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The capacitive voltage transformer (CVT) is a special measuring and protecting device, which is commonly applied in high-voltage power systems. Its measurement accuracy is affected seriously by the stray capacitances of the capacitance voltage divider (CVD) to ground and other charged parts. In this study, based on the boundary element method, a mathematical model was established firstly to calculate the stray capacitance. Then, the voltage distribution of the CVD was obtained by the CVD’s equivalent circuit model. Next, the effect of stray capacitance on the voltage distribution and the voltage difference ratio (VDR) of CVD was analysed in detail. We finally designed three types of shield and optimized their structure parameters to reduce VDR. The results indicated that the average deviation rate between calculated and experimental measured voltages is only 0.015%; that is to say, the method has high calculation precision. The stray capacitance of the CVD to ground is far larger than that of the CVD to the high-voltage terminal. It results in the inhomogeneous distribution of voltage and the increase of VDR. For the test CVT, its VDR exceeds the requirement of class 0.2. Among all of the three types of shield, the C type reduced the VDR of the test CVT the most. After optimizing the structure parameters of C-type shield, the VDR is further reduced to 0.08%. It is not only in accord with the requirement of class 0.2 but also has an adequate margin.

The Capacitor Voltage Transformer (CVT) has high dielectric strength, fast transient response, wide dynamic range, low power consumption, and nonferromagnetic resonance with power systems. It also can reduce the head steepness of lightning shock and be used as a coupling capacitor for the power carrier communication [

In recent years, various works have already been carried out for studying the effect of stray capacitance on the electric performance of a high-voltage device. The stray capacitor and the impulse voltage distributions of the HVDC converter valve are calculated by the field-circuit coupling method [

But, up to now, there are few studies about the effect of stray capacitance on the CVT. For the CVT applied in the 750 kV voltage level and above, the stray capacitance of the CVT to the high-voltage terminal increases the VDR of the CVT more than 0.1% [

Although great progress has been made for the research of the CVT, it is still hard to analyse the effect of stray capacitance on the VDR of the CVT accurately and quantitatively due to the complex configuration of the CVT [

The purpose of this paper is to present a new calculation method of stray capacitance and further analyse the effect of stray capacitance on the VDR of the CVT. In this context, a model based on the boundary element method (BEM) is established to calculate the stray capacitance of the capacitance voltage divider (CVD). The voltage distribution of the CVD is obtained by the equivalent circuit model of the CVD. The reliability of the method is confirmed by comparing the calculated voltage with experimental measured results. Then, the effect of stray capacitance on the VDR of the CVT is analysed. Finally, the structure and parameters of the shield are optimized to further reduce the VDR of the CVT. The research results can contribute to design the high-precision CVT more efficiently.

Currently, the most widely applied of CVT in the power system has a column structure as shown in Figure

Column CVT structure. 1- CVD, 2- EMU, 3- high-voltage terminal, 4- metal expander, 5- porcelain insulator, 6- high-voltage capacitor, 7- medium-voltage capacitor, 8- medium-voltage tap, 9- low-voltage terminal, 10- EMU box, 11- secondary terminal box, 12- compensation reactor, 13- damper, and 14- medium-voltage transformer.

The CVD is mainly composed of a high-voltage capacitor, a medium-voltage capacitor, an external metal expander, and a porcelain insulator. Both of the high- and medium-voltage capacitors consist of dozens or hundreds of capacitance units in series. Each capacitance unit is made of aluminum foil and insulating film which are stacked together and immersed in insulating oil [

In general, the total VDR of the CVT depends on the CVD, EMU, the temperature shift, power frequency variation, and proximity effects. Among them, it is believed that the CVD and EMU are the main factors [

Firstly, the CVD is divided into _{i} and _{i},

The abbreviation of equation (_{ij} or _{ji} (

The diagonal element _{ii} is the sum of the stray capacitance of unit _{ig} and the mutual capacitances of unit

The absolute value of the element in the first column of matrix _{i1} (

The main calculation methods of electrostatic field are the finite-element method (FEM) and the BEM. The BEM describes the mathematical and physical problems with boundary integral equations and solves them by the discrete technique of the FEM. It has higher accuracy than the FEM [

Firstly, the electric potentials of unit

Secondly, the lateral surface of all capacitance units were divided into _{k} at the center position _{k} of patch _{k0} and _{kl} are the electric potentials at point _{k} generated by the charges on patch _{0} is the vacuum permittivity, _{k} is the area of patch _{k} and _{k} are the density and quantity of charges on patch _{kl} is the distance between the center positions of patch _{l} is the area of patch _{l} is the density of charges on patch

For all patches, equation (

Then, the electric potential of all patches of unit _{k} can be obtained. Next, substituting _{k} into equation (

By repeating the abovementioned processes, the capacitance coefficient matrix

After obtaining the stray capacitance, the voltage distribution of the CVD was calculated in this part. Each capacitance unit was regarded as a voltage node. The electric potential of the node at the high-voltage terminal was assumed to be _{1}, and the low-voltage terminal was grounded directly. Taking the stray capacitance of units to ground and the high-voltage terminal into account, the equivalent circuit of the CVD was obtained, as shown in Figure _{i} is the capacitance of unit _{ig} is the stray capacitance of unit _{ih} is the stray capacitance of unit _{i1} in

Equivalent circuit of the CVD.

The node voltage equation of the CVD is as follows:

From Figure

Also, the node admittance matrix _{B} can also be derived:_{n} is the self-admittance of unit _{n} = _{n}, _{nh} is the admittance of unit _{nh} = _{nh}. _{ng} is the admittance of unit _{ng} = _{ng}.

Substituting equations (

The previous two sections presented the calculation method for the stray capacitance and the voltage distribution of the CVD. Next, we verify the proposed method by comparing the calculated result with the experimentally measured result.

The experimental schematic diagram of CVT voltage measurement is shown in Figure _{1}, the high-power-frequency input voltage of the CVT, is generated by using a frequency series resonance device, _{i} is the power grid voltage, _{1} is the excitation transformer, _{1}, _{1} is the adjustable reactor. The output voltage of the CVD is measured by using the voltage transformer calibrator.

Schematic diagram of voltage measurement of the CVT.

The test platform of the CVT is shown in Figure _{1} is an adjustable reactor with an adjustable range of 0∼110 H. _{f} is a series resonant capacitance with 1000 pF. The test CVT model is TYD110/0.01H. Its main structure and electrical parameters are as follows: the height of the CVD is 1.15 m, the output voltage of the CVD must be within the range of 15 kV to 25 kV to prevent damage to the insulation of the EMU, thus the adjustable position of the medium-voltage tap from ground is 0.162 m to 0.253 m (default position is 0.24 m), the average radius of the CVD is 0.30 m, the CVD is made up of 50 capacitance units in series (i.e., _{1} = 12574 pF and medium-voltage capacitor _{2} = 48853 pF).

Test platform of the CVT.

When _{1} = 110 kV and the total number of patches of all units

Voltage distribution of the test CVD.

The comparison of calculated voltages, measured voltages, and their maximum deviation rates at four different positions is shown in Table ^{−3} kV. As can be seen from Table ^{−3} kV, respectively. The maximum voltage difference is 0.0034 kV, and the deviation rate of voltage is as low as 0.0015%. For the four selected measurement positions, the maximum deviation rate of voltage is only 0.021%, and the average deviation rate of voltage is as low as 0.015%. Therefore, the method proposed in this paper had high accuracy, and it is suitable for calculating the stray capacitance and the voltage distribution of the CVD.

Comparison of calculated and measured voltages at four different medium-voltage tap positions.

Position ( | Measured voltage (kV) | Calculated voltage (kV) | Maximum deviation rate of voltage (%) |
---|---|---|---|

0.18 | 16.840 ± 1.5 × 10^{−3} | 16.842 | 0.021 |

0.20 | 18.706 ± 1.5 × 10^{−3} | 18.707 | 0.013 |

0.22 | 20.582 ± 1.5 × 10^{−3} | 20.581 | 0.012 |

0.24 | 22.461 ± 1.5 × 10^{−3} | 22.459 | 0.015 |

Figure _{h} decreases slowly from 56 pF to 8 pF. Near the low-voltage terminal, _{h}. But, near the high-voltage terminal, the difference between _{h} is not obvious. This may result in the inhomogeneous distribution of CVD voltage.

Distributions of _{h}.

The voltage drop on each capacitance unit of the test CVD is illustrated in Figure

Voltage drop on each capacitance unit of the test CVD.

As shown in Figure

The expression of VDR is as follows [_{out} is the output voltage of the CVD and _{N} is the ideal partial voltage ratio of the CVD.

_{out} can be changed by adjusting the position of the medium-voltage tap. Within the adjustable range of the medium-voltage tap (0.162 m to 0.253 m from ground), the VDR of the CVD is shown in Figure

VDR of the CVD at different medium-voltage tap positions. The “+” and “−” before the value on the vertical axis represent the positive deviation and the negative deviation, respectively.

As stated above, due to the effect of stray capacitance, the VDR of the test CVD exceeded the requirement of class 0.2 even adjusting the position of the medium-voltage tap. Some studies indicate that the metal shield and grading ring can compensate for the effect of stray capacitance, improve the distribution of electric field, and boost the voltage endurance and insulation strength of the high-voltage apparatus accordingly [

Three types of shield are designed for the test CVT in this study. They are A type (only one shield installed on the high-voltage terminal), B type (only one shield installed on the low-voltage terminal), and C type (two shields installed on both of the high- and low-voltage terminals), as shown in Figure

Three types of shield.

Figure

Effect of the shield type on the voltage drop and VDR of the CVD. (a) Voltage drop. (b) VDR.

To reduce the VDR of the CVD further, the optimization of structure parameters of the C-type shield is performed. Due to the internal insulation requirement and technology limitations of the CVT, the adjustable ranges of

The minimum VDR is the optimization goal. The optimization strategy is to optimize one of the parameters

Effect of shield parameters on VDR. (a)

As can be seen from Figure

According to the analysis mentioned above, the optimization of parameters for the C-type shield improves VDR greatly. The VDR of the CVD was reduced from about 0.2% before optimization to only 0.08% after optimization. Compared with the requirement of class 0.2 (0.2%), it has an adequate margin.

This paper proposed a method based on the boundary element method and the equivalent circuit of the CVD to calculate the stray capacitance and voltage distribution of the CVD. Then the effect of stray capacitance on the VDR of the CVD was studied. At last, the structure and parameters of the shield were optimized to reduce the VDR of the CVT further. The following conclusions can be drawn:

The proposed method has high precision. The average deviation rate between calculated voltage and experimental measured voltage was only 0.015%. It is a useful and reliable tool for the calculation of stray capacitance and the voltage distribution of the CVD.

For the test CVT, although its VDR was reduced from 0.292% to 0.273% by adjusting the position of the medium-voltage tap, it still did not satisfy the requirement of class 0.2.

All of the three types of shield reduced the VDR of the CVD effectively, in particular the C-type shield. After the optimization of structure parameters for the C-type shield, the VDR was reduced from about 0.2% to only 0.08%. The optimization results of shield parameters were

The research work in this paper can be used as a reference for studying the effect of stray capacitance on the performance of the CVD and is helpful to the optimal design of a high-precision CVT. However, the measurement accuracy of the CVT is affected by numerous and complex factors, and only the key factor of stray capacitance was considered in this paper. In future, we will focus on the effects of other factors on the measurement accuracy of the CVT, such as the phase-to-phase interference, the dielectric loss of the capacitor unit, the temperature shift, and the variation of power frequency.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was financially supported by the National Science Foundation of China (No. 51507025) and Fundamental Research Funds for the Central Universities (No. 3132019014).