influencing factors of electromagnetic leakage protection characteristics

1 Influence of compensation circuit parameters on leakage protection characteristics
Leakage protection features include leakage action value IDd and leakage action time td. The action value IDd should be less than the rated leakage action current IDn and greater than the rated leakage action current IDno, generally IDno= 0.5IDn, so the design value of IDd is generally 0.75IDn.

     In the design of leakage protection characteristics, the leakage action value IDd can be determined first, and then the action time under IDn can be designed. The leakage action time td consists of three parts: the time when the energy storage capacitor C2 voltage reaches the threshold voltage Uact of the discriminating circuit (that is, C2 charging time) tC, the magnetic release device action time tr, and the protective device mechanism action time tj. In general, tr and tj are smaller than tC, so the action time of the leakage protector is mainly determined by the charging time tC of the energy storage capacitor C2.

 

Matching relationship between compensating capacitance and compensating resistance
When the residual current transformer is determined, it is necessary to match the compensating resistance R1 and compensating capacitance C1 to meet the requirement of leakage action value. To simplify the analysis, the residual current transformer is assumed to work in the linear region,that is, the core permeability u is assumed to be constant, and the excitation inductance is
(1)

    Where W is the angular frequency of the leakage signal, and 314 rad/s under the power frequency; N2 is the second turn of the transformer. s is the cross-sectional area of the residual current transformer core; lm is the magnetic circuit length of the residual current transformer core.
As can be seen from FIG. 3a, the compensation circuit voltage UC1 in steady state depends on the excitation inductance L0, compensation resistance R1 and compensation capacitance C1 of the residual current transformer, and the steady state voltage UC1 is
(2)
Where, A ‘is the equivalent current amplitude converted from the primary current to the secondary current. When the leakage current is the action value IDd, that is, UC1=Uact in the case of A ‘=1.414IDd/N2, so the relationship between R1, C1 and L0 is
(3)
Where, C0 is the capacitance in the case of resonance, that is. The matching relationship curves of R1 and C1 can be obtained from equation (3), as shown in Figure 4.

                                                       Fig.4 Relationship between R1 and C1
As can be seen from Figure 4, when the residual current transformer is determined, the minimum value of compensating resistor R1 exists in R1min, and the lower limit of compensating capacitor C1 exists in C1min and the upper limit of C1max.

2 Influence of compensation circuit parameters on leakage action time

When the compensation capacitor C1 and the compensation resistor R1 meet the relationship in Figure 4, the leakage action value meets the requirements, but the leakage action time is different under different compensation capacitors and compensation resistors. The charging process of the energy storage capacitor is relatively complex, including two states as shown in FIG. 3a and FIG. 3b. The mathematical expression of the voltage change of the energy storage capacitor is relatively complex, but its change can be analyzed through simulation. The measured parameters of a leakage detection circuit are: residual current transformer turns N=1 200 turns, excitation inductance L0= 300 H, threshold voltage Uact=3 V, energy storage capacitance C2=363 nF, action value IDd=22 mA. The simulation was carried out under this parameter, and the matching relationship between R1 and C1 and the action time were obtained, as shown in Figure 5. As can be seen from FIG. 5, under different matching parameters R1 and C1, although the value of leakage action is the same, the time of leakage action is very different, and the shortest action time is less than half of the longest action time. Near the resonant point, the compensation resistance is the smallest, and the operation time is the longest, and the operation time changes in step with the increase of the compensation capacitance.

The voltage of compensation capacitor and energy storage capacitor under different R1 and C1 parameters was simulated to obtain the dynamic change process, as shown in Figure 6. When UC1=UC2 and the rectifier bridge is on, the output load of the remaining current transformer changes from R1 and C1 to R1, C1 and C2, and the equivalent capacitance becomes larger, resulting in a slower voltage rise (fall) speed, as shown in Figure 6a. When UC1 < UC2, the rectifier bridge is not on, and the energy storage capacitor is not charged, so the voltage of the energy storage capacitor rises in steps, as shown in Figure 6b.

                                     Fig.5 Relationship between R1 and C1 and tC when the iron core is linear

                                     Fig.6 Voltage of energy storage capacitor and compensation capacitor
The charging current simulation of the energy storage capacitor is carried out under different R1 and C1 parameters, and its waveform is shown in Figure 7. The It integral within a cycle is calculated to obtain the charging capacity of the capacitor during the cycle, as shown in Table 1.

                                       Fig.7 Charging current of energy storage capacitor

                                           Tab.1 Electric quantity of energy storage capacitor

As can be seen from Table 1, when the compensation capacitor is a resonant capacitor, the energy storage capacitor C2 charges the least amount of electricity in one charging cycle, so its operation time is the longest under the same threshold voltage. As can be seen from Figure 5, under the same compensation resistance, there are two compensation capacitors C1 matching it, one larger than the resonant capacitor C0 and one smaller than C0. The larger the compensation capacitor, the larger the shunt, and the smaller the charge capacity of the energy storage capacitor C2 in a cycle, so the voltage rise is slower and the leakage action is longer.

  Influence of excitation inductance on leakage protection characteristics under linear condition
The performance of residual current transformer mainly depends on core size, permeability and coil turns. If the residual current transformer operates in the linear region, the excitation inductance can be assumed to be constant. Therefore, the influence of residual current transformer performance on leakage protection characteristics can be analyzed through excitation inductance.
When the excitation inductance L0 increases, the resonant capacitance value C0 decreases, and vice versa. It can be seen from equation (3) that under different excitation inductance, although the matching relationship between the compensation capacitance and the compensation resistance changes, the change of the compensation capacitance is only related to the excitation inductance, that is, the matching relationship curve between R1 and C1 only shifts on the coordinate axis.
When the coil current of the transformer is 22 mA, the inductance value of the 1 200 turns transformer is measured between 150 and 450 H. Based on this, the equal step length method was adopted in the simulation, and the simulation analysis was carried out with 50 H as the step length. The matching relationship between R1 and C1 and the change curve of leakage action time under different L0 were obtained, as shown in Figure 8. It can be seen from Figure 8a that the matching curves of R1 and C1 under different excitation inductance L0 are exactly the same. As can be seen from Figure 8b, the change law of leakage action time is basically the same. The shortest action time tCmin appears at C1min, and the longest action time tCmax appears near the resonant capacitor C0. When 20 nF < C0 < 40 nF, the maximum action time ranges from 140 to 150 ms. When C0 > 40 nF, the maximum operation time is between 150 and 160 ms.
Under different excitation inductance L0, the shortest and longest operation time are slightly different, as shown in Figure 9. In an energy storage capacitor charging cycle, if the energy storage capacitor voltage does not reach the threshold voltage, it needs to wait for the next charging cycle. In the case of full wave rectifier charging, the charging cycle is 10 ms, so it can be seen from Figure 9 that there is a change of nearly 10 ms near a certain inductance value. It can be seen from Figure 5 that when C1=C1min, the action time is the shortest, and formula (3) shows that the compensation resistance at this time should be infinite. As can be seen from FIG. 9, with the increase of inductance, the minimum operation time tends to a smaller value, but when L0 > 400 H, the minimum operation time increases slightly, because when the inductance is large, the C1min calculated by equation (3) is already small, and may even change from 0 to negative value, while in practice, the capacitance cannot be negative value. Therefore, when the inductance is large, the minimum compensation capacitance is 0, which cannot reach the theoretical minimum value, resulting in a slight increase in the operating time. As can be seen from FIG. 8 and FIG. 9, due to the restriction of leakage protection action value, changing the excitation inductance does not change the change rule of leakage action time, that is, changing the magnetic properties of the core of the residual current transformer, such as increasing the permeability, will not change the leakage protection characteristics.

                                    Fig.8 Relationship between R1 and C1 and tC under different L0

                                           Fig.9 Shortest and longest tC under different L0

Influence of core magnetic properties on leakage protection characteristics under nonlinear conditions
In practice, the electromagnetic residual current transformer may work in the nonlinear region, and its excitation inductance is no longer constant. Therefore, a nonlinear residual current transformer model is established according to the saturation magnetic induction intensity Bs, residual magnetic induction intensity Br and coercivity force Hc, which are three characteristic parameters characterizing the magnetic properties of the core. The original parameters of residual current transformer and leakage detection circuit are shown in Table 2. Through simulation calculation under the parameters in Table 2, the relationship curves of R1 and C1 and corresponding action time can be obtained, as shown in Figure 10.

                       Tab.2 Original parameters of residual current transformer and leakage detection circuit

Fig.10 Relationship between R1 and C1 and tCwhen the iron core is non-linear 
Compared with FIG. 10 and FIG. 5, although there are differences in the matching relationship and operation time of R1 and C1 when the residual current transformer works in the linear region and the nonlinear region, their variation rules are the same. Therefore, the analysis under the assumption that the excitation inductance is constant is still instructive.
On the basis of the parameters in Table 2, the single factor rotation method is used to analyze the matching relationship between the compensation circuit parameters and the relationship between the operation time and the magnetic parameters of the core. When the magnetic parameters Bs are 0.4 ~ 1.3T, Br is 0.1 ~ 0.4t, and Hc is 0.3 ~ 1.0A /m, the simulation calculation is carried out, and the results are shown in Figure 11. As can be seen from FIG. 11, the matching relationship curves between compensation resistance and compensation capacitance under different magnetic characteristic parameters are not exactly the same, but they are all “U-shaped”, and the variation trend of operation time is basically the same as when the excitation inductance is constant.

                          Fig.11 Relationship between R1 and C1 and tC under different magnetic parameters

Experimental verification of R1, C1 matching relationship and action time

The actual measured parameters of a certain residual current transformer are shown in Table 3. Through the experiment, the IDd=22 mA is obtained by combining 5 groups of R1 and C1 parameters, and the corresponding action time is measured. Moreover, the action value and action time under the corresponding parameters are obtained through simulation, and the results are shown in Table 4.

                                 Tab.3 Parameters of residual current transformer and leakage detection circuit

                                           Tab.4 Parameters of R1 and C1 and operating time

It can be seen from Table 4 that under different compensation capacitors, the error of action value obtained by experiment and simulation is less than 5%, and the error of action time is less than 10%. Due to the inability to control the power supply closing phase during the experiment, the operation time when the compensation capacitor is 31.5nF differs greatly from the simulation result, but the error is within half a cycle. In addition, the error of other groups of data is less than 5%, which verifies the accuracy of the simulation method in this paper.

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