Distributed Real-Time Pricing Method Incorporating Load Uncertainty Based on Nonsmooth Equations for Smart Grid

Table 1

Numerical results of example given by the proposed algorithm and dual algorithm.

	Centralised algorithm			Decentralised algorithm		Dual algorithm			Maximum Electricity Demand	Minimum Electricity Demand
	Production level	Total energy consumption	Optimal price	Production level	Total energy consumption	Production level	Total energy consumption	Optimal price
1	186.865	183.593	1.868	169.606	172.666	186.862	183.508	1.869	514.743	102.949
2	184.583	181.174	1.856	166.011	169.76	185.152	181.73	1.852	504.603	100.921
3	183.343	180.070	1.833	165.618	169.481	183.391	179.945	1.834	503.677	100.735
4	171.073	167.657	1.712	152.235	156.083	171.143	167.723	1.711	465.047	93.009
5	186.357	182.971	1.867	169.611	173.445	186.523	183.173	1.865	517.132	103.426
6	189.874	186.482	1.904	171.915	175.167	190.19	186.758	1.902	523.195	104.639
7	181.414	178.134	1.813	165.016	168.886	181.407	178.029	1.814	501.598	100.32
8	177.081	173.663	1.774	161.123	164.166	177.214	173.856	1.772	489.198	97.8395
9	185.998	182.715	1.859	168.84	171.033	185.970	182.639	1.86	511.502	102.3
10	180.857	177.463	1.817	159.250	162.55	181.295	177.884	1.813	484.693	96.939
11	183.654	180.374	1.835	167.459	170.258	183.652	180.243	1.837	507.574	101.514
12	170.349	166.927	1.708	153.26	157.093	170.551	167.179	1.706	467.909	93.582
13	185.472	182.072	1.859	166.83	170.814	185.713	182.268	1.857	509.598	101.92
14	185.376	182.065	1.88	167.356	170.675	186.817	183.399	1.868	508.893	101.779
15	184.286	180.857	1.846	166.119	169.07	184.442	181.034	1.844	504.761	100.952
16	178.385	174.977	1.789	163.06	165.489	178.676	175.242	1.787	494.013	98.803
17	183.002	179.714	1.854	167.945	171.681	184.32	181.019	1.843	512.33	102.466
18	180.181	176.905	1.801	159.17	163.886	180.19	176.802	1.802	487.726	97.545
19	185.513	182.232	1.854	169.176	171.368	185.518	182.124	1.855	511.705	102.341
20	177.209	173.793	1.776	158.894	161.957	177.411	174.018	1.774	481.921	96.384
21	181.006	177.634	1.816	162.32	165.759	181.274	177.941	1.813	493.888	98.778
22	178.014	174.675	1.791	157.761	162.547	178.577	175.194	1.786	481.696	96.339
23	177.591	174.252	1.792	158.971	163.055	178.425	175.089	1.784	483.981	96.796
24	183.35	180.072	1.833	164.607	167.315	183.390	179.958	1.834	499.932	99.987