EXCITATION STABILIZERS FOR REDUCING SENSITIVITY OF SYNCHRONOUS MACHINES CONNECTED TO POWER SYSTEM

Abstract

Due to present-day extensive growth of electric power systems, the generators are required to operate satisfactorily under different operating conditions. Moreover, with the growing number of instances of dynamic oscillations in the power systems, it has been found necessary to improve the system damping. Essentially, the problem is one of improving the dynamic and transient performance of a synchronous machine over a wide range of operating conditions. In recent years different methods have been proposed for the control of synchronous machine through excitation and governor system using pole place ment techniques and optimal control theory. However, the existing pole placement techniques do not consider the sensitivity criterion while a few methods in optimalcontrol theory with sensitivity are available for power system applications. The drawback of these controllers is that they are designed at a particular operating point and their performance deteriorates with the change in operating Conditions. The suitability of such controllers for practical schemes will be proved only when these controllers obtained for a particular operating point are suitable for other widely different operating condi tions. Hence the present work is carried out to find suitable controllers which are useful over a wide range of operating conditions. The excitation stabilizers developed

in this work, using dominant-root approach, are found to have better dynamic and transient performance compared to the conventional excitation end optimal controllers for different operating conditions. The optimal sensitive stabilizer developed in this work using sensitivity cri terion, stabilizes the system for changes in operating condition as compared to the conventional excitation control. Further, non-linear gain optimal excitation stabilizers developed here are found to have better dynamic and transient performance as compared to those of conventional excitation control, standard optimal con trol or even sensitive optimal control. The approaches considered here to improve the response of synchronous machine connected to power system are (i) Dominant-root approach with sensitivity (ii) opti mal control with sensitivity and (iii) non-linear gain optimal controller. The first method aims at the design of a controller so as to assign, the overall system transfer function a cer tain number of dominant poles and the rest of the poles are placed far-off. This dominant configuration is nearly fixed over a wide range of operating conditions. This requires to find out the transfer functions at various operating points. State variable approach is used to find out the transfer functions of the machine. Two different methods

suggested using this technique are (a) single-input/singleoutput (b) single-input/multiple-output. In single-input/single-output case, different power system models and cases are considered. A synchronous machine with exciter connected to infinite bus through a transmission line is considered. For this model the dynamic stabilizer is designed using dominant root approach and the dynamic stability is found out for different operatingconditions. It is found to have better dynamic performance compared to the natural system.Even though, the stabilizer is designed from linearized model, it is studied for tran sient condition on non-linear machine model with realistic restrictions and it is found to have better transient per formance as expected. Then the governor loop is also included for the transient study and It is observed to have marginal improvement in the performance of the machine. This approach is further extended to the cases of synchronous machine with fast exciter neglecting its time constant and governor loop with single time constant and doubly-excited synchronous machine. In both these cases the dynamic stability study is carried out and it is found to have improved dynamic performance as compared to the natural system. In these cases the terminal voltage signal is used for feedback. The above method is extended to consider the rotor angle output for the design of dynamic stabilizer to improve

the performance of the machine. Different power system models of synchronous machine with and without exciter time constant are considered for the rotor feedback case. Dynamic and transient stabilit2r studies are carried out on these models for different operating conditions and it is found to have better performance compared to the natural system. The digital simulation results of the model without exciter time constant are compared with the experimental results of the optimal controller designed by Elmctwally et. al.[64jand it is observed that the performance of the proposed stabilizer is better particularly in the terminal voltage recovery and at leading power factor operation. If more than one output is available for feedback purposes then the minimum order of the compensator can be appreciably reduced. This is shown in two-output case where two signals, one the terminal voltage and the other field voltage signal are used for the design of the dynamic controller acting as a stabilizer in the excitation system. It is observed that the performance is improved as compared to the natural system. It is found that the order of the compensator is reduced by one. In the case of optimal control with sensitivity the feedback gains are chosen corresponding to low sensi tivity with respect to a parameter of the system. It is noted that the system settles down quickly corresponding

to the low sensitivity design. The non-linear gain approach developed in this work gives better performance over wide variations .in the operating conditions. This method is based upon expanding the gain matrix in Taylor's series expansion in the powers of the system variable. This leads to a feedback controller with gain elements which are adjusted as the variable varies and thus obtains the desired response. The variable chosen is the load angle 6. This controller behaves as an optimal controller at the nominal value and near optimal at other operating points. To study the performance of this proposed stabilizer, a system consisting of a synchronous machine connected to an infinite bus bar is considered. Dynamic and transient stability studios are carried out on this model for different operating conditions. The digital simulation results are compared with the experimental results of sensitive optimal controller[64]and it is seen that the performance of the proposed stabilizer is better. Then exciter and governor loops are included in the above model. It is observed that there is a marked improvement in the performance compared to sensitive optimal controller or standard optimal controller. This method is extended to cover the case of doublyexcited synchronous machine. It is found that better dynamic and transient performances are obtained with the proposed

stabilizers provided in the voltage, angle and governor loops The non-linear gain approach is generalized for a number of system variables and then applied to three-bus power system consisting of two generators and loads. Dynamic stability is carried out on this system at different load conditions and the results are compared with the natural system as well as with the standard optimal controller and it is observed that the performance is better. Thus the controller designed by dominant-root approach can give better results than those of pole placement methods or optimal control over a wide range of operating conditions. Further it does not require all the states to be fed back. The optimal stabilizer with sensitivity consi deration stabilizes the system at a faster rate as compared to the natural system. The non-linear gain optimal controller also improves the system performance over a wide range of operating conditions as compared to the optimal controller or sensitive optimal controller. This method is simpler to implement than that proposed by Galiana and Clavitsch[30] and can be successfully used for higher order systems.