Arid Zone Journal of Engineering, Technology and Environment, December, 2018; Vol. 14(4):713-726
Copyright © Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria.
Print ISSN: 1596-2490, Electronic ISSN: 2545-5818, www.azojete.com.ng

713

ASSESSMENT OF ELECTRICAL GRID FRAGILITY IN NIGERIA-31 BUS SYSTEM

P. O. Oluseyi*, T. O. Ajekigbe, O. M. Babatunde and T. O. Akinbulire
Department of Electrical/Electronics Engineering, University of Lagos, Akoka, Lagos, Nigeria
*Corresponding author’s e-mail address: poluseyi@unilag.edu.ng, drpeteroluseyi@gmail.com

Abstract
The grid fragility is a prevalent challenge in Nigeria electricity supply industry (NESI). It has resulted in
recorded incidents of voltage collapse which have been on the increase in the recent time. Meanwhile to
evaluate this events; thus the nexus between voltage collapse and network capacity was explored. To
actualize this, the load flow analysis was carried out on the Nigeria-31 bus system with the aid of the
Newton-Raphson iteration technique. Using the relevant parameters (such as bus voltage magnitude, bus
voltage angle, generated power, injected power as well as load magnitude) obtained from the analysis, the
line stability index and line stability factor were obtained for every line in the network. It was discovered
from the values of line stability index that Lines (26-2); (31-7); (10-11); (24-10) and (18-12) are weak and
fragile while for the line stability factor, the values obtained for Lines (10-8); (11-8); (11-10); (24-10) and
(18-12) indicate the fragility of some of the lines in the Nigerian Transmission Network. From this, it was
established that the weakest lines were those whose values range from 0.3051 to 0.8813 for the line
stability index. Correspondingly; any line that takes the value between 0.2737 and 0.9924 in respect of the
line stability factor was also marked as the weakest lines in the network. Thus it was noticed that for the
two line stability indices (i.e. stability factor and stability index); Line (11-10) i.e. from Oshogbo to Ikeja-
West bus is the most fragile line in Nigeria-31 bus transmission network while the nearest to it are lines
(24-10) i.e. from Ayede to Ikeja-West bus and (12-18) i.e. from Kaduna to Kano bus. This study is
potentially sufficient for determining the lines in the transmission network that require utmost
consideration for reinforcement in respect of the transmission expansion planning schemes.

Keywords: Transmission, fragility, stability index, collapse, electricity

1. Introduction
Electricity is the most crucial vehicle for socio-economic advancement in any nation. In
industries, it is established that electricity contributes about 35 percent to the total cost of
production. Therefore, lack of adequate electricity supply reduces the interest of investors due to
unprecedented costs of production (Oluseyi, 2010). This may have its attendant problem on the
increasing the rate of unemployment as well as complicate the human poverty index of a
community.
Almost 50 per-cent of the Nigeria’s population (precisely 76 million people) do not have access
to electricity in Nigeria (Egeruoh, 2012) while the rest of the percentage do not have adequate
supply of electricity. From the foregoing, it is therefore very crucial to look into steps to improve
electricity in such an environment. Efforts have been made over the years to improve electricity
supply in Nigeria. This has led to a number of policies in respect of the Electric Power Sector
Reforms Act (Oluseyi, 2010). One of these is the restructuring and deregulation of the power
sector to enhance access to electricity (Oluseyi et al., 2009). The principle of deregulation
involves provision of enabling environment for the investors to embark on electric power
generation. With the advent of this, pressure is placed on the national grid to wheel the generated
energy to the various Distribution Companies (Oluseyi et al., 2012). The effects of deregulation
on the grid are therefore highly profound and need to be carefully investigated (Oricha et al.,
2009). Several system collapse reports have been encountered in the recent times in the Nigerian
national grid. Quite a number of these abnormal functioning of the transmission network has
been related to poor network capacity of the transmission facilities (Samuel et al., 2014) Thus, it
has been quite impossible for the current Nigerian National grid to transport the recent total
generated capacity to the load end. In order to record tangible improvement in power supply, the
fragile Nigerian National grid has to be reinforced to ensure it has the capacity to wheel the
quantum of generated electric power.

mailto:poluseyi@unilag.edu.ng
mailto:drpeteroluseyi@gmail.com
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Oluseyi et al.: Comparative Analysis of Grid Fragility Indices in the Nigerian Transmission Network.
AZOJETE, 14(4):713-726. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

714

The review of the incidence of system collapse events on the transmission network have been
done in past studies which revealed that in the last ten years, the Nigerian national grid has
experienced an average of thirty-five system collapses per year (Awosope, 2014). Furthermore, a
thorough assessment of voltage instability has been well documented for purpose of improving
the phenomenon (Airoboman et al., 2015).
This study, by means of variously developed stability indices, examines the grid fragility on the
Nigerian Transmission Network. This is quite different from the previous approaches in a
number of ways. For instance; much more than lumping the network parameters into one
component while determining the fragility of the grid, this study developed a model for the
investigating the extent of fragility of each line in the grid. This provides empirical information
on the fragility status of lines in the entire network; thus facilitating establishing the identification
of weakest buses. Hence, it aids in locating the potentially weakest buses that may threaten the
system stability. Thus, this assists in prudent manipulation of the network operation for the
purpose of proffering practical approach to mitigating the challenges of voltage collapse
phenomenon. More importantly, this analysis of the grid fragility will serve as analytic
framework to various transmission expansion planning schemes; in which case the weak line
may be reinforced further to mitigate further voltage collapse in the network.

2. Materials and Methods
The primary material for this work is the bus and line data of the Nigeria-31 bus system (as it
currently operates). This was collected from the Transmission Company of Nigeria (TCN). In
order to evaluate this, the MATLAB™ Software Package (2012) would be employed. The
standard approach adopted for the analysis of the transmission network is analytical combined
with the simulation technique. In the case of the analytical methodology, this involves the
application of the outcome of the Newton-Raphson algorithm to the well-established
mathematical model for the evaluation of the line stability indices. The two main line stability
indices that would be used are Line stability index and Line stability Factor. So also the same
transmission network would be further evaluated using the Powerworld Simulator which is
interactive power system simulation package which is used to evaluate the contingency analysis
study of the transmission network.
The analysis of the Newton-Raphson load flow is carried out using the load flow equation (for N-
bus system). This is expressed in polar form as follows.

(1)

The current can thus be further simplified into real and reactive components as follows:

(2)

This can then be re-arranged as follows.

)(
11

**
ijjij

N

Nj
ji

N

i
iiiiii YVVSVIjQP

g

g

  
 (3)

Separating this into the real and the imaginary parts we then obtain the equations (4) and (5);
however note that the total number of buses irrespective of whether generator or load is N; hence
it is taken for granted that the iteration from i=1 to N is the limit of summation as depicted in the
following equations.

j

N

i
iji VYI 




1

*
i

ii
i V

jQP
I




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Arid Zone Journal of Engineering, Technology and Environment, December, 2018; Vol. 14(4):713-726.
ISSN 1596-2490; e-ISSN 2545-5818; www.azojete.com.ng

715

)(
1

*
ijjiijj

N

ij
j

ii CosYVVP  



(4)

)(
1

*
ijjiijj

N

ij
j

ii SinYVVQ  



(5)

The algorithm for computing involves:
Step 1: Formation of the Ybus
Step 2: Assume the initial values of bus voltage as 0V for all load buses (PQ) buses and bus
angle as 0

i for all the buses except the slack bus
Step 3: Compute Pi and Qi for each load bus using equations (4) and (5)
Step 4: Compute the scheduled errors (i.e. ΔPi and ΔQi for each load bus using the equations:

niPPP calc
i

spec
ii ...3,2,1; 

(6)
Where i= 1, 2, … N for PQ buses and

niQQQ calc
i

spec
ii ...3,2,1; 

(7)
Step 5: Compute the elements of Jacobian matrix










43

21

JJ
JJ

(8)
Where J2=J3=0

Step 6: From steps 6, 7 and 8; write the syetm equation as:



































V
V

J
J

Q
P 

4

1

0
0

(9)
Step 7: Expand the equation and thus obtain the values of Δδi and ΔVi from equation (9) so as to
modify the voltage magnitude and phase angle for each of the buses in the network (Oluseyi,
2010).
Step 8: Set up the equations for calculating the new voltage magnitude and angle as follows:

r
i

r
i

r
i VVV 1

(10)
)()()1( r

i
r
i

r
i  

(11)
Step 9: Commence a new iteration cycle from Step 2 with the new values of voltage magnitude
and phase angle obtained in Step 8.
Step 10: Continue this until the scheduled error is within the pre-set specified tolerance value.

i.e. 







)(

)( ;

r
i

r
i

Q
and
P





The ensuing power flow solution is then employed in the subsequent sections of the work.

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Oluseyi et al.: Comparative Analysis of Grid Fragility Indices in the Nigerian Transmission Network.
AZOJETE, 14(4):713-726. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

716

Figure 1: Flow Chart of the Newton-Raphson Load Flow Iteration Algorithm

START

READ SYSTEM DATA

COMPUTE Δ|V| AND Δδ USING EQUATIONS (10) AND (11)

FOR VOLTAGE-CONTROLLED BUSES: COMPUTE PiAND ΔPi
USING EQUATIONS (4) AND (6)

COMPUTE THE ELEMENTS OF J1AND J4USING EQUATION (9)

FOR LOAD BUSES, COMPUTE PiAND Qi USING EQUATIONS

(4) AND (5); ΔPiAND ΔQi FROM EQUATIONS (6) AND (7)

SPECIFY Pi spec AND Qi spec FOR LOAD BUSES

FORM Y- BUS MATRIX

SET |Vi| = 1.0, δi =0.0

CHECK FOR CONVERGENCE

PRINT RESULTS

DOES SOLUTION
CONVERGE?

YES

NO

STOP

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Arid Zone Journal of Engineering, Technology and Environment, December, 2018; Vol. 14(4):713-726.
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717

In the case of (N-1) contingency analysis test, the powerworld simulator is arranged as shown in
the flow chart shown in Figure 2.

Figure 2: Flow Chart of Contingency Analysis Algorithm (Scott, 2012)

The powerworld has a menu for contingency analysis in which case the contingency analysis
dialogue box is open. Then the line and bus data are then uploaded in which case the “run” mode
is thus activated so as to generate the relevant results (see Figure 2) along with the pictorial
display of the entire network as shown in Figure 4.

2.1 Detection of Weakest Lines Using Stability Indices
In the determination of grid fragility, there are several stability indices that can be employed
(Oluseyi, 2010). In this work, the line stability index and the line stability factor shall be
employed to detect the weakest lines in the Nigerian national grid. From this, the lines that
should be given greater priority in respect of network reinforcement in line with previous
comparative study of voltage stability indices are identified (Sinha and Hazarika, 2000). The
preferred load flow study for this analysis is the Newton–Raphson load flow approach. The
Newton-Raphson technique is chosen for obvious reasons, amongst which is that it has solutions
for cases of divergence in iteration (Oluseyi, 2010). Thus the Newton-Raphson iterative method
is used in load flow analysis and the results obtained are used to compute the above mentioned
indices (Goh, et al, 2015).

Base Case

Violation?

Run primary contingencies

Fix violations

Violation?

Model system
adjustment

Run secondary
contingencies

Apply ith primary
contingency

Violation?
YES

NO

NO

YES

YES

NO

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Oluseyi et al.: Comparative Analysis of Grid Fragility Indices in the Nigerian Transmission Network.
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718

2.2 Line Stability Index
The work of Moghavvemi and Omar (1998) on the conceptual modelling of the line stability
index was adopted for this calculation. The assumption made was that the power flow through a
single line. Thus by the use of the system reduction techniques to represent the entire
transmission network as a single line, as shown in Figure 3, the equivalent network analysis is
thus modelled as depicted equation (1) for the computation of the overall system stability
index.

Figure 3: Diagram of a Transmission Line with 2-Bus System (Goh et al., 2015)
The line stability index using this technique is given as:

 2
4
sin

R
mn

s

XQL
V δ


(12)

where:
VS is the sending end voltage
S and R are the phase angle at the sending and receiving buses respectively
X is the line reactance
θ is the line impedance angle

Based on the stability indices of lines, voltage collapse can be predicted. When the stability index
Lmn is less than 1, the system is stable and when this index exceeds the value 1, the whole system
loses its stability and voltage collapse occurs (Tran, 2009).

By extension, in the application to calculation of grid fragility for the purpose of this work, the
line stability index is computed for every line in the transmission network rather than
compressing the whole system into a single line equivalent. The lines with the stability index
closest to 1 will be identified as the most fragile lines in the system.

2.3 Line Stability Factor (LQP)
For proper and effective identification of the weakest lines in the transmission network, a further
analysis was performed on the network using another concept of the stability index. In this case,
the Line Stability Factor (LQP) was employed while the results are compared with those obtained
from the Line Stability Index earlier obtained. The stressed transmission network would
obviously results in voltage collapse, thus the network is better monitored to ensure that the
stability margin is not violated. This is best done by approaching the network stability analysis
using voltage stability index (Ratra, et al, 2018). Moreover, the LQP is also formulated so as to
enumerate the stability status of the transmission networks. This approach is thus applied to the
currently existing Nigeria-31 bus system using Equation (2). Similarly, Figure 1 is also valid for
this derivation of this calculation.

2
2 24 s R
s s

X XLQP P Q
V V

   
    

   
(13)

X is the line reactance
VS is the voltage magnitude at the sending end
Ps is the active power at the sending end
QR is the reactive power at the receiving end

In similarity to the application of the Line Stability Index, the lines with the line stability factor
closest to value of unity will be identified as the most fragile lines in the system. Thus the only

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Arid Zone Journal of Engineering, Technology and Environment, December, 2018; Vol. 14(4):713-726.
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acceptable evidence that a line is a threat to the voltage stability in a network is when the values
of both its stability index and stability factor equally violate the stability margin of the network.

3. Results and Discussion
This section presents the results obtained from deploying the procedure presented in section 2.
From this investigation, Table 1 shows the results obtained from the load flow analysis by
applying the Newton-Raphson iteration method. Thus Table 1 is the narration of the voltage
profile of the Nigerian transmission grid in which the comparison to the magnitudes and phase of
the various real and reactive power quantities of each of the buses that make up the Nigeria-31
bus system are displayed.

Table 1: System Voltage Profile with Power Magnitude at Each Bus of the Nigeria-31 Bus
System
Bus
No

V
(pu)

Angle
(Degree)

Injection
MW MVar

Generation
MW MVAr

Load
MW MVAr

1 1.0200 0.0000 825.4612 332.2438 332.2438 332.2438 0.0000 0.0000
2 0.9900 -2.9559 200.0000 -43.8762 -43.8762 -43.8762 0.0000 0.0000
3 1.0000 -2.3820 300.0000 11.3003 11.3003 11.3003 0.0000 0.0000
4 1.0000 -8.9140 250.0000 138.4051 138.4051 138.4051 0.0000 0.0000
5 1.0300 7.0762 490.0000 -52.6504 -52.6504 -52.6504 0.0000 0.0000
6 1.0400 7.3865 350.0000 -27.0382 -27.0382 -27.0382 0.0000 0.0000
7 1.0300 9.5870 450.0000 -35.4185 -35.4185 -35.4185 0.0000 0.0000
8 0.9953 -5.0357 -156.0000 -79.9000 -79.9000 0.0000 156.0000 79.9000
9 1.0402 4.6449 -8.6000 -5.6000 -5.6000 0.0000 8.6000 5.6000
10 0.9816 -5.6930 -429.9000 -258.4000 -258.4000 0.0000 429.9000 258.4000
11 1.0160 -0.5566 -201.0000 -136.7000 -136.7000 0.0000 201.0000 136.7000
12 1.0337 -1.1701 -166.2000 -97.8000 -97.8000 0.0000 166.2000 97.8000
13 1.0632 -6.4503 -58.4000 -28.4000 -28.4000 0.0000 58.4000 28.4000
14 0.9777 -11.2587 -144.7000 -88.4000 -88.4000 0.0000 144.7000 88.4000
15 0.9730 -10.8277 -115.2000 -42.0000 -42.0000 0.0000 115.2000 42.0000
16 0.9960 -4.8273 -82.1000 -44.5000 -44.5000 0.0000 82.1000 44.5000
17 0.9575 -12.7112 -112.6000 -50.0000 -50.0000 0.0000 112.6000 50.0000
18 0.9941 -8.0840 -184.9000 -60.0000 -60.0000 0.0000 184.9000 60.0000
19 1.0745 -10.6699 -102.9000 -17.5000 -17.5000 0.0000 102.9000 17.5000
20 1.0212 2.0303 -60.3000 -70.0000 -70.0000 0.0000 60.3000 70.0000
21 1.0058 -6.0171 -26.8000 -10.5000 -10.5000 0.0000 26.8000 10.5000
22 0.9775 -6.1333 -292.0000 -114.9000 -114.9000 0.0000 292.0000 114.9000
23 0.9977 -3.2197 -193.5000 -101.2000 -101.2000 0.0000 193.5000 101.2000
24 0.9927 -4.1225 -139.4000 -61.0000 -61.0000 0.0000 139.4000 61.0000
25 1.0003 -3.0052 -109.7000 -64.2000 -64.2000 0.0000 109.7000 64.2000
26 0.9956 -4.3557 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
27 0.9993 -4.6754 -64.3000 -44.2000 -44.2000 0.0000 64.3000 44.2000
28 0.9810 -10.9908 -119.3000 -65.7000 -65.7000 0.0000 119.3000 65.7000
29 1.0413 2.7845 -61.5000 -10.3000 -10.3000 0.0000 61.5000 10.3000
30 1.0445 4.8916 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
31 1.0401 4.9320 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

From the details of Table 1, as a representation of the voltage profile, it is evident that the
Nigeria’s Transmission Network as a whole is fragile requiring massive upgrades. Thus the
voltage magnitudes range from 0.95 pu to 1.08 pu (under normal operating conditions) which is

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Oluseyi et al.: Comparative Analysis of Grid Fragility Indices in the Nigerian Transmission Network.
AZOJETE, 14(4):713-726. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

720

technically unacceptable when compared to the acceptable international standard on electricity
operating policy with a permissible variation standards put at ±4 per cent of the nominal voltage
magnitude.
To further buttress the earlier statement in the preceding paragraph, the measurement of the line
stability indices for establishing the existing operating conditions of the Nigeria’s transmission
network was carried out. The results are thus presented below in Table 2. From this, it shows the
values of line stability factor (LQP) and line stability index (Lmn) obtained for each line of the
Nigerian Transmission Network. The lines with values of the stability indices closest to unity
depict the most fragile lines in the system. It is highly important to juxtaposing the results
obtained using the two stability indices techniques, hence, obtaining accurate results in each case.
In most cases, the Lmn reveals larger values than the LQP for stable lines (Lmn, LQP≤ 0.45).
Whilst the contrast is the case with regard to the fragile lines.

Table 2: Line Stability Indices for the Nigerian Transmission Network
S/N Line

From Bus To Bus
LQP Lmn

1 25 1 0.0863 0.0880
2 26 2 0.0213 0.4642
3 27 3 0.0063 0.0085
4 28 4 0.0831 0.0818
5 29 5 0.0322 0.0319
6 30 6 0.0134 0.0352
7 31 7 0.0253 0.6231
8 10 8 0.2737 0.1379
9 11 8 0.3132 0.2297
10 8 15 0.0850 0.0687
11 21 8 0.1830 0.1923
12 8 26 0.0005 0.0000
13 8 27 0.0037 0.0164
14 9 11 0.0782 0.0800
15 9 29 0.0138 0.0149
16 30 9 0.0003 0.0004
17 31 9 0.0002 0.0004
18 11 10 0.9924 0.8813
19 10 22 0.0133 0.0127
20 24 10 0.4379 0.4550
21 10 25 0.0311 0.0248
22 11 24 0.0878 0.0734
23 12 13 0.0949 0.0622
24 18 12 0.3339 0.3051
25 29 12 0.0515 0.0664
26 13 19 0.0551 0.0496
27 15 14 0.1823 0.1901
28 14 28 0.0103 0.0102
29 15 17 0.0647 0.0624
30 26 16 0.0334 0.0966
31 27 16 0.0138 0.0137
32 20 30 0.0112 0.0000
33 25 23 0.0084 0.0084

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From observation, the five most fragile lines while juxtaposing the LQP and the Lmn are shown in
bold prints in Table 2. It is evident from the two indices that the line from bus 11 to 10, Line (11-
10) which is from Oshogbo to Ikeja-West, is the most fragile line in the Nigerian Transmission
Network. Under normal operating conditions, the Lmn reveals a value of 0.8813 for the line from
Oshogbo to Ikeja-West while the LQP has a value of 0.9924 for the same line. It is also
discovered that the next two most fragile lines are the lines from Ayede to Ikeja-West, i.e. Line
(24-10) and from Kaduna to Kano, i.e. Line (12–18).
The values obtained for the Lmn and LQP for each line are very close; indicating the accurate
computation which further verifies the effectiveness of the two tests of the line stability as
deployed for the Nigerian Transmission Network. In case of the line from bus Egbin to Ajah, i.e.
Line (25-23), the values obtained for the two indices are in fact the same (0.0084). However, in
some cases, a difficulty arises in asserting the fragility of the line where the values obtained for
the two indices are contrasting as in the case of the Line (7-31). This is a rare case which can be
handled by further research that is not covered in this work.
Since voltage collapse is closely related to reactive power component of the line or network; thus
its consequence on the notably weak buses was determined. This provides information on the
extent of the proficiency of the methods. The result is as presented in Table 3.

Table 3: Characteristic behaviour of Nigeria Transmission Line to Stability Indices at Critical
Line with Variation in Reactive Power Magnitude (MVAr)

Q (MVAr) LQP Lmn

200
210

0.9912
1.0031

0.881
0.8845

220 1.0155 0.8885
230 1.0286 0.8931
240 1.0422 0.8981
250 1.0565 0.9034
260 1.0713 0.9089

Similarly, Table 4 provides information on the behaviour of the same transmission network to the
phenomenon of the real power flow. The values of both the stability factor (LQP) and line
stability indices (Lmn) are within the threshold on both sides of unity. The import of these values
is quite informative in regard of the influence of the realm power flow on the system collapse.
This would be further discussed later in this work.

Table 4: Characteristic behaviour of Nigeria Transmission Line to Stability Indices at Critical
Line with Variation in Real Power Magnitude (MW)

P (MW) LQP Lmn

250
260
270
280
290
300
310

0.9632
0.9979
1.0327
1.0676
1.1025
1.1375
1.1726

0.8504
0.8873
0.9248
0.9631
1.0022
1.0421
1.0828

From the foregoing, Tables 3 and 4 narrated the characteristic behaviour of the most fragile line
in relationship to the line stability indices, i.e. LQP and Lmn with varying values of real and
reactive power magnitudes respectively. Table 3 shows the variations of reactive power only
while Table 4 depicts that of the real power only. Further investigation was made by varying both
real power and reactive power at the same time within a specific value range. From this
consideration, thus Table 5 was generated; as presented.

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722

Table 5: Characteristic behaviour of Nigeria Transmission Line to Stability Indices at Critical
Line with Variations in both Real Power (MW) and Reactive Power (MVAr) Flow in the
network

Q (MVAr) P(W) LQP Lmn

200
210
220
230
240
250

250
260
270
280
290
300

0.9620
1.0086
1.0560
1.1040
1.1527
1.2021

0.8502
0.8905
0.9339
0.9804
1.0300
1.0828

Table 5 showed a more probable case of variations in both reactive and real power flow in the
network; especially with regard to the highly fragile lines. On this table, it is observed that the
LQP is more sensitive to load changes. From the table, as the load is increased to 210MW and
260MVAr, which is a meagre variation in load, it could be observed that the LQP increases
above unity which is a very grievous indication that collapse would occur in the network.
With the deployment of Figure 2, the powerworld simulation is obtained as displayed in Figure 4.
In the vivid pictorial illustration captured in Figure 4, the contingency analysis of the network
was easily evaluated using Powerworld simulator. Thus this aided in the identification of the
location of the weakest lines in the network. Hence from the Powerworld simulation of the
transmission network of the Nigeria-31 bus system, it is apparently confirmed that the same lines
that have been identified as the weakest buses (using the analytical technique). This is narrated
pictorially and illustrated by the limited flow of power to the adjoining lines in Figure 4.

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Arid Zone Journal of Engineering, Technology and Environment, December, 2018; Vol. 14(4):713-726.
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Figure 4: Powerworld Simulation of Nigeria-31 bus Transmission Network

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Oluseyi et al.: Comparative Analysis of Grid Fragility Indices in the Nigerian Transmission Network.
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The Nigeria- 31 bus system as presented in Figure 5 is shown below.

Figure 5: One Line Diagram of the Nigeria-31 Bus Transmission Network

From the outlook of Figure 4 which is developed from Figure 5, the Nigeria’s transmission
network is obviously weak though there are some lines that exhibit more fragility than others.
From this study; a number of the buses identified to be threatened by this fragile lines would
naturally not be able to supply continuous load to the load centres due to the blackout as the
evidence of voltage collapse. From the outlook of Table 2 and Figure 4; some of the weakest
lines in the system include Line (11-10) i.e. from Oshogbo to Ikeja-West (wherein LQP is equal
to 0.9924, Lmn is equal to 0.8813 for normal operating conditions), so also is Line (24-10) i.e.
from Ayede to Ikeja-West (LQP is equal to 0.4379, Lmn is equal to 0.4550 for normal operating
conditions) and Line (12-18) i.e. from Kaduna to Kano in which LQP is 0.3339 while Lmn is
0.3054 for normal operating conditions. From the pictorial output of the Powerworld simulation
as displayed in Figures 4; it is generally observed that those listed weak buses have terribly low
magnitude of flow of power from sending bus to the receiving bus which further affirm the test
of fragility obtained for the network. Hence, Table 6 is a narration of the influence of the
contingency analysis of the Nigeria’s transmission network. In which case, the critical lines were
identified along with the buses that are violated in the network. This gives the summary of the
fragility analysis of the network. Furthermore, when the two most fragile lines (i.e. Oshogbo to
Ikeja-West and Ayede to Ikeja-West) are subjected to contingencies (as depicted in Figure 2), the
buses at Kaduna, Jos, Gombe and Birnin-Kebbi are likewise violated (see Table 6).

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Arid Zone Journal of Engineering, Technology and Environment, December, 2018; Vol. 14(4):713-726.
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Table 6: Violations Recorded with Contingency on Critical Lines
S/N Critical Line Violated Buses
1 From Oshogbo to Ikeja-West Jos

Gombe
Birnin Kebbi
Kaduna

2 From Ayede to Ikeja-West Jos
Gombe
Birnin Kebbi
Kaduna

Considering the set of violation recorded by subjecting the critical lines to contingencies, it can
be concluded that the vulnerability of these lines to fragility is highly undesirable. This thus
implies that any small variation in the load at the buses adjoining the critical lines makes the
network to be susceptible to violation in a number of buses within the system. For instance for
the case at hand, it is evident from Table 6, that at least four buses in the grid experience security
margin violation. This therefore calls for an urgent upgrade of the critical lines in the system
because the weakest lines would determine the overall stability status of the whole network.

4. Conclusion
From the foregoing it was established the powerworld simulator’s flow analysis that that the line
with least flow across it are the weakest lines. This approach was used to determine the integrity
status of the network. This is as a further support to the stability indices which primarily tested
the stability margin of the network. Thus, this discovery then means that the Nigeria’s
transmission network has violated buses as Jos, Gombe, Birnin-Kebbi and Kaduna. This is
attributed to the influence of the poorly linked connection from Oshogbo to Ikeja-West and
Ayede to Ikeja-West. These lines are considered as the weakest connection which suggests that
they are the most critically fragile lines in the network.
In other words, the analysis has shown that two buses whose lines are adjoining the Ikeja-West
bus are highly fragile (i.e. Oshogbo and Ayede). It is therefore recommended that these lines
should be considered for reinforcement (using either transmission expansion programme or
deployment of the flexible alternating current transmission systems (FACTS) devices such as
SVC, UPFC, etc) as they are highly susceptible to voltage collapse.
In the same vein, in the Northern part of the country, i.e. the line from Kaduna to Kano should be
considered as primary target for the transmission expansion programme scheme. This will
improve the quantity and quality of electricity delivery to this part of the country. For a
wholesome solution to the challenges of electricity supply, the frontier of this research may be
further extended to consider the effects on vandalism on grid fragility whilst the study of the cost
analysis of implementing remedies to fragility in the network may be considered as area of future
research interest. Whilst the another simulator such as ETAP load flow software tool may be
deployed to solve this problem whose output could be compared with that of the Powerworld
simulator. The study has undoubtedly revealed the susceptibility of the Nigeria’s transmission
network to voltage collapse with empirical evidence of the locations that need to be fortified
against violation induced by the fragility of the network.

Acknowledgment
The authors wish to appreciate the Faculty of Engineering of University of Lagos, Akoka for the
privilege to access the design facilities in the LG Design Laboratory for conducting this study.

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Oluseyi et al.: Comparative Analysis of Grid Fragility Indices in the Nigerian Transmission Network.
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