Simulation characterization of measurement errors of the wide-range environmentally friendly current transformers

To accurately measure the hundreds of millions of dollars of electricity consumed, the accuracy, safety, environmental friendliness, and reliability of current transformers become crucial. In response to these problems, there is an urgent need to develop an environmentally friendly current transformer that can adapt to the needs of power systems with wide-range current fluctuations. Therefore, in this paper, the simulation model of a three-phase current transformer with a combined transformer is developed. Simulation and verification work for the relationship between the error characteristics of environmentally friendly current transformers and the influence of magnetic field changes in each phase and the magnitude of the load on the secondary side. We compared the measurement errors before and after active compensation, demonstrating that environmentally friendly current transformers can increase the range and measurement flat frequency range while ensuring their 0.2S class measurement accuracy. This in turn proves the feasibility of wide-range environmentally friendly current transformers.


Introduction
With the construction of the new power system, large amounts of new energy and power electronic equipment access, resulting in grid power quality and power load, presents a variety of unconventional changes, which puts forward higher requirements for the measurement accuracy of the current transformer.Conventional current transformers are difficult to meet demand and the wide-range current transformers are gradually needed by the power system.At the same time, with the development of society, the demand for the power industry has increased, the installation of gas-insulated equipment in the grid system is increasing, and the use of SF6 is also rapidly increasing.Although SF6 has good insulation properties, the United Nations stipulates that SF6 is one of the six greenhouse gases with the commissioning of insulated equipment, and overhaul process of the leakage of gases will make the SF6 into the atmospheric environment [1].There is an urgent need for green and environmentally friendly gases to replace SF6, which is of great significance to the implementation of the national dual-carbon policy and the promotion of green equipment [2].
Chen et al. [3] proposed to widen the range of the standard current transformer by changing the material of the core of the current transformer and appropriately increasing the cross-sectional area of the wire and core of the secondary winding.Currently, the research and exploration of new environmentally friendly gases that can replace SF6 with high pollution has become a new goal for many researchers [4].C4F7N gas was first proposed by 3M company, and the insulation capacity of C4F7N is about twice as much as SF6, which is non-flammable, non-toxic, and chemically stable.The GWP of C4F7N is only 1/10 of that of SF6, which can greatly alleviate the environmental problems caused by SF6.
Based on this, this paper proposes a kind of environmentally friendly current transformer suitable for metering by targeting the existing research situation and finds a suitable error compensation method for an environmentally friendly current transformer by analyzing the factors of measurement error.A new type of environmentally friendly gas is adopted instead of SF6, a model of the transformer is established in COMSOL, and its parameters are brought into the simulation model, for each phase of the magnetic field changes and the secondary side load size on the environmentally friendly current transformer error characteristics and the influence of the relationship between the simulation verification work.By comparing the size of the measurement error before and after the active compensation, we prove that the environmentally friendly current transformer can meet the metrological 0.2S level of accuracy and reduce the error rate, to achieve good measurement characteristics.

Structure and working principle of current transformer
Figure 1 is the actual structure of the current transformer.The transformer core is circular, the primary winding passes through the core, and the secondary winding is wound on the core.When the primary winding passes into the alternating current, the core will induce an alternating electromagnetic field, which will provide the secondary winding-induced electromotive force.The secondary winding connected to the load will produce a secondary current.The working principle of the current transformer and transformer is consistent.The current transformer equivalent circuit is shown in Figure 2 [5].According to the equivalent circuit, the equations for the input primary current and output secondary current of the current transformer can be obtained as: where Z1, Z2＇, Zm, and ZL＇ are the primary impedance, the secondary impedance converted to primary impedance, the excitation impedance, and the secondary impedance converted to primary load impedance of the current transformer, respectively; I1, I0, and I2＇ are the primary current, the excitation current, and the secondary current converted to primary current, respectively; E1 and E2＇are the primary induced electromotive force and the secondary induced electromotive force converted to primary induced electromotive force, respectively.

Analysis of the wide-range current transformer measurement error factors
According to the different iron core structures, three-phase three-element metering with a combination of transformers can be divided into the three-column iron core structure and independent iron core structure.A current transformer is mainly composed of a primary coil, a secondary, and an iron core [6].
In practice, both the core and the coil lose active power, which can cause capacitive or magnetic errors in the current transformer.2, the current transformer is equivalently analyzed so that it is easy to analyze the error.The presence of the excitation current I0 leads to the inequality of the primary current I1 and secondary current I2＇ of the current transformer, which results in an error.Equation (2) represents the complex error of the current transformer, where Kin is the current ratio, f is the ratio difference, and δ is the angular difference.The ratio difference is expressed as a percentage, and the angular difference is usually expressed in terms of a fraction, so the common equations for f and δ are Equations ( 3) and ( 4) respectively.
where I0 is the excitation current, I1 is the primary side current, l is the average magnetic circuit length of the iron core, Z2 is the secondary winding impedance, Zb is the secondary load impedance, F is the frequency of operation, μ is the magnetic permeability of the iron core, Ψ is the hysteresis angle of the iron core, α is the secondary side impedance angle, N is the number of turns of the secondary winding, and S is the cross-sectional area of the iron core [7].From the current transformer error calculation, Equations ( 3) and ( 4) can be seen on the impact of various parameters on the error, mainly including one or two secondary side winding parameters, iron core material, iron core structure parameters, and the first and second side of the current transformer current value [8].

Environmentally friendly current transformer error compensation methods
To improve the accuracy of the current transformer, in addition to improving its performance on the material and manufacturing process, we mainly take two kinds of compensation measures, passive compensation method and active compensation method.Passive compensation is fixed, and its role is limited.An active compensation method can be used for the size of the excitation current, that is, the size of the error tracking compensation and real-time satisfaction.This paper mainly focuses on active compensation research, which is divided into magnetic momentum compensation and electric potential compensation.Taking magnetic potential compensation as an example, the schematic diagram of the two-stage magnetic potential compensation current transformer is shown in Figure 3. where I is the main core, II is the auxiliary core, N1 and N2 are the primary and secondary windings, N4 is the detecting winding, N3 is the compensating winding, Z2 is the secondary load impedance, Zp is the leakage impedance of the compensating winding, Ee is the applied compensating power supply potential, and D is the measuring instrument.Magnetomotive force compensation can be summarized as adding a certain electromotive force to a certain impedance, generating a current through a certain winding, and providing the transformer with a magnetomotive force.Most of the active compensation methods used today are based on magneto-dynamic potential compensation.

Three-phase current transformer model
The three-phase current transformer model of the combined transformer is established in COMSOL to analyze the electromagnetic field current transformer model in the wide-range environmentally friendly combined transformers for metering.i.e., the outer diameter of the core is 90 mm, the inner diameter of the core is 70 mm, and the thickness of the core is 35 mm.The wire diameter of the secondary-side winding is set to be 2.25 mm, and the parallel winding with double windings is used.The load of the secondary side is set to 10 VA, and the frequency of the primary-side current is set to 50 Hz.The measurement errors brought about by the higher and lower currents are taken into account.The geometric model is shown in Figure 4 [9].Based on the wide-range three-phase current transformer wiring equivalent circuit, the Simulinkbased simulation model shown in Figure 5 is constructed.The measurement error of the wide-range current transformer is investigated under the effect of different influencing factors.The alternating current module is selected in Simulink software to generate the current required on the primary side of the transformer, and the secondary side load is represented by the RLC module connected to secondary side winding.The current module is utilized to measure the primary and secondary side currents of the transformer, and finally, the Fourier decomposition of this current is carried out by using the Fourier module.

Analysis of simulation results
As shown in Figure 6, the interphase interference of the magnetic current flow lines between the threephase current transformers is obvious, and the magnetic current flow lines in the core from the third phase to the first phase gradually change from almost all closed curves inside the core to broken nonclosed curves and extend to the outside of the core.Figure 7 clearly shows that at the same moment, the interactions between the leakage magnetic fields of the current transformers of the phases differ at different moments and three-phase current transformers arranged longitudinally can be used to minimize the effects of the leakage fields and interphase disturbances [10].This proves that the magnetic field is reasonable under the action of this environmentally friendly insulated gas current transformer.The simulation explores the current transformer error affected by the change of load on the secondary side.The results show that when the current increases in a certain range, the error of the current transformer decreases, but when the current increases to a certain extent, the iron core is saturated and the current transformer error will increase rapidly.The error is proportional to the size of the secondary load, and the larger the secondary load is, the larger the error is.The law is reflected in Figure 8.The simulation data are compared with the experimental platform test data to verify the correctness of the simulation results.The experimental platform data are tested ten times for each range and then averaged.Table 1 shows the simulation results of the wide-range environmentally friendly current transformer measured by the same method, taking the different ratios of the primary side current to the rated current as the nodes, measuring the current transformer error before and after the compensation, and comparing with the experimental values.It is obvious from Table 1 that, the ratio of the difference between the errors of the compensated ratio accounted for the experimental data is not more than 18%, and the angular difference of the ratio is not more than 15.5%, proving the correctness of the active compensation.The rated current accounted for the increase in the ratio of the error reduction rate after compensation is from high to low, with the error reduction rate of the difference of the lowest 75% and the highest 88.8%.The angle difference of the error reduction rate of 91.5% is the lowest, and 98.9% is the highest, proving the effectiveness of the active compensation.There is an error between the simulation data and the experimentally measured data, which may be because the experimental environment is not the same as the simulation environment, or the simulation model did not achieve a one-to-one reduction of the physical object when it was built, and the current simulation results meet the requirements of 0.2S level accuracy of the current transformer for metering as stipulated in GB/T 22071.1-2018.From the perspective of theoretical simulation, it illustrates the feasibility of wide-range current transformers that can improve the range and measurement flat frequency range under the condition of ensuring their measurement accuracy.

Conclusion
This paper carries out the wide-range measurement accuracy simulation verification of the environmentally friendly current transformer, analyzes the working performance of the environmentally friendly current transformer based on the simulation results of the measurement error, and obtains the following conclusions: (1) The wide-range environmentally friendly current transformer is just as reasonable as the conventional current transformer, whose error characteristics are affected by changes in the magnetic field of each phase and the size of the load on the secondary side, proving its reasonableness.
(2) The simulation results of the wide-range environmentally friendly current transformer show that it can effectively reduce the measurement errors of the specific and angular differences at the 0.2S level of metrology standard after active compensation, which proves its accuracy.

Figure 1 .
Figure 1.The actual structure of the current transformer.

Figure 2 .
Figure 2. Equivalent circuit of the current transformer.

Figure 3 .
Figure 3. Principle of magnetic potential compensation current transformer.

Figure 4 .
Figure 4. Longitudinal arrangement of three-phase current transformers.

Figure 8 .
Figure 8. Variation of conventional current transformer error with secondary side loading.

Table 1 .
Error data before and after active compensation.