Influence of line current limiting reactor on temporary overvoltage of 500 kV transmission line

In order to limit the temporary overvoltage, the method of the series current limiting reactor in the line is often used in the power grid to limit the overvoltage. The parameters of current limiting reactance directly affect the level of 50Hz overvoltage. The installation of a current limiting reactor changes the positive and zero sequence impedance parameters of the line, which has an impact on the temporary overvoltage of the line. Installing a current limiting reactor on the 500 kV Line’s overvoltage is studied by using electromagnetic transient calculation software EMTP. The simulation results show that the temporary overvoltage of the 500 kV Line can be reduced by adding a current limiting reactor.


Introduction
As the development and expansion of the power grid, the electrical connection is becoming closer and closer.The 500 kV power stations in Jiangsu are densely distributed, Short-current level of the main hub 500 kV substation is continuously improving.The 500kV bus's short-current is near to or exceeds the circuit break's capacity, so it is urgent to limit the short current level [1].Adding series reactance to relevant 500 kV lines can effectively reduce short-circuit current [2] and affect power flow distribution [3].
The installation of a line current limiting reactor can prolong the electrical distance between stations without changing the power grid's structure.However, after the installation of the line current limiting reactor, the positive sequence and the system's zero sequence will change, which will have a certain impact on the temporary overvoltage level of the system.[4] analyzes the overvoltage of a 500 kV Line after installing series reactance, without detailed calculation and analysis of asymmetric short overvoltage or load rejection overvoltage; [5] studies the influence of limiting reactor on temporary overvoltage of transmission line, and studies the capacitance effect of the no-load long line and the voltage rise caused by asymmetric short circuit respectively.However, due to the long research line itself and the installation of the shunt reactor, the calculated results of the combined action of temporary overvoltage current limiting reactor and shunt reactor, it does not quantitatively explain the relationship between temporary overvoltage and shunt reactor.
Taking a 500 kV transmission line as an example, the paper ressearches the effect of line current limiting reactor on temporary overvoltage by using electromagnetic transient calculation software EMTP.

Power Frequency Voltage Rise
Power frequency voltage rise is usually result from the line capacitance effect, asymmetric short circuit and load rejection [6].

No-load long line's Capacitance effect
When the transmission line is in no-load for a short time due to normal operation or fault operation of the system, the voltage rises of the line capacitance (ground capacitance) current on the conductor inductance and the system power supply makes the line voltage higher than the power supply voltage.
After omitting the line resistance and ground conductance, the line is represented by an equivalent T-type circuit, and the equivalent circuit is shown in Figure 1, the E is power potential, and its value is obtained from the normal operation state; X C is positive sequence equivalent capacitance reactance; X is equivalent circuit reactance of reactor L; u is the no-load line's terminal voltage .

Voltage rise after asymmetric short
Asymmetric short is the highest fault in the transmission line, in which the probability of a single phase earthing is highest, and the voltage boost of non-fault phase is also the most serious.After single-phase earthing, the three-phase fault voltage and current are asymmetric.The symmetrical component method is adopted and analyzed through the composite sequence network.We set phase a fault earthing and ignore the resistance of components in the system, and the negative reactance seen from the fault point is equal to the positive sequence reactance [7].Then the calculation of voltage boost of non-fault as Formulas ( 1) and ( 2).
where the E is the equivalent potential.U B and U C are the voltages of non-fault phases B and C after phase A one phase earthing.K W is earthing coefficient; X 0 and X 1 are the network sequence reactance's seen from the fault point.
It can be seen from Formulas (1) and ( 2) that in the case of the single-phase earthing fault, the rise of non-fault phase voltage is closely related to the system zero and positive sequence reactance's ratio.

Temporary overvoltage caused by load rejection
When the line transmits power, the potential of the generator at the sending end is higher than that of the high-voltage bus.After load rejection, the speed regulation effect can't be achieved rejection because the flux linkage of the generator cannot change suddenly, resulting in the increase of generator speed, resulting in the increase of potential, power frequency.However, in the short time of temporary overvoltage, the acceleration of the generator is not obvious, and the factor of potential rise caused by generator acceleration can often be ignored [8].

System Parameters and Simulation Model
In this paper, the total length of a 500 kV two circuit line on one tower is 49 km.The line model is built by EMTP software to calculate the specific parameters of the line; The power grid is equivalent to the system impedance; The limiting reactor is equivalent to inductance in the system, and the calculation model is simulated by the R-L-C circuit.

Model of the line
Assuming the line transmission parameters are as Figure 2 and Figure 3.

Temporary overvoltage Simulation
The limiting reactor shall be installed at the line' back.The calculation method in this paper selects one circuit suspended, and one circuit with no-load or earthing fault.

No load line capacitance effect temporary overvoltage
We compare and study the temporary overvoltage level caused by the line capacitance effect before and after the system is connected to the current limiting reactor, and simulate the voltage waveform when the capacitance effect at the end of the line under normal operation of 500 kV transmission, as shown in Figure 4.It is known from Figure 4 that the max-voltage at the no-load line's back due to the capacitance effect during the 500 kV transmission line without a current limiting reactor can reach 754.39 kV, which is 1.85 times higher than the rated voltage.When the current limiting reactor is increased by 0.15 Ω, the maximum overvoltage at the end of the no-load line can reach 735.26 kV, which is 1.76 times higher than the rated voltage.It can be seen that the temporary overvoltage of the line can be limited by connecting the current limiting reactor, and the size of the connected current limiting reactor determines the current limiting effect.  1 that the voltage rise at the end of the transmission line is obvious due to the capacitive effect.In particular, the maximum voltage rise during the closing process can reach 296.63 kV.Connecting the current limiting reactor can reduce the voltage rise at the end of the line, but the larger value of the connected current limiting reactor has no inhibitory effect.Therefore, it is necessary to calculate the specific value of the current limiting reactor to be connected according to the specific situation.

Power Flow on Induced Current and Voltage of single-phase short
We compare and study the temporary overvoltage level caused by a phase earthing fault before and after the system is connected to the current limiting reactor, and simulate the temporary overvoltage waveform at the end of the line under a single-phase earthing fault of the 500 kV transmission line, as shown in Figure 5.
From Figure 5 we know that the max-voltage the 500 kV transmission line due to single-phase earthing can reach 540.89 kV without a current limiting reactor, which is 1.325 times higher than the rated voltage.When the current limiting reactor is increased by 14 Ω, the maximum overvoltage of the no-load line can reach 513.81 kV, which is 1.26 times higher than the rated voltage, it can be seen that the temporary overvoltage of the line can be limited by connecting the limiting reactor, and the size of the connected limiting reactor determines the current limiting effect.oscillation of overvoltage will increase the overvoltage level to a certain extent.Therefore, in the case of a single-phase earthing fault, the specific value of the smaller current limiting reactor needs to be calculated and selected according to the specific situation.

Power Flow on Induced Current and Voltage of three-phase short
We compare and study the temporary overvoltage level caused by a three-phase short circuit of the line before and after the system is connected to the current limiting reactor, and simulate the overvoltage waveform caused by the capacitance effect at the end of the line under the three-phase short circuit of 500 kV transmission line, as shown in Figure 6 below.From Figure 7 we know that the max-current of a 500 kV line due to the three-phase short circuit can reach 43.16 kA without a current limiting reactor.When a 14 Ω current limiting reactor is added, the maximum overcurrent of the line can reach 39.82 kV.It can be seen that the current limiting reactor can well limit the short-circuit current of the line, and the size of the current limiting reactor determines the current limiting effect.3 we know thatthe reactor value's increase has a great impact on closing overcurrent.When the current limiting reactor reaches 150 Ω, the line overcurrent is only 4.53 kA, which is 43.16 kA higher than the maximum overcurrent without a current limiting reactor, which is 9.53 times higher than the former, and the limit effect is obvious.

Conclusions
In this paper, EMTP software is used to build a 500 kV Line's model to study the impact on temporary overvoltage before and after connecting the current limiting reactor.The following conclusions can be obtained: (1) Capacitance effect on the no-load line will cause the 50Hz voltage rise of the line, and the power grid voltage level at the power flow sending end is higher than that at the receiving end.It is equivalent to increasing the internal impedance of the power supply, and the temporary overvoltage rise is higher.It is recommended to install the current limiting reactor at the receiving end.And the reactance value should be smaller.
(2) The temporary overvoltage of single-phase earthing fault and non-fault phase is closely related to the system zero and positive sequence reactance ratio (x 0 /x 1 ), and the installation of current limiting reactor has an impact on the value of x 0 /x 1 .Installing current limiting reactor will increase the temporary overvoltage.
(3) For the current limiting reactor connected under a single-phase earthing fault, in order to avoid the increase of overvoltage caused by oscillation, the reactor with a larger value should be selected.
(4) In the case of 3-phase short circuit of a transmission line, the overvoltage is small but the overcurrent is large.Connecting the current limiting reactor can well limit the overcurrent, and the greater the reactor value is, the more obvious the limiting effect is.

Fig. 2
Fig. 2 Transmission line tower layout drawing Fig. 3 Line temporary overvoltage simulation model

Fig. 4
Fig. 4 Waveform of temporary overvoltage before and after connected to the current limiting reactor (a) Infinite current reactor (b) Connected to current limiting reactor Fig. 5 One phase earthing temporary overvoltage waveform before and after connected to current limiting reactor From Table 2 we know that the temporary overvoltage when single-phase earthing at the end of the transmission line is obvious, and the maximum overvoltage at the end of the line can reach 540.89 kV.Connecting the current limiting reactor can reduce the voltage rise at the end of the line, but the smaller the value of the connected current limiting reactor, it has no inhibitory effect, and the local NESP-2023 Journal of Physics: Conference Series 2592 (2023) 012062

Fig. 6
Fig. 6 Temporary overvoltage waveform caused by a three-phase short circuit of the line