23

IEEE Transactions on Energy Conversion, Vol. 14, No. 1, March 1999

Neural Network Observers for On-line Tracking of Synchronous Generator Parameters S. Pillutla, Student Member A. Keyhani, SM

I. Kamwa, Member

Department of Electrical Engineering The Ohio State University Columbus, OH 43210

IREQ, 1800 Lionel-Boulet Varennes (QC) Canada J3X 1S1

Abstract: This paper presents a methodology for implementing artificial neural network (ANN) observers in estimating and tracking synchronous generator parameters from time-domain online disturbance measurements. Data for training the neural network observers are obtained through off-line simulations of a synchronous generator operating in a one-machine-infinite-bus environment. Nominal values of parameters are used in the machine model. After training, the ANN observer is tested with simulated on-line measurements to provide estimates of unmeasurable rotor body currents and in tracking simulated changes in machine parameters. Keywords: Synchronous generators, parameter estimation, artificial neural networks, observers, parameter tracking. I. INTRODUCTION

In recent years, there has been a considerable interest in the online estimation of synchronous generator parameters [1-51. Online methods are particularly attractive since the machine’s service need not be interrupted and parameter estimation is performed by processing measurements obtained during the normal operation of the machine. The need for on-line parameter estimation arises because generator parameters tend to deviate substantially from nominal values obtained from off-line testing. These deviations are usually due to magnetic saturation [6-91, machine aging, internal temperature, the effect of centrifugal forces on winding contacts, and incipient faults within the machine. It is to be noted that although incipient faults can typically be detected by continuous or periodic monitoring of characteristic quantities [IO-123 (such as efficiency, fuel and oil consumption, impurities in the cooling stream, radio frequency noise level, temperature etc.), not all faults may manifest themselves in change of these quantities. However, parameter estimates obtained by processing online measurements are useful for generator condition monitoring [13]. For instance, a significant reduction in the field-to-stator turns ratio (and field PE-064-EC-1-09-1997 A paper recommended and approved by the IEEE Electric Machinery Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Energy Conversion. Manuscript submitted May 9, 1997; made available for printing October 3, 1997.

resistance) would indicate a shorted field-coil. By using an extensive database, online parameter estimates may be used to monitor generator condition and take preventative maintenance measures before complete breakdown occurs. Measurements acquired during synchronous generator testing are often a small subset of the machine’s state vector. The remaining unmeasurable components of the state vector are typically composed of currents in the rotor body circuits [14-171 which encapsulate high frequency sensitivity due to the flow of eddy currents in solid parts. In the absence of full-state measurement, the parameter estimation algorithm may require heavy computation to achieve convergence or may even fail to converge on a set of parameters, especially when poor initial estimates are used. However when the state vector is completely known, parameter convergence is guaranteed and recursive estimation algorithms may be used to estimate machine parameters. Observers are frequently used to estimate unmeasurable state vector components based on operating data. It must be recognized that the problem of estimating a system’s un-measurable states by processing its measurable states is essentially a system identification task and neural networks offer a promising means of achieving this (see reference [25]). In this paper, an ANN observer is developed to map sequences of measured machine outputs to un-measurable rotor body currents by processing data acquired during transient disturbances. Data for developing the neural network model are obtained through off-line simulations of the synchronous machine model connected to an infinite bus system. It is assumed that the structure and order of the machine model used in generating data for developing the observer is accurately known. Nominal parameter values are used in the machine model. These assumptions are reasonable because, over the years, significant advances have been made to accurately model synchronous generators based on well-established modeling and parameter estimation techniques [I-211. During training, all state variables of the machine model are assumed measurable. This would correspond to the stage when simulations are carried out to obtain a sufficiently accurate observer model. After developing the neural network observer, it can be used to estimate rotor body currents by processing measurements acquired on-line in an actual operating environment. 11. MACHINE MODEL DESCRIPTION AND

PROBLEM FORMULATION The structure of the synchronous machine model used in this study (Model 3’.3) is shown in Fig.1 and is based on the 0885-8969/99/$10.00 0 1997 IEEE

24

reciprocaI per-unit system in which all parameters are referred to the stator (see reference [20]). To use the above models with actual units of resistance and inductance in the estimation procedure, the following turns ratio transformation between the field and the stator should be used:

where ifd* the field winding current in ampere, vfd is the field voltage in volts, both quantities measured on the field side of the generator. Rfd* is the field winding resistance in ohm as measured on the field side. vd, vfd, and Rfd denote corresponding transformed quantities on the stator side of the generator through the field-to-stator turns ratio a.

Stage 1 : Estimation of linear model parameters. The first stage of the estimation process involves the estimation of armature circuit parameters from small excitation disturbance data. As described in reference [4], the armature resistance & , the mutual inductances Lad, and L,,, the field-to-stator turns ratio, a, and the field-resistance, Rid* can be estimated in this stage. Stage 2 : Development of neural network saturation model. In this stage, a multidimensional artificial neural network based non-linear mapping is established to map small excitation disturbance responses to a set of experimentally obtained mutual inductances over a wide range of operating conditions [5]. Stage 3: Observer based estimation of rotor body currents and estimation of rotor body parameters. Using armature circuit parameters obtained from stages 1 and 2, and nominal values of rotor body parameters in the machine model, simulated measurements will be generated to develop an artificial neural network (ANN) observer to estimate rotor body currents. The ANN observer will be used to estimate rotor body currents from large disturbance transient data. Following this, a recursive parameter estimation technique which utilizes measured large disturbance data and ANN estimated rotor body currents is used to update all machine parameters.

q-axis Fig. 1: Model 3'.3: On-line Model Structure

For discrete-time systems, the coupled state space representation of the models in Fig. 1 can be written as: X ( k + 1) = A ( @ ) *X ( k ) + B ( @ ) . U ( k )+ w ( k ) Y(k + 1) = C - X ( k + 1)+ v(k + 1)

(1)

wfi) and vfi) denote the process and measurement noise, respectively. In addition,

x = [i,

id ilq i2, i,,

i,,

Y = [i, i, i>17 ;

Ri

R!d

Rf21d

'l

Lad

U ,'

Define a suitable set of observer input patterns (machine variables) for the observation task. What should the training pattern be ? Is the observer robust to small deviations in synchronous generator parameters ? Is the observer robust to noisy input measurements ? 111. PROCEDURE FOR STATE VARIABLE DE-COUPLING UNDER LARGE DISTURBANCE CONDITIONS

iPld i;,Ir;

U = [ v , v , v;,]' ;

= LRa

Since the main intent of this paper is to describe the observer based parameter estimation technique, Stage 3 will be described in detail. The reader is referred to references [4,5] for details pertaining to stages 1 and 2 of the estimation process. In order to apply the concept of ANNs for estimating rotor body currents, the following issues need to be examined:

L!d

Lf21d

a

The A and B matrices and the parameter vector 0 are given in reference [20]. In the above formulation, all parameters are in actual units. Also, it is assumed that the machine power angle, 6, is available for measurement. The parameter vector 0 is estimated successively in three stages.

It is desirable to de-couple the d- and q-axis state-variables appearing in equation (1) so that corresponding orthogonal axis rotor body currents present during large disturbance transient events, can be observed through de-coupled forms of the machine state space equation given by equation (1). De-coupling the d- and q-axis equations also facilitates de-coupled estimation of machine parameters. It will now be shown that using a record of experimentally measured input-output data (vd, v,, id, i,, ifd*) obtained during a large disturbance transient event, it is possible to estimate stator

25

d- and q-axis flux-linkages , provided an estimate of stator resistance, & is known beforehand. An estimate of Ra can be obtained through small disturbance operating data using the procedure described in reference [ 4 ] . Under large disturbance conditions, the rate of change of stator flux linkages cannot be ignored. In such cases, machine stator voltage equations are arranged in a state-space form to solve for the flux linkages @d and aqusing numerical integration.

X ( k + 1) = A *X ( k ) + B . U ( k )

(2)

where X = [ a d Qq]T . Matrices A , B, U are defined in Appendix A.l. For computing initial flux linkages at steady state (prior to a transient disturbance), the following equations are used:

(3)

where Id Iq, Vd, Vq correspond to the steady-state stator d- and q-axis currents and voltages respectively. With estimates of stator d- and q-axis flux-linkages, the speed-voltage terms appearing in the d- and q-axis equivalent circuits (see Fig. 1) can be computed. This would facilitate in de-coupling equation (1) into two subsystems, one for each orthogonal axis: For the d a i s model,

where, X , = [id

ild ifild i;Ir ;

R;

For the q-axis model,

vq = vq - Odwr IV. ARTIFICIAL NEURAL NETWORK BASED ESTIMATION OF ROTOR BODY CURRENTS

The de-coupled system of equations (4) and ( 5 ) are assumed to be observable, linear and time-invariant. We propose a set of observers (one for each axis) which can map sequences of measurable currents and stator flux linkages to the unmeasurable rotor body currents. Let the vector of rotor body currents at any instant k be represented by

IEEE Transactions on Energy Conversion, Vol. 14, No. 1, March 1999

Neural Network Observers for On-line Tracking of Synchronous Generator Parameters S. Pillutla, Student Member A. Keyhani, SM

I. Kamwa, Member

Department of Electrical Engineering The Ohio State University Columbus, OH 43210

IREQ, 1800 Lionel-Boulet Varennes (QC) Canada J3X 1S1

Abstract: This paper presents a methodology for implementing artificial neural network (ANN) observers in estimating and tracking synchronous generator parameters from time-domain online disturbance measurements. Data for training the neural network observers are obtained through off-line simulations of a synchronous generator operating in a one-machine-infinite-bus environment. Nominal values of parameters are used in the machine model. After training, the ANN observer is tested with simulated on-line measurements to provide estimates of unmeasurable rotor body currents and in tracking simulated changes in machine parameters. Keywords: Synchronous generators, parameter estimation, artificial neural networks, observers, parameter tracking. I. INTRODUCTION

In recent years, there has been a considerable interest in the online estimation of synchronous generator parameters [1-51. Online methods are particularly attractive since the machine’s service need not be interrupted and parameter estimation is performed by processing measurements obtained during the normal operation of the machine. The need for on-line parameter estimation arises because generator parameters tend to deviate substantially from nominal values obtained from off-line testing. These deviations are usually due to magnetic saturation [6-91, machine aging, internal temperature, the effect of centrifugal forces on winding contacts, and incipient faults within the machine. It is to be noted that although incipient faults can typically be detected by continuous or periodic monitoring of characteristic quantities [IO-123 (such as efficiency, fuel and oil consumption, impurities in the cooling stream, radio frequency noise level, temperature etc.), not all faults may manifest themselves in change of these quantities. However, parameter estimates obtained by processing online measurements are useful for generator condition monitoring [13]. For instance, a significant reduction in the field-to-stator turns ratio (and field PE-064-EC-1-09-1997 A paper recommended and approved by the IEEE Electric Machinery Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Energy Conversion. Manuscript submitted May 9, 1997; made available for printing October 3, 1997.

resistance) would indicate a shorted field-coil. By using an extensive database, online parameter estimates may be used to monitor generator condition and take preventative maintenance measures before complete breakdown occurs. Measurements acquired during synchronous generator testing are often a small subset of the machine’s state vector. The remaining unmeasurable components of the state vector are typically composed of currents in the rotor body circuits [14-171 which encapsulate high frequency sensitivity due to the flow of eddy currents in solid parts. In the absence of full-state measurement, the parameter estimation algorithm may require heavy computation to achieve convergence or may even fail to converge on a set of parameters, especially when poor initial estimates are used. However when the state vector is completely known, parameter convergence is guaranteed and recursive estimation algorithms may be used to estimate machine parameters. Observers are frequently used to estimate unmeasurable state vector components based on operating data. It must be recognized that the problem of estimating a system’s un-measurable states by processing its measurable states is essentially a system identification task and neural networks offer a promising means of achieving this (see reference [25]). In this paper, an ANN observer is developed to map sequences of measured machine outputs to un-measurable rotor body currents by processing data acquired during transient disturbances. Data for developing the neural network model are obtained through off-line simulations of the synchronous machine model connected to an infinite bus system. It is assumed that the structure and order of the machine model used in generating data for developing the observer is accurately known. Nominal parameter values are used in the machine model. These assumptions are reasonable because, over the years, significant advances have been made to accurately model synchronous generators based on well-established modeling and parameter estimation techniques [I-211. During training, all state variables of the machine model are assumed measurable. This would correspond to the stage when simulations are carried out to obtain a sufficiently accurate observer model. After developing the neural network observer, it can be used to estimate rotor body currents by processing measurements acquired on-line in an actual operating environment. 11. MACHINE MODEL DESCRIPTION AND

PROBLEM FORMULATION The structure of the synchronous machine model used in this study (Model 3’.3) is shown in Fig.1 and is based on the 0885-8969/99/$10.00 0 1997 IEEE

24

reciprocaI per-unit system in which all parameters are referred to the stator (see reference [20]). To use the above models with actual units of resistance and inductance in the estimation procedure, the following turns ratio transformation between the field and the stator should be used:

where ifd* the field winding current in ampere, vfd is the field voltage in volts, both quantities measured on the field side of the generator. Rfd* is the field winding resistance in ohm as measured on the field side. vd, vfd, and Rfd denote corresponding transformed quantities on the stator side of the generator through the field-to-stator turns ratio a.

Stage 1 : Estimation of linear model parameters. The first stage of the estimation process involves the estimation of armature circuit parameters from small excitation disturbance data. As described in reference [4], the armature resistance & , the mutual inductances Lad, and L,,, the field-to-stator turns ratio, a, and the field-resistance, Rid* can be estimated in this stage. Stage 2 : Development of neural network saturation model. In this stage, a multidimensional artificial neural network based non-linear mapping is established to map small excitation disturbance responses to a set of experimentally obtained mutual inductances over a wide range of operating conditions [5]. Stage 3: Observer based estimation of rotor body currents and estimation of rotor body parameters. Using armature circuit parameters obtained from stages 1 and 2, and nominal values of rotor body parameters in the machine model, simulated measurements will be generated to develop an artificial neural network (ANN) observer to estimate rotor body currents. The ANN observer will be used to estimate rotor body currents from large disturbance transient data. Following this, a recursive parameter estimation technique which utilizes measured large disturbance data and ANN estimated rotor body currents is used to update all machine parameters.

q-axis Fig. 1: Model 3'.3: On-line Model Structure

For discrete-time systems, the coupled state space representation of the models in Fig. 1 can be written as: X ( k + 1) = A ( @ ) *X ( k ) + B ( @ ) . U ( k )+ w ( k ) Y(k + 1) = C - X ( k + 1)+ v(k + 1)

(1)

wfi) and vfi) denote the process and measurement noise, respectively. In addition,

x = [i,

id ilq i2, i,,

i,,

Y = [i, i, i>17 ;

Ri

R!d

Rf21d

'l

Lad

U ,'

Define a suitable set of observer input patterns (machine variables) for the observation task. What should the training pattern be ? Is the observer robust to small deviations in synchronous generator parameters ? Is the observer robust to noisy input measurements ? 111. PROCEDURE FOR STATE VARIABLE DE-COUPLING UNDER LARGE DISTURBANCE CONDITIONS

iPld i;,Ir;

U = [ v , v , v;,]' ;

= LRa

Since the main intent of this paper is to describe the observer based parameter estimation technique, Stage 3 will be described in detail. The reader is referred to references [4,5] for details pertaining to stages 1 and 2 of the estimation process. In order to apply the concept of ANNs for estimating rotor body currents, the following issues need to be examined:

L!d

Lf21d

a

The A and B matrices and the parameter vector 0 are given in reference [20]. In the above formulation, all parameters are in actual units. Also, it is assumed that the machine power angle, 6, is available for measurement. The parameter vector 0 is estimated successively in three stages.

It is desirable to de-couple the d- and q-axis state-variables appearing in equation (1) so that corresponding orthogonal axis rotor body currents present during large disturbance transient events, can be observed through de-coupled forms of the machine state space equation given by equation (1). De-coupling the d- and q-axis equations also facilitates de-coupled estimation of machine parameters. It will now be shown that using a record of experimentally measured input-output data (vd, v,, id, i,, ifd*) obtained during a large disturbance transient event, it is possible to estimate stator

25

d- and q-axis flux-linkages , provided an estimate of stator resistance, & is known beforehand. An estimate of Ra can be obtained through small disturbance operating data using the procedure described in reference [ 4 ] . Under large disturbance conditions, the rate of change of stator flux linkages cannot be ignored. In such cases, machine stator voltage equations are arranged in a state-space form to solve for the flux linkages @d and aqusing numerical integration.

X ( k + 1) = A *X ( k ) + B . U ( k )

(2)

where X = [ a d Qq]T . Matrices A , B, U are defined in Appendix A.l. For computing initial flux linkages at steady state (prior to a transient disturbance), the following equations are used:

(3)

where Id Iq, Vd, Vq correspond to the steady-state stator d- and q-axis currents and voltages respectively. With estimates of stator d- and q-axis flux-linkages, the speed-voltage terms appearing in the d- and q-axis equivalent circuits (see Fig. 1) can be computed. This would facilitate in de-coupling equation (1) into two subsystems, one for each orthogonal axis: For the d a i s model,

where, X , = [id

ild ifild i;Ir ;

R;

For the q-axis model,

vq = vq - Odwr IV. ARTIFICIAL NEURAL NETWORK BASED ESTIMATION OF ROTOR BODY CURRENTS

The de-coupled system of equations (4) and ( 5 ) are assumed to be observable, linear and time-invariant. We propose a set of observers (one for each axis) which can map sequences of measurable currents and stator flux linkages to the unmeasurable rotor body currents. Let the vector of rotor body currents at any instant k be represented by