In-depth analysis of voltage transformer fault compensation methods
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# In-depth analysis of voltage transformer fault compensation methods

Posted Date: 2024-02-05

Voltage transformer is equivalent to a transformer running without load in electromagnetic principle. The rated transformation ratio of the voltage transformer is:

kr=Upr/Usr

In the formula, Upr - rated primary voltage, V
Usr―Rated secondary voltage, V

This is the ideal state of a voltage transformer, but in reality voltage transformers have currents flowing through them, and they produce impedance voltage drops in the primary and secondary windings, causing the ratio of the primary and secondary voltages to deviate from the transformation ratio. There are also differences in phase, and these differences are the errors of the voltage transformer. The numerical differences are called voltage errors or ratio differences, and the differences in phase are called phase differences.

The national standard regulates the fault limit value of voltage transformers. If the fault of voltage transformers exceeds the specified limit, they need to be adjusted to within the limit, that is, fault compensation is performed.

The phase difference of the voltage transformer is usually small and does not require processing, while the voltage error is large and often exceeds the limit. This article only deals with the topic of compensation for negligence.

According to the definition in GB20840.3-2012, the voltage error of voltage transformer is the ratio difference.

ε is defined as:

ε=（kr・Us-Up）/Up×100，%
In the formula Up - actual primary voltage V
Us―The actual secondary voltage V when Up is applied

In most cases, the voltage error of the voltage transformer is negative, that is, the actual secondary voltage is lower than the corresponding primary voltage divided by the transformation ratio. Trying to increase the secondary voltage can change the error in the positive direction. A common method is to adjust the number of turns, often called turns compensation. Under a given voltage, reducing the number of primary turns will increase the potential of each turn, or increasing the number of secondary turns can increase the secondary voltage and reduce the negative voltage error.

The voltage transformer is connected in parallel on the high-voltage power grid. The primary voltage is the rated voltage of the system. The number of primary winding turns is generally designed to be tens of thousands of turns. For a 0.2-level voltage transformer, the number of primary winding compensation turns can reach several hundred turns, so the primary compensation is called Compensation for integer turns. Since the secondary voltage of the voltage transformer is very low (such as 57.7V or 100V) and the secondary winding only has a few dozen turns, even adjusting the percentage of voltage change caused by one turn may exceed the failure limit. Therefore, the secondary winding cannot use an integer. Turn compensation requires subdividing the potential of a single turn through an auxiliary voltage transformer to obtain the potential of several turns, which is equivalent to selecting fractional turns, and can also be called fractional turn compensation.

The following article discusses the fault compensation method of voltage transformer and the design and wiring of auxiliary voltage transformer for fault adjustment.

2. Several methods of voltage transformer fault compensation

There are many methods of voltage error compensation, and the following are commonly used.

2.1 Integer turn compensation

As mentioned before, this is a way to adjust the number of primary winding turns, usually by reducing the number of primary turns and obtaining positive error compensation, also known as reduced-turn compensation. The compensation principle is as follows.

If the electric potential of each turn before subtracting the turn is:

ezr=Upr/Npr

Then, the potential per turn after the turns are reduced will be:

ez=Upr/Np
In the formula, Upr——rated primary voltage, V
Npr - rated primary turns
Np - the actual number of primary turns after reducing the turns

Obviously, the percentage of potential increase per turn is the percentage of secondary voltage increase, then the voltage error compensation value is:

εb=（εz-εzr）/εzr=（Npr-Np）/Np

εb=Nb/Np×100，%

In the formula, Nb is called the compensation turns. Since Nb is generally very small, and the difference between the actual number of primary turns and the rated number of primary turns is also very small, the error compensation value is usually calculated using the following formula:

εb=Nb/Npr×100，%（1）

2.2 Auxiliary voltage transformer compensation

Auxiliary voltage transformer compensation is used to adjust the number of secondary turns, which is equivalent to the compensation of fractional turns. Depending on the way the auxiliary voltage transformer receives power (that is, the way the secondary winding of the main voltage transformer supplies power to the auxiliary voltage transformer is different), there are several compensation methods available.

2.2.1 Voltage transformer series compensation method

Only one turn of the auxiliary winding on the low-voltage side of the main voltage transformer supplies power to the auxiliary voltage transformer. The wiring diagram is shown in Figure 1. This compensation method is called series compensation.

In the two designs in Figure 1, the secondary winding Nf2 of the auxiliary voltage transformer is connected in series with the secondary winding of the main voltage transformer. This superimposes an electric potential in the secondary circuit of the main voltage transformer, thereby compensating for the error. effect. Changing Nf2/Nf1 in Figure 1(a) or Nf1 in Figure 1(b) can adjust the compensation value. Changing the polarity of Nf2 changes the sign of the compensation value, providing positive or negative compensation.

In the plan of (a), the cross section of the wire for winding Nf2 of the auxiliary voltage transformer should refer to Section 3.3 and be selected according to the sudden short-circuit current; while the secondary winding Nf2 of the auxiliary voltage transformer in Figure 1(b) only needs 1 turn or For a few turns, you only need to pass the secondary lead wire of the main voltage transformer through the core window of the auxiliary voltage transformer. Figure 1(b) is the commonly used plan.

Taking Figure 1(b) as an example, the number of turns of the primary winding of the auxiliary voltage transformer is Nf1. It is powered by an additional winding of only one turn on the low-voltage side of the main voltage transformer. The potential of each turn is efz=ezr/Nf1, where ezr =Usr/Nsr.

The secondary voltage of the auxiliary voltage transformer only has one turn, and it is connected in series with the secondary winding of the main voltage transformer, so the secondary voltage of the main voltage transformer gets the compensation voltage ub.

ub=ezr/Nf1，V

Therefore, the negligence compensation value is:

εb=ub/Usr=ub/（ezr・Nsr）

εb=1/（Nsr・Nf1）×100，%（2）

In the formula, Usr——the rated secondary voltage of the main voltage transformer, V

Nsr——Rated secondary turns of main voltage transformer

Nf1——The number of primary winding turns of auxiliary voltage transformer

The number of compensation turns is 1/Nf1 of the single turn of the secondary winding of the main voltage transformer.

2.2.2 Voltage transformer parallel compensation method

The entire secondary winding of the main voltage transformer supplies power to the auxiliary voltage transformer. The load of the auxiliary voltage transformer is similar to that of the main voltage transformer and is connected in parallel to the secondary side of the main voltage transformer. The wiring method is shown in Figure 2. The compensation method is called parallel compensation.

It can be seen from Figure 2 that the potential of each turn of the auxiliary voltage transformer is: efz=Usr/Nf1

The potential in the secondary winding Nf2 of the auxiliary voltage transformer is the compensation value for the secondary voltage of the main voltage transformer, so the compensation value of the voltage error by this compensation method is:

εb=（ef・zNf2）/Usr

εb=Nf2/Nf1×100，%（3）

In the formula, Nf1 and Nf2 are the number of turns of the primary and secondary windings of the auxiliary voltage transformer respectively.

The actual compensation voltage is Nf2/Nf1 of the secondary voltage of the main voltage transformer, so the number of compensation turns is Nf2/Nf1 of the secondary winding turns of the main voltage transformer, and the function is also fractional turn compensation.

2.2.3 Parallel compensation wiring method of auxiliary voltage transformer

For the secondary winding of voltage transformer without center tap, the wiring method of auxiliary voltage transformer parallel compensation is shown in Figure 2. For countries with a frequency of 60Hz, the requirements for voltage transformers are usually that the secondary winding has a tap. For the same winding, the secondary voltage has two voltages: 115V and 115/√3V (or 66.4V). Regarding this voltage transformer , when the accuracy requirements of the tap and full turns are the same, since the number of turns of the winding must be an integer during design, the ratio of the turns of the full turns and the taps cannot meet the multiple relationship of √3, thus resulting in a larger error difference between the taps and the full turns. If the difference is large, the difference itself sometimes exceeds the error limit. In this case, it is necessary to first use an auxiliary voltage transformer to separately perform fractional turn compensation on the tap or full turn, so that the error values ​​of the tap and full turns are close, and then start again from the first The integer turn compensation method is used to adjust the tap and full turn errors together to within the error limit. The wiring method for this excessive offset is shown in Figure 3.

Figure 3 (a), (b) and (c) show the auxiliary voltage transformer being connected between the secondary tap terminals X2-X3 of the main voltage transformer. Figure 3 (d), (e) and (f) show the Connect the auxiliary voltage transformer between the full-turn terminals X1-X3 of the main voltage transformer. The wiring in Figure 3 (c) and (e) is used to adjust the wiring to adjust the full-turn and tap errors at the same time. When Nf21=Nf22 The X3 lead can be used for compensation instead of using the X1 and If N13 and N23 are used to represent the number of full turns and tapped turns of the secondary winding of the main voltage transformer respectively, then, according to the analysis in Section 2.2.2, under each wiring method in Figure 3, the fault compensation value can be calculated as follows.

The wiring methods in Figure 3 (a) and (d) are tap power supply compensation tap and full turn power supply compensation full turn, calculated according to equation (3).

Figure 3(b) The wiring method is to use tap power supply to compensate for full turns, and the calculation method is:

εb=Nf2/Nf1・N23/N13×100，%（4）

Figure 3(e) The wiring method is a full-turn power supply compensation tap, and the calculation method is:

εb=Nf2/Nf1・N13/N23×100，%（5）

Figure 3(c) Wiring method, the error compensation values ​​of full turns and taps can be calculated according to equation (4) and equation (3) respectively.

Figure 3(f) Wiring method, the error compensation values ​​of full turns and taps can be calculated according to Equation (3) and Equation (5) respectively.

3. Design of parallel compensation auxiliary voltage transformer

The parallel compensation auxiliary voltage transformer (according to Figure 2) is generally designed with Nf1 evenly wound around the ring core, so that the leakage reactance is very small. The auxiliary voltage transformer circuit can be approximated as a pure resistance circuit, which affects the phase of the main voltage transformer. The negative impact can be ignored. The power supply voltage of the auxiliary voltage transformer is the secondary voltage of the main voltage transformer. The core cross-sectional area of ​​the auxiliary voltage transformer should be determined based on the secondary voltage and rated voltage factor of the main voltage transformer, and the auxiliary voltage should be determined based on the requirements of the fault compensation value. The number of primary turns of the transformer, and the primary winding wire of the auxiliary voltage transformer are selected based on the current that may appear in the primary winding of the auxiliary voltage transformer. The specific steps are as follows.

3.1 Recognition of primary winding turns

According to the error limit of level 0.2, the compensation range of the voltage error of the voltage transformer can be selected to be ± (0.05%~0.1%). According to Equation (3), Nf2=1 can be initially recognized for the primary winding turns of the auxiliary voltage transformer. The number Nf1 is 1000 turns to 2000 turns.

3.2 Core cross-sectional area recognition

According to the preliminary Nf1, the rated voltage Usr of the secondary winding of the main voltage transformer, the rated voltage factor k and the product operating frequency f, the core cross-section Sf is determined according to equation (6).

Sf=kUsr/（4.44fBNf1）×104（6）

In the formula, k——rated voltage factor

Usr——Rated secondary voltage, V
f——Rated frequency, Hz
B——Magnetic density in core under rated voltage factor, T
Nf1——The minimum number of turns of auxiliary voltage transformer

In addition to considering the linearity of the core function under normal operating conditions, the selection of the core cross section should also ensure that the core is not saturated at the rated voltage multiple times the rated voltage factor, generally making B ≤ 1.6T.

3.3 Primary winding wire diameter approval

According to the current of the secondary winding of the main voltage transformer being compensated, this current is also the current flowing in the secondary winding of the auxiliary voltage transformer. According to the balanced relationship between the primary and secondary ampere-turns of the auxiliary voltage transformer, the current in the primary winding can be determined, that is:

If1=If2・Nf2/Nf1（7）

In the formula, If1——the current in the primary winding of the auxiliary voltage transformer, A

Nf1——The number of primary winding turns of auxiliary voltage transformer
If2——The current in the secondary winding of the auxiliary voltage transformer, that is, the current in the secondary winding of the main voltage transformer, A
Nf2 - the number of secondary winding turns of the auxiliary voltage transformer, that is, the actual number of compensation turns

For the wires of the auxiliary voltage transformer, in addition to the temperature rise under normal conditions and multiple times of the rated voltage factor, it is also necessary to consider that the heat generated during the sudden short-circuit test does not exceed the limit. Since the short-circuit impedance of the voltage transformer is very small and the short-circuit current can reach hundreds of times the rated current, the wire should be selected first according to the short-circuit current and then the rated current density is calculated. When the short-circuit current and the maximum allowable short-circuit current density are known , the wire diameter can be determined by the following formula.

d=√4IkNf2（πNf1δk)(8）

In the formula, Ik - secondary short-circuit current of main voltage transformer, A

δk - Maximum allowable short-circuit current density, A/mm2. According to the standard, for copper wires, δk can be 160A/mm2.

4. Precautions when using auxiliary voltage transformer

From the above design of the auxiliary voltage transformer, we can know that the current in the primary winding of the auxiliary voltage transformer is determined by the secondary winding current of the main voltage transformer and the number of secondary turns of the auxiliary voltage transformer (that is, the actual number of compensation turns) and the primary turns. Determined by the ratio of the number, for a given product and selected auxiliary voltage transformer, according to equation (7), increasing the number of compensation turns will increase the primary current of the auxiliary voltage transformer. The primary winding of the auxiliary voltage transformer has selected wires The cross-section will constrain an increase in the number of compensating turns.

Regarding the temperature rise requirements that voltage transformers should meet under normal operating conditions, the rated current density is generally calculated with reference to each winding wire. According to experience, the current density of copper wires under long-term operation should not exceed 2A/mm2.

Regarding the wiring methods in Figure 3 (c) and (f), the current in the primary winding of the auxiliary voltage transformer should be converted into the superposition of the current in the primary winding of the auxiliary voltage transformer based on the tap and full turn currents of the main voltage transformer respectively. , in this method, it should be noted that the sum of the tap and full-turn compensation turns is limited by the cross-section of the primary winding conductor of the auxiliary voltage transformer.

5. Comparison of the effects of practical testing and theoretical analysis

In order to verify the analysis, the following preliminary tests are carried out with the help of the error adjustment process of the actual product, without considering the requirements of the accuracy level error limit. The basic parameters of the product and auxiliary voltage transformer are shown in Table 1.

5.1 The auxiliary voltage transformer is connected to the tap

Use the wiring in Figure 3(c) (Nf21=Nf22=4), and use the X3 terminal lead to pass through the auxiliary voltage transformer window to compensate 4 turns. The error effects before and after compensation are shown in Table 2.

For taps, the fault compensation value is calculated according to formula (3), and the compensation value is 0.33%. For full turns, the compensation value is calculated according to formula (4), and the compensation value is 0.19%. It can be seen that the calculation effect is the same as in Table 2 The amount of error change is close.

5.2 The auxiliary voltage transformer is connected to the full turn

Use the wiring in Figure 3(f) (Nf21=Nf22=5), and use the X3 terminal lead to pass through the auxiliary voltage transformer window for negative compensation of 5 turns. The error effects before and after compensation are shown in Table 3.

For full turns, the fault compensation value is calculated according to formula (3), and the compensation value is -0.416%. For taps, the compensation value is calculated according to formula (5), and the compensation value is -0.72%. It can be seen that the calculation effect is consistent with the table 3 The amount of negligent alteration is consistent.

In the measured results in Tables 2 and 3, the phase difference changes little before and after compensation, indicating that the auxiliary voltage transformer design structure recommended by the author in this article has small leakage reactance and has a negligible impact on the phase difference, consistent with the analysis results.

6. Conclusion

The test results show that the auxiliary voltage transformer design introduced above can be directly applied to product design, and the error compensation calculation formula given can also directly guide the error adjustment in product production.

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