Abstract

The Nigerian 330kV grid network is characterized with major problems like voltage instability (voltage profile violation), long transmission lines, nature of transmission lines and high power losses which affect power generation and distribution systems. This paper considered the load-flow study of the Nigerian 330-kV consisting of 32 buses, 11 generating stations and 36 transmission lines. Newton-Raphson iteration technique was used to carry out the analysis because of its fast convergence nature as compared to other iterative techniques. The data used for the study is obtained from Power Holding Company of Nigeria (PHCN). MATLAB/SIMULINK software was used to carry out the simulations. The results obtained shows that some of the bus voltages lie outside the prescribed limit of 0.95-1.05 pu (313.5 – 346.5kV). These buses include buses 16 (Kano 0.8721pu), 17(Kaduna, 0.9046pu), 18(Jos, 0.8580pu), 19(Gombe 0.8735pu) and 21(Katampe, 0.9167pu). The total active power loss is 268.622MW and that of reactive power loss is 2247.42Mvar. It is therefore inferred from the results obtained that the existing Nigerian 330-kV grid network is fraught with high line losses that require compensation using reactive power supports such as Flexible Alternating Current Transmission Systems (FACTS) devices, for effective line utilization.

1. Introduction

Since Electrical Energy is the pivotal upon which a country’s development is anchored, hence, the ever-increasing demand of electric power. Power is usually generated at specific locations far from load centers before it is delivered to consumers through transmission and distribution systems. The Nigerian power system network, like any other networks elsewhere is made up of the large interconnected network that spans across the country nationwide. One of the main challenges combating this network is the fact that most Northern parts of the system usually experience poor voltage profile as a result of shortage of reactive power support. Other challenges include fragile transmission lines, inability of transmission lines to transport more than 400MW of power, radial network and high losses ¹. This study classifies buses whose voltages are extremely below statutory limit of ±5% (346.6kV [1.05pu] to 313.5kV [0.95pu] as a result of reactive power shortage as “weak buses”. This problem is more amplified in relatively weak networks having high resistance to reactance ratios ^{1, 2}.

In load flow study, the main objective is to determine the complex bus voltages, and real and reactive power injected into the transmission system as well as real and reactive power at the slack bus with other parameters being specified. Load flow analysis usually finds its application during power network design and planning. It is also useful for obtaining the system behavior during operation in order to predict the loading conditions of transmission lines and equipment’s within the system. The system is usually assumed to be operating under a balance condition such that the analysis can be carried out using a balanced single-phase representation ³.

2. Nigeria 330kV Transmission Network

The increasing demand for electricity in Nigeria like many other developing countries, is extremely greater than what is been generated, which results to the transmission network being heavily loaded and stressed beyond permissible limits. The Nigeria grid network consist of few generating stations like many other developing countries and his located mostly in remote areas near the raw materials required for generation. Power Holding Company of Nigeria (PHCN) has the statutory function of generation, transmission, distribution and marketing of electricity in Nigeria. The single line diagram (Figure 1) of the Nigeria 330kV network consist of eleven (11) generating stations comprising of three (3) hydro and eight (8) thermal, twenty one (21) load stations and thirty six (36) transmission lines with a total installed capacity of 6500MW. The thermal generating stations are mainly located in the Southern part of the country like Okpai, Afam, Sapele, Delta (Ughelli), Egbin, Olorunshogo and Omotosho, while the hydro generating stations are located mainly in the Middle Belt/Northern part of the country like Kainji, Shiroro and Jebba ⁴.The Nigeria 330-kV grid network can be grouped into three (3) sections: North, South-east and South-west sections. The Northern and South-west are connected through one double circuit between Jebba TS and Oshogbo. The South-East is connected to the South-West through a single line from Osogbo to Benin and then one double circuit line from Ikeja West to Benin. The line diagram and data of the Nigerian 330kV grid network were sourced from the National Control Centre (NCC) of the PHCN, Oshogbo, Nigeria ⁵.

3. Data Collection

The data used for this study were obtained from Power Holding Company of Nigeria (PHCN) and are presented in Table 1 and Table 2. Computer software programmed using MATLAB/SIMULINK were used in conducting the simulation.

4. The Load-flow Modelling

Consider an n- bus power system shown in Figure 2. The transmission lines are shown by their equivalent model with the impedances converted to per unit admittances on a common MVA buses ⁶.

By applying Kirchhoff’s Current Law (KCL) to bus i, we obtain

(1)

Or

(2)

The real and reactive power at bus is

(3)

(4)

Substituting for I_i in eqn. 2 yields

(5)

The above mathematical formulation for load flow problems results in a system of nonlinear algebraic equations which must be solved by iterative methods. The commonly used methods for solving load flow problems are Gauss-Seidel, Newton-Raphson and Fast Decoupled techniques. In this paper, Newton-Raphson techniques is used because of its quadratic convergence property and ability to handle large power network ⁷ which are of paramount importance in solving nonlinear equations of power flow problems.

Equation. 2 can be re-written in terms of the bus admittance matrix as

(6)

In the above equations, j includes bus i. expressing this equation in polar form, we have

(7)

The complex power at bus i is

Substitute equation 3 into equation 7,

(8)

Separating the real and imaginary parts

(9)

(10)

The load flow equations using Newton-Raphson techniques can therefore be written as

In a compact form, it can be written as ²

(11)

Where J₁, J₂, J₃ and J₄ are sub-matrices of the Jacobian matrix, which are expressed as

For J₁

Diagonal element:

Off-diagonal element:

For J₂

Diagonal element:

Off-diagonal element:

For J₃

Diagonal element:

Off-diagonal element:

For J₄

Diagonal element:

Off-diagonal element:

The terms and are the difference between the scheduled and calculated values and represents the column vector of the control variables at the PV and PQ buses and are given by

(12)

(13)

Represents the column vector of the state variables at the PV and PQ buses. Gaussian elimination or triangular factorization method can be applied to equation 11 in order to determine the unknown vectors and updated value of the voltage angles at all buses except slack bus ⁸.

The complex power that flows through the transmission line connecting any two buses i and j as a result of the injection at bus i and j respectively are S_ij and S_ji. These can be expressed mathematically as

(14)

(15)

The power loss in line i-j is the algebraic sum of the power flow determined from equations 14 and 15, i.e.

(16)

5. Results and Discussion

The simulation results obtained are presented in Table 3 and Table 4. Table 3 presents the results of the voltage magnitudes and angles at various network buses while Table 4 presents the results obtained for the power flow and losses along the transmission lines within the network.

Figure 3 is a bar chart plot which shows the graphical display of the voltage magnitude against bus number for the Nigerian 330kV grid network.

The Nigerian 330kV consisting of 32 buses was simulated based on Newton-Raphson power flow algorithm using MATLAB/SIMULINK software. The data used for the study were obtained from Power Holding Company of Nigeria (PHCN). Based on the results obtained, it was found that the total active power loss from the power flow program solutions by Newton Raphson method is 268.622MW and that of the reactive power loss is 2247.420Mvar. The results obtained also identify some weak buses with values outside the statutory limit of 0.95 pu or 313.5kV and1.05pu or 346.5kV. These weak buses include: (Kano, 0.8721pu), (Kaduna, 0.9046pu), (Jos, 0.8731pu), (Gombe, 0.8735pu), (Yola, 0.8580pu) and (Katampe, 0.9167pu). The result further showed that the losses are still very high and these weak buses are located within the Northern part of the network. This could be as a result of the fact that they are very far from the location of generating stations within the system.

6. Conclusion

In this paper, the load flow study for the Nigerian 330-kV grid network using Newton-Raphson iteration techniques was modeled using MATLAB/SIMULINK software. The result shows that the Nigerian 330kV grid network is characterized with various problems like voltage instability (voltage profile violation), problem of long transmission lines, nature of transmission lines and poor power quality, most especially, within the Northern areas of the network under consideration. Also, the result reveals that the reactive power loss in the Nigerian 330kV grid network is still very high, hence, the need for reactive power compensation. Furthermore, more substations and additional lines should be introduced into the grid network to provide more loops in the existing 330kV such that the voltage profile of the network will be greatly enhanced, especially Kano, Kaduna, Jos, Gombe, Yola and Katampe where voltage dip is severe.

References