In this paper, the composite insulator for UHV transmission line is studied. A two-dimensional model is established in ANSYS to calculate the electric field. The boundary element type in the air domain is defined as the infinite boundary. Therefore, the bounded domain is transformed into open domain and the electric field distribution of insulators is solved. In ANSYS simulation, the insulator electric field calculation model consists of insulators, air, fiber reinforce plastic (FRP) rod and metal fittings. The relative dielectric constant and resistivity are shown in Table 1.
Table 1
The relative dielectric constant and resistivity
Physical medium
|
Insulators
|
Air
|
FRP rod
|
Metal fittings
|
Relative permittivity
|
3.0
|
1.02
|
5
|
1010
|
Resistivity /(Ω·m)
|
1013
|
1050
|
1015
|
8.7×10− 8
|
The length of the insulator string is far less than the AC wavelength under power frequency. The electric field is approximately stable at any time, so that the electrostatic field finite element method can be used to simulate and analyze the electric field distribution of insulators. The two-dimensional electrostatic field boundary can be expressed as Eq. (1).
$$\left\{ \begin{gathered} {\nabla ^2}\varphi {\text{=}} - \frac{\rho }{\varepsilon } \hfill \\ \varphi {\text{=}}{U_0}(x,y) \hfill \\ \frac{{\partial \varphi }}{{\partial n}}=0 \hfill \\ ({\varepsilon _1}\frac{{\partial \varphi }}{{\partial n}}) - ({\varepsilon _2}\frac{{\partial \varphi }}{{\partial n}})=\sigma \hfill \\ x,y \in G \hfill \\ \end{gathered} \right.$$
1
Where, φ is the scalar potential function of the electrostatic field; ρ is the Charge density; ε is dielectric constant of materials; U0 is the known potentials on the boundary; n is unit normal vectors at interfaces of different materials; σ is charge surface density; G is Pending field; Γ1 is Upper potential of insulator end fittings; Γ2 is sectional boundary of two-dimensional model; Γin is interface boundaries of different materials; x, y are two-dimensional model coordinates.
Equation (1) is transformed to Eq. (2).
$$\left\{ \begin{gathered} I(\varphi )=\iint\limits_{G} {(\frac{\varepsilon }{2}{{(\frac{{\partial \varphi }}{{\partial x}})}^2}+{{(\frac{{\partial \varphi }}{{\partial y}})}^2} - \rho \varphi }){\text{d}}x{\text{d}}y \hfill \\ {\left. \varphi \right|_{\Gamma 1}}={U_0}(x,y) \hfill \\ \end{gathered} \right.$$
2
By adopting interpolation in discretization, the variational problem is transformed into the extremum problem of multivariate function correlation. Therefore, Eq. (3) is obtained as:
$$K\varphi {\text{=}}P$$
3
Where, K is the N order matrix after the boundary condition is applied; φ is the N order potential vector; P is the N order load column vectors.
The potential values on the nodes of the finite field are solved by Eq. (3). Based on the results, the electric field intensity of the insulator is shown in Eq. (4).
$$E{\text{=-}}\nabla \varphi$$
4
Where, E is the electric field intensity value.
Figure 1 shows the electric field intensity distribution of UHV composite insulator string under the condition of good electrical performance, which means no zero insulators exist.
As shown in Fig. 1, the electric field distribution around the insulator string is non-uniform, which conforms to [18]. Because the electric field near the insulator wire and corona ring is relatively concentrated, the electric field intensity is as high as 380.48 V/mm. In comparison, the electric field value of insulator string in the middle is relatively low, about 11.544 V/mm. Moreover, the electric field intensity of insulators near the cross arm rises slightly, reflecting in Fig. 1 that the diagram slightly upwards at the rear. When the local electric field is too high, the electrical performance of the insulator tends to decrease, leading to local degradation.
Therefore, according to electric field distribution characteristics under normal working conditions, the 6th and 20th insulators starting from the high-voltage side are taken potentials to couple with freedom degrees. The zero insulators in the actual situation are analyzed to explore the influence of zero insulators on the overall electrical performance. The results are shown in Fig. 2.
Figure 2 shows that when zero insulators exist in the insulator string, the electric field intensity of zero insulators decreases sharply. While the electric field intensity of the insulator on both sides increases. It can be concluded that the farther away from the zero insulators, the smaller the influence.