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

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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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

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

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

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

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