Towards the prospection of an optimal thermal response of ZnO surge arrester in HV power system

Received May 20, 2020 Revised Dec 12, 2020 Accepted Dec 22, 2020 In order to understand the thermal and electrical properties of surge arrester under standard climatic conditions, it would be useful to evaluate the heating progression in its different elements. These are constituted of heterogeneous materials, which have physical and electrical nonlinear properties along the surge arrester. Temperature predicting solutions for zinc oxide ceramic blocks provide fundamental elements of the electrothermal material characteristics in view of the lifetime estimation. Electrothermal phenomenon analysis of surge arresters is based on empirically-determined parameter models, using finite element method (FEM) simulated on COMSOL Multiphysics software which is a more precise approach compared to the existing models. In this paper, the behavioural model has been developed to study the surge arresters in both cases: the steady state and overvoltage state (lightning). Previous published works validate the first simulation results. This work is therefore extended to consider other operating states, which illustrate the dependence of the type of surge on the amplitudes and durations of electrothermal phenomena.


INTRODUCTION
In the recent decades, surge arresters varistors based on zinc oxide (ZnO) have proved to playing a major role in electrical protection systems as they have remarkable electrical properties such as; low short response time, leakage current suppression, stability and reliability of electric systems, and high-energy absorption capability. This high energy-absorption capacity allows surge arresters to be sized on all networks, from electronics to very high voltage power transmission (225 or 400 kV) which indicates that their energy limits are beyond destruction for the two equipment protection types (overvoltages of Atmospheric originlightning and slow overvoltage switching surge) [1,2].
The varistors are semiconductor devices made of polycrystalline ceramic, with aparticular composition and microstructure [3]. They are variable and are characterized by a high nonlinear resistance to low applied voltage values. A varistor behaves like a high value resistance obeying the law Ohms law but, above a threshold voltage, the device becomes highly conductive with low impedance to the high tensions. When the resistance becomes conductive, it maintains the applied voltage to a maximum value indicated by the protected system, which can withstand it [4]. Indeed, the current-voltage relationship I(V) essentially reflects the quality of varistor from the non-linear and leakage current point of view [5]. The varistors are placed in a polymer or porcelain envelope, so that it is not affected by moisture or pollution. These envelopes have traditionally been made of porcelain, but today the trend is towards the use of synthetic insulators [6]. A porcelain surge arresters contains a large amount of dry air or gas (nitrogen), while a synthetic surge arrester does not have all the gas included. This means that the internal conditions against the electric and thermic phenomena must be resolved differently for both designs [7,8].
In the design of electrical equipment, particularly in protection systems, thermal evaluation is an important factor to increase the lifetime and reliability of this these systems [9]. This paper presents the thermal-electric model developed to study the behavior of ZnO porcelain surge arrester. The development of this model is relatively complex, as it takes into consideration the non-linearity of the electrical characteristic of ceramics, the non-linearity of thermal phenomena, as well as the coupling of electrical and thermal phenomena during surge arresters' operating. In this context, a procedure for calculating electric conductivity as a function of temperature and electric field is proposed by using an appropriate computer tool. To realize this study, a '2-D' finite element simulation model is developed in a steady state, using COMSOL Multiphysics software, with a detailed consideration of the electrical and thermal parameters, in other words, the relationship between temperature and electric field associated with the voltage distribution on the basis of existing approaches. The results are successfully validated by other work. The use of this simplified model requires the knowledge of natural convection and thermal radiation of these parts of the ZnO surge arrester.
To extend this work, cases of transient electrical operating conditions are examined to illustrate thermal behaviors under pulsed overvoltages. Finally, the results of last operating case are used to study natural cooling phenomenon. It is shown that, quality simulation results are obtained by finding the correlation between its electric and the thermal parameters.
Under normal operating conditions, ZnO surge arresters present low leakage current to ground [10]. When a surge arrester is subjected to a transient voltage, the ZnO elements absorb a large amount of energy and the temperature rises abruptly due to the unequal voltage distribution created by the surface leakage currents [11]. Furthermore, when the applied voltage is below a threshold temperature, the varistors reach a point of balance. From the literature, it is known that, the degree of control has practically no influence on the thermal stability limit of a surge arrester after injections of alternating energy [12,13]. Materials temperature is strongly related to power dissipation and temporary overvoltage. Therefore, there is a coupling between electrical behavior active elements (ZnO varistors) and the thermal impact of the whole structure.
The heat generated by the losses is in balance with the heat dissipated via the surge arrester towards the ambient air [14]. Whether the ambient temperature or the applied voltage change, the temperature margin may have other values, and consequently its value is not unique. However, if the applied voltage (electric field) exceeds this threshold, the current and the temperature have no balance point, and they will increase continuously until the destruction of the device. The thermal runaway takes place [15].
Protection against thermal runaway requires a prediction of the electrothermal behavior of its elements, that is to say, the estimated temperature margin in which the arrester is stable. The degradation of varistors, caused by the stray capacitances, result in an unequal voltage distribution along the resistance column [16]. This phenomenon reduces the stability zone by moving the upper point towards higher temperatures. Thus, the aging effect creates a new operating point that will evolve until both stability limits are combined, and the arrester can no longer dissipate (destruction) [17].
The majority of the electric models of the MO surge arrester existing in the literature, [18,19] presenting modifications on the equivalent electric circuits, allowed to obtain a set of the electrical parameters according to the approach of each model. The leakage currents flowing through the surge arrester ZnO block can be divided into resistive and capacitive leakage current [17]. Their density and magnitude are measured for an electric field value close to the nominal operating conditions [20,21]. Hence, the resistive leakage currents which generate a Joule effect in the ZnO block, are responsible for the temperature rising, and it is sensitive to the distribution of the voltage in the block [22,15]. Several techniques make it possible to calculate the resistive leakage current value, from the total leakage current [23][24][25]. The resistive current reaches the value of the total current in the moment when the voltage is at its maximum [26].

ELECTRIC PROPERTIES
The current-voltage characteristic is generally described by (1).
j is the electronic flux due to the electronic transport through potential barrier and j0 is a constant which can be a function of the temperature and Vf is the direct bias potential [27,28].

Int J Elec & Comp Eng
ISSN: 2088-8708  Towards the prospection of an optimal thermal response of ZnO surge arrester … (Abdelhakim Bendakir)

1867
The current density increment has two parts: One is due to the increase of the electric field at constant conductivity as (2).
The second is due to the increase increment in non-ohmic material, it can be written as (3).
Therefore, the semi-empirical equation is: σ0: is the electrical conductivity at room temperature, it calculate in the first ohmic region using the ohmic relation [2]. The electric field and the temperature are interrelated. Furthermore, nonlinear factor is proportional to the voltage barrier height level [29]. At low electrical fields ( < 1) the Ohm's law will be: At high fields, ( ) = 0 / , the conductivity increases with the electric field exponentially: The characteristic ( ) must represent the non-linear conductivity, and also temperature effect in the electric current low zone. ( ) is simulated by:  (7) and (8), which are used to represent the characteristic ( ), have the advantage of including both temperature effect and different electrical and physical quantities of materials. In order to solve these equations, an algorithm is proposed to find the curve of electrical conductivity according to temperature and electric field as shown in Figure 1.  Figure 1 demonstrates that the electrical conductivity of zinc oxide in the low current zone increases with the increase of electric field and temperature.The distribution of the temperature inside surge arrester influences the electric fields. Likewise, the distribution of the temperature between the individual elements of ZnO, both in normal operation and transient overvoltages, influences the voltage profile along the arrester. Therefore, a very complicated analysis is needed in the design of surge arresters. This analysis should cover mutual coupling between the thermal and electrical phenomena [30].
The heat diffusion equation takes the form [31]: is the diffusivity.
Since the thermal conductivity k(T) depends strongly on temperature [31], the scaled temperature T' is used, The temperature T' and the input heat Q presented in (9) depend on r (the radial distance from the disk center) and on t (time). The heat dissipates only radially by convection to air over the sidewall, since disks mounted in a surge arrester do not have significant axial heat conduction to neighboring disks [13].

The corresponding boundary condition
Electrothermal simulation requires knowledge of physical materials parameters. Comsol multiphysics has a database containing a set of numerical values for the different physical constants characterizing the materials. The values are taken directly from the literature [11].
The heat conduction equation in cylindrical co-ordinates for axial symmetry problems is:

ELECTROTHERMAL MODELING OF ZnO SURGE ARRESTER
The general configuration as depicted in Figure 2 is a 2D diagram of ZnO surge arrester; it represents the main components and their dimensions. In this device, three types of material regions are present: - The ZnO varistors column which has electrical characteristics μr and εr - The covers at each end, and the joints among two adjacent varistors is made in aluminum with characteristics σ, εa, and μa - The housing insulation material is made of porcelain σe, εe, and μe. The entire geometry of the model is surrounded by air. The electrothermal surge arrester model is developed in finite element method (FEM). It consists in coupling a thermal and electrical phenomenon. The COMSOL Multiphysics software works on heat flow, and electrical potential, resulting from an imposed voltage that passes through a resistive material. It solves the equations system arising from the electric charge conservation, and the thermal energy balance to calculate the temperature.
In this expression, V is the potential, σ is the electrical conductivity, ε 0 is the permittivity of the vacuum, and ε r is the relative permittivity of the material.

Heat transfer
The link between the two equations is the joule effect, defined by: where, Q: is the heat flux (W/m 3 ).

Model validation
The developed model is confronted to two different time constants. The thermal constant time is between 1h and 4h, while the constant time for electrical phenomenon is in the order of a few milliseconds. To calculate the thermal phenomena, the time step retained is about several dozen seconds. It should be noted that some adjustments are needed in the coupling of thermal and electrical phenomenon to observe their influences in ZnO varistor [32]. Moreover, under these conditions, the electrical study is assimilated to a continuous regime and its model contains only non-linear resistances. This representation is justified by the fact that electrical study has a dominant resistive behavior, which is mainly used to indicate high temperatures. Su-Bong Lee et al. [15] applied a voltage of 18 kV with a normal frequency of 50 Hz on surge arrester Figure 3

RESULTS AND DISCUSSION
The simulation results are shown in Figure 3(a) and Figure 4(a). In Figure 3(a), it can be observed that, the temperature distribution is similar to the results obtained experimentally in Figure 3(b). It has been revealed that, the temperature value in the electrodes is lower than in the middle. Accordingly, its maximum value is in the middle of the surge arrester (it reaches 50 °C experimentally and 48 °C by simulation).
In Figure 4(a), the thermal profile along the surge arrester is represented at different times, obtained by simulation. An increase of temperature is observed. From 80 minutes, the temperature difference between two successive periods of 20 minutes decreases. The temperature distribution of this simulation Figure 4(a) is close to the results obtained experimentally Figure 4(b) [15]. Furthermore, the general appearance is present in simulation results, although, the order of magnitudes is not directly compared, because the authors [20] do not indicate the electrical parameters, as well as relative permittivity as well as and non-linear conductivity of the varistors. Note, however, that the order of magnitude is well respected.
This set of results Figures 3 to 4(a), shows clearly a concordance between the results obtained from the two modelings which are different in the theoretical point of view. The Comsol Multiphysics software makes it possible to perform calculations, by solving the integral temperature equations, by the finite element method, taking into account the nonlinear conductivity of ZnO. This calculation is rigorous and carried out without any simplifying assumption.

APPLICATION OF THE MODEL TO A 110 KV SURGE ARRESTER 5.1. Under continuos operating
Under continuous operating conditions, the applied voltage is 110 kV to top electrode, at room temperature of 20 °C and the simulation time is 2 h 15 min. The obtained results are shown in Figures 5. From Figure 5, the temperature value is maximum in the middle of the surge varistor and minimal at the electrodes. Thus, the surge arrester temperature varies between 20 °C and 27 °C, and it remains stable when the applied voltage is about 110 kV. The power loss created by the leakage current is equal to the heat emitted into ambient air.  Figure 7, which illustrates the influence of height on temperature as a function of time. It is obvious that the temperature in interval [0, 100 min] varies proportionally with time. However, from 100 minutes, the temperature value remains constant with time increase, due to the equilibrium between generated and dissipated power. The study of thermal balance of a varistor must be carried out in all its operating regimes, because the danger of thermal runaway may occur at any time [2].

Transient analysis
Most of the time, surge arresters operating operate in a non-continuous mode. It is important to follow the thermal behavior in a transient mode (lightning, switching). A bi-exponential lightning voltage surge of 1.2/50 μs is applied; the waveform is given by (19): where, = 6.9, = 4.9 ,  = 0.98, 0 = 110 . The simulation lasts for 60 minutes; the result of the temperature distribution on the surge arrester is shown in Figure 8 and Figure 9. At transient regime, the ZnO blocks' temperature increases to 81 °C after 60 minutes. Figure 9 shows the thermal profile as a function of time. Temperature profile, along the symmetry axis of the arrester, at the point of the medium under transient conditions, reaches 75 °C. When the temperature of the ZnO blocks exceeds the limit, it causes a thermal imbalance between the production of heat and the released one which can lead to failures or thermal runaway. It is concluded that the degradation phenomena and the thermal runaway of the ZnO surge arrester block are directly related to the heat lossless, which determines the generation and temperature dissipation processes.

Cooling under voltage
The transient regime results are exploited as initial state in the cooling study under voltage of steady state for 3 hours. The result of the simulation is shown in the Figure 10. The characteristics of the thermal stability of this surge arrester can be determined from the amount of heat released directly by the surge arrester. The values obtained in the median part of ZnO varistors at ambient temperature of 20 °C, are illustrated in Figure 10. The cooling rate is very low (it takes 130 min) due to the low thermal conductivity. In addition, the heat can be dissipated to the housing surface with a low temperature gradient [32]. The distribution of heat as a function of time is given by: where, τ : Constant of time. T a : Ambient temperature 20 °C. t : Heat release time By fixing t=τ and entering the previous equation, the temperature value obtains T=40 ℃, this value will be projected on curve 18 to find τ=68min. During the first minutes of cooling, extreme ceramics temperature decreases very rapidly due to the heat dissipation by conduction towards the covers, and the large heat capacity of these covers. The central part cools in a uniform way, because the covers influence is minimal, for the order of the initial heating magnitude. In that case, most of the central part heat is evacuated by radiation, convection and conduction between the ZnO column and the porcelain.

CONCLUSION
The surge arrester operations are simulated by an electrothermal study, in order to predict its behavior under thermal factors' influence. This is one of the vital characteristics of surge arresters, that must ensure the proper power electrical network operating. The work covered in this paper consists essentially of two main parts: In the first part, the electrical and thermal properties of the different materials, used in the proposed model, were extracted from the COMSOL multiphysics software library. In addition, an algorithm is developed to implement the non-linear characteristics (electrical conductivity and thermal conductivity, thermal capacity) in this software. In the steady state after a few hours, a temperature skew distribution with higher temperatures in the middle area of surge arrester will then also occur.
From the obtained simulation results, it could be shown that the operating regime has a major influence on the average and maximum temperatures of the surge arrester, ie, an influence on the determined thermal stability limits. However, the temperature pattern along the arrester (maximum values in the medium and lower in the limits) is similar, and could be observed, whatever the injection regime is. This result confirms previous studies from the literature.