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Mathematical Problems in Engineering
Volume 2017, Article ID 6271341, 16 pages
https://doi.org/10.1155/2017/6271341
Research Article

Neural Adaptive Decentralized Coordinated Control with Fault-Tolerant Capability for DFIGs under Stochastic Disturbances

1School of Automation Engineering, Northeast Electric Power University, Jilin 132012, China
2School of Economics and Management, Northeast Electric Power University, Jilin 132012, China
3State Key Laboratory of Alternate Electric Power System with Renewable Power Source, North China Electric Power University, Beijing 102206, China

Correspondence should be addressed to Hong Cao; nc.ude.upecn@hc

Received 9 March 2017; Accepted 25 July 2017; Published 10 October 2017

Academic Editor: Mohammad D. Aliyu

Copyright © 2017 Xiao-ming Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

At present, most methodologies proposed to control over double fed induction generators (DFIGs) are based on single machine model, where the interactions from network have been neglected. Considering this, this paper proposes a decentralized coordinated control of DFIG based on the neural interaction measurement observer. An artificial neural network is employed to approximate the nonlinear model of DFIG, and the approximation error due to neural approximation has been considered. A robust stabilization technique is also proposed to override the effect of approximation error. A controller and a controller are employed to achieve specified engineering purposes, respectively. Then, the controller design is formulated as a mixed optimization with constrains of regional pole placement and proportional plus integral (PI) structure, which can be solved easily by using linear matrix inequality (LMI) technology. The results of simulations are presented and discussed, which show the capabilities of DFIG with the proposed control strategy to fault-tolerant control of the maximum power point tracking (MPPT) under slight sensor faults, low voltage ride-through (LVRT), and its contribution to power system transient stability support.

1. Introduction

During the last decade, wind power has shown world’s fastest growing rate compared to any other electric power generations, which causes the share of wind power to reach a considerable level [1]. DFIG is becoming the dominant type used in wind farms (WFs) for its maximizing wind energy conversion and flexible control to network support [2]. For ensuring that DFIG is integrated into the power network reliably and efficiently, it is necessary to provide DFIGs with suitable control strategies.

Power system is a geographically extensive large-scale system, and its controller design is commonly based on decentralized approach which only depends on local signals [35]. However, this simple approach reduces the controller capability and even leads to stability problems [6]. Considering this, a few of decentralized coordinated control strategies of power system have been proposed [711]. A hierarchical decentralized coordinated control strategy is proposed to control the excitation system of synchronous generator (SG), where the interaction terms are considered as bounded disturbances which are suppressed by a controller [8]. A direct feedback linearization based decentralized coordinated control of excitation and steam valve is proposed, where the upper bound of interaction terms is estimated [9]. A multiagent system based strategy is also used to control a multimachine power system [10, 11]. According methodologies used, decentralized coordinated control strategies of power system can be divided into two types, with and without communication system support. For the first type, the interaction terms are commonly considered as bounded disturbances which are completely suppressed, where the involved coordinated information has been neglected, while the second method needs communication system support, which may bring new stability problems caused by communication time delay and communication system fault.

It is generally recognized that mode decomposition based decentralized coordinated control strategy is more suitable for control over power systems, where the interaction term is modelled as a coordinated signal [12, 13]. This allows the system-wide state feedback control strategy to be replaced by using local state feedback control, which is a desired performance for power system controller design. This paper proposes a neural observer based decentralized coordinated control of DFIG, where a neural controller is used to compute the weightings. The mode decomposition technology is used to modelling power system and a mixed suboptimal control with regional pole placement and PI structure is employed to control a DFIG-based wind turbine. More concretely, the main contribution consists of the following aspects:(i)The mode decomposition is used to modelling power system, and the interaction measurement model of DFIG is introduced (where interaction measurement term has been considered as a coordinated signal). An ANN-based weighting controller is proposed to approximate the nonlinear model of DFIG, which achieves a closed-loop nonlinear adaptive approximation.(ii)The neural observer is proposed to approximate the nonlinear model of DFIG, where the approximation error due to the proposed neural approximation has been considered. A robust stabilization technique is proposed to override the effect of approximation error.(iii)For improving the fault-tolerant capability, a controller is employed to cope with the slight faults represented by bounded stochastic disturbances, and a controller with PI structure is also employed to achieve specified engineering purposes. Then, the controller design is formulated as a mixed suboptimal problem with regional pole placement which is used to further improve damping performance.(iv)The proposed control strategy combines the merits of conventional PI control, robust stabilization control, and mixed optimization. Simulation results show that the proposed controller not only improves the MPPT control with fault-tolerant capability bus also enhances system damping and LVRT capability, which greatly improves power system transient stability.

The rest part of this paper is arranged as follows. The neural interaction measurement observer of DFIG is proposed in Section 2. In Section 3, the mixed control with regional pole placement based on the obtained interaction measurement model is proposed. In Section 4, simulation results are presented and discussed, which demonstrate the capabilities of the proposed control strategy to enhance MPPT performance under external disturbances and its contribution on power system transient stability support. Finally, the conclusions are drawn in the Section 5.

2. Neural Adaptive Interaction Measurement Observer of DFIG

The proposed control strategy shown in Figure 1 is comprised of two parts, the neural interaction measurement observer of DFIG and the mixed controller. The neural interaction measurement observer is established at chosen operating conditions by considering the interactions from network, and a neural weighting controller is proposed to compute the weightings according the approximation error. Based on the obtained observer, the controller and controller are designed separately for specified engineering purposes. Then, the controller design is formulated as a mixed suboptimal problem with the constrains of PI controller structure and regional pole placement, and it can be solved easily by using LMI technology.

Figure 1: Neural PI control scheme.
2.1. DFIG Model with Stochastic Disturbances

For obtaining a good balance between the accuracy and simplification, the th DFIG nonlinear model is chosen as a third-order model [15], where the stator dynamic has been neglected.Dynamic equations:Output equations:where, , , is the internal voltage of the th generator, is the angle between the and the -axis of the synchronous coordinates, is the angle of impedance , and is the number of generators of a multimachine power system.

According the above equations, the th DFIG nonlinear model with unmeasurable stochastic disturbances and can be written as the following compact form:where is the state variable, is the output variable, is the input signal (control vector), and and are the interaction terms from network.

2.2. Approximation Error Considered Interaction Measurement Observer

The published literatures [16, 17] extend the classical SG based interaction measurement modelling to DFIG field. The interaction measurement model of DFIG with a certain weighting method can be written as the following form, where the model bank is established at chosen operating points (Table 3) [16]:where and , denotes the interaction matrix from the th node to the th node, is the weighting for the th model in the model bank, and is the number of model.

The terms and are interaction measurement vectors, which represents interactions from network and can be regarded as coordinated signals. It is seen that and only depend on local signals, which allows system-wide state feedback control to be replaced by using local state feedback method.

By combining (4)-(5), the approximation error considered interaction measurement model of DFIG can be rewritten aswhere

In order to cope with the nonlinearity of DFIG, a neural observer is introduced to estimate the state variables of DFIG, where a neural controller is used to compute the weightings according the tracking error.

According (5) and (6), the observer can be written aswhere is the output of the ANN, is the observer output, is the state estimation error, and

2.3. Neural Adaptive Weighting Controller

The Elman ANN can be described as the following equations [18]:where , , and are weight matrixes of input layer, context unit, and output layer, respectively, and are the input and output vectors, respectively, and are the input and output vectors of hidden layer, respectively, is the output vector of context unit, (•) and (•) are activation functions of hidden layer and output layer, and is the self-feedback gain of context unit.

This paper employs an ANN controller shown in Figure 1 to approximate the nonlinear model of DFIG according the tracking error , where denotes the th interval. The objective of the ANN controller is defined aswhere and are weighting matrixes and is the output vector of the ANN (which is also the weightings represented by vector form).

The gradient descent method is employed to minimize the objective shown in (15). Then, the output layer weighting matrix of the ANN controller can be updated as follows:where is the learning rate and is the gradient of with respect to .where is the observer output and .

The term can be computed by the backpropagation method and no difficulty is involved in it. With a similar approach, the weighting matrixes of input layer and context unit can be updated. Then, the weighting vector (which is also the output of the Elman ANN) can be updated adaptively according the mathematic model of the Elman ANN shown in (14). It is noted that, for obtaining the reasonable weightings, the activation function of the output layer is a sigmoid function , so that . By normalizing , the reasonable weightings can be obtained as and .

It can be seen that the weighting is regulated adaptively according the tracking error via a closed-loop approach. Considering the nonlinearity of ANN, the proposed weighting controller can be regarded as an adaptive nonlinear controller, which provides a desired approximation performance.

3. Controller Design

In this paper, the controller of rotor-side converter is chosen as the same structure as the conventional PI controller for taking its natural advantages of tracking control.where and are the respective proportion coefficient and integration coefficient, is the set point vector for the th DFIG, is the integral of tracking error, and

By combining (12)–(19), the closed-loop system model can be written as

By defining augment state vector , the compact form of (20) iswhere

Assumption 1. There exist bounding matrixes , , , , , , and such thatSince the parameters and are limited by the capacity of a DFIG, their upper bounds can be easily determined aswhere the details of and can be found in Appendix A.1.

According (23)–(30), we havewhere , , , , , , , , , , and .

3.1. Controller Design

The control is the common solution for external disturbance rejection, of which objective can be defined aswhere is a prescribed attenuation level and weighting matrixes and .

A Lyapunov function for system of (21) is chosen as following form:

By differentiating (40), we obtainwhere .

Lemma 2. Give two vectors and ; the following inequality is identical:

According Lemma 2, the following inequalities can be obtained:

By using (31)–(37), (44) can be rewritten as

According (43) and (45), (41) can be rewritten as

Then, the following result can be obtained.

Theorem 3. In the nonlinear augmented system (21), if is the common solution for the matrix inequalityfor , then the performance of the proposed controller shown in (39) is guaranteed for a prescribed .

Proof. From (47),From (46) and (48), we getBy integrating (49) from to , we have Then,From (51), it is seen that, under the constrain of (47), the control performance is achieved with a prescribed .

3.2. Controller Design

The controller (power regulator and automatic voltage regulator (AVR)) is developed, of which objective can be written as

Since that the external disturbances have been efficiently eliminated by the proposed controller, the controller should be designed without considering . For the approximation errors have been considered, it is hard to obtain the optimal solution of (52). Thus, a suboptimal method is employed to minimize its upper bound.

By substituting (18) into (52), we have where .

From (41) and (45), (53) can be rewritten asif

From (55), the upper bound of the objective is obtained as

Therefore, the suboptimal control can be formulated as following minimization problem:

3.3. Mixed Control with Regional Pole Placement

Since the and controllers have been developed separately, the mixed control is developed to satisfy both suboptimal performance in (56) and performance in (39). The proposed mixed controller can be formulated as the following suboptimization problem:

In order to further improve DFIG damping performance, the poles of closed-loop system of (21) are placed within the region shown in Figure 2, of which characteristic LMI can be written as following forms [19]: