Voltage Stability Analysis of 86-Bus 330KV Nigeria Power Grid Based on Reserved Energy Potential via Continuation Power Flow Technique

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Voltage Stability Analysis of 86-Bus 330KV Nigeria Power Grid Based on Reserved Energy Potential via Continuation Power Flow Technique

A Isdore Onyema Akwukwaegbu1,*, Fabian Izundu Izuegbunam2 , Michael Chukwudi Ndinechi3

1,2,3Department of Electrical /Electronic Engineering, Faculty of Engineering, Federal University of Technology, Owerri, Nigeria.

Abstract The Nigeria power system is being confronted by myriad of problems ranging from inadequate power generation capacity to meet demand, limited transmission corridor to evacuate generated power and insufficient reserves to sustain the existing capacity in times of sudden transients such as loss of generator/power plant. The objectives of this work include overview analysis of the procedures taken for the conversion of reserved energy resources of coal, natural gas and large hydro potentials into its equivalent electric power resource, evaluation of the reserved-based electric power resource, deployment of the reserved-based electric power resource into existing installed power generating capacity and voltage stability simulation of upgraded reserved-based electric power generating capacity model to enhance the totality of Nigeria power network stability. To meet the ever increasing power demand with increasing population, several megawatts (63,876.96 MW) from the reserved energy resources of large coal deposits (2,559 million tonnes or 12,081.96MW), unlimited reserved quantity of natural gas (5.4 trillion cubic meters or 39,270 MW) and abundant hydro reserve (12,525 MW) are deployed into the existing installed power generation capacity (12,682 MW) to form the reserved power potential injected Nigeria power network of 76,558.96 MW capacity. The introduction of 8,442 Km new transmission lines to the existing grid transmission lines of 5,988 Km were equally considered in this research in order to provide sufficient power evacuation corridor for efficient power flow management of the new network. The continuation power flow method which uses predictor, corrector and tangent techniques to generate the power voltage (P V) curves for the estimation of load ability limits to quantify voltage stability indices and determine the weak buses in the power network was deployed in the analysis. The results showed that majority of the network bus voltages met the acceptable voltage profile level of 5 % tolerance of rated voltage value, that is, (0.95 PU, 313.5 KV) < V

< (1.05 PU, 346.5 KV), with reduced transmission line congestion.

Keywords 86-bus 330 kV Nigeria power grid, voltage stability analysis, reserved energy resources, installed power generation capacity, voltage stability indices.component; formatting; style; styling; insert (key words)

  1. INTRODUCTION

    The existing Nigeria power network which comprises 5,988Km grid transmission lines (330 KV) is facing with the following problems: inability to effectively dispatch generated energy to meet the load demand; large number of uncompleted transmission line projects, reinforcement expansion projects in the power industry; poor voltage profile at the bus; inability of the existing transmission lines to wheel more than 4000 MW of power at present operational

    problems, voltage and frequency controls [1-5]. The grid system in Nigeria is almost radial single circuit lines, fragile and very long transmission line. Many of these lines experience total or partial system collapse when subjected to major disturbance and this makes voltage control difficult. Other problems include: poor network configuration in some regional work centres; ineffective control of the transmission line parameters; large numbers of overloaded transformers in the grid systems; the use of transmission lines beyond their thermal limits and frequent vandalism of 330KV transmission lines in various parts of the country [6,7]. Transmission-line voltage decreases when heavily loaded and increases when lightly loaded. This is line loadability. The line-loading limits are the thermal limits, the voltage-drop limit, and the steady- state stability limit. The existing power network must be transformed and expanded from radial to ring because of the high power losses associated with it and this help to maintain acceptable or allowable voltage violation drop of 5 % of nominal value in the system.

    Nigeria has sufficient reserved energy resources of coal, natural gas and new discovered hydro potentials that can serve as an input to all economic activities. Reserved energy resources of coal, natural gas and new discovered hydro potentials are the energy producing installations basket that contains power plants fired by fossil fuels (coal and natural gas) and hydro potentials[8,9]. The proven reserved coal in Nigeria is about 445 millions tones, consisting approximately of 81.05 % sub-bituminous, 4.81 % bituminous and 14.14 % lignite coals. The estimated reserved coal in Nigeria is about 2,559 million tonnes, consisting approximately of 42.32 % sub-bituminous, 45.17 % bituminous and 12.51 % lignite coals. The reserved proven coal and estimated coal can contribute 1,964 MW and 12,082 MW respectively to the grid system at 60 % capacity utilization for over 100 years. The total reserved proven natural gas in Nigeria are 4 trillion cubic meters (or 142 trillion standard cubic feet) and 5.4 trillion cubic meters (or 189 trillion standard feet) respectively. The reserved proven natural gas and estimated natural gas can contribute 29,505 MW and 39,270 MW respectively to the grid system at a capacity of 60 % for 100 years. The new discovered hydro potentials and the existing electricity generation capacity in Nigeria are about 12,525 MW and 12,682 MW respectively. The reserved estimated energy resources of coal, natural gas and new hydro potentials can contribute a total of 63,876.96 MW to the grid system, and when added to the existing installed capacity of 12,682 MW will give a total of 76,558.96 MW. Only 60.4 %

    (46,207 MW) of 76,558.96 MW is utilized in the current generation and transmission capacities expansion that gives expanded 86-bus network with the reserved energy resources.

    The continuation power-flow (CPF) techniques are used to investigate the voltage stability analysis of reserved power potential injected Nigeria power network. The continuation power-flow network is formulated, and then implemented using MATLAB SIMULINK Power System Analysis (PSAT) program. The purpose of the continuation power- flow is to find a continuum of power-flow solution for any change in load. The general principle behind the continuation power-flow is simple. It employs a predictor corrector scheme to find a solution path of a set of power-flow equations that have been reformulated to include a load parameter. It starts from a known solution corresponding to a different value of the load parameter. This estimate is then corrected using the same Newton Raphson technique employed by a conventional power flow. The local parameterization provides a means of identifying each point along the solution path and plays an integral path in avoiding singularity in the Jacobian [10-12].

    The solution power-voltage (P-V) curve is an important element in voltage stability analysis, which can be computed by continuation power flow method. The continuation power flow method is powerful and useful tool for obtaining solution power-voltage (P-V) curves for general non-linear algebraic equation by automatically changing the value of a parameter. These solutions power-voltage (P-V) curves are used to find the knee or critical point of voltage stability limit of a certain bus, which is at the nose of the curve. Voltage tability limit is the maximum loading point (MLP), which is computed by the continuation power flow method.

    Power Generation and Load Projection Capacities

    Power supply is either a source of generation or transformation from which the power is available to meet the load demand in megawatts. Presently, the total installed and on – going generating capacities in Nigeria is 12,682 MW whilst the available capacity is 3,863.5 MW or 31 %.This low average availability of the power plant is due to faulty generators, lack of machine maintenance and generally aging generators in the old power plants e.g. Kainji hydro power plant which was commissioned in 1968.

    There are a number of government owned and independent power plant projects under way to expand the generation and consequently the grid. The available installed capacities of existing and ongoing Nigerian power plants are estimated at 12,682 MW. This means that even with new plants and transmission lines being added, there may still be inefficient generation and transmission capacities due to demand increase.

    The word load is used to represent the present power consumption in the system and demand is used to represent the actual power need and future power consumption of the country. Load demand arises from the sudden load growth from industrial, commercial or residential development. The total load demand allocation for Nigeria power network estimation based on the total available generation capacity is about 3,152.31 MW with the total peak load demand of 3,927.5 7MW. The load allocation capacity in Nigeria is

    regional, comprising eight transmission regions of Lagos, Enugu, Osogbo, Port-Harcourt, Kaduna, Shiroro, Bauchi and Benin.

    Since this load allocation is regional, there was a need to adopt it to the network such that regions are associated with nodes. Table 1 shows the load nodal distribution for the demand forecast for years 2015, 2020 and 2025 with total load capacity of 3,603.47 MW. The total projected load capacities for 2015, 2020 and 2025 years are 13,157 MW, 18,280MW and 31,684 MW respectively, as shown in Table 1.

    Table 1 Nigeria power network 330KV voltage level load projection.

    Station

    Current Load (MW)

    %

    total load

    2015

    2020

    2025

    B.kebbi

    124.40

    3.45

    454.21

    631.07

    1093.80

    Jebba T.S

    7.47

    0.21

    27.27

    37.89

    65.68

    Osogbo

    129.77

    3.60

    473.82

    658.31

    1141.02

    Ayede

    190.43

    5.28

    695.30

    966.03

    1674.38

    Sakete

    140.43

    3.89

    511.17

    710.20

    1230.97

    Ikeja west

    230.78

    6.40

    842.62

    1170.72

    2029.16

    Akangba

    247.62

    6.87

    904.11

    1256.15

    2177.23

    Aja

    200.00

    5.55

    730.24

    1014.58

    1758.53

    Egbin

    200.00

    5.55

    730.24

    1014.58

    1758.53

    Ganmo

    42.83

    1.19

    156.38

    217.27

    376.59

    Kaduna

    203.71

    5.65

    743.79

    1033.40

    1791.15

    Shiroro

    73.39

    2.04

    267.96

    372.30

    645.29

    Katampe

    280.00

    7.77

    1022.34

    1420.41

    2461.94

    Jos

    82.59

    2.29

    301.55

    418.97

    726.18

    Kano

    292.66

    8.12

    1068.56

    1484.63

    2573.25

    Benin

    173.08

    4.80

    631.95

    878.02

    1521.83

    Ajaokuta

    68.16

    1.89

    248.87

    345.77

    599.31

    Gombe

    74.81

    2.08

    273.15

    379.50

    657.78

    New Heaven

    113.05

    3.14

    394.76

    573.49

    994.01

    Onitsha

    130.51

    3.62

    476.52

    662.06

    1147.53

    Aalaoji

    219.79

    6.10

    802.50

    1114.97

    1932.53

    Eket

    50.50

    1.40

    184.39

    256.18

    444.03

    Yola

    26.29

    0.73

    95.99

    481.57

    834.68

    Maiduguri

    14.70

    0.41

    53.67

    133.37

    231.16

    Port Harcourt

    286.93

    7.96

    1,065.64

    1,048.56

    1,817.44

    TOTAL (MW)

    3,603.47

    100.00

    13,157.00

    18,280.00

    31,684.00

  2. MATERIALS AND METHODS

    The work presented the overview analysis of the procedures taken for the conversion of reserved energy resources of coal, natural gas and large hydro potential into its equivalent electric power resource, evaluation of the reserved-based electric power resource, incorporation of the reserved-base electric power resource into existing installed power generating capacity and voltage stability simulation of the reserved-based electric power generating capacity model to enhance the totality of Nigeria power network stability.

    Overview Analysis of the Procedures Taken for Conversion of Reserved Resource of Coal, Natural Gas and Large Hydro Potential

    1. Coal Reserved Resource: Nigeria has a total proven coal energy reserve of 445 million tonnes comprising of sub-bituminous 361 million tonnes (81.05 %), bituminous

      21.42 million tonnes (4.81 %) and lignite 63 million tonnes (14.14 %), and a total estimated coal energy reserve of 2,559 million toes comprising of sub-bituminous 1,083 million tonnes (42.32 %), bituminous 1,156 million tonnes (45.17 %) and lignite 320 million tonnes (12.51%).

      The proven coal reserves of 445 million tonnes, located in various states Nigeria are expected to contribute a total computed equivalent electrical power value of 1,964 MW to the national grid system at 60% capacity utilization for over 100 years with the highest and lowest values of 757.24 MW and 113.95 MW recorded by Kogi state and Nassarawa state respectively as shown in Figure 1.

      Figure 1 Proven coal reserves in Nigeria and the computed values of electrical energy potentials.

      The estimated coal reserves of 2,559 million tonnes occurring in various states of Nigeria are expected to contribute a total computed equivalent electrical power value of 12,082 MW to the national grid system at 60 % capacity utilization for over 100 years with the highest and lowest values of 5,319.97 MW and 87.33 MW coming from Enugu state and Anambara state respectively as shown in Figure 2.

      Figure 2Estimate coal reserves in Nigeria and computed values of electrical energy potentials.

    2. Natural gas energy reserves: Nigeria has a total proven and estimated natural gas reserves of 4 trillion cubic meters (or 142 trillion standard cubic feet) and 5.4 trillion cubic meters (or 189 trillion standard cubic feet) respectively. The proven natural gas reserve would support 29,505 MW equivalent electrical capacity power plants operating at a

      capacity factor of 60 % for 100 years with River state and Imo or Abia state presenting the maximum and minimum values as shown in Figure 3.

      Figure 3 Proven gas reserves in Nigeria and computed values of electrical energy potentials.

      The estimated natural gas reserve would contribute a sum total of 39,270 MW equivalent electrical capacity power plants operating at a capacity factor of 60 % for 100 years with the highest and lowest values of 9,425 MW and 1,178 MW coming from River state and Abia state respectively as shown in Figure 4.

      Figure 4 Proven gas reserves in Nigeria and computed values of electrical energy potentials.

    3. Energy Reserves Resources Comparison: A total computed generation capacity value of 43,994.20MW is obtained by comparing the proven fuel reserves of coal, natural gas and large new discovered hydro potentials as shown in Figure 5.

    Figure 5 Comparison of electricity generation by proven fuel reserve.

    A total computed generation capacity value of 63,876.96 MW is obtained by comparing the estimated fuel reserves of coal (12,081.96 MW), natural gas (39,270 MW) and new large discovered hydro potential (12,525 MW)[13]. The existing and on-going electricity generation by coal (2,340 MW), natural gas (8,404 MW) and hydro (1,938 MW) would contribute a total of 12,682 MW to Nigeria grid system. Both the proven reserve capacity (43,994.20 MW), existing and on-going generation projects (12,682 MW) would offer a grand total of 56,676.20 MW to Nigeria grid system, whereas, the estimated reserve capacity (63,876.96 MW), existing and on-going generation projects (12,682 MW) would as well provide a grand total of 76,558.96 MW to Nigeria grid system.

    Evaluation and Deployment of Reserved-Based Electric Power Resource into Nigeria 28-bus Power Network

    The overall integrity of the existing Nigeria 28-bus power network in fast increasing population growth is continuously affected by acute shortages of electric power generation and transmission capacities. The existing Nigeria 28-bus power network has as built electrical generation and transmission capacities detail design parameters comprising 12,682 MW and 5,988 Km grid and transmission capacities, 28 buses or nodes, 10 electric power plants, 18 load (PQ) buses, 16 equal numbers of single and double lines and 4 loops as shown in Figure 6. The existing Nigeria 28-bus power network is reinforced and strengthened with additional 41 reserved electric power plants operating at 33,525 MW capacity, 5,723 Km new transmission capacities, 17 new load (PQ) buses, 58 new buses, 3 new loops, 18 new single lines and 42 new double lines as shown in Figure 7.

    The technical integrity of Nigeria power availability and evacuation capacities are restored by redesigning and redeveloping the 28-bus power network by deploying a grand total of 76,302.96 MW from the summation of the reserved estimated energy resources of coal(12,559×1010 tones or 12,081.96 MW), natural gas (5.32 trillion cubic meters or 189×1012 cubic feet or 39,270 MW, new discovered large hydro potentials(12,525 MW) and existing installed

    capacity(12,682MW) into the 28-bus test Nigeria power network to form improve and modernized reserved 86-bus electric power network.

    The improved and modernized 86-bus reserved- based electric power network is characterized with the sound electrical generation and transmission capacities detailed design parameters comprising 86buses or nodes, 46,207 MW and 11,711 Km grid and transmission capacities,35 load (PQ) buses,7 loops, 34 single lines and 58 double lines as shown in Figure 7.

    The process of modernization of the present Nigeria 28-bus power network with reserved energy sources would productively bring increase in industrial goods, agricultural products and quality life improvement of ever growing Nigeria population, which measure the annual per capita energy consumption from the energy availability and supply. Several numbers of coal-fired generating plants from the reserved energy sources are added into the present Nigeria 28-bus power network by looking at design technical features of new improved coal technology such as calorific value, weatherability, sulphur content, ash content, particle size, grindability index and caking quality.

    High firing temperatures, advanced cooling systems, advanced materials to withstand higher temperatures and more efficient compressors with transonic blades are design technical considerations for deploying natural gas from reserved energy sources for modernisation and improvement of 28-bus power network.

    Energy generation cost, capital cost of generators, capital cost of erecting and maintaining the transmission lines, and annual energy loss in transformation and transmission of electric power are considered for adding new hydro power generating plant from the reserved energy sources into 28-bus power network.

    Figure 6 The existing 28 bus 330KV Nigerian transmission grid [13].

    Where Ps, Qs are specified active and reactive powers of buses, and V are bus voltage angles and magnitudes respectively.

    Equation (1) can be expressed as,

    The reformulated power-flow equations, with provision for increasing generation as the load is increased, is expressed as,

    or

    (3)

    is the loading parameter. Equation (3) is set of nonlinear equations, which are solved by specifying a value of such that Where

    Figure 7 The improved and modernised 86-bus electric power network with the reserved energy resources [13].

    represents the critical load. Equation (3) is rearranged as,

    (4)

    The Continuation Power-Flow Analysis

    The continuation methods are developed, formulated and implemented in assessing the voltage stability analysis of the improved and modernised reserved 86-bus electric power network in order to justify its viability and utilization in Nigeria power industry.

    The Jacobian matrix of the conventional power-flow algorithms becomes singular at the voltage limit. These conventional power-flow algorithms are prone to convergence problems at operating conditions near the stability limit. The continuation power-flow analysis overcomes this problem by reformulating the power-flow equations so that they remain well-conditioned at all possible loading conditions. This allows the solution of the power- flow problem for stable (upper) and unstable (lower) portions (equilibrium points) of the P-V curves.

    The continuation power-flow method uses a locally- parameterized continuation method for solving nonlinear algebraic equations known as path-following methods [14 – 17].

    The continuation power-flow analysis uses an iterative process involving predictor and corrector steps. From a known initial solution, a tangent predictor is used to estimate the solution path for a specified pattern of load increase. The corrector step then determines the exact solution path using a conventional power-flow analysis with the system load assumed to be fixed. The voltages for a further increase in load are then predicted based on a new tangent predictor. If the new estimated load is now beyond the maximum load on the exact solution path, a corrector step with loads fixed would not converge; therefore, a corrector step with a fixed voltage at the monitored bus is applied to find the exact solution. As the voltage stability limit is reached, to determine the exact maximum load, the size of load increase is reduced gradually during the successive predictor steps.

    Mathematical formulation of a continuation algorithm:

    Powerflow equations can be represented as

    (1a)

    (1b)

    The computational procedures involved in continuation power-flow methods consist of predictor and corrector steps, as explained as follows:

    Predictor Step: In the predictor step, a linear approximation is used to estimate the next solution for a change in one of the state variables (i.e., , V, or ). Taking the partial derivatives of both sides of equation (4), with respect to the state variables (i.e., , V, or ) corresponding to the initial solution, will result in the following set of linear equations:

    Hence,

    (5a)

    Or,

    (5b)

    Or,

    (5c)

    Now,

    (6)

    is the solution of equation (4).

    Using the above in equation (5) and writing in matrix form, gives

    (7a)

    Or,

    (7b)

    Or,

    (7c)

    This can be written as,

    Or,

    (8a)

    Or,

    Or,

    Where:

    (8b)

    one equation that specifies the state variable selected as the continuation parameter. Thus, the new set of equation is

    J is the Jacobian matrix.

    is the tangent vector being sought.

    (12)

    is the partial derivative of F with respect to , V, .

    Near the point of voltage collapse, the Jacobian matrix, J approaches singularity; hence it is difficult to calculate J-1 near the collapse point. To overcome this problem, one more equation is added, assuming one of the variables as fixed. This problem is solved by setting one of the components of tangent vector, say d as ±1, depending on who the solution curve changes. When the tangent vector, d is equal to +1, the solution curve increases and when d is equal to -1, the solution curve decreases. This fixed variable is called the continuation variable. Assuming that the ith variable is the continuation variable, one can write,

    (9a)

    Or,

    (9b)

    is the vector having ith element as one and all other elements as zero.

    Rewriting equation (11), gives

    (10a)

    (10b)

    The difference vector is found from equation (10) and added with the initial assumption of vector to get the predictor. That is, the predicted value is computed by:

    (11a)

    Or,

    (11b)

    Where h is a scalar quantity representing the step size. In this study, the step size, h is assigned a constant value of 0.001. Hence, the procedures involved in predictor step are summarized as follows: specifying the step size h; finding the partial derivatives of F(, V, ) with respect to , V and respectively; using the step size h and partial derivatives to find the next point or predicted value (, V, ).

    Corrector step:In the corrector step, the original set of equations of F(, V, ) = augmented by

    is the assumed fixed/predicted value of the continuation variable, and Xi is the state variable chosen as continuation parameter.

    Thus, the system equations become,

    F(, V, ) = 0 and,

    (13a)

    (13b)

    Or,

    (13c)

    In the above, Xi is the state variable selected as the continuation parameter is the assumed fixed/predicted value of the continuation variable(Xi). This set of equations can be solved using a slightly modified Newton-Raphson power-flow method. The introduction of the additional equation specifying Xi makes the Jacobian non-singular at critical point and allows the computation of power flow solutions even beyond the critical point, i.e., in the lower portion of the P-V curve.

    The tangent component of positive for the upper portion of P-V curve, is zero at the critical point, and is negative beyond the critical point. Thus, the sign of the tangent component of will indicate whether or not the critical point has been reached. If the continuation parameter is the load increase, the corrector will be a vertical line on the P-V plane. If, on the other hand, a voltage magnitude is the continuation parameter, the corrector will be a horizontal line on the plane.

    Continuation power-flow allows the load voltage to be computed even when the power flow Jacobian matrix is singular. The complete P V curve, including the critical (knee) point and the lower part of the curve, can be drawn using continuation power-flow. The complete P V curves of the network are drawn using the MATLAB SIMULINK Power System Analysis Toolbox (PSAT) that uses continuation power flow.

    Selecting the continuation parameter: The best method of selecting the correct continuation parameter at each step is to select the state variable with the largest tangent vector component. The selected state variable must have the evidence of producing the maximum rate of change near a given solution.

    Application of Continuation Power-Flow Method to Investigate the Voltage Stability of Modernised reserved 86-Bus Electric Power Network

    The improved and modernised Nigeria reserved 330 KV transmission grid has 86 nodes, 51 generators, 35 load (PQ) buses, 67 transformers, 42,207 MW and 11,711Km grid and transmission capacities, 34 and 58 numbers of single and double lines and 7 numbers of loops as shown in Figure 7.

    The total loads on the modernised power network are 4,795.02 MW and 3,596.25 Mvar respectively. The buses are numbered so that bus no.1 becomes slack bus whereas, buses no.2 to 51 and buses 52 to 86 are PV and PQ (load) buses respectively. The designed MATLAB SIMULINK model for investigating voltage stability of improved and modernised Nigeria reserved 330kV 86-bus electric power network via continuation power flow method is shown in figure 8. The new electric power network is designed using electrical blocks contained in the SIMULINK library. The main components of electrical power system: generators, transformers, transmissions lines and loads blocks are used as the interface between the two buses as shown in Figure 8.

    The results obtained if favourable would prove its viability and utilization in Nigeria power industry. The input data for power/load flow analysis and CPF method is presented in Table 2. The continuation power flow method uses the conventional Newton Raphson method at the base case where =0=0 to compute the base power load data. Continuation power flow process is applied to 86 bus network system with reserved energy resources. Jacobian of the first load flow (Newton Raphson) is used in the predictor step to predict state variables for the next loading factor (LF or ). At the next loading factor (LF) and predicted state variables, the corrected state variables can be found in the corrector step. When the load flow solution is diverged, parametization step is activated at the last converged loading factor (LF). The complete system data is introduced in MATLAB code along with the generation and load profiles. The continuation power flow is run until the critical point is reached, that is when the maximum loading point/collapse point reaches, the continuation power flow will stop.

    voltage profiles of the system are presented in figures 9 to 10 respectively.

    Under normal operating conditions, the weakest bus is bus52 (Damaturu TS bus) with voltage profiles of 0.7946 pu (262.22 KV). Other weak buses include bus51 (Eboyi PS) and bus48 (Kasimbila hydro PS) with voltage profiles of 0.8323 pu (274.66 KV) and 0.8386pu (274.84 KV) as shown in Table 3 and Figure 9 respectively.

    Table 3 shows individual bus voltages, bus phase angles, and total maximum active power load and total reactive power load of the modernised reserved 86-bus electric power network computed under normal operating conditions as 15.983 pu (4,795.02 MW) and 11.9875 pu

    (3,596.25 Mvar) respectively.

    Figure 9(a) shows variation of bus voltage with increasing load factor, on the modernised reserved 86-bus electric power network under normal operating conditions. From the P V curve of Figure 9(a), maximum loadability point/ collapse point, of the bus system is 1.1753 pu (352.59 MW). It means that the maximum power expected for the modernised reserved 86-bus electric power network to be loaded under base load point/normal operatingconditions is 1.1753 pu (352.59 MW). The base load point is taken as 1pu = 300 MW = 300 Mvar. After that, the whole system might collapse at any time. At collapse point, only slack generator supplies the reactive power. Majority of the critical bus voltages of the modernised network fall within the acceptable voltage profiles range or voltage stability indices of ±5 % tolerance of the rated value, that is, 0.95 pu (313.5 KV) to 1.05 pu (346.5 KV) as shown in Table 3 and Figure 9 respectively. It means that the modernised reserved 86-bus electric power network is a stable network due to availability of adequate power generation and transmission capacities.

    The simulations of a large disturbance, a 3-phase fault

    Bus52

    Bus55

    Bus48

    Bus45

    Bus46

    Bus47

    Bus57

    at all generator buses and all lines are performed on the

    Bus39

    Bus53

    Bus64

    Bus56

    Bus1

    modernised reserved 86-bus electric power network using

    Bus38

    Bus54

    Bus40

    Bus41

    Bus43

    Bus42

    Bus58

    Bus44

    Bus59

    continuation power-flow method. The continuation power- flow results after the 3-phase faults simulations of generator

    Bus37

    Bus61

    Bus62

    Bus51

    Bus27

    Bus28

    bus 2 and line 2 – 83 of the modernised reserved 86-bus electric power network are shown in Tables 4 To 7,

    Bus60

    Bus63

    Bus34 Bus49

    Bus50

    Bus36

    respectively and the corresponding voltage violation results,

    Bus30

    Bus67

    Bus32

    Bus33

    Bus35

    Bus68

    Bus69

    Bus24

    Bus25

    Bus22

    Bus26

    P V curves and voltage profiles of the system are shown in

    figure 10 (a) and (b) , respectively.

    Bus31

    Bus29

    Bus66

    Bus12 Bus65

    Bus5

    Bus7

    Bus72

    Bus73

    Bus23 Bus21

    Bus20

    Bus70

    Bus14

    Bus15

    Bus16

    When a 3-phase fault occurred at generator bus 2, the continuation power-flow result, power-voltage (P V) graph

    Bus71

    Bus3

    Bus75

    Bus78

    Bus17

    and voltage profiles are shown in Table 4 and Figures 10

    Bus77

    Bus13

    Bus79

    respectively. The maximum loading point () / collapse point

    Bus74

    Bus6

    Bus4

    Bus76

    Bus11

    Bus82

    Bus83

    Bus2

    Bus85

    Bus86

    Bus19 Bus18

    increases from 1.1753 pu (352.59 MW) to 1.2166 pu (364.98 MW), indicating an improvement in the system voltage

    Bus8

    Bus9

    stability index/margin. Also, the overall/ total maximum

    Bus80

    Bus81

    Bus10

    Bus84

    active power load (P

    load

    ) increases from 15.9834 pu

    Fig 8: Designed MATLAB/SIMULINK circuit model for investigating voltage stability of improved and modernised reserved 330kV 86-bus electric power network via continuation power flow method.

  3. RESULTS AND DISCUSSION

The continuation power-flow result of the improved and modernised reserved 86 bus electric power network under normal operating conditions is shown in table 3 and the corresponding voltage violation result, P V curve and

(14,795.02 MW) to 16.5462 pu (4,963.86 MW), thus

indicating an improvement in the voltage stability margin for the system. Voltage stability results analysis of the modernised reserved 86-bus electric power network after3- phase fault at different generator buses are summarised in Table 5.

When a 3-phase fault occurred at line 2 83, the continuation power flow result is presented in table 6 and the voltage violation result, corresponding P V graph and

voltage profiles are shown in Figures 11 (a) and (b) respectively. The maximum loadability point recorded for a 3-phase fault occurred at line 2-83 is 1.1753 pu (352.59 MW). Voltage stability results analysis of the modernised reserved 86-bus electric power network after 3-phase fault at different transmission lines are summarised in Table 7.

These continuation power-flow results of the modernised reserved 86-bus electric power network recorded under normal operating conditions and after 3-phase faults at all generator buses and all lines indicated better voltage profile, better power quality, huge generation capacity and adequate power evacuation corridor.

1.3

1.2

1.1

V(p.u)

V(p.u)

1

0.9

0.8

0.7

0 0.2 0.4 0.6 0.8 1

Loading Parameter (p.u.)

(a)

(a)

(b)

Figure 10 Represents (a) P V curve of the modernised 86 bus network after 3-phase fault at generator bus 2, (b) Voltage profiles of the modernised 86 bus network after 3-phase fault at generator bus 2

1.3

1.2

1.1

V(p.u)

V(p.u)

1

0.9

(b)

Figure 9 Represents (a) P V curve of the modernised 86 bus network under normal operating conditions, (b) Voltage profiles of the modernised 86 bus network under normal operating conditions

0.8

0.7

0 0.2 0.4 0.6 0.8 1

Loading Parameter (p.u.)

(a)

lines loss by the same power network. The improved and modernised Nigeria reserved 86-bus electric power network presented an appreciable reduction in transmission line congestion, maintaining grid voltage stability and effective interconnectivity due to sufficient transmission and generation capacities.

REFERENCES

(b)

Figure 11 Represents (a) P V curve of the modernised 86 bus network after 3-phase fault at line 2-83, (b) Voltage profiles of the modernised 86 bus network after 3-phase fault at line 2-83

After a 3-phase fault at generator bus 2, the weakest bus is bus 52 (Damaturu TS bus) with voltage profiles of 0.8051 pu (265.68 KV). Other weak buses include bus43 (Kastina Ala1 hydro PS bus) and bus48 (Kasimbila hydro PS bus) with voltage profiles of 0.83067 pu (274.12 KV) and 0.86809 pu (286.47 KV) as shown in table 4 and Figure 11 (a) and (b) respectively.

The modernised reserved 86-bus electric power network recorded low and high voltage violations ranges of 5 % tolerance of rated 1pu (330 KV), that is, 0.95pu (313.5 KV) to 1.05pu (346.5 KV) at different lines loss as follows: a total number of 8 voltage violations at the base case and on 48-56 line; 9 voltage violations on 25 lines and 10 voltage violations on 31 lines, as summarized in Table 7.

Tables 2 to 7 containing both Bus Data and Line Data of the networks used as input for the Simulation can be seen in the Appendix.

IV CONCLUSIONS

The improved and modernised Nigeria reserved 86-bus electric power network solved the voltage instability problems by providing adequate and sufficient generation and transmission line capacities. The voltage stability investigation resuls of the modernised reserved330 kV 86- bus electric power network recorded under normal operating conditions and after 3-phase faults showed that majority of bus voltage profiles and line loadability limits of this network met the acceptable range of ±5 % tolerance of rated value due to sufficient power generation and transmission capacities of 42,207 MW and 11,711 Km. This network accepts more loading and still retains its voltage stability limit to a very large extend. Majority of bus voltages of the modernised reserved 86-bus electric power network recorded a total number of 9 low and high voltage violations of 5 % tolerance of rated 1pu (330KV), that is, 0.95pu (313.5 KV) to

1.05 pu (346.5 KV) at different generators loss contingencies. Whereas, a total number of 8 voltage violations at the base case and on 48-56 line, 9 voltage violations on 25 lines and 10 voltage violations on 31 lines are recorded at different

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  3. Nigeria Vision 2020 Program, Analysis for Power Generation capacity required to support 20; 2020 Economic vision, Report of the Energy Sector National Technical working Group.

  4. AS Sambo, B Garba, IH Zarma and MM Gaji. Electricity Generation and the Present Challenges in the Nigerian Power Sector, Energy Commission of Nigeria, Abuja, Nigeria, 2011.

  5. AS Sambo. Paper presented at the National Workshop on the Participation of State Government in The Power Sector: Matching Supply with Demand.

  6. Energy Profile of Nigeria, Available at: http://www.eoearth.org/article/energy profile of Nigeria published October 11, 2009.

  7. AO Cole. Restructuring the Electric Power Utility Industry in Nigeria, Proc:, 20th National Conference of the Nigerian Society of Engineers (Electrical Division), pp. 1-6 October 6-7, 2004..

  8. MMSD Coal Exploration and Power Generating Opportunities in Nigeria, the Ministry of Mines and Steel Development, Nigeria, 2010.

    , Available at: http://mmsd.gov.ng/downloads/coal.pdf.

  9. United State Development of Energy, Coal Our Most Abundant Fuel, 2011.

  10. CR Werner and VBA John. locally Parameterized Continuation Process, ACM Trans. On Mathematical Software, Vol. 9, no 2, PP. 215-235, 1983.

  11. MZ Laton, I Musirin, and TK Abdul Rahman. Voltage Stability Assessment Via Continuation Power Flow Method, International Journal of Electrical and Electronic Systems Research, Vol. 1, PP 71- 78, June 2008.

  12. HA Al-Awami. Power Flow Control to Determine Voltage Stability Limit by using the Continuation Method, EE 550, 062 Term Paper, Dept. Of Electrical Engineering, KFUPM, 2012.

  13. IO Akwukwaegbu, ENC Okafor, FI Izuegbunam and MC Ndinechi. Evaluation of the Reserved Energy Resource for Nigeria Power Generation and Transmission Capacities Improvement, International Journal of Research in Engineering and Technology, vol.5, Issue 5, pp.136-145, 2016.

  14. P Kundur. Power System Stability and Control, McGraw-Hill, pp.1012-1024, 1994.

  15. R Seydel. From Equilibrium to Chaos, Elsevier, New York, 1988.

  16. Rheinboldt, W. C., Numerical Analysis of Parameterized Nonlinear Equations, John Wiley and Sons, New York, 1986.

  17. IO Akwukwaegbu, ENC Okafor, FI Izuegbunam and MC Ndinechi. Voltage Stability Assessment of 330kV Nigeria Power System Using Continuation Power-flow Techniques, International Journal of Engineering Research and Management, vol. 3, Issue 6, pp. 222-233.

NAMES OF 5-9 REFEREES

  1. Dr. James Onojo., Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri., Nigeria., jamesonojo@yahoo.com

  2. Dr. Lazarus Uzoechi., Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri., Nigeria., lazarus.uzoechi@futo.edu.ng

  3. Prof. Damian Dike., Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri., Nigeria., damian.dike@futo.edu.ng

  4. Prof. E.N.C. Okafor., Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri., Nigeria., encokafor2000@yahoo.com

  5. Dr. Matthew Olubiwe., Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri., Nigeria., olubiwe.mathew@futo.edu.ng

  6. Dr. Nkwachukwu Chukwuchekwa., Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri., Nigeria., nkwachukwu.chukwuchekwa @futo.edu.ng

APPENDIX

Table 2 The modernised Nigerian reserved 330kV 86-bus transmission grid line data on a base of 100MVA.

td>

1

S/N

Lines Between buses

Bus No.

Length H(KM)

Circuit Type

Line Impendence (PU)

Tap Ratio

From

To

from

To

R(PU)

X(PU)

B/2(PU)

1

Mambilla

Jalingo

1

56

80

DC

0.0048

0.00373

0.99624

1

2

Egbin

Ikeja West

2

83

62

DC

0.0004

0.0029

0.771

1

3

Egbin

Eruka

2

84

42

SC

0.0004

0.00304

0.171

1

4

Egbin

Aja

2

85

16

DC

0.0007

0.0057

0.3855

1

5

Kainji

Birnin Kebbi

3

71

310

SC

0.004151

0.03041

1.8135

1

6

Kainji

Jebba TS

3

75

81

DC

0.000097

0.0082

0.924

1

7

Jebba GS

Jebba TS

4

75

8

DC

0.0001

0.0004

0.096

1

8

Shiroro

Katampe

5

60

144

DC

0.0009

0.0067

1.7933

1

9

Shiroro

Jebba TS

5

75

244

DC

0.0022

0.0234

1.3904

1

10

Shiroro

Kaduna

5

67

96

SC/SC

0.0011

0.0097

0.546

1

11

Zungeru

Jebba TS

6

75

90

DC

0.0054

0.0042

1.12077

1

12

Geregu

Ajaokuta

7

72

5

DC

0.00001

0.0005

0.057

13

Kwara Coal

Ilorin

8

76

30

DC

0.0018

0.0014

0.37359

1

14

Omotosho

Benin

9

73

120

SC

0.0014

0.0122

0.6841

1

15

Omotosho

Ikeja West

9

83

160

SC

0.0019

0.0162

0.9122

1

16

Papalanto

Aiyede

10

81

60

SC

0.0007

0.0061

0.3421

1

17

Papalanto

Ikeja West

10

83

30

SC

0.0004

0.003

0.171

1

18

Ondo Coal

Oshogbo

11

77

50

DC

0.003

0.002334

0.62265

1

19

Danko

Birnin Kebbi

12

71

18

DC

0.00108

0.00084

0.224154

1

20

Sapele

Benin

13

73

50

DC

0.0002

0.0015

0.936

1

21

Sapele

Aladja

13

79

63

SC

0.0008

0.0063

0.3585

1

22

Delta Coal

Delta PS

14

15

18

DC

0.00108

0.00084

0.224154

1

23

Delta PS

Gbarian

15

16

50

DC

0.003

0.002334

0.62265

1

24

Delta PS

Delta (gas)

15

19

18

DC

0.00108

0.00084

0.224154

1

25

Delta PS

Benin

15

73

107

SC

0.0008

0.0063

0.3585

1

26

Delta PS

Aladja

15

79

32

SC

0.0008

0.0063

0.3585

1

27

Delta PS

Aja

15

85

275

SC

0.0036

0.0269

1.6089

1

28

Gbarian

Rain/Ube

16

17

18

DC

0.00108

0.0084

0.224154

1

29

Gbarian

Omoku

16

22

60

DC

0.0036

0.0028

0.74718

1

30

Rain/Ube

Bayelsa (gas)

17

18

14

DC

0.00084

0.000653

0.17434

1

31

Egbema (gas)

Benin

20

73

18

DC

0.00108

0.00084

0.224154

1

32

Edo (gas)

Benin

21

73

18

DC

0.00108

0.00084

0.224154

1

33

Omoku

Edo

22

20

30

DC

0.0018

0.0014

0.37359

1

34

Okpai

Onitsha

23

68

80

DC

0.0002

0.0014

0.3736

1

35

Imo (gas)

Owerri

24

69

18

DC

0.0015

0.0012

0.312

1

36

Alaoji (hydro)

Aba

25

26

8

DC

0.0001

0.0004

0.096

1

37

Alaoji (hydro)

Onitsha

25

68

138

DC

0.00792

0.00616

1.6434

1

38

Alaoji (hydro)

Owerri

25

69

69

DC

0.0163

0.014

0.786

1

39

Afam (I V) gas

Rivers (gas)

27

28

18

DC

0.0004

0.0028

0.7472

1

40

Afam (I V) gas

Ikot Ekpene

27

57

90

DC

0.0054

0.0042

1.12077

1

41

Guarara (hydro)

Mabon (gas)

29

30

30

DC

0.0054

0.0042

1.1208

1

42

Mabon (gas)

Kaduna

30

67

18

DC

0.00108

0.00084

0.224154

1

43

Sarkin (hydro)

Kano

31

65

18

DC

0.00108

0.00084

0.224154

1

44

Lokoja (hydro)

Lokoja

32

63

20

DC

0.0012

0.000933

0.24906

1

45

Obajana (hydro)

Lokoja

33

63

23

DC

0.00138

0.001073

0.286419

1

46

Kogi (coal)

Lokoja

34

63

18

DC

0.00108

0.00084

0.224154

1

47

Onitsha2 (hydro)

Onitsha

35

68

10

DC

0.0006

0.000467

0.012453

1

48

Anambra (coal)

Onitsha

36

68

18

DC

0.00108

0.00084

0.224154

1

49

Plateau (hydro)

Jos

37

54

25

DC

0.0015

0.001167

0.311351

1

50

Bauchi (coal)

Jos

38

54

150

DC

0.009

0.007

1.86795

1

51

Gombe (coal)

Gombe

39

53

18

DC

0.00108

0.00084

0.224154

1

51

Bukuru (coal)

Jos

40

54

10

DC

0.0006

0.000467

0.012453

1

53

Plateau (coal)

Jos

41

54

18

DC

0.00108

0.00084

0.224154

1

54

Adamawa (coal)

Yola

42

64

18

DC

0.00108

0.00084

0.224154

1

55

Katsina Ala (hydro)

Makurdi

43

58

98

DC

0.00588

0.004574

1.220394

1

56

Benue (coal)

Makurdi

44

58

18

DC

0.00108

0.00084

0.224154

1

57

Ikom (hydro)

Calabar

45

46

25

DC

0.0015

0.001167

0.311351

1

58

Ibom (gas)

Ikot Ekpene

46

57

18

DC

0.00108

0.00084

0.224154

1

59

Kasimbela (hydro)

Jalingo

47

56

18

DC

0.00108

0.00084

0.224154

1

60

Katsina Ala2 (hydro)

Makurdi

49

58

100

DC

0.006

0.004667

1.2453

1

61

Enugu (coal)

New Heaven

50

59

18

DC

0.00108

0.00084

0.224154

1

62

Ebonyi (coal)

New Heaven

51

59

70

DC

0.0042

0.003267

0.87171

1

63

Damturu (coal)

Gombe

51

53

30

DC

0.0018

0.0014

0.37359

1

64

Dmaturu (coal)

Maiduguri

51

55

308

SC

0.0002

0.0029

0.1649

1

65

Gombe TS

Jos

53

54

265

SC

0.004

0.0302

1.8018

1

66

Jos

Gwagwa

54

61

180

SC

0.0032

0.027

1.515

1

67

Jos

Makurdi

54

58

230

DC

0.0013

0.0099

2.3517

1

68

Jalingo

Kasimbila (hydro)

56

48

150

DC

0.0017

0.0126

3.0069

1

69

Jalingo

Yola

56

64

132

SC

0.00792

0.00616

1.6434

1

70

Ikot Ekpene

New Heaven

57

59

143

DC

0.0016

0.0134

0.7515

1

71

Makurdi

Gwagwa

58

61

201

DC

0.0005

0.0033

3.5618

1

72

Makurdi

Aliade

58

62

50

DC

0.0014

0.0107

2.8644

1

73

New Heaven

Aliade

59

62

150

DC

0.0003

0.0023

0.6227

1

74

Katampe

Gwagwa

60

61

30

DC

0.0009

0.007

1.8681

1

75

Gwagwa

Lokoja

61

63

140

DC

0.0018

0.0014

0.3736

1

76

Kano

Zaria

65

66

147

SC

0.0008

0.0065

1.7435

1

77

Kano

Kaduna

65

67

81

SC

0.000097

0.0082

0.924

1

78

Zaria

Kaduna

66

67

81

SC

0.000097

0.0082

0.924

1

79

Onitsha

Owerri

68

69

137

DC

0.0019

0.0144

0.8307

1

80

Onitsha

Benin

68

73

137

SC

0.0008

0.0064

1.7062

1

81

Owerri

Egbema (gas)

69

20

30

DC

0.0016

0.0139

0.781

1

82

Birnin Kebbi

Sokoto

71

74

142

SC

0.0002

0.0014

0.3736

1

83

Ajaokuta

Benin

72

73

195

SC/SC

0.0019

0.0139

0.8307

1

84

Benin

Oshogbo

73

77

251

SC

0.0023

0.0198

0.748

1

85

Benin

Eyaen

73

78

5

DC

0.0003

0.0254

1.431

1

86

Jebba TS

Ilorin

75

76

84

SC

0.0001

0.0002

0.0623

1

87

Jebba TS

Oshogbo

75

77

157

SC/SC

0.0011

0.0083

0.4914

1

88

Ilorin

Oshogbo

76

77

90

SC

0.0019

0.00159

0.8955

1

89

Sakete

Ikeja West

80

83

70

SC

0.0012

0.0088

0.5165

1

90

Akangba

Ikeja West

82

83

18

SC/SC

0.00084

0.00709

0.3991

1

91

Aja

Alagbon

85

86

26

DC

0.0007

0.0057

0.3855

1

Table 3 Continuation power flow result of the modernised reserved 86-bus electric power network under normal operating conditions.

Bus No

V

[pu]

phase [rad]

P gen [pu]

Q gen [pu]

P load [pu]

Q load [pu]

Bus1

0.89653

0

-12.4627

3.359

0

0

Bus2

1.0012

0.99459

1.153

1.6714

0

0

Bus3

1.0011

0.98753

1.1529

-2.9634

0

0

Bus4

1.0015

0.97031

1.153

1.2907

0

0

Bus5

1.0009

1.0022

1.153

0.12667

0

0

Bus6

1.0009

1.0043

1.1529

-1.6757

0

0

Bus7

1.0009

1.004

1.1526

9.09

0

0

Bus8

1.0008

1.0071

1.1529

-1.4166

0

0

Bus9

1.0008

1.0077

1.1529

-1.9497

0

0

Bus10

1.0008

1.0079

1.1529

-1.3942

0

0

Bus11

1.0009

1.0043

1.1529

-1.6757

0

0

Bus12

1.0012

0.99479

1.1529

2.99

0

0

Bus13

1.0009

1.0022

1.1529

-2.0713

0

0

Bus14

1.0009

1.0022

1.1529

-2.0713

0

0

Bus15

1.0008

1.008

1.1529

-0.9887

0

0

Bus16

1.0007

1.0175

1.153

-0.19376

0

0

Bus17

1.0006

1.0183

1.1529

-1.6837

0

0

Bus18

1.0007

1.0174

0

0

1.1564

0.86732

Bus19

1.0007

1.0175

1.1529

-0.93657

0

0

Bus20

0.99761

0.96593

1.1529

-1.6801

0

0

Bus21

0.99765

0.96629

1.153

-0.19555

0

0

Bus22

0.99753

0.95597

1.1529

-1.5857

0

0

Bus23

1.0009

0.97423

1.153

0.1196

0

0

Bus24

0.99759

0.95452

1.153

0.73989

0

0

Bus25

0.99949

0.95132

1.1529

-1.3686

0

0

Bus26

0.98469

0.91792

1.1529

-1.1618

0

0

Bus27

0.98469

0.91797

1.1529

-1.1786

0

0

Bus28

0.98468

0.91789

1.1529

-1.1501

0

0

Bus29

1.0007

1.0175

1.1529

-1.4705

0

0

Bus30

1.0007

1.0176

1.1529

-1.6758

0

0

Bus31

0.94361

0.83243

1.1529

-0.36053

0

0

Bus32

0.94458

0.83448

1.1529

-1.436

0

0

Bus33

0.83664

0.46964

1.1532

4.5109

0

0

Bus34

1.0014

0.97424

1.1529

4.685

0

0

Bus35

0.94349

0.8322

1.153

1.4546

0

0

Bus36

0.94354

0.83231

1.153

0.11555

0

0

Bus37

0.97961

0.90231

1.1529

-1.8999

0

0

Bus38

0.8500

0.40231

1.1518

-10.8459

0

0

Bus39

0.97943

0.90104

1.1529

-3.431

0

0

Bus40

0.99776

0.9661

1.1529

-1.525

0

0

Bus41

0.99778

0.9657

1.153

1.208

0

0

Bus42

0.9977

0.9639

1.1529

1.8863

0

0

Bus43

0.85063

0.27351

1.1533

14.1567

0

0

Bus44

0.97962

0.90234

1.1529

-1.8863

0

0

Bus45

0.99675

0.95421

1.1529

-0.35171

0

0

Bus46

0.99477

0.9224

1.1529

-1.5871

0

0

Bus47

0.99452

0.92018

0

0

1.1564

0.86732

Bus48

0.83286

0.46937

0

0

1.1564

0.86732

Bus49

0.83424

0.47007

0

0

1.1564

0.86732

Bus50

0.94281

0.83223

0

0

1.1564

0.86732

Bus51

0.83231

0.46725

0

0

1.1564

0.86732

Bus52

0.7946

0.27454

0

0

1.1564

0.86732

Bus53

1.0004

0.96379

0

0

1.1564

0.86732

Bus54

1.0023

0.90053

0

0

0

0

Bus55

1.0019

0.92211

0

0

1.1564

0.86732

Bus56

1.0014

0.97541

1.1529

-1.1041

0

0

Bus57

1.0018

0.94757

0

0

1.1564

0.86732

Bus58

0.98225

0.91065

0

0

1.1564

0.86732

Bus59

0.99479

0.91655

0

0

1.1564

0.86732

Bus60

0.98461

0.91766

0

0

1.1564

0.86732

Bus61

0.85094

0.40094

0

0

1.1564

0.86732

Bus62

0.99957

0.95106

0

0

1.1564

0.86732

Bus63

1.003

0.9495

0

0

1.1564

0.86732

Bus64

0.99748

0.95422

0

0

1.1564

0.86732

Bus65

1.0007

1.0173

0

0

0

0

Bus66

1.0007

1.0178

0

0

0

0

Bus67

1.001

1.0019

1.153

0.24436

0

0

Bus68

1.0007

1.0081

0

0

1.1564

0.86732

Bus69

1.0012

0.97037

0

0

1.1564

0.86732

Bus70

1.001

1.0019

0

0

1.1564

0.86732

Bus71

1.001

1.0019

0

0

1.1564

0.86732

Bus72

1.0005

0.96937

0

0

1.1564

0.86732

Bus73

1.0012

0.97424

0

0

1.1564

0.86732

Bus74

0.99981

0.97511

0

0

1.1564

0.86732

Bus75

1.0015

0.98629

0

0

1.1564

0.86732

Bus76

1.002

0.98194

0

0

1.1564

0.86732

Bus77

1.0006

1.0028

0

0

1.1564

0.86732

Bus78

1.0014

0.97504

1.153

1.2332

0

0

Bus79

0.99719

0.98821

0

0

1.1564

0.86732

Bus80

1.0005

0.99389

0

0

1.1564

0.86732

Bus81

0.99759

0.98945

0

0

1.1564

0.86732

Bus82

1.0009

0.99462

0

0

1.1564

0.86732

Bus83

1.0009

0.99446

0

0

1.1564

0.86732

Bus84

1.0004

0.9953

0

0

1.1564

0.86732

Bus85

0.99761

0.99117

0

0

1.1564

0.86732

Bus86

1.001

0.99964

1.153

-0.04158

0

0

Total

18.1499

6.983

15.9834

11.9875

Table 4 Continuation power-flow result of modernised reserved 86-bus electric power network after 3-phase fault at generator bus 2.

Bus No

V

[pu]

phase [rad]

P gen [pu]

Q gen [pu]

P load [pu]

Q load [pu]

Bus1

0.78648

0

-5.1715

1.5681

0

0

Bus2

0.9916

1.6498

0.50621

1.4049

0

0

Bus3

0.99187

1.6438

0.50624

-0.77326

0

0

Bus4

0.98931

1.6248

0.50612

0.54199

0

0

Bus5

0.99357

1.6615

0.50613

0.1309

0

0

Bus6

0.99381

1.664

0.50618

-0.4892

0

0

Bus7

0.99375

1.6637

0.50689

3.2377

0

0

Bus8

0.99432

1.6671

0.50617

-0.40957

0

0

Bus9

0.99443

1.6677

0.50619

-0.5875

0

0

Bus10

0.99447

1.6679

0.50617

-0.40385

0

0

Bus11

0.99381

1.664

0.50618

-0.4892

0

0

Bus12

0.98997

1.65

0

0

0

0

Bus13

0.99359

1.6614

0.50619

-0.5796

0

0

Bus14

0.99359

1.6614

0.50619

-0.5796

0

0

Bus15

0.99448

1.6681

0.50615

-0.27448

0

0

Bus16

0.99539

1.6816

0.50613

-0.01669

0

0

Bus17

0.99551

1.6822

0.50617

-0.51181

0

0

Bus18

0.99539

1.6819

0

0

0.48665

0.36499

Bus19

0.99537

1.682

0.50615

-0.2625

0

0

Bus20

0.99266

1.6214

0.50618

-0.47863

0

0

Bus21

0.99274

1.6219

0.50613

0.01159

0

0

Bus22

0.9883

1.6054

0.50619

-0.39523

0

0

Bus23

0.98971

1.6295

0.50613

0.1441

0

0

Bus24

0.98795

1.604

0.50611

0.37412

0

0

Bus25

0.9878

1.6003

0.50618

-0.31726

0

0

Bus26

0.98267

1.5525

0.50617

-0.1996

0

0

Bus27

0.98269

1.5525

0.50618

-0.20439

0

0

Bus28

0.98266

1.5525

0.50617

-0.19634

0

0

Bus29

0.99539

1.6815

0.50617

-0.44032

0

0

Bus30

0.99542

1.6817

0.50617

-0.50871

0

0

Bus31

0.95989

1.4378

0.50611

0.27437

0

0

Bus32

0.96094

1.4391

0.50621

-0.05359

0

0

Bus33

0.87497

0.85828

0

0.50459

2.3524

0

Bus34

0.98956

1.6294

0.50621

1.5104

0

0

Bus35

0.95983

1.4377

0.50607

0.41098

0

0

Bus36

0.95977

1.4376

0.50597

0.80995

0

0

Bus37

0.87026

0.74092

0.50933

-1.7527

0

0

Bus38

0

0.9791

1.534

0.50623

-0.39972

0

Bus39

0.97866

1.5329

0.50639

-0.91253

0

0

Bus40

0.99272

1.6221

0.50617

-0.42794

0

0

Bus41

0.99264

1.6217

0.50613

0.47706

0

0

Bus42

0.99226

1.6193

0.50613

0.70537

0

0

Bus43

0.83067

0.56773

0.50188

5.1216

0

0

Bus44

0.97911

1.5341

0.50623

-0.39531

0

0

Bus45

0

0.9874

1.6036

0.50614

0.00471

0

Bus46

0.98379

1.5637

0.5062

-0.34485

0

0

Bus47

0.97847

1.5614

0

0

0.48665

0.36499

Bus48

0.86809

0.85846

0

0

0.48665

0.36499

Bus49

0.87407

0.85921

0

0

0.48665

0.36499

Bus50

0.95953

1.4377

0

0

0.48665

0.36499

Bus51

0.86562

0.85489

0

0

0.48665

0.36499

Bus52

0.36499

0.8051

0.56889

0

0

0.48665

Bus53

0.99152

1.6192

0

0

0.48665

0.36499

Bus54

0.97872

1.5325

0

0

0

0

Bus55

0.36499

0.9837

1.5634

0

0

0.48665

Bus56

0.98987

1.6306

0.50616

0

-0.2681

0

Bus57

0.36499

0.9864

1.5949

0

0

0.48665

Bus58

0.98126

1.546

0

0

0.48665

0.36499

Bus59

0.98435

1.5558

0

0

0.48665

0.36499

Bus60

0.98253

0.36499

1.5522

0

0

0.48665

Bus61

0.87057

0.36499

0.48665

0.73992

0

0

Bus62

0.36499

0.48665

0

0.9877

1.6

0

Bus63

0.98844

0

1.598

0

0.48665

0.36499

Bus64

0.98759

0.36499

1.6037

0

0

0.48665

Bus65

0.99537

0

1.6814

0

0

0

Bus66

0.99547

0

1.6818

0

0

0

Bus67

0.99342

0

1.6617

0

0.50613

0.1518

Bus68

0.99439

0.36499

1.6682

0.48665

0

0

Bus69

0.98899

0.36499

1.6248

0.48665

0

0

Bus70

0.36499

0.48665

0.9934

0

1.6617

0

Bus71

0.99356

0.36499

1.6611

0

0

0.48665

Bus72

0.98801

0.36499

1.6235

0

0

0.48665

Bus73

0.98934

1.6294

0

0

0.48665

0.36499

Bus74

0.98925

1.6305

0

0

0.48665

0.36499

Bus75

0.99195

1.6427

0

0

0.48665

0.36499

Bus76

0.98954

1.636

0

0

0.48665

0.36499

Bus77

0.99322

1.6621

0

0

0.48665

0.36499

Bus78

0.98975

1.6305

0.50612

0.42647

0

0

Bus79

0.98512

1.6417

0

0

0.48665

0.36499

Bus80

0.99076

1.6489

0

0

0.48665

0.36499

Bus81

0.98591

1.6432

0

0

0.48665

0.36499

Bus82

0.99058

1.6499

0

0

0.48665

0.36499

Bus83

0.98955

1.6495

0

0

0.48665

0.36499

Bus84

0.98957

1.651

0

0

0.48665

0.36499

Bus85

0.98572

1.6457

0

0

0.48665

0.36499

Bus86

0.99287

1.6574

0.50613

0.20764

0

0

Total

18.6163

7.1937

16.5462

12.4097

Table 5 summary of voltage stability results analysis of the modernised reserved 86-bus electric power network after3-phase fault at different generator buses.

-5.2267

Loss of Generator

Maximum loading factor/ Collapse Pt (pu)

Total generation

Total load

Total losses

Voltage Violations

Real power Ptotal (pu)

Reactive power Qtotal (pu)

Real load power Ptotal (pu)

Reactive load power Qtotal (pu)

Real power loss Ploss (pu)

Reactive power loss Qloss (pu)

2

1.2166

18.6163

7.1937

16.5462

12.4097

2.0701

-5.216

9

3

1.2176

18.6417

7.2024

16.5599

12.42

2.0817

-5.2176

9

4

1.2175

18.6397

7.1995

16.5584

12.4188

2.0813

-5.2192

9

5

1.2177

18.642

7.2131

16.5604

12.4203

2.0816

-5.2072

9

6

1.2176

18.6403

7.2002

16.5591

12.4193

2.0812

-5.2192

9

7

1.2166

18.6151

7.1892

16.5455

12.4091

2.0696

-5.2199

9

8

1.2176

18.6395

7.2004

16.5586

12.419

2.0809

-5.2186

9

9

1.2166

18.6143

7.1821

16.5452

12.4089

2.0691

-5.2268

9

10

1.2166

18.6161

7.1923

16.5461

12.4096

2.07

-5.2173

9

11

1.2166

18.6163

7.1822

16.5452

12.4089

2.0711

9

12

1.2177

18.6437

7.2163

16.5609

12.4207

2.0828

-5.2044

9

13

1.2165

18.6133

7.1773

16.5447

12.4086

2.0686

-5.2313

9

14

1.2165

18.6126

7.1751

16.5443

12.4082

2.0683

-5.2331

9

15

1.2163

18.6091

7.1719

16.5417

12.4062

2.0675

-5.2344

9

16

1.2162

18.606

7.1701

16.5401

12.4051

2.0659

-5.235

9

17

1.2161

18.6048

7.1692

16.5393

12.4045

2.0654

-5.2353

9

18

1.2161

18.6045

7.169

16.5392

12.4044

2.0653

-5.2354

9

19

1.2165

18.6126

7.1751

16.5443

12.4082

2.0683

-5.2331

9

20

1.2165

18.6133

7.1771

16.5448

12.4086

2.0685

-5.2315

9

21

1.2165

18.6133

7.1771

16.5448

12.4086

2.0685

-5.2315

9

22

1.2162

18.6051

7.1698

16.5396

12.4047

2.0655

-5.235

9

23

1.2163

18.6086

7.1636

16.5419

12.4065

2.0667

-5.2428

9

24

1.2163

18.6081

7.1625

16.5416

12.4062

2.0665

-5.2437

9

26

1.2166

18.615

7.1731

16.5459

12.4094

2.0691

-5.2364

9

27

1.2175

18.636

7.1787

16.5581

12.4186

2.0778

-5.2399

9

28

1.2175

18.636

7.1785

16.5582

12.4186

2.0778

-5.2401

9

29

1.2176

18.6399

7.2121

16.559

12.4193

2.0809

-5.2071

9

30

1.2176

18.641

7.2138

16.5597

12.4198

2.0813

-5.206

9

31

1.2178

18.6405

7.2199

16.5623

12.4217

2.0829

-5.2019

9

32

1.2171

18.6319

7.2199

16.5519

12.4139

2.08

-5.1941

9

33

1.2171

18.6319

7.2198

16.5519

12.4139

2.08

-5.1941

9

34

1.2171

18.6319

7.2199

16.5519

12.4139

2.08

-5.1941

9

35

1.2163

18.6088

7.1637

16.5421

12.4066

2.0667

-5.2428

9

36

1.2163

18.6085

7.1635

16.5419

12.4064

2.0666

-5.2429

9

37

1.2137

18.5941

7.2358

16.5066

12.3799

2.0875

-5.1441

9

38

1.2137

18.5932

7.2333

16.5064

12.3798

2.0868

-5.1465

9

39

1.1374

17.4973

5.7411

15.4685

11.6014

2.0288

-5.8603

9

40

1.2137

18.5936

7.2358

16.5059

12.3794

2.0877

-5.1436

9

41

1.2137

18.594

7.2359

16.5064

12.3798

2.0876

-5.1439

9

42

1.1341

17.216

5.2227

15.424

11.568

1.7919

-6.3454

9

43

1.2172

18.6367

7.2329

16.5537

12.4153

2.0829

-5.1824

9

44

1.2177

18.6455

7.2385

16.5604

12.4203

2.0851

-5.1818

9

45

1.2177

18.6392

7.1799

16.5603

12.4202

2.0789

-5.2403

9

46

1.2177

18.6394

7.1801

16.5604

12.4203

2.079

-5.2402

9

47

1.2176

18.6377

7.1805

16.5591

12.4193

2.0786

-5.2388

9

48

1.0978

16.6323

4.1426

14.9299

11.1974

1.7024

-7.0548

9

49

1.2172

18.6336

7.2329

16.4153

12.4153

2.0829

-5.1824

9

50

1.2177

18.6441

7.215

16.5612

12.4209

2.0829

-5.2059

9

Table 6 Continuation power-flow result of modernised reserved 86-bus electric power network after 3-phase fault at line 2 83.

Bus No

V

[pu]

phase [rad]

P gen [pu]

Q gen [pu]

P load [pu]

Q load [pu]

Bus1

0.80498

0

-5.286

1.6361

0

0

Bus2

0.99349

1.666

0.48827

0.85559

0

0

Bus3

0.99324

1.6573

0.48837

-0.90576

0

0

Bus4

0.99086

1.6363

0.48825

0.52821

0

0

Bus5

0.99501

1.6775

0.48826

0.09744

0

0

Bus6

0.99526

1.6806

0.4883

-0.50361

0

0

Bus7

0.99522

1.6802

0.48883

3.0601

0

0

Bus8

0.99567

1.6836

0.48829

-0.42276

0

0

Bus9

0.99576

1.6842

0.48831

-0.60077

0

0

Bus10

0.99579

1.6844

0.48829

-0.41681

0

0

Bus11

0.99526

1.6806

0.4883

-0.50361

0

0

Bus12

0.9941

1.6721

0.48827

0.78146

0

0

Bus13

0.99502

1.6774

0.48832

-0.63039

0

0

Bus14

0.99502

1.6774

0.48832

-0.63039

0

0

Bus15

0.9958

1.6845

0.48828

-0.2764

0

0

Bus16

0.99643

1.697

0.48826

-0.02611

0

0

Bus17

0.99655

1.6978

0.4883

-0.52332

0

0

Bus18

0.99645

1.6973

0

0.4701

0.35257

0

Bus19

0.99643

1.6974

0.48828

-0.27273

0

0

Bus20

0.99355

1.6197

0.48831

-0.48709

0

0

Bus21

0.99362

1.6201

0.48826

0.00362

0

0

Bus22

0.98971

1.6142

0.48831

-0.409

0

0

Bus23

0.99112

1.6409

0.48826

0.13819

0

0

Bus24

0.98941

1.6128

0.48825

0.36088

0

0

Bus25

0.98938

1.6091

0.4883

-0.33275

0

0

Bus26

0.98423

1.5557

0.4883

-0.20937

0

0

Bus27

0.98424

1.5557

0.4883

-0.21508

0

0

Bus28

0.98422

1.5556

0.4883

-0.20547

0

0

Bus29

0.99643

1.6969

0.48829

-0.44982

0

0

Bus30

0.99645

1.6971

0.4883

-0.51841

0

0

Bus31

0.96298

1.4368

0.48823

0.27804

0

0

Bus32

0.96392

1.4381

0.48833

-0.0765

0

0

Bus33

0.88491

0.85253

0.48678

2.4383

0

0

Bus34

0.99097

1.6408

0.48835

1.6464

0

0

Bus35

0.96287

1.4366

0.48811

0.86005

0

0

Bus36

0.96292

1.4367

0.48819

0.43104

0

0

Bus37

0.88063

0.73472

0.49136

-2.0047

0

0

Bus38

0.98092

1.5357

0.48835

-0.41362

0

0

Bus45

0.98889

1.6123

0.48827

0.00693

0

0

Bus39

0.98054

1.5346

0.48848

-0.90873

0

0

Bus40

0.99361

1.6203

0.4883

-0.43637

0

0

Bus41

0.99354

1.6199

0.48826

0.46924

0

0

Bus42

0.99321

1.6176

0.48826

0.6973

0

0

Bus43

0.84473

0.55649

0.48416

5.3797

0

0

Bus44

0.98093

1.5357

0.48835

-0.40928

0

0

Bus46

0.98564

1.5641

0.48832

-0.36281

0

0

Bus47

0.98057

1.5618

0

0

0.4701

0.35257

Bus48

0.87832

0.85274

0

0

0.4701

0.35257

Bus49

0.884

0.85348

0

0

0.4701

0.35257

Bus50

0.96262

1.4367

0

0

0.4701

0.35257

Bus51

0.87598

0.84936

0

0

0.4701

0.35257

Bus52

0.81835

0.55793

0

0

0.4701

0.35257

Bus53

0.9925

1.6175

0

0

0.4701

0.35257

Bus54

0.9806

1.5341

0

0

0

0

Bus55

0.98556

1.5638

0

0

0.4701

0.35257

Bus56

0.99124

1.642

0.48829

-0.26726

0

0

Bus57

0.98791

1.6029

0

0

0.4701

0.35257

Bus58

0.98302

1.5492

0

0

0.4701

0.35257

Bus59

0.98629

1.5565

0

0

0.4701

0.35257

Bus60

0.9841

1.5554

0

0

0.4701

0.35257

Bus61

0.88102

0.73363

0

0

0.4701

0.35257

Bus62

0.98929

1.6088

0

0

0.4701

0.35257

Bus63

0.99011

1.6069

0

0

0.4701

0.35257

Bus64

0.98907

1.6125

0

0

0.4701

0.35257

Bus65

0.99641

1.6967

0

0

0

0

Bus66

0.99652

1.6973

0

0

0

0

Bus67

0.99485

1.6776

0.48826

0.13815

0

0

Bus68

0.9957

1.6846

0

0

0.4701

0.35257

Bus69

0.99054

1.6363

0

0

0.4701

0.35257

Bus70

0.99483

1.6775

0

0

0.4701

0.35257

Bus71

0.99501

1.677

0

0

0.4701

0.35257

Bus72

0.98961

1.6351

0

0

0.4701

0.35257

Bus73

0.99074

1.6408

0

0

0.4701

0.35257

Bus74

0.99063

1.642

0

0

0.4701

0.35257

Bus75

0.99344

1.656

0

0

0.4701

0.35257

Bus76

0.99184

1.6528

0

0

0.4701

0.35257

Bus77

0.99469

1.6784

0

0

0.4701

0.35257

Bus78

0.99115

1.6419

0.48825

0.50538

0

0

Bus79

0.98783

1.6581

0

0

0.4701

0.35257

Bus80

0.99268

1.6651

0

0

0.4701

0.35257

Bus81

0.98855

1.6596

0

0

0.4701

0.35257

Bus82

0.99299

1.666

0

0

0.4701

0.35257

Bus83

0.99369

1.6717

0

0

0.4701

0.35257

Bus84

0.9933

1.6722

0

0

0.4701

0.35257

Bus85

0.98965

1.6671

0

0

0.4701

0.35257

Bus86

0.99447

1.6734

0.48826

0.09154

0

0

Total

18.1499

6.9847

15.9834

11.9875

Table 7 Summary of voltage stability results analysis of the modernised reserved 86-bus electric power network after3-phase fault at different transmission lines.

Loss of LINES

Maximum loading factor/ Collapse Pt (pu)

Total generation

Total load

Total losses

Voltage Violations

Real power Ptotal (pu)

Reactive power Qtotal (pu)

Real load power Ptotal (pu)

Reactive load power Qtotal (pu)

Real power loss Ploss (pu)

Reactive power loss Qloss (pu)

Base case/ normal

1.1753

18.1499

6.983

15.9834

11.9875

2.1665

-5.0045

8

2-83

1.1753

18.1499

6.9847

15.9834

11.9875

2.1665

-5.0028

9

2-85

1.1753

18.1505

6.9885

15.9837

11.9877

2.1665

-4.9993

9

4-75

1.2174

18.6438

7.2436

15.9837

11.98

2.0867

-5.1743

10

6-75

1.2175

18.6444

7.2442

16.5579

12.4184

2.0865

-5.1742

10

7-72

1.2165

18.6192

7.234

16.5442

12.4081

2.075

-5.1741

10

8-76

1.2175

18.6437

7.2445

16.5574

12.4181

2.0862

-5.1736

10

9-73

1.1754

18.149

6.9602

15.9853

11.989

2.1637

-5.0288

9

9-83

1.1758

18.1538

6.9839

15.9876

11.9907

2.1662

-5.0068

9

11-77

1.2165

18.6205

7.2269

16.544

12.408

2.0765

-5.811

10

12-71

1.2176

18.6478

7.2598

16.5597

12.4198

2.0881

-5.16

10

13-73

1.1753

18.1499

6.9846

15.9834

11.9876

2.1665

-5.003

9

13-79

1.1753

18.1498

6.9831

15.9834

11.9875

2.1665

-5.004

9

14-15

1.2164

18.6168

7.2207

16.5429

12.4072

2.0739

-5.1865

10

15-16

1.1768

18.2256

7.468

15.9985

11.9985

2.2271

-4.5308

9

15-19

1.2164

18.6168

7.2207

16.5429

12.4072

2.0739

-5.1865

10

15-73

1.1753

18.1496

6.9862

15.9833

11.9875

2.1663

-5.0013

9

15-79

1.1753

18.15

6.9852

15.9834

11.9875

2.1666

-5.0023

9

15-85

1.1755

18.1514

6.9829

15.9863

11.9897

2.1651

-5.0069

9

16-22

1.1751

18.1456

6.9838

15.9811

11.9858

2.1645

-5.002

9

17-18

1.216

18.6087

7.2146

16.5378

12.4034

2.0709

-5.1888

10

20-73

1.2164

18.6175

7.2226

16.5434

12.4076

2.0741

-5.185

10

21-73

1.2164

18.6175

7.2226

16.5434

12.4076

2.0741

-5.185

10

22-70

1.1753

18.1484

6.9526

15.9842

11.9881

2.1623

-5.0355

9

23-68

1.2162

18.6128

7.2098

16.5405

12.4054

2.0723

-5.1956

10

24-69

1.2162

18.6122

7.2086

16.5402

12.4051

2.0721

-5.1966

10

25-26

1.2165

18.6192

7.2192

16.5444

12.4083

2.0747

-5.1891

10

25-68

1.1752

18.1497

7.7989

15.9832

11.9874

2.1665

-4.1885

9

25-69

1.1753

18.1497

7.3733

15.9832

11.9874

2.1665

-4.6141

9

27-28

1.2175

18.6404

7.2207

16.5574

12.4181

2.083

-5.1973

10

29-30

1.2175

18.6441

7.2549

16.558

12.4185

2.0861

-5.1636

10

31-65

1.2178

18.6493

7.2621

16.5613

12.421

2.088

-5.1589

10

32-63

1.217

18.6363

7.26

16.5514

12.4135

2.0849

-5.1535

10

33-63

1.217

18.6362

7.26

16.5513

12.4135

2.0849

-5.1535

10

34-63

1.217

18.6363

7.26

16.5514

12.4135

2.0849

-5.1535

10

35-68

1.2162

18.613

7.2099

16.5407

12.4055

2.0723

-5.1956

10

36-68

1.2162

18.6126

7.2097

16.5404

12.4053

2.0722

-5.1956

10

37-54

1.2137

18.5983

7.2713

16.5064

12.3798

2.0919

-5.1086

10

38-54

1.2137

18.5975

7.2687

16.5063

12.3797

2.0911

-5.111

10

39-53

1.1374

17.4991

5.7542

15.4683

11.6012

2.0308

-5.847

9

40-54

1.2137

18.5979

7.2712

16.5058

12.3793

2.0921

-5.1081

10

41-54

1.2137

18.5983

7.2713

16.5063

12.3797

2.092

-5.1084

10

42-64

1.1341

17.2173

5.2325

15.424

11.568

1.7934

-6.3355

9

43-58

1.2172

18.641

7.2725

16.5533

12.415

2.0877

-5.1425

10

44-58

1.2176

18.6499

7.2781

16.56

12.42

2.0899

-5.1419

10

45-46

1.2176

18.6436

7.2222

16.5595

12.4197

2.0841

-5.1975

10

48-56

1..0978

16.6336

4.1521

14.9296

11.1972

1.704

-7.0451

8

49-58

1.2172

18.641

7.2724

16.5533

12.4149

2.0877

-5.1425

10

50-59

1.2177

18.6484

7.2554

16.5606

12.4205

2.0878

-5.1651

10

54-58

1.1619

18.1604

9.7075

15.8016

11.8512

2.3587

-2.1437

9

54-61

1.1726

18.1569

7.9748

15.9475

11.9607

2.2094

-3.9859

9

58-61

1.1733

18.1769

9.2275

15.957

11.9677

2.2199

-2.7403

9

65-66

1.1752

18.1457

7.8062

15.9833

11.9875

2.1625

-4.1812

9

65-67

1.1753

18.1454

7.3516

15.9835

11.9876

2.1619

-4.636

9

66-67

1.1753

18.1468

7.185

15.9842

11.9882

2.1626

-4.8032

9

68-69

1.1753

18.1502

7.2177

15.9836

11.977

2.1667

-4.77

9

68-73

1.1783

18.2535

7.2667

16.0148

12.0111

2.2386

-3.7444

9

69-70

1.1751

18.1461

7.3749

15.9811

11.9858

2.15

-4.6109

9

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