Pressure Characteristics in the Nitrogen-Sealed Power Transformers under Internal Faults

Abstract

The explosion-proof performance is an important index for oil-immersed transformers. The nitrogen-sealed transformer is a new type of transformer with nitrogen gas in the upper space, which can buffer against internal stress increase caused by arc faults. However, the pressure changes in the transformer under internal faults are unclear. The authors of this study propose a method based on finite element simulation to analyze the pressure changes and the stress on the tank. First, the calculation process of arc energy and the pressure of the bubbles caused by the arc are derived. Second, the dynamic pressure wave propagation model and acoustic-solid coupling model are established. Last, the finite element simulation model is built to analyze the pressure characteristics. Taking the winding turn-to-turn and phase-to-phase short circuit faults as the analysis situations, the pressure changes in the 110 kV/20 MVA nitrogen-sealed transformer are simulated. Due to the pressure wave refraction and reflection, the pressure changes show oscillatory characteristics with time after the occurrence of an internal short circuit fault. The pressure wave travels from the arc fault position to the periphery. Compared to the conventional transformer, the pressure changes with slower variations under an internal short circuit fault and the tank suffer less stress, which indicates that the nitrogen-sealed transformer is more effective in the explosion-proof performance.

1. Introduction

The oil-immersed transformer is an important equipment for a power transmission system. When an internal fault occurs, the high-energy arc may generate and a large amount of energy will be released, which can cause the insulating oil to decompose and evaporate rapidly. Since the growth of the bubble volume is limited by the surrounding insulating oil, the pressure at the oil and gas boundaries suddenly rises, which stimulates the dynamic pressure wave impact on the body and tank of the transformer. In general, the time from the occurrence of an internal fault to the tripping of a circuit breaker is about 60–120 ms [1], and the strong impact of the pressure wave perhaps causes the oil tank to bulge. In serious cases, the oil tank may rupture, oil will be sprayed and fire breaks out, endangering the safety of personnel and nearby equipment. There will also be huge economic losses [2].

In order to reduce the explosion probability of transformer tanks, much research has been completed. The research can be divided into three directions. One is the transformer defect detection and condition assessment methods. One is the transformer protection method research. The other is the transformer structure and material research.

When the internal fault occurs, there are many signals produced, such as sound, electromagnetic wave, heat and chemical signals. According to the transformer defect phenomenon, there are mainly three types of defects, including mechanical defects, partial discharge (PD) defects and overheating defects. To detect mechanical defects, the vibration spatial distribution characteristics of the transformer vibration under normal conditions, partial looseness of the winding, global looseness and winding deformation have been studied [3]. The voiceprint features of vibration sound signals within power transformers under different operational conditions were studied, and a multi-fault recognition module was built, which can be used to identify the patterns of mechanical defects [4]. The progress in mechanical state recognition was introduced, and it covered sensor deployment, sensor specialization and equipment integration [5]. State-of-the-art machine learning and signal processing techniques were utilized to build a diagnosis model to distinguish transformer operating conditions based on vibration signals [6]. In order to detect partial discharge defects inside the transformer, the discharge characteristics, three kinds of sensors and many discharge diagnosis methods have been studied. The distinctive sensors and technologies based on acoustic, ultra-high-frequency, electric and hybrid methods were compared, and their advantages and limitations were pointed out [7]. The response of high-frequency current transformer (HFCT) sensors due to surface, oil corona and air corona were analyzed, and the sensitivity of PD detection can be increased by increasing the number of turns [8]. The ultra-high-frequency (UHF) PD frequency range was obtained from investigating laboratory experiments and on-site measurements, and measurements using either valves or window antennas were feasible [9]. A new PD localization method based on UHF sensors was proposed by determining the critical sites and solving the time differences of arrival (TODA) equations, which can simplify the computational complexity and improve the accuracy [10]. The application of microfiber coupler sensors (MFCSs) to detect ultrasonic signals was introduced, and an optimized support vector machine (BSO-SVM) was built to recognize the PD patterns [11]. The sub-scene monitoring method was designed, the partition model of a transformer was established and the best monitoring point location was determined, which can improve the feasibility and accuracy under complicated environments [12]. The current state-of-the-art methods for PD detection and localization techniques were reviewed, and different partial discharge measurement techniques were analyzed [13]. A straightforward method based on the distance between the vertexes of the hyperbolic surfaces and their intersection point was proposed to find the best positions on the tank to install the sensors [14]. An ultra-wideband (UWB) monopole PD sensor that can be installed in the oil tank seam was designed, and the signal strength detected by the seam sensor was greater than that of the bow-tie antenna [15]. For transformer overheating defects, the dissolved gases analysis (DGA) is the main method. The values of gas ratios and values of the percentage content of gases were analyzed based on 344 transformers and shunt reactors with low-temperature overheating defects [16]. The ranges of gas percentage and gas ratio values under high temperature overheating defects accompanied by discharges with different intensity were determined based on 259 transformers, and 15 nomograms were drawn to recognize different defects [17]. In addition, the DGA is used widely in overheating and PD defect detection. The uncertain and unresolved issues in diagnosis accuracy were analyzed, and the solutions for addressing issues were reviewed, including the application of intelligent techniques [18]. In order to analyze these gases and diagnose transformer fault types, many methods have been developed, such as the Key Gas Method, Method of Duval, IEC 60599 Method, Method of Dornenburg, Method of Rogers, deep belief networks, etc. [19]. To assess the overall condition of a transformer, some methods were proposed, such as the evidential reasoning approach, artificial intelligence expert system and health index calculation model [20,21,22]. In addition, the optical characteristics of the arc in oil were measured, which can help us timely detect the internal arc [23]. These studies focus on defect detection methods and do not improve the transformer explosion performance essentially. Based on the above studies, most defects can be detected, but it is difficult to determine rapid development-type defection. Therefore, the defect detection accuracy and severity assessment should be improved.

According to the physical quantities, the transformer protection methods can be divided into electrical and non-electrical quantity protection methods. A power differential protection scheme based on the fault component network (FCN) was proposed that was free from inrush detection [24]. The unidirectional index and quartering-based similarity index were proposed to discriminate the fault conditions and other non-fault conditions [25]. The hydrodynamic analysis of the safety device’s behavior in a gas relay using computational fluid dynamics techniques was performed, and the performance for failures was obtained [26]. To analyze Buchholz relay maloperation and failure to act in time, an experiment based on a 25 MVA/110 kV transformer was performed, and the response of a Buchholz relay under gas generation faults of different severities inside the transformer’s oil tank was obtained, which revealed that the gas accumulation relay had high sensitivity but insufficient speediness [27]. To analyze the performance of the oil pressure relief valve (PRV) under external short circuit faults, experimental and numerical analyses were performed on a real full-scale 50 MVA/110 kV transformer, and the sustained vibrations can result in PRV malfunctions [28]. The pressure distribution clouds inside the tank of AC 220 kV, AC 500 kV and DC ± 800 kV oil-immersed transformers were analyzed [29]. A detailed investigation using the nonlinear finite element analysis of a 210-MVA transformer high-pressure experiment was presented, which indicates the true stress–strain curve was recommended [30]. These researches aim to put the transformer out of operation before tank rupture. However, there are loopholes in the protection provided for the transformer [31].

In order to improve the transformer explosion-proof performance, many scholars have studied the insulation material, transformer tanks and new transformer structures. Vegetable oil characteristics and application were studied, which can reduce the possibility of fire due to its high flash point [32,33]. The transformer tank equipped with a mockup active part was designed for arc resistance [34], and the application of polymer matrix composites in large power transformer tanks was studied, which can make it more resilient [35]. In addition, a new type of transformer was designed with the gas layer, in which the upper space is filled with nitrogen and the gas contacts with the insulating oil directly. This type of transformer is referred to as the nitrogen-sealed transformer [36]. Compared to the researches in the first two directions, these studies change the structure and material of the transformers, which can reduce the tank rupture probability fundamentally. However, the application is less, and the effectiveness should be further validated.

Among the above studies, the nitrogen-sealed transformer has the most obvious changes and is considered to be very promising in explosion-proof performance. The gas pressure was calculated under varying load conditions, and the gas layer volume design principle is proposed [36]. In order to determine the performance of transformers under overload conditions, model tests were conducted to check the characteristics of nitrogen gas pressure, moisture content in the insulation paper for winding and air bubble generation temperature, and the results showed that designing the nitrogen gas pressure was effective [37]. An apparatus was developed for sampling the head space, which was useful to analyze the condition of nitrogen-sealed transformers [38]. These studies are effective for normal operation and slowly evolving faults of transformers, but are difficult to apply to rapidly evolving faults. In sudden fault analysis, the pressure change characteristics caused by the presence of a large number of bubbles due to internal arcs are unclear.

This paper takes the stress fields of the arc caused by a winding short circuit fault in the nitrogen-sealed transformer as the object of research. We theoretically analyze and deduce the arc energy based on the topology of the circuit. Moreover, we analyze the source of pressure at the fault point and the propagation process from the fault point to the wall of the tank. A model of the transfer of pressure in the transformer is established using a finite element software. We seek to obtain the dynamic pressure changes on the wall of the tank when the arc develops. Based on the simulation results, the protection method can be designed to ensure the operational safety of the transformer.

This paper is structured as follows: Section 2 mainly introduces the structure of the nitrogen-sealed transformer and its tank rupture process. Section 3 manly discusses the arc characteristics, gas generation mechanism and pressure propagation equations. Section 3.1 is the calculation process of the arc energy generated due to winding short circuit faults. Considering the arc heat energy conversion coefficient, the gases produced in the arc faults and the pressure wave propagation are analyzed in Section 3.2. In order to obtain the transformer explosion-proof performance, the stress on the transformer tank is analyzed in Section 3.3. Section 4 mainly provides a detailed introduction of establishing a finite element model using simulation models. Section 5 is divided into three sections to analyze the simulation results. Section 5.1 presents the arc energy under different faults, and Section 5.2 analyzes the pressure wave and the pressure on the tank. Section 5.3 compares the differences between the nitrogen-sealed transformer and the conventional transformer.

2. The Nitrogen-Sealed Transformer

2.1. Transformer Structure

In the nitrogen-sealed transformer, the volume of nitrogen gas is designed to meet the thermal expansion and contraction requirements of insulating oil. The molecular structure of nitrogen gas is stable and can be used as a protective gas to realize the sealing and moisture-proof of transformers [36].

The schematic diagram of the nitrogen-sealed transformer is shown in Figure 1. The nitrogen gas contacts the oil directly, and the gas content in the oil is related to temperature and pressure. The winding and core are submerged in insulation oil, and the winding leads are led out of the tank through long tail bushes.

2.2. Internal Faults and Tank Rupture Process

In oil-immersed transformers, the insulating oil and insulating paper gradually age after long-term operation, and the insulation strength is reduced. When there are defects in the transformer, the deterioration of the insulation oil and paper intensifies. If the actual field strength exceeds the tolerance field strength, the insulation material will break down, and short circuit current occurs with arcs.

Since the temperature of the arc is very high, the oil will be decomposed and evaporated quickly. The bubble volume expands and the pressure rises because of the limitation of the insulating oil around the fault point. Therefore, the dynamic pressure wave passes through the oil and the body to the tank. If the stress exceeds the tank wearing strength, the oil tank ruptures. The oil will leak and make contact with the air, and when the temperature of the oil exceeds the ignition point, the fire will occur [39]. The transformer tank rupture process is shown in Figure 2.

There are mainly two types of internal faults in transformers. One is the winding phase-to-phase or phase-to-ground short circuit, with a long arc. The other is the winding turn-to-turn short circuit, with a short arc. The arc presents the resistance characteristics, and the resistance is usually nonlinear. To avoid the transformer tank rupture, the analysis on the pressure propagation and the pressure on the tank during the arc duration process is important.

3. Transient Model of Dynamic Pressure Wave Propagation in Oil

3.1. Arc Energy Calculation Method

When a short circuit fault occurs in a transformer, the short circuit arc occurs between the fault points, and the arc energy can be calculated as follows:

$$W_{\mathrm{arc}}={\displaystyle {\int }_0^{\Delta t}{u}_{\mathrm{arc}}\left|i_{\mathrm{arc}}\right|dt}$$

(1)

where W_arc is the arc energy, u_arc is the arc voltage, i_arc is the arc current, Δt is the arc duration time and | | represents the absolute value operation. Generally, u_arc is set to be a positive value.

The arc voltage is related to arc length and severity. For long arcs in phase-to-phase or phase-to-ground short circuits, experimental studies have found that the arc voltage is related to the arc length and the relative pressure at the depth of the arc in the oil [40]. The arc voltage calculation formula is shown in the following formula:

$$u_{\mathrm{arc}}=55l_{\mathrm{arc}}\sqrt{P}$$

(2)

where l_arc and P represent the arc length and the relative pressure.

For the short arc between adjacent turns, the arc voltage is calculated according to Equation (2). As the arc expands, the number of turns in the short circuit may increase, representing a parallel shunt relationship, and the arc voltage based on Equation (2) can be corrected by multiplying three to five times.

Take the turn-to-turn short circuit fault as an example, and the equivalent circuit is shown in Figure 3 [41,42]. The arc resistance is represented as r_arc. According to Kirchhoff’s current law, the arc current is the sum of the primary-side current i₁₁ and the circulating current i₁₂ in the faulted turns.

$$i_{\mathrm{arc}}=i_{11}+i_{12}$$

(3)

For a turn-to-turn short circuit fault, the fault arc energy can be expressed as follows:

$$W_{\mathrm{arc}}=55l_{\mathrm{arc}}\sqrt{P}{\displaystyle {\int }_0^{\Delta t}\left|i_{11}+i_{12}\right|dt}$$

(4)

3.2. Dynamic Pressure Propagation Model in Oil

In the arc energy, the percentage used to make oil evaporate is about 15~40% [40], which is called the conversion coefficient. The remaining energy is used to transfer heat with oil. The quantity of oil vapor produced by arcs in the oil can be calculated based on the following equation:

$$m_{\mathrm{oil}}=\alpha W_{\mathrm{arc}}/\Delta H_{\mathrm{oil}}$$

(5)

where m_oil is the quantity of oil vapor, α is the conversion coefficient and ∆H_oil is the enthalpy increase of insulating oil from liquid to a vapor state.

The arc energy conversion coefficient is inversely proportional to the duration time and can be expressed by several functions. Set the arc duration time from 0 to 0.08 s, and the conversion coefficient curves in the four different functions are shown in Figure 4.

For simplicity, the arc energy conversion coefficient in this paper follows the exponential function F₃.

$$\alpha =(2\times {10}^{-10}{)}^{t/2}/2.5$$

(6)

In the process of the oil from liquid to gases, the enthalpy increase equation can be expressed in the following formula:

$$\Delta H_{\mathrm{oil}}=C_{\mathrm{oil}}({\theta }_2-{\theta }_1)+\Delta H_2+C_{\mathrm{gas}}({\theta }_3-{\theta }_2)$$

(7)

where θ₁ is the oil temperature in a normal operation situation, θ₂ is the vaporization temperature of the insulating oil, θ₃ is the maximum temperature of the oil vapor, C_oil is the specific heat of the insulating oil, C_gas is the specific heat of the oil vapor and ∆H₂ is the latent heat of vaporization of the insulating oil. In general, θ₁ is from 60 °C to 80 °C, θ₂ can be up to 400 °C, θ₃ is about 1700 °C and ΔH₂ is 250.8 kJ/kg.

The approximate relationship between the fault energy and the volume of gas was obtained by the French company SERGI through experiments [43] and can be expressed in the following formula:

$$V_{\mathrm{gas}}=[0.44\ln (W_{\mathrm{arc}}+5474.3)-3.7874]$$

(8)

Assuming that the gas aggregates into spherical bubbles rapidly, the equal radius can be calculated based on the following formula:

$$r_{\mathrm{gas}}={(\frac{3V_{\mathrm{gas}}}{4\pi })}^{1/3}$$

(9)

Due to the mass conservation of the oil and the vapor, the oil vapor density can be calculated based on the following formula:

$${\rho }_{\mathrm{gas}}=\frac{\alpha W_{\mathrm{arc}}}{\Delta H_{\mathrm{oil}}{V}_{\mathrm{gas}}}$$

(10)

Assuming that the insulating oil vapor is the ideal gas, the pressure at the fault point is expressed as follows:

$$p_{\mathrm{gas}}=\frac{({\gamma }_{\mathrm{gas}}-1){\mu }_{\mathrm{gas}}}{\Delta H_{\mathrm{oil}}}\cdot \frac{\alpha W_{\mathrm{arc}}}{V_{\mathrm{gas}}}$$

(11)

where p_gas is the internal pressure of the oil vapor, γ_gas is the ratio between the specific heat ratio of oil and vapor and μ_gas is the specific internal energy of the oil vapor. The data of μ_gas can be set at 5.68 MJ/kg.

Due to the expansion inertia of the insulating oil around the bubbles, the pressure inside the bubbles increases dramatically with the continuation of the arc, resulting in a huge pressure difference at the interface between the oil and gas phases and propagating to the surrounding area in the form of pressure waves. The pressure can be calculated based on the following formula:

$$\Delta p=p_{\mathrm{gas}}-k{p}_0-p_{\mathrm{oil}}-2{\sigma }_{\mathrm{oil}}/r_{\mathrm{gas}}$$

(12)

where p₀ is the atmospheric pressure, σ_oil is the bubble surface tension coefficient, p_oil is the pressure at the bubble surface caused by oil and k is the equivalent factor for different transformer forms. For conventional transformers, k is equal to 1, and for nitrogen-sealed transformers, k is relative to the nitrogen volume. Generally, σ_oil is set at 0.027 N/m.

The pressure difference at the interface between the oil and gas will produce a dynamic pressure wave that propagates around. The pressure wave reflected by the oil tank and the dynamic pressure wave superpose, constituting the tank internal acoustic pressure field in the oil. The transient pressure acoustic equation of the dynamic pressure wave transmitted to the surrounding oil can be expressed in the following formula:

$$\frac{1}{\rho c^2}\frac{{\partial }^2{p}_t}{\partial t^2}-\nabla \cdot \left[\frac{1}{\rho }(\nabla p_t-q_{\mathrm{d}})-\frac{\delta }{\rho c^2}\frac{\partial \nabla p_t}{\partial t}\right]=Q_{\mathrm{m}}$$

(13)

$$\delta =\frac{1}{\rho }(\frac{4\mu }{3}+{\mu }_{\mathrm{B}})$$

(14)

$$p_t=p_{\mathrm{b}}+\Delta p$$

(15)

where c is the pressure wave propagation speed, ρ is the oil medium density, ρc² is the bulk elastic modulus, t is the time, μ is the dynamic viscosity, μ_B is the intrinsic viscosity coefficient, q_d is the dipole domain source, Q_m is the monopole domain source, p_t is the total pressure field strength, p_b is the background pressure field strength and Δp is the scattered sound pressure field.

Pressure wave propagation is impeded and reflected by tank walls, internal insulation and metal structures. Then, the sound hard boundary conditions can be expressed as follows:

$$-n\cdot \left[\frac{1}{\rho }(\nabla p_t-q_{\mathrm{d}})\right]=0$$

(16)

where n is the normal unit vector.

3.3. Solid Mechanics and Acoustic-Solid Coupling Model

The tank wall will obstruct and reflect the pressure wave, causing tank suffer stress and deform, which leads to tank rupture in severe cases. The transient equilibrium equation of the tank wall caused by the fault pressure can be expressed as follows:

$${\rho }_{\mathrm{t}}\frac{{\partial }^{2}u}{\partial t^2}=\nabla \cdot S+F_{\mathrm{V}}$$

(17)

where ρ_t is the tank wall density, u is the micro-element displacements of the tank wall, S is the stress on the tank wall micro-element and F_V is the pressure density of the tank wall micro-elements.

During the transient stress deformation, the tank stress–strain relationship can be expressed as follows:

$$S-S_0=C:(\epsilon -{\epsilon }_0-{\epsilon }_{\mathrm{p}})$$

(18)

where S₀ and ε₀ are the initial stress and strain, respectively, C is the stress–strain tensor relationship related to Young’s modulus and Poisson’s ratio and ε_p is the plastic deformation tensor of the tank material.

The relationship between the total strain tensor of the tank and the micro-element displacement is expressed as

$$\epsilon =\left[{(\nabla u)}^{\mathrm{T}}+\nabla u\right]/2$$

(19)

During the pressure wave impact, the micro-element displacement of the tank confinement area is zero, the tank wall undergoes linear elastic deformation and the acoustic-solid coupling surface of the oil and tank wall generates pressure loss and pressure transfer, which can be expressed as follows:

$$-n\cdot \left(\frac{1}{\rho }\left(\nabla p_t-q_{\mathrm{d}}\right)\right)=-n{u}_{\mathrm{tt}}$$

(20)

$$F_{\mathrm{A}}=P_{t}n$$

(21)

where u_tt is the second-order derivative of the tank wall micro-element displacement, and F_A is the pressure surface density on the tank wall micro-elements.

Through the dynamic pressure model and acoustic-solid coupling model, the pressure wave propagation in the transformer caused by the internal arc can be simulated, and the stress and the deformation of the tank wall can be calculated.

4. Finite Element Simulation of the Pressure in the Tank

In order to simulate the pressure changes in the transformer, a finite element simulation model is built. The transformer is simplified to reduce the computational complexity. The tank, the winding and the core are in the model.

Take a 110 kV/20 MVA transformer as an example, the overall geometric model of the tank is shown in Figure 5. The tank can be divided into two parts. The lower part represents the space filled with oil. Its length is 4.23 m, its width is 1.45 m and its height is 2.585 m. The upper part is filled with nitrogen gas. The gas is stored in the cuboid and cylinder spaces. The size of the cuboid part is 3.335 m × 1.45 m × 0.342 m. The height and the radius of the cylinder part are 2.1 m and 0.895 m. The thickness of the wall of the tank is 10 mm. A model of the core and the winding is provided inside the tank, and stiffeners are installed at suitable positions outside it.

This model is used to simulate the pressure distribution in the transformer after an internal arc fault occurs, and the observation point is at the middle position of the fuel tank near the conservator.

The winding with an iron core is shown in Figure 6. The core is composed of multiple sheets of silicon and steel. The coil can be divided into primary and secondary coils. In the model, the arc occurrence positions are set, which is the source of transient pressure wave.

A finite element mesh division is used, as shown in Figure 7. Based on the finite element model, the pressure changes inside the transformer tank and the stress on the wall of the tank can be simulated, and we can analyze the propagation of the pressure wave based on a diagram of the contours of the pressure distribution.

5. Simulation Analysis

5.1. Internal Arc Energy Calculation in the Nitrogen-Sealed Transformer

To analyze the transformer tank performance, considering the internal and external faults superimposed as the analysis condition. In this section, the internal arc energy in a 110 kV transformer is calculated.

The transformer coupling group is YNd11. The rated voltage of high-voltage and low-voltage winding is 110 kV and 10.5 kV, respectively. The rated capacity is 20 MVA, and the short circuit impedance is 10.5%. The number of primary winding pies is 70. For the sake of simplicity, the arc resistance is set to be constant, and the arc energy can be calculated by the steady-state values of the voltage and current. The system short circuit capacity is set to be 9000 MVA, and the system short circuit impedance can be calculated. The impedance is 1.34 Ω, with the resistance at 0.5 Ω and the inductance at 4 mH.

The high-voltage side winding turn-to-turn short circuit simulation model is shown in Figure 8. The third and fourth pies are shortened. In the conventional transformer, the depth at the fault is 2.6 m, the arc length is 4 mm and the oil medium density at 60 °C is 0.860 kg/m³. According to the arc voltage calculated and current simulated, the arc resistance can be calculated at 0.027 Ω, and the arc current can be obtained.

The arc current obtained in the transformer is shown in Figure 9. The root mean square value of the steady-state arc current is about 4.87 kA.

Assume the pressure in the nitrogen layer is 18.7 kPa and the oil medium density at 60 °C is 0.860 kg/m³, so the equivalent depth can be calculated as 2.2 m. The depth at the fault is 0.94 m and the arc length is 4 mm. According to the formula, the arc voltage can be calculated, and the arc current can be simulated.

Based on the simulation model and the above formulas in Section 3, the arc voltage, arc current and arc energy are shown in

Table 1. Arc energy under turn-to-turn faults in the nitrogen-sealed transformer.

	Short Circuit Condition	Uarc (kV)	Iarc (kA)	Warc (MJ)
1	high-voltage side B-phase turn-to-turn short circuit superimposed with low-voltage side three-phase short circuit	0.148	4.87	0.058
2	high-voltage side B-phase turn-to-turn short circuit superimposed with low-voltage side a-phase short circuit	0.185	8.30	0.123

. The arc energy is of the same order of magnitude as it was in the paper published in [44].

When the phase-to-phase short circuit fault occurs, the arc energy can be calculated, which is shown in

Table 2. Arc energy under phase-to-phase faults in the nitrogen-sealed transformer.

	Short Circuit Condition	Uarc (kV)	Iarc (kA)	Warc (MJ)
1	high-voltage side B–C phase-to-phase short circuit superimposed with low-voltage side three-phase short circuit	1.053	17.5	1.475
2	high-voltage side B–C phase-to-phase short circuit superimposed with low-voltage side a-phase short circuit	1.053	17.6	1.483

. It is higher than the arc energy under a turn-to-turn fault.

5.2. Pressure Characteristics in the Nitrogen-Sealed Transformer

Using the pressure acoustic transient module and solid mechanics module of COMSOL 5.6 software, the models of the nitrogen-sealed transformer are built. The fault point and the pressure observation points are set in the model. The material of the tank is the steel plate Q355B, which yield strength is 510 MPa.

Set the initial pressure values for each area, and the oil pressure at the depth of the arc position is applied to the surface of the bubble directly. For the nitrogen-sealed transformer, the pressure in the nitrogen layer is set at 0.185 atm (standard atmospheric pressure).

The model is built based on COMSOL Multiphysics 5.6. In the model, the free mesh partitioning is used and tetrahedral meshes are automatically generated on volumes. The simulation is set from 0 to 80 ms, and the time interval is 0.25 ms. The occurrence time of the arc is 0 ms. The processor of the server is Intel(R) Xeon(R) Gold 6248R CUP @3.00 GHz, and the RAM is 768 GB.

5.2.1. Turn-to-Turn Short Circuit Simulation

When a high-voltage side B-phase turn-to-turn short circuit superimposed with a low-voltage side three-phase short circuit occurs, the arc energy is 0.123 MJ in the nitrogen-sealed transformer, according to Table 1. The arc bubble model can be simulated along the winding turns, which is shown in Figure 10.

The simulated distribution of the pressure on the transformer tank wall is shown in Figure 11. The pressure spreads from the arc position to the tank wall after the fault occurs. The propagation speed of the pressure waves in oil can reach up to 1.4 m/ms, and the transformer tank will withstand the pressure in a short period of time after the fault. The pressure on the wall of the transformer tank continues to change with time. Due to the reflection and refraction of the pressure wave during the propagation, the pressure on the tank does not change linearly, and there are some local areas where the pressure is larger. When the tank wall is under pressure, the wall of the tank expands and deforms under the action of the pressure. The maximum pressure is 109 MPa and occurs at 66.5 ms, which means that the tank will not rupture.

5.2.2. Phase-to-Phase Short Circuit Simulation

When a high-voltage side B–C phase-to-phase short circuit superimposed with low-voltage side a-phase short circuit occurs, the arc energy is 1.483 MJ, according to Table 2. The arc bubble model is simulated in the space between B and C phase winding, which is shown in Figure 12.

The simulated distribution of the pressure on the transformer tank wall is shown in Figure 13. According to the arc energy in Table 1 and Table 2, the arc energy of the phase-to-phase short circuit fault is larger. Compared to the pressure changes in Figure 11, the pressure propagation process and characteristics are similar. The maximum pressure is 162 MPa and occurs at 66 ms. The pressure on the tank is less than the yield strength of the steel, and the tank is safe.

5.3. Comparison with the Pressure Changes in a Conventional Transformer

5.3.1. Arc Energy in the Conventional Transformer

Based on the simulation model and the above formulas in Section 3, the arc voltage, arc current and arc energy in the conventional transformer are shown in

Table 3. Arc energy under turn-to-turn faults in the conventional transformer.

	Short Circuit Condition	Uarc (kV)	Iarc (kA)	Warc (MJ)
1	high-voltage side B-phase turn-to-turn short circuit superimposed with low-voltage side three-phase short circuit	0.133	4.87	0.052
2	high-voltage side B-phase turn-to-turn short circuit superimposed with low-voltage side a-phase short circuit	0.165	8.30	0.110

and

Table 4. Arc energy under phase-to-phase faults in the conventional transformer.

	Short Circuit Condition	Uarc (kV)	Iarc (kA)	Warc (MJ)
1	high-voltage side B–C phase-to-phase short circuit superimposed with low-voltage side three-phase short circuit	0.941	17.5	1.316
2	high-voltage side B–C phase-to-phase short circuit superimposed with low-voltage side a-phase short circuit	0.941	17.6	1.324

.

Compared to the arc energy in the nitrogen-sealed transformer, it is a little smaller due to the pressure difference at the arc occurrence position.

5.3.2. Turn-to-Turn Short Circuit Simulation

The pressure distribution characteristics on the two different transformer tanks are shown in Figure 14 and Figure 15. For the conventional transformer, the maximum pressure at 1.5 ms is about 20.3 MPa, the maximum pressure during the arc duration process occurs at 80 ms and the pressure is 157 MPa. The tank wall begins to bulge and deform at 1.5 ms after the fault time. However, for the nitrogen-sealed transformer, the maximum pressure at 1.25 ms is about 26.1 MPa, and the maximum pressure during the arc duration process occurs at the time 66.5 ms, which is about 109 MPa. The tank wall begins to bulge and deform at 1.25 ms after the fault time. The stress on the nitrogen-sealed transformer tank is lower than the pressure on the convention transformer tank. The maximum pressure on the conventional and nitrogen-sealed transformer tank is 157 and 109 MPa, respectively, which is lower than the yield strength of the steel plate Q355B. The two types of transformer tanks only undergo elastic deformation.

5.3.3. Phase-to-Phase Short Circuit Simulation

The pressure distribution on the two different transformer tanks is shown in Figure 16 and Figure 17. The maximum pressure on the conventional and nitrogen-sealed transformer tanks is 635 and 162 MPa, respectively. The pressure of the conventional transformer is higher than the yield strength of the steel plate Q335B, and the tank will rupture. However, the tank of the nitrogen-sealed transformer will not rupture.

5.3.4. Pressure Change Comparison Analysis

In Figure 18 and Figure 19, the pressure on the tank of the conventional transformer and the nitrogen-sealed transformer is shown. The observation point is at the middle position of the fuel tank near the conservator.

When the turn-to-turn short circuit occurs, the pressure increases obviously in the conventional transformer, and the pressure is relatively stable in the nitrogen-sealed transformer. When the phase-to-phase short circuit occurs, the pressure increases rapidly in the conventional transformer, while the pressure is still stable and increases slowly.

The volume and pressure of bubbles at the fault point change with the energy of the arc, and the propagation of pressure waves is affected by the bending and reflection effects of metal components and insulation fibers, which cause the pressure curves to exhibit oscillatory characteristics.

According to the data analysis, the setting of the nitrogen layer in the nitrogen-sealed transformer has good compressibility and plays a significant role in reducing the pressure, so the internal pressure rise rate is gentle and the amplitude is low throughout the entire arc duration process.

6. Conclusions

In this paper, the pressure changes in the nitrogen-sealed transformers under turn-to-turn and phase-to-phase short circuit faults are analyzed, and their explosion-proof performance is compared to the conventional transformer.

(1)

The arc energy caused by phase-to-phase faults is larger than turn-to-turn faults, and the proportion can reach tens of times more. For the 110 kV/20 MVA transformer studied in this paper, the arc energy is lower than 0.2 MJ when the winding turn-to-turn short circuit fault occurs, and it is about 1.4 MJ when the winding phase-to-phase short circuit fault occurs.

(2)

After the arc occurrence in the nitrogen transformer, the pressure wave spreads from the position of the initial arc to all four sides. Because the pressure wave propagation speed is nearly 1.4 m/ms, the tank will withstand stress for about several milliseconds. Due to the pressure wave refraction and reflection, the transient pressure at any point is the superposition of the vectors of the pressure waves. The pressure changes show oscillatory characteristics, and the maximum pressure appears at a certain moment during the process.

(3)

Compared to the conventional transformer, the arc energy is a little different because of the pressure difference at the arc position. The pressure in the nitrogen-sealed transformer has a slower change trend, and the pressure acting on the tank wall of the conventional transformer continues to increase over time, which is different from the change in the nitrogen-sealed transformer.

(4)

The tank of the nitrogen-sealed transformer will not rupture under the faults studied in this paper. However, the tank of the conventional transformer will rupture when the winding phase-to-phase short circuit fault occurs, which indicates that the nitrogen-sealed transformer has excellent explosion-proof performance. In the future, the non-electrical protection methods should be studied based on the pressure distribution.