A CHEMICAL REACTION OPTIMIZATION ALGORITHM FOR PHASOR MEASUREMENT UNIT PLACEMENT

Carniel, Aileen; Mestria, Mario

doi:10.1590/0101-7438.2021.041.00231454

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ARTICLES • Pesqui. Oper. 41 • 2021 • https://doi.org/10.1590/0101-7438.2021.041.00231454 copy

A CHEMICAL REACTION OPTIMIZATION ALGORITHM FOR PHASOR MEASUREMENT UNIT PLACEMENT

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Optimal Phasor Measurement Unit (PMU) Placement (OPP) aims to reduce equipment costs while maintaining electrical systems observability. PMUs synchronized phasor data provide electrical systems information with high quality and frequency enabling the implementation of faster than real-time state estimators. We applied Chemical Reaction Optimization (CRO) method at OPP problem, testing it successfully at IEEE power system databases (14, 30, 57 and 118 bars) through two distinct models. The relationships between CRO parameters and the occurrence of elementary reactions was exploited, achieving better results through specific reactions. Due to problems similarity and larger scales, the software was adapted to Beasley OR-Library Set Covering (SC) problems. In the process to achieve GAPs smaller than 10% for some files, we tried out dedicated local searches, disturbance recurrence limits and stop condition changes. However, we suggest continuing to evaluate CRO method adherence to SC problem using different data structures to decrease computational times.

Keywords:
Combinatorial Optimization; Phasor Measurement Unit; Observability; Smart Grids; Chemical Reaction Optimization

Parameter	Description	Function
PopSize	Population size	Initial CRO population size.
MAX_ITER	Stopping criterion	Defines the maximum number of CRO algorithm iterations to be executed.
initialKE	Initial kinetic energy	Defines the amount of initial kinetic energy for each created molecule. The kinetic energy is related to the tolerance of the system in accepting worse solutions.
KELossRate	Rate of kinetic energy loss	Defines the percentage of molecule kinetic energy lost at each collision suffered.
iniBuffer	Environment energy buffer	Sets the initial amount of energy available at the environment.
MoleColl	Decision variable between collision types	MoleColl is compared to a randomly generated parameter to choose between unimolecular (decomposition and on-wall ineffective collision) or intermolecular (intermolecular ineffective collision and synthesis) operations.
Alpha	Decision variable between unimolecular operations	Defines the decomposition criterion limit (NumHit - MinHit> α). If the chosen molecule meets the criterion, the decomposition operation is performed; otherwise, on-wall ineffective collision takes place.
Beta	Decision variable between intermolecular operations	Defines the synthesis criterion limit $(KE \leq β)$ . If both chosen molecules meet this criterion, synthesis operation is performed; otherwise, intermolecular ineffective collision takes place.

Routine	Description	Source
2XChange	Select a random bit from the molecule solution (w) and change its value for a smaller position bit value.	^{Lam & Li (2012}15. LAM AYS & LI VOK. 2012. Chemical Reaction Optimization: A tutorial. Memetic Computing, 4(1): 3-17. Available at: https://doi.org/10.1007/s12293-012-0075-1 https://doi.org/https://doi.org/10.1007/... )
Random 2XChange	Perform a random number (between 0 and 50) of bit pair exchanges in the molecule solution (w). The positions of the bits that are changed are randomly selected.	Authors
OneResource Change	Randomly selects two positions from the molecule solutions array (w). Looks for the first bit that is set after the first position and for the first not-set bit after the second position. Both bits are exchanged for the output solution.	Lam & Li (2011)
OneResourceRandomChange	Select a random bit from the molecule solution (w) and change its value	Lam & Li (2011)
HalfRandom Change	Creates two new binary solutions (w1 and w2) similar to the original molecule (w). Changes the even bits values for molecule w1 and changes the odd bits values for molecule w2.	Lam & Li (2011)
OnePosition XChange	Selects a random position of the array as a cut-off point to be applied at the input molecules (w1 and w2). Creates a new molecule that combines the solutions from w1 and w2. Its solution incorporates all the bits before the cut-off point from w1, discarding the rest of the array, and concates them with all the bits after the cut-off point of w2.	Lam & Li (2011)
Exhaustive Change	Runs every position from the molecule solution (w), changing its value and testing its results. If a best result is met, it becomes the new solution (w). It continues the search at the new solution (w) until the last array position is verified.	Authors

Parameter	Values
PopSize	1, 10, 100
MAX_ITER	100, 500, 1000 *(number of nodes from the test files)
iniBuffer	3000, 5000, 10000
initialKE	Molecule initial PE, set as objective function value
KELossRate	0,3, 0.5, 0.8
MoleColl	0.2, 0,3, 0.5, 0.8, 0.9
Alpha	10, 100, 200*( number of nodes from the test files)
Beta	200, 500, 800*( number of nodes from the test files)

CRO Parameters							IEEE 14 Buses		IEEE 30 Buses		IEEE 57 Buses		IEEE 118 Buses
Population Size	MAX ITER	Alpha	Beta	KELoss Rate	MoleColl	Buffer	BS: 4 PMUs		BS: 10 PMUs		BS: 17 PMUs		BS: 32 PMUs
Population Size	MAX ITER	Alpha	Beta	KELoss Rate	MoleColl	Buffer	AE (%) Penalty	AE (%) Model (1)(2)	AE (%) Penalty	AE (%) Model (1)(2)	AE (%) Penalty	AE (%) Model (1)(2)	AE (%) Penalty	AE (%)Model (1)(2)
1	500	200	20	0.9	0.0	1000	0.00	0.00	20.00	0.00	9.02	0.00	9.17	0.63
1	700	150	50	0.8	0.0	0	3.33	0.00	30.00	0.00	4.31	0.00	9.79	0.42
10	700	150	2	0.7	0.0	1000	3.33	0.00	15.33	0.00	8.24	0.00	11.25	1.04
10	700	150	500	0.8	0.0	1000	0.00	0.00	25.33	0.00	6.67	0.00	9.38	2.29
10	700	500	2	0.9	0.0	0	6.67	0.00	22.67	0.00	7.84	0.00	9.17	2.29
10	700	500	50	0.9	0.0	1000	10.00	0.00	23.33	0.00	6.67	0.00	9.58	1.67
1	100	100	500	0.8	0.2	10000	21.67	0.00	7.33	0.00	13.33	0.00	14.17	4.38
1	100	200	800	0.8	0.3	5000	18.33	0.00	9.33	0.00	11.76	1.18	14.58	3.33
1	500	200	500	0.8	0.3	3000	26.67	1.67	18.67	0.00	14.90	0.78	19.58	1.04
10	500	100	200	0.8	0.5	5000	18.33	26.67	7.33	0.67	12.94	1.18	17.92	1.46
100	1000	100	800	0.8	0.2	10000	15.00	36.67	7.33	0.67	10.20	2.35	15.00	1.04
100	1000	200	200	0.8	0.5	5000	13.33	1.67	6.00	0.00	12.55	0.78	15.83	0.83

	Our paper	^{Xu et al. (2013}28. XU J, WEN MHF, LI VOK & LEUNG K-C. 2013. Optimal PMU Placement for Wide-Area Monitoring Using Chemical Reaction Optimization. 2013 IEEEPES Innovative Smart Grid Technologies Conference (ISGT). Available at: https://www.eee.hku.hk/∼hfwen/papers/ISGT-OPP-2013.pdf https://www.eee.hku.hk/∼hfwen/papers/ISG... )
CPU	Intel Core i7 3.6GHz	Intel Core Duo 2.66 Hz
CPU Single Thread Rating	2904	743
Time IEEE 118 bus system (seconds) - algorithm	0.376 s - CRO	3.1s - CRO 1.1s - SCRO
Time IEEE 118 bus system (seconds) normalized	1.46 s - CRO	3.1s - CRO 1.1s - SCRO

Test Group Number	Number of instances by group	Problem Scale	Cost Variation	Density	Optimal solution is known?(Yes/No)
4	10	200 x 1000	1-100	2%	Yes
5	10	200 x 2000	1-100	2%	Yes
6	5	200 x 1000	1-100	5%	Yes
A	5	300 x 3000	1-100	2%	Yes
B	5	300 x 3000	1-100	5%	Yes
C	5	400 x 4000	1-100	2%	Yes
D	5	400 x 4000	1-100	5%	Yes
NRE	5	500 x 5000	1-100	10%	No
NRF	5	500 x 5000	1-100	20%	No
NRG	5	1000 x 10000	1-100	2%	No
NRH	5	1000 x 10000	1-100	5%	No
E	5	50 x 500	-	2%	Yes
CLR.10	1	511 x 210	-	2%	No
CLR.11	1	1023 x 330	-	5%	No
CLR.12	1	2047 x 495	-	2%	No
CLR.13	1	4095 x 715	-	5%	No
CYC.6	1	240 x 192	-	2%	Yes
CYC.7	1	672 x 448	-	5%	No
CYC.8	1	1792 x 1024	-	10%	No
CYC.9	1	4608 x 2304	-	20%	No
CYC.10	1	11520 x 5120	-	2%	No
CYC.11	1	28160 x 11264	-	5%	No

Parameter	Values
PopSize	10
MAX_ITER	15*(Number of columns of the Set Covering problem)
iniBuffer	10000
initialKE	50000
KELossRate	0.3
MoleColl	0.3
Alpha	0.5*(Number of columns of the Set Covering problem)
Beta	1*(Number of columns of the Set Covering problem)

Instance	Mean Computational Time (s)	Lines (Search Space elements)	Columns (available subsets)	Best Known Solution ^{Yu et al. (2014}29. YU JJQ, LAM AYS & LI VOK. 2014. Chemical Reaction Optimization for the Set Covering Problem. Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, p. 512-519. Available at: https://doi.org/10.1109/CEC.2014.6900233 https://doi.org/10.1109/CEC.2014.6900233... )	Best Found Solution	GAP (%)	Mean Solution Value	Mean Error (%)
41	167	200	1000	429	432	0.70%	449.60	4.80%
42	168	200	1000	512	525	2.54%	555.40	8.48%
43	160	200	1000	516	531	2.91%	546.53	5.92%
44	175	200	1000	494	530	7.29%	543.93	10.11%
45	176	200	1000	512	522	1.95%	548.40	7.11%
46	169	200	1000	560	568	1.43%	592.33	5.77%
410	161	200	1000	514	548	6.61%	563.33	9.60%
51	1077	200	2000	253	271	7.11%	278.27	9.99%
55	1085	200	2000	211	221	4.74%	225.53	6.89%
510	1054	200	2000	265	270	1.89%	276.07	4.18%
61	299	200	1000	138	144	4.35%	150.47	9.03%
65	286	200	1000	161	171	6.21%	176.93	9.90%
a4	4296	300	3000	234	246	5.13%	254.40	8.72%
a5	4268	300	3000	236	240	1.69%	247.20	4.75%
b1	5466	300	3000	69	77	11.59%	81.73	18.45%
b5	5444	300	3000	72	75	4.17%	80.93	12.41%
c1	10108	400	4000	227	232	2.20%	242.73	6.93%
c5	10475	400	4000	215	224	4.19%	233.20	8.47%
clr10	29	511	210	25	30	20.00%	31.73	26.93%
clr11	132	1023	330	23	31	34.78%	32.33	40.58%
d1	13158	400	4000	60	65	8.33%	69.73	16.22%
d5	12564	400	4000	61	66	8.20%	71.73	17.60%
e1	34	50	500	5	6	20.00%	6.87	37.33%
e2	35	50	500	5	6	20.00%	6.87	37.33%
e3	36	50	500	5	6	20.00%	6.53	30.67%
e5	36	50	500	5	6	20.00%	6.80	36.00%
nre4	31434	500	5000	28	31	10.71%	33.53	19.76%
nre5	31369	500	5000	28	31	10.71%	32.93	17.62%
nrf1	45501	500	5000	14	16	14.29%	17.87	27.62%

Instance	Disturbance Limit	Computational time (s)	Best Known Solution ^{Yu etal. (2014}29. YU JJQ, LAM AYS & LI VOK. 2014. Chemical Reaction Optimization for the Set Covering Problem. Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, p. 512-519. Available at: https://doi.org/10.1109/CEC.2014.6900233 https://doi.org/10.1109/CEC.2014.6900233... )	Best Solution Found	Error (%)	Mean SolutionValues	Mean Error(%)
42	10	111	512	2755	438.09	569.80	11.29
42	20	143	512	1587	209.96	559.60	9.30
42	50	209	512	530	3.52	555.40	8.48
65	10	116	161	178	10.56	819.50	223.91
65	20	147	161	171	6.21	982.70	288.42
65	50	236	161	173	7.45	184.10	14.35
e1	10	82	5	7	40.00	8269.30	3746.19
e1	20	88	5	7	40.00	6990.60	3151.44
e1	50	103	5	6	20.00	5471.30	2444.79
clr11	10	128	23	31	34.78	8925.20	14531.48
clr11	20	160	23	31	34.78	8750.80	14245.57
clr11	50	246	23	31	34.78	6667.80	10830.82
clr11	50	246	23	31	34.78	6667.80	10830.82

Instance	Number of nodes	CROIteration Number	Computational time (s)	Best Known Solution ^{Yu et al.(2014}29. YU JJQ, LAM AYS & LI VOK. 2014. Chemical Reaction Optimization for the Set Covering Problem. Proceedings of the 2014 IEEE Congress on Evolutionary Computation, CEC 2014, p. 512-519. Available at: https://doi.org/10.1109/CEC.2014.6900233 https://doi.org/10.1109/CEC.2014.6900233... )	Best Solution Found	Error (%)	Mean Solution Values	Mean Error (%)
51	1000	10000	272	253	608	140.32	2414.0	854.15
51	1000	15000	406	253	274	8.30	1618.4	539.68
51	1000	20000	516	253	277	9.49	819.5	223.91
51	1000	25000	649	253	278	9.88	982.7	288.42
65	2000	10000	159	161	174	8.07	184.1	14.35
65	2000	15000	232	161	175	8.70	180.0	11.80
65	2000	20000	319	161	175	8.70	180.0	11.80
65	2000	25000	402	161	166	3.11	178.8	11.06
a4	1000	10000	541	234	2675	1043.16	5855.8	2402.48
a4	1000	15000	835	234	2226	851.28	5854.0	2401.71
a4	1000	20000	1133	234	1963	738.89	4644.1	1884.66
a4	1000	25000	1379	234	241	2.99	1874.6	701.11
e1	4000	10000	67	5	6	20.00	7.4	48.00
e1	4000	15000	102	5	6	20.00	6.9	38.00
e1	4000	20000	137	5	6	20.00	6.8	36.00
e1	4000	25000	171	5	6	20.00	6.6	32.00
clr11	500	10000	162	23	31	34.78	31.9	38.70
clr11	500	15000	245	23	31	34.78	32.3	40.43
clr11	500	20000	327	23	31	34.78	32.0	39.13
clr11	500	25000	410	23	31	34.78	31.6	37.39

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