# Study on Fault Characteristics of Layer Short Circuit of Dry-Type Air-Core Series Reactor

Authors: Yang Guo; Richang Xian; Xuebing Leng; Yan Hao; Zhi Li
Journal: Mobile Information Systems
 (2022)

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## Abstract

Aiming at the layer short circuit fault of dry-type air-core series reactor winding, in order to reveal the characteristics of electrical parameters when the fault occurs and improve the accuracy of online detection, this paper uses ANSYS Maxwell software to study the changes of electrical parameters when the layer short circuit fault occurs in dry-type air-core series reactor. The changes of equivalent resistance, equivalent reactance, and power factor are simulated and analyzed when the layer short circuit fault occurs in normal operation and different positions of winding. The simulation results show that with the different locations of layer short circuit fault points, the variation laws of electrical parameters of reactors are also different, in which the variation amplitude of power factor is obvious and the variation trend is consistent, which can provide important theoretical support for the online detection and protection of layer short circuit fault of dry-type air-core series reactors.


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## Body

## 1. Introduction

The dry-type air-core series reactor is an indispensable type of power equipment in power system, which has the functions of filtering harmonics and limiting short circuit current, and is generally used for reactive power compensation [1, 2]. In recent years, with the rapid development of the power grid, dry-type air-core reactors have been more and more widely used in power system due to their advantages of good linearity, strong antisaturation ability, simple structure, high-cost performance, and less operation and maintenance workload [3]. Layer short circuit fault is a fault form that is easy to occur in dry-type air-core reactor when it is used for a long time. If it cannot be effectively detected, it is easy to cause reactor damage and cause great harm [4, 5]. In view of the above situation, it is particularly important to study the changes of electrical parameters in the Layer short circuit fault of dry-type air-core reactor and improve the fault monitoring sensitivity and protection ability of reactor [6].At present, the research on online monitoring methods for reactor insulation faults mainly includes the following methods: temperature monitoring method, equivalent impedance method, magnetic field monitoring method, and zero-sequence amplitude comparison method. Huo et al. scholars have studied the application of temperature monitoring method in the fault detection of dry reactor [7, 8], but the current technology can only measure the average temperature rise of the reactor, and the local temperature rise monitoring is still limited. [8]. Zhuang verified the feasibility of inter-turn short circuit detection method of reactor based on impedance variation through experiments, but it cannot accurately evaluate the detection of small turn short circuit fault. Zheng proposed the application scheme of the magnetic field monitoring method in the early development period of reactor inter-turn [9]. However, in the actual power grid operation, the measurement results of this method are vulnerable to the interference of complex electromagnetic fields in the field, and the accurate value of flux change cannot be obtained. Chen et al. put forward the zero-sequence amplitude comparison monitoring method of inter-turn protection scheme [10], the scheme is mainly aimed at the problem of small turn number inter-turn protection of high voltage reactor and cannot be used more widely.In the past, the research on reactor fault monitoring and protection mainly focused on inter-turn short circuit fault, while the research on layer short circuit fault characteristics of dry-type air-core series reactor was rarely reported. In this paper, the research focuses on the layer short circuit of the reactor that has received less attention in the past. The equivalent circuit model and voltage equation of the normal and layer short circuit faults are established to carry out the theoretical analysis of the basic fault of the reactor. The ANSYS Maxwell software is used to simulate and study the variation law of the electrical parameters of the dry-type air-core reactor (including the equivalent resistance, equivalent impedance, and power factor) when the layer short circuit fault occurs at different positions, and to reveal the variation law of the electrical parameters when the layer short circuit fault occurs, so as to provide a scheme for the further monitoring and protection of the reactor.


## 2. Methodology

Dry-type air-core reactor is essentially composed of multilayer coaxial coils in parallel. At 50 Hz, the equivalent capacitance of its equivalent circuit can be ignored, so the reactor can be equivalently represented by multiple resistors and inductors in series [11]. Assuming that the reactor has n layers of coil, the equivalent circuit model of the reactor under normal insulation can be drawn by analyzing the structural characteristics of the reactor, as shown in Figure 1. In Figure 1, Ri is the equivalent resistance of the layer i coil, Li is the inductance of the layer i coil, Mi represents the mutual inductance of other layer coils to the layer i coil, Ii is the current component of each branch, and IL is the current flowing through the dry-type air-core reactor. According to the established equivalent circuit model, voltage equation can be obtained:(1)R1+jωL1⋮jωMi,1⋮jωMn,1⋯⋮⋯⋮⋯jωM1,i⋮Ri+jωLi⋮jωMn,i⋯⋮⋯⋮⋯jωM1,n⋮jωMi,n⋮Rn+jωLnI1⋮Ii⋮In=UUUUU.In the above equation, Mi,j is the mutual inductance between the coil of i layer and the j layer and U is the external voltage of the reactor. According to the equivalent circuit model of reactor, IL=I1+I2+…+Ii+…+In can be obtained.Figure 1
Equivalent circuit of reactor at normal operating conditions.When the layer circuit fault occurs in the dry-type air-core reactor, it is assumed that the layer short circuit fault occurs between the encapsulation of layerm and layer m+1. At this time, the equivalent resistance and equivalent inductance of the fault layer are divided into two parts, and the equivalent circuit structure changes. The equivalent circuit model of the layer short circuit fault of the reactor can be drawn through analysis, as shown in Figure 2. In the figure, Rk and Rk+1 are the two equivalent resistances divided after the layer short circuit of the equivalent resistance Rm of the original layer m encapsulation and Rk+2 and Rk+3 are the two equivalent resistances divided after the layer short circuit of the equivalent resistance Rn of the original layer n encapsulation. Lk and Lk+1 are the two equivalent inductances divided by the equivalent inductance Lm of the original layer m encapsulation after interlaminar short circuit, Lk+2 and Lk+3 are the two equivalent inductances divided by the equivalent inductance Ln of the original layer m+1 encapsulation after interlaminar short circuit and Ik, Ik+1, Ik+2 and Ik+2 represent the current flowing through each equivalent resistance, respectively.Figure 2
Equivalent circuit of reactor at layer short circuit conditions.According to the equivalent circuit model of layer short circuit fault, the following equation voltage equation can be obtained:(2)R1+jωL1⋮jωMk,1jωMk+1,1jωMk+2,1jωMk+3,1⋮jωMn,1⋯⋯⋯⋯⋯⋯jωM1,k⋮Rk+jωLkjωMk+1,kjωMk+2,kjωMk+3,k⋮jωMn,k⋯⋮⋯⋯⋯⋯⋮⋯jωM1,k+3⋮jωMk,k+3jωMk+1,1+3jωMk+2,k+3Rk+3+jωLk+3⋮jωMn,k+3⋯⋯⋯⋯⋯⋯jωM1,n⋮jωMk,njωMk+1,njωMk+2,njωMk+3,n⋮Rn+jωLnI1⋮IkIk+1Ik+2Ik+3⋮In=U⋮U1U2U1U2⋮U.In the above equation, U1 and U2 are the upper voltage and the lower voltage of the short circuit layer, respectively. The following equation can be obtained by analyzing the fault equivalent circuit model:(3)Rm=Rk+Rk+1Rn=Rk+2+Rk+3Lm=Lk+Lk+1Lm=Lk+2+Lk+3IL=I1+I2+⋯+Ik+Ik+2+⋯+In=I1+I2+⋯+Ik+Ik+2+⋯+InU=U1+U2.Due to the layer short circuit fault of the reactor, the two equivalent resistances and equivalent inductances of the adjacent two layers of coils are short circuit ed into four equivalent resistances and equivalent inductances. The change of circuit structure makes the current in the coil also change. Therefore, the mutual inductance will be generated between the coils of the normal layer, between the new equivalent inductances generated by the normal layer and the short circuit layer, and between the new equivalent inductances generated by the short circuit layer [12, 13].The total currentI of the main circuit of the reactor can be obtained by adding the current of each branch obtained from the solution, and the calculation formula is shown in the following equation:(4)I=∑i=1nIi.In the above formula, n is the number of coil layers of the reactor; Ii is the current of each branch of the reactor.The equivalent impedance calculation formula of reactor is shown in the following equation:(5)Z=R+jωX=UI.In the following formula, U is the external voltage, I is the total current of the main circuit of the reactor, R is the equivalent resistance of the reactor, ω is the angular frequency, andL is the equivalent inductance of the reactor.The loss factortanδ can be obtained by comparing the equivalent resistance R of the above reactor with the equivalent reactance ωL, and the calculation formula of reactor power factor cosφ is shown in the following equation:(6)cosφ=cosπ2−arctanδ=cosπ2−arcRωX.


## 3. Experimental Details and Results

In order to study the influence of electrical parameters on layer short circuit fault of dry-type air-core reactor winding, this paper uses ANSYS Maxwell electromagnetic simulation software transient field (Transient) to model, simulates the dry-type air-core reactor, and explores the changes of equivalent resistance, equivalent impedance, and power factor under the condition of normal operation and layer short circuit fault between different adjacent envelopes at different positions. The modeling and simulation object is a dry air-core reactor of CKGKL-50/10–5%, and its specific technical parameters are shown in Table1.Table 1
Rated parameters of reactor.
ParameterParameter valueRated voltage/kV10Rated current/A157.5Rated capacity/kvar50Frequency/Hz50Diameter inside coil/mm545Diameter outside coil/mm843.1Height of coil/mm450Number of phases1Number of envelopment4Number of branches encapsulated 15Number of branches encapsulated 24Number of branches encapsulated 34Number of branches encapsulated 45


### 3.1. Establishment of Two-Dimensional Finite Element Model

According to the rated parameters and structural parameters of the above reactor, since dry-type air-core reactor has axisymmetric characteristics in actual structure, the cylindrical coordinate system (Cylindrical about Z) in the 2D module is selected. According to the actual situation of the reactor and the equivalent circuit model, the two-dimensional axisymmetric model of the dry-type air-core reactor is established, as shown in Figure3. The coils of each layer of the reactor are represented by a rectangular section, and the short circuit part is plotted at the corresponding position of the adjacent two layers of coils with layer short circuit. The coils in the upper part of the short circuit part and the coils in the lower part of the short circuit part are represented by a rectangular surface.Figure 3
Finite element model of reactor.


### 3.2. Boundary Conditions and Excitation Settings

For the simulation analysis of dry-type air-core series reactor in this paper, unbounded domain is adopted, which is realized by adding boundary condition ballon to region.After setting the number of turns and coil ports, the excitation loading is set by using the external circuit function.


### 3.3. Establishment of External Circuit Model

According to the above analysis of the circuit structure of the reactor under normal operation and layer short circuit, the circuit model of the reactor is established by using the Circuit Editor. According to the simulation requirements, a total of 24 layer short circuit fault circuit models are created according to the different short -circuit positions. Taking the layer short circuit fault at the axial height of 7H/8 between layers 1 and 2 as an example, the layer short circuit model is plotted in the external circuit editor, as shown in Figure4.Figure 4
Simulation circuit model of reactor layer short circuit fault.In the circuit shown in Figure4, the first and second layers are adjacent two layers of coils with layer short circuit fault. Among them, LWinding1 and LWinding1_DLand LWinding2 and LWinding2_DL represent the two groups of new coils that are divided into the first and second layers after layer short circuit fault. R20 and R62and R23 and R68 are the two groups of new resistors that are divided into the first and second layers after layer short circuit fault. The sum of the two groups of new resistors is equal to the original resistance value.


### 3.4. Layer Short Circuit Fault Setting of Reactor

In this paper, the fault layer group is set up between layer 1 and layer 2, between layer 4 and layer 5, between layer 7 and layer 8, between layer 10 and layer 11, between layer 14 and layer 15, and between 17 layer and layer 18. At the same time, the layer short circuit fault is set at the axial height of the coil H/2, 5H/8, 3H/4, and 7H/8, and is recorded from the middle to the end as 1, 2, 3, and 4. Taking the layer short circuit fault at the axial height of 7H/8 between layer 1 and layer 2 as an example, the fault location is set as shown in Figure5, and the ANSYS simulation cloud image is shown in Figure 6.Figure 5
Reactor fault setting.Figure 6
Reactor simulation cloud map.


### 3.5. Analysis of Simulation Results

When layer short circuit fault occurs at different locations in dry-type air-core series reactor, the change rate and change of equivalent electrical parameters relative to normal state, as shown in Figures7–9.Figure 7
Equivalent resistance change rate.Figure 8
Equivalent impedance change rate.Figure 9
Power factor change rate.When interlayer short-circuit fault occurs in a dry-type air-core series reactor, according to the simulation results, it can be seen that the change rates and changes of equivalent resistance, equivalent impedance, and power factor are different. This section further expounds the detailed changes of various electrical parameters and explains the reasons. The change rates and trends of the equivalent resistance, equivalent impedance, and power factor are different, and the specific changes are as follows:(1)
In the direction of axial height from the middle to both ends, the change rate of equivalent impedance decreases gradually when layer short circuit fault occurs, and when layer short circuit fault occurs between the same two layers, the change rate of equivalent impedance at the end position is the smallest, ranging from 0.2% to 1.4%.The reason for the gradual decrease in the change rate of equivalent impedance is mainly that the system voltage of the reactor does not change before and after the layer short circuit fault. As the fault occurs in the axial position from the middle to both ends, the change rate of the total current of the circuit is smaller and smaller after the short circuit, so the change rate of equivalent impedance is also smaller.(2)
In the direction of axial height from middle to both ends, the change rate of equivalent resistance and power factor increase gradually when layer short circuit fault occurs, and the change rate of end position is the largest when layer short circuit fault occurs between the same two layers. The equivalent resistance change rate ranges from −90% to 2%, and the power factor change rate ranges from −97% to 28%.(3)
In the radial position from the inner to the outer direction, the absolute values of equivalent impedance, equivalent resistance, and power factor change rate show a gradually increasing trend when the layer short circuit fault occurs in the reactor. The main reason is that with the change of the fault position from the inner layer to the outer layer, the coupling degree of the fault coil and other coils is getting higher and higher.


## 3.1. Establishment of Two-Dimensional Finite Element Model

According to the rated parameters and structural parameters of the above reactor, since dry-type air-core reactor has axisymmetric characteristics in actual structure, the cylindrical coordinate system (Cylindrical about Z) in the 2D module is selected. According to the actual situation of the reactor and the equivalent circuit model, the two-dimensional axisymmetric model of the dry-type air-core reactor is established, as shown in Figure3. The coils of each layer of the reactor are represented by a rectangular section, and the short circuit part is plotted at the corresponding position of the adjacent two layers of coils with layer short circuit. The coils in the upper part of the short circuit part and the coils in the lower part of the short circuit part are represented by a rectangular surface.Figure 3
Finite element model of reactor.


## 3.2. Boundary Conditions and Excitation Settings

For the simulation analysis of dry-type air-core series reactor in this paper, unbounded domain is adopted, which is realized by adding boundary condition ballon to region.After setting the number of turns and coil ports, the excitation loading is set by using the external circuit function.


## 3.3. Establishment of External Circuit Model

According to the above analysis of the circuit structure of the reactor under normal operation and layer short circuit, the circuit model of the reactor is established by using the Circuit Editor. According to the simulation requirements, a total of 24 layer short circuit fault circuit models are created according to the different short -circuit positions. Taking the layer short circuit fault at the axial height of 7H/8 between layers 1 and 2 as an example, the layer short circuit model is plotted in the external circuit editor, as shown in Figure4.Figure 4
Simulation circuit model of reactor layer short circuit fault.In the circuit shown in Figure4, the first and second layers are adjacent two layers of coils with layer short circuit fault. Among them, LWinding1 and LWinding1_DLand LWinding2 and LWinding2_DL represent the two groups of new coils that are divided into the first and second layers after layer short circuit fault. R20 and R62and R23 and R68 are the two groups of new resistors that are divided into the first and second layers after layer short circuit fault. The sum of the two groups of new resistors is equal to the original resistance value.


## 3.4. Layer Short Circuit Fault Setting of Reactor

In this paper, the fault layer group is set up between layer 1 and layer 2, between layer 4 and layer 5, between layer 7 and layer 8, between layer 10 and layer 11, between layer 14 and layer 15, and between 17 layer and layer 18. At the same time, the layer short circuit fault is set at the axial height of the coil H/2, 5H/8, 3H/4, and 7H/8, and is recorded from the middle to the end as 1, 2, 3, and 4. Taking the layer short circuit fault at the axial height of 7H/8 between layer 1 and layer 2 as an example, the fault location is set as shown in Figure5, and the ANSYS simulation cloud image is shown in Figure 6.Figure 5
Reactor fault setting.Figure 6
Reactor simulation cloud map.


## 3.5. Analysis of Simulation Results

When layer short circuit fault occurs at different locations in dry-type air-core series reactor, the change rate and change of equivalent electrical parameters relative to normal state, as shown in Figures7–9.Figure 7
Equivalent resistance change rate.Figure 8
Equivalent impedance change rate.Figure 9
Power factor change rate.When interlayer short-circuit fault occurs in a dry-type air-core series reactor, according to the simulation results, it can be seen that the change rates and changes of equivalent resistance, equivalent impedance, and power factor are different. This section further expounds the detailed changes of various electrical parameters and explains the reasons. The change rates and trends of the equivalent resistance, equivalent impedance, and power factor are different, and the specific changes are as follows:(1)
In the direction of axial height from the middle to both ends, the change rate of equivalent impedance decreases gradually when layer short circuit fault occurs, and when layer short circuit fault occurs between the same two layers, the change rate of equivalent impedance at the end position is the smallest, ranging from 0.2% to 1.4%.The reason for the gradual decrease in the change rate of equivalent impedance is mainly that the system voltage of the reactor does not change before and after the layer short circuit fault. As the fault occurs in the axial position from the middle to both ends, the change rate of the total current of the circuit is smaller and smaller after the short circuit, so the change rate of equivalent impedance is also smaller.(2)
In the direction of axial height from middle to both ends, the change rate of equivalent resistance and power factor increase gradually when layer short circuit fault occurs, and the change rate of end position is the largest when layer short circuit fault occurs between the same two layers. The equivalent resistance change rate ranges from −90% to 2%, and the power factor change rate ranges from −97% to 28%.(3)
In the radial position from the inner to the outer direction, the absolute values of equivalent impedance, equivalent resistance, and power factor change rate show a gradually increasing trend when the layer short circuit fault occurs in the reactor. The main reason is that with the change of the fault position from the inner layer to the outer layer, the coupling degree of the fault coil and other coils is getting higher and higher.


## 4. Conclusion

In this paper, the equivalent circuit model and voltage and current equation of dry-type air-core reactor under normal operation and layer short circuit fault are studied and discussed. ANSYS Maxwell is used to simulate and analyze the changes of electrical parameters of dry-type air-core reactor under layer short circuit fault in different axial and radial positions. The conclusions are as follows:(1)
The change rates of power factor, equivalent resistance, and equivalent inductance are all related to the different fault locations of the layer short circuit of dry-type air-core series reactors. With the fault location moving from the middle to the end in the same axial direction, the change rates of equivalent resistance and power factor have an increasing trend, while the change rate of equivalent impedance has a decreasing trend.(2)
In the same radial direction, as the fault location moves from the inside to the outside, the absolute values of equivalent resistance, equivalent impedance, and power factor change rate all show an increasing trend.(3)
In summary, when the dry-type air-core series reactor occurs layer short circuit fault at the end of the outermost layer, the overall change rate of its electrical parameters is the largest, and the harm to the reactor is also the largest. Therefore, the further protection of the reactor can be realized by enhancing the heat dissipation capacity at the upper and lower ends of the outer layer of the reactor, timely inspection, and improving the production process. In addition, among the above parameters of the reactor, the power factor is the most sensitive response to the layer short circuit fault of the reactor and has a closer relationship with the short circuit position. Therefore, the power factor of the reactor can be calculated by collecting the calculated voltage and current signals, and the power factor can be used as a monitoring parameter for more accurate and timely online monitoring and protection of the reactor.According to the research results of layer short circuit fault of reactor in this paper, more theoretical support can be provided for the fault monitoring research of dry-type air-core reactor, and it can be improved to make the fault coating coverage of reactor fault monitoring and protection in the future wider rather than just for inter-turn short circuit fault, with higher accuracy, and enhance the economy, security, and reliability of power grid operation.



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*Source: 5429807-2022-06-30.xml*