Horse Herd Optimization Algorithm for Fuel Constrained Day-ahead Scheduling of Isolated Nanogrid

Figures & data

Figure 1. (a). Pseudo code of the recommended HOA. (b). Flowchart of HOA.

Table 1. Fuel delivered (liter) to diesel generators obtained from HOA with fuel constraints

Interval	$Fd{g}_1$	$Fd{g}_2$
1 2 3 4 5 6	8.6625 2.1625 9.0671 8.5923 8.4710 9.2896	11.3375 17.8375 12.9329 16.4077 13.5290 10.7104

Table 2. Fuel delivered (liter) to diesel generators obtained from SGEO with fuel constraints

Interval	$Fd{g}_1$	$Fd{g}_2$
1 2 3 4 5 6	7.7092 7.0027 9.7082 8.5863 4.4807 9.6353	12.2908 12.9973 12.2918 16.4137 17.5193 10.3647

Table 3. Fuel delivered (liter) to diesel generators obtained from HPSO-TVAC with fuel constraints

Interval	$Fd{g}_1$	$Fd{g}_2$
1 2 3 4 5 6	8.8212 9.2395 9.2827 9.7192 6.3402 8.7186	11.1788 10.7605 12.7173 15.2808 15.6598 11.2814

Table 4. Comparison of performance

		Best price ($)	Average price ($)	Worst price ($)	CPU time (s)
With fuel constraints	HOA	137.1420	137.1524	137.1648	7.44
	SGEO	137.1875	137.1982	137.1996	8.05
	HPSO-TVAC	137.2230	137.2352	137.2487	8.38
	FCEP	137.3685	137.3769	137.3832	7.25
	DE	137.5102	137.5301	137.5437	7.47
Without fuel constraints	HOA	136.5432	136.5543	136.5677	6.78
	SGEO	136.6293	136.6389	136.6478	7.11
	HPSO-TVAC	136.7158	136.7288	136.7399	7.46
	FCEP	136.9600	136.9715	136.9802	6.39
	DE	136.9979	136.9998	137.0132	6.43

Figure 2. Power generation acquired from diesel generators, solar PV plants, PEVs and BESS considering fuel constraints using HOA.

Figure 3. Power generation acquired from diesel generators, solar PV plants, PEVs and BESS considering fuel constraints using SGEO.

Figure 4. Power generation acquired from diesel generators, solar PV plants, PEVs and BESS considering fuel constraints using HPSO-TVAC.

Figure 5. Power generation acquired from diesel generators, solar PV plants, PEVs and BESS without fuel constraints using HOA.

Figure 6. Power generation acquired from diesel generators, solar PV plants, PEVs and BESS without fuel constraints using SGEO.

Figure 7. Power generation acquired from diesel generators, solar PV plants, PEVs and BESS without fuel constraints using HPSO-TVAC.

Figure 8. Cost convergence characteristics considering fuel constraints.

Figure 9. Cost convergence characteristics without fuel constraints.

Table

Unit$\mathrm{P}d{g}^{min}$ $\mathrm{P}d{g}^{max}$$a_d$ $b_d$ $c_d$ $U{R}_d$ $D{R}_d$ KW KW $/h $/KWh $/ KW^2h KW/h KW/h

1 0 15 2.0350 0.0602 0.000044 3 3 2 0 25 1.1825 0.0653 0.000044 5 5

Table

Unit ${\eta }_d$ ${\delta }_d$ ${\mu }_d$ $Fd{g}^{min}$ $Fd{g}^{max}$ $Vd{g}^{min}$ $Vd{g}^{max}$ $Vd{g}^0$ liter/h liter/MWh liter/(MW)^2h liter liter liter liter liter

1 2.00669 0.060200 0.00010033 0 10 0 20 15 2 1.33779 0.060200 0.00005017 0 20 0 40 20

Table

Hour	Power (KW)	Temperature$\left({\hspace{0.17em}}^{0}C\right)$	Hour	Power (KW)	Temperature$\left({\hspace{0.17em}}^{0}C\right)$	Hour	Power (KW)	Temperature$\left({\hspace{0.17em}}^{0}C\right)$
1 2 3 4 5 6 7 8	37 39 35 37 40 42 45 47	23 23 24 25 25 25 26 27	9 10 11 12 13 14 15 16	49 47 48 47 49 50 50 49	27 28 29 29 29 28 28 27	17 18 19 20 21 22 23 24	47 46 44 42 40 39 38 37	26 25 24 24 24 24 23 23

Table

Interval Duration $F{D}_d$ (h) (liter)

1 4 20 2 4 20 3 4 22 4 4 25 5 4 22 6 4 20