Influence of Temperature on Brushless Synchronous Machine Field Winding Interturn Fault Severity Estimation

Abstract

There are numerous methods for detecting interturn faults (ITFs) in the field winding of synchronous machines (SMs). One effective approach is based on comparing theoretical and measured excitation currents. This method is unaffected by rotor temperature in static excitation SMs. However, this paper investigates the influence of rotor temperature in brushless synchronous machines (BSMs), where rotor temperature significantly impacts the exciter excitation current. Extensive experimental tests were conducted on a special BSM with measurable rotor temperature. Given the challenges of measuring rotor temperature in industrial machines, this paper explores the feasibility of using stator temperature in the exciter field current estimation model. The theoretical exciter field current is calculated using a deep neural network (DNN), which incorporates electrical brushless synchronous generator output values and stator temperature, and it is subsequently compared with the measured exciter field current. This method achieves an error rate below 0.5% under healthy conditions, demonstrating its potential for simple implementation in industrial BSMs for ITF detection.

1. Introduction

In power generation applications, brushless synchronous machines (BSMs) usually consist of a main machine and an exciter, mechanically coupled on the same shaft. The exciter’s function is to supply the necessary field power to the main machine for its operation. In the conventional topology, the exciter’s field winding is rolled around the stator poles, and its armature is an AC winding located on the rotor. The AC output of the exciter armature is converted into the DC excitation input for the main machine by a rotating diode rectifier bridge. The field winding of the main machine is located on the rotor and its armature on the stator.

Currently, several excitation systems for BSMs are identified by the field power source supplied to the exciter [1,2,3]. The primary advantages of removing brushes and slip rings in the excitation system [4] are reduced maintenance costs and increased operational safety, as no sparks are produced. In some facilities, such as oil refineries and chemical plants, the use of BSMs is mandatory.

The market for BSMs is extensive. High-power BSMs are widely used in nuclear power plants, while low-power units are employed in emergency diesel generators and hydro power plants [5,6]. Furthermore, BSMs can address issues arising from the high penetration of renewable generation plants in the grid, such as the reduction of the short-circuit ratio (SCR). BSMs used as synchronous condensers can help maintain a minimum SCR level in global grids [7,8], especially those equipped with a PMG as a pilot exciter. Additionally, BSMs can help renewable power plants comply with various grid code requirements, which are largely based on specific standards [9,10,11].

In all these applications, BSMs must meet industry reliability standards, including protection against faults and abnormal operating conditions [12,13]. BSMs are susceptible to various faults due to their operating conditions. This manuscript focuses on the influence of temperature on estimating the theoretical field exciter excitation current, with the ultimate goal of detecting interturn faults (ITFs) in the field winding of BSMs. The number of ITFs is directly proportional to the severity of the fault [14,15].

The main difficulty in detecting ITFs is that they do not usually result in large overcurrent in the machine, so the machine can operate normally if the interturn fault severity level is lower than a tolerable limit. However, the existence of a magnetic unbalance causes additional mechanical stress on the machine, which can lead to large vibrations that can damage the generator.

The main origin of ITFs is the weakness of the insulation [16,17]. A short-circuit between turns is usually caused by deterioration of the insulation, which is usually caused by the high stresses applied to the insulation. The ITFs cause a drop in the electrical resistance between the poorly insulated turns, which leads to an increase in the excitation current of the generator.

Differences in electrical potential, mechanical stresses due to vibrations and frictions, and thermal stresses due to a temperature gradient are the causes of high stresses in the insulation, which can lead to damage to it. In addition, the presence of fine particles or liquids such as water or acids can increase the likelihood of ITFs.

There are some previous model-based approaches for rotor ITF detection and severity estimation in BSMs [14,15]. Some of these methods are based on the comparison of two variables: the theoretical model estimation obtained from the machine electrical output values and the measured exciter field current. This comparison is very useful for attesting deviations from the healthy condition and for calculating the fault severity level employing the relative difference between both values. So, accurate assessment of the excitation current in BSMs is essential for proper machine characterization. This significance arises from the inherent nature of brushless excited SMs, where the field winding becomes physically inaccessible during operation, making direct measurement of the field current extremely challenging.

Another previous article [18] investigates the idea of implementing deep neural network (DNN) algorithms to detect ITFs in BSMs. The combination of large numbers of experimental data and the use of deep learning methods achieves excellent results for detecting ITFs in BSMs. However, preceding algorithms fail to account for the impact rotor winding temperature may have on field current estimation. During machine operation, a notable increase in rotor winding temperature occurs, gradually causing a decline in the field current. It is interesting to highlight that, while extensive studies have explored field current estimation, limited research investigates temperature-induced alterations in these values. In [19], field current and field winding temperature are estimated using a machine model, and then the estimates are compared with the actual currents measured in the stator and adjusted through a correction mechanism using a Kalman filter, demonstrating efficacy in simulations. In [20], field current and temperature estimation is achieved through the DC link current, initially computed via an algorithm and afterward fed back to the controller and compared with the measured value. The resulting error facilitates temperature estimation refinement, thereby improving both field and DC link current estimates.

Furthermore, due to the difficulty of accurate modeling posed by SMs combined with recent advancements in computational learning, contemporary studies explore methodologies such as neural networks for identifying faults within the field winding. Works such as [18,21] collect healthy machine data alongside post-fault data to use these data for early fault detection. Nonetheless, these methods do not work in the absence of real-time consideration of BSM operating temperatures, as situations may arise where a fault between turns in a cold machine exhibits field current values like those of a healthy machine operating at high temperatures.

Taking into account this difficulty, the main objective of this work is to demonstrate and verify the influence of temperature on the exciter excitation current estimation algorithm. This will substantially improve the results studied in previous works [18], where a neural network model was presented that allowed the estimation of the excitation correlation of a brushless machine but did not consider the rotor temperature. Considering how the rotor temperature affects the excitation current of the machine, the results obtained by taking into account the machine temperature as input to the model will be much closer to the real machine measurements. The second objective is to validate the use of stator temperature instead of rotor temperature in the estimation algorithm. This is a very important validation because the stator temperature can be measured during operation in industrial BSMs, where it is not possible to measure the rotor temperature.

For this purpose, this paper proposes using DNN architecture algorithms. It was decided to use DNNs to estimate the excitation current because the introduction of artificial intelligence in the field of diagnosis of synchronous machines is on the rise, as can be seen in several recent research works [22,23,24].

The developed DNN uses voltage, active and reactive power, and temperature (U, P, Q, and θ) as inputs of the model to estimate the field excitation current of the BSM. The proposed method was developed using a special laboratory setup, firstly to collect all the necessary data to train the DNN under healthy conditions.

In Section 2, the influence of temperature is analyzed in different excitation systems of synchronous machines (SMs). It also highlights the importance of considering temperature as an input in developing the theoretical excitation current estimation model of a BSM. The proposed method and the steps to develop the estimation method are discussed in Section 3. Then, Section 4 describes the experimental setup and the experimental tests performed on it under healthy conditions. Finally, Section 5 summarizes the paper’s conclusions.

2. Influence of Rotor Temperature on Different Excitation Systems of SMs

This section presents the need to consider the rotor temperature in the model to estimate the exciter field current for detecting ITFs in BSMs.

In an SM with static excitation, as shown in Figure 1, the excitation current (I_f) is controlled directly by a controlled rectifier which modifies the field winding voltage (U_f). As the temperature increases, the excitation field winding resistance increases, and consequently, the excitation voltage must be raised to maintain a constant excitation current.

However, in a BSM, as can be seen in Figure 2, the main machine field winding current is regulated through the exciter. When the temperature increases, the resistance of the field winding of the main machine increases, following Equation (1) [25]:

$$R_{\theta }=R_{{\theta }_0}· \left[1+\alpha ·\left(\theta -{\theta }_0\right)\right]$$

(1)

where $R_{\theta }$ is the resistance at the operating temperature $\theta$, $R_{{\theta }_0}$ is the resistance at the reference temperature ${\theta }_0$, and $\alpha$ is the temperature coefficient of resistance for the conductor material.

This increase in the field winding resistance leads to an increase in the field winding voltage (U_f), assuming the excitation current (I_f) remains constant. Therefore, to maintain the same operating point (I_f constant), it is necessary to increase the exciter excitation current (I_fe) to raise the induced voltage in the armature winding of the exciter and consequently the field winding voltage (U_f). Additionally, because, as said, the resistance of the exciter field winding increases with the exciter’s temperature, this also affects the exciter field voltage (U_fe).

3. Inclusion of Temperature in the DNN Model-Based Method

3.1. Foundations

This section pursues two main objectives. The first is to utilize DNN algorithm architectures to predict the value of the theoretical exciter field current in a BSM, considering the effect of temperature on the machine, with temperature as an additional input. This approach aims to improve the results obtained in other research [18]. The results shown in this previous article are good because of the short-term tests in which the machine did not have time to warm up and the effect of temperature on the estimation of fault severity was not too high. However, in the current work it has been verified that if continuous monitoring of the BSM is to be carried out, the effect of the rotor temperature must be considered, as shown in Section 5.

The second objective is to validate the feasibility of using the stator temperature in the model instead of the rotor temperature, since measuring rotor temperature in industrial BSMs is not possible.

Based on the principles described in [18], the theoretical exciter field current (I_fe,cal) is estimated using a DNN model under healthy condition calculations. The inputs to this model are a combination of machine output voltage (U) and current (I) measurements that fully define a [U, P, Q] operating point. In addition to these inputs, the machine temperature measurement (θ) will be included as an input in the present work, following the reasoning presented in Section 3. The comparison of I_fe,cal with the actual measured exciter field current (I_fe,mea) enables ITF severity (α) estimation, as the ratio of faulty turns is directly related to the field current increase imposed by the automatic voltage regulator (AVR) with respect to the estimated current. Equation (2) shows the explicit calculation of the severity of the interturn fault in a BSM:

$$\alpha \left[\%\right]={\displaystyle \frac{N_{Faulty}}{N_{total}}}·100=\left({\displaystyle \frac{I_{fe, cal}}{I_{fe,mea}}}-1\right)·100$$

(2)

where $N_{Faulty}$ is the number of equivalent faulty turns with R_f = 0 Ω, and $N_{total}$ is the total number of turns.

Figure 3 illustrates the simplified layout of the field winding ITF detection and severity estimation technique, with inclusion of the influence of temperature.

The purposely developed DNN allows one to adaptively model the complex relationships among the mentioned variables through approximation of non-linear functions, with a reduced error. In accordance with the complexity of the problem, the DNN model is composed of four neurons in the input layer, one for each input variable (U, P, Q, and θ), and one output neuron which employs the sigmoid as the activation function. The developed DNN has two hidden layers, with their neurons using the rectified linear unit (ReLU) activation function, and was optimized for computational efficiency.

To determine the optimal number of neurons in each hidden layer, the model was trained with all combinations of neurons ranging from 3 to 20 per layer, utilizing the backpropagation method. The backpropagation learning rate was set at 0.001, and the number of epochs was fixed at 40.000. The optimum configuration was selected by evaluating the trained DNNs based on the minimization of the mean square error (MSE) and the minimization of points with errors greater than 5%. The general form of the involved DNN architecture is presented in Figure 4.

The main features of the development stages (data collection and processing, training with validation, and testing) are described in the following subsections.

3.2. Data Collection and Processing

The data were obtained through experimental testing on a special laboratory test bench, as described in Section 4, under healthy conditions for BSMs. This dataset was collected by conducting several series of long-term tests, with different grid voltage (380 ≤ U ≤ 420 V), real power (0 ≤ P ≤ 3000 W), and reactive power (−2000 ≤ Q ≤ 3000 var) values.

V, P, and Q were obtained using a Camile Bauer SINEAX converter M563, and temperatures were measured using Pt−100 commercial sensors with converters. The converters of the temperature sensors and the transducer give an output signal proportional to the measured variables in the range of [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] mA. To adapt these signals to the measurement range of the Arduino © microcontroller, a series resistor of 249 ohms was connected to each current signal, so the signals are finally in the range [1,2,3,4,5] V, which is a suitable range for the Arduino © microcontroller. Finally, I_fe,mea was measured using a Hall effect sensor (INA219) directly compatible with the Arduino © microcontroller.

After acquisition, the data were filtered to remove anomalous measurements. In total, approximately 400,000 refined records were analyzed under healthy conditions. The removed data include transients, anomalous measures, and communication failures.

This data pool was randomly divided into three subsets for training, validation, and testing, as shown in Figure 5.

3.3. Training with Validation

The feed-forward DNN is trained using the popular backpropagation method [25,26,27], in order to align the outputs (I_fe,cal) as closely as possible with the measured values (I_fe,mea). Backpropagation is an iterative gradient descent optimization technique applied to the network’s weight space, enabling the weights to be updated in each iteration and to progressively minimize the cost function (CF).

At the first stage of each epoch, forward propagation is performed, where the inputs (U, P, Q, and θ) are fed to the DNN and the output value is calculated based on those inputs and with the initialization values of the weight, as stated in Equation (3).

$$I_{fe,cal}=F·\left[\sum _{k=1}^K{w}_{F, 2k}{h}_{2k}\left(\sum _{j=1}^J{w}_{2k, 1}{h}_{1j}\left(w_{1j,U}·U+w_{1j,P}·P+w_{1j,Q}·Q+w_{1j,\theta }·\theta +w_{j,0}\right) +w_{k,0}\right)+w_{F,0}\right]$$

(3)

where $wF,2k$, $w2k,1$, and $w1j,U$, $w1j,P$, $w1j,Q$, $w1j,\theta$ are the synaptic weights from the neurons of the second hidden layer to the output neuron, from the neurons of the first hidden layer to the second hidden layer, and from the neurons of the input layer to the ones of the first hidden layer, respectively.

To summarize Equation (3), it is better to write the weights vector as in Equation (4):

$$W_t=\left[w_{F, 2k }{w}_{2k, 1j }{w}_{1j, U }{w}_{1j, P }{w}_{1j, Q }{w}_{1j, \theta }\right]$$

(4)

with j from 1 to J, and k from 1 to K.

At the second stage, the algorithm calculates the value adopted by the CF and subsequently evaluates its gradient by propagating the errors from the output layer back to the input layer through the chain rule. Through stochastic gradient descent, accordingly, moving towards the negative direction of the gradient, the iteration is concluded by updating the weights and biases.

The progressive adjustment of the network is performed by minimizing the mean square error (MSE) between the predicted and the measured exciter field currents, serving as the CF. The cost function calculation is shown in (5).

$$CF={\displaystyle \frac{1}{N}}\sum _{n=1}^N{\left(I_{fe, cal}-I_{fe, mea}\right)}^2$$

(5)

The adaptive moment estimation (ADAM) algorithm, which employs the exponential moving average of both the gradient or first momentum (∇CF) and the squared gradient or second momentum (∇²CF), is used for gradient descent optimization. The diagram of the employed backpropagation method is provided in Figure 6.

Also, the following equations allow the weights vector at epoch t to be determined from the vectors at the previous epoch (t − 1):

$$W_t=W_{t-1}-l·{\displaystyle \frac{\widehat{m_t}}{\sqrt{\widehat{v_t}+\epsilon }}}$$

(6)

$$\widehat{m_t}=m_t·{\displaystyle \frac{1}{1-{\beta }_m}}$$

(7)

$$m_t={\beta }_m· m_{t-1}+\left(1-{\beta }_m\right)·\nabla CF$$

(8)

$$\widehat{v_t}=v_t·{\displaystyle \frac{1}{1-{\beta }_v}}$$

(9)

$$v_t={\beta }_v·v_{t-1}+\left(1-{\beta }_v\right)·{\left(\nabla CF\right)}^2$$

(10)

where l represents the learning rate that allows speeding up of the convergence of the CF to its minimum, $v_t$ and $m_t$ are variables updated in each epoch, and ε, ${\beta }_m$, and ${\beta }_v$ are constant.

After training, hyperparameter tuning is performed to achieve the best-fitting network. During this validation phase, various neural networks were evaluated to determine the optimal number of hidden layers and nodes in each layer. The network that reduced the maximum absolute error (MAE) to 0.1% was selected.

3.4. Tests

After the training and validation process, an unbiased evaluation of the model performance was carried out. The absolute maximum error is approximately 0.5%, so if this method was used to detect ITFs, faults with a severity greater than 0.5% could be detected. In other words, because 0.5% is the smallest severe detectable fault, the tripping limit should never be fixed beneath this value.

Table 1. Results obtained from the DNN predictions under healthy conditions.

Set of Data	MAE [%]	RMSE [mA]
Tests under healthy conditions	0.1	0.04

shows the evaluation results of the DNN network for the machine in healthy conditions, including the value of the mathematical metrics used to evaluate its accuracy: the mean average error (MAE) and the root mean square error (RMSE).

The errors obtained through DNN prediction are significantly beneath the errors obtained in previous papers where the temperature was not considered as an input in the model [16]. An MAE of 0.1% shows that the trained DNN has a fairly high overall estimation accuracy, in terms of overall closeness to null error values, while an RMSE of 0.06 implies a fair mean value of prediction dispersion with respect to the actual values, as this metric penalizes outliers or large deviations.

4. Experimental Tests

4.1. Experimental Setup

Numerous long-duration tests under constant operation points (P, Q, and U) were carried out on a special 4-salient pole, 5-kVA, 400-V BSM. A simplified diagram of the machine is shown in Figure 7.

This BSM was modified by adding 5 slip rings and brushes to permit access to the field winding of the main machine and to the “rotating” diodes (which were actually made static in this setup and placed outside of the machine). This modification allows for the measurement of the voltage (U_f) and the current (I_f) of the field winding of the main machine and consequently the temperature by observing variations in its resistance. Additionally, two Pt−100 type temperature sensors were installed at both ends of the armature windings of the main synchronous machine, and these temperatures were also recorded.

From the armature currents and voltages, the values of stator voltage (U), active power (P), and reactive power (Q) are measured by a commercial 3-channel programmable transducer, SINEAX M563. Finally, the exciter field current is measured using a Hall effect sensor. All these measurements are recorded on a computer through an Arduino© microcontroller, communicating via the COM port of the computer.

During the long-duration test, the temperature of the rotor and the stator of the main synchronous machine increased. To maintain the machine at the same operating point, the exciter excitation current (I_fe) needs to be increased as the temperature rises.

The ratings of the main machine and the exciter are detailed in

Table 2. Main machine data.

Alternator Type	Synchronous 3-Phase
Rated power	5	kVA
Rated speed	1500	rpm
Rated voltage	400	V
Rated current	7.2	A
Pole pairs	2
Rated frequency	50	Hz
IP	21
Insulation class	F
Rated excitation voltage	33	V
Rated excitation current	4.1	A

and

Table 3. Exciter data.

Alternator Type	Synchronous 3-Phase
Rated power	277	VA
Rated speed	1500	rpm
Rated voltage	40	V
Rated current	4	A
Pole pairs	4
Rated frequency	100	Hz
IP	21
Insulation class	F
Rated excitation voltage	33	V
Rated excitation current	0.61	A

, respectively.

The experimental laboratory setup is shown in Figure 8. The BSM (1) and the exciter (2) are mechanically coupled with a common shaft. The diodes (3) are located outside the machine in this layout to be accessible.

There are five slip rings and brushes (4): three are connected to the armature winding of the exciter, and the other two are connected to the main machine’s field winding. The voltage and current of the main machine’s field winding are measured (5). The temperature of the main machine’s armature windings is monitored by two Pt−100 sensors (6). These sensors are placed in the end winding of the machine at both sides of the generator, the non-drive end NDE and the drive end DE. In element 6 of Figure 8, there is a zoom of this area. This is the best non-invasive location of the temperature sensors that allows estimating an average temperature with which to compare the estimations of the DNN.

This modified synchronous machine is actioned by an induction motor (7), which is controlled with a frequency variable converter. A DC source provides the excitation power to the machine, and the machine is connected to the grid.

4.2. Experimental Results

Numerous tests have been conducted to verify that the measured exciter field current (I_fe) must be significantly increased in BSMs under warm conditions to maintain a constant reactive power delivered by the machine. The tests involve initially setting an operating point for the BSM in terms of active and reactive power, and then allowing the machine to operate as it warms up, while continuously keeping the reactive power constant. To maintain constant Q as the temperature rises, it is necessary to increase the exciter field current (I_fe).

All the aforementioned electrical variables (P, Q, U, U_fe, I_fe, I_f, and U_f) and the rotor and stator temperatures are continuously monitored. Figure 9 illustrates the increase in the exciter field winding current due to the rising rotor temperature during a test.

Since it is impossible to access the voltage and current of the field winding of the main machine in industrial BSMs and consequently to calculate the rotor temperature, the stator temperature was measured to assess whether it could be used instead of the rotor temperature to estimate the excitation current (I_fe).

Figure 10 and Figure 11 show the exciter field winding current variation with the increment of the stator and rotor temperatures, respectively. It can be seen that, in this BSM, the exciter field current (I_fe) consumption increases by 0.75% every 10 K degrees of temperature rise. Thus, to develop a model capable of estimating the excitation current consumption at an electrical operating point of the machine, in the case of BSMs it is necessary to add the machine temperature variable in the estimation model, as said above.

Comparing Figure 10 and Figure 11, it is verified that the variation in excitation current consumption with increases in stator and rotor temperatures is very similar. Importantly, the slope remains constant with both temperatures, indicating that it is feasible to use the stator temperature in the estimation model.

Additionally, Figure 12 displays the rotor and stator temperatures during a constant reactive power test. The difference between them is also represented. This difference is not constant and varies depending on the machine temperature.

As described in Section 4, to validate that this method is significantly more efficient when using temperature as an input to the model, a DNN was trained with real operating points measured using the experimental system described in the previous subsection.

Figure 13 shows the measured excitation current, I_fe,mea (in blue), and the calculated excitation current, I_fe,cal (in orange), for all test operational points. The calculated excitation current value is derived from the DNN previously trained with the machine operational data under healthy conditions.

As shown in Figure 13, the DNN excitation current prediction is highly accurate, with a maximum error of 3 mA, which is an error of 1.5%. The MSE obtained is 0.5%, which means that the minimum detectable fault severity is 0.5%, considering the fault severity of Equation (2).

5. Conclusions

In BSMs, rotor temperature is a crucial variable for detecting ITFs based on exciter field current estimation. As the machine heats up, the rotor’s resistance increases, necessitating a rise in the rotor field voltage to maintain a constant field current and reactive power. Consequently, the exciter field current must also be increased.

Previous research did not consider the rotor temperature as a variable in the development of the online model-based fault severity estimation algorithm for BSMs. This omission is significant, as the presented results indicate that the exciter excitation current varies by 0.75% for every 10 °C increase in temperature. This could result in errors exceeding 5% in an industrial machine, where the normal operating temperature range can vary from 20 °C in cold conditions to 100 °C in warm conditions. This fact implies that the algorithm could only detect faults from 5% fault severity or higher if unwanted trips are to be avoided.

To enhance the accuracy of the detection method, an alternative online model has been developed for detecting ITFs in BSMs, incorporating the machine’s temperature. Given the difficulty of measuring rotor temperature, the use of stator temperature was evaluated as an alternative, yielding satisfactory results.

To validate the equivalence of using rotor versus stator temperature, the variation in the excitation current with different temperatures was compared in several laboratory tests, using 400,000 operational points for training the neural network.

The results obtained in this paper indicate that the DNN using stator temperature as an input can estimate the exciter field current with errors below 0.5%. Consequently, ITFs with a severity of approximately 0.5% or higher can also be detected.

However, this study leaves the gates open to future research, which should focus on carrying out tests with known interturn faults in the brushless generator. Thus, the DNN developed for this article could be used to verify the accuracy of the model as a function of the severity of the fault.