Investigation of Impact of Contingencies on Power Plant and Transmission Lines

Contingency analysis are widely applied to predict the effect of outages in power systems, like tripping of equipment in power plants and transmission lines. Using off line analysis to predict the effect of individual contingency is a tedious task on power system containing large number of components. Practically, only selected contingencies will lead to severe conditions in power system, like violation of voltage and active power flow limits. Simultaneously, the value of active power flow before and after severe transmission and power plant contingencies was analysed using Genetic Eigenvalue Analysis Technique. This was achieved by simulating the Simulink of Nigerian 330KV 48 bus power system using m-file programme in MATLAB environment.The result of the simulation for the power flow solution for transmission line outage contingencies shows that the voltage trajectory at bus 11 stood at 0.3934 p.u, at bus 15 is0.4986 p.u, and bus of 23 is 0.4647 p.u while for the contingencies on power plant, there voltage trajectories stood at 0.2342 p.u for bus 11, 0.3987 p.u for bus 23. The result shows that the impact on power plant is higher than that of transmission line by 40%, 20%, 14%for sampled buses 11, 15, and 23 respectively.

to minimize the PSS control gains with constraints to move the unstable eig10nvalues to the stable region while not changing the stable eigenvalues. This approach assumed that PSSs were installed at every machine.
During severe disturbance, a PSS may actually cause the generator under its control to lose synchronism in an attempt to control its excitation [8].
GAGenetic Algorithm has been applied successfully to various power system problems and the recent approach is to integrate the use of GA and fuzzy logic systems in order to design power system stabilizer [3].The coordination between genetic based fuzzy logic power system stabilizer (GFLPSS) and CPSS provide good damping characteristics during small disturbance and large disturbances for local as well as inter area modes of oscillations The closed-loop performance of the system model was evaluated for an input disturbance in the mechanical torque. The results show that the optimal output controller exhibits better performance than the conventional controller. Results also show the robustness and the validity of the output optimal controller. The usage of optimal control is discussed [9]. The Nigerian 330KV, 48-bus system was modeled as the case study power system for the simulation test, to validate the stability analysis technique and the proposed power system damping controller. The MATLAB Simulink environment is used for the modeling and development of the case study interconnected power system damping controller and for programming the genetic-eigenvalue stability analyzer. For the testing and evaluation of the solution, different transient disturbances were simulated and injected into the MATLAB model of the case study power grid to investigate the performance of the system. Simulations are carried out to determine the effect on the power system angle stability, voltage stability and frequency stability of the case study of power system. The Simulink model of Nigerian 330KV, 48-bus interconnected system was developed for load flow studies, to see the base case voltage profile of the network and for further simulations on the implementation of genetic eigenvalue algorithm

3.2Development of Simulink Model of the Case Study Power system
The Nigerian 330KV, 48-bus was modeled using MATLAB Simulink tool box. This shows 48-bus for further simulations on the network as shown on fig 2.System data for the existing 48-bus Nigeria 330kV power networks obtained from Power Transmission Company of Nigeria (TCN) Osogbo, were used as input data which provided the values of series impedances, admittances of the transmission lines, transformer ratings and impedances required for the power/load flow study. These parameters were modeled and simulated in MATLAB/SIMULINK power system analysis using Newton-Raphson power flow algorithm.

Load/ Power Flow solution for 48-bus network.
Nigerian 330KV 48-bus modeled using MATLAB/SIMULINK Simulation power toolbox.The MATLAB M-file program was then used to carry out load flow solution of the 48-bus 330KV interconnected power system. The source code of the software. The load flow software implements the Newton-Raphson load flow algorithm. The load flow was done to obtain the base case voltage profile of the case study power system. From the load flow investigation, it can be seen that 27 buses are below the 5% voltage drop limit. This shows substantial weakness in the power system under investigation. However, this does not give much information regarding the distribution of instabilities in the system. The power system stability is now analyzed under generator outage condition. The MATLAB SIMULINK synchronous generator block was configured to trip the generator within a set time. The block is configured to trip generator 4 within 1.5secs of the simulation. The result of associated eigenvalue analysis is as analyzed below.

Mathematical Model of Power Flow and Eigenvalue Analysis
Power system matrices are required for the stability analyses of genetic eigenvalue analysis program, hence the mathematical model were derived as shown Q is the reactive power with the following notation: The mismatch power at bus K is given by: The K P and K Q are calculated from equations (3.13) and (3.14) The Newton -Raphson method solves the partitioned matrix equation: The eigenvalues associated with a mode of voltage and reactive power variation can provide a relative measure of proximity to voltage instability. Then, the participation factor can be used to find out the weak nodes or buses in the system. Equation (15) can be written as:   The appropriate definition and determination as to which modes or buses participates in the selected mode become very important. The participation factor is computed to identify the weakest nodes or lead buses that are making significant contribution to the selected modes. The participation factor is given by

RESULTS
The base data for this paper are system parameters of Nigerian 330KV 48-bus system from Transmission Company of Nigeria. There are 14 synchronous generators in the system. The base voltage is 330KVA and 100MVA. The generator, line and bus parameters used for simulation and computations are listed in table 1.

Figure. 4: Voltage Profile of the Base Case of Nigerian 330KV Power System
From the load flow result, it can be seen that 27 buses are below the 5% voltage drop limit. This shows substantial weakness in the power system under investigation which might lead to instability.. However, this does not give much information regarding the distribution of instabilities in the system. Hence further simulations were carried out using the hybrid of Genetic and Arnoldi Eigenvalue analysis technique to find the eigenvalues, the damping ratios and the participation factors in the power system for proper placement of Power System Stabilizers Result of Pflw solution on outage of transmission line without stabilizer.

Simulation and Analysis of Voltage Stability
Simulations were carried out to determine the base voltage stability levels at the buses of the case study power system, and the ability of the system to operate stably and also to remain stable following the injection of simulated contingencies. The Eigenvalue analysis program was applied to the case study power system modeled in MATLAB simulink as shown in figure 2, The MATLAB m-file code of the eigenvalue program interfaces with the MATLAB/SIMULINK model of the case study power system via the MATLAB program Workspace.
The bus eigenvalues, bus participation factor, and bus damping ratios were computed for the case study power system base operational state (i.e. For the power system steady state -without contingency or disturbances) is listed in table 4. The Eigenvalue ( ) give information about the proximity of the system to instability. The participation factor measure the participation of a state variable in a certain mode of oscillation [12]. The bus participation factor The Genetic Eigenvalue computation program was called during the simulation to compute the system eigenvalue, damping ratio and participation factor at the system buses. The power flow program was activated to carry out power flow solution of the current state of the power system. From result of the eigenvalue analysis almost all the real part of the complex eigenvalue listed in table 4 lie on the right half of the S-plain. That is the real parts of the complex eigenvalue are almost all positive. This is an indication that the system is unstable. The damping ratios of the eigenvalue are very small. The negative value of most of the damping ratios is a further indication of the instability of the system. Bus 11 shows the most negative (smallest) damping ratio (being the weakest bus even at steady state) the damping ratio of most of the buses in the power system during the disturbance are below the 5% minimum and the 0.2 damping threshold .The listing in table 5 confirms the information from the eigenvalue analysis.
The values in table 6 show that there is serious voltage degradation at the buses of the power system. The voltages in most of the buses are degraded. These result indicate that the exciters on the generators alone cannot stabilize the oscillation in the power system. The voltage magnitudes in table 6 do not give complete information of variation of voltage at the buses. The eigenvalues and the damping ratios indicates that the power system is unstable. This means that voltage at nodes of the power system are oscillating.
The trajectory of the voltage at the buses 11, 15 and 23, as a result of the transmission line outage contingency, are shown on figures 5 -7 respectively. Figures 8 -14, shows the load angle responses of generators 1, 3, 5, 7,9,11 and 13 respectively . Figures 15 -17 shows the terminal voltage responses of generators 1, 3, and 5 respectively in that order to the transmission      15-17) indicates the failure of the generators excitation system and the generators AVRs to stabilize the generators output terminal voltages. These factors combine to cause the instabilities of the entire power grid as reflected in the eigenvalues and damping ratios of the buses in the power system.
The situation here requires the integration of the power system stabilizers to compliment the generator excitation system. The power system stabilizers will help to damp out the oscillations to the generator angle and the terminal voltages.

Outage of a Power Plant
The power system stability is now analyzed under generator outage condition. The MATLAB SIMULINK synchronous generator block was configured to trip the generator within a set time. The block is configured to trip generator 4 within 1.5secs of the simulation. The result of associated eigenvalue analysis is listed in table 8   7, it can be seen that real part of the complex eigenvalues lie on the right-half of the S-plane. This shows that the real part of the complex eigenvalue are all positive. The damping ratios are all negative. This information indicates that the power system is unstable. Furthermore the instability from the generator outage seem to be more severe than that resulting from the transmission line outage. This is due to the fact that the real parts of the eigenvalue in  Table 8 gave the output of the power flow solution carried out by P-flow using the generator outage disturbance data.  8 showed that the severity of the voltage degradation is more than that in table 6.The severity of the degradation is worse than that of the base power system. For instance referring to the voltage levels in the result of the power flow solution in tables 6, it can be seen that for the transmission line outage contingency, the voltage of bus 11 stood at 0.3934 p.u , that of bus 15 stood at 0.4986p.u and that of bus 23 stood at 0.4647 after the transmission line outage contingency. However for the power plant outage table 4.13, the voltage of bus 11 stood at 0.2342p.u, that of bus 15 stood at 0.3987p.u while that of bus 23 stood at 0.3987p.u. The margin gives an indication of the level of severity of the instability resulting from the outage of the power plant. This fact is shown by the very high negative damping ratio resulting from all the real parts of the bus eigenvalues lying on the right-half of the S-plane. The real parts of the eigenvalue in table 5 are very much positive than the real parts of the eigenvalues in table 7.   Figure 18 -20 showed that the impact on the voltage levels and their stability is more severe than those of figure 5-7 in the case of the transmission line outage. Figure 18 -20 indicate that the voltage instability of the power system is (as seen in the level of voltage oscillations) is higher than when the power system was impacted by the transmission line outage.
The same can be said of the severity of the instability of the load angle of the generator as shown in figure 21 -23 (for generators 1, 3, and 5), when compared to the instabilities in the case of the transmission line outage as shown in figure 8-10. As figures 24-26 indicate the terminal voltages of the generators were heavily impacted by the power plant outage contingency more than they were impacted by the transmission line outage contingency as shown in figure 15 -17. These results agree with the eigenvalue and damping ratio computed for the case of the transmission line outage event and the power plant outage event on the case study power plant 5.1 conclusion It is very important to re-establish baseline values for key stability parameters for the Nigerian power system. This will enable the establishment of ground of service assessment index. From the Eigenvalue and power flow resultsof the transmission line voltage trajectories, generator terminal voltages and load angles, it is observed that the contingency impact on power plant is more severe than that of the transmission lines. This demands the need to use appropriate technique for a choice of selection of stability analysis for placement of PSS on generators with high participation factor to support the exciters of the generators. Genetic eigenvalue technique is recommended for its heuristic behavior in optimal location of eigenvalues.