645485	13.76%	−1.84%	†
23:30	5484.05	5586.3543	1.87%	220.2	186.35301	15.35%	24.91	30.340156	21.80%	29.97726871	20.34%	1.46%	*
Average	5645.03	5666.4993	1.38%	222.7	202.50737	11.24%	30.9	33.627043	15.30%	32.15269162	13.25%	2.05%	‡
Variance	555.278	556.16377	1.31%	88.95	61.797993	7.83%	16.48	16.42647	10.62%	15.36874818	10.98%	8.04%