Elsevier

European Journal of Control

Volume 57, January 2021, Pages 172-178
European Journal of Control

Application of a novel adaptive sliding mode control method to the load frequency control

https://doi.org/10.1016/j.ejcon.2020.03.007Get rights and content

Abstract

In this paper a novel adaptive sliding mode control method has been designed and applied to the load frequency control. Firstly, a novel adaptive sliding mode control method is designed. Secondly, the stability of this method has been proved mathematically. Finally, one numerical simulation example is presented to verify the effectiveness of the proposed control scheme. At the same time, the proposed new adaptive sliding mode control method is compared with the classical adaptive sliding mode control method. From the simulation results, it is confirmed the validity of the proposed adaptive sliding mode control method in terms of external disturbances and parameter variation. It is also verified the superiority of the proposed adaptive sliding mode control method in terms of chattering, overshoot and response time in comparison with classical adaptive sliding mode control method.

Introduction

As an advanced control method, sliding mode control is a kind of robust control method. The sliding mode control is composed of equivalent control which maintains the trajectories on the sliding surface, and variable structure control which forces the trajectories reach on the sliding surface. Sliding mode control method has been applied to many systems, such as nonlinear system [2], [7], [15], [22], [26], Markovian system [19], [29], [32], [33], discrete system [10], [11], [21], [23], [30], switched system [31] and fuzzy system [25], [27]. Also it has been applied to the power electronics [13], [16], [24], power system [3], [5], [20] and DC motor [6], [8], [28]. In real applications, sliding mode control has been applied to the power electronics successfully.

Although traditional sliding mode control has the above merit, it has the drawback of chattering handling [18]. The main drawback of sliding mode control method is the chattering phenomenon, which is provoked by a high-frequency switching nature in the presence of unmodelled dynamics. High order sliding mode control can attenuate the chattering effect by increasing the input-output degree. However, sliding mode control laws all contain signum function often pre-multiplied by a gain, so the chattering is not totally eliminated even by increasing the relative degree. Usually during the design process, conservative upper bounds, which often are not exactly known, are used to guarantee that sliding will take place, but this conservatism yields increasing the control gains and alleviates chattering associated with the unmodelled dynamics. Also the traditional sliding mode control method can not handle the parameter variation in the process and external disturbance very well. These disadvantages have inspired research in what could be described as adaptive sliding mode control method. Adaptive control method has the ability of handling parameter variation [4], [9], [12], [17]. In [9], the adaptive control method has the computational complexity. In [17], the adaptive sliding mode control needs the measurement. In [12], the adaptive control method is hard to design. Adaptive control method can combine the robustness of sliding mode control with tracking capability. In order to overcome these disadvantages, we design a novel adaptive sliding mode control method, which has the benefits of resisting unknown external load disturbance and parameter variation, but also can attenuate the chattering effect. In order to prove this, one numerical example is designed and simulated. The example is the application of this method to the load frequency control based on different areas interconnected power system with non-reheat turbine.

The contribution of this paper is as follows. Firstly, a novel adaptive sliding mode control method is proposed which can be treated as resisting unmodelled dynamics, parameter variation and external disturbance. It also has the benefit of attenuating chattering effect. Secondly, this new method has been applied to the load frequency control based on different areas power system. Finally, the chattering effect, response time and overshoot can be more decreased by using the proposed adaptive sliding mode control method, which confirms the superiority of this new method comparing to the traditional adaptive sliding mode control method [1], [14]. Additionally, the proposed method is robust to the parameter variations.

The remaining of this paper is listed as follows. The proposed adaptive sliding mode control method is designed and the stability of this method is analyzed at the same time in Section II. The load frequency control based on different areas power system by the proposed adaptive control method is designed in Section III. The simulation results of the example with the new adaptive sliding mode control method is presented in Section IV and compared with the classical adaptive sliding mode control method. The concluding remarks are made finally in Section V.

Section snippets

A novel adaptive sliding mode controller design and stability analysis

As an advanced control method, sliding mode control method has wide application in many systems, which has the benefits of resisting parameter variation and load disturbance. The main purpose of sliding mode control is to let the trajectory reach and maintain on the sliding surface.

Now consider a nonlinear system given byz(n)=f(z,z˙,z¨,z,z(n1),t)+b(z,t)u(t)where z(t) is the state vector, f(z, t) and b(z, t) are nonlinear functions, u(t) is the control input, n indicates the highest order of

The LFC design based on the new adaptive sliding mode control method

In this section, the novel adaptive sliding mode control method has been applied to the load frequency control based on different areas interconnected power system. The interconnected power system contains nonlinearities.

The load frequency control is an important factor in the power system, it reflects the stability of the power system and influences the quality of the power system. Frequency deviation will cause the short life of the appliance or in more serious case, it will cause the

Simulation Results

The simulation is based on the different areas interconnected power system with non-reheat turbine by the proposed adaptive sliding mode control method and compared with the traditional adaptive sliding mode control method [1]. The system parameters are presented in the appendix.

The simulation is firstly based on two areas system with non-reheat turbine. In Case C1, a step load disturbance is set as 0.008p.u. at t=2s in the first power control area, a step load disturbance is set as 0.003p.u.

Conclusion

In this paper, a novel adaptive sliding mode control problem as well as studied the convergence of this method have been addressed. The new method has been used to control the load frequency control based on different areas power system with non-reheat turbine. Through the simulation results, it is clear to see that the desired results have been obtained under different load disturbances and parameter variations. However, there exist some limitations due to the computational complexity and the

Compliance with Ethical Standards

Conflict of Interest: The authors declare that they have no conflict of interest.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (61803102).

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