IMO-based novel adaptive dual-mode controller design for AGC investigation in different types of systems

Figures & data

Figure 1. Transfer function model of the three-area thermal system with DMPID controller

Figure 2. Structure of the proposed dual-mode PID controller

Figure 3. Nature of movement of ions

Table 1. Optimal gains of IMO tuned PID and DMPID controllers with application of an SLP of 0.01 p.u. in area 1

Algorithm	Control area 1			Control area 2			Control area 3
	$Z_p$	$Z_i$	$Z_d$	$Z_p$	$Z_i$	$Z_d$	$Z_p$	$Z_i$	$Z_d$
PID	1.4709	0.2649	0.2548	2.0000	0.1000	1.1474	2.0000	0.1000	0.8863
DMPID	1.6480	0.3995	1.3459	1.4415	0.9336	0.6244	1.5274	1.6974	0.7682
BFOI (Nanda et al., 2009)	$Z_{i1}$= 0.4465			$Z_{i2}$= 0.2191			$Z_{i3}$= 0.2799

Table 2. Performance evaluative factors with different controllers due to a SLP of 0.01 p.u. in area 1

Frequency deviations	Performance evaluative factors	BFOI (Nandaet al., 2009)	PID	Dual-mode PID
Δf1	Overshoots (Hz)	0.0096	0.0063	0.0000
	Undershoots (Hz)	−0.0199	−0.0148	−0.0090
	$T_s$in sec (0.05% band)	25.6986	8.0403	3.6745
Δf2	Overshoots (Hz)	0.0050	0.0000	0.0000
	Undershoots (Hz)	−0.0096	−0.0046	−0.0026
	$T_s$in sec (0.05% band)	20.8329	8.4370	5.9987
Δf3	Overshoots (Hz)	0.0018	0.0000	0.0000
	Undershoots (Hz)	−0.0083	−0.0036	−0.0021
	$T_s$in sec (0.05% band)	11.9358	8.7657	6.5810
ΔPtie1-2	Overshoots (PU)	0.0018	0.0001	0.0001
	Undershoots (PU)	−0.0131	−0.0073	−0.0038
	$T_s$in sec (0.05% band)	21.6156	15.2116	10.8073
ΔPtie1-3	Overshoots (PU)	0.0027	0.0015	0.0008
	Undershoots (PU)	−0.0015	0.0000	0.0000
	$T_s$in sec (0.05% band)	11.8672	5.1508	3.1068
ΔPtie2-3	Overshoots(PU)	0.0021	0.0011	0.0006
	Undershoots (PU)	−0.0002	0.0000	0.0000
	$T_s$in sec (0.05% band)	5.7982	4.2108	3.6745

Figure 4. Frequency deviation in area 1 with application of an SLP of 0.01 p.u. in area 1

Figure 5. Frequency deviation in area 2 with application of an SLP of 0.01 p.u. in area 1

Figure 6. Frequency deviation in area 3 with application of an SLP of 0.01 p.u. in area 1

Figure 7. Tie-line power deviation between areas 1 and 3 with application of an SLP of 0.01 p.u. in area 1

Figure 8. Tie-line power deviation between areas 1 and 2 with application of an SLP of 0.01 p.u. in area 1

Figure 9. Frequency deviations in area 1 due to an SLP of 0.01 p.u. in all areas simultaneously

Figure 10. Tie-line power deviations between area 1&3 due to an SLP of 0.01 p.u. in all areas simultaneously

Table 3. Performance evaluative factors of$\mathrm{\Delta }{f}_1,\mathrm{\Delta }{f}_2$and$\mathrm{\Delta }{f}_3$for different loading conditions in area 1

$\mathbf{\Delta }{P}_L$	$\mathbf{\Delta }{f}_1$			$\mathbf{\Delta }{f}_2$			$\mathbf{\Delta }{f}_3$
	${\mathit{U}}_{\mathit{s}\mathit{h}}$in Hz	${\mathit{O}}_{\mathit{s}\mathit{h}}\times {10}^{-3}$in Hz	${\mathit{T}}_{\mathit{s}}$in sec	${\mathit{U}}_{\mathit{s}\mathit{h}}$in Hz	${\mathit{O}}_{\mathit{s}\mathit{h}}\times {10}^{-3}$in Hz	${\mathit{T}}_{\mathit{s}}$in sec	${\mathit{U}}_{\mathit{s}\mathit{h}}$in Hz.	${\mathit{O}}_{\mathit{s}\mathit{h}}\times {10}^{-3}$in Hz	${\mathit{T}}_{\mathit{s}}$in sec
1% SLP	−0.0090	0.05842	3.6745	−0.0026	0.05064	5.9987	−0.0021	0.05079	6.5810
2% SLP	−0.0179	0.1129	5.1110	−0.0053	0.1014	9.1548	−0.0043	0.1016	9.5281
3% SLP	−0.0268	0.1680	6.1924	−0.0079	0.1523	10.7268	−0.0065	0.1525	11.0850
4% SLP	−0.0357	0.2224	6.9971	−0.0105	0.2030	11.5288	−0.0087	0.2033	11.8743
5% SLP	−0.0445	0.2776	7.5706	−0.0132	0.2529	12.2421	−0.0109	0.2535	12.5755

Figure 11. Frequency deviations in area 1 due to parameter variations

Figure 12. Tie-line power deviation between areas 1 and 3 due to parameter variations

Figure 13. Random loading pattern in area 1

Figure 14. Frequency deviations in area 1 due to random loading in area 1

Figure 15. Tie-line power deviation between areas 1 and 3 due to random loading in area 1

Figure 16. Frequency deviations in area 1 considering time delay

Figure 17. Tie-line power deviation between areas 1 and 3 considering time delay

Table 4. Performance indices with a SLP of 0.01 p.u. in area 1

Controllers	IAE	ITAE	ISE	ITSE
Dual-mode PID	0.0276	0.1687	6.3476e-005	1.5702e-004
PID	0.0376	0.2397	9.7597e-005	3.5915e-004
BFOI (Nanda et al., 2009)	0.0792	0.5549	4.2105e-004	9.9779e-004

Table 5. Optimum gains of DMPID controllers of multi-source power system tuned by IMO algorithm

Controller	Thermal			Hydro			Gas
	$Z_p$	$Z_i$	$Z_d$	$Z_p$	$Z_i$	$Z_d$	$Z_p$	$Z_i$	$Z_d$
DMPID controller	3.9384	3.9576	2.4849	3.3857	0.1000	0.9020	3.4855	4.0000	2.2436
PID (Mohanty et al., 2014)	0.779	0.2762	0.6894	0.5805	0.2291	0.7079	0.5023	0.9529	0.6569

Figure 18. Transfer function model of the multi-source power system with PID/DMPID controller

Figure 19. Frequency deviation of area 1 of multi-source system considering 1% SLP in area 1

Figure 20. Frequency deviation of area 2 of multi-source system considering 1% SLP in area 1

Figure 21. Tie-line power deviation of multi-source system considering 1% SLP in area 1

Nanda, J., Mishra, S., & Saikia, L. C. (2009). Maiden application of bacterial foraging-based optimization technique in multiarea automatic generation control. Power Systems, IEEE Transactions, 24(2), 602–609. doi:10.1109/TPWRS.2009.2016588

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Mohanty, B., Panda, S., & Hota, P. K. (2014). Controller parameters tuning of differential evolution algorithm and its application to load frequency control of multi-source power system. International Journal of Electrical Power & Energy Systems, 54, 77–85. doi:10.1016/j.ijepes.2013.06.029

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