Variable structure control for power systems stabilization

https://doi.org/10.1016/j.ijepes.2009.06.017Get rights and content

Abstract

The application of variable structure control (VSC) for power systems stabilization is studied in this paper. It is the application, aspects and constraints of VSC which are of particular interest. A variable structure control methodology has been proposed for power systems stabilization. The method is implemented using thyristor controlled series compensators. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller. The results demonstrate the effectiveness of the methodology proposed as an useful tool to suppress the oscillations in power systems.

Introduction

Variable structure control has its roots in relays and bang–bang control theory. The minimum time control problem can be solved for simple systems using the bang–bang control law as discussed in Refs. [1], [2].

Time-optimal control is of practical importance in providing a design of nonlinear feedback controls to damp machine swings. The case of time-optimal control of series capacitors requiring multiple switchings is investigated in Ref. [3], where it is demonstrated, for a single machine infinite bus system, and for an interconnected system.

Energy functions were developed for assessment of stability of multimachine power systems. In Ref. [4] is developed a switching control strategy for suppression of oscillations of power systems. This strategy is based on energy function using shunt and series compensators for lossy multimachine power systems. The switching control design is on the basis of maximizing the convergence rate of an energy function. Fast multimode damping and the monotonic convergence of the energy is demonstrated on a three machine power system.

A new design approach for bang–bang sliding control of a class of single –input bilinear systems is introduced in Ref. [5]. The sliding function is determined by the pole-assignment-based method for linear time-invariant systems.

In Ref. [6] a nonlinear, variable structure control theory is employed for series capacitor control and braking resistor control to improve the transient stability of a single machine infinite-bus system.

Variable structure control techniques with optimal sliding modes have been used to improve the dynamic stability of a synchronous machine-connected to an infinite bus [7], where the performance of the variable structure controller has been investigated and also compared with that of a conventional power system stabilizer and a linear optimal controller.

A technique for designing variable structure controllers to damp out multimodal oscillations in a multimachine power system consisting of three machines, is presented in Ref. [8], where three variable structure controllers are applied. The design was based on linearised dynamic model of a single generator supplying an infinite bus through an external impedance.

In Ref. [9] is designed a nonlinear observer-based excitation controller for power system comprising a single synchronous generator connected to an infinite bus with local load. The controller proposed is based on the using first singular perturbation systems concepts and then sliding mode control technique combining with block control principle.

This paper develops the design of nonlinear controllers to suppress the postfault oscillations in power system. A variable structure control methodology for power systems stabilization is developed. The method is implemented using thyristor controlled series element changing the effective line inductance. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller.

Section snippets

Variable structure control (VSC)

The variable structure control (VSC) is a high speed switching feedback control, i.e. the control on the feedback path switches between two values in accordance with a defined rule. The variable structure control provides a robust and efficient means for the control of nonlinear plants. Variable structure control theory started with the general principles in relays and bang–bang control. At the present time control engineers are interested in the practical implementation of variable structure

Multimachine power system

Consider the multimachine power system presented in Fig. 2.

In a multimachine power system, the output and hence the accelerating power of each machine depend upon the angular positions of all the machines of the system. A multimachine power system can be represented as in Ref. [12]:Mid2δidt2+Didδidt=Pi-j=1;jim(EiEjBijsinδij+EiEjGijcosδij)

for i = 1, 2,…m

where:Pi=Pmi-Ei2Gii

The standard simplifying assumptions are to neglecting damping and to consider that the transfer conductances are negligible.

Boundary lines of sliding mode

For the variable structure controller 1 we have:S12S˙12<0that is:P1M1S12-E1E2(X12+εu12)1M1+1M2sinδ12S12-E1E3M1(X13+εu13)sinδ13S12-P2M2S12+E2E3M2X23sinδ23S12+λδ˙12S12<0

The existence region S12S˙12<0, is therefore delimited by two lines that mark the limits of the region, which are obtained by setting u12=0,u13=0 and u12=1,u13=1, respectively in the Eq. (38), such that S˙12=0, the switching line S12 = 0 intersects the boundary lines.

The boundary lines 1, 2 are given by the mathematical expressions:

Asymptotic stability towards the region of existence

The reachability of the existence region of the sliding mode is guaranteed for a finite region of initial conditions. Auxiliary controls are required to ensure the system is driven close enough to the origin so that the conditions for sliding will be met. One option for the auxiliary control outside the sliding region is to use a velocity feedback controller. So u12 is controlled such that the term:sin(δ1-δ2)δ˙12X12+u12is as negative as possible.

When the system trajectories intersects the

Simulation results

The multimachine power system is shown in Fig. 2. Where for simulation studies of the variable structure control for the multimachine power system model (45), the power system data are given in Table 1.

The sampling rate was set to 10 ms to model that fact that the thyristor firing can only occur once every 10 ms for a 50 Hz power system. The values of Xij = 1.0 and ɛ = 0.3 corresponding to effective line reactances varying from 1.0 to 1.3 p.u.

The steady state operating point uij = 0 is chosen to give

Discussion

The oscillations damping of the multimachine power system can be improved with a steep switching line. Outside of the reachability region it is desirable to damp oscillations rather than slide. In that case the switching line needs to be more horizontal near the origin that is close to the velocity equal zero line. Outside of the sliding convergence region the controls have a significant section of velocity feedback and therefore expected is good damping contribution that is because suggesting

Conclusions

The application of variable structure control for power systems stabilization was studied in this paper. A variable structure control methodology has been proposed for power systems stabilization. The method is implemented using thyristor controlled series element changing the effective line inductance. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller.

The results demonstrate the

References (13)

  • J. Fernández-Vargas et al.

    Switching control strategy for power systems with losses

    Int J Elect Power Energy Syst

    (2007)
  • J. Cabrera-Vazquez et al.

    Robust controller for synchronous generator with local load via VSC

    Int J Elect Power Energy Syst

    (2007)
  • W.L. Brogan

    Modern control theory

    (1985)
  • Barnett S, Cameron RG. Introduction to mathematical control theory, Oxford applied mathematics and computing science...
  • J. Chang et al.

    Time-optimal control of power systems requiring multiple switchings of series capacitors

    IEEE Trans Power Syst

    (1998)
  • Y.P. Chen et al.

    Stability analysis and bang–bang sliding control of a class of single-input bilinear systems

    IEEE Trans Automat Contr

    (2000)
There are more references available in the full text version of this article.

Cited by (37)

  • PID controller design for hydraulic turbine based on sensitivity margin specifications

    2014, International Journal of Electrical Power and Energy Systems
  • Enhanced design of an indirect adaptive fuzzy sliding mode power system stabilizer for multi-machine power systems

    2014, International Journal of Electrical Power and Energy Systems
    Citation Excerpt :

    On the other hand, it is well known that robust control provides an effective approach to deal with uncertainties introduced by variations of system parameters as well as changes of operating conditions. Among many techniques available in the control arsenal, sliding mode control has been reported as one of the most effective control methodologies for nonlinear power system applications [18–22] in improving power system stability due to its invariance properties and robustness. In this paper, following similar approach in [23,24], a new indirect adaptive fuzzy sliding mode stabilizer (AFSMPSS) is designed for enhancing oscillations damping in nonlinear multi-machine power system using nonlinear models while many papers use linear model with perfectly known parameters as [25,26] or address single machine systems [27,28].

  • Decentralized coordinated control for large power system based on transient stability assessment

    2013, International Journal of Electrical Power and Energy Systems
    Citation Excerpt :

    Many nonlinear control methods also have been proposed in controller design for the large power systems [21–25]. But the nonlinear control schemes are so complicated that they are unsuitable as well as unfeasible for real applications [26–28]. For improving transient stability of large power systems, taking into account feasibility and effectiveness of control, in this paper, much attention has been paid to both design scheme and control method when we design a decentralized coordinated controller.

  • A practical design sliding mode controller for DC-DC converter based on control parameters optimization using assigned poles associate to genetic algorithm

    2013, International Journal of Electrical Power and Energy Systems
    Citation Excerpt :

    The multiple control structures are designed so that trajectories always move toward a switching condition, and hence the ultimate trajectory will not exist entirely within one control structure. Instead, the ultimate trajectory will slide along the boundaries of the control structures [2]. The motion of the system as it slides along these boundaries is called a sliding mode.

  • Perturb and Observe MPPT algorithm with a current controller based on the sliding mode

    2013, International Journal of Electrical Power and Energy Systems
    Citation Excerpt :

    In this paper the low frequency-ripple mitigation has been achieved by using the sliding mode control (SMC). Such a non-linear control technique represents an effective control method which provides extreme robustness and fast response not only in applications involving switching converters [6,7] but also for more complex power electronic systems [8–10]. It is based on the implementation of a control equation which forces the system’s variables to stay on a selected surface called “sliding surface”.

  • Dynamic soft variable structure control of singular systems

    2012, Communications in Nonlinear Science and Numerical Simulation
    Citation Excerpt :

    In recent years, the researches of VSC theory have been developed into time-delay systems [19,20], stochastic systems [21,22], chaotic systems [23,24] and other complex systems. VSC has been successfully applied to a wide variety of practical systems, such as robot control [25], economic systems [26], satellite attitude control [27] and power systems [28]. VSC is based mainly on the arrival conditions of sliding modes, guaranteeing the motion trajectory of the control systems from arbitrary initial state onto the switching plane in finite time according to the arrival conditions of sliding modes, then VSC is designed by applying the reaching law, which is also named to be sliding mode VSC.

View all citing articles on Scopus
View full text