Neural network based power system stabilizers - Semantic Scholar

Neural Network Based Power System Stabilizers T. T. Lie and H. B. Gooi School of Elect. and Elec. Engineering Nanyang Technological University Nanyang Avenue Singapore 2263

A. M. Sharaf' Department of Electrical Engineering The University of New Brunswick Fredericton, NB Canada

signals (Ig). Conventional fixed structure, fixed parameter PSS designs are inherently limited and degradation in theirs stabilizing effectiveness is expected under different loading, contingencies resulting in network topology changes due to short circuit faults, generation-load mismatch, and network switching. New techniques [5 - 181 such as adaptive, selftuning, variable structure, nonlinear linearized control, Lyapunov based PSS designs, robust control, expert system rule based, fuzzy logic and neural network designs result in more robust, effective PSS designs. However, such new design techniques require extensive knowledge of power system dynamics, accurate models, and on-line predictive and estimation stages. This result is slower stabilizing action and the limited online application due to noisy measurements and power system nonlinearities. The paper is structured in the following sequence, following the introduction a sample one machine power system model is presented, then the two ANN based PSS designs are discussed with digital simulation results for two different disturbances. The paper ends with conclusions.

Abstract Novel power system neural network (ANN) based stabilizers (PSS) are presented. The two ANN-PSS designs are driven by the speed error and its rate of change. Other supplementary Stabilizing signals such as voltage deviation, ezcursion error, and PSS output rate of change are utilized to ensure the best matching between the ANN-PSS design and the optimized conventional analog PSS bench-mark model. The use of A N N based PSS stabilizers are motivcited b y their noise rejection and robustness under varying network topologies, loading conditions, parametric variations, and model uncertainties.

Keywords: Power System Stabilizer, Neural Networks.

1 Introduction The paper presents two novel PSS feed forward neural network stabilizers. The ANN block represents a nonlinear mapping between the effective damping signal vector and the resultant PSS corrective action Upss. The ANN network acts aa a nonlinear function approximator and is trained using the best performance of a conventional PSS bench-mark model. Conventional analog PSS designs are fixed structure, fixed parameter stabilizers with lead-lag, washout, and gain stages. Analog PSS are usually optimized for a given external network topology, system parameters, and loading conditions. This in turn cause excessive degradation in their stabilizing influence under varying network and load conditions. Power system stabilizers (PSS) [l - 41 are utilized in interconnected AC power system to enhance the synchronous stability, by damping the unstable oscillatory modes of oscillations including machine local, intra-area or inter-machines, and inter-area (tieline). These modes of oscillations are characterized by low mechanical natural frequencies in the limited range from (0.3 - 3 Hz.). Damping torque components are effected via the machine excitation system. These conventional PSS types utilize effective modulating signals such as speed deviation (Au),accelerating power (AP,,), generator active and reactive powers (APG,A&G),or current

2

and output

'Currently a Visiting Professor, faculty of Electrical Engineering Nanyang Technological University, Singapore 2263.

306

0-8186-4260-2/93 $03.000 1993 IEEE

Power System Model

A sample single machine infinite bus system of Figure 1 with the excitation and speed control blocks is simulated using the MATLAB software package. The analog optimized bench-mark PSS model shown in Figure 2 is utilized to train the two ANN based PSS designs. The ANN-PSS designs are shown in Figure 3. Both designs utilize the speed deviation (error) e, as the main modulating signal with other generic signals for fitting and output stabilization. The input vector for the two designs are:

T h e Dynamic Model

2.1

The enerator is adapted as a third first order different iaf equations given below:

6 = wow 1 LI = - ( P M + G + K ~ w - P , ) M 1 = - ( E f d - ( Z d - 2L)id - E:) Ti0

5Exciter]

(1) (2) (3)

where

E,

=

id

-ECOS~

2.2

Figure 1: Sample One Machine Infinite Bus System

= E:+

E,

+

zq

(29

-z&)id

E'Esin6

p, = 4 t, xi

+

1+sTl

AW

Figure 2: Structure

For the AVR and exciter, the following dynamic model is adapted.

UCPSSI

where

Conventional Bench-Mark Analog PSS

Vt'dG

and where d is the difference or rate operator d z = x(t) z(k - 1 ) and

=

vd

x q Esin6 2,

e, e,,

A"-PSS Design # 1

G=

[

a+-

b l+sTg]'

(5)

For the conventional PSS, the following transfer function is considered.

[

"

][

u p s s = - -K J - l+sT1] 8 K A ~ + s T Q l+sT2

NPSSI

3

A"-PSS Design # 2

zq

For the governor, the following transfer function is considered.

e,, de, define the per unit (pu) speed error deviation Aw and its rate of change. e,, is the pu incremental 'error' change in machine terminal voltage. U N p S S l and Up~pss2are the pu output of the two ANN based PSS blocks. The system was simulated with sampling period of 10 ms using the MATLAB-NNET Tool Box. e,.,

+

Vq = E: - ZLid

= AW=W-W~ = &%TZG

(6)

ANN Based PSS Designs

The two proposed ANN-PSS desi ns are based on the speed deviation (error) signal. O&er input signals and generic stabilizin signals are added to ensure an effective mapping an% curve fitting using MATLAB NNET Tool Box for feed forward neural networks [14]. The ANN network was trained using the back error propagation (BEP) algorithm, each has one hidden layer of tansigmoid activation functions and an output layer with one neuron and purelinear activation function. The ANN network was trained using the offline data ensemble generated by the optimized benchmark conventional PSS design for a number of excursions such as generation-load mismatch, short circuit

UNPSS2

Figure 3: ANN Based PSS

307

Timc (uc)

Tims (sec)

Figure 4: Response to a Short Circuit Fault without PSS

Figure 5: Response to a Short Circuit Fault with Conventional PSS

fault, and external network equivalent driving point impedance ze changes. Before data collection and ANN-PSS training the conventional bench-mark model parameters were tuned iteratively to minimize a performance index J,,

where N =

4

with

tjinol

= 3 - 5 seconds.

speed Dennuan

Figure 6: Response to a Short Circuit Fault with ANN-PSS Design 1

Sample Simulation Results

In all of the dynamic simulations shown in Figure 4 - 10, a short circuit fault was applied at time=5 sec. and was cleared after 0.1 sec. and a 0.6 pu step change increase in ze and noisy data were applied from time = 5 sec. to the the final time of the simulations (10 sec.).

5

"

f

"

1

I

b

as-

$ T m (U&)

Conclusions

The paper presents two novel ANN based PSS designs. These designs utilized an optimal benchmark conventional PSS for neural network training and function approximation. They differ in the use of a number of supplementary dampi1.g signals based on speed deviations. The proposed ANN-PSS stabilizers offer the added advantages of noise tolerance, adaptiveness to varying network and loadin conditions, flexibility, possible on-line training an retraining wing actual field measurements. Hybrid p3wer system stabilizers and combined conventional and ANY-based structure are the most effective designs.

$o'.im 4.05

JO'+O

Spccd "n,

rims (Icf)

Figure 7: Response to a Short Circuit Fault with ANN-PSS Design 2

%

Acknowledgement The Authors wish to acknowledge the support of Nanyang Technological University, Singapore and The University of New Brunswick, Canada.

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spcs4 Dsnstlrm

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~ u n c(-=)

Figure 8: Response to a 0.6 pu Step Change Increase in 2 e with Conventional PSS and Noisy data

308

(4

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Time (ur)

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-

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(=4

Figure 9: Response to a 0.6 pu Step Change Increase in x e with ANN-PSS Design 1 and Noisy Data

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(-1

Figure 10: Response to a 0.6 pu Step Change Increase in x e with ANN-PSS Design 2 and Noisy Data

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