Analysis of Calculation of Artificial Neutral Point Resistance for Open-circuit Testing

This article focuses on the artificial neutral point device with ZN connection (ZN type connection refers to the way that the primary winding adopts a zigzag connection and the neutral point is led out). In the process of breaking test, the arc energy is an important criterion. For three-phase four-wire transformers, the test loop can be built by connecting the N-pole with a pure resistance. However, for three-phase transformers, the loop needs to be built through the artificial neutral point. By analyzing the calculation and actual test data, the calculation method for the artificial neutral point resistance used in the experiment is clarified. It is confirmed that the resistance of the artificial neutral point will not change with the change of input voltage, making the calculation of expected fault current more accurate in daily use.


Introduction
According to GB/T 14048.1-2012"Low-voltage Switching and Control Equipment Part 1: General Requirements" and GB/T 14048.2-2020.Low-voltage switchgear and controlgear -Part 2: Circuit breakers, when conducting switching and short-circuit performance tests on electrical equipment, metal wire mesh should be set up at various points around the equipment to simulate a possible breakdown phenomenon.This wire mesh should be connected to the N-terminal of the circuit and equipped with a fusible element as well as a limiting resistor to restrict the fault current [1].For circuits composed of three-phase transformers without a N-phase, it is not possible to form an arcing loop through the neutral point.Therefore, an artificial neutral point must be used to connect with the metal wire mesh, and a variable resistor can be used to limit the expected fault current.The test circuit is shown in figure 1.If the arc detection fuse melts, it means that the arc energy has exceeded the bearable range and will be judged as failed in the test result judgment.As the use conditions of the artificial neutral point during the test are different from those of the ZN-type connected grounding transformer, the calculation method of the current limiting resistor in the artificial neutral point circuit is also different from the traditional method.Correctly calculating the resistance of the artificial neutral point device and configuring a reasonable variable resistor can not only improve the accuracy of the switching test results but also avoid excessive configuration of the current limiting resistor, thereby controlling the volume of the entire device within a certain range.Artificial neutral point devices are not widely used as experimental equipment, and most of the transformers used for experiments are three-phase four-wire transformers.However, as a special experimental device, it is necessary to exist.With the continuous improvement of testing requirements, the requirements for artificial neutral point devices are also constantly increasing.Through experiments and calculations, it can also provide some help for the future design and development of this device.

Introduction to the Artificial Neutral Point Device
The artificial neutral point device consists of a transformer with a ZN-type connection and a variable current-limiting resistor, connected to each other via a contactor as shown in the figure2.The transformer's ABC phases are connected to the test port's ABC phases, and the N phase is connected to the metal mesh via a fusible element.The transformer's ZN-type connection allows for the expected fault current to balance between the two series-connected windings.The transformer parameters used for this test are shown in table 1.According to GB/T 14048.1-2012"Low-voltage switchgear and controlgear-Part 1: General rules", the minimum expected fault current is 50 A and the maximum expected fault current is 1500 A (Allow a deviation of ±10%.)[2].The variable resistor has a fineness of 5 mΩ and a total of 13 settings, including 5 mΩ,10 mΩ,20 mΩ,40 mΩ,80 mΩ,160 mΩ,320 mΩ,640 mΩ,1280 mΩ,2560 mΩ,5120 mΩ,10240 mΩ, 10240 mΩ.

Analysis of Factors Influencing the Resistance of the Artificial Neutral Point Device
Compared with traditional transformers, the artificial neutral point device has different usage methods.The voltage of the primary winding is not always maintained consistent during operation, and the zerosequence resistance may change with the variation of the input voltage, thereby affecting the calculation of the expected fault current [3].
The usage methods are also different from those of grounding transformers.After the three-phase input of the grounding transformer, the N-terminal acts as the grounding end and is connected to the grounding device.The DC resistance can be measured through the relationship between voltage and current.However, for the artificial neutral point transformer, the N-terminal is connected to the test device's arcing net cylinder.In the event of a short circuit, it is momentarily connected to any of the source terminals on the primary side.Therefore, its resistance cannot be simply derived from the relationship between voltage and current [4].
Based on the above analysis, the same current limiting resistor will be used under each voltage setting to observe the relationship between input voltage and output current.Then, the actual impact on the expected fault current will be calculated using a formula, and finally, the calculated reliability will be verified through actual working conditions.

Traditional Method of Measuring the Resistance of the Artificial Neutral Point Device(Direct Current Resistance Measurement)
Transformer is a device that utilizes the principle of electromagnetic induction to change the voltage of an alternating current [5].It mainly consists of a primary coil, a secondary coil, and a core composed of iron or magnetic material, with the primary coil located inside the secondary coil.When a primary coil is supplied with an alternating current, the core produces a varying magnetic field, which induces a voltage in the secondary coil.The voltage induced in the secondary coil is proportional to the number of windings in the primary and secondary coils and the strength of the magnetic field.By using coils with different numbers of windings, it is possible to change the voltage of the induced current without changing the frequency or waveform of the input current.This process can be used to transform highvoltage alternating current to low-voltage alternating current for use in homes and industries, or to transform low-voltage alternating current to high-voltage alternating current for long-distance power transmission.The transformer can also be used to change the ratio of voltage in an alternating current circuit.The power transformer winding can be simplified and equivalent to a series connection of an inductor L and a resistor R.
The artificial neutral point device consists of a transformer and a variable resistor.The traditional method of measurement connects the ABC phases of the artificial neutral point device to the positive terminal of a DC voltage source, and the N phase is connected to the negative terminal.The variable resistor is a fixed resistor, and the input voltage is measured to calculate the resistance using Ohm's law.However, the conventional method has a low voltage (approximately 380V) and cannot prove whether the resistance changes with changes in voltage.Moreover, in practical use, AC power is used, and the measurement method of DC resistance is not reference.This experiment connects the transformer to a power source with a matching operating condition by using input voltages close to the designed values and calculates the resistance based on the actual current.The purpose is to prove whether the transformer resistance is related to the input voltage.First, the variable resistor is set to a fixed value of 640 mΩ (the actual resistance is 630 mΩ).Then, the ABC phases of the artificial neutral point device are connected in parallel to the A phase of the input power supply, and the N phase is connected to the B phase of a three-phase power supply.The voltage is adjusted by regulating the power supply and transformer settings, and the results are shown in table 2.    From the above data(figure3, figure4, figure5)it can be seen that the influence of different input voltages on the resistance value of artificial neutral point transformers is extremely small.As the input voltage increases, there is a slight deviation in the resistance value of the artificial neutral point transformer due to differences in wiring methods.Testing has identified the interference factor of input voltage on resistance, and in practical circuit tests, the number of tests to confirm resistance can be reduced.However, due to differences between this measurement method and actual usage conditions, further testing is still necessary.

Computing the Resistance of the Artificial Neutral Point Device Using Formulas
The artificial neutral point is connected to the ABC phases of the power supply in real situations, resulting in a fault current that short circuits with any one phase of the power supply.However, due to the connection of the adjustable resistor, the neutral point undergoes a shift, which affects the calculation of the resistance.According to Kirchhoff's current law, the sum of the currents flowing into a node is equal to the sum of the currents flowing out of the node.The equation can be converted as follows: In the formula, Ua, Ub, Uc are the phase voltages of the power supply terminals, U0 is the N-phase voltage, Z is the reactance of the neutral point transformer, R is the adjustable current-limiting resistor, and the sum of the three phase voltages at the test port is balanced to be zero.The voltage impact on Z is negligible and can be regarded as the resistance r.Transforming the formula to: The current flowing through the adjustable current limiting resistor R is I, and the following formula can be obtained: By using the above formula, it can be calculated that the current limiting resistor and the artificial neutral point resistance are not simply added together.The expected fault current is only related to the artificial neutral point resistance, the current limiting resistor, and the circuit voltage.Here, the circuit voltage should be the phase voltage of the test circuit rather than the line voltage.Calculations also show that when the current is high, the influence of the artificial neutral point resistance on the entire expected fault current is extremely small, so attention should be paid to avoiding calculation errors during actual experimental circuit testing.

Calculating the Resistance of the Artificial Neutral Point Device Using the Test Loop
First, according to the transformer resistance value provided by the manufacturer, the artificial neutral point device is matched with a relatively large current limiting resistor to avoid damage due to excessive current.After powering on, the expected current is obtained, and the actual measured current is used to correct the designed value of the transformer resistance.Through practical testing, the resistance values of the transformer are obtained, as shown in table 3, which also proves that the resistance of the artificial neutral point device at each position cannot be measured by direct current resistance.The actual test loop was used to verify the artificial neutral point device and test its ability.The adjustable resistor was adjusted using the formula in Section 3.2, and the parameters in table 4 were tested.

Figure 2 .
Figure 2. Structure of the artificial neutral point device.

Table 1 .
Parameters of transformer with manual neutral point device.

Table 2 .
Parallel test results of artificial neutral port.

Table 3 .
Transformer resistance correction values for each setting.