Q01052136142

IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE)
e-ISSN: 2278-1676,p-ISSN: 2320-3331, Volume 10, Issue 5 Ver. II (Sep – Oct. 2015), PP 136-142
www.iosrjournals.org
DOI: 10.9790/1676-1052136142 www.iosrjournals.org 136 | Page
Contingency Evaluation of a Peturbed Electric Network
J. N. Onah1
, T.C Madueme2
and V.C Ukwueze3
1,2,3
(Department Of Electrical Engineering,University Of Nigeria, Nsukka. Enugu State-Nigeria )
Abstract: A single line contingency analysis and generator(s) outages were carried out on a 330kV power
network using MATPOWER 4.1 embedded in MATLAB to carry out fast decoupled load flow studies in order to
identify the voltage violation at various buses, determine power losses at the transmission lines and to compute
the performance indices. The performance indices were further ranked in accordance with their severity indices.
Voltages less than 0.95pu were assumed to be low voltages and voltages greater than 1.05pu were also assumed
to be high voltages. It was also assumed that power losses greater than 5% are unacceptable. So a base case
comparative analysis of the load flow studies using three conventional methods showed that Gauss Seidel could
not converge in 0.93seconds and 1000 iterations, Newton Raphson converged in 0.15seconds and 6 iterations.
However, Fast Decoupled Load Flow (FDLF) converged in 0.01second and 28 iterations. Further, a single line
contingency analysis was also carried out on the transmission lines to investigate the performance indices of the
lines which were later ranked in accordance with their severity. The outcome of the simulations showed that at
a time when there was an outage of Kainji-GS, low voltages were found at Kano, Jos, Gombe, Kaduna,
Katampe, Oshogbo, Ajaokuta, New Haven, Aiyede, Ikeja-West, Onitsha, and Akangba buses. And there were
also power losses greater than 5% at Ikeja-West to Egbin, Ikeja-West to Benin, Oshogbo to Benin, Kaduna to
Shiroro, Kano to Kaduna, Jos to Kaduna and Jos to Gombe.
Key Words: Contingency Evaluation, FDLF, Performance Index, Power Loss, Line outage.
I. Introduction
A typical issue that confronts the integrated power project is outages on the transmission lines. Outages
diminish the productivity of the transmission system as they cause power disturbance and interference [1].
Moreover, the incessant and unprecedented vandalisation of the power equipment of the Nigerian power
systems resulting in cascaded outages of either the transmission line or the generator(s) in the recent time leaves
much to be desired. Consequently, contingency evaluation is necessary to showcase the areas that may lead to
total system voltage collapse and power losses. We are to carry out Fast Decoupled Load flow to determine the
voltage magnitudes, real and reactive powers that enabled us to calculate the performance indices of each of the
transmission lines and later rank them based on their severity. The study involves (N-1) secure otherwise called
single line contingency evaluation on the Nigerian 330kV transmission grid. Contingency analysis is the study
of the outage of elements such as transmission lines, transformers and generators, and investigation of the
resulting effects on line power flows and bus voltages of the remaining system [2].
II. Overview Of Contingency Evaluation
Nnonyelu et al [2] looked at the overloading at various transmission lines but could not bring to lime
light the voltage instability of the network as well as the effect of power losses in the transmission lines. It has
been established by Chan et al [3] that some transient-stability analysis concerns the transient behaviour of the
power system when moving from the pre-contingency to post-contingency operating point. However, owing to
computational economics, both direct methods [4, 5] and artificial-intelligence methods [6] have often been
proposed for use in online transient-stability assessment. However, it is not easy to apply these methods to larger
power systems involving complex models of plant and contingencies. But an application of a conventional load
flow method, gives a fast and a reliable result. However, Newton-Raphson method may be used to solve the
network equations but the method is computationally expensive because it needs to calculate the Jacobian at
each iteration of the algorithm. To improve the computational performance, a fast decoupled solution technique
is used to solve AC network equations iteratively [7]. It is a very fast and efficient method of obtaining power
flow problem solution. In this method both speed as well as sparsity is exploited. It is an extension of N-R
method formulated in polar coordinate with certain approximations which result into a fast algorithm for power
flow solution. This method exploits the property of the power system where the MW flow-voltage angle and
MVAR flow –Voltage magnitude is loosely coupled. In order words a small change in the magnitude of bus
voltage does not affect the real power flow at the bus and similarly a small change in phase angle of the bus
voltage has hardly any effect on reactive power flow. On the account of loose physical interaction between the
MW and the MVAR flows in a power system, the MW-δ and MVAR-V calculations can be decoupled resulting

to a very simple, fast and reliable algorithm [7]. The fastness is on the account of the sparsity feature of the
admittance matrix that minimizes the computer memory requirement.
Most of the early iterative techniques were based on the Y-matrix of the G-S method [8]. It requires
minimum computer storage and needs only a small number of iterations for small networks. However, as the
size of the network is increased the number of iterations required increases dramatically for large systems. In
some cases the method does not provide solution at all [9]. Hence the slow convergence of G-S method and its
frequent failure to converge in ill- conditioned situations caused the development of Z-Matrix methods [10]. In
spite of the fact that these methods have considerably better converging characteristics, they also have the
demerit of needing a significantly large computer storage memory owing to the fact that Z-matrix is full,
contrary to the Y-Matrix which is sparse. Consequently, the shortcomings led to the development of N-R
algorithm to solve the simultaneous quadratic equations of power network .Contrary to the G-S algorithm, it
needs a large time per iteration but only a few iterations and is significantly independent of the network size.
However, in a realistic power system, there may be a large number of buses, for instance, 100 or more but each
bus is connected to only a small number usually two or more of the remaining buses. That is to say that of
a large power system is very sparse. This implies that it has a large number of zero elements, hence the sparcity
feature of minimizes the computer memory requirement as only non-zero terms are considered for storage
and results in faster computation. This idea leads to the development of Fast Decoupled power flow method. It
is a very fast, reliable and efficient method of obtaining power flow problem solution. It exploits speed and
accuracy in its methodology [5]. It has a compatible accuracy with that of N-R method. For the sake of brevity,
FDPF is an extension of N-R method formulated in polar coordinates with certain approximation which results
in algorithm for power flow solution.
It has been stated by Ekwue et al [11] that power Systems are generally nonlinear in nature and some
primary elements such as generator, branch outage etc contribute to the severity of the nonlinearity. So
considering the merits of FDPF aforementioned, we intend to look at the line flows, losses in the line, voltage
violation constraints and the performance indices which were found missing in the work of the various authors
reviewed above using the fast decoupled power flow algorithm.
III. The Network Under Study And Data
A single line diagram of the 330Kv Nigerian Power grid used in the study is shown in figure 1. It
comprises nine generator buses, eighteen load buses, twenty nine transmission lines of the Nigerian 330kV
transmission system.
Figure 1: One line diagram of Nigerian 330kV transmission grid [2]

Tables 1, 2 and 3 show generator data, load data and line data respectively that are used for the simulations
Table 1: Generator Data
S/No. Bus name PG(MW) Rated
1 Kainji GS 756
2 Shiroro 413
3 Jebba GS 339
4 Sapele 70
5 Egbin 967
6 Afam 316
7 Delta GS 498
8 AES 235
9 Calabar 0
Source: [2 ]
Table 2: Load Data
Source: [2 ]

Table 3: Line Data
Branch No. From To R(pu) X(pu) B(PU)
1 10 1 0.02676 0.06576 1.178
2 8 5 0.00300 0.02100 0.300
3 9 24 0.00216 0.00530 0.2570
4 1 15 0.00699 0.01718 0.308
5 3 15 0.00069 0.0017 0.033
6 15 17 0.01355 0.0333 0.597
7 17 21 0.02167 0.05324 0.521
8 17 20 0.00993 0.02439 0.437
9 20 21 0.01183 0.02906 0.521
10 21 25 0.00147 0.0361 0.065
11 21 5 0.00535 0.01315 0.257
12 5 26 0.00138 0.00339 0.257
13 21 22 0.02417 0.05939 1.162
14 22 4 0.00432 0.01061 0.208
15 4 27 0.00544 0.01336 0.239
16 7 27 0.00276 0.00679 0.239
17 7 22 0.00924 0.0227 0.239
18 18 22 0.0145 0.03564 0.208
19 17 22 0.02167 0.05324 0.954
20 2 15 0.02106 0.05176 0.927
21 2 16 0.01243 0.03055 0.308
22 14 2 0.00829 0.02036 0.364
23 11 14 0.01985 0.04879 0.874
24 12 14 0.01692 0.04158 0.927
25 12 13 0.002279 0.056 1.01
26 22 23 0.01183 0.02906 0.521
27 19 23 0.00829 0.02036 0.365
28 23 24 0.01191 0.02927 0.524
29 24 6 0.00216 0.0053 0.104
Source: [2 ]
IV. Methodology
The power flow study of the 330kV line was carried out comparatively, using various techniques such
as Gauss-Seidel, Newton Raphson and Fast Decoupled Load Flow. However, Gauss-Seidel could not converge
after 0.93seconds and 1000 iterations. Newton Raphson Converged in 0.15seconds and 6 Iterations but as a
matter of fact, Fast Decoupled load flow converged in 0.01seconds and 28 Iterations. Hence, because of its time
for numerical iteration and its capacity to hold as many data as possible, we utilized the FDLF for the research
work. To compute the performance indices, one of the lines was removed and the load flow analysis was carried
out in order to see the effect on the network. This was done by calculating the performance indices and ranking
them based on highest severity and thus, the operation continued until no severe contingencies are found. The
performance indices are given by
(1)
Moreover, the has got to do with the violation of the line active power flow and it is given by:
AiP = ∑i=1
N
(
Api
Api
max )2x
(2)
Where, = Active power performance index
=Active power flow in line i
Api
max
= Maximum active power flow in line i
N = The total number of transmission lines in the system.
x = the specific exponent where x is assumed to be unity.
And the maximum power flow in each line is given by (3)
Where, Vj = voltage at bus j got from FDLF solution, = Voltage at bus k obtained from FDLF solution. And
= impedance of the line connecting bus j and k.
However, (4)

(5)
Figure 2 shows a bar chart that represents voltage drops at various branches when Kainji- generating
station was not committed. The result shows that the following buses are experiencing low voltages. They are:
Kano, Jos, Gombe, Kaduna, Katampe, Oshogbo, Ajaokuta, New Haven, Aiyede, Ikeja-West, Onitsha and
Akangba.
V. Simulation, Results And Discussion
The input data for the case to be simulated are specified in a set of data matrices packaged as the fields
of a Matlab struct, referred to as a “Matpower case" and denoted by the variable mpc. The struct is typically
defined in a case file called M-file whose return value is mpc struct. The solver was invoked by calling the
simulation function “runpf” and passing in a case file name as the first argument. So the FDLF was ran by
typing runpf(„case27‟) . By default, the results of the simulation are pretty to the screen, displaying a system
summary, bus data, branch data and, for the power flow, binding constraint information. The bus data comprises
the voltage, angle, total generation and load at each bus. The branch data shows the power flows and power
losses in each branch. Then the performance indices were computed using equations 1,2,3,4 and 5. The voltage
drops and the power losses are respectively shown in figure 2 and figure 3.
Figure 2: Voltage drop at the outage of kainji GS
At the outage of Kainji GS, the following branches experienced power losses. They are: Ikeja-West to
Egbin, Ikeja-West to Benin, Oshogbo to Benin, Kaduna to Shiroro, Kano to Kaduna, Jos to Kaduna and Jos to
Gombe.
Figure 3: Power loss at the various branches when kainji- generating station was not committed.

Power losses greater than 5% were observed at Ikeja-West to Egbin, Ikeja-West to Benin, Oshogbo to
Benin, Kaduna to Shiroro, Kano to Kaduna, Jos to Kaduna and Jos to Gombe transmission lines.
VI. Computing The Performance Indices
The calculation of the performance indices was done using equation 1. The simulation results provided
the requisite parameters such as those given in equations 2, 3, 4 and 5.The results are tabulated in Table 4.
Table 4: Performance indices of the various lines of the network and the ranking based on the severity of the
lines
Branch No.
1 1-10 40.41 0.900 41.31 11
2 8-5 24.85 0.410 25.26 17
3 9-24 6.68 0.40 7.08 24
4 1-15 8.56 0.52 9.08 22
5 3-15 0.16 0.32 0.48 29
6 15-17 4.65 0.88 5.53 25
7 17-21 138.59 0.87 139.46 6
8 17-20 116.43 0.44 116.84 7
9 20-21 85.40 0.01 85.41 8
10 21-25 4.19 16.45 20.64 18
11 21-5 1.08 0.64 1.74 27
12 5-26 1.64 1.08 2.72 26
13 21-22 18.75 20.38 39.13 12
14 22-4 9.37 66.08 75.45 9
15 4-27 13.61 14.30 27.91 13
16 7-27 13.27 12.98 26.25 16
17 7-22 164.42 14.81 179.23 3
18 18-22 9.68 17.80 27.49 14
19 17-22 159.11 18.08 177.19 5
20 2-15 1.34 25.10 26.44 15
21 2-16 60.51 1.02 61.53 10
22 14-2 214 6.52 220.52 1
23 11-14 0.75 0.24 0.99 28
24 12-14 175..62 2.14 177.76 4
25 12-13 9.62 4.34 13.96 20
26 22-23 10.21 2.32 12.53 21
27 19-23 12.41 3.25 15.66 19
28 23-24 6.24 1.22 7.46 23
29 24-6 196.42 4.56 200.98 2
6.2 Relationship Between Performance Indices And Outages
The relationship between the performance indices and outages is plotted in figure 5 below. It has been
shown in Table 4 that contingency has been ranked by considering the line with the highest performance
indices. Kaduna to Shiroro having the highest performance indices is ranked first and Jebba GS to Jebba TS
having the least performance indices is ranked the last. However, the most severe contingency which is clearly
shown in figure 4, should be given priority attention.
Figure 4: Performance indices plotted against line outage numbers.

VII. Conclusion
Considering the number of numerical iteration per time taken, Fast Decoupled load flow method has
proven to be excellent in the load flow analysis of the 27-bus Nigerian 330kV transmission grid. Hence, owing
to its time for numerical iteration, its capacity to hold as many data as possible and its merit of having a matrix
alteration formula that can be incorporated and used to simulate problem of contingencies involving power
system equipment outages without involving the inversion of the Jacobian matrix for all iteration, then FDLF is
considered extensively in the research work. The load flow studies identified buses with low voltages. At the
outage of Kainji generator bus, it was observed that Birnin-Kebbi, Jos, Gombe, Kaduna, Katampe, Oshogbo,
Ajaokuta, New Haven, Aiyede, Ikeja-West, Onitsha and Akangba have voltages less than 0.95pu which was
regarded as low voltages. Power losses greater than 5% were also observed at Jebba TS to Oshogbo, Ikeja-West
to Egbin, Ikeja-West to Benin, Oshogbo to Benin, Kaduna to Shiroro, Kano to Kaduna, Jos to Kaduna and Jos to
Gombe. At the outage of Sapele GS and Calabar GS, low voltages were noticed in the same buses given above
and also power losses greater than 5% in the same line above. However, a single line contingency evaluation
shows that a transmission line from Kaduna to Shiroro has the highest severity index and hence ranked number
one (1). The ranking continued until the line with the least performance index. Furthermore, it can be seen that
the outages of one or more generators give low voltages at the same bus and power losses at the same
transmission lines. Hence, it becomes expedient to compensate the lines.
References
[1]. O. A. Ezechukwu. “Expansion planning for Nigerian‟s South East Electric Power Transmission Network”. The International
Journal of Engineering and Science (IJS) Volume 2, Issue 9, pp.1804-1805, 2013.
[2]. C. J. Nnonyelu, T. C. Madueme and B. O. Anyaka “Power System Contingency Analysis”: A study of Nigerian 330kV
Transmission Grid. Proceedings of the 4th
Electrical Engineering National Conference on Energy sources for power generation, 21-
23 July. University of Nigeria,Nsukka. pp. 250, 2013.
[3]. K. W. Chan, R.W. Dunn, A.R. Daniels, J.A. Padget, A.O.Ekwue, E. H. Buxton and M. J. Rawlins. “On-line dynamic-security
contingency screening and ranking”. IEE Proceedings.-Generation, Transmission and Distribution. Vol. 144, No. 2, pp. 132-138,
March 1997.
[4]. A. A Fouad, and V. Vittal, „Dynamic security assessment utilizing the transient energy function method‟, IEEE Trans.Power
Syst.Vol.34, No. 1, pp. 284-291, 1986.
[5]. P. Seaux, M. Pavella, E. Euxibie, B. Heilbronn, and J. F. Lesigne, „Extended equal-area criterion revisited‟. Proceedings of IEEE
Power Engineering Society Summer Meeting, pp. 422-426, 1991.
[6]. El-Kady, M. A. Tang, C. K. Carvalho, V.F. Cauley, G. Kumar, A. Brandwajn and A. Ipakchi, “Artificial intelligence applications in
on-line dynamic security assessment”. Proceedings of PSCC 11, Vol. 2, pp. 881-887, 1993.
[7]. J. B. Gupta. “A Course in Power Systems” S. Chand and Company Ltd. India pp. 625, 2013.
[8]. J. A. Treece. “Boot strap Gauss-Seidel load flow”. Proceedings of the IEEE. Vol. 116, pp. 866-870, 1969.
[9]. J. B. Ward and H. W Hale. “Digital Computer Solution of Power Flow Problems”.Trans.Am.Inst.Electr.Eng.Part375, pp. 398-404,
1956.
[10]. G. W. Stagg and A. G. Phadke. “Real Time Evaluation of Power System Contingencies Detection of Steady State Overloads”. IEEE
Power Eng. Soc. Summer power meet, 1970, Paper. No. 70, pp. 692, 1970.
[11]. A. O. Ekwue, H. B. Wan, D. T. Y. Cheng and Y. H. Song. “Voltage Stability Analysis on the NGC System”. Electric Power
Systems Research Vol. 47,Issue 6, pp. 173–180, 1998.

Q01052136142

More Related Content

What's hot (20)

Viewers also liked (14)

Similar to Q01052136142 (20)

More from IOSR Journals (20)

Recently uploaded (20)

Q01052136142