Research Paper ANALYSIS OF POWER SYSTEM STABILITY FOR MULTIMACHINE SYSTEM D. Sabapathi a and Dr. R. Anita b Address for Correspondence a Research Scholar, Department of Electrical & Electronics Engineering, M.P.N.M.J. Engineering College, Chennimalai India ABSTRACT This paper proposes Power System Stabilizer (PSS) in addition to the existing AVR and Governor for power system stability. The variations of rotor angle, voltage and frequency of TNEB system are taken as comparison parameters. The system is simulated with the existing and the proposed for three phase fault and single phase fault using ETAP software. The combination of AVR, Governor and PSS maintains synchronism during all kinds of faults. KEYWORDS: AVR, Governor, PSS, Power system stability and ETAP. 1. INTRODUCTION In recent years, there has been considerable interest in designing excitation, Governors along with Power System Stabilizers (PSS) which are expected to give better dynamic performance for large scale power system over a wider range of system and operating conditions. Voltage and frequency is a very important index of power supply in power system operation. Both utility equipment and consumer equipment are designed to operate within a certain voltage and frequency range. A system is said to be synchronously stable (i.e., retain synchronism) for a given fault if the system variables settle down to some steady-state values with time, after the fault is removed [1]. Prolonged operation of the equipment at voltages and frequencies outside the allowable range could adversely affect its performance and possibly cause damages to the equipment. The generator excitation system and the governor system are the most important means of voltage and frequency control in a power system. It should maintain the generator terminal voltage and frequency at a constant value under normal operating conditions and regulate to its prefault steady value quickly and effectively once the fault occurs. Many drawbacks of AVR/PSS have already been discussed in [2, 3]. The delineates alternative designs that use differential geometric control theories, namely, exact and partial feedback linearizing techniques [4]. The intent of that was to explore the potentiality of nonlinear exciters. Any synchronous generator in a power system is traditionally equipped with an Automatic Voltage Regulator (AVR), to sustain the generator terminal voltage, and a PSS, to provide damping torque and this combination does not meet out the stability criteria in all aspects. Analysis of nonlinear voltage regulators [5] in an SMIB system over a wide range of system and operating conditions and the synchronizing and damping torques analysis have been shown only for SMIB system. The proposed controller aims to improve the voltage control, stability and frequency control for a multi-machine infinite bus system under small signal disturbances and transient conditions. Simulation is performed for different cases using above software and results are analysed and compared for transient and small signal disturbance [6]. In the First Case, Large Fault (three phase fault) at 400 kv is considered to verify the transient stability. In the Second Case, Small Fault (single line to ground fault) at 400 kv is considered for analysis. 2. SYSTEM DATA Tamilnadu Electricity Board (TNEB) system was considered to evaluate the performance of the proposed Automatic Voltage Regulator (AVR), Governor and PSS. 2.1 System TNEB 400 kv Grid system consists of 57 Buses out of which 40 are 400 kv buses and 52 transmission lines. The entire generators which are directly evacuated at 400 kv are modelled with their generator transformer. Totally 11 generating stations with one or more units at each generation plant is modelled. The generator transformer is also modelled with its leakage reactance. Generator is modelled with transient model, considering direct axis sub transient reactance, direct axis transient reactance, direct axis synchronous reactance, armature resistance, and open loop time constants for both transient and sub-transient model and inertia constant for the generator. Koodankulam 1000 MW Nuclear Power Plant, Coastal Energen 660 MW, Mettur and North Chennai, Neyveli are the important generating stations. The above power plants are located at Tamilnadu, India. Generator Transformer is modelled with its leakage reactance, X/R ratio and OLTC is modelled with its minimum and maximum tap and tap step. Transmission line is modelled with nominal Pi model with series resistance and reactance and shunt half line charging susceptance. All the loads are lumped at 400 kv and the load is modelled as a combination of constant impedance, constant current and constant power loads. The generator consists of AVR, governor and PSS which plays crucial role in stability. Since the generating stations of various locations are installed in various years, the very old power plant consists of dc excitation system and (remove with here) less than a decade generating station consists of either static or brushless excitation. All the AVRs are modelled as per manufacturer block diagram and transfer function. Governor also ranges from old governors in the power plants which are operating more than 20 years to recent governors in the recently commissioned power plants. Electronic governors are used in the recent power plants. PSS is not present in the old power plants. Whereas separate PSS is available in some power plants and PSS is a part of AVR in the very recent power plants. 3. Modelling of Power System AVR, Governor & PSS are modelled for transient stability in ETAP software as shown below: 3.1 AVR
AVR with its rectifier time constant T rec and gain constant K a and associated time constant T a, exciter gain K e and its associated time constant T e are modelled as shown in Fig. 1. Figure 1. Block diagram for AVR The output of the rectifier is compared with the reference voltage and then multiplied by gain. The output of the rectifier is fed to a limiter, which restricts the minimum and maximum output to prevent the components failure. The exciter gain and time constant is given to field limiter which restricts the field voltage within its minimum and maximum limit so that the field current is limited to prevent the rotor damage, as in Eqs. (1) and (2). The modelling problem of a truly multi-machine, multi-order representation is not a simple matter and the algebra behind it will be quite cumbersome as the number of machines increase. Depending on the chosen model for a given machine, several coefficients associated with the differential and algebraic equations may or may not exist depending on the kind of model used for the rest of the machines. In fact, the whole mathematical representation will differ for each study case [7]. 3.2 Governor Governor works based on the changes in speed, as in Eqs. (3) and (4). In thermal power plants, the governor consists of three stages of turbine (High Pressure HP, Intermediate Pressure - IP and Low Pressure LP) for normal technology and four stages (Very High Pressure VHP, High Pressure HP, Intermediate Pressure IP and Low Pressure LP) for critical technology. If there exists a difference between total generation and load, the mismatch of these will reflect as change in frequency and hence the change in speed of the machines. Governor will adjust the turbine valve to reduce the mismatch between generation and load. 3.3 Power system stabilizer Figure 2. Block diagram for thyristor excitation system Fig. 2. shows the block diagram representation for thyristor excitation system with PSS. PSS is the most widely used device for resolving oscillatory stability problems [8]. The development of general concepts associated with applying power system stabilizers utilizing shaft speed, ac bus frequency and electrical power inputs and root locus involved shifting of Eigen values related to the power system modes of oscillation by shifting the poles and zeros of the stabilizer [9]. Stabilizer consists of three blocks such as, PSS Gain, Washout Time constant and Phase compensation. This limits the speed and magnitude of AVR to ensure that the oscillations are damped out quickly. PSSs utilizing shaft speed, ac bus frequency and electrical power inputs to regulate the field voltage are given in Eqn. (6).Voltage dependence on angular speed changes is demonstrated. These changes contribute to changes in the electric power supplied by the machine. This effect enhances the stability of the system. This is true if the field voltage is constant. However, machine terminal voltages are the negative feedback to the exciters. Therefore, change of voltages due to angular speed increments tend to reduce the field voltage and vice versa. This has negligible effects on machines connected to infinite bus as the speed changes will eventually vanish. However, for multi-machine isolated systems, the angular speed changes should settle to a final value depending on the perturbation [10]. Therefore, the voltage frequency dependence tends to destabilize the system. A positive feedback from angular speed changes to the exciter can overcome this problem. A feedback gain in the range of unity can be sufficient to stabilize the uncontrolled (without PSS) system [11].
4. SIMULATION AND RESULTS Various contingencies are simulated on the TNEB as given below. The contingencies include large transient event like three phase fault and contingencies like single line to ground fault are considered. The system has been modeled with existing AVR, governor and PSS and studies are carried out. Rotor angle, voltage and frequency oscillations are considered as key criteria (parameters) to compare the results. Then this system with various AVR, Governor and PSS model and parameters are considered to evaluate their behavior. Best suitable model and parameters of AVR, Governor and PSS is identified based on the above said criteria. 4.1 Three phase fault Though there are rare, very severe faults in power system, the fault, which in general used to find out the critical clearing time, is three phase faults. In general rotor angle stability is taken as index, but the concept of transient stability, which is the function of operating condition and disturbances, deals with the ability of the system to remain intact after being subjected to abnormal deviations. Three phase to ground fault at very important 400 kv substations (Sriperumpudur and Salem located in Tamilnadu, India) in Tamil Nadu Electricity Board (TNEB) system are simulated. Rotor angle oscillations of generators and frequency are verified. The graph shows the rotor angle oscillation of various generators for a fault at 400 kv sriperumpudur substation for the duration of 100 ms. with existing system parameters and proposed parameters. Results show that the proposed parameters reduce the rotor angle oscillation to great extent as shown in Figs. 3-8. Figure 3. Rotor angle Variations of TNEB systems with existing during 3 phase fault. Figure 4. Rotor angle Variations of TNEB systems with proposed during 3 phase fault. Figure 5. Voltage at 400 kv bus in TNEB systems with existing during 3 phase fault. Figure 6. Voltage at 400 kv bus in TNEB systems with proposed during 3 phase fault.
Figure 7. Frequency at 400 kv bus in TNEB systems with existing during 3 phase fault. Figure 8. Frequency at 400 kv bus in TNEB systems with proposed during 3 phase fault. 4.2 Single line to ground fault Quite frequent fault in power system is single line to ground fault. In general, single line to ground fault does not have much to do with the critical clearing time and so rotor angle oscillation was compared. Single line to ground fault at few 400 kv substations (Udumalpet, Almati, Sriperumpudur and Salem) in TNEB system is simulated. Rotor angle oscillations of various generators and frequency are compared with existing system and proposed. The graph shows the rotor angle oscillation of various generators and frequency for a fault at 400 kv Sriperumpudur substation for the duration of 100 ms. with existing system parameters and proposed parameters. Classical approach to solution of stability analysis problems in power system is based on analysis of properties of a system of equations, representing dynamic behavior of a power system as a whole. This general approach being adequate and efficient in application to dynamic analysis of small and medium-size power systems meets with difficulties when applied to solution of these problems in large power interconnections. Results show that the proposed parameters reduce the rotor angle oscillation to great extent as shown in Figs. 9 and 10. Figure 9. Rotor angle variations of TNEB systems with existing during single line to ground fault. Figure 10. Rotor angle variations of TNEB systems with proposed during single line to ground fault. Graph shows that the rotor angle oscillation is greatly seconds after clearance of the fault with proposed reduced and suppressed with proposed., whereas the oscillation persists with For a three phase fault the system is unstable (i.e existing. Since the system considered is Rotor angle goes beyond 180 0 ) with the existing large, the impact of the frequency and voltage by the which is made stable with proposed proposed is not significant, but still that and the maximum rotor angle oscillation improves the voltage profile as tabulated below in is limited to 170 0. In addition, the oscillation occurs 5 Table 1.
Since 400 kv system is solid earth system, the fault current is almost close to three phase fault current. For a Single line to ground fault the system is stable with the existing however the angle of rotor reaches maximum of 172 0 which is reduced to 160 0 with proposed. It clearly indicates that the proposed are able to improve stability and reduce the angle of oscillation. The rotor oscillation continues for larger time after clearance of the fault with existing, whereas proposed suppress the oscillation quickly. Since the system considered is large the impact of the frequency and voltage by the proposed are not significant but still that improve the voltage profile as tabulated in Table 2. Table 1. Three phase fault Parameters Existing Proposed Rotor angle in degree Unstable 170 Voltage in volts 0.37 0.43 Frequency in hz 50.5 50.4 Table 2. Single line to ground fault Parameters Existing Rotor angle in degree 172 160 Proposed Voltage in volts 0.7 0.82 Frequency in hz 50.3 50.2 5. CONCLUSIONS In this paper, the variations of rotor angle, voltage and frequency of TNEB system have all been taken as comparison parameters. The system has been simulated with ETAP software for a fault of 100 milliseconds duration from 3 to 3.1 seconds. System is analyzed over the duration of 10 seconds. The system has been simulated with the existing and the proposed for three phase fault and single phase fault. From the simulation results, it has been ascertained that, the existing controller was not able to maintain the synchronism of the system during the above said faults but the proposed controller maintains the synchronism. REFERENCES 1. Gundala Srinivasa Rao, Dr. A.Srujana, Transient Stability Improvement of Multi-machine Power System Using Fuzzy Controlled TCSC, International Journal of Advancements in Research & Technology, vol. 1, Issue 2, July 2012. 2. Y. Cao and O.P. Malik, A nonlinear variable structure stabilizer for power system, IEEE Trans. Energy Convers., vol. 9, no. 3, pp. 489-495, Sep. 1994. 3. F.K. Mak, Design of nonlinear generator excitors using differential geometric control theories, in Proc. 31st IEEE conf. Decision Control, Tuscon, AZ, 1992, pp. 1149-1153. 4. C. Zhu, R. Zhou and Y. Wang, A new nonlinear voltage controller for power systems, Int. J. Elect. Power Energy Sys., vol. 19, pp. 19-27, 1997. 5. J.W.. Chapman, M.D. Ilic, C.A. King, L. Eng, and H. Kaufman, Stabilizing a multimachine power system via decentralized feedback linearizing excitation control, IEEE Trans. Power Syst., vol. 8, no. 3, pp. 830-839, Aug. 1993. 6. Edward Wilson Kimbark, Power System Stability, vol. III, February 1995, Wiley-IEEE Press. 7. Carlos E. Ugalde-Loo, Enrique Acha, Eduardo Licéaga-Castro, Multimachine power system state space modelling for small-signal stability assessments,science Direct, Applied Mathematical Modelling vol. 37, 2013. 8. P.Kundur, Power system stability and control McGraw Hill Inc. 1993. 9. E.V.Larsen and D.A.Swann, Applying Power System Stabilizers Part-I: General Concepts, IEEE Transactions on Power Apparatus and Systems, vol.pas-100, no. 6, 1981. 10. Oleg Soukhanov, Igor Yadykin and Dmitry Novitsky, Method of steady-state stability analysisin large electrical power systems 17th Power Systems Computation Conference, Stockholm Sweden, August 2011. 11. Jawad Talaq, Optimal power system stabilizers for multi machine systems, Science Direct, Electrical Power and Energy Systems, vol. 43, 2012.