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Overhead line fault with mutual induction

Model description

This example considers two independent 220 kV power systems with de-grounded neutral consisting of double-circuit overhead lines (overhead lines) with two-way supply from substations A and B. In the first power system, the overhead lines are modelled by Double-Circuit Transmission Line, which is a U-shaped substitution diagram taking into account the mutual induction between the circuits. In the second power system, the overhead line is modelled by Three-Phase PI Section Line, which is a conventional U-shaped substitution diagram.

Mutual induction between overhead line circuits can significantly affect the results of some asymmetrical calculations. For example, when calculating the settings of the first stage of the zero sequence current directional protection (ZSCP). One of the conditions of adjustment against tripled zero sequence current (NSC), passing in the place of protection installation, are [1]:

  1. in case of a ground fault on the busbars of the opposite substation;
  2. in case of an earth fault on the busbars of the opposite substation, if the parallel circuit is disconnected and earthed at both ends and the mutual induction between the lines cannot be neglected.

Further the above mentioned scenarios will be shown, the process of running and setting up the model from the script development environment using command control, processing of simulation results, visualisation of simulation results and suggested scenarios for independent work with the model. Logging of current values is performed and their time plots are shown. Setting up the model for each of the scenarios is carried out by changing the positions of switches in the "Switching Experiments" subsystems. Model appearance:

mutual_inductance_line_1730214998115.png

Power systems are modelled by the Voltage Source (Three-Phase) block, steady state is set by specifying the effective line voltage and phase shift. The forward and zero-sequence resistances of the power systems are modelled by the Coupled Lines (Three-Phase) block. Short circuit is modelled by the block Fault (Three-Phase), in the settings of this block using the drop-down menu Failure mode it is possible to select the type of short circuit. The system parameters are set according to Appendix B1 "Functional test programme for 110-220 kV short-circuit protection and 110-220 kV LVDC" [2]:

Element Parameter
System A Equivalent EMF $E_{А} = 239\angle0° кВ$
System B Equivalent EMF $E_{Б} = 239.24\angle10.5° кВ$
Line A-B $L = 70км$
$R_1+jX_1=0.0788 + j 0.4155 Ом/км$
$R_0+jX_0=0.3356 + j1.151 Ом/км$
$R_M+jX_M=0.15 + j0.684 Ом/км$

Experience with earth fault on the busbars of the opposite substation

Import the necessary modules for working with graphs:

In [ ]: 
using Plots
gr();

Loading the model:

In [ ]: 
model_name = "mutual_inductance_line";
model_name in [m.name for m in engee.get_all_models()] ? engee.open(model_name) : engee.load( "$(@__DIR__)/$(model_name).engee");

Setting up the model for the first experiment for a 1-f short-circuit on the busbars of substation B with two working overhead line circuits is done by changing the values of the constants blocks connected to the circuit breakers in the "Switching Experiments" subsystems. If the value of the constant is equal to zero, the circuit breaker is in the closed state, otherwise it is open. Thus, to connect the second circuits from the busbars of PS A and PS B and to disconnect the earthing at both ends, the following values of constants must be set:

In [ ]: 
enable_step_name = "Переключение опытов/Enable";
grounding_step_name = "Переключение опытов/Grounding";
# Включение выключателей ПС
engee.set_param!(model_name*"/"*enable_step_name, "Value" => 0);
# Отключение заземляющих выключателей 
engee.set_param!(model_name*"/"*grounding_step_name, "Value" => 1);

Starting the loaded model:

In [ ]: 
results = engee.run(model_name);

To import the simulation results, logging of the required signals has been enabled in advance and their names have been set. Convert the instantaneous values of the currents of the variable results into separate vectors:

In [ ]: 
# вектор времени симуляции
sim_time = results["i_a_1"].time;
# вектора токов в точке измерения №1
i_1mut = hcat(results["i_a_1mut"].value,results["i_b_1mut"].value,results["i_c_1mut"].value,results["sum_i_1mut"].value);
i_1 = hcat(results["i_a_1"].value,results["i_b_1"].value,results["i_c_1"].value,results["sum_i_1"].value);
# вектора токов в точке измерения №2
i_2mut = hcat(results["i_a_2mut"].value,results["i_b_2mut"].value,results["i_c_2mut"].value,results["sum_i_2mut"].value);
i_2 = hcat(results["i_a_2"].value,results["i_b_2"].value,results["i_c_2"].value,results["sum_i_2"].value);

Graphs of currents at measuring point 1 (beginning of circuit 1 on the side of substation A):

In [ ]: 
p1 = plot(sim_time, i_2mut[:,1:3], label = [L"I_a" L"I_b" L"I_c"],
title = "Токи (система 1)", ylabel = "I, А", xlabel="Время, c");
p2 = plot(sim_time, i_2[:,1:3], label = [L"I_a" L"I_b" L"I_c"],
title = "Токи (система 2)", ylabel = "I, А", xlabel="Время, c")
plot(p1, p2, layout=(2,1), legend = true, linecolor = [:orange :green :red], size = (700,440))
Out[0]:

Plots of tripled zero sequence currents at measurement points 1 and 2 (beginning of overhead line on the A side of the substation):

In [ ]: 
p1 = plot(sim_time, [i_1mut[:,4] i_1[:,4]], label = [L"3I_0(система\,1)" L"3I_0(система\,2)"],
title = "Утроенные токи НП в точке измерения 1", ylabel = "I, А", xlabel="Время, c")
p2 = plot(sim_time, [i_2mut[:,4] i_2[:,4]], label = [L"3I_0(система\,1)" L"3I_0(система\,2)"],
title = "Утроенные токи НП в точке измерения 2", ylabel = "I, А", xlabel="Время, c")
plot(p1, p2, layout = (2,1), size = (700,440))
Out[0]:

When taking into account the mutual induction, the tripled zero-sequence current becomes smaller due to the increase of the total resistance of the overhead line MV.

Experience a ground fault on the busbars of substation B if the parallel circuit is disconnected and earthed at both ends:

Set up the model for the second experience for a short-circuit on the busbars of substation B with one disconnected and earthed circuit similar to the previous experience:

In [ ]: 
# отключение вторых цепей от шин ПС А и ПС Б и заземление с обоих концов
enable_step_name = "Переключение опытов/Enable";
grounding_step_name = "Переключение опытов/Grounding";
# Отключение выключателей ПС
engee.set_param!(model_name*"/"*enable_step_name, "Value" => 1);
# Включение заземляющих выключателей 
engee.set_param!(model_name*"/"*grounding_step_name, "Value" => 0);

Running the loaded model and importing the results:

In [ ]: 
results = engee.run(model_name);
# вектора токов в точке измерения №1
i_1mut = hcat(results["i_a_1mut"].value,results["i_b_1mut"].value,results["i_c_1mut"].value,results["sum_i_1mut"].value);
i_1 = hcat(results["i_a_1"].value,results["i_b_1"].value,results["i_c_1"].value,results["sum_i_1"].value);
# вектора токов в точке измерения №2
i_2mut = hcat(results["i_a_2mut"].value,results["i_b_2mut"].value,results["i_c_2mut"].value,results["sum_i_2mut"].value);
i_2 = hcat(results["i_a_2"].value,results["i_b_2"].value,results["i_c_2"].value,results["sum_i_2"].value);

Graphs of tripled zero-sequence currents at measuring points 1 and 2 (beginning of the overhead line on the side of substation A):

In [ ]: 
p1 = plot(sim_time, [i_1mut[:,4] i_1[:,4]], label = [L"3I_0(система\,1)" L"3I_0(система\,2)"],
title = "Утроенные токи НП в точке измерения 1", ylabel = "I, А", xlabel="Время, c")
p2 = plot(sim_time, [i_2mut[:,4] i_2[:,4]], label = [L"3I_0(система\,1)" L"3I_0(система\,2)"],
title = "Утроенные токи НП в точке измерения 2", ylabel = "I, А", xlabel="Время, c")
plot(p1, p2, layout = (2,1), size = (700,440))
Out[0]:

The graph shows that due to mutual induction, the first circuit induces NP currents in the second circuit. When the mutual induction is taken into account, the tripled NP current becomes larger. In this mode, the impedance of the two-circuit overhead line is minimal. As can be seen from the experiments, taking into account the mutual induction between overhead line circuits can have a strong influence on the currents, and as a consequence, on the calculation of protection tripping settings.

Addendum

Try changing the following model parameters yourself and investigate how this affects the simulation results:

  1. overhead line length by 140 km;
  2. type of fault in the Fault (Three-Phase) block;
  3. specific inductive resistance of mutual induction by 1 Ohm/km.

Conclusions

In this example, the tools for command control of the Engee model and uploading of the simulation results were used and the work with the Plots module was shown. Measured currents were imported into the Workspace from the result variable and then plotted on time plots. The use of the Double-Circuit Transmission Line block, which takes into account the mutual induction between overhead line circuits, is shown and compared with a conventional overhead line block.

References

  1. Methodology of calculation and selection of tuning parameters (setpoints) and algorithms of functioning of reserve protections in the cabinet of type SHE2607 021. URL: https://ekra.ru/product/docs/rz-ps-110-750kv/zashchita-lin/she2607-she2710/Рекомендации%20по%20расчету%20уставок%20КСЗ%20110-220%20кВ.pdf?ysclid=m2oicx6k7852299404 (дата обращения 28.10.2024)
  2. Standard of the organisation PJSC FGC UES. СТО 56947007-29.120.70.241-2017. Technical requirements for microprocessor-based RPA devices. URL: https://www.rosseti.ru/upload/iblock/bc9/wgavy1h2g4grcll6x2rmxfltcjatlcfk.pdf (date of circulation 28.10.2024)

Blocks used in example