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Artificial neural network based auto-regressive controller for a voltage-source converter.

1 INTRODUCTION

The switch-mode voltage-source converter (VSC) topology has gained wide acceptance for application in electric power generation, transmission, and distribution systems [1], [2]. Conventionally a VSC is operated as a current-controlled voltage source and real- and reactive-power components are controlled through the VSC instantaneous current components [3]-[5].

Conversion of abc-frame currents to dq current components requires a phase-locked loop (PLL) system to determine the phase angle of the rotating -frame. If dynamics of PLL is ignored in the VSC control design, the control system must be adequately robust to compensate for the unaccounted PLL dynamics.

Using current components as dynamic variables result in a nonlinear VSC-control model which in turn adds to the complexity of the control design [5], [6].Various linear and nonlinear VSC control methods have been proposed/adopted in the technical literature [3]-[9].

Among linear control methods, state feedback based methods do not necessarily provide robust controllers since control provisions (e.g., stability margins), are not readily formulated in these methods [6]. A root locus analysis approach is proposed in [6] to ensure robustness of designed controllers based on state feedbacks. Another drawback is that such PI-based controllers are often designed based on trial and error [3]. Among nonlinear control approaches, feedback linearization method is not robust since it requires precise cancellation of VSC model nonlinearities [5]. In this context, an integral control to eliminate steady state error, and a passivity-based control to enhanced robustness of VSC nonlinear control are presented in [8] and [5], respectively.

NARMA L2 [10] is a good candidate for control since it has a capability to transform a nonlinear dynamical system into a linear one by revoking both the nonlinearities and dynamic of the system.

There are many PWM techniques. The most common strategy discussed compares a high frequency periodic triangular waveform, the carrier signal, with a slow-varying waveform known as the modulating signal that instigates VSC valve switching and this is achieved with a two-level converter is covered basically. But in this novel the switching signals are generated using the NARMA-L2 controller directly instead of above PWM techniques

Digital simulations of the various switched three-phase converter configurations with PWM slow down the speed of solution. An averaged model is presented that represents the averaged ac side terminal power and the averaged dc side power of the PWM three-phase converter in a simplified model that avoids switching in simulation, thus speeding up the solution. The average VSC model is said to be adequately accurate for dynamic analysis and control design [11].

The familiar dq frame or transformation is used. In the dq frame of reference for the VSC control, the signals are closer to dc in steady-state operation, allowing simpler control functions to be applied.

A DC-bus voltage controller for the controlled DC-voltage power port VSC has been designed based on [11] to ensure that dc-side voltage is tracking its reference.

2 SYSTEM DESCRIPTION

Single line diagram of Study system in this paper is shown in Fig. 1. In this diagram the DC voltage source connected to the Point of Common Coupling through interface VSC, [R.sub.t] and [L.sub.t] as low pass filter and power transformer. The impedance of transformer is added to [R.sub.t] and [L.sub.t].

There is also a local load connected to the PCC and AC voltage source connected to PCC via the [R.sub.s] and [L.sub.s]. Parameters of the system are represented in Table 1[12][13].

3 CONTROLLER MODEL

The undesirable start-up transient can be avoided if the control is augmented with a feed-forward compensation scheme, as shown in Fig. 2. The feed-forward scheme augments the compensator output with a measure of [V.sub.s] which can be obtained from a voltage transducer whose (dynamic) gain is [G.sub.ff](s), where [G.sub.ff](0) = 1. Therefore, at the start-up instant when the compensator output is zero, the AC-side terminal voltage to be generated starts from a value equal to [V.sub.PCC], and the AC-side current remains at zero. The feed-forward compensation can also decouple dynamics of the converter system from those of the AC system with which the converter system is interfaced [11].

The control structure of VSC converter including NARMA-L2 controller is shown in Fig. 2. The proposed control structure produce control signals using the PCC voltage, interface impedance currents and reference currents.

Fig. 3 shows how reference currents determined using PCC voltage and active/reactive reference signals. The Current Reference Generator created based on two below formulas:

[i.sub.dref](t) = [k.sub.d][P.sub.erf](t) + [k.sub.q][Q.sub.ref](t) (1)

[i.sub.qref](t) = [k.sub.q][P.sub.ref](t) + [K.sub.d][Q.sub.ref](t) (2)

where [k.sub.d] and [k.sub.q] are equal to [2/3][[V.sub.d]/[V.sup.2.sub.d] + [V.sup.2.sub.q]] and [2/3][[V.sub.q]/[V.sup.2.sub.d] + [V.sup.2.sub.q]] respectively [11].

4 NARMA L2 CONTROLLER

Because of the learning and approximation capabilities, Artificial Neural Networks have became popular structures is in identification and adaptive control of dynamical systems. One of the most appropriate architectures for prediction and control of time variant nonlinear systems is NARMA-L2 [14]. NARMA-L2 has the advantage of fast and accurate output regulation due to its mapping capability. This control technique is based on input output linearization [15]. There are two basic in NARMA-L2, the first step is identification of the system to be controlled and the second step is to design control system.

4.1 System Identification

In identification step, to describe behavior of discrete-time nonlinear system, the following nonlinear autoregressive moving average (NARMA) model is employed:

y(k + d) = F(y(k), y(k - 1), ..., y(k - n + 1), u(k), u(k - 1), ..., u(k - m + 1))

where u(k) and y(k) are the system input and output respectively and d is the relative degree. The positive integer's m and n are respectively the number of measured values of inputs and outputs. Taylor expansion of F(.) yelid to [16]:

y(k + d) = f (y(k), y(k - 1), ..., y(k - n + 1), u(k - 1), ..., u(k - m + 1))

+ [??](y(k), y(k - 1), ..., y(k - n + 1), u(k - 1), ..., u(k - m + 1)).u(k) (4)

In NARMA-L2 two MLP neural networks [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are used as approximates to identify the system of (3) to get prediction of y(k + d) as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Fig. 4 shows the two sub networks are used for the model approximation; NN1 and NN2 which are used to approximate nonlinear functions f and g respectively. The plant model identification in NARMA-L2 Control starts off with a dataset of input output data pairs collected experimentally. If necessary, the data pairs are preprocessed. Again, the collected dataset is divided into two parts; one for the training of the neural nets and the other for cross validating the resulting neural model.

As an averaged model represents the averaged ac side terminal power and the averaged dc side power of the PWM three-phase converter in a simplified model that avoids switching in simulation, thus speeding up the solution [11]. So the averaged model have been used to collect data for training reason.

Here, the NN1 sub network is a feed forward neural network with one hidden layer with p neurons of hyperbolic tangent (tanh) activation function and an output layer of one neuron with linear activation function. Also, the NN2 sub network is a feed forward neural network with q tanh hidden layer neurons and one output neuron.

For each sub network, the number of past output n and the past input m; which compose the input vector and the number of neurons (p and q) of the hidden layer are determined. Subsequently, the selected neural network structure is trained using the input pattern and the desired output from the dataset. Here, the parameters (weights and biases) of the two MLP sub networks that properly approximate the nonlinear modeling representing the system are estimated. The optimization technique that will be used to update the parameters is also importantly determined. Finally, to measure the success at approximating the dynamical system plant model using the neural network model, the prediction error ek should be uncorrelated with all linear and nonlinear combination of past inputs and outputs. Thus, the validation and cross validation tests are carried out to ascertain the validity of the obtained neural network model.

4.2 Controller Design

Controller design is done based on (4) and is quite straightforward. The system output should follow a reference trajectory yr (k + d). Substituting y(k + d) within (4), control signal can be obtained as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

The control rule (6) is not realizable since input computation of u(k) requires the output signal y(k). A more practical form can be represented as the following [17].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

which is realizable for d [greater than or equal to] 2. Block diagram of NARMA-L2 controller is shown in Fig. 4.

Theoretically, this control structure is simple and its implementation is not particularly demanding. Thus, favorably, NARMA-L2 control has the advantage to reduce the amount of memory and computation time. Faster and accurate output regulation is expected due to its mapping capability, where the output becomes a linear function of a new control input. Basically, there are two steps involved when using NARMA L2 control: system identification and control design. In the system identification stage design, a neural network of the plant that needs to be controlled is developed using two sub networks for the model approximation. The network is then trained offline in batch form using data collected from the operation of the plant. Next, the controller is simply the rearrangement of two sub networks of the plant model. Computation of the next control input to force the plant output follows a reference signal is materialized through simple mathematical equation.

5 PERFORMANCE EVALUATION

5.1 Tracking capability

Tracking capability of the designed controllers is examined by applying a step command to [Q.sub.ref], from 0 to -1 p.u., to the closed-loop system of Fig. 1. Fig. 5 shows the dc-side voltage and the VSC reactive power responses to the step in [Q.sub.ref]. Fig. 5(a) shows that the q(t) tracking rise time is less than 1 cycle ([t.sub.r] = 2ms), its overshoot is less than 5%,. Fig. 5(b) shows a maximum of 0.03-p.u. voltage drop in the dc-side voltage which is recovered in less than 1 cycle. Steady state errors in both reactive power and dc-side voltage are zero. Time responses of variables q(t) and [V.sub.dc](t) of Fig. 5 do agree with the corresponding responses obtained based on conventional [i.sub.q](t) and [i.sub.d](t) control as reported in [18].

5.1 Disturbance Rejection Capability

1) DC-Side Load Energization: The ability of the control system to reject a dc-side disturbance is verified by connecting [R.sub.P] = 4.5[ohm] in parallel to the dc capacitor (Fig. 1). [R.sub.p] Dissipates 500 kW (0.5 p.u.) at the rated dc-side voltage which is half of the VSC rated power. This scenario, can represent variations in power exchange due to a disturbance in a back-to-back VSC configuration (e.g., in the converter system of a doubly-fed induction machine-based wind energy conversion unit [19]).

Fig. 6 shows variations of the dc-side voltage and the corresponding reactive power flow, subsequent to the dc-side disturbance. Fig. 6(b) shows that the VSC control system reverts the capacitor voltage to its reference value in less than two cycles and maintains the dc-side voltage within 3% of the rated value. Fig. 6(a) illustrates that q(t) deviates less than 0.1 p.u. (10% of the converter rating).

2) AC-Side Load Change: To investigate the VSC controllers' performance in response to a disturbance due to a load change, the load of Fig. 1 is divided into two equal sections. The load change is imposed short circuiting half of the load it means [R.sub.l] and [L.sub.l] are changed to [R.sub.l]/2 and [L.sub.l]/2 respectively. Fig. 7 depicts the effect of the load change on reactive power at the PCC and the dc-side voltage. Fig. 7 shows that reactive power and dc-side voltage have no sensible deviation. Fig. 7 demonstrates the ability of the designed controllers to reject an ac-side disturbance.

5 CONCLUSIONS

A new neural network controller for a voltage-source converter (VSC) is presented. The VSC control system, based on conventional dq-frame model, consists, an outer loop to control dc-side voltage through real-power control.

The proposed neural network controller is applied to a study system to demonstrate its tracking, disturbance rejection and robustness capabilities. The study results indicate that the controller has the ability to fulfill the desired tracking and disturbance rejection specifications and shows a great robustness to the system parameter. Accuracy of the model and effectiveness of the proposed controller are validated based on time-domain simulation studies of a test system in the MATLAB software environment.

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[19.] Hansen. L. H, Helle. L, Blaabjerg. F, Ritchie. E, Munknielsen. S, Bindner. H, Sorensen. P and Bak-Jansen B., Conceptual Survey of Generators and Power Electronics for Wind Turbines. Roskilde, Denmark: Riso Nat. Lab., December 2001.

Adel Akbarimajd, Reza Dolatabadi

Department of Electrical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

akbarimaid@gmail. com, re. dolatabadi@yahoo. com

Table 1. VSC, Local load and grid parameters

Parameter                         Value

[R.sub.l]                         30 [ohm]
[L.sub.l]                         50 mH
[R.sub.s]                         1 [ohm]
[L.sub.s]                         10 mH
[R.sub.t]                         1.5 m[ohm]
[L.sub.t]                         300 [micro]H
VSC rated power                   1 MW
PWM carrier frequency             3,960 HZ
[F.sub.0]                         60 HZ
VSC terminal voltage              600 V
DC voltage                        1500 V
C                                 9625 [micro]F
Nominal grid Line-Line voltage    13.8 kV (rms)
Transformer voltage ratio         0.6/13.8 kV
Transformer rated power           1 MW
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Author:Akbarimajd, Adel; Dolatabadi, Reza
Publication:International Journal of Emerging Sciences
Article Type:Report
Geographic Code:7IRAN
Date:Sep 1, 2014
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