Study on Oil Flow Characteristics and Winding Temperature Distribution of Oil-immersed Transformer

Ye Chen¹, Chuan Luo², Wenjiao Xu³, Guipeng Zhang⁴, Biao Tang¹, Ling Wei¹ and Zhengang Zhao^2,*

¹Electric Power Research Institute of Yunnan Power Grid Co. Ltd, Kunming 650217, China

²Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650500, China

³Kunming Electric Power Supply Bureau, Kunming 650011, China

⁴Yunnan Power Grid Co, Ltd, Kunming 650041, China

E-mail: zhaozhengang@kmust.edu.cn

*Corresponding Author

Received 05 March 2021; Accepted 08 March 2021; Publication 17 April 2021

Abstract

The stability and effective functioning of a power grid depend upon the reliability as well as safety prospects of a transformer which is the principal component of the power system. The natural oil circulation in the oil-immersed transformer drifts the oil flow by the change in the density which is again caused by the change in temperature. But the pressure is comparatively low with respect to the oil pump causing the lower down of velocity which in turn dissipates unimpressionable heat. In this paper, a noble attempt has been made to build a natural oil circulation layer-type winding transformer based on a fluid-solid coupling heat transfer model pertaining to the internal temperature field and flow field by using the fluid mechanics’ simulation software. In the next stage, the authors have analyzed the temperature distribution, hot spot, position condition of the variable winding, the horizontal the oil channel width as well as the temperature of the winding transformer. The paper is of great significance as it examines the influence of the flow characteristics of oil channel on the winding temperature distribution. The outcome can significantly improve the structure of heat dissipation and the operating environment of the transformer.

Keywords: Oil-immersed transformer, fluid-structure coupling, horizontal oil channel, winding temperature rise.

1 Introduction

Power transformers constitute the most critical power equipment in power systems. The stability of their operating state directly affects the safety of the whole power system. According to statistics, accidents caused by power transformers in the distribution system accounted for 90% [1]. The fault caused by the transformer winding accounts for more than 70% [2–4] attributed to the high frequency of failure. This is because the losses generated during the operation of the transformer will cause the internal temperature of the transformer to rise. In this process, the iron core, the windings, and the internal parts are in a high-temperature condition for a long time. According to the National Standard of the People’s Republic of China GB1094.2-2013 [5], for the A Class insulation material used in oil-immersed transformers, the service life of the transformer will be shortened by half for every 6 $^{\circ}$ C increase in the winding temperature in the range of 80 $^{\circ}$ C to 140 $^{\circ}$ C. The windings of the power transformer are mostly pie-type structures, and the horizontal oil channel is the main cooling channel between the windings, and the horizontal oil channel width has a large influence on the convective heat transfer between the transformer windings and the interstitial oil flow [6, 7].

In 2013, Dursun applied fluid dynamics calculation software ‘Comsol’ to simulate oil-immersed transformer flow field and discussed the influence of transformer oil properties on winding temperature variation is discussed [8]. In 2013, Wang et al. used Fluent to build a two-dimensional model for a non-steering transformer with a vertical oil channel in order to obtain a horizontal oil channel velocity vector [9]. Guo et al. built a two-dimensional model of the oil channel and winding, and changed the vertical oil channel width for calculation and analysis. It was found that the average temperature rise of the winding was significantly reduced when the vertical oil channel width was increased [10]. In 2015, Chen et al. used Fluent to calculate the two-dimensional flow field of the transformer and set a different number of oil baffles for the transformer. It was found that the distribution of the temperature field was ideal when 9 sets of oil baffles were set up [11]. In 2015, Li et al. proposed using the electromagnetic-fluid-temperature coupling method to perform simulation calculations, and the loss of internal heat source was attributed to the fluid-temperature field coupling analysis. The winding calculation model takes the 1/48 3D model of the overall model. The rise in temperature and position of the winding hot spot can be determined by calculating the temperature rise and oil flow distribution of transformer windings through the finite volume method [12]. In 2017, Xu et al. simplified the winding calculation model and calculated its winding temperature using the fluid network method [13].

This paper takes the model of SZ11-10000/35 three-phase double-winding load-regulating power transformer produced by a company in Yunnan as the research object, theoretically analyzes the heat source and the internal heat transfer principle of the transformer, and analyzes the oil flow without an oil channel. The numerical calculation of the temperature distribution of the winding is carried out. Considering the change of the physical property parameters of the transformer oil under temperature change, a numerical model of three-dimensional heat transfer inside an oil-immersed transformer was established. In this research work, the Fluid mechanics’ simulation software ANSYS CFX has been adopted for simulation of the heat flow coupling in the winding area of the transformer and analysis of oil flow situation at different width levels. This also measures the impact of the rise of temperature on winding. The fiber winding temperature measurement means (temperature sensor) is used to directly detect the temperature of the transformer winding, and the experimental results are compared with the simulation results to verify the validity of the simulation results.

2 Oil-immersed Transformer Structure and Heat Source Analysis

As an important equipment in power transmission and transformation systems, oil-immersed transformers are mainly composed of iron cores, windings, fuel tanks, etc. The structure diagram is shown in Figure 1. When the transformer is functioning, the core and windings generate losses and transfer heat to the transformer oil, so they can be used as a heat source in the internal temperature and oil flow calculation of the transformer [14]. The loss in the transformer consists of the idling loss generated by the iron core and the load loss generated by the high and low voltage windings, which is expressed by the following formula [15]:

P_{T} = P_{L} + P_{C}

(1)

where $P_{T}$ is the total loss, P $_{L}$ is the load loss, P $_{C}$ is the idling loss.

Figure 1 Oil-immersed transformer structure diagram.

The idling loss is mainly composed of the hysteresis loss and eddy current loss of the core. Hysteresis and eddy current loss are related to material quality and magnetic density of silicon steel sheet [16]. Hysteresis loss due to hysteresis in ferromagnetic materials during repeated alternating magnetization. Its magnitude is proportional to the square of the maximum magnetic induction density of hysteresis coefficient, alternating magnetization frequency, the core volume and alternating flux. Hysteresis loss can be expressed by the following formula

P_{h} = γ f B_{\max}^{2} V

(2)

where $γ$ is the hysteresis coefficient of the core material, f is the frequency, B $_{m a x}$ is the maximum magnetic induction density of the core alternating magnetic flux, V is the total volume of the core.

Eddy current loss is not only related to induced potential and maximum magnetic density, but also to the resistivity and thickness of the silicon steel sheet. Therefore, in the design and manufacture of the iron core, reducing the thickness of the silicon steel sheet can reduce eddy current loss, and the eddy current loss Pe can be expressed as

P_{e} = γ d^{2} f^{2} B_{m a x}^{2} V

(3)

where $d$ is the thickness of the silicon steel sheet. Therefore, the idling loss $P_{C}$ is:

P_{C} = P_{h} + P_{e} = γ f B_{m a x}^{2} V + γ d^{2} f^{2} B_{m a x}^{2} V

(4)

The load loss of the transformer, also known as copper loss [17], is the loss generated when the primary and secondary windings respectively flow through their respective load currents. During the operation of the transformer, the load loss is

P_{D} = 3 I_{1 N_{φ}}^{2} r_{1, 75^{\circ} C} + 3 I_{2 N_{φ}}^{2} r_{2, 75^{\circ} C}

(5)

where P $_{D}$ is copper loss, $I_{1 N_{φ}}$ and $I_{2 N_{φ}}$ are the phase current of the primary and the secondary winding, respectively, $r_{1, 75^{\circ} C}$ is the total resistance of the primary winding at 75 $^{\circ}$ C, and $r_{2, 75^{\circ} C}$ is the total resistance of the secondary winding at 75 $^{\circ}$ C.

Figure 2 Transformer structure and heat dissipation diagram.

Through the analysis of the heat generation and heat conduction of the transformer, both the iron core and the winding generate heat. During this process, the transfer of heat takes place due to conduction and convection. In a similar process, the heat generated by the core and the windings are also transferred to the transformer oil. Then, the heat of the transformer oil is directly transmitted to the air through the tank wall. Similarly, transformer oil brings internal heat to the heat sink fins, which ultimately transfers heat to the air through the heat exchange between the heat sink and the air.

3 Fluid-solid Coupling Model of the Oil-immersed Transformer

The oil-immersed power transformer provided by Yunnan Tongchang Electric is used in this study. According to the actual core, winding structure and material parameters of the transformer, the finite element analysis software ANSYS is used to establish the three-dimensional temperature calculation model of the core and winding.

Table 1 Structural parameters of various components of the transformer

Component	Structural Parameters
Iron Core	Diameter	440 mm
	High	860 mm
	Three pillar center distance	78 mm
Low Voltage Winding	Height per pie	7.5 mm
	Total thickness	56.5 mm
	Spacing from the core	14 mm
High Voltage Winding	Height per pie	7.5 mm
	Total thickness	65 mm
	Spacing from the low voltage winding	20 mm
Horizontal Oil Channel	High	2 mm

Table 2 Transformer material properties

			Thermal	Specific
		Density	Conductivity	Heat Capacity
Component	Material	(kg/m $^{3}$ )	(W/mK)	(J/kg K)
Iron core	Silicon steel	$7.42 \times 10^{3}$	21	485
Low voltage winding	Copper	$8.93 \times 10^{4}$	398	386
High voltage winding	Copper	$8.93 \times 10^{4}$	398	386

Establishing a three-phase model of the transformer, the core is simplified into a cylinder, the outside is low and high voltage winding, the high-low voltage winding is 55 layers, the winding height of each layer is 7.5 mm, and the oil channel height between each layer 2 mm, the total height of the winding is 520.5 mm. According to the actual parameters of the iron core and the winding the simplified three-dimensional physical model of the transformer. The three-dimensional model is shown in Figure 3(a). The iron core is simplified into a cylinder. The division is divided into grids as shown in Figure 3(b).

Figure 3 Three-dimensional model of the iron core and winding.

The heat loss of each heat source is converted into body load, assume that the loss of the transformer core and winding is evenly distributed, and can be calculated and applied to the iron core according to the volume of the transformer core and the high and low voltage windings. The unit heat loss is 1074 W/m $^{3}$ , and the unit heat loss of the high and low voltage windings is 64875 W/m $^{3}$ .

If you want to accurately obtain the flow state of the transformer oil and the temperature rise of the winding, you need to establish a fluid-solid coupling heat transfer model to resolve the calculation, and the model needs to be simplified [16],

(1) The external environment of the transformer is constant as 25 $^{\circ}$ C;

(2) Iron core and winding are evenly heated;

(3) Ignore the influence of other phase windings on adjacent windings;

The thermal lift force driving the oil circulation in the natural oil cycle is derived from the density change of the transformer oil, and the flow state of the transformer oil almost determines the heat dissipation effect inside the transformer. The material properties of the fluid need to be set before the model is numerically solved. The physical properties of transformer oil vary with temperature as shown in Table 3.

Table 3 Transformer oil physical parameters

Physical Properties	Fitting Formula
Density (kg/m $^{3}$ )	$ρ$ $=$ $-$ 0.58T+893.09
Dynamic viscosity (kg/m s)	$η = 8 \times 10^{- 5}$ T ${}^{2}- 4.8 \times 10^{- 3}$ T $+$ 0.1
Thermal conductivity (W/mK)	k $= - 8.049 \times 10^{- 5}$ T $+$ 0.133
Specific heat capacity (J/kgK)	C $=$ 4.207T $+$ 1763.4

The temperature field of an object is a scalar field. The object temperature is generally expressed as a function of space coordinates and time, which can be expressed in a Cartesian coordinate system [18]

T = f (x, y, z, t)

(6)

where $x, y, z$ is a space rectangular coordinate; $t$ is time. When the temperature difference exists in the iron core and winding in the solid domain, the microscopic particles undergo thermal motion and heat conduction occurs. In the heat conduction phenomenon, the heat passing through a given section is proportional to the temperature change rate perpendicular to the cross section in a unit of time. And the cross-sectional area, and the direction of heat transfer is opposite to the direction in which the temperature rises. The thermal conductivity of the solid domain satisfies Fourier’s law

q = \frac{Φ}{A} = - λ \frac{\partial T}{\partial n} n

(7)

where q is the heat flux density; $Φ$ is the conduction heat flow; A is the cross-sectional area perpendicular to the heat transfer direction; $λ$ is the thermal conductivity.

In a rectangular space coordinate system, (7) can be expressed as

q = - λ_{x} \frac{\partial T}{\partial x} i - λ_{y} \frac{\partial T}{\partial y} j - λ_{z} \frac{\partial T}{\partial z} k

(8)

where $λ_{x}$ , $λ_{y}$ , $λ_{z}$ is the thermal conductivity of $x, y, z$ component in the direction.

For solids, the differential equation of heat conduction can also be expressed as

\frac{\partial T}{\partial t} = \frac{λ}{ρ c} (\frac{\partial^{2} T}{\partial x^{2}} + \frac{\partial^{2} T}{\partial y^{2}} + \frac{\partial^{2} T}{\partial z^{2}}) + \frac{Φ + S_{h}}{ρ c}

(9)

where c is the specific heat capacity of the substance; $ρ$ is the density of matter; S $_{h}$ is the internal heat source in the object.

At the interface between the solid domain and the fluid domain of the transformer, the fluid-solid coupling between the iron core, the winding and the transformer oil is carried out by convection heat transfer. Convection heat transfer is actually a heat exchange process that occurs under the combined action of heat transfer and heat convection on fluid and solid surfaces, the premise of heat exchange is the temperature difference between the fluid and the solid surface. The basic equation describing the convection heat transfer heat q is the Newtonian cooling formula, which can be expressed as

q = α Δ T

(10)

where $α$ is the surface convection heat transfer coefficient; $Δ$ T is the temperature difference between the fluid and the solid surface.

In the measurement of fluid-solid coupling of the transformer, convection heat transfer occurs on the contact surface of the iron core, high and low voltage windings and transformer oil. Through the software, the convection heat transfer coefficient of the outer part of the tank wall has been calculated. In this context, the air contact part needs to be calculated manually.

The calculation formula of the convection heat transfer coefficient is [19, 20]

$α = \frac{N_{u} λ}{L}$	(11)
$N_{u} = {0.825 + \frac{0.387 R_{a l}^{1 / 6}}{{[1 + (0.429 / \Pr) 9 / 16]}^{8 / 27}}}^{2}$	(12)
$R_{a l} = \frac{g β (T_{w} - T_{\infty}) L^{3}}{k v}$	(13)

where Nu is the Nusselt number; L is the height of the tank wall, m; $λ$ is the thermal conductivity of the fluid. P $_{r}$ is the Prandtl number; R $_{d}$ is the Rayleigh number. g is the gravity acceleration; $β$ is the thermal expansion coefficient of air; T $_{w}$ is the tank wall temperature; $T_{\infty}$ is the air temperature; v is the dynamic viscosity of air.

4 Simulation Calculation and Analysis of Transformer Internal Temperature Field

After creating a two-dimensional interface in the CFX post-processing section CFX-Post, the XY section of the winding horizontal oil channel and the flow velocity diagram of the ZX section can be obtained shown in Figure 4.

Figure 4 Oil flow rate diagram of horizontal oil channel XY section and ZX section.

It can be seen in Figure 4 that the oil flow rate of the horizontal oil channel is much lower than that of the vertical oil channel, and the oil flow rate of the horizontal oil channel of the low-pressure winding is lower than the oil flow rate of the horizontal oil channel of the high-pressure winding. Due to the small pressure difference between the oil flows on both sides of the winding, the oil velocity in the horizontal oil channel between the two-wire layer is relatively low, which easily causes the oil flow to stagnate, forming a dead oil zone, causing the temperature of the wiring layer to rise to cause the local temperature of the transformer too high.

Through the solution calculation of the fluid-solid coupling heat transfer model of the transformer temperature rise and oil flow, the calculation results of the winding temperature distribution of the transformer single-phase three-dimensional model are obtained. Figure 5 shows the winding temperature distribution.

Figure 5 Winding temperature profile.

It can be seen from the three-dimensional distribution of the transformer winding that the temperature distributions of the high and the low voltage winding are approximately equal. Further, the temperature rise of the upper winding is the highest. As the winding height decreases, the winding temperature also decreases, which is mainly due to the convection of transformer oil. The heat dissipation causes the heat to flow upwards. The difference between the oil temperature and the winding temperature decreases in the wake of the height increases, and the heat dissipation effect deteriorates. This causes the temperature at the top of the winding to be higher than the lower part. Simultaneously, since the top of the winding is no more heating, and the oil channel is wide, besides, transformer oil has good heat dissipation conditions. Therefore, the winding hot spot temperature is located above the winding, but not at the top.

5 Oil-immersed Transformer Layer Winding Temperature Rise Experiment

To accurately obtain the temperature variation of the transformer winding, besides, to verify the effectiveness of this calculation method for fluid-solid coupling, this paper conducts a temperature rise test for the oil-immersed transformer and uses the fiber Bragg grating temperature sensor to monitor the winding temperature of the transformer.

An FBG is essentially a wavelength-selective filter, which consists of a short segment of single mode optical fiber with a photo-induced periodically modulated index of refraction in the core of the fiber, as shown in Fig. 6. The Bragg wavelength $λ_{B}$ depends both on the physical characteristics of the fiber and geometrical characteristics of the gratin.

Figure 6 Spectrum modulation schematic diagram of the optical fiber Bragg grating.

In the experiment [21, 22], with the aim to reduce the influence of the sensor on the temperature rise test result and accurately detect the winding temperature rise, the temperature sensor is installed in the block of the winding oil channel, leaving the sensor pigtail and placing the spacers on the winding temperature measuring point. Five temperature sensors are arranged in the winding from top to bottom. The installation method of temperature sensors is shown in Figure 7. The site construction is shown in Figure 8.

Figure 7 Sensor installation and layout.

Figure 8 Installation photos of FBG temperature sensor.

The experiment conducted temperature tests on windings of different heights. The experimental results are shown in Table 4 below.

Table 4 Winding temperature rise experimental data and numerical calculation values

Winding Position/cm	Experimental Data/K	Numeral Calculations/K
1	323.65	322.21
7	No	325.88
13	329.35	328.59
25	335.35	336.11
37	339.75	340.59
45	No	342.51
49	340.85	341.31

Figure 9 is the graph of winding temperature as a function of winding position as a function of winding temperature rise simulation.

Figure 9 Winding temperature rise numerical calculation curve.

Since the parameter settings of the simulation calculation are different from the actual parameters and the environment, there are certain errors in the numerical calculation. It can be seen from the experimental data that as the winding position increases, the winding temperature also rises. The position of the sensor closest to the hot spot temperature is 37 cm and 49 cm from the bottom. When the hot spot of the simulation curve is at 45 cm from the winding, the simulation is performed. The hot spot temperature obtained is the same as the measured temperature, so the measured temperature is slightly lower than the simulation result.

6 Study on the Influence of Horizontal Oil Channel Height on Winding Temperature Rise

In the design and manufacture of the oil-immersed transformer structure, reducing the height of the horizontal oil channel can reduce the winding height, save the winding material and reduce the manufacturing cost, but harms the heat dissipation of the transformer and the temperature rise of the winding. According to the design principle of the transformer winding, the height of the horizontal oil channel can provide more heat dissipation space, which is beneficial to heat dissipation.

In this paper, three-dimensional models of three types of transformers with horizontal oil channel heights of 3 mm, 4 mm, and 5 mm are established. Keeping the other settings unchanged, the fluid-solid coupling model of the transformer is calculated to obtain the winding temperature distribution at different levels of oil channel height. Figure 10 shows the temperature rise diagram of the transformer winding with a horizontal oil channel height of 3 mm to 5 mm. Figure 10 shows that the change in the horizontal oil channel height does not have much influence on the longitudinal oil temperature trend of the winding, and the winding hot spot position does not change, but the overall temperature rise of the winding is reduced, simultaneously, the temperature of the winding hot spot is also lowered. It helps to protect the voltage transformer insulation, thus extending the operating life of the transformer.

Figure 10 Temperature distribution of windings at different oil channel heights.

Figure 11 Winding temperature profile of different oil channel widths.

Figure 11 is a graph showing the temperature distribution of windings at different oil channel widths. It can be seen that as the height of the horizontal oil channel is widened, the winding temperature is reduced. This is because the heat exchange between the winding and the transformer oil is intensified, which reduces the temperature rise of the hot spot of the winding and rise of the average temperature. It can also be seen that changing the horizontal oil channel height, the high and low voltage winding temperature distribution remains unchanged, besides, the hot spot position of the winding will not alter. As the height of the oil channel increases further, the winding hot spot temperature rise trend is also slowing down, indicating that the increase of the oil channel height has a certain limit on the improvement of the oil flow of the oil channel and the effect of the temperature rise of the winding. The oil height channel is 2 mm. The oil flow and winding heat dissipation are greatly improved within the range of 4 mm. When the oil channel height is greater than 4 mm, the influences on the winding temperature rise and the oil flow is gradually reduced.

7 Conclusion

In this research work, the experiment pertaining to the rise in temperature for the oil-immersed transformer, using the basic theories of heat transfer and fluid dynamics, combined finite element simulation, a fluid-solid coupling heat transfer calculation model for the natural oil circulation oil-immersed transformer was established.

The simulation calculation and the actual measurement error are in the range of 1K, which proves that the numerical calculation model is feasible. On this basis, the influence of the horizontal oil channel oil flow velocity on the winding temperature distribution is analyzed. The results show that the oil flow rate of the horizontal oil channel of the low-pressure winding of the oil-immersed transformer is lower than the oil flow rate of the horizontal oil channel of the high-voltage winding, which leads to the temperature rise of the low-voltage winding is slightly higher than the high-voltage winding at the same height. Simultaneously, the oil flow velocity of the oil channel is different, resulting in the high and low voltage winding has different temperature distributions. As the width of the oil channel increases, the oil flow resistance between the line layers decreases which increases the oil flow rate. The convection heat transfer of the layers and the oil flow is therefore increased, and the hot spot of the winding is gradually reduced.

Acknowledgment

This project was jointly supported by the National Natural Science Foundation of China under Grant 51667011, the Applied Basic Research Project of Yunnan province under Grant 2018FB095, and the National Natural Science Foundation of China under Grant 51567013.

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Biographies

Ye Chen works at Electric Power Research Institute of Yunnan Power Grid Co. Ltd. She received a master’s degree in Power systems and automation from Kunming University of Science and Technology in 2017, engaged in electric energy, electrical measurement, and thermal engineering professional work. She is a member of the High-precision Electrical Parameter Laboratory, Spark Power Research Studio, Intelligent Perception Innovation Studio, and Key Laboratory of CSG for Electric Power Measurement.

Chuan Luo was born in Sichuan, China, in 1992. He received the B.Eng. degree from the Institute of Automation and Information Engineering, Sichuan University of Science & Engineering, Zigong, China, in 2016. He is currently working toward a Ph.D. degree with the Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, China. He is presently working in the fields of optical fiber sensors and measurement technology.

Wenjiao Xu obtained a bachelor’s degree in system and automation from Kunming University of Science and Technology in 2011. He is currently working in the Kunming Power Supply Bureau of Yunnan Power Grid Co., Ltd., and engaging in substation operation.

Guipeng Zhang received a double bachelor’s degree in engineering and administration from Northeast Power University in China. He is a specialist in the Operation and Equipment Management Department, Yunnan Power Grid Co., Ltd. He focuses on power supply reliability management and distribution automation management, and he has been working in transmission lines management, distribution network management for 12 years.

Biao Tang, the first-level technical assistant expert of Yunnan Power Grid Company, is a senior engineer with a master’s degree. His work unit is the Electric Power Research Institute of Yunnan Power Grid Co., Ltd. His main research fields include thermal instrument measurement, measurement basis, and Internet of things technology application of power equipment.

Ling Wei received a master’s degree in control engineering and control theory from Kunming University of Science and Technology in 2014. As a visiting scholar of China and the United States, she went to the United States for exchange from 2012 to 2013. He works at EPRI of Yunnan Power Grid Co., Ltd, P.R. China as a senior research fellow in metrology. Her research interests include power system automation and energy metering.

Zhengang Zhao was born in Inner Mongolia, China, in 1981. He received the B.Eng., M.Eng., and Ph.D. degrees in electronic science and technology from the University of Harbin Institute of Technology, Harbin, China, in 2005, 2007, and 2012, respectively. He is currently a professor with the Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming, China. His current research interests include micronano detection technology, optical fiber sensors, and measurement technology.

Distributed Generation & Alternative Energy Journal, Vol. 35_3, 173–194.
doi: 10.13052/dgaej2156-3306.3531
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