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For the generator excitation control system which is equipped with static var compensator (SVC) and unknown parameters, a novel adaptive dynamic surface control scheme is proposed based on neural network and tracking error transformed function with the following features: (1) the transformation of the excitation generator model to the linear systems is omitted; (2) the prespecified performance of the tracking error can be guaranteed by combining with the tracking error transformed function; (3) the computational burden is greatly reduced by estimating the norm of the weighted vector of neural network instead of the weighted vector itself; therefore, it is more suitable for the real time control; and (4) the explosion of complicity problem inherent in the backstepping control can be eliminated. It is proved that the new scheme can make the system semiglobally uniformly ultimately bounded. Simulation results show the effectiveness of this control scheme.

With the development of power system, the requirements of the load are increasing. However, the ability of the transmission network is limited and the electric power system has gradually reached its operating limit; the world power systems tend to extend power grid scale and develop larger power system. However, the power systems are more likely to encounter some problems such as oscillations and complex nonlinear phenomena due to the extension of power grid scale and some emergencies. Therefore, ways of maintaining the reliability and stability of power system are attracting more and more research interest [

The most common method for designing generator excitation system controller is the direct-feedback-linearization, which transforms the nonlinear model into a linear one by some mathematical ways. However, it is only effective to the system when special conditions are satisfied [

Motivated by the previous work ([

the tracking error of the power angle and voltage at the SVC can be transformed to an arbitrarily prespecified performance by an error transformed function;

the neural network based adaptive dynamic surface controller is designed without doing any linearization to the excitation generator model. Therefore, the design procedures and the final control law are greatly simplified and the control accuracy is improved;

by using the neural network, the structure and the parameters of the control system can be totally unknown;

by estimating the norm of the weighted vector of neural network instead of the weighted vector itself, the computational burden is greatly reduced and it is more suitable for the real time control.

This paper is organized as follows. In Section

Assume that the SVC device is installed in a single-machine infinite-bus system; the structure and the equivalent circuit diagram are shown in Figure

Single machine infinite bus system with SVC.

To proceed, the following assumptions are made.

Ignoring the dynamic process of rapid excitation equipment means the control voltage

The mechanical power of generators remains unchanged in transient stability process; that is,

Then, the mathematical model of the generator excitation control system equipped with SVC can be described as follows [

When the system encounters the external disturbances, the stability of the power angle and SVC access point voltage can be effectively improved by combining the regulation of SVC with generator-excitation adjustment. In this paper, we take increment of the power angle and accessing point voltage as the output value of the system to design our adaptive dynamic surface controller; that is,

Based on the above descriptions, let

Now, we can design our adaptive dynamic surface control law of the power system based on the following assumptions.

The value of

The reference signal

Assumptions

In general, the neural network is a multi-input single-output system [

RBFNN is a universal approximator in the sense that, given any real continuous function

We define the tracking error:

As (

Note that the case

According to the mathematical model of the generator excitation system that is shown in (

Let the first surface error and the tracking error as (

Consider the following quadratic function:

In order to avoid “differential explosion,” the new variable

Define the second surface error:

Consider the following quadratic function:

Define the third surface error:

Similarly, we design controller for the voltage subsystem (

We emphasize our dynamic surface control scheme which, combined with tracking error transformed function (

This section will conduct stability analysis for dynamic surface control scheme on the generator excitation system. Although the control law is simple, the stability analysis is relatively complex due to the introduction of first-order low-pass filters. For the first subsystem in (

Consider the closed-loop control system composed by object (

The derivative of

Similar to the second subsystems, we substitute (

As a result, all the signals such as

The single machine infinite bus power system with SVC is shown in Figures

The equivalent circuit diagram.

System parameters are

In the simulation the initial values of the states are

We suppose that three-phase short-circuit occurred on the terminal of the line at

Tracking error and the performance function.

The actual control law

The actual voltage control law

The rotor angle

The rotor speed

The transient EMF

The estimated norm of the weighted vector

The estimated norm of the weighted vector

The estimated norm of the weighted vector

The access point voltage increment

The comparison of our NN based dynamic surface control scheme and backstepping.

The controllers that have been proposed in [

This paper proposed a novel neural network and tracking error transformed function based on adaptive dynamic surface control scheme for the generator excitation control system which is equipped with SVC. In this scheme, both the designing procedures and the control law are simplified because it does not need to make any transformation to the excitation generator model. The prespecified tracking performance can be guaranteed by using the tracking error transformed function. The norm of the weighted vector of neural network is estimated which replaces the estimation of the weighted vector itself; therefore, the computational burden is greatly reduced. Also, the explosion of complicity problem inherent in the backstepping control can be eliminated. It is proved that the new scheme can make the system semiglobally uniformly ultimately bounded.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The research is supported by Natural Science Foundation (no. 61304015), China Postdoctoral Science Foundation (no. 2013M540839), Outstanding Young Scholar Project of Jilin City (no. 2013625002), “Twelfth Five Year” Scientific Research Plan of Jilin Province (no. [2014]111), and Nature Science Foundation of Jilin Province (no. 20140101059).