Synthesis and control of UPFC system using PI-D and (NEWELM and NIMC) based adaptive control for compensation power in Transmission Line

Flexible Alternating Current Transmission System devices (FACTS) are power electronic components. Their fast response offers potential benefits for power system stability enhancement and allows utilities to operate their transmission systems even closer to their physical limitations, more efficiently, with improved reliability, greater stability and security than traditional mechanical switching technology. The unified Power Flow Controller (UPFC) is the most comprehensive multivariable device among the FACTS controllers. According to high importance of power flow control in transmission lines, new controllers are designed based on the Elman Recurrent Neural Network (NEWELM) and Neural Inverse Model Control (NIMC)with adaptive control. The Main purpose of this paper is to design a controller which enables a power system to track reference signals precisely and to be robust in the presence of uncertainty of system parameters and disturbances. The performances of the proposed controllers (NEWELM and NIMC) are based neural adaptive control and simulated on a two bus test system and compared with a conventional PI controller with decoupling (PI-D). The studies are performed based on well known software package MATLAB/Simulink tool box. . Keyword FACTS, UPFC, PI-D, NEWELM, NIMC, Neural Adaptive Control, Synthesis, Stability, Robustness.

To be able to lead to a reliable command of the system, it is indispensable to proceed to a decoupling of the two components. The decoupling of two loops is obtained by subtracting the term ( ) through a reaction against .It is then conducted to a rule which provides a command with decoupling (PI-D) of the currents I d and I q with a model which can be rewritten in the following form: The design of the control system must begin with the selection of variables to adjust and then that of the control variables and their association with variables set. There is various adjustment techniques well suited to the PI controller.
The structure of the PI controller is represented by the first block diagram of Figure 4. In control, we obtain the following controller, depending on the damping coefficient ξ and the frequency : There are two well-known empirical approaches proposed by Ziegler and Tit for determining the optimal parameters of the PI controller TABLE I. The method Ziegler-Nichols [31] used in the present article is based on a trial conducted in closed loop with a simple analogy proportional controller. The gain Kp of the regulator is gradually increased until the stability limit, which is characterized by a steady oscillation. Based on the results obtained, the parameters of the PI controller given by  For each of the control systems, a simulation model is created which includes the required PWM .The parameters of the simulation model are selected to be equal to the parameters of a laboratory UPFC model , which are listed in TABLE III.   The te a disturb system h   Where u (t) is the control vector, x (t) the state vector, and y (t) the output vector of dimension for a discrete system to the sampling process parameters T e at times of T e sample k are formalized as follows: The system is of order 1, so it requires a single state variable x. this state variable represents the output of an integrator as shown in Fig. x(t) = y(t) x * (t) = y*(t) Fig. 11. . Block diagram of the state representation of the UPFC The transfer function G s Y s U s ⁄ of our process UPFC can be written as: We deduce the equations of state representation of the UPFC: * With: U t e t k x t Let: X t 1 x t e t (17) (18) The dynamics of the process corrected by state space is presented based on the characteristic equation of the matrix [A d -B d K], where K is the matrix state space controlled process.
Our system is described in matrix form in the state space: Where: * The identification makes it possible to obtain a mathematical model that represents as faithfully as possible the dynamic behavior of the process [4-5-7]. A process identified will then be characterized by the structure of the model, of its order and by the values of the Settings .It is therefore, a corollary of the process simulation for which one uses a model and a set of coefficients in order to predict the response of the system.
The figure shows the network Elman consisting of three layers: a layer of entry, hidden layer and a layer of output. The layers of entry and exit interfere with the outside environment, which is not the case for the intermediate layer called hidden layer. In this diagram, the entry of the network is the command U (t) and its output is Y (t) .The vector of state X (t) from the hidden layer is injected into the input layer. The state vector X (t) from the hidden layer is injected into the input layer. We deduce the following equations: When an input-output data is presented to the network at iteration k squared error at the output of the network is defined as: (22) For the whole training data u (t), y d (t) de t = 1, 2… N, the summed squared errors is: The weights are modified at each time step for W 0 : .
The latter we obtain: 1 Equation shows that there is a dynamic trace of the gradient. This is similar to back propagation through time. Because the general expression for weight modification in the gradient descent method is: The dynamic back propagation algorithm used to identify a state space model of the UPFC for NEWELM (Elman network) can be summarized as follows: (29) . .
If the dependence of X (t-1) on W i is ignored, the above algorithm degrades is the standard back propagation algorithm: Note that the performance of the identification is better when the input signal is sufficiently high in frequency to excite the different modes of process. The three weights W o ,Wr and W h which are respectively the matrices of the equation of state of the process system (UPFC) [C, A and B] became stable after a rough time t = 0.3s and several iterations fig. 9.

Remarque:
For the NEWELM is assumed through the vector is zero (D = 0). In online learning Elman network, the task of identifying and correcting same synthesis are one after the other. Or correction of the numerical values of the parameters is done repeatedly so the estimation error Fig. 10 takes about almost a second (t = 1s) to converge to zero i e regulation in pursuit.

b. Estimation of the parameters:
The input used of the Echelon type, is envisaged for identification systems [19].It is obvious that the entry is better than on the other (rail, Sinusoid……) from the point of view of the identification. In order to allow an identification by entries to excite the maximum of the modes of the system without too disrupt its normal operation, if it wants to pull a lot of information, in particular the excite in the entire frequency band interesting, one uses in general a variation in the niche market of pseudorandom binary sequence (PRBS) Superim The design of a system of efficient regulation and robust requires knowing the dynamic model of the process, which describes the relationship between the variations of the command and the variations of the measure. The dynamic model can be determined by direct identification.
The classic method type "Response Level" requires signals of excitation of large amplitudes; its accuracy is reduced, and does not allow the validation of the model. The current methods, with algorithms for recursive identification on micro computers offer a better precision and operate in open or closed loop mode with excitation signals of very low amplitude (0.5 to 5 per cent of the op pseudo random binary sequence (PRBS), and rich in frequency. The Pseudo Random Binary Sequence (PRBS) is a signal consisting of rectangular pulses modulated randomly in length, which approximate a white noise discreet, therefore rich in frequency and average value of zero, not amending the operating point of the process. Easy to generate; it is commonly used in the identification procedures. Posed on useful signal. Therefore, in our project it was used for the identification of the parameters of the system a network neuron said network of Elman with three layers .As has already been seen. Note that the performances of the identification are best when the input signal is rich enough in frequencies to excite the different modes of process. To obtain its results, a pseudo random binary sequence ( PRBS) is used as the excitation signal and are of the estates of rectangular pulses modulated in width, which are approximate to a white noise discrete which have a rich content of frequencies.
For the simulation it was chosen:  Network Elman (NEWELM) to three layers [Entry, hidden and output] is respectively [vector command, the vector of state and output vector]  A rich signal of frequency pseudorandom binary sequence is of languor in 1023 and of amplitude 1V.  A PRBS signal fig 14. Is input to system to provide reasonable convergence of the neural network weights for the controller to start with.
The error of characterization (or modeling) the system that represents the difference between the system and its model is represented by the term: (34) The errors signal w (t) rebuilt the disturbance D (t) and the error of characterization following the command u (t): . (35) So we can say that the stability of the whole when R(s) and are stable For an ideal model and a perfect pursuit of trajectory , ∀ d (t) An online estimate of unmeasured disturbances (36) b. Neural Inverse Model Control Design: It is quite obvious that this excludes many cases, and thus the effective implementation of the IMC structure goes through techniques which are in two general principles:  Minimize the sensitivity of the IMC structure for maximum disturbance rejection  Maximizing the complementary sensitivity for a better pursuit In the basic principle of the internal model control, the closer the model is to reality the more the structure approaches an open-loop structure.
A closed loop type corrector can therefore compensate for this handicap while enlarging the class of systems for which the structure is applicable. On the other hand, the gap between the actual system and its behavioral model may be due to multiple reasons, so it is more reasonable to consider this signal as exogenous to the control. The structure of Figure 16 is modified as shown in Figure 17

+ -
The low-pass filter (Filtering model), obviously has an impact on the behavior of the closed-loop system; on the model-following as well as on the disturbance rejection ability. The model M is determined by the Widrow-Hoff learning law [27].
The training of the network consists in modifying, with each step, the weights and bias in order to minimize the quadratic errors at output by using the law of Windrow-Hoff. With each step of training, the error at output is calculated as the difference between the required target t and the output y of the network. The quantity to be minimized, with each step of training k, is the variance of the error at the output of the network.

2
(37) T e : The sampling time is equal to 1ms .This time will be maintained throughout this study. The estimation of output and the error are calculated by: The learning of the network of neuron is to modify, at each sampling, the weight and bias (estimation of parameters) in order to minimize the quadratic criterion of the squares of the errors in the output.
The inverse model controller y (t) is given by the following equation: Adaptive Neural Feedback Control (ANFC) is a hybrid control that has allowed them to control any variation in tracking, regulation or stability. The results of the simulation showed the strength of our neural adaptive controller (NAC).We can say that the decoupled PI regulator would be ideal for the UPFC system control if the ± 30% variation of the reactance did not degrade its dynamic performance, as pointed out in this article. The process model is never perfect.
The results of this analysis of the two controls by neural networks at ± 30% of XL fig.19 are summarized in the following points:  All control strategies indicate that the proposed regulators have better dynamic performance and are much more robust than the traditional PI controller. They seem to be very high performance dynamic regulators.  Thanks to the generalization capacity of network neurons, the use of a neural identification regulator allows an improvement in the dynamic performance of the regulator approached. It has even been demonstrated by simulation that a neural identification regulator can solve the problem of the incapacity of parametric variations regulator PI of the line.

V. CONCLUSION
In this article, our UPFC system based on three robust control methods has been proposed. As the controller (PI -D) and approach the control of neural adaptive applied on (NEWELM and NIMC). These control strategies introduce enough flexibility to set the desired level of stability and performance. Practical constraints were considered by introducing appropriate uncertainties. The methods above have been applied to a typical test of a single-phase power system bridge. Simulation results showed that designed regulators were able to ensure a robust stability and performance a wide range of uncertainty of parameters of transmission .but line orders two hybrid (NACSSS-ERNN and NACIMS) in case of modification of the parameters of the system and an excellent ability to improve the stability of the system under small disturbances.