Abstract
The electric field distribution of insulator surface is nonuniform, and the maximum electric field is visible around two terminals of the insulator. Using a microvaristor layer is one of the methods of field control that can reduce the electric field stresses to prevent an extension of discharges on the insulator surface and a complete flashover caused by the subsequent development of arcing. This study targets the effect of zinc oxide (ZnO) microvaristors on the electric field distribution along the contaminated and clean composite insulators that have been investigated. In addition, the impact of the insertion of microvaristor layers on the critical flashover voltage (CFO) of the insulators through a mathematical formula has been presented for the first time. The estimation of electric field distribution is conducted through finite element method (FEM) on a 400 kV insulator using COMSOL Multiphysics, in which the optimal dimensions of the microvaristor layer were obtained using the accelerated particle swarm optimization (APSO) algorithm. Then, for the first time, the analysis of the influence of the ZnO insertion on the transient performance of the insulator, i.e., the outage rate of the network, is performed in EMTP software for the insulator with the optimized insertion of the microvaristor layer. Modelling techniques were used to simulate the components of a transmission network according to the valid models. Finally, by setting different values for CFO, Monte Carlo simulation, and linking EMTP and MATLAB software, the lightning flashover rate (LFOR) and the failure risk (F.R.) of the different insulator models are calculated. It is shown that the proposed method reduces the maximum electric field of the inside and outside of the insulator, which in turn leads to a reduction in the outage rate of the power network and the insulation risk of the insulator, and an increase in CFO of the insulator.
1. Introduction
Quick advancements in power network insulation have persuaded power utilities to replace composite insulators with old ones. Compared to traditional porcelain and glass insulators, composite insulators are superior in breakage resistance, lightness, performance in pollution, and so on [1–3]. However, composite insulators are subject to electrical, mechanical, and environmental stresses. Both normal and transient conditions arose by switching operation and lightning strokes lead to the electrical stress in composite insulators [4]. The electrical stress is vital in the presence of a strong field around the electrodes, i.e., the high voltage (HV) and the ground terminals of the insulator [5–7]. Extension of discharges on the insulator surface and the following development of arcing imposed by the high electric field may finally cause an insulation failure or a complete flashover [8].
Since field magnitudes around the terminals of insulators are higher than the middle sections, reducing the electric field in vicinity of the terminals is effective for better performance of the insulators [5]. In other words, uniform the electric field distribution and decrement of the electric aim in improving CFO of the insulator. In recent years, using the technology has developed the meaning of electric stress control. Applications of microvaristor for electrical machines and transmission lines and their performance improvement have been presented in [9, 10]. In research [4], improvement due to the microvaristor layer reported a 21% increase in flashover voltage in breakdown tests.
ZnO microvaristor as a semiconductor with a large direct band gap (3.37 eV) and high binding energy of 60 meV at room temperature as semiconductor material [11] is widely applied in the area of high voltage [12]. For example, introducing nanoparticles such as ZnO into transformer oils brings out some merits including improved partial discharge properties; better AC, DC, and impulse breakdown performances; better performance of transformer cooling; making less sensitive to moisture; and increased thermal conductivity [13]. Duzkaya and Beroual [14] showed that natural ester-based nanofluids with ZnO nanoparticles as semiconductive can make the AC breakdown performance better. Recently, Xie et al. [15] reveal that the SiR/ZnO composites have a significant smoothing effect on nonuniform AC electrical field at the tip and suppress corona discharge. In [16], by using ZnO varistor as a material with nonlinear conductivity, the electric field in the cable terminal accessory was diminished.
The microvaristor conductivity increases above a threshold field domain, and hence, it can be applied to decrease the maximum electric field experienced at critical sections of the insulator [17]. The use of a microvaristor layer with two different thicknesses in a composite insulator with FEM modelling and laboratory test has been presented in [18] in which the results demonstrate the effectiveness of the microvaristor in decreasing the electric field intensity in the regions near to the insulator terminals. Also, the investigations on the effect of a thin layer of microvaristor on polluted and clean composite insulators are available in [19], and the results showed a significant decrement in field magnitude on the insulator surface. Recently, authors in [20] applied nonlinear composites as the field grading material (FGM) in polymeric outdoor insulators and obtained the simulations and experimental results. Applying nonlinear field-dependent conductivity to reduce the high electric field issue in an envisaged 25 kV high-density wide bandgap power module was proposed by authors in [21].
So far, electric field control has been achieved utilizing microvaristors; however, the following issues arise in this literature: (a) How does the microvaristor layer affect the failure risk of insulators and LFOR of the power network? (b) How could a mathematical expression represent the impact of a microvaristor on CFO which indeed can result in the network outage rate? (c) How to calculate the costs related to the improvement of the insulator dielectric strength? In accordance with the above-discussed literature, this paper is aimed at addressing these concerns and the research gap for the first time to the best of our knowledge. To this aim, the proposed insulator model is simulated by the EMTP package, and the CFO value of the model is determined by a new mathematic formulation. In this study, a suitable location where the microvaristor layer must be inserted into the housing of the composite insulator is determined so that the electric field along the insulator is minimized. In order to go through this, the electric field distribution is obtained from FEM using COMSOL software. The microvaristor dimension is optimized by connecting MATLAB to COMSOL and the use of APSO algorithm for transient analysis. Also, regarding the probabilistic nature of the lightning wave, Monte Carlo method is introduced to calculate the values of CFO updated with the link between EMTP and MATLAB. The contributions of this study can be briefly summarized as follows: proposing a new mathematical formulation taking into account the variations of the electric field distribution caused by the presence of microvaristors in order to calculate the insulator’s the CFO value; performing an optimal strategy via a link between COMSOL and MATLAB software; employment of microvaristors potential for analyzing the failure risk of insulators and LFOR of the network caused by insulators with microvaristors through a link between EMTP and MATLAB.
2. Finite Element Modelling
2.1. Simulation of Insulator
In this research, FEM investigation is done by applying the electrostatic (es) module in COMSOL Multiphysics.
Composite insulators commonly comprise four main components: (i) fiber-reinforced polymer (FRP) rod; (ii) polymer sheath on the rod; (iii) polymer weather sheds; (iv) metal and fitting [22]. The composite insulator is considered as a symmetric 400 kV insulator, so an axisymmetric model is used to simulate the insulator (Figure 1).
Simulation dimensions of the 400 kV composite insulator used in this paper according to [23] are detailed in Table 1.
The microvaristor applied in this simulation exhibits an extremely nonlinear characteristic (see Figure 2).
As can be depicted in Figure 2, if the applied field oversteps the field threshold, the conductivity of the microvaristor increases and enters the conduction region. Also, to model the contamination, an unchangeable layer with a 0.5 mm width is assumed on the surface of the insulator, while its conductivity is set to , and its relative permittivity of 80 is used [24].
The geometry and electrical properties of materials used in the proposed insulator are indicated in Figure 3 and Table 2, respectively.
In this study, by changing the place of microvaristor injection, its impact on the maximum field has been investigated. Five different modes of insulators with their various injection places have been demonstrated in Figure 4.
2.2. Finite Element Analysis
The finite element analysis is an acceptable numerical method for analyzing many problems of physics and engineering [25–27]. Using a variety of mathematical theorems, a discrete differential equation with given conditions for the electric field, FEM produces a linear/nonlinear system of equations that should be solved. FEM proceeds from the following step to build and solve the equations to calculate electric fields: step 1: definition of the insulator geometry; step 2: meshing of the geometry; step 3: determination of material type; step 4: definition of boundary conditions; step 5: electric field computation on the insulator profile. To calculate the electric potential and field on the insulator surface, the electrostatic form of the Maxwell’s equation [28] is solved, and to compute the electric potential, the electric field of the insulator surface should be calculated (see [29] for further details).
2.3. Modelling Results
Using the existing governing equations, five different insulator modes are simulated in COMSOL environment.
In this paper, the effect of microvaristor layer presence on the maximum field and dissipated power of different insulator models (Figure 4) is investigated, and its results are shown in Table 3. Also, based on the relations in [4], the dissipated power is calculated in the volume unit of the insulator ().
Regarding the results presented in Table 3, it can be seen that the injection of the microvaristor layer has a positive effect on reducing the maximum field of the insulator surface and dissipated power of all models. Based on the maximum field and dissipated power values in Table 3, the worst and the best modes are seen in 3rd and 5th insulator modes, respectively. Also, comparing 1st and 5th mode results, it is clear that the injection of a large amount of microvaristor does not necessarily lead to better results.
By considering the high electric field density in the vicinity of the insulator terminals and Table 3, mode 5 is selected as the proposed model of insulator. Therefore, the microvaristor is placed between the core and silicone housing of the insulator in the vicinity of the insulator terminals.
Figures 5 and 6 show the equipotential contours around the HV terminal for the insulator model without and with microvaristor, respectively. As can be observed from these figures, the density of the equipotential contours at two terminals in the insulator without microvaristor is higher than the insulator with microvaristor. Also, the displacement of the equipotential line from two terminals of the insulator to central sections of the insulator can be seen in Figure 6; thus, the reason for reduction in the electric field near the terminals is the displacement of contours that leads to a decrease in the gradient.
3. Optimization
The optimal dimensions of the injected microvaristors are necessary to obtain the lowest electric field accumulation. Hence, because of the hugeness of problem space, the evolutionary algorithm is needed. One of the useful intelligent algorithms for resolving the designing problem of high-voltage equipment is APSO optimization algorithm. APSO algorithm is a simplified version of the standard PSO which can speed up the convergence due to the use of the global best. The general steps of the optimization process adopted from [30, 31] are as follows:
Step 1: generating the initial population
Step 2: computing and evaluating the objective function
Step 3: creating the new population
Step 4: investigating constraints
Step 5: selection
Step 6: going to step 3 and repeating until the convergence criterion is met
The optimization of microvaristor layers in order to improve the maximum field is done by establishing a link between COMSOL and MATLAB software. In fact, the insulator with ZnO microvaristor layers is simulated in COMSOL to calculate the maximum field. Then, the obtained results are transmitted to MATLAB in order to evaluate the objective function.
3.1. Objective Function
The purpose of the optimization algorithm is to minimize the maximum electric field density () of insulator with injecting microvaristor. Therefore, function is described as follows:
The width and height of the injected microvaristor layers are the optimization variables; in this way, and are the width and height of the injected microvaristor layer in the vicinity of the HV terminal, respectively (see Figure 3). Also, and are the width and height of the microvaristor layer near the earth terminal, respectively.
The flowchart of the used algorithm is shown in Figure 7.
3.2. Results of Optimization
Table 4 presents the maximum value of the electric field, the ratio of the maximum field to the average field of the insulator (Schwaiger factor), and the dissipated power before and after optimization.
By comparing the results shown in Table 4, it can be realized that the presence of microvaristor layers reduces the maximum field and moreover provides a more uniform field on the surface of the insulator than the insulator without microvaristor layers. As can be seen in the table, the results show a 13.3% decrease in the maximum field and a 20.7% decrease in the Schwaiger factor when ZnO microvaristor-optimized layers are injected into the structure of the insulator.
Also, it can be seen that the dissipated power () is decreased by 25% nearly, which indicates a reduction in the temperature and heat at the insulator surface.
In this work, also the effectiveness of microvaristor layers on the insulator under clean surface conditions has been investigated, and its results can be seen in Table 5.
According to Table 5, the maximum electric field of the insulator with ZnO microvaristor has been reduced from 37.10 kV/cm to 32.86 kV/cm.
The field distribution of the insulator with and without ZnO microvaristor under contaminated surface conditions is plotted in Figure 8.
As can be observed in Figure 8, with the approach used in this study, in addition to the reduction of the electric field near the terminals, the field distribution on the insulator surface becomes more uniform correspondingly as the electric field is increased in the central areas of the insulator with ZnO microvaristor. The uniform distribution of the field and maximum reduction of the electric field lead to the reduction of the surface discharge probability on the insulator surface and improve the performance of the insulator.
4. EMTP Modelling
To figure out the effect of microvaristor layer injection on the network outage rate, the optimized insulator should be properly modelled in EMTP.
To calculate the variation of CFO, the program needs to use one of the outputs of COMSOL Multiphysics. This is while the electric field is one of the main results. Hence, an approach is necessary to present a link between the electric filed and the mentioned index. It is clear that in uniform fields can be expressed as
where and are applied voltage and distance between two electrodes, respectively. According to [32], the “Schwaiger factor” as the efficiency of the electric field can be defined as follows:
Since the maximum field intensity of insulator surface is equal to the breakdown of the air (), the above equation can be revised as
In the above expression, is the breakdown voltage [32]. After substituting (2) and (3) in (4)
Equation (5) is particularly beneficial to estimate the CFO of an insulator. Therefore, reducing and controlling the maximum field could be a useful technique to increase the CFO of an insulator. The CFO values, as presented in Table 6, are calculated by using Equation (5) and the obtained results from Tables 4 and 5.
The disruptive effect (DE) model is utilized to determine the effect of the injected ZnO microvaristor layer leading to the variation CFO. Therefore, having CFO, an appropriate DE model, can be simulated in EMTP.
The insulator string can be modelled by [33]:
where is the criterion to recognize the breakdown event when exceeds the critical disruptive effect , (kV) is the minimum required voltage where breakdown occurrence starts, and (μs) is the moment that the instantaneous voltage is higher than .
5. Simulation Results
The effect of ZnO microvaristor on the outage rate or LFOR and the failure risk is investigated. These evaluations have been done on a 400 kV transmission line by EMTP-like tool which has the ability to link to MATLAB. The needed parameters to simulate in EMTP are defined as follows.
5.1. Lightning Parameters
The peak current, , rise time, , and tail time, , are the major parameters of the lightning waveforms. Having main parameters of the lightning waveform, the lightning current surge can be proposed by the Heidler function [34]:
where is the peak value of current, is the current steepness factor, is the correction factor of the peak current, and and , and are time constants for determining the rise and decay time of lightning, respectively.
5.2. Tower Footing Impedance
In this work, the footing impedance is expressed as a nonlinear resistance. It is given by [35]:
where is the footing resistance at low current and low frequency, is the stroke current through the resistance, is the limiting current to initiate sufficient soil ionization, is the soil resistivity (ohm.m), and is the soil ionization gradient (400 kV/m).
5.3. Transmission Tower and Line
Figure 9 shows the schematic diagram of the tower of the 400 kV test line and its multistory model in this work. The characteristics of the line conductors are shown in Table 7.
(a)
(b)
In the multistory model, is assumed as the tower top to the phase arm impedance, and is presumed as the phase arm to the tower underneath impedance. Also, the other parameters of this multistory model can be found in [36].
In this simulation, in order to prevent reflections, a line termination with 30 km length is added at each side.
Regarding the probabilistic nature of the lightning wave, a probabilistic evaluation based on a statistical approach similar to Monte Carlo simulation has been utilized. To create the main lightning parameters, each of these parameters () is approximated by a log-normal probability density function as follows [34]:
where is the average of and is the standard deviation.
The parameters of log-normal distribution are shown in Table 8.
The convergence of Monte Carlo simulation is obtained after 30000 runs. Figure 10 shows the distribution of randomly created variables for current magnitude and rise time.
5.4. Computation of Outage Rate and Failure Risk
By using the calculated CFO in previous section, the outage rate and the failure risk are calculated, and the impact of microvaristor on these parameters is evaluated. In following, formulizations of the aforementioned parameters have been presented.
The lightning performance of transmission line can be evaluated by LFOR and calculated as the following:
where (flashes/km2 year) is the ground flash density and 1 km and are the number of flashovers in runs. Further details can be found in [38].
The line outage cost is an important parameter in the lightning issues. The annual outage costs can be calculated as follows [39]:
where (kW) is the outage power due to line trip-out, (h) is the average of failure duration, and is the average of annual cost of undelivered energy per kWh. In this paper, MW, min, and $/kWh.
Also, the insulator failure risk can be obtained by the following expression [40]:
where is the probability density function of overvoltage occurrences and is the probability of disruptive discharge. The normal distribution function is considered for the function:
The mean of over voltages () and standard deviation () are achieved by running of Monte Carlo for 30000 times.
function containing the value of CFO and standard deviation () can also be calculated as follows:
5.5. Simulation Results and Discussion
According to the results of Table 6, evaluations are investigated in four different models: (i) model of insulator with ZnO microvaristor under clean surface conditions; (ii) model of insulator with ZnO microvaristor under contaminated surface conditions; (iii) model of insulator without ZnO microvaristor under clean surface conditions; (iv) model of insulator without ZnO microvaristor under contaminated surface conditions.
Table 9 presents LFOR and the outage cost for four different cases of the insulator by using Monte Carlo simulation with different footing resistance (). The CFO values of the insulator are adopted from the results in Table 6. The failure risk of different insulators is calculated and summarized in Table 10.
Based on the obtained results, it can conclude that a microvaristor layer in the structure of the insulator can improve and change the flashover rate and the failure risk of insulator compared to the insulator without microvaristor. Also, it is obvious that the outage rate and risk are increased in the certain CFO value when footing impedance increment, which is the expected result.
Applying the insulator with microvaristor reduces the outage rate so that under the same circumstances, the outage rate of the insulator without microvaristor in the footing resistance is twice more than the outage rate of the insulator with microvaristor. The results reveal that using microvaristor not only optimizes the performance of the insulator but also decreases the outage rate, outage expenses, and the risk. In other words, it enhances the system’s reliability.
According to the obtained results, the use of microvaristor technology for optimizing the insulator performance has been evaluated positively.
6. Conclusion
This paper is aimed at investigating the effects of the microvaristor layer injection on the network, the outage rate, and other electrical parameters. Accordingly, through the analysis of the simulation results, the following conclusions were obtained.
The optimized microvaristor layers cause the decrement of the maximum electric field and the uniformity of the field distribution on the insulator surface, and the reduction of the maximum intensity of the field reduces the contamination deposition around the electrodes.
The dissipated power in the volume of the insulator decreases in the presence of microvaristor, which means a reduction in the temperature and heat on the insulator surface.
By changing the value of , also changes; therefore, the number of outages and the costs related to it reduce.
Generally, according to the above results, the microvaristor layer prevents premature aging of composite insulators and increases the insulator lifetime. Also, it can also reduce the network outages, which means increasing the degree of reliability and decreasing the risk.
Data Availability
The original/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by national funds through FCT (Fundação para a Ciência e a Tecnologia), under project UIDB/50021/2020. The authors want to acknowledge the support of Masoumeh Abdali.