Analyze the difference between Rogowski coil and current transformer from the principle and its application

 

 

summary:

Rogwski coil can be said to be a new type of “current transformer”. Since the structure of Rogwski coil is mainly a coil without iron core, it has the advantages of unsaturation, low delay, good frequency characteristics and safe insulation compared with ordinary current transformers. Now the smart grid is promoted, and the smart grid needs to use electronic transformers to change the analog signal output by the traditional ordinary current transformer (current transformer, referred to as CT) into a digital signal output by the electronic transformer, so as to facilitate the data transmission of the smart grid. The main technology of the electronic transformer is Rogwski coil technology (of course there are also low-power transformers, optical fiber transformers, etc.). However, the development of electronic transformers is not as fast as imagined. What is the reason? Obviously, Rogwski coils are not that simple and still cannot replace traditional current transformers. This article analyzes the difference between Rogwski coils and traditional current transformers by comparing their principles, and finds the development positioning of the two transformers based on the current technological development.

 

 

 

 

1.The principle of Rogowski coil (for the convenience of introduction, “Rogowski coil” will be written as “RCT” below)

Figure 1 Working principle diagram of RCT with a circular cross section

The theoretical basis for RCT current measurement is Faraday’s law of electromagnetic induction and Ampere’s loop law (see Figure 1: RCT working principle). We list the formula for RCT secondary voltage u

u=2πf*μ*S*n*I1/N=6.28f*μ*S*n*I1 (Formula 1)

Formula 1 is the output calculation formula of RCT, where u is the coil output voltage value, μ is the vacuum magnetic permeability : 4π*10 -7 , S is the cross-sectional area of the coil, n is the number of coil turns per unit length (i.e. winding density), I1 is the primary current value, and N is the primary turns. It can be seen from Formula 1 that the coil secondary output voltage value u and f, S, n, I 1 These four key factors are directly proportional.

The higher the frequency f, the higher the voltage value output by the RCT. For example, when testing 60HZ, the output voltage value is 1.2 times that of 50HZ. Coil cross-sectional area S: The larger the coil cross-sectional area, the larger the output signal. To obtain a larger output signal, a skeleton with a larger cross-section can be used. Winding density n: The winding density is proportional to the output. The more wires are wound per unit length, that is, the larger the winding density n, the greater the output. In other words, it is not the case that the longer the RCT is and the more turns it has, the larger the output signal will be. Instead, the more wires are wound per unit length, the greater the output will be. Primary current I 1 : This is easy to understand. RCT, like CT, has linear output, and the secondary output increases with the increase of primary current.

 

 

 

 

2.The principle of traditional current transformer (i.e. with iron core) (For the convenience of introduction, “traditional current transformer” will be written as “CT” below)

Figure 2: Working principle of CT

 

 

Basically the same as that of transformer. The number of turns of primary winding (N1 ) is small, and it is directly connected in series with the power supply line. When the primary current I1 passes through the primary winding, the alternating magnetic flux generated induces a proportionally reduced secondary current I2 ; the number of turns of secondary winding N2 is large, and it is connected in series with the secondary load (Z) of the current coil of the instrument, relay, transmitter, etc. to form a closed loop, as shown in Figure 2. When CT is working, its secondary side loop is always closed, so the impedance of the measuring instrument and the series coil of the protection loop is very small, and the working state of CT is close to short circuit. CT converts the large current on the primary side into a small current on the secondary side for measurement, and the secondary side cannot be open.

 

 

Since CT relies on the principle of electromagnetic induction, there must be secondary induced electromotive force, and the iron core must have magnetic flux. The magnetic flux per unit area is called magnetic flux density B, also called magnetic induction intensity. When the current reaches a certain value, the magnetic flux density in the iron core reaches the highest, and the CT will be saturated at this time. Therefore, the magnetic density is the parameter that determines whether the CT is saturated. According to the law of electromagnetic induction, the relationship between magnetic density B and induced electromotive force can be listed.

 

 

B=2252*E2/(f*Sc*N2 ) (Formula 2)

Where E2 is the secondary induced electromotive force, which is composed of secondary impedance and secondary current I2 , f is the operating frequency, S C is the cross-sectional area of the core, and N2 is the number of secondary turns.

At the same time, we list the CT error formula as follows:

ε=25.3*Z2*Lc/(Sc*u*N22 ) (Formula 3)

Where Z2 is the secondary impedance of the transformer and LC is the magnetic path length of the core.

 

 

 

 

3.Analyze RCT and CT from multiple aspects

Below we compare the advantages of both parties in nine aspects: output signal, overload capacity, load capacity, frequency range, error, linearity, anti-interference ability, response ability, and safe use.

 

 

3.1 Output signal

The signal output by CT is an AC current signal. If it is a primary transformer, it generally outputs a 5A/1A signal. If it is a secondary transformer in an electric meter, it generally outputs an AC signal of 1mA-5mA. RCT outputs a very small voltage signal, generally 0-100mV for 1kA output, which can be tested with a high-impedance voltmeter. If an integrator is added, the output signal is generally 0-10V, which is selected according to customer requirements. Of course, there are also customers who need RCT to output 1A or even 5A signals, in which case an external power amplifier must be connected.

 

3.2 Overload capacity

RCT has no iron core or its iron core is air. Air will not saturate the magnetic field, so RCT will not saturate, which is also the advantage of RCT. However, since CT has an iron core, once the magnetic density B in the iron core reaches the highest, the magnetic permeability of CT will continue to decrease and eventually disappear. At that time, CT is likely to burn out in the case of demagnetization. (See Figure 9: As the magnetic field increases, the magnetic permeability will not increase at first and then continue to reach the lowest level.)

 

 

3.3 Load capacity

The load capacity is different from the overload capacity. If we only look at CT, the one with strong overload capacity generally has strong load capacity. However, the comparison between RCT and CT is another case. As mentioned in 3.1 above, RCT basically outputs a very small voltage signal. Once the load is added, the voltage value will drop very quickly. This is why RCT needs a high impedance voltmeter to test. CT is different. CT is actually equivalent to a transformer with only one primary coil. It has an iron core and can output a certain amount of power. Of course, this is also related to the material of the iron core. For example, the magnetic density of silicon steel can reach 2T, while that of ultrafine crystal is about 1T. Therefore, the load capacity of silicon steel is basically about 1 times that of ultrafine crystal.

 

 

3.4 Frequency range

Both CT and RCT are inductors. The difference is that CT has a larger inductance due to the iron core. According to the impedance formula Z L=2πfL, the larger the inductance L, the greater the impedance; the higher the frequency, the greater the impedance. At the same frequency, the impedance of CT is very large, while the impedance of RCT is very small, so RCT can easily respond to higher frequency currents, thereby more realistically restoring the primary current.

 

 

3.5 Error

To be more convincing, we selected two products for comparison.

The following is a comparison of data tested using test equipment.

 

3.5.1 Test data of RCT without integrator and with integrator 20-1000A

Input current (A)	20	40	60	80	100	200	400	600	800	1000
100mV/KA (Unit: mV)	2.5	4.2	6.1	8.0	10.0	20.2	40.2	60.2	80.2	100.4
With integrator 1V/KA (Unit V)	0.021	0.041	0.061	0.080	0.100	0.201	0.402	0.604	0.806	1.008

 

 

3.5.2 Test data of split-type transformer 1000A/1A (transformer tester)

Input current (A)	10	50	200	1000	1200
error(%)	-0.25	-0.047	0.032	0.086	0.09

 

 

3.5.3 Based on this, draw their error linear comparison graph

 

Figure 6: Linearity comparison between RCT and KCT85

 

From this error bar graph we can draw the following conclusions:

1) The error of RCT is very large in the lower current range. For example, below 100A, the error reaches 25%. However, the error of kCT85 is very small

2) After the RCT is equipped with an integrator, the error at the low end is lower than that without an integrator because the signal output by the integrator is larger, but this does not mean that the error can be reduced by installing an integrator.

3) Many people say that the linearity of RCT is better than that of CT. In theory, it is, but it may not be the case in practical applications, because RCT will be subject to greater interference errors due to the lack of an iron core (see Figure 8). The specific linearity will be analyzed in 3.6.

Figure 3: The linearity of RCT fluctuates while the linearity of open-close CT is relatively stable

 

 

 

 

 

3.6 Linearity

According to Formula 1, the output of the RCT u = 6.28f*μ*S*n*I1 should be a linear output on the same coil because the magnetic permeability of the vacuum does not change, and S and n are fixed in the same coil.

However, the output accuracy formula of CT is ε=25.3*Z2*Lc/(Sc *u*N22 ), where Z2 , Lc, Sc , and N2 are relatively fixed values on the same coil, and the magnetic permeability u will change with the current, resulting in changes in accuracy (see Figure 4).

 

 

Figure 4: Magnetic permeability versus magnetic field strength

Theoretically, the error of CT should be greater than that of RCT. However, in the actual test process, RCT will be affected by the specific position, and its output accuracy will also change greatly. Therefore, due to the non-fixed position, the linearity of RCT will also be greatly affected, which is also a major disadvantage of RCT (see Figure 10: Error diagram of RCT at different positions).

 

 

 

 

 

Figure 10: Error diagram of different RCT positions

 

Now many manufacturers use magnetic skeletons to increase the output of RCT, that is, to increase the magnetic permeability of RCT, which is very inappropriate. First of all, according to Figure 9, it can be found that the magnetic permeability changes with the change of magnetic field, until the magnetic field is saturated and the magnetic permeability drops to the lowest point, then the output of RCT is no longer linear. That is, the linear trend of the output is the same as the trend of the magnetic permeability. Can RCT still be used in that case? If you must use a magnetic skeleton, then the magnetic permeability of the magnetic skeleton must be constant, that is, constant magnetic permeability, which is achievable. (Now there are ultra-fine crystals with constant magnetic permeability, which are processed by transverse and longitudinal magnetic fields to make the magnetic permeability of the magnetic core change less within a certain range.) However, except for the vacuum magnetic permeability, all materials can only have constant magnetic permeability within a certain range. Then after using this material, the unsaturated advantage of RCT is lost.

 

 

3.7 Anti-interference capability

RCT has no iron core and is easily interfered by signals, especially small current errors are very large. As shown in Figure 6, the interference is large at the low end, resulting in relatively large errors. Therefore, RCT needs to be properly shielded to achieve better output. Although CT is also interfered by signals, it has a very strong magnetic field, which is equivalent to a filter, so the interference is relatively small.

 

 

 

3.8 Responsiveness

Responsiveness is an important characteristic of the transformer. Generally, since CT contains an iron core, the iron core will produce hysteresis effect, which has two hazards: one is that the transformer will heat up, and even burn the transformer when the hysteresis effect is serious; the other is that the transformer’s responsiveness will be weakened due to the hysteresis effect, and it cannot always convey the information of the primary current, which is particularly harmful to the protection CT. This is precisely an advantage of RCT, because it has no iron core, so it has no hysteresis reaction, so its instant responsiveness is very high, which is also an important reason why it can test high-frequency current.

 

 

 

3.9 Security

CTs usually have a nameplate before leaving the factory, which says “Secondary open circuit is strictly prohibited” . Because CT secondary open circuit will generate high voltage, which will seriously damage the equipment and human life safety. Therefore, the secondary of the transformer can only be short-circuited but not open-circuited. Of course, the secondary side fuse cannot be short-circuited. However, the secondary side output of RCT is a very small voltage value, so there is no need to consider the secondary open circuit. Therefore, in terms of safety performance, RCT is much higher than CT.

 

 

To sum up, the relative differences between RCT and CT are now summarized in a table.

type	3.1 Output signal	3.2 Load capacity	3. Overload capacity	3.4 error	3.5 Linearity	3.6 Anti-interference	3.7 Responsiveness	3.8 frequency scope	3.9 Security
RCT	weak	weak	powerful	Difference	powerful	Difference	quick	Width	high
CT	powerful	powerful	weak	powerful	Strong	Strong	slow	narrow	Low

 

 

 

 

 

 

 

4.Development trend of RCT

This article analyzes the difference between RCT and CT and finds that RCT cannot replace CT at present. So in what occasions can RCT be used? According to our summary, although RCT has large errors, it is not saturated, so it can replace the protective CT. Of course, in the field of measurement, RCT has good high-frequency characteristics, fast response, and can be used to measure leakage current, fault current, pulse current, lightning current, or harmonics in current. It is also hoped that with the continuous enhancement of RCT technology, large-scale development, production and application of electronic transformers can be achieved.

 

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