Stability Studies of the Nigerian 330 KV Integrated Power System

Transient stability is concerned with the effect of large disturbances due to fault(s) that occur in power system. The most severe is the three phase fault. One way of improving transient stability in power systems is by increasing bus voltage above its nominal value [1], thus making the machine to decelerate fast. This maintains the transmission voltage at the most optimal point or mid-point after a fault is cleared. Transient stability studies involves the determination of whether or not synchronism is maintained after the machine has been subjected to severe disturbance, and this depends on the location and kind of fault in the network. This may be sudden application of load, loss of generation, loss of large load or a fault on the system [2]. Transient stability studies determines the machine power angles, speed deviations, electrical frequency, power flow of machines, lines, transformers and the bus voltage levels [1]. The swing equation is used for transient stability studies (rotor angle stability) and it is seriously affected by the type and location of fault. The nature of the fault means whether it is a three phase or a single phase short circuit fault and the location means whether the fault is on the largest machine in the network or on any other machine(s). Three-phase short circuit fault at the generator bus is the most severe type, as it causes maximum acceleration of the connected machine [3].


Introduction
Transient stability is concerned with the effect of large disturbances due to fault(s) that occur in power system. The most severe is the three phase fault. One way of improving transient stability in power systems is by increasing bus voltage above its nominal value [1], thus making the machine to decelerate fast. This maintains the transmission voltage at the most optimal point or mid-point after a fault is cleared. Transient stability studies involves the determination of whether or not synchronism is maintained after the machine has been subjected to severe disturbance, and this depends on the location and kind of fault in the network. This may be sudden application of load, loss of generation, loss of large load or a fault on the system [2]. Transient stability studies determines the machine power angles, speed deviations, electrical frequency, power flow of machines, lines, transformers and the bus voltage levels [1]. The swing equation is used for transient stability studies (rotor angle stability) and it is seriously affected by the type and location of fault. The nature of the fault means whether it is a three phase or a single phase short circuit fault and the location means whether the fault is on the largest machine in the network or on any other machine(s). Three-phase short circuit fault at the generator bus is the most severe type, as it causes maximum acceleration of the connected machine [3].

Literature Review
The swing equation is the basic equation used to investigate power system transient stability studies.Various numerical methods based on the relevant mathematical modeling of the network and differential evaluation of the machines are applied to solve this equation. It issolved using various numerical methods expressed mainly in time domain. These include: Euler method, Modified Euler method, Runge-stability. Matlab/Simulink isused to consider stable, critically stable and unstable state of a multi-machine power system and obtained the individual generator angles [8].
Various control methods and controllers have been developed over time to ensure that, after a very sudden and large disturbance, the system still maintains stability by adjusting its protective schemes and control actions [9]. The transient stability control scheme is very difficult to implement because a disturbance that causes instability can only be controlled if a significant amount of computation (analysis) and communication is accomplished [10]. Time domain simulation method using the swing equation was used by [8] to assess the transient stability by setting the fault clearing time (FCT) randomly to determine whether the system is stable or unstable after a fault is cleared.

Equations relevant to the study
The swing equation, torque equation, equal area criteria, and the determination of the time response equivalent to the rotor angle of the machines.

Swing equation (Rotor angle determination)
This is the fundamental equation that determines rotor dynamics in transient stability studies and it is a non linear differential equation that is solved accurately using digital computer program. The equation is given below: Changes in any of these quantities in the two (2) equations causes the rotor speed and acceleration to fall into the three conditions as shown in the below Table 1.

Equal area criteria
Thiscriteria means all energy gained from the turbine during acceleration period must be returned back to the system by the rotor. It is also used to determine the critical clearing angle. This is given in the equation below The critical clearing time is given as

Basic numerical equation used to determine time response equivalent to rotor angle
It gives the corresponding time of the rotor angular displacement. It is obtained based on the mathematical concept and it makes use of numerical integration packages based on mathematical concepts. The equation for the basis of the numerical method used is given below Where n δ and 1 n δ − ∆ are rotor angle changes. ∆t is a very small time interval (usually 0.05 sec). It gives a detailed numerical solution of the swing equation and requires little iteration. Hence, it is simple, easy to understand and gives minimal round off errors.

Etap (Transient analyzer)
ETAP is a dynamic stability program that incorporates comprehensive dynamic models of prime movers and other dynamic systems. It has an interactive environment for modeling, analyzing, and simulating a wide variety of dynamic systems. It provides the highest performance for demanding applications, such as large network analysis which requires intensive computation, online monitoring and control applications. It is particularly useful for studying the effects of nonlinearity on the behavior of the system, and as such, it is an ideal research tool [9].
Performing power system transient stability is a very comprehensive task, that requires the knowledge of machine dynamic models, machine control unit models (such as excitation system and automatic voltage regulators, governor and turbine/engine systems and power system stabilizers) numerical computations and power system electromechanical equilibrium phenomenon.

Aim
To investigate transient stability limits of the generators in the Nigeria 330 Kv integrated power project (NIPP) before, during and after system disturbances due to fault of the generating station(s) in the network in time domain. Etap 4.0 (power station transient stability analyzer) is used to model and solve the network and machine differential equation interactively.

Methodology
The stability limits of Nigeria 330 KV power network consist of Seventeen (17) Generating Stations, Fifty Two (52) buses and Sixty Four (64) Transmission lines is studied to investigate the limits of stability before, during and after disturbance. A one line diagram as well as the transmission line parameters and generator installed and available capacitiesof the network are shown in appendix A, B and C respectively. In this study, three phase (3-θ) short circuit fault on the largest generator (EGBIN with available output capacity of 1320 MW) is considered and analyzed graphically.The impact it will have on other generators rotor angles, exciter currents, exciter voltages, electrical power, mechanical power, frequencies, terminal currents and the entire stability of the network are also determined. Theswing equationexpressed in time domain is solved using the Runge-kutta (using the predictor-corrector routines) and equal area criteria approach in ETAP environmentis used for the analysis. In cases of fault(s), it randomly set up a fault clearing time (FCT) for the machines in the network and solves all the complex differential equations of all equipment in the network.

Modeling the Nigeria 330 KV Integrated Power Network Using Etap
The Integrated Nigerian 330 KV Integrated Power Project (NIPP) interconnects all the generating stations and load centers. The system consists of synchronous generators, motors, transmission lines, transformers, loads and protective devices. Figure 1 below shows the model of the network used for this study. This is obtained by modeling the parameters (bus voltages, transmission line parameters transformers ratings and their loadings, generators ratings and their power limits) as obtained from Power Holding Company of Nigeria (PHCN), while Figure 2 shows the transient stability simulation results obtained.
The simulation time is set from 0 sec-10.0 secs while subjecting EGBIN to a three-phase short circuit fault, and the behavior of the network is obtained graphically as shown in Figures 2-13 below.

Results and Discussions
The Nigeria 330KV integrated power network consisting of seventeen (17) generating stations, sixty four (64) transmission lines and fifty two (52) buses is studied, to investigate the limits of stability before, during and after three phase (3-θ) fault on Egbin power station. When 3-θ short circuit fault occurred at Egbin generator, the system dynamics changes, thus affecting the quadrature axis. This change in the quadrature axis affects the generator's exciter current, exciter voltage, electrical power, mechanical power, frequency, rotor angle and terminal current. Tables 2a, 2b and 2c shows the results obtained and gives the stability limits of these electrical quantities before, during and after a three phase (3-θ) fault. Figures 2-13 shows a plot of how this fault affects the behavior of the other generators in the network. It was observed that before the 3-θ pre-fault, the peak values obtained between time range of 0.000 Secs-0.0600 Secs operates within the              45 Hz at nominal frequency of 50 Hz. Moreso, the net power (difference between electrical and mechanical power) is small and the rotor angle is within 90 degrees, thus satisfying stability criteria. During the fault (0.061 secs-0.042 secs), it was observed that the net power was large and the frequency was gradually moving out of its allowable tolerable limit. However, the various electrical quantities peak values indicates that if the fault is not cleared after 0.042 secs, the system become unstable and loss synchronism between the generators, that will eventually lead to system collapse as shown in

Conclusion/Recommendation
Transient stability study of the Nigeria 330 KV integrated power network consisting of Seventeen (17) generating stations, Fifty Two (52) buses and 64 Transmission lines was carried out using ETAP 4.0 Transient analyzer. The impact of three phase short circuit fault of the largest power station (EGBIN) on the entire system stability was considered. The system was analyzed before, during and after the fault. It was observed that before the fault (0.000-0.0060 secs), the system was still stable until it got to 0.042 sec. At this time, four generating stations (Omotosho, Sapele, AES and Delta) were almost getting out of synchronism. However, when the fault was cleared, the system returned to its stability. The obtained result showed that the fault when allowed to last beyond 0.042 seconds causes buses connected to four (4) generating stations (AES, Sapele, Delta and Omotosho) to swing away from the stability region hence operating outside the allowable tolerable voltage limit of 314.45 KV-346.45 KV.