PSS Design Based on RNN and the MFAFEP Control Strategy - PDF by ijcsis


									                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                              Vol. 8, No. 2, May 2010

PSS Design Based on RNN and the MFA\FEP
             Control Strategy

      Rebiha Metidji and Boubekeur Mendil
        Electronic Engineering Department
      University of A. Mira, Targua Ouzemour,
               Bejaia, 06000, Algeria.

                                                                    The main problem in control systems is to
Abstract –    The conventional design of PSS (power
system stabilizers) was carried out using a linearized          design a controller that can provide the appropriate
model around the nominal operating point of the                 control signal to meet some specifications
plant, which is naturally nonlinear. This limits the            constituting the subject of the control action. Often,
PSS performance and robustness.
    In this paper, we propose a new design using RNN            these specifications are expressed in terms of speed,
(recurrent neural networks) and the model free                  accuracy and stability. In the case of neuronal
approach (MFA) based on the FEP (feed-forward                   control, the problem is to find a better way to adjust
error propagation) training algorithm [15].                     the weights of the network. The main difficulty is
    The results show the effectiveness of the proposed          how to use the system output error to change the
approach. The system response is less oscillatory with          controller parameters, since the physical plant is
a shorter transient time. The study was extended to             interposed between the controller output and the
faulty power plants.
                                                                scored output.
Keywords-Power Network; Synchronous Generator;
Neural Network; Power System Stabilizer; MFA/FEP                    Several learning strategies have been proposed
control.                                                        to overcome this problem such as the supervised
                                                                learning, the learning generalized inverse modeling,
              I. INTODUCTION                                    the direct modeling based on specialized learning,
                                                                and so on [14]. In this work, we used our MFA/FEP
    Power system stabilizers are used to generate
                                                                approach because of its simplicity and efficiency
supplementary control signals for the excitation
                                                                [15]. The aim is to ensure a good damping of the
system, in order to damp the low frequency power
                                                                power network transport oscillations. This can be
system oscillations. Conventional power system
                                                                done by providing an adequate control signal that
stabilizers are widely used in existing power
                                                                affects the reference input of the AVR (automatic
systems and have made a contribution in enhancing
                                                                voltage regulator). The stabilization signal is
power system dynamic stability [1]. The parameters
                                                                developed from the rotor speed or electric power
of a classical PSS (CPSS) are determined based on
a linearized model of the power system around its
nominal operating point. Since power systems are                     The section II presents the power plant model.
highly nonlinear with time varying configurations               The design of the neural PSS is described in section
and parameters, the CPSS design cannot guarantee                III. Some simulation results are provided in section
good performance in many practical situations.                  IV.

    To improve the performance of CPSSs,                              II. THE POWER PLANT MODEL
numerous techniques have been proposed for their
design, such as the intelligent optimization methods                The standard model of a power plant consists of
                                                                a synchronous generator, turbine, a governor, an
[2], fuzzy logic [3,4,5], neural networks [7,8,9] and
                                                                excitation system and a transmission line connected
many other nonlinear control techniques [11,12].                to an infinite network (Fig.1). The model is built in
The fuzzy reasoning using qualitative data and                  MATLAB/SIMULINK environment using the
empirical information make the fuzzy PSS (FPSS)                 power system Blockset. In Fig.1, PREF is the
less optimizing compared with the neural PSS                    mechanical power reference, PSR is the feedback
(NPSS) performance. This is our motivation.                     through the governor, TM is the turbine output

                                                                                         ISSN 1947-5500
                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                       Vol. 8, No. 2, May 2010

torque, Vinf is the infinite bus voltage, VTREF is
terminal voltage reference, Vt is terminal voltage,
VA is the voltage regulator output, VF is field
voltage, VE is the excitation system stabilizing
signal, ∆w is the speed deviation, VPSS is the PSS
output signal, P is the active power, and Q is the
reactive power at the generator terminal.                                              Figure 4. Block diagram of DTRNN.

   The switch S is used to carry out tests on the
power system with NPSS, CPSS and without PSS
(with switch S in position 1, 2, and 3, respectively).

    The synchronous generator is described by a
seventh order d-q axis of equations with the
machine current, speed and rotor angle as the state
variables. The turbine is used to drive the generator                              Figure 5. Illustration of the state feedback.
and the governor is used to control the speed and
the real power. The excitation system for the                                            III. THE NPSS DESIGN
generator is shown in Fig.2 [4].                                             In this work, we used a neural architecture used
                                                                         primarily in the field of modeling and systems
    The CPSS consists of two phase-lead                                  dynamic control; namely the DTRNN (Discrete
compensation blocks, a signal washout block, and a                       Time Recurrent Neural Network). This is analogous
gain block. The input signal is the rotor speed                          to the Hopfield network (Fig.4).
deviation ∆ω [16]. The block diagram of the CPSS
is shown in Fig.3.                                                       W : global synaptic weight vector.

                                                                         S : weighted sum, called potential.

                                                                         U : output or neuron response.

                                                                         f : activation function.

                                                                         υ: external input.

                                                                              This is a neural network with state feedback. It
                                                                         has a single layer network with the output of each
                                                                         neuron is feed back to all other neurons. Each
                                                                         neuron may receive an external input [14]. This is
                                                                         well shown in Fig.5.

         Figure 1. The control system configuration.
                                                                         A. DTRNN network Equations

                                                                            Originally, the equations governing this network
                                                                         type are the form:

                                                                         U k 1         f∑ W         U k      ν k
                                                                         If we consider that the inputs ν are weighted as in

                                                                         Fig.4, (1) can be rewritten as follows:

                                                                          U k      1        f∑      W       U k                         (2)
      Figure 2. Block diagram of the excitation system.                  With

                                                                                                1    j 0
                                                                          U k                 U k   j 1, … , n
                                                                                        ν      k  j n 1, … , n                m

             Figure 3. Block diagram of CPSS.                            U k 1 :      i      Network    state                      variable

                                                                         ν k : j External input (j=1… m).
                                                                         (i=1… n).

                                                                                                     ISSN 1947-5500
                                                (IJCSIS) International Journal of Computer Science and Information Security,
                                                Vol. 8, No. 2, May 2010

n : number of neurons in the network.

U k =1 : inner threshold.
m : dimension of the input vector, V.

    The outputs are chosen among the state
variables. Learning is done using dynamic training
algorithms that adjust the synaptic coefficients
based on presented examples (corresponding
desired inputs \ outputs) and taking into account the
feedback information flow [17].                                                    Figure 6. MFA/FEP control structure.

    In this work, we used the MFA training                                        Y(k) = [y1(k), y2(k),…,yr(k)]T
structure of Fig.6. The idea is to evaluate the output
error (i.e. the gap between the system output and its                                     = [U1(k), U2(k),… Ur(k)]T                             (5)
desired value) to the controller input and to spread
them directly from input to output, to get the hidden                The standard quadratic error over the pth
layers and the output layer errors. This can be                   sequence is given by
realized by the feed forward error propagation                                 J (W) = ∑                      ∑        y (k)           y (k)    (6)
algorithm (FEP) crafted specifically for this
purpose. This allows direct and fast errors                       Where
calculation of consecutive layers, required for the
                                                                       : is the length of the pth training sequence,
controller parameters adjustment.
                                                                  r : is the number of the network outputs,
B. Training the DTRNN controller based on the                     y (k) : is the jth network output,
   algorithm FEP                                                  y (k) : is the desired value corresponding to y (k).
                                                                  The weights are updated iteratively according to
     The approach MFA / FEP is an effective
alternative for training controllers. Direct injection                                                                           (    )
                                                                              W (k        1) = W (k)                   μ             ( )
of the input error can provide error vector
components required to the network weight update.
The FEP formulation is given in the following                     where µ is the learning rate. The gradient in (7) is
paragraph.                                                        calculated using the chain rule:
    Let consider a DTRNN given by (2) and (3).                                                (    )           (   )
The global input vector, X (k), of the network                                                          =                                       (8)
                                                                                                  ( )           ( )         ( )
consists of the threshold input, d=1, the external
inputs, xi (k), and network state feedback variables,
Ui (k).                                                           Where
                                                                                           ∂U      ∂f s (k) ∂s (k)
                                                                                          ∂W (k)    ∂s (k) ∂W (k)

              1    X     (k)                                                                                = f s (k) . x (k)                   (9)
            X (k)  X     (k)                U (k)
              .          .                  U (k)                                     (   )
              .          .                    .                   The term                        in (8) is the sensitivity of Jp(w) to
X (k) =
                                                                                      ( )
           X (k) =       .      and U (k) =   .
          u (k 1)
                                                                  the node output, Ui(k). Let the error, calculated
                         .                    .
              .          .                    .                   between the network output and desired output, be
              .          .                  U (k)
          u (k 1)  X     (k)
                                                                                      (k) = Y(k)                   Y (k) = ∆Y(k)               (10)

                                                                         As in the back-propagation algorithm, the term
                                                                     (    )
                                                                               can be interpreted as the equivalent
   Then, we can write                                                ( )
                                                                  error, ε (k), with (i=1,2,…,n). Hence, we write
 U (k     1) = f S (k) = f ∑        W . X (k)        (4)
                                                                              (   )                                        ( )
The outputs are chosen among the state variables.                                     = ε (k) = ∑                          ( )
                                                                                                                                  ∆y (k)       (11)
                                                                               ( )
For the simplicity of notation, let consider the first r
state variables as outputs.                                          The error vector, E0(k), can be calculated at the
                                                                  input ; since the network receives the output vector,
                                                                  Y(k), as input through the state feedback. The

                                                                                                            ISSN 1947-5500
                                                      (IJCSIS) International Journal of Computer Science and Information Security,
                                                      Vol. 8, No. 2, May 2010

equivalent error vector components, ε k , are                           -The nominal Power : Pn = 3.125×106 (VA).
computed using (11), through the forward
propagation of E0(k).                                                   -The nominal voltage : Vn =2400 (V).

C.     NPSS design using the MFA / FEP approach                         -The nominal frequency : fn = 50 (Hz).

                                                                           To evaluate the performance of the
     The aim is to ensure an optimal control of
                                                                        NPSS, the system response of the NPSS is
power system output voltage. The MFA / FEP
                                                                        compared with the cases where there is no PSS and
learning structure is illustrated by Fig.7.
                                                                        with a CPSS in the system.
  The adequate structure of the NPSS network
consists of 3 neurons. The input vector X=
[d=1,dw, w, UT]T , where U(3x1) is its own state
vector, d is the threshold input, w is the angular
velocity, and dw is its variation. The NPSS output,
VNPSS, chosen as the first state variable, is applied to
the automatic voltage regulator input. The learning
rate is fixed at µ = 0.2.

    The training procedure is summarized by the
followed steps:

Step1- Initialize the weights to small values in an
interval [0, 0.1]. The synaptic weight matrix is of
size 3 × 6 (3 outputs and 6 inputs).

Step 2- Initialization the state variables.                                         Figure 8. Terminal voltage response.

Step 3- Compute NPSS output.

Step 4- Application to the single-machine infinite
bus (SMIB) process.

Step 5- Compute the output error and update the
NPSS weights.

Step 6- Go to step 3 or stop if the learning is

                                                                                      Figure 9. Machine angular speed.

                                                                           From these results, we can see that the response
                                                                        of the system stabilizes at the reference value after
                                                                        2 sec. But, the NPSS provide a better voltage
                                                                        response with reduced overshoot and rise time.
     Figure 7. The NPSS training structure based on MFA / FEP
                             approach.                                       In order to evaluate the performance of the
                                                                        different PSS in the presence of defects, let us
                                                                        consider, as an example, a temporary short circuit,
                                                                        at t = 5s, that lasts 0.1s (time required for switching
              IV. SIMULATION RESULTS                                    the circuit breaker protection).

    The parameters of the machine model used hang
the simulation are:

                                                                                                 ISSN 1947-5500
                                                      (IJCSIS) International Journal of Computer Science and Information Security,
                                                      Vol. 8, No. 2, May 2010

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                     V. CONCLUSION

    In this paper, we have developed another way to
design PSS. The NPSS is a DTRNN trained using
our MFA / FEP learning structure. The results show
the effectiveness and the best performance of the
resulting stabilizer.

[1] S. M. Pérez, J. J. Mora, & G. Olguin, ‘’ Maintaining Voltage
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                                                                                                    ISSN 1947-5500

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