Application of Newton Raphson Method to Voltage Stability Analysis of the Nigeria 330kV Transmission Grid

DOI : 10.17577/IJERTV12IS010087

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Application of Newton Raphson Method to Voltage Stability Analysis of the Nigeria 330kV Transmission Grid

Peter .O. Ohiero

Department of Electrical and Electronic Engineering, Cross River University of Technology,

Calabar, Nigeria

Abstract This paper presents the voltage stability analysis of the Nigeria 330kV transmission network using Newton Raphson load flow method. A model of the existing 56-bus transmission network was developed and simulations have been carried out using Electrical Transient and Analyzer Program (ETAP) software. The simulation results show that the voltage magnitudes of buses; Aliade (0.9469pu-26.180), Damaturu (0.8961pu-39.390), Gombe (0.9000pu-37.040), Jalingo (0.8721pu-25.510), Jos (0.9112pu-32.950), Kaduna (0.8833pu- 34.560), Kano (0.7805pu-44.590), Makurdi (0.9432pu-27.660),

Maiduguri (0.8961pu-39.380), Yola (0.8920pu-23.390) fall below the acceptable voltage limit of 0.95pu. These buses are the weak buses in the existing Nigeria 330kV transmission network that contribute more to system collapse and blackouts. This work also demonstrates the effectiveness of voltage stability analysis in proper identification of weak buses and proper location of reactive power compensation devices. Hence, in order to improve on the stability of the power system network, there is need for reactive power compensation devices to be located on these buses.

Keywords Voltage Stability, Voltage Instability, Voltage Collapse, Newton Raphson load flow method, Nigeria 330kV Transmission Grid.

  1. INTRODUCTION

    Voltage and frequency are important parameters used to determine the stability, security, quality and performance of a power system network. Power system network and it components are designed to operate at a constant and specified value of voltage and frequency. This is achieved when there is a balance between the power generation and power demand. In other words, the power generation must be equal to power demand and losses.

    In Nigeria, electricity is transmitted through transmission lines at a high voltage of 330kV. This voltage is to be maintained at the acceptable operational value of 330kV±5% that is, between 315.5kV and 346.5kV or 0.95pu to 1.05pu stability limit. However, numerous challenges facing the Nigeria power system have been forcing the transmission network to operate out of the stability limit. Some of these challenges are inability to maintain a balance between power generation and power demand; the power generation is less than power demand due to increasing population and industrialization, sudden increase in load, increasing reactive power demand without adequate reactive power support, slow

    pace of rehabilitation and expansion, erratic power supply, long radial, fragile transmission lines with limited transmission wheeling capacity without redundancies, aged power system equipment, high losses [1].

    At present, there are twenty three (23) power generating plants with a total installed capacity 10,396MW connected to the Nigeria national grid but with only available capacity of 6,056MW [2]. Even if all the existing generating plants are operational, there is a great limitation to dispatch the generated power by the transmission and distribution infrastructures. The transmission network has a theoretical wheeling capacity of 7,500MW and a current transmission wheeling capacity of 5,300MW which is overstressed and overloaded. When the generated reactive power is greater than or less than the demanded reactive power, the voltage level goes up and down and results to voltage instability. Voltage instability is direct opposite of voltage stability. Voltage instability occurs when a power system is unable to maintain its bus voltages within the acceptable operational limit under normal condition and after being subjected to disturbance. Voltage instability causes overheating, excessive voltage drop and power losses, and force the components of the power system to operate above their thermal limits and consequently reduces power quality, efficiency, reliability and performance and leads to a wide scale supply disruptions, resulting to grid collapse and blackout. In a power system, some components and buses are more prone to voltage variation than the other because of their location with regards to the sources of electricity and load demand. A power bus which voltage fall outside of the acceptable voltage range of

    ±5% of nominal value is a weak bus. Weak buses poses great challenge in the operation, reliability and security of power system. A weak bus cannot support additional loads and have negative effect on generation, transmission and distribution of electricity to industrial and residential customers. Several studies and methods have been used to know the operational voltage and identify weak buses in power system network [3][4][5][6].

    Voltage stability can be analyzed using power flow analysis, continuation power flow, bifurcation diagram, V-P curves, P- Q sensitivity analysis, Q-V modal analysis, Q-V curves, and minimum singular value methods, modal/eigen value, Fast Voltage Stability Indices (FVSI). Voltage Stability Analysis

    of Nigerian 330kV Power Grid using Static P-V Plots was investigated in [7]. In their approach, the real power P of electric load, at a particular area or bus is varied in steps at a fixed power factor while the value of the voltage V is recorded. The plot of the PV curve is used to determine the voltage stability of the system. Two solutions were arrived at for the voltage, one for the high voltage but within the voltage stability limit which is the stable solution and the other one is the low voltage but outside the minimum voltage stability limit which the unstable solution. Their results showed the maximum power point, at which the two solution

    Newton Raphson method is an iterative method in which a set of linear simultaneous equations is obtained from a set of nonlinear simultaneous equations by successive approximation using Taylors series expansion [13]. It is widely applied to solving load flow problems and only first approximation is taken. It begins with an initial estimate or a guess at the solution and at the end of an iteration, the solution is checked of its closeness to the actual solution, the solution is updated until the solution converges and a final solution is obtained.

    for voltage is equal beyond which increase in real power P and reactive power Q will make the voltage unstable. In

    Considering an

    ith bus as shown in a single line diagram in

    another work, the fast voltage stability indices (FVSI) was

    Fig. 1 below, the current injection into the

    ith

    bus Ii is a

    analysed and presented [8]. They used the fast voltage

    function of the voltage at

    i bus V and the impedance of

    stability indices (FVSI) to identify the critical lines and buses to install the FACTS controllers. The line stability indices

    the line

    Zij

    th

    between the ith

    i

    bus and another bus say jth bus

    were evaluated for each loading condition and line outage.

    The line that gives FVSI value close to one were taken to be the most critical line corresponding to the bus causing the power system to tend towards instability. The simulation results by using PSAT software for the IEEE-14 bus system shows the proper location of UPFC as identified by the FVSI in a particular line connected to the most critical bus to maintain the stability of the system. When a power system network is subjected to voltage instability, there is need for reactive power compensation, expansion an upgrade. The problem of voltage instability can be solved with reactive power compensating devices such as shunt capacitors, UPFC, SVC, FACTS and under load tap changing (ULTC) transformer [9][10]. The location of reactive power compensating devices must be accurately known and located to improve the stability of the power system network. The challenge most power system operators and engineers faced

    given as;

    G

    I Vi

    i Z

    ij

    Fig. 1. Single line diagram of a two bus system.

    Load

    (1)

    is the proper and optimal location of the point where voltage instability originates from and the correct placement of reactive power compensator [11]. Reference [12] studied the compensation effect on the interconnected Nigerian Electric Power grid and concluded that concentrating the

    In order to eliminate the burden of calculation in (1), the relationship between impedance and admittance can be used and (1) becomes;

    compensation on the problem buses gives best results. Hence, there is need to investigate the voltage stability of the entire power system network to know in advance the parts or buses likely to contribute more to voltage instability and system

    Where,

    Ii Vi yij

    yij is the admittance of the line between bus i and j.

    (2)

    collapse or blackouts in order to correctly locate voltage compensation devices. In this paper, the load flow method approach is used to analyse voltage stability. It involves carrying out a load flow analysis to know the voltage

    In an n-bus power system, the current injection into ith

    calculated based on Kirchhoff Current Law (KCL) as;

    n n

    bus is

    i i ij

    j ij

    magnitude and angle at each bus, the real and reactive power

    of the generator and loads and the power flow and losses along the transmission lines. Once, the bus voltage magnitude

    I V y

    j 0

    • V y

    j 1

    j i

    (3)

    and angle is known, it becomes easier to know the buses whose voltage limit is violated.

  2. FORMULATION OF NEWTON RAPHSON LOAD

    Equation (3) can be written in terms of the bus admittance matrix Yij as;

    n

    FLOW METHOD

    Load flow analysis can be carried out using any of the following; Newton Raphson, Gauss Seidel and Fast Decoupled methods. Among these, Newton Raphson is

    Ii

    j 1

    YijVj

    , for i 1, 2, 3,…n

    (4)

    widely used because it has better accuracy, less iterative time and very fast convergence speed.

    Where Vi

    and Vj are given as,

    Vi Vi i Vi (cosi j sin i )

    (5)

    2

    And

    Vj Vj j Vj

    (cos j j sin j )

    (6)

    P2 .

    . .

    Yij Yij ij Yij

    (cosij j sinij )

    (7)

    . .

    .

    n

    Substituting equations (6) and (7) into equation (4), the

    P

    V2

    current injected into the

    ith

    bus can be expressed in polar

    n

    Q2

    J V

    2

    (13)

    form as

    . .

    n

    Ii Yij

    Vj ij j

    (8)

    . .

    . .

    j 1

    The complex power at ith bus is given by,

    Q1n

    V1n

    n

    0 0

    P jQ

    V *I

    V * Y V

    (9)

    V

    0

    i i i i i ij j

    j 1

    1n

    Where, J is the Jacobian matrix which element is divided

    P jQ

    V *I

    V

    n

    Y V

    (10)

    into sub-matrices; J1, J2 , J3 , J4 as shown in (14).

    i i i i i i

    j 1

    ij j ij j

    Where, Pi

    is the real power in bus-i and Qi is the reactive

    Pi J1

    J2 i

    (14)

    i

    power in bus-i and V * is the conjugate of the voltage at bus-i

    Qi J3

    J4 Vi

    Substituting equations(5), (6) and (7) into (10) and simplify, the real and reactive power at ith bus are given by;

    n

    Where, Pi is the real power mismatch, Qi is the reactive power mismatch, i is the changes in the bus voltage angle,

    Pi Yij Vj

    Vi cos(ij j i )

    (11)

    Vi

    is the changes in the bus voltage magnitude. At each

    j 1

    n

    Qi Yij

    j 1

    Vj Vi sin(ij j i )

    (12)

    iteration a jacobian matrix is formed and sub-matrices are

    computed with the partial derivatives of the real and reactive power (11) and (12) with respect to small changes in the bus voltage magnitude and angle given. The element of the sub-

    Equations (11) and (12) are nonlinear equations with voltage

    matrices J1, J2 , J3 and J4

    can be expressed as;

    magnitude V and voltage angle and are called power flow equations. These equations can be solved iteratively by

    The diagonal element of

    J1 is

    Newton Raphson method starting with an initial estimate.

    P n

    Assuming that the slack bus is the first bus with a fixed

    i Y V V

    cos(

    )

    (15)

    voltage angle/magnitude, the voltage magnitude and angle at each bus or area of the power system is determined by the

    i

    j 1 j i

    ij j i ij j i

    matrix form of Newton Raphson method as;

    The off-diagonal element of

    J1 is

    Pi

    Y V V

    sin(

    )

    (16)

    j

    ij j i ij j i

    The diagonal element of J2 is

    P

    i ij ii

    n

    ij j ij j i

    i

    Vi

    2 V Y

    cos

    • Y V

    j 1

    cos(

    ) (17)

    j i

    The off-diagonal element of J2 is

    Pi

    V Y

    cos(

    )

    (18)

    Vj

    i ij ij j i

    The diagonal element of J3 is

    k 1

    i

    i

    k k

    (26)

    Q n

    ij j i ij j i

  3. MATERIALS AND METHOD

    i

    i

    j 1

    Y V V

    cos(

    )

    (19)

    In order to carry out voltage stability analysis of the existing Nigeria transmission network, it is necessary to first perform

    j i

    The off-diagonal element of

    J3 is

    load flow analysis. For this research, the load flow analysis is

    based on Newton Raphson method performed using Electrical Transient and Analyzer Program (ETAP) software. ETAP is a computer-aided software suitable for design, modelling, simulation and analyzing generation, transmission

    Qi

    Y V V

    cos(

    )

    (20)

    and distribution power system as well as renewable energy

    j

    ij j i ij j i

    generation. The single line diagram of the existing 330kV Nigeria Transmission network used in this study was drawn as shown in Fig. 2. A model of the 56 bus system of the Nigeria 330kV transmission network was developed in ETAP software. The model requires input data, which are the real

    and reactive power of the generating plants, the voltages and power rating of the transformers, voltages, real and reactive

    The diagonal element of

    Q

    J4 is

    n

    power of the loads, the length of transmission lines, real and reactive power of generator buses. The input data of the

    i ij ii

    ij j ij j i

    generators and loads as obtained from the Transmission

    i

    Vi

    2 V Y

    sin

    • Y V

    j 1 j i

    sin(

    )

    (21)

    Company of Nigeria is shown in Table 1. The transmission line model in ETAP requires basic data such as the type of

    The off-diagonal element of

    J4 is

    conductor, the length of lines, the voltage rating of the lines,

    the number of parallel lines, the type and configuration of circuits (e.g. single and double circuit), the number of

    Qi

    V Y

    sin(

    )

    <>(22)

    conductor per phase, the height of towers, the spacing of

    Vj

    i ij ij j i

    conductors in the bundle and spacing between phases. The

    type of conductor used in the existing 330kV overhead transmission lines in the Nigeria power system network is

    The iteration continues until it converges thereby reaching a

    satisfactory solution. The changes in the bus real power, Pi and reactive power, Qi are the mismatches which are the difference between the calculated and scheduled values of the real and reactive power given as;

    350mm2 Aluminium Conductor Steel Reinforced (ACSR) twin conductor bundle Bison conductor with an average spacing of the conductor in the bundle as 400mm and the spacing between the phases as 10.5m [12]. The supporting structure are made of steel towers and spanned at an average distance of 500m apart, with a height of 75 metres for the

    double circuits and 54 metres for the single circuit [11].

    Pi

    k

    Pi

    sch

    • Pi

    k

    (23)

    These data were inputted into the transmission line model in ETAP and the transmission line parameters were obtained as

    Qi

    k

    Qi

    sch

    Qi

    k

    (24)

    shown in Table 2. All the components were adequately represented in the model of the transmission network as

    i

    Where, Psch and

    i

    Q sch are the scheduled real ad reactive

    shown in Fig. 3 and Fig. 4. With Egbin power plant as the slack bus because of its location in the far western part of the

    power while

    i

    Pk and

    Q

    k

    i

    the calculated real and reactive

    country, these data were used for the simulation analysis. The

    power respectively. From (23) and (24), the new estimates for

    bus voltages and angles, real and reactive power flow and

    the voltage magnitude

    V k 1 and angle k 1 are given by

    losses under steady state were recorded.

    V k 1

    (k

    Vi

    (k

    • Vi

    (25)

    Fig. 2. Single line diagram of the 56-bus Nigerian 330kV Transmission Network.

    Table 1. Generator and Load Bus Data for the existing Nigerian 330kV Transmission Grid

    SN

    Bus Name

    Bus Nominal Voltage (V)

    Generation

    Load

    From

    Max. Active Power (MW)

    Active Power Schedule (MW)

    Active (MW)

    Reactive (MVAr)

    1

    AES

    330

    270

    200

    2

    Afam GS

    330

    776

    500

    3

    Ayiede

    330

    270

    166.10

    4

    Aja

    330

    220

    103

    5

    Ajaokuta

    330

    96

    45

    6

    Akamgba

    330

    471

    156.071

    7

    Aladja

    330

    167

    20

    8

    Alaoji

    330

    1079

    450

    266.18

    155

    9

    Alaogbon

    330

    220

    103

    10

    Aliade

    330

    136

    84

    11

    B.Kebbi

    330

    112

    60

    12

    Benin

    330

    298

    131.2

    13

    Benin North

    330

    80

    50

    14

    Calabar

    330

    561

    240

    110.75

    60.37

    15

    Damaturu

    330

    75

    259.18

    16

    Delta I -IV

    330

    960

    620

    17

    Egbema

    330

    378

    200

    18

    Egbin PS

    330

    1320

    610

    19

    Egbin TS

    330

    20

    Erunkan

    330

    14.5

    8.93

    21

    Ganmo

    330

    270

    223.35

    22

    Geregu

    330

    434

    200

    23

    Gombe

    330

    180

    100

    24

    Gwagwalada

    330

    75

    65

    25

    Ihovbor

    330

    451

    182

    26

    Ikeja West

    330

    510

    115

    27

    Ikot Abasi

    330

    195

    0

    28

    Ikot Ekpene

    330

    45.8

    20

    29

    Jalingo

    330

    75

    50

    30

    Jebba GS

    330

    590

    475

    31

    Jebba TS

    330

    360

    180

    32

    Jos

    330

    141

    155

    33

    Kainji

    330

    760

    313

    34

    Kaduna

    330

    193

    144

    35

    Kano

    330

    180

    100

    36

    Katampe (Abuja)

    330

    290

    60

    37

    Lokoja

    330

    75

    65

    38

    Makurdi

    330

    75

    37.7

    39

    Maiduguri

    330

    70

    50

    40

    New Haven

    330

    140

    10

    41

    New Haven South

    330

    40

    27

    42

    Olorunshogo

    330

    335

    195

    43

    Omotosho

    330

    335

    220

    44

    Omoku

    330

    150

    75

    45

    Oshogbo

    330

    201

    150

    46

    Okpai

    330

    480

    330

    47

    Onitsha

    330

    162

    28

    48

    Owerri

    330

    100

    60

    49

    Papalanto

    330

    1020

    450

    50

    PortHarcourt

    330

    200

    100

    316

    159

    51

    Sapele

    330

    1020

    550

    52

    Sakete

    330

    145

    70

    53

    Shiroro

    330

    600

    450

    54

    Shiroro TS

    330

    97.5

    22.75

    55

    Ugwuaji

    330

    75.7

    46.8

    56

    Yola

    330

    112

    65

    Table 2. Transmission Line Data (of Bison, two conductors per phase & 2×350 mm2 X-section Conductor) for the 330KV Lines obtained from ETAP.

    td>

    21

    SN

    Bus Name

    Length (km)

    Type of Circuit

    R1

    (/km)

    X1

    (/km)

    Y1

    (S/km)

    R0

    (/km)

    X0

    (/km)

    Y0

    (S/km)

    From

    To

    1

    Afam GS

    Alaoji

    25

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    2

    Afam GS

    Ikot Ekpene

    90

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    3

    Afam GS

    PortHarcourt

    45

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    4

    Ayiede

    Oshogbo

    115

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    5

    Ayiede

    lkeja West

    137

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    6

    Ayiede

    Papalanto

    60

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    7

    Aja

    Egbin PS

    14

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    8

    Aja

    Alagbon

    26

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    9

    Ajaokuta

    Benin North

    195

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    10

    Ajaokuta

    Geregu

    5

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    11

    Ajaokuta

    Lokoja

    38

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    12

    Akamgba

    Ikeja West

    18

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    13

    Aladja

    Sapele

    63

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    14

    Aladja

    Delta PS

    32

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    15

    Alaoji

    Owerri

    60

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    16

    Alaoji

    Onitsha

    138

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    17

    Alaoji

    Ikot Ekpene

    38

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    18

    Aliade

    New Haven South

    150

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    19

    Aliade

    Makurdi

    50

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    20

    B.Kebbi

    Kainji

    310

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    Benin

    Ikeja West

    280

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    22

    Benin

    Sapele

    50

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    23

    Benin

    Delta PS

    41

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    24

    Benin

    Oshogbo

    251

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    25

    Benin

    Onitsha

    137

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    26

    Benin

    Benin North

    20

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    27

    Benin

    Egbin PS

    218

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    28

    Benin

    Omotosho

    51

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    29

    Benin North

    Eyaen

    5

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    30

    Calabar

    Ikot Ekpene

    72

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    31

    Damaturu

    Gombe

    135

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    32

    Damaturu

    Maiduguri

    140

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    33

    Egbema

    Omoku

    30

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    34

    Egbema

    Owerri

    30

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    35

    Egbin PS

    Ikeja West

    62

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    36

    Egbin PS

    Erunkan

    30

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    37

    Erunkan

    Ikeja West

    32

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    38

    Ganmo

    Oshogbo

    87

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    39

    Ganmo

    Jebba TS

    80

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    40

    Gombe

    Jos

    264

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    41

    Gombe

    Yola

    240

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    42

    Gwagwalada

    Lokoja

    140

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    43

    Gwagwalada

    Shiroro

    114

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    44

    Gwagwalada

    Katampe

    30

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    45

    Ikeja West

    Oshogbo

    252

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    46

    Ikeja West

    Omotosho

    200

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    47

    Ikeja West

    Papalanto

    30

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    48

    Ikeja West

    Sakete

    70

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    49

    Ikot Abasi

    Ikot Ekpene

    75

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    50

    Ikot Ekpene

    New Haven South

    143

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    51

    Jalingo

    Yola

    132

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    52

    Jebba TS

    Oshogbo

    157

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    53

    Jebba TS

    Jebba GS

    8

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    54

    Jebba

    Kainji

    81

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    55

    Jebba

    Shiroro

    244

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    56

    Jos

    Kaduna

    196

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    57

    Jos

    Makurdi

    230

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    58

    Kaduna

    Kano

    230

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    59

    Kaduna

    Shiroro TS

    96

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    60

    Abuja (Katampe)

    Shiroro GS

    144

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    61

    New Haven

    Onitsha

    96

    Single

    0.03809

    0.033368

    3.42768

    0.23426

    1.09356

    1.75899

    62

    New Haven

    New Haven South

    5

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    63

    Okpai

    Onitsha

    60

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

    64

    Onitsha

    Owerri

    137

    Double

    0.01879

    0.14976

    8.08147

    0.17972

    1.02342

    1.93438

  4. RESULTS AND DISCUSSIONS

    The developed model was simulated based on Newton Raphson load flow method using ETAP software as shown in Figs. 3 and 4 below. The simulation results of the bus voltage magnitudes and angles were recorded and presented as shown in Table 3. The voltage profile in Fig. 5 shows the buses which voltages violates the acceptable bus voltage limit of 0.95pu 1.05pu. They are Aliade (0.9469pu-26.80),

    Damaturu (0.8961pu-39.390), Gombe (0.9000pu-37.040), Jalingo (0.8721pu-25.510), Jos (0.9112pu-32.950), Kaduna (0.8833pu-34.560), Kano (0.7805pu-44.590), Makurdi (0.9432pu-27.660), Maiduguri (0.8961pu-39.380), Yola (0.8920pu-23.390). These buses contribute more to the voltage instability been experienced in the Nigeria 330kV transmission network.

    Fig. 3. A simulation model of the Nigerias 330kV Transmission network using Newton Raphson Method.

    Fig. 4. A Zoomed section of the simulation model of the Nigerias 330kV Transmission network using Newton Raphson Method.

    Table 3. Simulation Results of Bus Voltages

    S/N

    Bus Name

    Bus Nominal Voltage (kV)

    Operational Voltage (%)

    Operational Voltage (kV)

    V (pu)

    Angle (0)

    1

    AES

    330

    99.24

    327.492

    0.9924

    -2.99

    2

    Afam GS

    330

    96.93

    319.869

    0.9693

    -15.57

    3

    Ayiede

    330

    96.90

    319.77

    0.9690

    -14.93

    4

    Aja

    330

    99.52

    328.416

    0.9952

    -0.458

    5

    Ajaokuta

    330

    96.10

    317.13

    0.9610

    -27.48

    6

    Akamgba

    330

    95.74

    315.942

    0.9574

    -13.01

    7

    Aladja

    330

    99.25

    327.525

    0.9925

    -20.48

    8

    Alaoji

    330

    97.08

    320.364

    0.9708

    -15.63

    9

    Alaogbon

    330

    99.06

    326.898

    0.9906

    -0.886

    10

    Aliade

    330

    94.69

    312.477

    0.9469

    -26.18

    11

    B.Kebbi

    330

    98.51

    325.083

    0.9851

    -23.39

    12

    Benin

    330

    97.73

    322.509

    0.9773

    -19.32

    13

    Benin North

    330

    95.76

    316.008

    0.9576

    -21.68

    14

    Calabar

    330

    96.59

    318.747

    0.9659

    -17.5

    15

    Damaturu

    330

    89.61

    295.713

    0.8961

    -39.39

    16

    Delta

    330

    100.0

    330.00

    1.0000

    -20.26

    17

    Egbema

    330

    97.68

    322.344

    0.9768

    -10.64

    18

    Egbin PS

    330

    100.0

    330.00

    1.0000

    0

    19

    Erunkan

    330

    98.08

    323.664

    0.9808

    -5.51

    20

    Ganmo

    330

    95.40

    314.82

    0.954

    -20.75

    21

    Geregu

    330

    96.01

    316.833

    0.9601

    -27.5

    22

    Gombe

    330

    90.00

    297.00

    0.9000

    -37.04

    23

    Gwagwalada

    330

    95.84

    316.272

    0.9584

    -29.11

    24

    Ihovbor

    330

    96.61

    318.813

    0.9661

    -19.14

    25

    Ikeja West

    330

    97.04

    320232

    0.9704

    -11.48

    26

    Ikot Abasi

    330

    96.55

    318.615

    0.9655

    -17.39

    27

    Ikot Ekpene

    330

    96.64

    318.912

    0.9664

    -17.38

    28

    Jalingo

    330

    87.21

    287.793

    0.8721

    25.51

    29

    Jebba GS

    330

    100

    330.00

    1.0000

    -18.5

    30

    Jebba TS

    330

    99.65

    328.845

    0.9965

    -18.79

    31

    Jos

    330

    91.12

    300.696

    0.9112

    -32.95

    32

    Kainji

    330

    100.9

    332.97

    1.0090

    -17.25

    33

    Kaduna

    330

    88.33

    291.489

    0.8833

    -34.56

    34

    Kano

    330

    78.05

    257.565

    0.7805

    -44.59

    35

    Katampe (Abuja)

    330

    95.75

    315.975

    0.9575

    -29.28

    36

    Lokoja

    330

    95.95

    316.635

    0.9595

    -28.38

    37

    Makurdi

    330

    94.32

    311.256

    0.9432

    -27.66

    38

    Maiduguri

    330

    89.61

    295.713

    0.8961

    -39.98

    39

    New Haven

    330

    97.0

    320.10

    0.9700

    -20.13

    40

    New Haven South

    330

    97.01

    320.133

    0.9701

    -20.09

    41

    Olorunshogo

    330

    101.8

    335.94

    1.018

    -10.37

    42

    Omotosho

    330

    100.0

    330.00

    1.0000

    -16.50

    43

    Omoku

    330

    97.79

    322.707

    0.9779

    -10.64

    44

    Oshogbo

    330

    97.41

    321.453

    0.9741

    -18.92

    45

    Okpai

    330

    98.61

    325.413

    0.9861

    -17.84

    46

    Onitsha

    330

    98.23

    324.159

    0.9823

    -17.81

    47

    Owerri

    330

    97.6

    322.08

    0.976

    -13.45

    48

    Papalanto

    330

    97.09

    320.397

    0.9709

    -12.97

    49

    PortHarcourt

    330

    95.69

    315.777

    0.9569

    -16.69

    50

    Sapele

    330

    98.31

    324.423

    0.9831

    -19.04

    51

    Sakete

    330

    95.22

    314.226

    0.9522

    -13.31

    52

    Shiroro

    330

    95.51

    315.183

    0.9551

    -28.22

    53

    Ugwuaji

    330

    96.89

    319.737

    0.9689

    -20.21

    54

    Yola

    330

    89.20

    294.36

    0.892

    -23.39

    Fig. 5. Voltage profile of the existing Nigeria 330kV transmission network

  5. CONCLUSION

The voltage stability of the Nigeria 330kV transmission network have been simulated and analysed. The results revealed the buses that operates at voltage outside the acceptable operational voltage limit of 330kV±5% which is between 313.5kV 346.5kV. These buses constitute the weak buses that cause voltage instability and system collapse in the network and require serious attention. It is therefore necessary to put in place adequate reactive power compensation in these buses to reduce or avoid voltage stability problems and system collapse.

REFERENCES

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2014), PP 76-82 www.iosrjournals.org

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2056-5860.

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