 Open Access
 Authors : Ogundare Ayoade Benson , Adejumobi Isaiah Adediji , Oludare Nathaniel Adeyinka , Adebeshin Azeez Ishola
 Paper ID : IJERTV11IS020159
 Volume & Issue : Volume 11, Issue 02 (February 2022)
 Published (First Online): 05042022
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Assessment of Transmission Lines Operational Resilience Using Power Transfer Distribution Factor Index for Proactive System Operational Planning
Ogundare Ayoade Benson
Lagos State Polytechnics: Dept.of Electrical and Electronics Engineering
LASPOTECH,
IkoroduLagos State,Nigeria
Adejumobi Isaiah Adediji
Federal University of Agriculture: Dept. of Electrical and Electronics Engineering
FUNAAB,
Abeokuta OgunState, Nigeria
Abstract The Electricity Reform Act of 2005 in Nigeria was instituted due to the continuous rapid increase in electrical power demand from over 200 million Nigerian. The reform encouraged private sector participation in the generation of more electrical energy. Unfortunately, expansion of transmission network (TN) was given less attention by the Government. Hence, the transmission network was over loaded, and in critical condition that cannot accommodate all the power generated simultaneously. This paper estimates the resilience of transmission network of Nigeria 30bus grid system under this condition using Power Transfer Distribution Factor Index (PTDFI). The NewtonRalphson iterative power flow technique was used to determine the steady state condition of the TN. As the generation and load were varied, the line flows on each transmission line keep changing. The variation in power flow on each transmission line is sensitive to the strength of the line. The simulation results showed that the most critical line is from Jos to Kaduna with PTDFI of 1.3271 and the most strengthened line is from Ikeja West to Benin with PTDFI of 0.2085. From this result, it is discovered that Jos to Kaduna transmission line needs urgent enhancement, closely followed by Gombe to Jos. The PTDFI is a good approach to fast track transmission network expansion and resilience enhancement for power system operation.
Keywords Electricity reform act, Transmission network expansion, Transmission line resilience enhancement, Power Transfer Distribution Factor Index

INTRODUCTION
Power system consists of generation, transmission and distribution. Generated power is carried out at generating station while consumers are at the distribution end of the power system chain. If the transmission network is not capable to accommodate all the power generated, it will cause stranded generation and results to load shedding. On the other hand, if the transmission lines are underutilized, it will leads to loss of
Oludare Nathaniel Adeyinka
Lagos State University: Dept.of Computer and Electronics Engineering
LASU,
OjoLagos State,Nigeria
Adebeshin Azeez Ishola
Lagos State Polytechnics: Dept.of Electrical and Electronics Engineering
LASPOTECH,
IkoroduLagos State,Nigeria
resources. Therefore, for optimum power system operation, transmission network is designed to accommodate power generated and transfer quality power to consumers at minimum loss [1 2].
In 2005,the Nigeria power system was privatized. The aim was to cope with rising in load of consumers and to get reliable power supply. This served as an opportunity for the private investors to be involved in electricity generation and distribution while transmission is still regulated. This has led to insufficient capacity of the transmission lines to accommodate the available generated power to the consumers. Hence, it led to overstressing the transmission lines, poor voltage gradient and high losses [3].
To operate any power system efficiently, and to carry out possible future expansion on the transmission network of the system, the strength of each transmission line of the network must be ascertained. The steps involved for the determination of the strength of transmission line commence with power flow analysis to obtain steady state solution. The next is to consider variation in load and variation in generation to match. While the loads and generations are varied, the power flow as well as the line flow must be maintained at steady state to obtain quality power supply. This implies that none of the transmission lines or cables is overstressed and voltage magnitudes and voltage angles are not violated. If the thermal loading limit of transmission line is exceeded, it will lead to increase in the conductor temperature [4]. This will increase the sag of the transmission lines between the towers and if it is not checked may results in irreversible stretching. Therefore, such lines are described as critical and overstressed. Variation in generation or load at a bus or switching on/off of a line or a transformer will reach other places in the network through transmission lines thereby changing the power flow on all
transmission lines [5]. The consequences of the changes in line flow may be experienced in various degrees on different transmission lines, depending on electrical characteristics of the lines and the interconnection [6]. The response of each transmission line to change in loading condition depends on the fragility (strength or weakness) of such line. This fragility of the transmission line is determined in this paper using PTDFI. The PTDFI measures the strength or the weakness of the transmission line and can be employed to determine the strength of the transmission network.
Many researchers have proposed different model and tools to obtain the strength of the transmission line which include linear and nonlinear mixed integer optimization programming techniques.
Determination of the strength of transmission line is a complex task, which often involves the use of sophisticated mathematical modeling and optimization techniques [4]. The solution to the sophisticated mathematical modeling is usually broken down into steps.
In a realistic power system network, the committed units of power plants are at different location from load centre. Under steady state condition, the generation capacity is equal to the load demand plus loses [7]. Thus, there are many ways of scheduling generation to feed the loads.
k n
PG Vj YjkVj cos jk j k
k 1
(1)
k n
P V Y V cos
D k kj k kj k j
k 1
(2)
The power demanded is given in (2).
Where, V is voltage magnitude, Y is the admittance, is the voltage angle and is the load angle. For a steady state
condition, total power generated is equal to total power demanded plus total losses on the transmission lines as given in (3).
(3)
Where nd is the load buses and ng is the generating plant. Power loss (PL) on the transmission line is presented by the author in [11] as given in (4).
ij i j
n n R cos
Authors in [8] worked on Nigerian transmission network
PL V V
Pi Pj QiQj
(4)
using long term load forecast algorithm. This approach broke down the system to artificial neural network and Monte Carlo
i1
j 1
i j
simulations and takes into consideration how the probabilistic growing load could be effectively accommodated.
In [9], the authors carried out study on power transmission network for the Nigerian South East Electric Power system using Power World Simulator software. He analysed transmission network using contingency analysis of NI criteria to evaluate potential transmission system and help in selecting the best plan for overall system security.
Recenly, a comprehensive and novel methodology based on power transfer distribution factor is presented by authors in [10]. The work considered a linearized power system network and avoids the use of voltage angle at the network nodes. Consequently, both the computational and time complexities are reduced significantly as the number of constraints are reduced compared to the optimizationbased approach..

METHODOLOGY
where R is the resistance of the line, Q is the reactive power,
V is the voltage and is the voltage angle. To determine the strength of each transmission line, generation and load were varied to maintain steady state operation. The power loss was neglected since sensitivity index was considered to study the change in power flow on each line. Also, the variation in generation is limited by the inequality constraint in (5).
Pi(min) Pi Pi(max) i 1,2,3……..n
(5)
where Pi (min) and Pi (max) is the minimum and maximum generating limit for plant i. When losses are negligible in (3) and using the inequality in (5), we have (6).
ng
Pk
If the system operator is desired to increase generation into
the infinite busbar, the valve must be opened more to increase steam into the turbine couple to the generator thereby increasing the shaft mechanical power. As a consequence, the
k 1 1
nd
Pi
i1
(6)
electrical output power increases and so the voltage angle increases. The PTDFI is described as the relationship that exists between the amount of power generated and the power flow on a line as the load also varied. It is described as sensitivity approach since it computes the amount of a change in generation and load to change in power flow on the line. Any transmission line that has value of PTDFI greater than one or equal to one is considered to be weak and vice versa.
Consider real power P generated at bus j and taken out at load buses k, as given in (1).
Hence, the measure of power flow on any transmission line to varying generation with varying load is given by (6).
Equation (6) gives the power flow index on the transmission lines. Hence, the transmission line with the largest PTDFI is the most critical line within the network.

STRUCTURE OF THE NIGERIAN 330 KV TRANSMISSION SYSTEMS
Figure 1 (sample network) shows the structure of the Nigerian 30bus 330 kV transmission network. It contains the
Ikeja west
76.12
23.99
79.81
0.55
47.63
Ikeja west
475.15
47.39
477.51
6.90
48.39
Ikeja west
196.20
49.33
202.31
1.26
4.46
Ikeja west
366.80
76.20
374.63
8.20
5.89
Jebba GS
247.50
27.25
249.00
0.11
0.05
Jebba TS
112.67
21.36
114.68
0.78
27.08
Jebba TS
112.67
21.36
114.68
0.78
27.08
Jebba TS
247.39
27.20
248.88
0.11
0.05
Jebba TS
248.72
27.19
250.20
1.84
3.79
Jebba TS
321.46
36.13
323.48
9.02
14.97
Jos 24
137.16
114.85
178.90
6.56
16.95
Jos 24
207.46
167.55
266.68
8.16
29.31
Kaduna
229.44
173.89
287.89
8.84
30.99
Kaduna
319.03
257.73
410.13
6.75
31.35
Kanji GS
116.58
38.78
122.87
2.08
47.12
Kanji GS
250.56
30.98
252.47
1.84
3.79
Kano 26
220.6
142.90
262.84
8.84
30.99
Katampe
145.05
72.50
162.16
0.90
13.61
Newhaven
177.90
133.4
222.36
2.11
0.54
Okapi
750.00
249.83
790.51
45.58
302.56
Omotoso
482.05
95.78
491.47
6.90
48.39
Omotoso
72.05
99.13
122.54
0.33
1.06
Onitsha 2
131.00
229.98
264.68
3.90
2.76
Onitsha
495.61
42.36
497.42
16.5
95.66
Onitsha
180.01
133.94
224.38
2.11
0.54
Osogbo
76.68
23.63
80.23
0.55
47.63
Osogbo
90.18
22.17
92.87
0.76
46.64
Osogbo
147.96
40.22
153.33
1.05
15.34
Osogbo
111.89
48.44
121.92
0.78
27.08
Osogbo
111.89
48.44
121.92
0.78
27.08
Papalanto
197.47
53.79
204.66
1.26
4.46
Papalanto
144.63
102.21
177.11
1.12
3.47
Sapele
255.54
61.61
262.87
1.59
1.77
Sapele
141.75
85.27
165.42
0.51
6.87
Sapele
141.75
85.27
165.42
0.51
6.87
Shiroro
312.43
51.10
316.58
9.02
14.97
Shiroro
145.95
58.89
157.38
0.9
13.61
name of the each bus, eleven generating stations, nineteen load buses and fiftythree transmission lines.
Fig. 1. Nigeria Power Network (Source:National Control Centre,Power Holding Company of Nigeria,2015)

RESULTS AND DISCUSSION
The 330 kV, 30bus Nigerian power system was simulated using NewtonRalphson power flow method. Table I shows the power flow and losses on the transmision lines for initial power flow.
TABLE I. THE INITIAL POWER FLOW AND LOSSES ON THE
TRANSMISSION LINES
BUS
P (MW)
Q
(Mvar)
S (MVA)
P LOSS (MW)
Q LOSS
(Mvar)
AES 9
375.00
82.09
383.88
8.20
5.89
Afam 3
189.25
403.08
445.29
1.82
8.20
Aiyede 16
14.63
52.49
54.49
0.09
26.62
Aiyede 16
146.91
55.56
157.07
1.05
15.34
Aiyede 16
143.52
98.75
174.21
1.12
3.47
Aja 10
137.20
102.90
171.50
0.16
2.06
Ajaokuta
6.90
5.15
8.61
0.02
41.17
Akangba
172.35
129.25
215.43
0.31
1.19
Aladja 14
353.63
9.02
353.75
1.37
3.73
Aladja 14
257.13
63.38
264.83
1.59
1.77
Alaoji 18
512.11
138.02
530.38
16.50
95.66
Alaoji 18
564.25
331.54
654.44
30.17
189.81
Alaoji 18
187.43
394.88
437.11
1.82
8.20
Benin 15
150.73
21.16
152.20
2.34
40.38
Benin 15
6.92
36.02
36.68
0.02
41.17
Benin 15
90.94
24.47
94.17
0.76
46.64
Benin 15
127.10
232.74
265.19
3.90
2.76
Benin 15
72.38
100.18
123.59
0.33
1.06
Benin 15
311.11
4.82
311.14
3.89
5.84
Benin 15
141.23
92.14
168.63
0.51
6.87
Benin 15
141.23
92.14
168.63
0.51
6.87
Benin 15
6.92
36.02
36.68
0.02
41.17
BininKebi
114.50
85.90
143.14
2.08
47.12
Calabar
594.42
141.74
611.08
30.17
189.81
Calabar
704.42
52.74
706.39
45.58
302.56
Delta 2
355.00
12.75
355.23
1.37
3.73
Delta 2
315.00
10.67
315.18
3.89
5.84
Egbin 1
137.36
100.84
170.40
0.16
2.06
Egbin 1
402.22
246.11
471.54
4.71
23.42
Gombe 22
130.60
97.90
163.22
6.56
16.95
Ikeja west
406.93
222.68
463.87
4.71
23.42
Ikeja west
172.66
128.06
214.97
0.31
1.19
Ikeja west
148.39
19.22
149.63
2.34
40.38
Ikeja west
14.53
25.88
29.68
0.09
26.62
Table II shows the ranking of the transmission lines according to their sensitivity using PTDFI for varying load and generation. It shows that the most critical line is Jos to Kaduna with PTDFI of 1.3271 and the least fragile line is Ikeja West to Benin with PTDFI of 0.2085.
TABLE II. THE RANKING OF TRANSMISSION LINES
From Bus
To Bus
PTD F
Ranki ng
From Bus
To Bus
PTD F
Ranki ng
Jos
Kaduna
1.32
71
1
Ikeja West
Omoto so
0.67
01
18
Gombe
Jos
1.16
11
2
Aiyed e
Papala nto
0.64
29
19
Kaduna
Kano
1.07
28
3
Benin
Oshog bo
0.55
68
20
Kanji GS
BirninK ebbi
1.03
05
4
Kanji GS
Jebba TS
0.51
52
21
Benin
Onitsha
1.01
95
5
Oshog bo
Jebba TS
0.51
41
22
New Haven
Onitsha
1.01
68
6
Shiror o
Katam pe
0.50
53
23
Okpai
Calabar
1.00
00
7
Delta
Benin
0.50
37
24
Alaoji
Onitsha
0.99
72
8
Akang ba
Ikeja West
0.50
12
25
Alaoji
Calabar
0.99
32
9
Egbin
Aja
0.50
08
26
Delta
Aladja
0.86
30
10
Ajaok uta
Benin
0.50
05
27
Shiroro
Jebba TS
0.77
12
11
AES
Ikeja West
0.50
00
28
Benin
Omotoso
0.75
68
12
Afam
Alaoji
0.50
00
29
Egbin
Ikeja West
0.74
98
13
Jebba GS
Jebb TS
0.50
00
30
Aiyede
Oshogbo
0.74
53
14
Ikeja West
Oshog bo
0.49
44
31
Shiroro
Kaduna
0.72
80
15
Ikeja West
Aiyede
0.43
24
32
Sapele
Aladja
0.71
42
16
Sapele
Benin
0.30
81
33
Ikeja West
Papalant o
0.69
77
17
Ikeja West
Benin
0.20
85
34

CONCLUSION
In this article, a new approach to evaluate the power system transmission line resilience and vulnerability to the variation of increased power generation and loading is investigated using 330 kV, 30bus Nigerian power system. The 330 kV, 30bus, Nigerian transmission lines are often overstressed due to more than enough generation unit. This condition of operation is abnormal for power system operation. The PTDFI technique has the ability to monitor a quite number of network transmission lines, which have significant influence on the network operation in avoiding the network line overloading to enhance the transmission line resilience for sustainable uninterruptible power supply. The applicability of the proposed PTDFI model to the sample network serves as a reliable pointer to ranking the transmission lines. Also, this model serves as a useful tool in making faster decisions for proper transmission network expansion for sustainable power system operation.
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