Comparative performances evaluation of FACTS devices on AGC with diverse sources of energy generation and SMES

Figures & data

Figure 1. Transfer function model of multi-source multi-area power system.

Figure 2. Schematic diagram of SSSC connected in series with the tie-line.

Figure 3. Structure of SSSC as a frequency controller.

Figure 4. A schematic diagram of a two area interconnected power system with TCPS in series with tie-line.

Figure 5. Structure of TCPS as frequency stabilizer.

Figure 6. Schematic diagram of two area interconnected power system with UPFC.

Figure 7. Structure of UPFC as frequency stabilizer.

Figure 8. Schematic diagram of IPFC.

Figure 9. Structure of IPFC as a frequency controller.

Figure 10. SMES circuit diagram.

Figure 11. Structure of SMES as frequency stabilizer.

Figure 12. Structure of Fuzzy PID controller.

Figure 13. Membership function for the two inputs and two outputs with gains of −1 to 1 and −10 to 10, respectively.

Table 1. Fuzzy rules for the inputs and outputs

ACE	ΔACE
	NB	NS	Z	PS	PB
NB	NB	NB	NB	NS	Z
NS	NB	NB	NS	Z	PS
Z	NB	NS	Z	PS	PB
PS	NS	Z	PS	PB	PB
PB	PB	Z	PS	PB	PB

Figure 14. Flowchart of Grey Wolf Optimizer (GWO) algorithm.

Table 2. GWO optimized Fuzzy PID controller parameters of power system-1 without physical constraints

Methods	Area 1 = Area 2
GWO optimized controller	Thermal	Hydro	Gas
Fuzzy PID controller	K1 = 1.6974	K1 = 0.5428	K1 = 1.5258
	K2 = 1.8336	K2 = 0.0605	K2 = 0.1659
	K3 = 0.4935	K3 = 1.0157	K3 = 0.3308
	K4 = 1.0103	K4 = 1.1712	K4 = 1.0340

Figure 15. (a) Frequency deviation in Area 1 subjected to a step load change of 0.01 p.u. in Area 1, (b) Frequency deviation in Area 2 subjected to a step load change of 0.01 p.u. in Area 1 and (c) Tie-line power flow deviation subjected to a step load change of 0.01 p.u. in Area 1.

Figure 16. (a) Frequency deviation in Area 1 subjected to a step load change of 0.01 p.u. in Area 1 and their comparison for proposed GWO optimized Fuzzy PID control scheme with TLBO optimized Output feedback SMC scheme, (b) Frequency deviation in Area 2 subjected to a step load change of 0.01 p.u. in Area 1 and their comparison for proposed GWO optimized Fuzzy PID control scheme with TLBO optimized Output feedback SMC scheme and (c) Tie-line power flow deviation subjected to a step load change of 0.01 p.u. in Area 1 and their comparison for proposed GWO optimized Fuzzy PID control scheme with TLBO optimized Output feedback SMC scheme.

Table 3. GWO optimized Fuzzy PID controllers parameters of power system-2 with HVDC link, GRC and reheat turbine

Methods	Area 1 = Area 2
GWO optimized controller	Thermal	Hydro	Gas
Fuzzy PID controller	K1 = 0.2393	K1 = 1.1126	K1 = 1.8334
	K2 = 0.5789	K2 = 0.4438	K2 = 1.4036
	K3 = 1.8669	K3 = 1.3002	K3 = 0.3902
	K4 = 1.4068	K4 = 1.4014	K4 = 1.3604

Table 4. Performance evaluation of proposed GWO optimized Fuzzy PID controller by settling time, minimum undershoot and maximum overshoot

Controllers and parameters		Proposed GWO fuzzy PID controller	TLBO optimized output feedback SMC scheme (Mohanty, 2015)
		Value	Value
Settling times (0.002% band) (s)	ΔF1	4.42	20
	ΔF2	4.54	9.92
	ΔPTie	3.5	20.33
MUS (p.u.)	ΔF1	−0.00983358	−0.0123
	ΔF2	−0.00175890	−0.0035
	ΔPTie	−0.00078422	−0.0038
MOS (p.u.)	ΔF1 × 10^−4	0.0020060735	2.7741
	ΔF2 × 10^−4	0.00010095	1.2757
	ΔPTie × 10^−4	0.00005726	8.4175
Performanceindices	ITAE	0.0478	0.3684
	ITSE	1.9551 × 10^−5	9.3287 × 10^−4
	ISE	3.3554 × 10^−5	4.412 × 10^−4
	IAE	0.0138	0.0611

Figure 17. (a) Frequency deviation of Area 1 without and with SMES subjected to load change of 0.01 p.u. in Area 1, (b) Frequency deviation of Area 2 without and with SMES subjected to load change of 0.01 p.u. in Area 1 and (c) Tie-line power flow deviation without and with SMES subjected to load change of 0.01 p.u. in Area 1.

Table 5. System modes, minimum damping ratio, for multi-source multi area power system with HVDC link, GDB, GRC and Reheat turbine without and with SMES

Methods	GWO Fuzzy PID without SMES	GWO Fuzzy PID with SMES
System Modes	−2.0000	−2.0000
	−0.0348	−2.0000
	−5.0000	−0.0348
	−2.0000	−3.3333
	−0.0348	−3.3333
	−3.3333	−0.1000
	−3.3333	−12.5000
	−0.1000	−5.0000
	−12.5000	−0.1000
	−0.1000	−12.5000
	−12.5000	−0.0348
	−5.0000	−5.0000
	−19.9809	−36.7400 +23.9350i
	−2.2222 + 5.1856i	−36.7400 −23.9350i
	−2.2222 −5.1856i	−36.6879 +23.9109i
	−2.4483 +4.9497i	−36.6879 −23.9109i
	−2.4483 −4.9497i	−20.0148
	−4.5159	−4.5858
	−2.1734	−3.4205 +1.3882i
	−1.0459	−3.4205 −1.3882i
	−0.4667	−3.3076 +1.3945i
	−0.1084	−3.3076 −1.3945i
	−0.1435	−0.3401
	−5.0000	−0.1098
	−2.0000	−0.1431
	−2.0000	−1.0409
		−2.2554
		−1.5745
		−1.5505
		−5.0000
		−2.0000
		−2.0000
MDR	0.3939	0.8378

Table 6. Performance evaluation of proposed GWO optimized Fuzzy PID controller by settling time, minimum undershoot and maximum overshoot of multi-source multi area nonlinear power system without and with SMES

Controllers and parameters		Without SMES	With SMES
Settling times (2% tolerance band) (s)	ΔF1	4.42	1.75
	ΔF2	4.54	3.68
	ΔPTie	3.5	2.38
MOS (p.u.)	ΔF1 × 10^−4	20.0607	1.846
	ΔF2 × 10^−4	1.0095	1.0521
	ΔPTie × 10^−4	0.5726	0.6377
MUS (p.u.)	ΔF1 × 10^−3	−9.83358	−3.60876
	ΔF2 × 10^−3	−1.75890	−0.88572
	ΔPTie × 10^−3	−0.78422	−0.44698

Table 7. Optimal gains of controller for different FACTS devices

Methods	Area 1 = Area 2			Area 1 = Area 2
GWO optimized fuzzy PID controller	Thermal	Hydro	Gas	SMES constants	FACTS constants
SSSC	K1 =  1.6291	K1 = 0.5978	K1 = 1.8000	T1 = 0.0048	T1 = 0.2933
	K2 = 0.3561	K2 = 0.1037	K2 = 0.7356	T2 = 0.0178	T2 = 0.0516
	K3 = 1.6633	K3 = 0.7323	K3 = 0.9476	T3 = 0.2393	T3 = 0.5041
	K4 = 0.1372	K4 = 0.2603	K4 = 1.6671	T4 = 0.0295	T4 = 0.7684
				Ksmes = 0.3649	KSSSC = 0.2830
				Tsmes = 0.0405	TSSSC = 0.2254
TCPS	K1 = 1.8279	K1 = 1.7430	K1 = 0.2655	T1 =  0.4554	Kϕ = 1.9004
	K2 = 0.3036	K2 = 0.4515	K2 = 0.4514	T2 = 0.0509
	K3 = 1.8793	K3 = 1.7688	K3 = 1.8824	T3 = 0.4097	TPS = 0.0172
	K4 = 1.9604	K4 = 0.5784	K4 = 0.1095	T4 = 0.0265
				Ksmes = 0.8695
				Tsmes = 0.2268
UPFC	K1 = 1.9347	K1 = 1.8720	K1 = 0.2627	T1 = 0.5942	TUPFC = 0.0201
	K2 = 0.3568	K2 = 0.3125	K2 = 0.6757	T2 = 0.0587
	K3 = 1.2961	K3 = 1.3503	K3 = 1.7661	T3 = 0.4635
	K4 = 1.9822	K4 = 0.5819	K4 = 0.3135	T4 = 0.0280
				Ksmes = 0.8872
				Tsmes = 0.1571
IPFC	K1 = 1.9669	K1 = 1.5336	K1 = 0.2389	T1 = 0.5766	KIPFC1 = 0.0270
	K2 = 0.3811	K2 = 0.4944	K2 = 0.5364	T2 = 0.0683	KIPFC2 = 0.0016
	K3 = 1.5876	K3 = 1.9892	K3 = 1.6987	T3 = 0.4558	TIPFC = 0.0450
	K4 = 1.8540	K4 = 0.6728	K4 = 0.3353	T4 = 0.0220
				Ksmes = 0.8149
				Tsmes = 0.4599

Figure 18. (a) Frequency deviation of Area 1 with SMES and FACTS subjected to a step load change of 0.01 p.u. in Area 1, (b) Frequency deviation of Area 2 with SMES and FACTS subjected to a step load change of 0.01 p.u. in Area 1 and (c) Tie-line power flow deviation with SMES and FACTS subjected to a step load change of 0.01 p.u. in Area 1.

Table 8. Performance criteria for multi-source multi area nonlinear power system with SMES and FACTS

Objective function and parameters		SSSC	TCPS	UPFC	IPFC
ITAE		0.0086	0.0072	0.0098	0.0077
ISE		4.5798 × 10^−6	7.4202 × 10^−7	1.8377 × 10^−6	7.7629 × 10^−7
ITSE		9.7544 × 10^−6	1.4507 × 10^−6	2.6448 × 10^−6	1.5436 × 10^−6
IAE		0.0068	0.0028	0.0043	0.0029
Settling times (2% band)	ΔF1	2.34	1.55	1.59000	1.29
	ΔF2	3.5	2.01	4.51000	2.25
	ΔPTie	2.9	0.66	1.41000	1.41
MUS	ΔF1	−0.00503375	−0.00182222	−0.00110808	−0.00217230
	ΔF2	−0.00266690	−0.00050430	−0.00175894	−0.00036766
	ΔPTie	−0.00125826	−0.00026595	−0.00111744	−0.00018922
MOS	ΔF1	0.0000014191	0.0002340791	0.0000357620	0.0001321079
	ΔF2	0.00000145	0.00005316	0.00021740	0.00005974
	ΔPTie	0.00000091	0.00002438	0.00011378	0.00002815

Table 9. System modes, minimum damping ratio, for multi-source multi area nonlinear power system with SMES and FACTS

Methods	SSSC	TCPS	UPFC	IPFC
System modes	−2.0000
	−3.3333	−2.0000	−2.0000	−2.0000
	−3.3333	−2.0000	−2.0000	−2.0000
	−0.1000	−0.0348	−0.0348	−0.0348
	−12.5000	−3.3333	−3.3333	−3.3333
	−0.1000	−3.3333	−3.3333	−3.3333
	−12.5000	−0.1000	−0.1000	−0.1000
	−2.0000	−12.5000	−12.5000	−12.5000
	−0.0348	−5.0000	−5.0000	−5.0000
	−5.0000	−0.1000	−0.1000	−0.1000
	−0.0348	−12.5000	−12.5000	−12.5000
	−5.0000	−0.0348	−0.0348	−0.0348
	−67.1216	−5.0000	−5.0000	−5.0000
	−67.1825	−58.0422	−49.3395	−29.0688 +39.9748i
	−22.1978 +21.1799i	−28.4684 +56.0027i	−27.3788 +77.0634i	−29.0688 −39.9748i
	−22.1978 −21.1799i	−28.4684 −56.0027i	−27.3788 −77.0634i	−29.1235 +39.9402i
	−22.6587 +21.1097i	−28.4778 +55.7861i	−27.4911 +75.2695i	−29.1235 −39.9402i
	−22.6587 −21.1097i	−28.4778 −55.7861i	−27.4911 −75.2695i	−22.2410
	−19.9981	−20.0000	−20.0001	−20.0018
	−19.1607	−2.4292 +1.8917i	−5.1713	−4.5571
	−3.9637 +4.3612i	−2.4292 −1.8917i	−5.2122	−3.2550 +1.7917i
	−3.9637 −4.3612i	−2.5270 +1.8526i	−4.4276	−3.2550 −1.7917i
	−3.6414 +4.1798i	−2.5270 −1.8526i	−2.1960 +2.1065i	−3.3576 +1.7678i
	−3.6414 −4.1798i	−0.2774	−2.1960 −2.1065i	−3.3576 −1.7678i
	−4.4629 +0.0469i	−0.1104	−1.9270 +1.6704i	−1.0307
	−4.4629 −0.0469i	−0.1428	−1.9270 −1.6704i	−0.2917
	−0.3006	−1.0288	−1.0164	−0.1103
	−0.1098	−2.1721	−0.1858	−0.1429
	−0.1430	−4.3603	−0.1122	−2.1915 +0.0234i
	−1.0203	−4.8129	−0.1413	−2.1915 −0.0234i
	−1.3976	−4.7465	−2.1659	−2.1701
	−2.1496	−5.0000	−5.0000	−5.0000
	−5.0000	−2.0000	−2.0000	−2.0000
	−2.0000	−2.0000	−2.0000	−2.000
	−2.0000
MDR	0.5569	0.4532	0.3348	0.5881

Figure 19. Random load pattern with respect to time.

Figure 20. (a) Frequency deviation in Area 1 subjected to random load in Area 1 with GWO optimized Fuzzy PID controller, (b) Frequency deviation in Area 2 subjected to random load in Area 1 with GWO optimized Fuzzy PID controller and (c) Tie line power deviation obtained subjected to random load in Area 1 with GWO optimized Fuzzy PID controller.

Figure 21. Sinusoidal load pattern with respect to time.

Figure 22. (a) Frequency deviation in Area 1 subjected to sinusoidal load pattern in Area 1 with GWO optimized Fuzzy PID controller with and without FACTS, (b) Frequency deviation in Area 2 subjected to sinusoidal load pattern in Area 1 with GWO optimized Fuzzy PID controller with and without FACTS and (c) Tie line power deviation subjected to sinusoidal load pattern in Area 1 with GWO optimized Fuzzy PID controller with and without FACTS.

Figure 23. Transfer function model of interconnected three area thermal power system.

Figure 24. Structure of UPFC as frequency stabilizer for three area power system.

Figure 25. Structure of IPFC as frequency stabilizer for three area power system.

Table 10. Optimal gains of controller for different FACTS devices for three area thermal power system

Methods	Area 1	Area 2	Area 3	FACTS constants
GWO optimized fuzzy PID controller without FACTS	K1 = 0.6293	K1 = −0.276	K1 = −0.4377
	K2 =  −0.1808	K2 = 0.7097	K2 = 0.6156
	K3 =  −0.217	K3 = 0.0711	K3 = −0.1324
	K4 = 0.7757	K4 = −0.2862	K4 = −0.6008
GWO optimized fuzzy PID controller with UPFC	K1 = 0.9979	K1 = 0.3061	K1 = 0.6104	TUPFC_1 = 0.0302
	K2 = 0.0456	K2 = 0.0737	K2 = 0.0368	TUPFC_2 = 0.0044
	K3 = 0.9998	K3 = 0.1513	K3 = 0.052	TUPFC_3 = 0.9999
	K4 = 0.2096	K4 = 0.8659	K4 = 0.5553
GWO optimized fuzzy PID controller with IPFC	K1 = 0.7572	K1 = 0.7655	K1 = 0.5097	TIPFC_1 = 0.0442
	K2 = 0.0843	K2 = 0.3992	K2 = 0.1513	TIPFC_2 = 0.0452
	K3 = 0.9997	K3 = 0.3735	K3 = 0.0098	TIPFC_3 = 0.2809
	K4 = 0.2232	K4 = 0.7232	K4 = 0.5523	Ka1 = 0.9349, Kb1 = 0.2095
				Ka2 = 0.9673, Kb2 = 0.9129
				Ka3 = 0.0806, Kb3 = 0.0452

Figure 26. (a) Frequency deviation in Area 1 subjected to SLP of 1% in Area 1 with GWO optimized Fuzzy PID controller with and without FACTS, (b) Frequency deviation in Area 2 subjected to SLP of 1% in Area 1 with GWO optimized Fuzzy PID controller with and without FACTS and (c) Frequency deviation in Area 3 subjected to SLP of 1% in Area 1 with GWO optimized Fuzzy PID controller with and without FACTS.

Mohanty, B. (2015). TLBO optimized sliding mode controller for multi-area multi-source nonlinear interconnected AGC system. International Journal of Electrical Power & Energy Systems, 73, 872–881.10.1016/j.ijepes.2015.06.013

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