Impacts of Atmospheric and Load Conditions on the Power Substation Equipment Temperature Model

Abstract

Infrared thermography is a predictive maintenance tool used in substations to identify a disturbance in electrical equipment that could lead to poor operation and potential failure in the future. According to Joule’s law, the temperature of electrical equipment is proportional to the current flowing through it. Other external factors, such as solar incidence, air humidity, wind speed, and air temperature, can interfere with its operating temperatures. Based on this premise, this article aims to analyze the influence of atmospheric and load conditions on the operational cycle of thermography-monitored equipment in order to describe the operating temperature of the object using only external data and to show the impacts of external influences on the final temperature reached by the object. Five multivariate time series regression models were developed to describe the maximum equipment temperature. The final model achieved the best fit between the measured and model temperature based on the Akaike information criterion (AIC) metric, where all external variables were used to compose the model. The proposed model shows the impacts of each external factor on equipment temperature and could be used to create a predictive maintenance strategy for power substations to avoid failure.

1. Introduction

Predictive maintenance aims to prevent damage and predict equipment failures before they occur [1,2,3]. Its uniqueness lies in how it applies analysis techniques to reduce maintenance costs significantly. However, predictive maintenance needs to be performed through periodic monitoring and analyzing equipment to verify its operation and define its future state. This makes detecting an anomaly in the early stage easier, preventing component breakdown or complete system shutdown. Predictive maintenance is useful in many fields, including electrical power systems [1,3,4].

Infrared Thermography (IRT) is one of these forms of predictive maintenance. IRT is a method that uses equipment that can pick up electromagnetic radiation in the infrared spectrum. The electromagnetic radiation is taken as thermal images, allowing for the investigation of the object’s temperature [5]. This technique has significant benefits as an electrical system inspection tool, as it is a non-destructive, non-invasive method that may be applied not only locally but also in remote monitoring systems [5,6]. Among the benefits of IRT in electrical systems, the identification and pinpointing of equipment problems, analysis of equipment in full operation, inspections carried out remotely, and avoiding exposure to hazardous areas can be highlighted [5,7,8]. Studies researching IRT for predictive maintenance of electrical equipment are essential and have a broad scope of research and application [9,10,11]. Takeuchi et al. (2022) used IRT to monitor an electrical substation for overheated areas, indicating potential electrical equipment failures. On the other hand, using high-quality cameras to capture IRT images can be costly, and manual analysis needs specialized technical knowledge. The article suggests using image processing techniques and artificial intelligence algorithms to detect and classify problems. Computational analysis of IRT images detects overheated areas and other anomalies automatically, eliminating the need for manual analysis. The article presents four image segmentation methods for detecting overheated areas (Otsu, Histogram-Based Threshold, Cluster K-means, and Fuzzy C-means), each suitable for a different type of image. In a real-world substation, segmentation methods yielded satisfactory fault identification results [9].

IRT can be used in condition-based maintenance (CBM) to identify significant changes in variables such as temperature that may indicate future failures, according to Balakrishnan et al. (2022). On the other hand, the text emphasizes the difficulties encountered when using IRT in electrical equipment inspections, such as the need for high-quality cameras and the difficulty in correctly interpreting the captured images. The text also goes over the most common induction motor failures and how IRT can be used to detect them. Furthermore, the text emphasizes the importance of combining IRT with artificial intelligence to improve CBM preventive maintenance and decision-making, presenting methods such as the K-Means Algorithm and Support Vector Machine (SVM) [11].

Cardinale-Villalobos et al. (2022) discussed how fault detection in photovoltaic panels (PV) systems is critical to ensuring proper performance and maintenance over their lifetime. Shade, dirt, and electrical failures can all reduce energy production and cause irreversible damage to solar modules. Visual inspection, IRT, and electrical analysis are some of the fault detection techniques that have been proposed. However, the effectiveness of these techniques in detecting various types of faults remains unknown. This study compares the effectiveness of three fault detection techniques (visual inspection, IRT, and electrical analysis) in detecting partial shading, dirt, and electrical failures. IRT detected dirt and partial shading with a 78% accuracy, while electrical analysis had a 73% accuracy. To maximize fault detection, the text concludes combining techniques such as IRT with visual inspection or electrical analysis is required. The text discusses how IRT detects faults in PV systems and emphasizes the importance of combining different techniques to maximize fault detection [10].

However, IRT has some external factors that can interfere with its measurements, such as the type of thermal image, emissivity, cavity effect, viewing angle, load current, solar incidence, rain, air humidity, wind speed, air temperature, component dimensions, and distance, among others [12,13,14,15,16,17,18,19]. These impacts are changing the infrastructure traditionally designed as the means of wastewater maintenance [20], the productivity of agriculture [21], and climate change impacts electricity transmission and distribution infrastructure [22]. In that last paper, the authors show the impacts of climate change on the electricity transmission and distribution infrastructure in the USA. The authors verified the increase in electrical infrastructure cost, generating annual spending on climate change increasing by up to 25%. There are possibilities to develop mathematical or known statistical techniques to be used in measurement devices to correct the external effects as used by Salazar et al. [23] (2017). They analyzed three polynomial functions obtained based on the heat radiation of the half-voltage disconnect for thermal camera images limited in a range between −3 and 39 degrees. The regression analysis showed a relationship between the pixel number image in the camera and temperature was evaluated for mean square error for linear regression. However, these authors did not consider the local atmospheric influence.

Two years later, in 2019, Shi and Ling proposed a space-time analysis identification analysis approach to detecting and locating anomalies in distribution networks through support vector machines (SVMs), a Principal Component Analysis (PCA)-based dimension reduction algorithm, and long short-term memory for anomaly detection and location in distribution network data. All these techniques are important. However, the interference of external variables, such as atmospheric variables, was not evaluated, knowing that these influence the equipment in an open field, such as the electrical power substation [24].

On the other hand, in 2022, the authors Ovsyannikov and Ovsyannikov, when considering thermal imaging devices [25], developed an advanced method for predicting the threshold sensitivity of thermal imaging devices. The technique consists of calculating the noise-equivalent temperature difference considering a thermal stratification of the atmosphere and corresponds to actual operating conditions of thermal imaging devices. The analysis was carried out under the photon noise resulting from the radiation of the elements of the thermal imaging device itself. However, doubt remains about the tremendous atmospheric changes over the day or hours.

When working with the classic weather station, it becomes possible to understand the dynamics between the time series referring to the temperatures collected by the thermal camera and the atmospheric variables. Independent mathematical, physical, or electrical contexts used in thermal images are essential to understand the real impact of variable atmosphere in collected thermal data. In this sense, this work contributes to approaching a behavior dynamical regression evaluation when the atmospheric variable is inputted in a regression, such as air temperature, solar incidence, wind speed, and air humidity, to model the maximum temperature of a power substation disconnect.

2. Materials and Methods

To develop this work, it was necessary to use a professional thermal camera and a weather station and to collect electrical current from a power substation disconnect. The disconnect is a piece of equipment located in an unsheltered power substation, meaning it is located in an uncontrolled environment and susceptible to weather conditions, such as variable air temperatures, rain, and wind, among others. This equipment and substation belong to Copel-Companhia Paranaense de Energia, an electric utility company. For statistical computation, we used the packages of R Software that test for structural change in linear regression models [26,27].

2.1. Infrared Thermal Acquisition

The thermal camera, FLIR A700, was installed in the studied substation and pointed at 5 m to a three-phase 69 kV disconnect. The parameters set in the FLIR^® A700 thermal camera for the study were: emissivity = 0.85, reflected temperature = 20 ${}^{\circ }$C, external optics transmittance = 1, and external optics temperature = 20 ${}^{\circ }$C. The lens used was a 24${}^{\circ }$, with a field of view of 24${}^{\circ }$× 18${}^{\circ }$, and a focal length of 18.9 mm.

The methodology for the equipment temperature measurement involves a manual design of masks to accurately delimit the area of interest, given the camera has a fixed position within the power substation. The masks were designed to avoid excessive equipment segmentation, and a Gaussian function was proposed to define the region of interest to account for any possible manual errors. The center of the Gaussian function is positioned at the point of highest temperature density and has a confidence interval of three standard deviations, covering 99.73% of the area. This technique effectively eliminates low temperatures from the sky and high temperatures from the sun, resulting in consistent values of maximum, average, and minimum temperatures for the objects of interest.

The original thermogram provided by the A700 camera is used to extract thermal data, which is then compared with the manually created masks. The relevant data, including the date and time of acquisition, as well as the specific object to which the temperature pertains, are recorded in dataframe spreadsheets using Python code.

In Figure 1 (middle), a sample thermal image is presented, while Figure 2 shows three masks and their respective segmented areas from Figure 1 (middle). The area resulting from the technique was compared with that obtained using the original masks, and it was found that the method eliminates between 10 and 20% of the pixels from the original masks. Although this technique needs further improvement, as some high temperatures are being discarded, it is still more effective than the pure use of the original masks, which can have peaks throughout the day due to the appearance of the sun behind the equipment.

2.2. Disconnect Current

The disconnect currents (three phases) are data already acquired by Copel before this work, as they are regular data for every power substation equipment. Figure 3 shows only phase A current, as the other phases have the same profile. The currents were acquired at every minute for 17 days. Figure 3 shows the time in samples. Analyzing the figure is possible to notice there are two moments of high demand for each day, around 12 h and around 19 h. It can also be observed that there is just one moment of very low energy consumption every day, which is around 4 h.

2.3. Weather Station

A weather station was used to acquire climate data, namely the wind speed (m/s), solar incidence W/m${}^2$, air humidity (%), and air temperature (${}^{\circ }$C). At a distance of 12 m from the relevant equipment and 17 m from the fixed thermographic camera, the weather station was mounted inside the substation perimeter. The weather station has a pyranometer, an anemometer, and a thermograph/hygrograph; see Figure 4. All measurements are registered every minute, and they were used to form the seventeen-day time series, resulting in times series: wind speed = $Win{d}_{Vel}$, solar incidence = $In{c}_{Sol}$, air humidity = $Humid$, and air temperature = $T_{air}$.

2.4. Multivariate Time Series Regression Model

Considering a multivariate time series vector:

$${\mathbf{Z}}_t={[Z_{1,t},Z_{2,t},Z_{3,t},\cdots Z_{n,t}]}^{{}^{\prime }}$$

(1)

where the subscript indicates the n-dimensional component of a vector in time t. The covariance matrix is $\mathrm{\Gamma }\left(k\right)=Cov({\mathbf{Z}}_t,{\mathbf{Z}}_{t+k})$, where k is the time delay of each sample. Each component $z_{i,t}$ of the vector represents a unique i-nth variable on the time sample evolution of t [28,29,30].

The first step of the statistical time series analysis was to apply a classical Box–Jenkis method for each variable in our study; the method can be found in [31,32].

The second step was to create a vector auto-regression VAR(p) application in p-order [28,33,34,35]. This is a generalized statistical time series model version, and this technique extends the idea of uni-variate auto-regression to multivariate regression [28] achieving the following format:

$$\mathsf{\Phi }\left(B\right){\mathbf{Z}}_t={\mathsf{\Phi }}_0+{\mathbf{e}}_t$$

(2)

where $\mathsf{\Phi }\left(B\right)$ has a p-order auto-regressive operator [28,34] and ${\mathbf{e}}_t$ is the errors vector.

Supposing a first-order model, VAR(1), there is just one equation as follows [28]:

$${\mathbf{Z}}_t={\mathsf{\Phi }}_0+\mathsf{\Phi }·{\mathbf{Z}}_{t-1}+{\mathbf{e}}_t$$

(3)

In the studied problem, it was necessary to add to the equipment temperature all climate variables plus the disconnect current. Every time we add a variable, it is also added an equation, which means, when inputting a new variable in the equations, it should have $n+1$ equations; this was the third step.

In a generalized way, it is possible to have a system with n-variables:

$$\begin{array}{ccc}{Z}_{1\left(t\right)}& =& {\varphi }_{1\left(0\right)}+{\varphi }_{1\left(1\right)}·Z_{1(t-1)}+{\varphi }_{1\left(2\right)}·Z_{2(t-1)}+\cdots +{\varphi }_{1\left(n\right)}·Z_{n(t-1)}+e_{1\left(t\right)}\\ Z_{2\left(t\right)}& =& {\varphi }_{2\left(0\right)}+{\varphi }_{2\left(1\right)}·Z_{1(t-1)}+{\varphi }_{2\left(2\right)}·Z_{2(t-1)}+\cdots +{\varphi }_{2\left(n\right)}·Z_{n(t-1)}+e_{2\left(t\right)}\\ & \cdots & \\ Z_{n\left(t\right)}& =& {\varphi }_{n\left(0\right)}+{\varphi }_{n\left(1\right)}·Z_{1(t-1)}+{\varphi }_{n\left(2\right)}·Z_{2(t-1)}+\cdots +{\varphi }_{n\left(n\right)}·Z_{n(t-1)}+e_{n\left(t\right)}\end{array}$$

(4)

where the variable $Z_1$ is an independent variable and $Z_2$, $Z_3$, and $\cdots Z_n$ are dependent variables. In the second equation, $Z_2$ will be independent, while $Z_1$ will be a dependent variable, as are the others. Applying the method to the studied problem, it has $n=6$ and each equation is associated with one variable: maximum temperature ($Z_1$), electrical current ($Z_2$), air temperature ($Z_3$), wind speed ($Z_4$), solar incidence ($Z_5$), and air humidity ($Z_6$).

The main equation under analysis was maximum temperature as an independent variable, as the main objective is to understand the behavior of the maximum temperature under the influence of current and atmospheric variables.

The last step was to analyze the adjustment quality’s models through metric techniques to choose to best multivariate time series model for $Z_1\equiv T_{max}$ [36]. The goal was not a prediction, but the behavior of thermal data collected under the action of weather variables.

2.5. Metrics

There are some statistical techniques for adjustment quality. The determination coefficient $R^2$ can be cited, which indicates the percentage of the variance of a dependent variable by the co-variables in a regression.

Although the determination coefficient is a good and well-known metric, it was also applied the AIC criterion, as it measures the best statistical model [37,38]. Every time a variable is added to a mathematical model, the AIC criterion must be applied to verify if the new variable inclusion improved or not the model. In statistics, parsimony is paramount and the AIC criterion is used to verify it. Therefore, the smallest AIC value defines the model with the best-fitting goodness, which means the method compares different possible models and determines which one is the best fit between them, being given by [37,38]:

$$AIC=2k-2ln\widehat{L}$$

(5)

where k is the number of parameters of the model and $\widehat{L}$ the maximal likelihood value. Not only this work used the AIC criterion, but in recent research, other studies evaluated meteorological variables applying AIC criterion [39], which may be used for selecting a forecast model of sea surface temperature in coast [40] or choose the best cosmological interactions models [41], as examples.

To complement the metrics, well-known assessment metrics for checking the degree of fitting between maximum temperature and the developed model were performed through the following error indicators:

(a)

Mean Square Error (MSE): Evaluate the mean square error between real observations and a proposed theoretical model:

$$MSE=\frac{1}{n}\sum {(Y-\widehat{Y})}^2$$

(6)

(b)

Mean Absolute Error (MAE): Evaluate the mean absolute error between real observations and predicted data:

$$MAE=\frac{1}{n}\sum |Y-\widehat{Y}|$$

(7)

(c)

Absolute Mean Percentage Error (MAPLE):

$$MAPLE=\frac{100\%}{n}\sum \frac{|Y-\widehat{Y}|}{Y}$$

(8)

(d)

Median Absolute Derivation (MAD):

$$MAD=median\left(\right|Y-\widehat{Y}\left|\right)$$

(9)

When including the atmospheric variables in the regression multivariate time series, the reduction of errors in adjustments is indicative of model improvement. The greater approximation of real data Y with the response of the proposed model $\widehat{Y}$ could be measured by the metrics above, where the smaller the error indicator, the better the proposed new model [36].

3. Results and Analysis

Multivariate time series regression models applied to exogenous variables are difficult to achieve due to the climatic nature of the variables [42]. In this matter, the proposed metrics above must help to choose the best time series regression model. In this way, this section presents the evolution of developed models that consider the addition of the external variables providing not only the best model but also which variable is more important to the model. Figure 5 shows the difference between maximum temperature collected (black) and air temperature (red).

For each model, the AIC criterion was used as a comparison technique between current and previous models. When a lower value is found, it indicates the best model. The first model considered only the Joule effect with the relationship between the temperature emitted by the disconnect and its square current. The determination coefficient, or $R^2$, provides information about a model’s fitting goodness. For this first model, the multiple R-squared was $R^2=38.72\%$ for the following adjusted Model 1:

$$T_{ma{x}_A;t}=14.39+0.00002646I_{A_{t-1}}^2\left(\mathrm{phase}\mathrm{A}\right)$$

Looking at Figure 6, it can be concluded that the model is poor and it can not estimate the maximum temperature with high fidelity. For all figures, the trace in black means the maximum temperature registered by the thermal camera, and the trace in red means the model result. The AIC criterion was the biggest of all models with $AIC=164.50$, indicating the model should be improved.

The second model included the air temperature in Model 1. Applying the methodology, the following max temperature equation was found:

$$T_{ma{x}_A;t}=-1.637+0.00001691I_{A_{t-1}}^2+1.468T_{ai{r}_{t-1}}$$

Looking at Figure 5, it is possible to observe the air temperature behavior. It also becomes clear that the model started to better follow more significant variations in the equipment temperature, as can be seen for higher temperatures before around sample 14,000 and after this for lower temperatures, see Figure 7.

The metrics can also be analyzed. The multiple R-squared increased from $R^2=38.72\%$ to $R^2=80.57\%$. This means that the air temperature makes up a large part of the max temperature. The error indicators found were $MSE=12.28$, $MAE=2.84$, $MAD=2.44$, and $MAPLE=0.12$, with improvements of 74.90%, 48.57%, 47.92%, and 53.42%, respectively. The mean square error was the most impacted indicator. The AIC’s criterion was better than the previous model with $AIC=130.29$, showing that the inclusion of the variable is significant to the model, see

Table 1. Comparative table for all metrics.

Model	${\mathbf{R}}^2(\%)$	$\mathbf{AIC}$	MSE	MAE	MAD	MAPE
Model 1	32.72	164.50	49.05	5.51	4.69	0.26
Model 2	80.57	130.29	12.28	2.84	2.44	0.12
Model 3	87.22	126.55	10.57	2.57	2.25	0.10
Model 4	91.01	117.60	7.38	2.14	1.81	0.08
Model 5	92.95	106.13	5.73	1.88	1.59	0.07

.

After the inclusion of the wind speed in the dynamical model, the following equation was obtained:

$$T_{ma{x}_A;t}=-1.006+0.00001881I_{A_{t-1}}^2+1.464T_{ai{r}_{t-1}}-1.880Win{d}_{Ve{l}_{t-1}}$$

It can be observed that $Win{d}_{Ve{l}_{t-1}}$ has a negative contribution for the $T_{ma{x}_A,t}$ model, as expected. Figure 8 shows the wind speed. When analyzing the multiple R-squared, it became 87.22%. This is an improvement of almost 7% in the model. It is not a very high improvement when compared to the air temperature variable, but it plays an important role and really improves the model when the period is significantly windy. This can be seen in Figure 9 just between the two blue lines. These were very windy days and it can be observed the model fitted much better when compared to Model 2.

Model 4 was developed with the inclusion of solar incidence. This element contributes to the increase of the thermal payload due to infrared radiation. For each 50 W/m${}^2$, the temperature increases +0.5 ${}^{\circ }$C. Figure 10 shows there is only solar incidence during the days. The solar incidence does not influence the equipment temperature at night, as expected. However, it can also be observed that the solar incidence is very noisy. Until Model 3, the model could not fit the noisy peaks. It can be seen in Figure 11, as highlighted in the red box, that after the solar incidence inclusion, the model started to better fit the noisy segments.

For Model 4, the multiple R-squared calculated was 91.01% with $AIC=117.60$. This result was a low contribution compared to the multiple R-squared previous cases. It was also expected as the metric is global and does not see specific segments, as it only occurs during daylight. Therefore, the presence of solar incidence produces disturbance in captured thermal emission times series on the first maximum of the current period, i.e., during the first diary demand. See the red box in Figure 11.

$$\begin{array}{ccc}\hfill T_{ma{x}_A;t}& =& 1.674+0.00001938I_{A_{t-1}}^2+1.217T_{ai{r}_{t-1}}-0.3077Win{d}_{Ve{l}_{t-1}}+0.009385In{c}_{So{l}_{t-1}}\hfill \end{array}$$

The air humidity was the last variable included in the multiple time series linear model; see Figure 12 for air humidity behavior. When including all atmospheric variables in the model, the final model equation was:

$$\begin{array}{ccc}\hfill T_{ma{x}_A;t}& =& 14.79+0.00001662I_{A_{t-1}}^2+1.135T_{ai{r}_{t-1}}-4.084Win{d}_{Ve{l}_{t-1}}\hfill \\ \hfill & +& 0.006756In{c}_{So{l}_{t-1}}-0.1227Humi{d}_{t-1}\hfill \end{array}$$

The multiple R-squared also shows improvements, reaching 92.95%. If all atmospheric variables are included, the multiple regression time series model had a reduction in all error indicators, as can be seen in Table 1.

The max temperature registered for the camera is a composition of thermal irradiation of electrical current mixed with atmospheric variables (air temperature, wind speed, solar incidence, and air humidity). Compare both figures for Model 1 (see Figure 6) with the full model (see Figure 13).

In the comparison between the first model ($T_{max}=f\left(I^2\right)$) with the last model ($T_{max}=f\left(allvariables\right)$), the error reduction is more visible, with 88.31% for MSE, 65.88% for MAE, 66.09% for MAD, and 73.07% for MAPLE; see Table 1. The determination coefficient criterion $R^2$ shows an improvement when a new atmospheric variable was included. The most contribution was the air temperature on Model 2 from 32.72% to 80.57%. For the other sequential inclusions, atmospheric variables do not increase in this magnitude, but they have importance in specific periods.

The minor AIC criteria were the full model when all atmospheric variables were included. Note that by adding a new variable, the AIC criterion tends to decrease, showing better fitting of the model. Finally, the error’s relationship for each model may be seen in the comparative Table 1. If the order inclusion of atmospheric variable on the multivariate time series linear model is altered, the numeric results of the error measures indices are modified too. However, the reduction of each error in the sequence should always be reduced.

4. Conclusions

The purpose of this study was to develop a model that correlates the maximum temperature emitted by a power substation disconnect with its electrical current and environmental variables, such as air temperature, solar incidence, wind speed, and air humidity. To do so, a methodology was proposed based on statistical concepts, such as the classical Box–Jenkis method and a multivariate time series regression model. To evaluate the results, very well-known metrics were used, such as the determination coefficient $R^2$, but also a more suitable metric, called the AIC criterion.

The results revealed that incorporating these variables into a multi-linear time series regression model improved the maximum temperature estimation accuracy. When air temperature, wind speed, solar incidence, and humidity were all taken into account, the best-fit model had a multiple R-squared of 92.95%, which shows that the model is satisfactory. Wind speed and air humidity contributed negatively, while solar incidence contributed modestly to increasing the estimated temperature. When the temperature of the environment was taken into account, the mean square error improved by 74.9% in all models. The AIC criterion also showed that all variables contributed to the model, resulting in good fitting goodness.

This study opens up the possibility of further research into thermal imaging in power substations to investigate the effect of other environmental factors on the thermal performance of the equipment, such as rain or windstorm. Furthermore, the proposed model could be used to create a predictive maintenance strategy for power substations, lowering maintenance costs while increasing power grid reliability.