With the higher voltage level of electric power system in China, the distribution of power frequency electric field in the substation is strengther^[1].About the distribution of power frequency electric field in the substation, there are a lot of research. For on-site measurement study[2-7], the results are not nearest the real results, because of the limitation of measurement guide. For numerical study[8-13], such as by using FEM[10-11] and BEM[12-13], the electrodes are not always considered. Beside the connecting wire, the one earth electrodes which make the electric field distorted, based on this, the present study on the distribution of power frequency electric field in the substation has great limitations and shortcomings. For example, the EHV substation power frequency electric field field measurement, field measurements for the around pillars of the station equipment to be subject to greater limitations. Although based on the finite element method and boundary element method based on literature document[10-13], simulation calculation and analysis for distribution of the power frequency electric field in the substation, does not consider the metal earth electrode of electrical equipment of all kind of switch yards in the substation affect of the distribution of power frequency electrical field.

As for the deeper research on the distribution of power frequency electric field in the substation, the electrode and its affections should be taken into account. Only under these consideration, the power electric field in substation is much more closer to that of the real distribution in the substation. So this kind of study is significant in the study of the distribution of electric field.

Because of the complexity of the switching yard in the EHV substation, the 3D charge simulation method is used for the efficiency computing in the substation[14].

Suppose a linear charge L (as shown in the Fig.1) is in space with the two ends coordinates P1 (x1, y1, z1), P2 (x2, y2, z2), the linear charge simulation parameters are given by

(1)

Where: 0≤u≤L, and

(2)

In order to analyze the current-carrying conductor of various directions in the substation, the global coordinate and local coordinate are used. At first, a charged segments using local coordinate field calculation, then, by using the coordinate transformation, the local coordinates of the results will be integrated into the global coordinates.

In the local coordinates, the linear charge density can be expressed as

(3)

Where: a、b are constants to be determined.

Therefore the potential of the linear charge L at any point in space is deduced as follows

(4)

Where: D is the distance from the source point to the field point, if u = Lt, then

(5)

From Eq. (3)~Eq. (5), we can get[11]

(6)

Where:

In order to save computer storage space and to speed up the computation process. An improved charge simulation algorithm is presented in this paper, which regards the finite length linear charge as constant, the charge density of the two points P1 and P2 are equal

(7)

From Eq. (6)、Eq. (7), we can get

(8)

When using the improved charge simulation method, the equivalent model is divided into a plurality of finite length segments. The potential coefficient of each linear unit with each matching point is calculated, and the known potential are used as boundary conditions. The equation is given as follows

(9)

Where: P is the potential coefficient matrix, τ is the charge simulation column vector, φ is the potential column of the matching point.

Through calculating the charge simulation and division of the conductors, the power frequency electric field intensity of the point P in each directions in space can be derived

(10)

(11)

(12)

According to the superposition theorem, the electric field strength is generated by three-phase conductor segments, and they are added in sequence in X, Y, Z direction. The electric field strength generated by all conductor segments at point P in each direction is expressed as

(13)

Finally, according to the electric field intensity of any point in space in X, Y, Z direction, the total electric field strength E can be calculated

Now taking a 500kV switch yard in the substation as an example for analysis and calculation, the plane configuration of substation is shown in Fig.2. The vertical dashed lines represent position of the set observation lines.

Because of the complexity of the switch yard in the substation. When modeling the distribution of power frequency electric field to calculate its switching field, we make the following simplifying processing: regarding the bus, inlet and outlet lines as linear type wire, potential equal to the wire of voltage, set the ground to be zero potential. The relevant model parameters are set as follow: the height of in-line is 30m, spaced 8m, line height is 26m, spaced 7.5m, 1M, 2M bus modeling height is 16.2m, distance 100m, during normal operation the phase voltage is 303.12kV. The simplified model is shown in Fig.3.

Results and analysis is only considering the overhead line the distribution of power frequency electric field in 500kV switch yard.

Applying the charge simulation method, the aforementioned model information is imported into computer, then the simulation of 3D and color block spatial distribution of power frequency electric field at the height of 1.5m is computed. respectively, as shown in Fig.4 and Fig.5[15].

As can be seen from Fig.5 and Fig.6, the field strength of power frequency electric field mostly at 5~9kV/m, less than 12kV/m in the substation. The value of electric field distortion occurs mostly in the outside under in and out line, and by comparing the electric field strength under the three-phase in and out lines, the electric field values are relatively small under the phase B, this is because of the 120° phase lag are arranged in sequence, the electric field strength produced by the middle phase of B three-phase are superposition and offset. The maximum electric field values are concentrated at the junction of the bus and the in and out lines, this is because of the factors that the height of line, conductor structure, the height of electric field point to be calculated lead to the result. The electric field strength even more than 10kV/m in some part area, so in the design phase of the substation, it should avoid the patrol road located in the lager area of the electric field strength as far as possible.

Wires, isolating switch, circuit breaker, grounding switch and transformers, etc, in the switchyard in the substation are supported by pillars, as shown in Fig.6. These pillars will obviously change the distribution of power frequency electric field. So it is an important way to get close to the actual distribution of power frequency electric field, considering the effects caused by these pillars in switchyard.

Due to complex of electrical equipment, the structure of the model should be simplified when modeled, the influence of all kinds of metal earth electrodes in the switchyard on the surrounding electric field mainly is considered. The parameters are set to: the potential of the grounding body is set to 0, the radius of the earth electrodes is set to 0.13m, the metal earth electrodes of the different electrical equipment with different heights (the hight of post insulator is 5.1m, isolating switch is 5.1m, circuit breaker is 4m, grounding switch is 5.1m and transformer is 3.2m). After considering the metal earth electrode the model of 500kV switchyard is shown in Fig.7.

After the earth electrode is considered in the switchyard, so the distribution of power frequency electric field in the modeling is calculated, the distribution of power frequency electric field at the height of the 1.5m above the ground are shown in Fig.8 and Fig.9.

As can be seen from Fig.8 and Fig.9, the earth electrodes of all kinds of electrical equipment are considered, the power frequency electric field near the earth electrode in the switchyard distort, making the power frequency electric field in the switchyard becomes more and more complex. The maximum electric field value of power frequency is 18.415kV/m in the switchyard which located in the near the earth electrode below the first back incoming line. By comparing Fig.4 and Fig.8, we can get the distribution of the power frequency electric field undergone major change when the earth electrode is considered. The distribution of power frequency electric field is relatively gently (Fig.4 and Fig.5) when the earth electrode is not considered, while considering the earth electrode, the distribution of power frequency electric field of the local peak value appeared more convex (Fig.8 and Fig.9). Obviously, the modeling and the calculation results considered the earth electrode is in good agreement with the actual distribution of power frequency electric field in switch yard.

In order to further study the effect that the earth electrodes of all kinds of electric equipment have an effect on the distribution of power frequency electric field in the switchyard, the electric field of power frequency under the C phase of the first incoming line (the position marked by the vertical dashed lines in Fig.2) were calculated, and the calculation results are shown in Fig.10.

As can be seen from Fig.10, after considering the earth electrode, the electric field of power frequency around the earth electrode is subject to greater impact. The earth electrode of electrical equipment makes power frequency electric field occur larger changes, appearing local larger distortion. This is due to the discontinuity of surface normal direction of electric field supported the conductor and the supported conductor is earthed.

(1) A more concise three dimensional charge simulation method calculated the distribution of the electric field is derived in this paper, we can use the method to calculate the distribution of power frequency electric field in 500kV switch yard. The efficiency of calculation of this method is higher, avoiding to set the complicated boundaries of the finite element, boundary element method and limit the range of calculation. The calculation results meet the requirements of engineering accuracy.

(2) Considering various of grounding metal holders in 500kV switch yard, thus we establish the calculation model of power frequency electric field in switch yard which include the transmission line, bus and the earth electrodes of all kinds of electrical equipment that is in good with the actual model, we use the method derived in this article to calculate and analysis the distribution of power frequency electric field in switch yard. This work provides an effective, rapid means of researching the electric field distortion around the earth electrodes of all kinds of electric equipment and analyzing of power frequency electric field distribution in the actual substation.

(3) By studying the distribution of power frequency electric field in switch yard that is more close to the actual switch yard, we can find the region that the field strength is stronger and make suggestions of environment security for making an inspection tour in station.