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A neural diagnostic system for the monitoring of transformer heating
Measurement Vol. 18, No. 1, pp. 35 46, 1996
PH: S0263-2241 (96) 00043-7
ELSEVIER
Copyright © 1996 Elsevier Science Ltd Printed in The Netherlands. All rights reserved 0263-2241/96 $15.00 +0.00
A neural diagnostic system for the monitoring of transformer heating P. Daponte a,., D. Grimaldi
b,# A. Piccolo b, D.
Villacci c
a Dip. di. lng. dell'Informazione ed Ing. Elettrica, Universitfi di Salerno, 84084 Fisciano, SA, Italy b Dip. di Elettronica, Informatica e Sistemistica, Universitfi della Calabria, 87030 Rende, CS, Italy c Dip. di Ing. lndustriale, Universitfi di Cassino, 03043 Cassino, FR, Italy
Abstract
A new method to monitor and estimate heating of the transformers in electrical power systems is proposed. It is based on neural identification techniques and was tested for a real transformer operating under typical environmental and load conditions. Finally, some considerations on the applicability of the method to real protection and control systems in electrical power networks are also made. Copyright © 1996 Elsevier Science Ltd. Keywords: Diagnostic; Transformer heating; Neural network
strategy. This is becoming ever more necessary due to: (i) more and more stringent environmental constraints on new overhead lines, (ii) greater difficulties in finding free space to locate transformers and to lay new power cables in highly populated urban areas [ 3 - 5 ] , and (iii) problems of electromagnetic compatibility with other systems (telecommunication, transport, etc.) [6]. It is possible to intervene in this sense because (i) the performances of components that use new technologies have improved and (ii) real component operating conditions are generally less onerous than planned. All these elements have encouraged operators, especially private ones, to increase the load levels of existing networks. The need to know with increasing accuracy the behaviour and the real operating limits of components has thus risen [ 1]. To pursue these objectives, use must be made of (i) a distributed measurement and diagnostic
1. Introduction
The real need for advanced power system automation is associated with (i) the growing demand for reliable and flexible power supply systems, and (ii) the desire for optimised network operation in both normal and emergency conditions [-1,2]. Historically, utilities have used transmission and distribution systems conservatively, providing high reliability through moderate loading levels and redundancies. These strategies imply limited exploitation of the components and require considerable investments compared to the service given. Recently, however, a critical revaluation is being made of the degree to which components are underused and of the obsolescence investment
* E-mail: d a p o n t e @ n a d i s . d i s . u n i n a . i t * E-mail: g r i m a l d i @ c c u s c l . u n i c a l . i t 35
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P. Daponte et al.
system for monitoring on-line both the quantities that are of interest (electrical, environmental and others) and network component operation [3], and (ii) protection and control systems based on component models that are capable of taking into account both real network and environmental operating conditions. Power transformers are among the components that prove more interesting to be monitored: they are currently subjected to reduced load levels especially in transmission networks (normally 60-70% of the rated value [7,8]) and nowadays perform better due to new materials and more evolved construction techniques. It should be borne in mind that power transformers are the "bottlenecks" in a network's thermal overload capability in the same way as power cables: better use of these produces a direct improvement in the network thermal overloading capability. The benefits are particularly noticeable since transformers are widespread in both transmission and distribution networks. Unlike research on overhead and underground power lines which gives rise to problems related to defining boundary conditions and the signals to be transmitted over long distances, research on transformers allows attention to be more closely focused on aspects such as (i) measurement signal gathering, (ii) signal processing, and (iii) diagnostics [3,9]. Furthermore, transformers have more definable boundary conditions, more compact dimensions and a reduced number of quantities to be considered: all these allow the solutions that will be proposed to be applied with significant advantages. The main limiting factor in a transformer's loading capability is determined by the temperature of the hottest part of its windings (hot-spot temperature). Therefore it is necessary to know this temperature and how it varies over time in order to be able to either decide if the load level is appropriate or evaluate if a short- or long-term overload can be attempted [10-12]. The definition of the insulation state, the identification of the components' real residual thermal life and the overload capability of the transformer itself depend on the accuracy with which these temperatures are evaluated. Unfortunately, accurate hot-spot temper-
ature evaluation is an objective that is very difficult to reach. In numerous studies carried out on the subject, the difficulties encountered in setting up adequate thermal models are clearly underlined [13-16]. These difficulties are due to the heat transfer process in the transformer which is distributed over many complex surfaces made up of different materials. Also, for natural cooling of the transformer when much of the heat is transferred by convection, the steady-state equilibrium equations are nonlinear. Hence, in this case too, the mathematical description of the temperature distribution in the transformer is very complex. The methods used nowadays to determine transformer loading capabilities are in general the ones proposed by Standards Organisations such as the International Electrotechnical Commission (IEC), the American National Standard Institute (ANSI) and the National Electrical Manufacturer Association (NEMA) [13]. They are based on different simplifying hypotheses such as: (i) a linear temperature increase for the oil inside the winding; (ii) a constant difference between the average winding temperature rise and the oil gradient at any position along the winding; (iii) the hot-spot temperature as the sum of the top-oil temperature and the average winding temperature rise corrected by a conservative factor; (iv) the influence of solar thermal energy being taken as negligible. Because of these approximations the ability of these models to predict transformer temperature under realistic loading conditions is obviously limited [ 13,17]. If more accurate results are required, it is necessary to follow a different approach. One possibility is offered by the use of on-line measurement and monitoring systems which enable Artificial Neural Network (ANN) recursive techniques to be used to identify the real thermal model needed to evaluate transformer thermal capability. In this paper an approach that uses ANN-based identification techniques is proposed. Recent studies have proved that ANN-based identification techniques are particularly suitable for modelling complex nonlinear systems [18-22]. These techniques can be applied to any type of transformer and are capable of providing useful results [23-26]. Beginning with direct measurements of hot-spot
P. Daponteet al. temperatures and the quantities that determine transformer heat generation and thermal exchange, the method proposed in this paper allows identification of the equivalent thermal model for each transformer and is then capable of updating it on-line as the boundary conditions change. Once the thermal model is known it is possible directly to determine transformer hot-spot temperature against load and environmental condition variations. In order to (i) verify the proposed method, (ii) optimise the ANN design, and (iii) improve the training-set technique selected, a laboratory test was carried out.
2. Neural identification of the transformer heating model A suitable transformer heating model must furnish the winding hot-spot temperature in relation to (i) the RMS values of load current, (ii) the transformer design characteristics and (iii) the environmental conditions. The construction characteristics of a transformer are geometrical shape and type of cooling system. The weather conditions comprise environmental temperature, the thermal flux associated with solar radiation and wind speed, If I(t) is the vector representing the RMS values of load current, W(t) is the vector for the weather conditions and H'(t) is the hot-spot temperature at time t, then for fixed transformer design characteristics the transformer heating model can be regarded as a nonlinear function f whereby: H'(t) = f[I(7), W(t)] = f[-X(t)]
(1)
with X being the vector of all inputs. Although the current is the main cause of the transformer heating, there are undoubtedly additional undesired heating phenomena in the transformer itself, for example due to eddy current, higher harmonic currents, etc. Nevertheless these additional heating phenomena can be considered negligible compared to the joule effect determined by l(t), as is the case for power cables, switchgears and motors, etc. Because of the high complexity and non-linearity of the electrical and non-electrical phenomena it is very difficult to set up a traditional analytical
37
model capable of accurately giving the hot-spot temperature. On the other hand ANNs offer an alternative methodology for determining the winding hot-spot temperature. In fact in other cases they have provided accurate results characterised by nonlinear complex phenomena [ 18,26,27]. The neural network equivalent transformer heating model is outlined in Fig. 1, for fixed transformer characteristics. The ANN is a parallel distributed network comprising many interconnected processing elements (neurons) characterised by input vectors W(t), I(t) and a single output vector H'(t). Each neuron processes information in a predetermined manner and furnishes the results as the ANN output or to another neuron. The expression for the non-linear input/output transfer characteristic of the ith neuron is:
hi=g(a~=1wijxij-bi)
(2)
where hi is the ith neuron output signal, wi~ is the weight of the connection between the ith neuron and the jth neuron of the previous layer, xia is the input signal to the ith neuron from the jth neuron of the previous layer, n is the number of neurons in the previous layer, and bi is the ith neuron bias. By means of many cross-connections between the neurons they are combined to form: (i) a set of input layer neurons, (ii) a set of output layer neurons and (iii) a set of hidden layer neurons. The choice of the number of input/output neuron layers is closely connected to the desired accuracy. The number and dimensions of the hidden layers depend only on the ANN performance reached in terms of model fidelity and operating speed. In order to train the ANN model transformer heating it is necessary: (i) to specify the "learning set" constituted by an adequate number of input [-Wj(t),Ij(t)] and target output I-Hi(t)] vector
I H'(t Fig. 1. Transformerheating modeling:production phase.
38
P. Daponte et al.
pairs (with j = 1, 2. . . . . No, where N¢ is the number of samples) and (ii) to minimise the objective function defined as the relative difference, normally in the Euclidean sense, between the actual ANN output H'(t) and the target outputs H(t) (Fig. 2). It is possible to minimise the objective function by using a "learning algorithm". The strategy of the "learning algorithm" is devoted: (i) to determining the input/output transfer characteristic of each neuron by a supervised learning section, (ii) to modifying the connection weights and the neuron bias by means of an adaptive process (error backpropagation) which minimises the output neuron errors ei on the basis of the following relationships: wu(k) = wij(k -
1)+ ~ e . i ( k - 1 ) h i ( k -
bi(k) = b i ( k - 1 ) + ~ e i ( k -
1)
(3)
1)
where k is the current learning algorithm iteration and c~is the "learning coefficient". This phase ends when the ANN furnishes the outputs necessary for the learning set. Suitable software developed in a TurboPascal environment to simulate a feed-forward ANN was used to produce the neural transformer heating model according to the previous considerations. An ANN with neurons characterised by the following input/output transfer characteristic (a
Hct)
H'(~0
sigmoidal function) was considered: g(x) -
1 l + e ,x
(4)
- -
where a is the sigmoid steepness. Progress in the ANN learning phase was monitored through a decrease in the maximum relative error ME defined as: [-IHi(t)[- Ini(t)17 ME=max L ]H~-t~ .j
i = 1.... ,No.
(5)
Some efforts must be devoted to determining the "learning set" in order to obtain a high ANN accuracy. In the validation phase (Fig. 3), this ANN accuracy is tested using new input and output vector pairs called the "validation set". These vector pairs are different from the learning phase ones, but have similar characteristics. If the ANN performance does not reach the desired level of accuracy a new learning phase and a modified learning set are necessary. The modified learning set must additionally take into account any new information obtained by the previous set. After the learning and validation phases, a new phase, called the production phase begins in which the ANN is used to provide the corresponding outputs required for any input (Fig. 1). The ANN trained in this manner represents a valid model of the transformer heating for which it has been trained. Using this trained ANN for different transformers, even if they have similar design characteristics, could give less accurate results. Nevertheless, training the neural network for a specific transformer could constitute the
H(t)
Learning algorithm
Fig.2. Transformerheatingmodeling:learningphase,hot-spot temperaturetrend -- real H(t), estimatedH'(t).
Fig. 3. Transformerheatingmodeling:validationphase.
39
P. Daponte et al.
starting point for training the ANN on transformers with the same design characteristics, which would undoubtedly give the advantage of reduced training times.
Table 1 Main characteristics of the transformer Nameplate rating
25 kVA 10 kV/380 V 195 W 776 W 73,1 C 136 kg 62 kg 310 kg 64x 16x80cm ONAN MACE/87
Vp.m~,/ V~o.d~y
3. Experimental application In order to optimise the ANN architecture, and to develop the best learning strategy, various experiments are necessary. Figure4 shows the measurement station utilised to acquire the transformer input primary current, the hot-spot temperature and the environmental condition data. The experiments were carried out on an oil-immersed distribution transformer whose main characteristics are reported in Table 1. There is no precise general rule to determine exactly the position in which to measure the hotspot temperature, since the hot-spot position varies depending on the transformer size and design characteristics. Hence the manufacturer's specifications must be referred to, since they are capable, for each type and size of transformer, of indicating the most probable positions of the hot-spot. Thus in the transformer under test, two type k thermocouples were installed (Fig. 5): in the Medium (T0 and Low voltage (TI0 windings on the core central column at the predicted winding hot-spot locations (the upper side of the windings between the second and third coils) and protruding into the inner oil
Iron losses* Copper losses (full load)* Top oil temperature rise at full load* Weight of core and coil assembly Weight of oil Total weight Length, width and height of tank Type of cooling Factory/year * Values reported to 75°C. ~ With environmental temperature of 21°C.
)t
ement
(a)
MV winding )il duet LV winding
(b)
j I
I I
"~
~
I
Iref(t)
~
1
~
Hot-spot measurement
N'.:tt~N
Regulator I(t)_..2_~ Hot-spo';and
Data
~
acquisition
andeonttolunit l
N -'N
environmental data ~
~
C
o
Transforrnerunder test Fig. 4. Measurement station.
n
I
i Fig. 5. Position of the thermocouples.
40
P. Daponte et al.
ducts adjacent to the hot-spot locations. A Microstar DAP 2400e data acquisition board was used as a data acquisition unit and controller for the transformer tap-changer. Its main characteristics are shown in Table 2. The current transducer was a Scientific Columbus transducer with AC input 0-5 A - - 50 Hz; DC output 1 mA, and load resistance 0-10 kf~.
3.1. Learning and validation phases In order to build the learning set, the heating test input/output vectors consider only the loading current and the environmental temperature. The contributions to hot-spot heating due to additional losses present in the transformer and hysteresis phenomena are automatically taken into account by the hot-spot measurement and thus will be implicitly included in the function f of equation ( 1 ). To correctly reproduce the heating process, various real daily loading current patterns were monitored in urban distribution electrical networks. That used in the learning phase is shown in Fig. 6, where the relative amplitude has been referred to the nameplate rating of the transformer under test. In particular, Fig. 6 shows a daily loading current versus time, including one of the possible transformer overload conditions. Regarding the trend of the environmental temperature considered in the laboratory tests, among all the possible temperature trends a sinusoidal one was chosen. This can be considered as being
Table 2 Data acquisition board characteristics Microstar DAP 2440e data acquisition I/O characteristics Analog inputs Samples Analog outputs Samples Control section Microprocessor RAM Processing section DSP RAM
16 166 kHz 2 166 kHz 80166/16 MHz 1024 kbytes 5600/1 MHz 6 kbytes
a real hypothesis according to the IEC loading guide. On the basis of the chosen selected loading curves and the environmental temperature, successive input and target output vector pairs were specified to train the ANN. The criteria used to establish the input vector elements take into account the need to furnish information capable of giving the ANN an adequate accuracy during the production phase. In particular, it is necessary to supply the ANN with the existing correlation between the current and hot-spot temperature trends. As a matter of fact power transformers show "thermal-memory behaviour"; consequently at time to in order to estimate the hot-spot temperature at time t~ = (to + At) it is necessary to take into account the "thermalmemory effect". Thus, at time t o the ANN input is constituted by the load current and the environmental data measured at time to and by the load current and the environmental data recorded during the N time-steps (At) previous to time t~. As shown in Fig. 7, these values can be produced for successive time intervals, starting at to. As proven by the calculation results the values of the load current must be squared; furthermore, the input vector also includes environmental values. The output vector is constituted only by the hot-spot temperature H(t). On the basis of the input/output vector characteristics, the ANN architecture was organised with X = 2(N + 1) input neurons. Furthermore, in order to improve the "neuron-memory capacity" recurrent connections (back-connections) into a set of hidden neurons, as shown in Fig. 7 were introduced [-28,29] At the end of the learning phase the ANN structure which furnishes accurate evaluation of the hot-spot temperature trend consists of: X = 40 input neurons; one hidden layer, including Y= 81 neurons, according to the adopted rule Y = 2X + 1 to avoid "minimum local error" during the learning phase; and only one neuron in the output layer. The number of nodes in the input and output layers were fixed on the basis of the number of input/output signal samples necessary to describe the system dynamic behavior. As regards the number and dimensions of the hidden layers, they
P. Daponte et al.
41
(a)
lp.u.l
1.2 Nameplate J
rating
of transformer
i L
0.8
I
II IS ¢
0.4
\
J
06.00
[°CI
i
J
i
10.00
14.00
18.00
X
(b)
i
22.00
02.00
T i m e [h]
(measured)
90
70
_..j/'//
50
30 06.00
E lp.ul
0.04
i
i
i
14.00
18.00
22.00
(c)
0.04 0
i
10.00
l
x% .g
02.00
T i m e [h]
&,.%/,z~,/"~a"
4,
rj
| V L /J 06.00
10.00
14.00
18.00
22.00
02.00 T i m e [h]
Fig. 6. Learning phase. (a) Learning current curve versus time with overloading conditions, (b) hot-spot temperature trends and (c) relative error E between the measured H and calculated H ' hot-spot temperature values.
were obtained by applying a trial and error procedure, starting from empirical suggestions given by the ( Y = 2 X + 1) rule and paying particular
attention to the accuracy of the learning and validation phases [18,21,22]. Subsequently, in order to ensure that the ANN "learning phase"
P. Daponte et al.
42
I2
W
j'-
I
] ' - " \ Current / ~-::~-Environment / \ . , / '/~temperature
/~
!~/ ,....
/ J
\ ,
L t-
' ,, /[ ". . . . / [ '\\
/
'-\/~
"
',
....
(t0-NAt)o . ° (to-kAt). . (t0-At) tO \X\ I2(ti ) WO O / / / I if, ) \ /--/
.
\
.
.
.
.
.
.
.
.
.\.~
.
\
/
S
/j~J~
.
.,
Weights .~ I ]'
[ H (tO+l)
('~'~F~ Lh~l" ~ (" h i ")
Fig. 7. Concise representation of input data (currents and environmental temperatures).
begins and progresses and that there is a minimum output error, the learning coefficient ~ and steepness of the sigmoidal activation function were assumed to be constant. Furthermore the following values were assumed: the time interval amplitude (At) was fixed at 15 min; the sigmoid steepness was 1.5; the learning coefficient ~ was 0.01. Higher learning coefficient values would have made the learning phase quicker, but they would have compromised algorithm stability and therefore the accuracy required. Ten thousand learning algorithm iterations were carried out, thereby guaranteeing a maximum relative error ME of less than 0.06 p.u. One iteration corresponds to one 24 h observation period training set, and is composed of Nc = 290 input and target output vector pairs.
The final results of the learning phase are shown in Figs. 6b and c. The first shows the trends of measured H(t) and calculated H'(t) hot-spot temperatures, the second shows their relative differences: Ei--
] H ' i ( t ) l - IH,(t)i IHi(t)l
i = 1. . . . . No.
(6)
It is possible to observe that the maximum absolute ANN error is lower than 3°C, while the maximum relative ANN error, ME, is lower than 0.06 p.u. This result allows the ANN to be considered as ready to accurately reproduce transformer hotspot heating. The validating phase uses test data which were
43
P. Daponte et al.
I
[p.u.l
(a) Nameplate rating of transformer
0.8
1
0.4
J
i
06.00
[°CI
10.00
(b)
i
14.00
18.00
22.00
02.00
Time [h]
H (measured)
70
//~/
o~J'~ ~"':',I\.,
50
30
E [p.ul 0.~
0.04
i
6.00
t
10.00
14.00
18.00
22.00
(c)
" V 06.00
i
02.00
Time [h]
,~4-v'"......
\
14.00
18.00
22.00
02.00
Time [h]
Fig. 8. Validation phase. (a) daily current against time, (b) hot-spot temperature trends and (c) relative error E between the measured H and calculated H' hot-spot temperature values.
not input to the ANN in the learning phase. Figs. 8 and 9 show two different validation sets, according to environmental conditions which vary with a
daily sinusoidal trend. In particular, Fig. 9 shows an overload current condition. Hot-spot temperatures obtained by the ANN
44
P. Daponte et al.
I
(a)
[p.u.]
1.2 Nameplate rating of transfer
0.8
0.4
i
06.00
[°C]
10.00
(b)
=
I
14.00
--
I
_ _
18.00
22.00
02.00
Time [h]
18.00
22.00
02.00
Time [h]
H (measured)
(calculated) 70
\, 50
30
6.00
10.00
14.00
E [p.u] /
0.04 I~(c)
06.00
,
10.00
14.00
18.00
l
22.00
02.00
Time [hi
Fig. 9. Validation phase. (a) daily current against time including overload conditions, (b) hot-spot temperature trends and (c) relative error E between the measured H and calculated H ' hot-spot temperature values.
P. Daponte et al.
were compared to the real detected temperatures obtained for the same transformer loading values. Figures 8 and 9 show the relative error between the real hot-spot temperature and the one predicted by the ANN. In these cases the ANN performance also proved to be satisfactory.
4.
Concluding remarks
This paper has proposed a new method to monitor and estimate the transformer heating in power systems based on identifying Artificial Neural Networks (ANNs). The ANN design and learning process have been optimised and validated in relation to a real transformer. The ANN model of the transformer heating provides the winding hot-spot temperature trend as the transformer load current and environmental conditions vary. The results obtained were verified experimentally and showed the accuracy of the approach. Because of its characteristics the method can be used by plant operators to fix acceptable transformer loads and overload limits. The greater accuracy of the ANN thermal model compared to the traditional thermal models shown in the load guides undoubtedly allows the exploitation margins of the power transformers to be increased. In any case it must be borne in mind that the method can only be applied if the winding hot-spot temperature, the load current and the environmental conditions can be monitored. Moreover it must be noted that the use of neural networks for transformers could become even more widespread in the light of recent studies. In these studies, neural networks have been used with very encouraging results to carry out monitoring and control tasks for: • real-time analysis of the dissolved gases in the over-heating transformer oil, from which it is possible to detect and diagnose the type of degradation occurring within the transformer [30,31]; • selective detection of partial discharges arising from pulse-shaped noise signals which are normally present in transformers and which can
45
give low level reliability to measurements carried out using traditional instrumentation [32]; • setting up a measurement system capable of discriminating currents arising from internal transformer faults and from magnetising inrush currents (the presence of the latter often cause false tripping of the currently-used differential protection systems [33]). These considerations could enable integrated transformer protection and control systems to be developed in the future, based on the contents of the different elementary diagnostic and protective functions already implemented using different ANNs.
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Transformers), Survey of power transformer overload field practices 161 (1995) 147-179. CIGRE, Working Group 12.09 (Thermal Aspect of Transformers), A survey of facts and opinion on the maximum safe operating temperatures under emergency conditions, Paris (1995) 25-48. G.L. Alegi and W.Z. Black, Real-time thermal model for an oil-immersed forced-air cooled transformer, IEEE Trans. Power Deliv. 2 (1990). F. Lindsay, Temperature rise of an oil-filled transformer with varying load, IEEE Trans. Power Appar. Syst. 9 (1984) 2530-2535. C.M. Arturi, Calcolo perfezionato delle temperature nei trasformatori in olio, L'Energia Elettrica 6 (1981) 242-251. W.P. Linden, Predicting liquid filled transformer loading capability, IEEE Trans. Indust. Applic. 1 (1994) 170-178. CIGRE, Working Group 12.09 (Thermal Aspect of Transformers), Analytical determination of transformer windings hot-spot factor, Electra 161 (1995) 29-33. A. Anderson and E. Rosenfeld, Neurocomputing: Foundations of Research, MIT Press, Cambridge, MA (1988). R. Hecht-Nielsen, Neurocomputing, Addison-Wesley, U.S.A. (1990). T. Khanna, Foundation of Neural Networks, AddisonWesley, U.S.A. (1990). E. Sanchez-Sinecio and L. Lau, Artificial Neural Networks, IEEE Press, Piscataway, NJ (1992). J.A. Freeman and D.M. Skapura, Neural Networks: Algorithms, Applications and Programming Techniques,
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[23] S.R. Chu, R. Shoureshi and M. Tenorio, Neural networks for system identification, IEEE Control System Magazine 2 (1990) 31-35. [24] K.S. Narendra and K. Parthasarathy, Identification and control of dynamical systems using neural networks, IEEE Trans. Neural Networks 1 (1990) 4-27. [25] D.F. Specht, A general regression neural network, IEEE Trans. Neural Networks 6 (1991) 568 576. [26] A. Bernieri, M. D'apuzzo, L. Sansone and M. Savastano, A neural network approach for identification and fault diagnosis on dynamic systems, IEEE Trans. Instrumentation and Measurement 6 (1994) 867-873. [27] A. Bernieri, P. Daponte and D. Grimaldi, ADC neural modeling, IEEE Trans. Instrumentation and Measurement April (1996) 627-633. [28] S. Grossberg, Some networks that can learn, remember and produce any number of complicated space-time patterns, J. Math. Mechanics 1 (1991) 115-120. [29] S. Santini, A. del Bimbo and R. Jain, Block-structured recurrent networks, Neural Networks 1 (1995). [30] N. Takeki, Y. Yoshihide, I. Hideo and A. Yoshihiro, Gas discrimination method for detecting transformer faults by neural network, IEEE Trans. Power Deliv. (1994). [31] J.J. Dukarm, Transformer oil diagnosis using fuzzy logic and neural networks, IEEE, CCEGE/CCGEI (1993). [32] H. Borsi, E. Gockenbach and D. Wenzel, Separation of partial discharges from pulse-shaped noise signals with the help of neural networks, IEE Proc. Sci. Meas. Technol. 1 (1995) 57 63. [33] L. Perez, A.J. Flechsig, J.L. Meador and Z. Obradovic, Training an artificial neural network to discriminate between magnetizing inrush and internal faults, IEEE/PES Winter Meeting (1993).
PH: S0263-2241 (96) 00043-7
ELSEVIER
Copyright © 1996 Elsevier Science Ltd Printed in The Netherlands. All rights reserved 0263-2241/96 $15.00 +0.00
A neural diagnostic system for the monitoring of transformer heating P. Daponte a,., D. Grimaldi
b,# A. Piccolo b, D.
Villacci c
a Dip. di. lng. dell'Informazione ed Ing. Elettrica, Universitfi di Salerno, 84084 Fisciano, SA, Italy b Dip. di Elettronica, Informatica e Sistemistica, Universitfi della Calabria, 87030 Rende, CS, Italy c Dip. di Ing. lndustriale, Universitfi di Cassino, 03043 Cassino, FR, Italy
Abstract
A new method to monitor and estimate heating of the transformers in electrical power systems is proposed. It is based on neural identification techniques and was tested for a real transformer operating under typical environmental and load conditions. Finally, some considerations on the applicability of the method to real protection and control systems in electrical power networks are also made. Copyright © 1996 Elsevier Science Ltd. Keywords: Diagnostic; Transformer heating; Neural network
strategy. This is becoming ever more necessary due to: (i) more and more stringent environmental constraints on new overhead lines, (ii) greater difficulties in finding free space to locate transformers and to lay new power cables in highly populated urban areas [ 3 - 5 ] , and (iii) problems of electromagnetic compatibility with other systems (telecommunication, transport, etc.) [6]. It is possible to intervene in this sense because (i) the performances of components that use new technologies have improved and (ii) real component operating conditions are generally less onerous than planned. All these elements have encouraged operators, especially private ones, to increase the load levels of existing networks. The need to know with increasing accuracy the behaviour and the real operating limits of components has thus risen [ 1]. To pursue these objectives, use must be made of (i) a distributed measurement and diagnostic
1. Introduction
The real need for advanced power system automation is associated with (i) the growing demand for reliable and flexible power supply systems, and (ii) the desire for optimised network operation in both normal and emergency conditions [-1,2]. Historically, utilities have used transmission and distribution systems conservatively, providing high reliability through moderate loading levels and redundancies. These strategies imply limited exploitation of the components and require considerable investments compared to the service given. Recently, however, a critical revaluation is being made of the degree to which components are underused and of the obsolescence investment
* E-mail: d a p o n t e @ n a d i s . d i s . u n i n a . i t * E-mail: g r i m a l d i @ c c u s c l . u n i c a l . i t 35
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P. Daponte et al.
system for monitoring on-line both the quantities that are of interest (electrical, environmental and others) and network component operation [3], and (ii) protection and control systems based on component models that are capable of taking into account both real network and environmental operating conditions. Power transformers are among the components that prove more interesting to be monitored: they are currently subjected to reduced load levels especially in transmission networks (normally 60-70% of the rated value [7,8]) and nowadays perform better due to new materials and more evolved construction techniques. It should be borne in mind that power transformers are the "bottlenecks" in a network's thermal overload capability in the same way as power cables: better use of these produces a direct improvement in the network thermal overloading capability. The benefits are particularly noticeable since transformers are widespread in both transmission and distribution networks. Unlike research on overhead and underground power lines which gives rise to problems related to defining boundary conditions and the signals to be transmitted over long distances, research on transformers allows attention to be more closely focused on aspects such as (i) measurement signal gathering, (ii) signal processing, and (iii) diagnostics [3,9]. Furthermore, transformers have more definable boundary conditions, more compact dimensions and a reduced number of quantities to be considered: all these allow the solutions that will be proposed to be applied with significant advantages. The main limiting factor in a transformer's loading capability is determined by the temperature of the hottest part of its windings (hot-spot temperature). Therefore it is necessary to know this temperature and how it varies over time in order to be able to either decide if the load level is appropriate or evaluate if a short- or long-term overload can be attempted [10-12]. The definition of the insulation state, the identification of the components' real residual thermal life and the overload capability of the transformer itself depend on the accuracy with which these temperatures are evaluated. Unfortunately, accurate hot-spot temper-
ature evaluation is an objective that is very difficult to reach. In numerous studies carried out on the subject, the difficulties encountered in setting up adequate thermal models are clearly underlined [13-16]. These difficulties are due to the heat transfer process in the transformer which is distributed over many complex surfaces made up of different materials. Also, for natural cooling of the transformer when much of the heat is transferred by convection, the steady-state equilibrium equations are nonlinear. Hence, in this case too, the mathematical description of the temperature distribution in the transformer is very complex. The methods used nowadays to determine transformer loading capabilities are in general the ones proposed by Standards Organisations such as the International Electrotechnical Commission (IEC), the American National Standard Institute (ANSI) and the National Electrical Manufacturer Association (NEMA) [13]. They are based on different simplifying hypotheses such as: (i) a linear temperature increase for the oil inside the winding; (ii) a constant difference between the average winding temperature rise and the oil gradient at any position along the winding; (iii) the hot-spot temperature as the sum of the top-oil temperature and the average winding temperature rise corrected by a conservative factor; (iv) the influence of solar thermal energy being taken as negligible. Because of these approximations the ability of these models to predict transformer temperature under realistic loading conditions is obviously limited [ 13,17]. If more accurate results are required, it is necessary to follow a different approach. One possibility is offered by the use of on-line measurement and monitoring systems which enable Artificial Neural Network (ANN) recursive techniques to be used to identify the real thermal model needed to evaluate transformer thermal capability. In this paper an approach that uses ANN-based identification techniques is proposed. Recent studies have proved that ANN-based identification techniques are particularly suitable for modelling complex nonlinear systems [18-22]. These techniques can be applied to any type of transformer and are capable of providing useful results [23-26]. Beginning with direct measurements of hot-spot
P. Daponteet al. temperatures and the quantities that determine transformer heat generation and thermal exchange, the method proposed in this paper allows identification of the equivalent thermal model for each transformer and is then capable of updating it on-line as the boundary conditions change. Once the thermal model is known it is possible directly to determine transformer hot-spot temperature against load and environmental condition variations. In order to (i) verify the proposed method, (ii) optimise the ANN design, and (iii) improve the training-set technique selected, a laboratory test was carried out.
2. Neural identification of the transformer heating model A suitable transformer heating model must furnish the winding hot-spot temperature in relation to (i) the RMS values of load current, (ii) the transformer design characteristics and (iii) the environmental conditions. The construction characteristics of a transformer are geometrical shape and type of cooling system. The weather conditions comprise environmental temperature, the thermal flux associated with solar radiation and wind speed, If I(t) is the vector representing the RMS values of load current, W(t) is the vector for the weather conditions and H'(t) is the hot-spot temperature at time t, then for fixed transformer design characteristics the transformer heating model can be regarded as a nonlinear function f whereby: H'(t) = f[I(7), W(t)] = f[-X(t)]
(1)
with X being the vector of all inputs. Although the current is the main cause of the transformer heating, there are undoubtedly additional undesired heating phenomena in the transformer itself, for example due to eddy current, higher harmonic currents, etc. Nevertheless these additional heating phenomena can be considered negligible compared to the joule effect determined by l(t), as is the case for power cables, switchgears and motors, etc. Because of the high complexity and non-linearity of the electrical and non-electrical phenomena it is very difficult to set up a traditional analytical
37
model capable of accurately giving the hot-spot temperature. On the other hand ANNs offer an alternative methodology for determining the winding hot-spot temperature. In fact in other cases they have provided accurate results characterised by nonlinear complex phenomena [ 18,26,27]. The neural network equivalent transformer heating model is outlined in Fig. 1, for fixed transformer characteristics. The ANN is a parallel distributed network comprising many interconnected processing elements (neurons) characterised by input vectors W(t), I(t) and a single output vector H'(t). Each neuron processes information in a predetermined manner and furnishes the results as the ANN output or to another neuron. The expression for the non-linear input/output transfer characteristic of the ith neuron is:
hi=g(a~=1wijxij-bi)
(2)
where hi is the ith neuron output signal, wi~ is the weight of the connection between the ith neuron and the jth neuron of the previous layer, xia is the input signal to the ith neuron from the jth neuron of the previous layer, n is the number of neurons in the previous layer, and bi is the ith neuron bias. By means of many cross-connections between the neurons they are combined to form: (i) a set of input layer neurons, (ii) a set of output layer neurons and (iii) a set of hidden layer neurons. The choice of the number of input/output neuron layers is closely connected to the desired accuracy. The number and dimensions of the hidden layers depend only on the ANN performance reached in terms of model fidelity and operating speed. In order to train the ANN model transformer heating it is necessary: (i) to specify the "learning set" constituted by an adequate number of input [-Wj(t),Ij(t)] and target output I-Hi(t)] vector
I H'(t Fig. 1. Transformerheating modeling:production phase.
38
P. Daponte et al.
pairs (with j = 1, 2. . . . . No, where N¢ is the number of samples) and (ii) to minimise the objective function defined as the relative difference, normally in the Euclidean sense, between the actual ANN output H'(t) and the target outputs H(t) (Fig. 2). It is possible to minimise the objective function by using a "learning algorithm". The strategy of the "learning algorithm" is devoted: (i) to determining the input/output transfer characteristic of each neuron by a supervised learning section, (ii) to modifying the connection weights and the neuron bias by means of an adaptive process (error backpropagation) which minimises the output neuron errors ei on the basis of the following relationships: wu(k) = wij(k -
1)+ ~ e . i ( k - 1 ) h i ( k -
bi(k) = b i ( k - 1 ) + ~ e i ( k -
1)
(3)
1)
where k is the current learning algorithm iteration and c~is the "learning coefficient". This phase ends when the ANN furnishes the outputs necessary for the learning set. Suitable software developed in a TurboPascal environment to simulate a feed-forward ANN was used to produce the neural transformer heating model according to the previous considerations. An ANN with neurons characterised by the following input/output transfer characteristic (a
Hct)
H'(~0
sigmoidal function) was considered: g(x) -
1 l + e ,x
(4)
- -
where a is the sigmoid steepness. Progress in the ANN learning phase was monitored through a decrease in the maximum relative error ME defined as: [-IHi(t)[- Ini(t)17 ME=max L ]H~-t~ .j
i = 1.... ,No.
(5)
Some efforts must be devoted to determining the "learning set" in order to obtain a high ANN accuracy. In the validation phase (Fig. 3), this ANN accuracy is tested using new input and output vector pairs called the "validation set". These vector pairs are different from the learning phase ones, but have similar characteristics. If the ANN performance does not reach the desired level of accuracy a new learning phase and a modified learning set are necessary. The modified learning set must additionally take into account any new information obtained by the previous set. After the learning and validation phases, a new phase, called the production phase begins in which the ANN is used to provide the corresponding outputs required for any input (Fig. 1). The ANN trained in this manner represents a valid model of the transformer heating for which it has been trained. Using this trained ANN for different transformers, even if they have similar design characteristics, could give less accurate results. Nevertheless, training the neural network for a specific transformer could constitute the
H(t)
Learning algorithm
Fig.2. Transformerheatingmodeling:learningphase,hot-spot temperaturetrend -- real H(t), estimatedH'(t).
Fig. 3. Transformerheatingmodeling:validationphase.
39
P. Daponte et al.
starting point for training the ANN on transformers with the same design characteristics, which would undoubtedly give the advantage of reduced training times.
Table 1 Main characteristics of the transformer Nameplate rating
25 kVA 10 kV/380 V 195 W 776 W 73,1 C 136 kg 62 kg 310 kg 64x 16x80cm ONAN MACE/87
Vp.m~,/ V~o.d~y
3. Experimental application In order to optimise the ANN architecture, and to develop the best learning strategy, various experiments are necessary. Figure4 shows the measurement station utilised to acquire the transformer input primary current, the hot-spot temperature and the environmental condition data. The experiments were carried out on an oil-immersed distribution transformer whose main characteristics are reported in Table 1. There is no precise general rule to determine exactly the position in which to measure the hotspot temperature, since the hot-spot position varies depending on the transformer size and design characteristics. Hence the manufacturer's specifications must be referred to, since they are capable, for each type and size of transformer, of indicating the most probable positions of the hot-spot. Thus in the transformer under test, two type k thermocouples were installed (Fig. 5): in the Medium (T0 and Low voltage (TI0 windings on the core central column at the predicted winding hot-spot locations (the upper side of the windings between the second and third coils) and protruding into the inner oil
Iron losses* Copper losses (full load)* Top oil temperature rise at full load* Weight of core and coil assembly Weight of oil Total weight Length, width and height of tank Type of cooling Factory/year * Values reported to 75°C. ~ With environmental temperature of 21°C.
)t
ement
(a)
MV winding )il duet LV winding
(b)
j I
I I
"~
~
I
Iref(t)
~
1
~
Hot-spot measurement
N'.:tt~N
Regulator I(t)_..2_~ Hot-spo';and
Data
~
acquisition
andeonttolunit l
N -'N
environmental data ~
~
C
o
Transforrnerunder test Fig. 4. Measurement station.
n
I
i Fig. 5. Position of the thermocouples.
40
P. Daponte et al.
ducts adjacent to the hot-spot locations. A Microstar DAP 2400e data acquisition board was used as a data acquisition unit and controller for the transformer tap-changer. Its main characteristics are shown in Table 2. The current transducer was a Scientific Columbus transducer with AC input 0-5 A - - 50 Hz; DC output 1 mA, and load resistance 0-10 kf~.
3.1. Learning and validation phases In order to build the learning set, the heating test input/output vectors consider only the loading current and the environmental temperature. The contributions to hot-spot heating due to additional losses present in the transformer and hysteresis phenomena are automatically taken into account by the hot-spot measurement and thus will be implicitly included in the function f of equation ( 1 ). To correctly reproduce the heating process, various real daily loading current patterns were monitored in urban distribution electrical networks. That used in the learning phase is shown in Fig. 6, where the relative amplitude has been referred to the nameplate rating of the transformer under test. In particular, Fig. 6 shows a daily loading current versus time, including one of the possible transformer overload conditions. Regarding the trend of the environmental temperature considered in the laboratory tests, among all the possible temperature trends a sinusoidal one was chosen. This can be considered as being
Table 2 Data acquisition board characteristics Microstar DAP 2440e data acquisition I/O characteristics Analog inputs Samples Analog outputs Samples Control section Microprocessor RAM Processing section DSP RAM
16 166 kHz 2 166 kHz 80166/16 MHz 1024 kbytes 5600/1 MHz 6 kbytes
a real hypothesis according to the IEC loading guide. On the basis of the chosen selected loading curves and the environmental temperature, successive input and target output vector pairs were specified to train the ANN. The criteria used to establish the input vector elements take into account the need to furnish information capable of giving the ANN an adequate accuracy during the production phase. In particular, it is necessary to supply the ANN with the existing correlation between the current and hot-spot temperature trends. As a matter of fact power transformers show "thermal-memory behaviour"; consequently at time to in order to estimate the hot-spot temperature at time t~ = (to + At) it is necessary to take into account the "thermalmemory effect". Thus, at time t o the ANN input is constituted by the load current and the environmental data measured at time to and by the load current and the environmental data recorded during the N time-steps (At) previous to time t~. As shown in Fig. 7, these values can be produced for successive time intervals, starting at to. As proven by the calculation results the values of the load current must be squared; furthermore, the input vector also includes environmental values. The output vector is constituted only by the hot-spot temperature H(t). On the basis of the input/output vector characteristics, the ANN architecture was organised with X = 2(N + 1) input neurons. Furthermore, in order to improve the "neuron-memory capacity" recurrent connections (back-connections) into a set of hidden neurons, as shown in Fig. 7 were introduced [-28,29] At the end of the learning phase the ANN structure which furnishes accurate evaluation of the hot-spot temperature trend consists of: X = 40 input neurons; one hidden layer, including Y= 81 neurons, according to the adopted rule Y = 2X + 1 to avoid "minimum local error" during the learning phase; and only one neuron in the output layer. The number of nodes in the input and output layers were fixed on the basis of the number of input/output signal samples necessary to describe the system dynamic behavior. As regards the number and dimensions of the hidden layers, they
P. Daponte et al.
41
(a)
lp.u.l
1.2 Nameplate J
rating
of transformer
i L
0.8
I
II IS ¢
0.4
\
J
06.00
[°CI
i
J
i
10.00
14.00
18.00
X
(b)
i
22.00
02.00
T i m e [h]
(measured)
90
70
_..j/'//
50
30 06.00
E lp.ul
0.04
i
i
i
14.00
18.00
22.00
(c)
0.04 0
i
10.00
l
x% .g
02.00
T i m e [h]
&,.%/,z~,/"~a"
4,
rj
| V L /J 06.00
10.00
14.00
18.00
22.00
02.00 T i m e [h]
Fig. 6. Learning phase. (a) Learning current curve versus time with overloading conditions, (b) hot-spot temperature trends and (c) relative error E between the measured H and calculated H ' hot-spot temperature values.
were obtained by applying a trial and error procedure, starting from empirical suggestions given by the ( Y = 2 X + 1) rule and paying particular
attention to the accuracy of the learning and validation phases [18,21,22]. Subsequently, in order to ensure that the ANN "learning phase"
P. Daponte et al.
42
I2
W
j'-
I
] ' - " \ Current / ~-::~-Environment / \ . , / '/~temperature
/~
!~/ ,....
/ J
\ ,
L t-
' ,, /[ ". . . . / [ '\\
/
'-\/~
"
',
....
(t0-NAt)o . ° (to-kAt). . (t0-At) tO \X\ I2(ti ) WO O / / / I if, ) \ /--/
.
\
.
.
.
.
.
.
.
.
.\.~
.
\
/
S
/j~J~
.
.,
Weights .~ I ]'
[ H (tO+l)
('~'~F~ Lh~l" ~ (" h i ")
Fig. 7. Concise representation of input data (currents and environmental temperatures).
begins and progresses and that there is a minimum output error, the learning coefficient ~ and steepness of the sigmoidal activation function were assumed to be constant. Furthermore the following values were assumed: the time interval amplitude (At) was fixed at 15 min; the sigmoid steepness was 1.5; the learning coefficient ~ was 0.01. Higher learning coefficient values would have made the learning phase quicker, but they would have compromised algorithm stability and therefore the accuracy required. Ten thousand learning algorithm iterations were carried out, thereby guaranteeing a maximum relative error ME of less than 0.06 p.u. One iteration corresponds to one 24 h observation period training set, and is composed of Nc = 290 input and target output vector pairs.
The final results of the learning phase are shown in Figs. 6b and c. The first shows the trends of measured H(t) and calculated H'(t) hot-spot temperatures, the second shows their relative differences: Ei--
] H ' i ( t ) l - IH,(t)i IHi(t)l
i = 1. . . . . No.
(6)
It is possible to observe that the maximum absolute ANN error is lower than 3°C, while the maximum relative ANN error, ME, is lower than 0.06 p.u. This result allows the ANN to be considered as ready to accurately reproduce transformer hotspot heating. The validating phase uses test data which were
43
P. Daponte et al.
I
[p.u.l
(a) Nameplate rating of transformer
0.8
1
0.4
J
i
06.00
[°CI
10.00
(b)
i
14.00
18.00
22.00
02.00
Time [h]
H (measured)
70
//~/
o~J'~ ~"':',I\.,
50
30
E [p.ul 0.~
0.04
i
6.00
t
10.00
14.00
18.00
22.00
(c)
" V 06.00
i
02.00
Time [h]
,~4-v'"......
\
14.00
18.00
22.00
02.00
Time [h]
Fig. 8. Validation phase. (a) daily current against time, (b) hot-spot temperature trends and (c) relative error E between the measured H and calculated H' hot-spot temperature values.
not input to the ANN in the learning phase. Figs. 8 and 9 show two different validation sets, according to environmental conditions which vary with a
daily sinusoidal trend. In particular, Fig. 9 shows an overload current condition. Hot-spot temperatures obtained by the ANN
44
P. Daponte et al.
I
(a)
[p.u.]
1.2 Nameplate rating of transfer
0.8
0.4
i
06.00
[°C]
10.00
(b)
=
I
14.00
--
I
_ _
18.00
22.00
02.00
Time [h]
18.00
22.00
02.00
Time [h]
H (measured)
(calculated) 70
\, 50
30
6.00
10.00
14.00
E [p.u] /
0.04 I~(c)
06.00
,
10.00
14.00
18.00
l
22.00
02.00
Time [hi
Fig. 9. Validation phase. (a) daily current against time including overload conditions, (b) hot-spot temperature trends and (c) relative error E between the measured H and calculated H ' hot-spot temperature values.
P. Daponte et al.
were compared to the real detected temperatures obtained for the same transformer loading values. Figures 8 and 9 show the relative error between the real hot-spot temperature and the one predicted by the ANN. In these cases the ANN performance also proved to be satisfactory.
4.
Concluding remarks
This paper has proposed a new method to monitor and estimate the transformer heating in power systems based on identifying Artificial Neural Networks (ANNs). The ANN design and learning process have been optimised and validated in relation to a real transformer. The ANN model of the transformer heating provides the winding hot-spot temperature trend as the transformer load current and environmental conditions vary. The results obtained were verified experimentally and showed the accuracy of the approach. Because of its characteristics the method can be used by plant operators to fix acceptable transformer loads and overload limits. The greater accuracy of the ANN thermal model compared to the traditional thermal models shown in the load guides undoubtedly allows the exploitation margins of the power transformers to be increased. In any case it must be borne in mind that the method can only be applied if the winding hot-spot temperature, the load current and the environmental conditions can be monitored. Moreover it must be noted that the use of neural networks for transformers could become even more widespread in the light of recent studies. In these studies, neural networks have been used with very encouraging results to carry out monitoring and control tasks for: • real-time analysis of the dissolved gases in the over-heating transformer oil, from which it is possible to detect and diagnose the type of degradation occurring within the transformer [30,31]; • selective detection of partial discharges arising from pulse-shaped noise signals which are normally present in transformers and which can
45
give low level reliability to measurements carried out using traditional instrumentation [32]; • setting up a measurement system capable of discriminating currents arising from internal transformer faults and from magnetising inrush currents (the presence of the latter often cause false tripping of the currently-used differential protection systems [33]). These considerations could enable integrated transformer protection and control systems to be developed in the future, based on the contents of the different elementary diagnostic and protective functions already implemented using different ANNs.
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