International Journal of Computational Engineering Research(IJCER)

International Journal of Computational Engineering Research||Vol, 03||Issue, 9||
||Issn 2250-3005 || ||September||2013|| Page 99
Prediction of Voltage Instability in Nigeria Interconnected
Electric Power System Using V-Q Sensitivity Method
Enemuoh F. O.1
, Madueme T. C.2
, Onuegbu J. C.1
and Anazia A. E.1
1.
Department of Electrical Engineering, Nnamdi Azikiwe University, Awka, Nigeria
2. Department of Electrical Engineering, University of Nigeria, Nsukka Nigeria
I. INTRODUCTION
For many years, the demand for and consumption of energy in many countries of the world has been on
the increase. The major portion of the energy needs of these nations is electric energy. In Nigeria and other
industrial developing nations, the demand for supply of electrical power has been on the increase, which may be
as a result of improved economic activities of the people. To satisfy the increasing demand for electricity,
complex power system networks have been built. The most usual practice in electric power transmission and
distribution is an interconnected network of transmission lines usually referred to as a grid system that links
generators and loads to form a large integrated system that spans the entire country. In many countries of the
world including Nigeria, generating stations are located thousands of kilometers apart and operate in parallel.
The generating stations‟ output is connected and transmitted through the grid system to load centers nationwide.
One of the several problems confronting the efficient performance of an interconnected system is voltage
stability. Voltage stability issues are of major concern worldwide because of the significant number of black-
outs that have occurred in recent times in which it was involved. For many power systems, assessment of
voltage stability and prediction of voltage instability or collapse have become the most important types of
analysis performed as part of system planning, operational planning and real-time operation. Voltage stability is
defined as the ability of a power system to maintain steady acceptable voltages at all buses in the system under
normal operating conditions, and after being subjected to a disturbance [1].
The ability to transfer reactive power from production sources to consumption sinks during steady
operating conditions is a major aspect of voltage stability. The consumers of electric energy are used to rather
small variations in the voltage level and the system behaviour from the operators‟ point of view is fairly well
known in this normal operating state. Equipment control and operation are tuned towards specified set points
giving small losses and avoiding power variation due to voltage sensitive loads. Once outside the normal
operating voltage band many things may happen of which some are not well understood or properly taken into
account today. A combination of actions and interactions in the power system can start a process which may
cause a completely loss of voltage control. It is known that to maintain an acceptable system voltage profile, a
sufficient reactive support at appropriate locations must be found. Nevertheless, maintaining a good voltage
profile does not automatically guarantee voltage stability. On the other hand, low voltage although frequently
associated with voltage instability is not necessarily its cause [2] and [3]. Voltage stability studies of a power
system is now essential and is intended to help in the classification and the understanding of different aspects of
power system stability [4].
ABSTRACT
The need to predict power system stability as it concerns voltage status is very important for
the system planning, operation and control. This paper presents the prediction of voltage instability in
Nigerian interconnected electric power system using V-Q sensitivity method. The method makes use of
the least eigenvalue of the Jacobian matrix of the power system to calculate the V-Q sensitivity of the
system. The highest sensitivity is an indication of the bus prone to voltage instability. The result from
our calculations showed that Nigerian power system has the highest V-Q sensitivity of 0.1474 at the
Maiduguri bus followed by Gombe, Kano and Jos with 0.1312, 0.0823 and 0.0370 respectively. It is
very clear that the first bus that will collapse on the same percentage of loading will be Maiduguri
followed by Gombe then Kano and Jos.
KEYWORDS: Eigenvalue analysis, prediction, voltage instability/collapse, voltage stability, V-Q
sensitivity

Prediction Of Voltage Instability…
Voltage stability evaluation requires the determination of:
(i) The parameters and a stress test that establish the structural causes of voltage collapse and instability in
each load area (exhaustion of reactive reserves in a reactive reserve basin).
(ii) A method of identifying each load area (voltage collapse and instability area) that has a unique voltage
collapse and instability problem, and
(iii) A measure of proximity to voltage collapse for each load area (a measure of reactive reserve or voltage
control areas with zero reserves in the reactive reserve basin)
One of the operating goals of an electric power system is to attend the power demand keeping the
system‟s voltages as well as the frequency close to rated values. Deviation from these nominal conditions may
result in abnormal performance of or even damage to the supplied equipment. An unacceptable voltage level
means voltage instability. The voltage instability, also known as voltage collapse of power systems appears
when the attempt of load dynamics to restore power consumption is just beyond the capability of the combined
transmission and generator system [5]. The problem is also a main concern in power system operation and
planning. It is characterized by a sudden reduction of voltage on a set of buses of the system. In the initial stage
the decrease of the system voltage starts gradually and then decreases rapidly.
The following can be considered the main contributing factors to the problem [6]:
1. Stressed power system; i.e., high active power loading in the system.
2. Inadequate reactive power resources.
3. Load characteristics at low voltage magnitude and their difference from those traditionally used in stability
studies.
4. Transformers tap changer response to decreasing voltage magnitudes at the load buses.
5. Unexpected and or unwanted relay operation may occur during conditions with decreased voltage
magnitudes.
So, there is a requirement to have an analytical method, which can predict the voltage collapse problem
in a power system. As a result, considerable attention has been given to this problem by many power system
researchers. A number of techniques have been proposed in the literature for the analysis of this problem [7]. In
this paper, a V-Q sensitivity method has been used to predict voltage instability of Nigerian 330kV, 30bus
interconnected electric power system.
II. POWER FLOW PROBLEM
The power flow or load flow is widely used in power system analysis. It plays a major role in planning
the future expansion of the power system as well as helping to run existing systems to run in the best possible
way. The network load flow solution techniques are used for steady state and dynamic analysis programme [3]
and [4]. The solution of power flow predicts what the electrical state of the network will be when it is subject to
a specified loading condition. The result of the power flow is the voltage magnitude and the angle of each of the
system nodes. These bus voltage magnitudes and angles are defined as the system state variables. That is
because they allow all other system quantities to be computed such as real and reactive power flows, current
flows, voltage drops, power losses, etc … power flow solution is closely associated with voltage stability
analysis. It is an essential tool for voltage stability evaluation. Much of the research on voltage stability deals
with the power-flow computation methods. The power flow problem solves the complex matrix equation:
I=YV= *
*
V
S
(1)
The Newton-Raphson method is the most general and reliable algorithm to solve the power-flow problem. It
involves interactions based on successive linearization using the first term of Taylor expansion of the equation
to be solved. From equation (1), we can write the equation for node k (bus k) as derived in [8].
      2sincos
1



n
m
mkkmmkkmmkK
BGVVP 
      3cossin
1



n
m
kkmmkkmmkk
mBGVVQ 
This mismatch power at bus k is given by:
)4(k
sch
kk
ppP 

k
sch
kk
QQQ  (5)
The Pk and Qk are calculated from Equation (2) and (3)
The Newton – Raphson method solves the partitioned matrix equation:
















V
J
Q
P 
(6)
Where,
ΔP and ΔQ = mismatch active and reactive power vectors.
ΔV and ΔӨ = unknown voltage magnitude and angle correction vectors.
J = Jacobian matrix of partial derivative terms
III. EIGENVALUE ANALYSIS
The Eigenvalue analysis mainly depends on the power-flow Jacobian matrix of equation (6). Gao,
Morison and Kundur [9] proposed this method in 1992. It can predict voltage collapse in complex power system
networks. It involves mainly the computing of the smallest eigenvalues and associated eigenvectors of the
reduced Jacobian matrix obtained from the load flow solution. The eigenvalues are associated with a mode of
voltage and reactive power variation which can provide a relative measure of proximity to voltage instability.
The analysis is expressed as follows:
Equation (6) can be rewritten as:






















VJJ
JJ
Q
P 
2221
1211
(7)
By letting 0 P in Equation (7)
,0 1211
VJJP   VJJ 

12
1
11
 (8)
and
VJJQ  2221
 (9)
Substituting Equation (8) in Equation (9):
VJQ R
 (10)
Where
 12
1
112122
JJJJJ R

 (11)
R
J is the reduced Jacobian matrix of the system.
Equation (10) can be written as
QJV R

1
(12)
IV. V – Q SENSITIVITY ANALYSIS
The relationship between system voltage stability and eigenvalues of the JR matrix is best understood
by relating the eigenvalues with the V-Q sensitivities of each bus (which must be positive for stability). JR can
be taken as a symmetric matrix and therefore the eigenvalues of JR are close to being purely real. If all the
eigenvalues are positive, JR is positive definite and the V-Q sensitivities are also positive, indicating that the
system is voltage stable.
V – Q sensitivity analysis calculates the relation between voltage change and reactive power change from
equation (12).
QJV R


.
1
ΔV incremental change in bus voltage magnitude (vector)
ΔQ incremental change in bus reactive power injection (vector)
JR reduced Jacobian matrix
The elements of the inverse of the reduced Jacobian matrix JR are the V – Q sensitivities. The diagonal
components are the self sensitivities
i
i
Q
V


and the nondiagonal elements are the mutual sensitivities
i
k
Q
V


The sensitivities of voltage controlled buses are equal zero. Positive sensitivities: stable operation, the smaller
the sensitivity the more stable the system. As stability decreases, the magnitude of the sensitivity increases,
becoming infinite at the stability limit (maximum loadability).

Negative sensitivities: unstable operation. The system is not controllable, because all reactive power control
devices are designed to operate satisfactorily when an increase in Q is accompanied by an increase in V.
V. SYSTEM DESCRIPTION OF NIGERIAN 330KV, 30-BUS INTERCONNECTED
ELECTRIC POWER SYSTEM
The electrical utility is probably the largest and most complex industry in the world. The electrical
engineer, who researches in this industry, will encounter challenging problems in designing future power
systems to deliver increasing amounts of electrical energy in a safe, clean and economical manner [10].
The transmission network in Nigeria is characterised by several outages leading to disruption in the lives of the
citizenry. According to Anil et al [11], the level of disruption is a function of the dependency of people on
electricity, which can be very high for a developed country and not as much as developing countries. In Nigeria,
the available energy generated is not enough to meet the demands of the users leading to constant load shedding
and blackouts. The Nigerian power stations are mainly hydro and thermal plants. Power Holding Company of
Nigeria.(PHCN) generating plants sum up to 6200MW out of which 1920MW is hydro and 4280MW is
thermal-mainly gas fired[12].The transmission grid system in Nigeria is predominantly characterised by radial,
fragile and very long transmission lines, some of which risk total or partial system collapse in the event of major
fault occurrence and make voltage control difficult. These lines include Benin-Ikeja West (280Km) Oshogbo-
Benin (251km), Oshogbo-Jebba (249km) Jebba-Shiroro (244km), Birnin-Kebbi-Kainji (310km), Jos-Gombe
(265Km) and Kaduna-Kano (230km) [13].These lines experience high voltages under light load conditions and
very low voltages under high loading conditions [12]. The Nigerian Electricity Network comprises 11,000km
Transmission lines (330kV and 132kV), the sub-transmission line (33kV) is 24,000km, the distribution line
(11kV) is 19000km, while the substations are 22,500 [14].
VI. SYSTEM DISTURBANCES/COLLAPSES IN NIGERIAN INTERCONNECTED
POWER System
Electricity supply situation in Nigeria is inadequate and unstable; the problems cut across generation,
transmission and distribution/commercial operation. Voltage instability and collapse are the major issues in
today‟s electric power operations. Table 1 shows the system disturbances/collapse in Nigerian Power System
from 2000 to 2011. Transmission and generation faults and their effects caused most of the voltage collapse.
Table 1 Summary of System Disturbances from January to December (2000 to 2011)
S/N Years (Jan-Dec) No. of Disturbances Cause of Collapse
1. 2011 19 Transmission
2. 2010 42 Generation/Transmission
Source [15]
VII. SAMPLE SYSTEM SIMULATION, RESULTS AND ANALYSIS
The V-Q sensitivities analysis method has been successfully applied to Nigerian power systems. A
power flow program based on Matlab is developed to:
1. Calculate the power flow solution
2. Analyze the voltage stability based on eigenvalue analysis
3. Generate the V-Q sensitivities to predict voltage instability or collapse

The Nigerian 330kV, 30Bus Interconnected Power System (NIPS) is shown in the appendix, the model is
achieved using elements arrangement. The data required for the simulation are as follows: Line data represented
in Table 2; while Table 3 represents load distribution.
The calculated voltage profile of the Power Holding Company of Nigeria (PHCN) 330kV, 30bus interconnected
network system is shown in figure 1.
Table 2 Line Data for Nigeria Integrated Power System (NIPS)
Length 1KM
Source [11]
Table 3 Load Distribution for Nigeria Integrated Power System (NIPS)
S/N ID Name From To R(1), Ohm X(1), Ohm C(1), uF B(0), Us
1. 373 L373 B11 B6 13.26402 21.75822 0.000245 0.077
2. 389 L389 B6 B8 0.835 6.52 0.0012 0.377
3. 405 L405 B12 B8 0.7623 5.5466 0.0034 1.068
4. 413 L413 B20 B28 2.2869 16.63992 0.001685 0.529
5. 421 L421 B9 B8 5.21631 39.26934 0.001751 0.55
6. 429 L429 B19 B29 5.21631 39.2693 0.00175 0.55
7. 437 L437 B3 B9 0.20691 1.60083 1.8e-005 0.006
8. 445 L445 B17 B9 1.0291 7.7265 0.0014 0.44
9. 453 L453 B24 B26 2.05821 15.45291 0.000693 0.218
10. 461 L461 B17 B18 10.08414 76.79628 0.000864 0.271
11. 469 L469 B17 B19 7.81001 66.30921 0.000743 0.233
12. 477 L477 B19 B20 12.82842 96.57252 0.001082 0.34
13. 485 L485 B2 B8 0.20691 1.60083 1.8e-005 0.006
14. 493 L493 B12 B13 4.61736 35.19648 0.000396 0.124
15. 501 L501 B12 B14 9.62676 80.3682 0.000904 0.284
16. 509 L509 B13 B14 5.0094 38.3328 0.000496 0.156
17. 517 L517 B14 B21 2.9948 22.5423 0.004 1.257
18. 541 L541 B22 B21 2.0854 15.6925 0.0028 0.88
19. 549 L549 B29 B26 2.0854 15.6925 0.0028 0.88
20. 557 L557 B21 B1 0.5391 4.0239 0.00072 0.226
21. 573 L573 B21 B23 2.9294 22.0523 0.00098 0.308
22. 589 L589 B23 B24 5.79348 44.15895 0.000497 0.156
23. 597 L597 B24 B5 1.06722 8.03682 9.02e-005 0.028
24. 605 L605 B10 B14 0.6534 5.31432 0.000211 0.066
25. 613 L613 B10 B14 0.6534 5.31432 0.000211 0.066
26. 621 L621 B10 B16 0.3267 2.40669 0.000108 0.034
27. 629 L629 B10 B15 3.29967 24.78564 0.000278 0.087
28. 637 L637 B14 B15 0.35937 145.0548 0.000122 0.038
29. 645 L645 B14 B15 0.35937 145.0548 0.000122 0.038
30. 661 L661 B1 B25 2.70072 20.26629 0.000227 0.071
31. 669 L669 B1 B7 2.85318 21.75822 0.000245 0.077
32. 677 L677 B7 B25 1.11078 8.37441 9.38e-005 0.029
33. 685 L685 B4 B10 0.60984 4.82427 0.000884 0.278
34. 732 L732 B23 B26 3 20 0.000332 0.104
35. 829 L829 B30 B9 0.5391 4.0239 0.00072 0.226
36. 175409 L175409 B11 B27 1.4265 10.879 0.00049 0.154
S/N ID Name LF Type P, MW Q, MVAR
1. 182 Load 11 PQ 56.4 42.3
2. 207 Load 14 PQ 332 249
3. 201 Load 13 PQ 133 97.5
4. 213 Load 10 PQ 80 60
5. 286 Load 16 PQ 95 71.25
6. 298 Load 25 PQ 20 15
7. 292 Load 15 PQ 228 171
8. 316 Load 23 PQ 86 64.5
9. 310 Load 24 PQ 264.8 198
10. 304 Load 26 PQ 90 67.5
11. 334 Load 9 PQ 109.6 82.2
12. 322 Load 21 PQ 124.2 93.3

Source [11]
The voltage profile of all buses of the PHCN 30 Bus system as obtained from the load flow result.
To have clear indication of voltage collapse on the system loading the V-Q sensitivities calculation was carried
out using the system eigenvalues. For a 30bus network with 7generator buses the expected eigenvalues will be
23 since voltage stability is load dependent we expect the eigenvalues at the 23 load buses. Table 4 is the
calculated eigenvalues while Figure 2 is the plot of the eigenvalues. From Table 4, all the eigenvalues are
positive and this is an indication that the system is stable. For the determination of the buses in the system that
will collapse with system loading, the least eigenvalue of 3.4951 will be used. .
Table 4 PHCN 30 Bus system eigenvalues
Table 5 The V-Q Sensitivities for the Network System
13. 340 Load 17 PQ 390 0
14. 364 Load 19 PQ 65 48.75
15. 370 Load 20 PQ 132.8 99.6
16. 764 Load 18 PQ 130 60
17. 779 Load 12 PQ 144.9 108.68
18. 773 Load 8 PQ 7.9 5.93
19. 175351 Load 22 PQ 20 15
20. 175420 Load 27 PQ 56.4 42.3
21. 175457 Load 30 PQ 130 60
22. 175482 Load 29 PQ 83.45 61.22
23. 175506 Load 28 PQ 80 60
S/N Eigenvalue S/N Eigenvalue
1. 3.4951 13. 183.4425
2. 12.0129 14. 194.8132
3. 21.1896 15. 198.2067
4. 23.1243 16. 214.9579
5. 34.6424 17. 223.3135
6. 49.2926 18. 289.0459
7. 51.1237 19. 420.3368
8. 58.8551 20. 495.4999
9. 107.3404 21. 1104.0739
10. 120.5424 22. 1215.5813
11. 128.6551 23. 1449.9396
12. 131.8992 - - - - - - - -
S/N ID Name Sensitivity,
Mvar
1. 175463 N175463-
maiduguri-
B28
0.1474
2. 53 B-53-
Gombe-
B20
0.1312
3. 148 N148-
Kano-B18
0.0823
4. 45 N45-Jos-
B19
0.0370

Figure 1 Voltage Profile of (PHCN) 30-Bus System Figure 2 The eigenvalues of the 23 buses
The calculated V-Q sensitivities are represented in Table 5, while Figure 3 is V-Q sensitivities graph
representation. The bus with highest sensitivity of 0.1474 is Maiduguri followed by Gombe, Kano and Jos with
0.1312, 0.0823 and 0.0370 respectively. It is now clear that the first bus that will collapse on the same
percentage of loading will be Maiduguri followed by Gombe then Kano before Jos.
Figure 3 The V-Q sensitivities of all Buses
VIII. CONCLUSION
Voltage instability or collapse is a common feature in Nigerian interconnected electric power system.
The problem cut across generation, transmission and distribution. Prediction of power system stability as it
concerns voltage state is very important for the system planning, operation and control. In this work, V-Q
sensitivity was carried out on the Nigerian 330kV 30Bus interconnected power system. .The calculation was
done using the least eigenvalue of the Jacobian matrix. The calculated values shows that Nigerian power system
has the highest V-Q sensitivity of 0.1474 at the Maiduguri bus followed by Gombe, Kano and Jos with 0.1312,
0.0823 and 0.0370 respectively. It is very clear that the first bus that will collapse on the same percentage of
loading will be Maiduguri followed by Gombe then Kano and Jos . V-Q sensitivity is a good method for the
prediction of voltage instability of an interconnected power system, it is used in combination with eigenvalue
analysis.

REFERENCES
[1] Taylor, C.W; „Power System Voltage Stability; MacGraw-Hill, 1994
[2] Y. Tamura, H. Mori and S. Iwamoto, “ Relationship between Voltage Stability and Multiple Load Flow
Solution in Electric Systems,” IEEE Trans. On Power Apparatus and Systems, Vol. PAS-102, pp.1115-1123, May 1983.
[3] P.A Lof, T. Smed, C. Anderson and D.J.Hill, “ Fast Calculation of a Voltage Stability Index,” IEEE Trans. on Power Systems,
Vol.7, pp59-64, Feb.1992.
[4] CIGRE Task Force 38-01-10,: “Modelling of Voltage Collapse including dynamic phenomenon”, 1993.
[5] Abhijit Chakrabarti and Sunita Halder “Power System Analysis Operation and Control” PHI Learning Private Limited, New Delhi,
2008.
[6] P.A. Lof, G. Anderson and D.J. Hill, “Voltage Stability Indices For Stressed Power
System”, IEEE Trans. on Power Systems, Vol. 8, 326-335, Feb. 1993.
[7] V. Ajjarapu, and B. Lee “Bibliograph on voltage Stability” IEEE Trans. on Power Systems, vol. 13 pp 115- 125, 1998.
[8] F.O. Enemuoh, J.C. Onuegbu and A.E. Anazia “Modal Based Analysis and Evaluation of Voltage Stability of Bulk Power System
[9] B. Gao, G.Morison and P. Kundur, “Voltage Stability Evaluation Using Modal Analysis”, IEEE Trans. On Power Systems, Vol.7,
No.4, pp. 1423-1543, Nov. 1992.
[10] J. D. Glover and M.S. Sarma, “ Power System Analysis and Design”. 3rd
Edition Wadsworth Group, Brooks Cole, a division of
Thomson Learning Inc.
[11] P. Anil, H. Mark and T.R. Gaunt “Estimation of Outages in Overhead Distribution Systems of South Africa and of Manhattan,
Kansas, USA.7th
International Conference on Power System Operation and planning, Cape Town, South Africa. 2007
[12] O. S. Onohaebi, “ Power Outages in the Nigeria Transmission Grid Research Journal of Applied Sciences 4(1): 1-9, 2009 ISSN.
1815-932X Medwell Journals, 2009.
[13] O.S. Onohaebi and S.O. Igbinovia “ Voltage Dips Reduction in the Nigeria 330kV Transmission Grid” Journal of Engineering and
Applied Sciences 3(6):496-503, ISSN: 1816-949X
Medwell Journals, 2008.
[14] J. Sadoh “ Ph.D. Thesis on Power System Protection : Investigation of System Protection Schemes on the 330kV of Nigeria
Transmission Network” Unpublished University of Benin, pp.27.

~
~
N12-Birnin Kebbi-
B11
L1754
09 N-175397-Sokoto-
B27
N148-Kano-B-18
L-
764N175463-Maiduguri-
B28L46
1
L41
3 L-
175506Gombe-
B20
L-
370
L-
182Sm-
160
N16-Kainj-
B6
B49-Jebba-GS-
B2
Ms-
176
L-773
N20-Jebba-TS-
B8
L48
5
L38
9
L42
1
L-
334
L-
175420
L-
373
Sm-347
B-93
ShiroroGS-B3
N152-kaduna-
B17
N144-Shiroro TS
B9
L43
7 L44
5
L-
340
L46
9 B-53
L47
7Jos-
B19
N45
L-
364N175427 Abuja
B30
L-
175427B-89 Ajaokuta
B22
L54
1B85-Bennin-B21
L40
5
N28-Oshogbo-
B12
N28-Ibadan-
B13
L-779
L40
5
L-
201
L50
9B33 Ikeja West
B14
L50
1L51
7
L-
322
L55
7
L42
9 Makurdi-
B29
N1754
75
L54
9
L-
175482
B-77-Enugu-
B26
L-
304
L57
3 B69-Onitsha-
B23
L73
5
L45
3
L-
316
L57
3N65-Aba -B24
N61 Sapele B1
~ L-
669N81 Delta-
B7
L66
1Sm-137202 L-
597
~
N73 Afam-B5
Sm-
823
L67
7N57-Aladja
B25
L64
5
L63
7
L67
7B41 Akangba
B15
L61
3
L60
5
L-
629
L-
292N136 Egbin TS-
B10
L-
213
L62
1
L68
5N140 Egbin GS-
B4
B37 Aja-
B16
L-
286
~
Sm-
245


L-
310

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