International Journal of Electrical Power & Energy Systems
An improved direct feedback linearization technique for transient stability enhancement and voltage regulation of power generators
Introduction
Operating conditions of modern large-scale power systems are continuously varying in order to satisfy different load demands. Power system stabilization has been dealt with for many years by both control and power systems communities. The goal is to design controllers for synchronous generators such that they provide within stringent tolerances, an uninterrupted supply of power at a specific frequency and voltage to the loads present in power systems. On the other hand, control system teams develop quite more complicated algorithms which may be difficult to implement in the industry. This justifies the fact that automatic voltage regulation and power system stabilizer (AVR/PSS) have been extensively used in modern power systems to enhance system damping and to improve the overall system stability [1], [2], [3], [4]. But since the AVR/PSS are designed separately, both voltage regulation and system stability enhancement is difficult to achieve simultaneously [4]. Moreover, the controllers are designed according to approximately linearized power systems models which are dependent on certain operating conditions and will suffer from performance degeneracy when the operating condition changes [5]. In [4], internal model control (IMC) theory is used to propose a robust coordinated AVR/PSS which allows an effective trade-off between voltage regulation and damping improvement but the problem of linearized models remains.
In order to improve power system stability and performance, nonlinear excitation controllers using feedback linearization technique have been proposed [5], [6], [7], [8]. The problem of the direct feedback linearization technique (DFL) controller is that it cannot achieve voltage regulation and system stability simultaneously [8]. To overcome this problem, switching of different feedback control laws are proposed in [7]. But the switching of different feedback control laws may cause a high-frequency disturbance to power systems. Another solution to this voltage regulation problem is to use the DFL technique and robust control theory [8].
Some recent results can be found in [9], [10], [11], [12], [13], [14], [15], [16]. In [9], a finite-element model of a turbine-generator infinite-busbar system is used to assess the robustness and performance capabilities of a PSS/AVR scheme. The numerical model incorporates simulation of rotor motion, iron magnetic nonlinearity and eddy currents in the solid rotors of turbine generators. In order to circumvent the lack of real power systems, finite-element models are suitable tools of validation of new control designs under nearly true conditions that exist in real plants. It is shown that robust control designs, obtained with small order models, keep their good performance characteristics when applied to the actual machine. In [10], an new passivity-based controller design approach for the excitation control of synchronous generators is investigated and it is shown that the proposed method can enlarge both the estimates and the actual domain of attraction, thus increases critical clearing time for faults. Unfortunately, the passive output is a nonlinear function of the system states and the commonly unknown operating point makes unfeasible the direct implementation of passive controllers [13]. In [11], an intelligent based LQR controller design has been developed for power system stabilization but the voltage regulation has not been considered. In [12], an interesting method based on nonlinear feedback linearization is proposed for transient stabilization and voltage regulation of power generators with unknown parameters. The main drawback of the latter method is that, it requires the power angle reference signal to be at least and this requirement may be difficult to fulfill in practice. In addition, a method/guideline for the selection of the controller parameters has not been described. In [13], an excitation controller for a single generator based on modern multi-loop design methodology is presented. It has been shown that the proposed two-loop excitation control scheme enlarges the potential region of attraction of the operating point. Therefore, this approach is able to provide local damping of swing oscillations and asymptotic terminal voltage regulation about a given setpoint. In [14], a generalized neuron-based PSS and adaptive PSS have been used for power systems transient stabilization but the problem of voltage regulation has not been addressed. In [15], an output feedback controller is proposed to enhance the transient stability of nonlinear multimachine power systems using high-order sliding-mode technique and robust high-order sliding-mode differentiator. But in this latter approach, the voltage regulation problem has not been investigated and the implementation of the control law may be difficult in practice since the switching of the control law may cause a high-frequency disturbance to power systems. In [16], Immersion and Invariance control strategy has been applied to design a nonlinear controller that provides asymptotic stabilization of a single machine infinite bus system using a controllable series capacitor. But in this approach, the problems of voltage regulation and real-time experiment have not been addressed.
Moreover, most of control algorithms assume that the mechanical power and power angle are available by measurements. For the measurement of power angle, the main problem is the detection of the rotor position. Various techniques have been used [17], [18], [19], [20], [21]. The power angle instrument presented in [17], [18], uses a toothed gear mounted on the rotor shaft, with a magnetic type toothed gear pickup to detect the rotor position. The technique described in [19], uses an optical encoder to detect the rotor position. But in some cases, mounting a toothed gear on the rotor shaft can be very complicated, and coupling an encoder is almost impossible [21]. An approach to power angle measurement discussed in [20] is based on a photoelectric sensor installed on the stator to detect the rotor position and has been tested on a small laboratory machine. A new approach discussed in [21], was developed for power angle determination of the salient pole synchronous machine and is based on air gap measurements. However, the value obtained under steady-state condition using this technique, is corrupted with periodical oscillations which can affect the accuracy of the power angle measurement. The zero phase filter [22] can be used to eliminate these oscillations in order to improve the accuracy but this technique is only convenient for off-line applications. Moreover, the presence of these sensors increases the cost and complexity of the control system and reduces the robustness of the overall system.
In addition, most of the control systems developed consider that the operating points are exactly known and are more complicated and may be difficult to implement in real-time. While most of the above control algorithms have been successfully proven in numerical simulation, there is still a lack of experimental results which are the only way to verify the effectiveness of those methods. These are the main motivations of the proposed nonlinear control algorithm in this paper.
Our main goal is to propose an improved DFL adaptive control algorithm which can achieve both voltage regulation and transient stability simultaneously and can be easily implementable in real-time by using the works of [12], [23]. The third-order nonlinear model for power generator [24] is used and the power angle and mechanical power input are not assumed to be available. The main advantage of the proposed method is that when an equivalent linear system is obtained, a variety of proven linear-control design techniques can be applied to complete the control design.
In Section 2, the dynamic model of the power system is described as well as the problem statement. The design procedure of the improved direct feedback linearization technique is presented in Section 3. Experimental results are presented in Section 4 to illustrate the performance of the proposed control scheme and its robustness properties compared to those of AVR/PSS scheme. Finally, in Section 5, some concluding remarks end the paper.
Section snippets
Dynamic model description
Consider a single-machine infinite-bus (SMIB) power system as shown in Fig. 1. The dynamics of this single-machine infinite-bus power system are given by the following third-order model [2], [25], [24]which is valid over the region defined by . The first two equations represent the mechanical dynamics of the power generator and the third equation gives the electrical
Actual DFL technique
In this section, we describe the DFL technique under the assumption that the power angle and the mechanical power input are available. If we letwhere , the second equation of (1) becomes
Thus the third model (1) has been linearized. The mapping (5) is invertible over the normal working region . The DFL compensation law can be deduced from (5) as follows:
Experimental results
The experimental setup is illustrated by the block diagram of Fig. 2 which includes a development system DSP1103, an input/output electronics board (for analog/digital conversions) and a Personal Computer (PC). This PC is used to program the DSP, to store and display experimental data.
The three phase electrical network is the local “Electricté De France (EDF)” low voltage network (136 V/50 Hz). The synchronous generator connected to EDF network whose data are reported in Appendix B has been used.
Conclusion
In this paper, a simple improved direct feedback linearization design method for transient stability and voltage regulation of power systems has been described. Starting with the classical direct feedback linearization technique currently applied to power systems, an adaptive nonlinear excitation control of synchronous generators has been proposed. This method is based on a standard third-order model of a synchronous generator which requires only information about the physical available
Acknowledgment
The main part of the experimental setup used in this work has been supported by the “Département Énergie, École Supérieure d’Électricité, Gif-sur-Yvette, Paris, France”.
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