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INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
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ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue VI, June 2026
Voltage-Instability Bus Identification in Power Transmission
Networks Using an Improved Strength Pareto Evolutionary
Algorithm
1
Ashiru S.K.,
2
Amos Ibrahim S.,
3
Akpan I.J.,
4
Adebayo A.A.,
5
Olaoluwa I.A.,
6
Ijaola M.O.,
7
Mafiana
C.K.,
8
Odia Akhere K.
12356
National Space Research and Development Agency, Cooperative Information Network, Obafemi
Awolowo University, Ile-Ife South-West Nigeria
7,8
Centre for Transport and Propulsion, Epe, Lagos
DOI:
https://doi.org/10.51583/IJLTEMAS.2026.150600269
Received: 13 July 2026; Accepted: 18 July 2026; Published: 03 August 2026
ABSTRACT
Voltage instability remains a major operational challenge in stressed transmission networks because reactive
power deficiencies and contingency events can force bus voltages outside acceptable operating limits. This paper
presents an Improved Strength Pareto Evolutionary Algorithm (ISPEA) for the identification of voltage-
instability buses in transmission systems under steady-state and contingency loading. A Newton–Raphson load-
flow model was first used to obtain the operating point of the network. Contingency severity is represented by a
90% increase in reactive demand at load buses, after which the ISPEA ranks buses using a multi-objective fitness
structure based on voltage magnitude deviation, maximum loading capacity, and generator operating constraint
penalties. ISPEA runs for 200 generations with a population of 100, an archive of 100, and a Newton–Raphson
convergence tolerance of 10⁻⁵ p.u. The method was evaluated on the IEEE 30-bus and Nigerian 31-bus networks
using MATLAB R2023a. Under base-case conditions, the IEEE 30-bus system reaches its minimum voltage at
Bus 5 (0.9360 p.u.), whereas the Nigerian 31-bus system records its lowest voltage at Bus 21 (0.9430 p.u.). After
contingency loading, the number of under-voltage buses increased from 2 to 8 in the IEEE system and from 2 to
9 in the Nigerian system. ISPEA identifies Buses 5, 7, and 23 as the most critical in the IEEE 30-bus system,
and Buses 5, 11, and 21 in the Nigerian 31-bus system. Compared with LVSI and VCPI screening, ISPEA yields
the lowest maximum loading capacity values across all evaluated buses, confirming the superior identification
of genuinely vulnerable buses for reactive power compensation siting.
Keywords — Voltage instability; weak-bus identification; contingency analysis; transmission networks; multi-
objective optimization; Improved Strength Pareto Evolutionary Algorithm; Newton–Raphson load flow;
reactive-power planning
INTRODUCTION
Voltage stability is the ability of a power system to maintain acceptable voltage magnitudes under normal
operating conditions and after any disturbances. When the system is heavily stressed, reactive power shortages,
unfavorable power transfers, and topology changes can reduce the voltage stability margin and trigger
progressive voltage decline or collapse (Zeitawyeh et al., 2025; Kobibi et al.,2022; Bharathi et al.,2023).
Contemporary work continues to emphasize that contingency-aware voltage stability assessment remains
essential because line outages and load increases can materially change the stability margin and ranking of
vulnerable buses (Luo et al., 2024; Sobayo et al., 2024; Angadi et al., 2023).
The need for reliable weak-bus identification is especially critical in transmission systems that operate near
security boundaries (Ismail et al., 2022; Puhan et al., 2024). In the Nigerian grid context, poor voltage profiles
and network fragility remain operationally relevant concerns (Alayande et al., 2024; Adeyemi et al., 2025). A
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recent Nigerian study also linked node-voltage improvement and reactive power support with improved grid
security and resilience under contingencies (Okampo et al., 2022).
Classical approaches for locating voltage-vulnerable buses include the direct inspection of bus-voltage profiles,
voltage stability indices, modal methods, continuation-power-flow-based critical-bus studies, and fuzzy or
index-based ranking procedures (Valuva et al., 2023; Mamari et al., 2021; Putranto et al., 2024). Voltage stability
indices are widely used to identify weak buses, estimate maximum loadability, and rank critical lines or areas
(Ismail, 2022; Baleboina, 2024). Modal analysis is still used to identify the weakest buses using eigenvalues and
participation factors (Ibrahim et al., 2021; Nappu et al., 2020). The continuation power flow remains a standard
method for tracing P–V curves and determining the maximum loading points and weak buses, especially under
contingencies (Wang, 2024). Fuzzy and index-based ranking procedures
They also continue to appear in decision support and compromise-solution selection for voltage-stability-
constrained operation (Kyomugisha et al., 2022; Zhang et al., 2020; Kyomugisha et al.,2021).
These tools are valuable but are often used as deterministic screening instruments rather than explicit multi-
objective decision frameworks (Alayande et al., 2024; Zhang et al., 2020). In practice, the weakest bus is rarely
defined by voltage magnitude alone because operators also care about reactive power behavior, collapse
proximity, maximum loading capacity, and compensation feasibility (Mokred et al., 2022; Adegoke et al.,2022;
Adetokun et al.,2023). Recent studies have increasingly formulated voltage stability improvement and reactive
power dispatch as constrained multi-objective optimization problems that balance voltage deviation, losses, cost,
and security margins (A. A. Liu et al., 2024; Hu et al., 2026). Generator operating conditions and reactive power
reserves are now also treated as part of the voltage stability assessment rather than peripheral details (B. B. Liu,
2023; Miyazaki et al.,2025).
This study addresses this gap by reformulating weak-bus identification as a constrained multi-objective search
problem and solving it using an Improved Strength Pareto Evolutionary Algorithm (ISPEA). The central premise
is that critical buses should be identified not only by their depressed voltage profile but also by their simultaneous
association with a low voltage-security margin, lower maximum loading capacity, and tighter interaction with
generator operating limits. The main contributions are as follows: (i) a Newton–Raphson–ISPEA voltage
instability bus identification framework; (ii) a constraint-aware objective structure that explicitly incorporates
generator operating limits; (iii) validation on both the IEEE 30-bus system and the Nigerian 31-bus network;
and (iv) interpretation of selected buses as candidate locations for reactive power compensation.
METHODOLOGY
Power-Flow Formulation
For each test network, the steady-state operating point was obtained using the Newton–Raphson method. The
active and reactive power balance equations are Pᵢ = Vᵢ Σⱼ Vⱼ (Gᵢⱼ cos δᵢⱼ + Bᵢⱼ sin δᵢⱼ) and Qᵢ = Vᵢ Σⱼ Vⱼ (Gᵢⱼ sin δᵢⱼ
− Bᵢⱼ cos δᵢⱼ). The Newton–Raphson correction step [Δδ, ΔV] ᵀ = J⁻¹[ΔP, ΔQ]ᵀ iterates until mismatches fall
below 10⁻⁵ p.u. PV buses that reach Qmax are switched to the PQ type for the remainder of the iteration,
consistent with the standard PV-to-PQ conversion practice.
Contingency Model
The contingency severity is represented by Q^c_{L,i} = 1.9 Q⁰_{L,i}, where Q⁰_{L,i} is the base-case reactive
load. This 90% reactive increase intentionally compresses the voltage security margin. The generator loading
was simultaneously monitored against a 125% megavolt-amperes (MVA) ceiling.
ISPEA-Based Weak-Bus Identification and Flowchart
The weak-bus identification problem is posed as a constrained multiobjective optimization with three
coordinated objectives: (i) minimize voltage deviation |Vᵢ − 1.0|; (ii) maximize loading capacity (equivalently,
minimize its negative); and (iii) minimize generator-operating-limit penalty. The ISPEA begins with a
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population P of 100 solutions and an empty archive A. Each member x is assigned a strength S(x) = | {y ∈ P ∪
A | x ≺ y} |, raw fitness R(x) = Σ_{y≺x} S(y), density D(x) = 1/ (σᵏ + 2), and overall fitness F(x) = R(x) + D(x)
+ ρΠ(x) with ρ = 1.0. Buses with F(x) < 1 after 200 generations are candidates for voltage instability. The
"improved" aspects relative to standard SPEA are: (i) adaptive crossover (initial probability 0.90); (ii) Gaussian
mutation (probability 0.01); and (iii) minimum distance archive truncation with next-smallest-distance tie-
breaking. Figure 1 shows the full comparison analysis flowchart used in this study.
Figure 1. Flowchart of the Newton–Raphson–ISPEA comparison analysis framework
Bus-Ranking Rule
At convergence, the buses are ranked in ascending order of F(x). Buses with F(x) < 1 are non-dominated and
classified as voltage instability candidates, and those with F(x) ≥ 1 are excluded from the critical set.
Case Studies and Computational Setup
The IEEE 30-bus system has two generators, three synchronous condensers, 15 PQ load buses, and 37 branches.
The Nigerian 31-bus system has seven generation plants, 24 load buses, and 60 transmission lines. Voltage limits
of 0.95–1.05 p.u. and a 125% generator MVA ceiling were enforced. Table 1 shows the case study (CS)
summaries for all ISPEA settings; stability was verified over 10 independent runs.
Table 1. Studies and Computational Setup CS. ISPEA computational parameters
Parameter
Value
Notes
Population size (|P|)
100
Fixed for both test systems
Archive size (|A|)
100
Maximum non-dominated solutions
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Max. generations
200
Stopping criterion
NR convergence tolerance
10⁻⁵ p.u.
Active/reactive mismatch threshold
Crossover probability
0.90
Adaptive single-point crossover
Mutation probability
0.01
Gaussian perturbation
Penalty coefficient ρ
1.0
Constraint-violation weighting
Voltage limits (p.u.)
0.95 – 1.05
±5% statutory band
Generator MVA ceiling
125% rated
Generator loading limit
Contingency loading
90% Q increase
Applied to all load buses
Independent runs
10
Solution stability verification
Software
MATLAB R2023a
Simulation environment
RESULTS AND DISCUSSION
Base-Case Load-Flow performance
Table 2 presents the base-case Newton–Raphson results for both networks. Under base-case conditions, the IEEE
30-bus network exhibits its lowest voltage at Bus 5 (V = 0.9360 p.u.), whereas Bus 23 registers V = 1.0570 p.u.,
both outside the ±5% statutory band. The total active and reactive losses were 324.31 MW and 228.85 MVAr,
respectively. The Nigerian 31-bus network reaches its minimum at Bus 21 (V = 0.9430 p.u.), whereas Bus 5
exceeds the upper limit at V = 1.0700 p.u. No generator reactive limits were active in either system under the
base conditions. The total losses for the Nigerian system were 341.93 MW and 257.69 MVAr. The maximum
loading capacities at the two vulnerable IEEE buses are 45.13 MVAr (Bus 5) and 14.25 MVAr (Bus 23),
confirming that the reactive headroom is already constrained before the contingency stress.
Table 2. Base-case load-flow results. Buses marked * fall outside the 0.95–1.05 p.u. statutory band.
IEEE 30-Bus System — Base Case
Bus No
Bus Type
V Mag (p.u.)
V Angle (°)
P Load (MW)
Q Load (MVAr)
Max Load Cap.
(MVAr)
1
Swing
1.0000
0.0000
0
0
0
2
PV
0.9630
1.5160
21.7
12.9
30.64
3
PQ
0.9780
1.6270
2.4
1.2
2.28
4
PQ
1.0240
0.6750
7.6
1.6
6.46
5
PQ
0.9360*
1.6700
0
0
45.13
6
PQ
1.0210
2.9380
0
0
46.08
7
PQ
0.9970
1.9510
22.8
7.9
24.13
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8
PQ
1.0160
1.9530
30.0
30.0
71.25
9
PQ
0.9830
1.9520
0
0
2.28
10
PQ
0.9930
0.9360
5.9
2.0
4.75
11
PQ
1.0320
1.1170
0
0
17.81
12
PQ
1.0130
0.4970
11.2
7.5
24.51
13
PQ
1.0410
2.4740
0
0
17.81
14
PQ
1.0290
2.8950
6.2
1.6
9.12
15
PQ
1.0370
2.5940
8.4
2.5
10.83
16
PQ
1.0150
0.5880
3.5
1.8
3.61
17
PV
0.9820
2.5440
9.0
4.8
11.40
18
PQ
1.0220
2.9100
3.2
0.9
3.04
19
PQ
0.9950
0.6270
9.5
3.4
16.86
20
PQ
0.9910
0.5990
4.2
0.7
3.80
21
PQ
0.9890
3.4470
19.7
5.2
3.61
22
PQ
0.9880
2.4370
0
0
5.70
23
PQ
1.0570*
1.4210
3.2
1.6
14.25
24
PQ
0.9630
1.3450
18.0
5.7
15.91
25
PQ
0.9580
1.3660
1.0
0
0.38
26
PQ
1.0290
3.4320
2.5
2.3
14.25
27
PQ
1.0250
0.6320
0
0
12.73
28
PQ
1.0130
2.4520
0
0
9.12
29
PQ
0.9980
2.0770
3.7
0.9
3.61
30
PV
0.9940
1.0370
12.0
1.9
4.51
Nigerian 31-Bus System — Base Case
Bus
No
Bus
Type
V Mag
(p.u.)
V Angle (°)
P Load
(MW)
Q Load
(MVAr)
Max Load Cap.
(MVAr)
1
Swing
1.0500
0.000
68.9
51.7
108.4
2
PV
1.0000
3.3950
0
0
13.64
3
PQ
0.9550
-0.2860
274.4
205.8
431.5
4
PV
0.9730
0.5060
344.7
258.5
538.5
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5
PQ
1.0700*
0.9160
633.2
494.9
988.7
6
PQ
0.9990
2.4750
13.8
10.3
21.7
7
PQ
0.9650
0.8260
96.5
72.4
150.7
8
PQ
0.9850
3.8390
383.3
287.5
600.5
9
PQ
0.9950
1.5840
275.8
216.8
431.4
10
PV
1.0100
2.0940
201.2
170.9
315.6
11
PQ
1.0130
0.7490
52.5
39.4
81.6
12
PQ
1.0150
0.1500
427.0
320.2
664.4
13
PQ
0.9850
0.0780
177.9
133.4
278.6
14
PQ
0.9600
2.7980
184.6
138.4
288.3
15
PQ
0.9850
3.9570
114.4
85.9
178.7
16
PV
1.0050
1.5900
130.6
99.5
203.1
17
PQ
1.0200
1.2290
130.6
97.9
203.4
18
PQ
1.0300
0.5300
0
0.001
13.04
19
PQ
1.0150
-2.1200
70.3
52.7
109.8
20
PQ
1.0180
4.8480
193.0
144.7
301.9
21
PQ
0.9430*
2.2840
7.0
0.25
8.8
22
PQ
0.9950
-4.4480
199.8
149.9
312.3
23
PQ
1.0150
-0.1480
320.1
256.1
513.3
24
PQ
0.9780
1.5920
20.6
15.4
32.0
25
PV
1.0150
3.9400
130.0
89.0
175.1
26
PQ
1.0190
2.7520
290.0
145.0
404.9
27
PV
1.0100
2.5520
0
0
12.73
28
PQ
1.0150
3.7960
0
0
9.12
29
PQ
1.0170
3.8550
0
0
128.8
30
PQ
1.0270
3.9740
0
0
4.51
31
PQ
1.0210
-1.3550
0
0
6.98
Contingency-Case Load-Flow Performance
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Table 3 presents the contingency-voltage profiles. The minimum voltage in the IEEE 30-bus system dropped
from 0.9360 p.u. to 0.9000 p.u. (Buses 5, 16, 23, 24, 26, and 29), while the Nigerian 31-bus minimum drops
from 0.9430 p.u. to 0.9001 p.u. (Bus 5). The under-voltage bus count increases from 2 to 8 in the IEEE system
and from 2 to 9 in the Nigerian system. IEEE 30-bus active losses rise from 324.31 to 541.66 MW (+67.1%),
and Nigerian 31-bus active losses rise from 341.93 to 684.52 MW (+100.2%). These results confirm that the
90% reactive contingency constitutes a severe stress that materially degrades the voltage security margin of both
networks.
Table 3. Contingency-case load-flow results (90% reactive-load increase). Buses marked * fall below 0.95 p.u.
IEEE 30-Bus System — Contingency
Bus No
Bus
Type
V Mag (p.u.)
V Angle
(°)
P Load (MW)
Q Load
(MVAr)
Max Load Cap.
(MVAr)
1
Swing
1.0000
0.0000
8.76
7.68
0.38
2
PV
0.9500
0.5620
47.09
27.87
31.23
3
PQ
0.9600
0.6272
5.18
2.59
2.56
4
PQ
0.9500
0.7209
16.42
3.46
7.44
5
PQ
0.9000*
0.5919
7.2
4.08
68.60
6
PQ
0.9500
0.9203
7.2
2.94
50.04
7
PQ
0.9202*
0.9322
49.25
17.07
36.68
8
PQ
0.9501
1.0412
64.8
59.04
78.30
9
PQ
0.9501
1.0421
7.2
6.36
2.47
10
PQ
0.9600
0.3803
12.75
4.32
5.22
11
PQ
0.9500
0.1102
7.2
6.41
17.97
12
PQ
0.9573
0.9418
24.13
16.2
27.26
13
PQ
0.9600
1.5691
7.2
6.43
17.97
14
PQ
0.9500
0.9062
11.16
2.88
9.85
15
PQ
0.9601
0.6127
7.87
1.82
10.96
16
PQ
0.9000*
0.8402
25.92
4.11
6.65
17
PV
0.9500
1.5316
19.44
10.37
12.10
18
PQ
0.9601
1.9734
6.91
1.95
3.08
19
PQ
0.9200*
0.0231
20.52
7.35
17.05
20
PQ
0.9600
0.0967
9.07
1.51
3.98
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PQ
0.9501
2.4572
28.37
7.90
5.49
22
PQ
0.9600
0.3311
7.2
6.42
5.96
23
PQ
0.9000*
1.0643
6.91
1.355
21.66
24
PQ
0.9000*
0.4235
38.88
12.31
24.18
25
PQ
0.9500
0.3783
2.16
6.72
0.90
26
PQ
0.9000*
0.0469
5.4
5.26
21.66
27
PQ
0.9500
0.0282
7.2
6.28
13.35
28
PQ
0.9500
1.4124
7.22
6.54
9.86
29
PQ
0.9000*
1.1942
18.15
5.20
5.49
30
PV
0.9500
0.1219
7.56
3.89
4.86
Nigerian 31-Bus System — Contingency
Bus
No
Bus Type
V Mag
(p.u.)
V Angle
(°)
P Load
(MW)
Q Load
(MVAr)
Max Load Cap.
(MVAr)
1
Swing
1.0500
0.0000
148.74
111.67
108.4
2
PV
0.9500
0.3463
7.92
5.45
13.64
3
PQ
0.9055*
0.9323
592.71
444.53
489.08
4
PV
0.9522
0.0053
744.06
558.36
538.5
5
PQ
0.9001*
0.9742
1266.80
1068.98
1127.56
6
PQ
0.9500
0.7012
29.81
22.25
21.7
7
PQ
0.9500
0.3043
208.44
156.38
150.7
8
PQ
0.9531
0.5443
827.93
621.0
600.5
9
PQ
0.9041*
0.8362
595.73
468.29
490.17
10
PV
0.9500
0.6392
434.59
369.14
315.6
11
PQ
0.9060*
0.9061
113.4
85.11
81.6
12
PQ
0.9500
0.0365
922.32
691.63
664.4
13
PQ
0.9003*
0.0772
384.24
288.15
316.48
14
PQ
0.9501
0.0763
398.74
298.94
288.3
15
PQ
0.9541
0.8343
247.10
185.55
178.7
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16
PV
0.9500
0.6964
282.10
214.92
203.1
17
PQ
0.9534
0.9558
282.10
211.86
203.4
18
PQ
0.9201*
0.0773
8.06
6.73
19.82
19
PQ
0.9501
0.8023
151.85
113.83
109.8
20
PQ
0.9500
0.8662
416.88
312.11
301.9
21
PQ
0.9101*
0.9540
15.12
5.4
0.59
22
PQ
0.9541
0.0832
431.57
323.78
312.3
23
PQ
0.9561
0.9780
691.42
553.18
513.3
24
PQ
0.9504
0.0690
44.50
33.26
32.0
25
PV
0.9500
0.0427
280.8
192.24
175.1
26
PQ
0.9400*
0.2026
626.4
313.20
343.44
27
PV
0.9500
0.8046
8.06
5.45
12.73
28
PQ
0.9601
0.8301
7.92
6.61
9.12
29
PQ
0.9500
0.8025
8.29
7.63
128.8
30
PQ
0.9350*
0.1640
8.17
5.17
6.86
31
PQ
0.9500
0.0536
7.92
4.66
6.98
ISPEA Weak-Bus Ranking
Tables 4 and 5 present the core ISPEA weak-bus rankings, respectively. Figure 2 (IEEE) and 3 (Nigerian) show
the corresponding total power losses after the ISPEA application. In the IEEE 30-bus network, ISPEA identifies
Buses 5, 7, and 23 as the most critical under contingency loading (ISPEA fitness: 0.96, 0.84, 0.76; max loading
caps: 50.63, 28.01, 18.04 MVAr). Bus 7 migrated into the critical set only under contingency, revealing
contingency-sensitive vulnerability. In the Nigerian 31-bus network, buses 5, 11, and 21 are the most vulnerable
(fitness: 0.94, 0.76, 0.65; max loading caps: 902.31, 74.86, 0.48 MVAr). Bus 21 had the lowest fitness value
(0.65) with near-zero reactive headroom (0.48 MVAr), indicating extreme sensitivity to reactive stress.
Table 4. ISPEA weak-bus ranking — IEEE 30-bus system.
Bus
V Mag
(p.u.)
Max Load Cap.
(MVAr)
ISPEA
Fitness
Base-Case
Rank
Contingency
Rank
Rank Shift
5
1.0000
50.63
0.96
1
1
0 (persistent)
7
1.0000
28.01
0.84
3
2
+1 (contingency-
sensitive)
23
1.0000
18.04
0.76
2
3
-1 (less critical under
stress)
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24
0.9500
10.83
1.00
4
4
0
26
0.9500
14.24
1.00
5
5
0
29
0.9500
2.71
1.00
6
6
0
Figure 2. Total active and reactive power losses of the IEEE 30-bus system after ISPEA application: Active =
440.23 MW, Reactive = 325.82 MVAr
Table 5. ISPEA weak-bus ranking — Nigerian 31-bus system.
Bus
V Mag
(p.u.)
Max Load Cap.
(MVAr)
ISPEA
Fitness
Base-Case
Rank
Contingency
Rank
Rank Shift
5
1.0000
902.31
0.94
1
1
0 (persistent)
11
1.0000
74.86
0.76
3
2
+1 (contingency-sensitive)
21
1.0000
0.48
0.65
2
3
-1 (severe, near-zero
headroom)
26
0.9503
275.50
1.00
4
4
0
30
0.9501
6.86
1.00
5
5
0
3
0.9501
390.98
1.00
6
6
0
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Figure 3. Total active and reactive power losses of the Nigerian 31-bus system after ISPEA application: Active
= 490.59 MW, Reactive = 391.34 MVAr
Voltage-Profile Comparison (Figure 2 and 3)
Figure 2 compares the voltage magnitudes across all buses for the IEEE 30-bus system under steady-state,
ISPEA, LVSI, and VCPI conditions. With ISPEA, buses 5, 7, and 23 each achieved 1.0000 p.u. In contrast,
LVSI produces 0.9500 p.u. at buses 5, 16, and 23, whereas VCPI yields magnitudes of 0.8862, 0.7312, and
0.7793 p.u. at buses 5, 11, and 21, respectively. Figure 3 shows the corresponding comparison for the Nigerian
31-bus system. The ISPEA maintains 1.0000 p.u. at buses 5, 11, and 21; the LVSI produces 0.9503 p.u. at buses
5 and 21; and the VCPI achieves 0.9824, 0.9510, and 0.9822 p.u. at buses 5, 11, and 29, respectively. ISPEA
consistently provided the strongest voltage recovery at the identified critical buses.
Figure 4. Comparison of voltage magnitude across all buses — IEEE 30-bus system under steady-state, ISPEA,
LVSI, and VCPI conditions
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Figure 5. Comparison of voltage magnitude across all buses — Nigerian 31-bus system under steady-state,
contingency, ISPEA, LVSI, and VCPI conditions.
Practical Implication for Compensation Placement
The ISPEA-selected buses constitute priority candidate locations for corrective reactive power support because
they are not merely low-voltage buses; they are buses whose voltage weakness persists after loadability and
generator operating constraints are incorporated. For the IEEE 30-bus system, a hybrid STATCOM/SVC at
Buses 5, 7, and 23 with sizes 5.03, 7.38, and 7.78 kVAr restores all voltages to 1.0000 p.u. and reduces active
losses to 265.92 MW (−50.9% from the contingency). For the Nigerian 31-bus system, STATCOM/SVC sizes
of 7.38, 14.34, and 14.34 kVAr at Buses 5, 11, and 21 similarly restored voltages to 1.0000 p.u. and reduced
active losses to 316.10 MW (−53.8% from contingency). ISPEA consistently yielded the lowest loading capacity
values across all evaluated buses, which is an operationally meaningful outcome when the goal is to prioritize
buses that are most susceptible to reactive power collapse.
CONCLUSION
This paper presents an Improved Strength Pareto Evolutionary Algorithm for voltage instability bus
identification in transmission networks under steady-state and contingency loading. By combining the Newton–
Raphson load-flow analysis with a constraint-aware multiobjective ranking structure, the ISPEA identifies weak
buses using three coordinated criteria: voltage magnitude behavior, maximum loading capacity, and generator
operating constraints. Application to the IEEE 30-bus and Nigerian 31-bus systems demonstrates that ISPEA is
an effective decision-support tool for locating critical buses that should be prioritized for voltage-support
interventions.
This method reframes weak-bus identification as an optimization problem rather than a single-index screening
exercise. Under reactive power stress, the most problematic bus is the one that combines poor voltage with a low
security margin and high exposure to operating constraints. A comparison with LVSI and VCPI confirmed that
ISPEA yielded the lowest loading-capacity values across all evaluated buses, demonstrating superior
prioritization of genuinely vulnerable locations. Future studies should validate the rankings against alternative
contingencies, multiple loading patterns, and additional multi-objective optimizers.
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Author Statements
Data availability: Derived from the IEEE 30-bus test system and Nigerian 31-bus transmission network dataset.
Available from the corresponding author on reasonable request.
Code availability: MATLAB R2023a scripts are available. Available from the corresponding author on
reasonable request.
Conflict of interest: The authors declare no conflicts of interest.
Funding: This research did not receive any external funding.
REFERENCES
1. Adegoke, S. A., & Sun, Y. (2022). Power system optimization approach to mitigate voltage instability
issues: A review. Cogent Engineering. https://doi.org/10.1080/23311916.2022.2153416
2. Adetokun, B. B., Muriithi, C., Ojo, J., & Oghorada, O. (2023). Impact assessment of increasing
renewable energy penetration on voltage instability tendencies of power system buses using a QV-based
index. Scientific Reports, 13. https://doi.org/10.1038/s41598-023-36843-5
3. Adeyemi, N. A., & Adebayo, I. (2025). Power System Stability Development and Application of
Mathematical Model of Reactive Power Loss Index as a Measurement of Voltage Stability in Nigerian
Transmission System. LAUTECH Journal of Engineering and Technology.
https://doi.org/10.36108/laujet/5202.91.0302
4. Alayande, A. S., Hassan, A., Olobaniyi, F., Osokoya, S. O., Adebeshin, A. I., & Ogundare, A. B. (2024).
L-Index-Based Technique for Voltage Collapse Prediction and Voltage Stability Enhancement in
Electrical Power Systems. ABUAD Journal of Engineering Research and Development (AJERD).
https://doi.org/10.53982/ajerd.2024.0701.27-j
5. Angadi, R. V., Mangai, J. A., Manohar, V., Daram, S. B., & Rao, P. (2023). Ensemble-based data mining
model for contingency analysis of power system under STLO. International Journal of Applied Power
Engineering (IJAPE). https://doi.org/10.11591/ijape.v12.i4.pp349-358
6. Babu, R., Raj, S., Dey, B., & Bhattacharyya, B. (2021). Optimal reactive power planning using
oppositional grey wolf optimization by considering bus vulnerability analysis. Energy Conversion and
Economics. https://doi.org/10.1049/enc2.12048
7. Baleboina, G. M., & Rudramoorthy, M. (2024). Stability analysis of power system under n-1 contingency
condition. Bulletin of Electrical Engineering and Informatics. https://doi.org/10.11591/eei.v13i4.6133
8. Bharathi, Atla, C. S. R., & M. R. S. (2023). Power System Voltage Collapse Mitigation Employing
Optimization-Based Dynamic Voltage Stability Analysis. U.Porto Journal of Engineering.
https://doi.org/10.24840/2183-6493_009-003_001645
9. Chi, Y.-Q., Tao, A., Xu, X., Wang, Q., & Zhou, N. (2023). Adaptive Many-objective Robust
Optimization Model of Dynamic Reactive Power Sources for Voltage Stability Enhancement. Journal of
Modern Power Systems and Clean Energy. https://doi.org/10.35833/mpce.2022.000431
10. Hu, Y., Hu, W., Li, X., Shi, Y., Jin, J., Ren, X., Fan, X., & Yang, T. (2026). Optimal reactive power
dispatch based on a multitask-assisted constrained multimodal multi-objective evolutionary
algorithm. iScience, 29. https://doi.org/10.1016/j.isci.2026.115434
11. Hu, Y., Hu, W., Li, X., Shi, Y., Jin, J., Ren, X., Fan, X., & Yang, T. (2026). Optimal reactive power
dispatch based on a multitask-assisted constrained multimodal multi-objective evolutionary
algorithm. iScience, 29. https://doi.org/10.1016/j.isci.2026.115434
12. Ibrahim, M., & Jasim, A. (2021). Voltage Collapse Prediction of IEEE 30-Bus System. Tikrit Journal of
Engineering Sciences. https://doi.org/10.25130/tjes.28.1.10
13. Ismail, B., Wahab, N. A. A., Othman, M., Radzi, M., Vijyakumar, K. N., & Naain, M. N. M. (2020). A
Comprehensive Review on Optimal Location and Sizing of Reactive Power Compensation Using
Hybrid-Based Approaches for Power Loss Reduction, Voltage Stability Improvement, Voltage Profile
Enhancement, and Loadability Enhancement. IEEE Access, 8, 222733-222765.
https://doi.org/10.1109/access.2020.3043297
www.rsisinternational.org
Page 3676
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue VI, June 2026
14. Ismail, B., Wahab, N., Othman, M. L., Radzi, M., Vijayakumar, K. N., Rahmat, M., & Naain, M. M.
(2022). New Line Voltage Stability Index (BVSI) for Voltage Stability Assessment in Power System:
Comparative Studies. IEEE Access, 10, 103906-103931. https://doi.org/10.1109/access.2022.3204792
15. Izzati, T. N., Soeprijanto, A., Syifa, B. N., Aryani, N. K., & Rahayu, P. (2025). Voltage Stability
Enhancement Using NCPI-Based Optimal Reactive Power Compensation during Critical Line
Outages. 2025 International Seminar on Intelligent Technology and Its Applications (ISITIA), 755-760.
https://doi.org/10.1109/isitia66279.2025.11137457
16. Kobibi, Y. D., Djehaf, M. A., Khatir, M., & Ouadafraksou, M. (2022). Continuation Power Flow
Analysis of Power System Voltage Stability with a Unified Power Flow Controller. Journal of Intelligent
Systems and Control. https://doi.org/10.56578/jisc010106
17. Kyomugisha, R., Muriithi, C., & Nyakoe, G. (2022). Performance of Various Voltage Stability Indices
in Stochastic Multiobjective Optimal Power Flow Using Mayfly Algorithm. J. Electr. Comput. Eng.,
2022, 7456333:1-7456333:22. https://doi.org/10.1155/2022/7456333
18. Luo, Y., & Liu, C. (2024). Power Systems Static Voltage Stability Assessment Considering N-1
Contingencies Based on Holo-morphic Embedding Method. 2024 IEEE Power & Energy Society
General Meeting (PESGM), 01-05. https://doi.org/10.1109/pesgm51994.2024.10761098
19. Luo, Y., & Liu, C. (2024). Power Systems Static Voltage Stability Assessment Considering N-1
Contingencies Based on Holo-morphic Embedding Method. 2024 IEEE Power & Energy Society
General Meeting (PESGM), 01-05. https://doi.org/10.1109/pesgm51994.2024.10761098
20. Mamari, A. S. A., Toha, S., Ahmad, S., & Mamari, A. (2021). Modal analysis based on reactive power
compensation on 6-bus Oman electrical grid. International Journal of Power Electronics and Drive
Systems (IJPEDS). https://doi.org/10.11591/ijpeds.v12.i2.pp757-764
21. Miyazaki, M., Aoki, M., & Nakamura Y. (2025). Voltage Stability Estimation Considering Variability
in Reactive Power Reserves Using Regression Trees. Energies. https://doi.org/10.3390/en18051260
22. Mokred, S., Wang, Y., & Chen, T.-L. (2023). A novel collapse prediction index for voltage stability
analysis and contingency ranking in power systems. Protection and Control of Modern Power Systems,
8, 1-27. https://doi.org/10.1186/s41601-023-00279-w
23. Mossie, M. A., Yetayew, T., Bitew, G. T., Yenealem, M. G., & Beza, T. M. (2025). Machine learning
algorithms for voltage stability assessment in electrical distribution systems. Scientific Reports, 15.
https://doi.org/10.1038/s41598-025-15791-2
24. Nappu, M. B., Arief, A., Alam, N., & Zulfachri, M. (2020). Voltage stability assessment of the Southern
Sulawesi power system in Indonesia for 2020 using modal analysis. IOP Conference Series: Earth and
Environmental Science, 473. https://doi.org/10.1088/1755-1315/473/1/012097
25. Nascimento, S., & Gouvêa, M. (2021). Multi-objective Adaptive Evolutionary Algorithm to Enhance
Voltage Stability in Power Systems. International Journal of Control, Automation and Systems, 19, 2596
- 2610. https://doi.org/10.1007/s12555-020-0095-4
26. Nascimento, S., & Gouvêa, M. (2021). Multi-objective Adaptive Evolutionary Algorithm to Enhance
Voltage Stability in Power Systems. International Journal of Control, Automation and Systems, 19, 2596
- 2610. https://doi.org/10.1007/s12555-020-0095-4
27. Okampo, E., Nwulu, N., & Bokoro, P. (2022). Optimization of Voltage Security with Placement of
FACTS Device Using Modified Newton–Raphson Approach: A Case Study of Nigerian Transmission
Network. Energies. https://doi.org/10.3390/en15124211
28. Olasunkanmi, O. G., Barron, A. R., White, A. O., & Todeschini, G. (2024). Evaluation of HVDC
Interconnection to Improve Voltage Stability of Nigerian Transmission Network. Journal of Electronics
and Electrical Engineering. https://doi.org/10.37256/jeee.3120243799
29. Puhan, S. S., Sharma, R., & Mallick, M. (2024). Ensuring grid resilience: Voltage stability analysis and
contingency ranking in electric power systems. e-Prime - Advances in Electrical Engineering,
Electronics and Energy. https://doi.org/10.1016/j.prime.2024.100696
30. Puppala, V., & Chandrarao, D. T. P. (2018). Voltage stability assessment considering power system
contingencies using continuation power flow method with regression.
31. Putranto, L. M., & Azhar, I. F. (2024). A proposed PMU-based voltage stability and critical bus detection
method using an artificial neural network. Energy Informatics, 7. https://doi.org/10.1186/s42162-024-
00302-w
www.rsisinternational.org
Page 3677
INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
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32. Sobayo, A. S., Adejumobi, O. I., Adebisi, I. A., & Adams, D. O. (2024). Contingency Approach for
Static Security Assessment on the Nigerian 330 Kv Electric Power Transmission Grid. Advances in
Science and Technology, 154, 203 - 212. https://doi.org/10.4028/p-stvce4
33. Valuva, C., Chinnamuthu, S., Khurshaid, T., & Kim, K.-C. (2023). A Comprehensive Review on the
Modelling and Significance of Stability Indices in Power System Instability Problems. Energies.
https://doi.org/10.3390/en16186718
34. Zeitawyeh, R. A., & Faza, A. (2025). Optimal Reactive Power Planning Using FACTS Devices for
Voltage Stability Enhancement in Power Transmission Systems. Energy Sci. Eng., 13.
https://doi.org/10.1002/ese3.70064.
35. Zhang, M., & Li, Y. (2020). Multi-objective optimal reactive power dispatch of power systems by
combining classification-based multi-objective evolutionary algorithm and integrated decision-
making. IEEE Access, 8, 38198-38209. https://doi.org/10.1109/access. 2020.2974961, 1(5): 186–200.
