Wide-Band Characteristic Analysis and Compensation Research of Electromagnetic Current Transformer

Abstract

In order to realize the wide frequency applicability of the electromagnetic current transformer in a ‘double high’ power system, the equivalent circuit model of the electromagnetic current transformer under wide frequency is established. The complex permeability method is used to obtain the excitation impedance value on the basis of the existing core parameters. Secondly, according to the equivalent circuit of the current transformer in the broadband domain, the error transfer function of the electromagnetic current transformer is derived. Through simulation calculation, the ratio difference and angle difference in the electromagnetic current transformer at 50 Hz–3000 Hz are obtained. The correctness of the theoretical analysis and simulation model is verified by comparing it with the existing model and measurement. The simulation and test results show that the electromagnetic current transformer has good linearity when the frequency is in the frequency range of 50 to 650 Hz. When the frequency exceeds this frequency, the ratio difference and angle difference in the current transformer will not reach the accuracy standard, which indicates that it is difficult to accurately measure the high frequency current. Aiming at the correlation of frequency characteristics, this paper proposes a method of optimizing parameters, which provides a certain reference for the error compensation and structural design of electromagnetic current transformers.

1. Introduction

In recent years, the proportion of nonlinear loads in the distribution network has continued to rise, resulting in a large number of harmonics of multiple frequencies flooding into the system, causing serious harmonic pollution. At present, as the mainstream electromagnetic transformer in the distribution network, the current transformer mainly uses the electromagnetic coil to realize the signal conversion. This kind of equipment is very sensitive to harmonic interference, and it is easy to make the transformer produce measurement deviation. This measurement error will cause a chain reaction, which will seriously affect the accuracy of subsequent equipment control, action execution, and measurement based on transformer data.

As the core component of the electric energy metering system, the electromagnetic current transformer plays an important role in smart meters and electronic metering devices. The transmission performance of the transformer under different signal conditions will have a direct impact on the measurement results of the energy meter, which in turn affects the accuracy of the energy measurement. In recent years, with the continuous development of the power system, various power semiconductor devices and their converter devices have been widely deployed in the power system, resulting in the continuous deterioration of power quality [1,2,3]. The problem of electric energy measurement accuracy under non-power frequency complex signals needs to be solved urgently.

Error is the core index to measure the performance of the electromagnetic current transformer. It is mainly affected by the excitation characteristics of ferromagnetic materials and the structure of equipment. Together, these factors determine the measurement accuracy of the transformer. Due to the continuous friction between magnetic domains, the iron core will produce a hysteresis effect and cause hysteresis loss during the magnetization process so that the magnetic field intensity and the magnetic induction intensity show a multi-valued nonlinear correlation [4]. In essence, when the iron core constructs an alternating magnetic flux, the instantaneous power loss that overcomes the magnetic domain steering is the hysteresis loss, and its size is related to the operating frequency. When the frequency changes, the hysteresis loss changes, which will inevitably affect the hysteresis loop and then act on the core excitation characteristics.

At present, although electromagnetic current transformers are widely used in power systems, related research is still insufficient for the transmission characteristics of high-frequency signals. In contrast, many achievements have been accumulated in the field of capacitive voltage transformers, Rogowski coils, and industrial current transformers [5,6,7]. Under the condition of the fundamental wave (50 Hz), the electromagnetic current transformer exhibits high measurement accuracy, conforming to its specified accuracy class with typically negligible ratio and phase errors. However, its performance degrades significantly in the presence of harmonics, and the influence of harmonics on its measurement accuracy needs to be further explored.

Reference [8] only deduced the current transformer (CT) measurement error from the theoretical formula and did not verify the analysis results by simulation. In Reference [9], the CT high-frequency equivalent model was constructed experimentally, but the simulation results showed that the output did not meet the expectations. Reference [10] studied the frequency characteristics of industrial current transformers. By improving the signal source device, the excitation signal with more abundant spectrum components can be output. At the same time, high-precision synchronous sampling technology is used to realize the accurate synchronous acquisition of the primary and secondary side signals of the current transformer. After obtaining the sampling data, through systematic processing and analysis, the current transformer passband range is successfully determined. Based on the research results, the literature further proposes a series of optimization methods for the actual demand for the problem of bandwidth expansion. Reference [11] proposed a new measurement method for measuring the transmission characteristics of the input current fundamental wave superposition harmonic test. The experimental test focuses on the frequency characteristics near the power frequency, and the ranges of some data analyses are only extended to seven times the original.

Compared with the existing studies, this paper presents a broadband equivalent circuit model for electromagnetic current transformers that explicitly addresses the frequency-dependent excitation impedance via complex permeability. Unlike existing models, our approach is validated over a wide range (50–3000 Hz), showing significantly higher accuracy beyond 300 Hz. The systematic analysis of parameter impacts offers practical insights into CT error compensation and structural design [12].

2. Wide-Band Modeling of Electromagnetic Current Transformer

Under the power frequency (50 Hz) condition, the equivalent circuit model of the electromagnetic current transformer mainly includes the leakage inductance, leakage resistance, and excitation impedance of the primary and secondary sides. The corresponding equivalent circuit is shown in Figure 1 [13], where $R_1$ and $L_1$ are the primary winding resistance and leakage inductance; $R_2$ and $L_2$ are the secondary winding resistance and leakage inductance; and $R_m$ and $L_m$ represent the core loss resistance and magnetizing inductance, respectively.

In the power frequency operation state, the magnetic coupling effect of the electromagnetic coil inside the CT is dominant [14]. At this time, the stray capacitance between the windings and the stray capacitance to the ground are very small, and the influence on the operation of the equipment can be neglected. However, as the current frequency gradually increases, the influence of the ground capacitance of the primary and secondary windings of the CT and the stray capacitance between the windings on the measurement accuracy is more and more significant, which cannot be ignored. The primary current of the instrument’s current transformer is at the ampere level, the secondary current is at the milliampere level, and the number of secondary side turns is more than 2000 turns. At this time, the distributed capacitance between the secondary coils is about tens to hundreds of micrometers [15]. In the low frequency band of 1~200 Hz, the distributed capacitance can be ignored, but in the middle frequency and high frequency band, its influence cannot be ignored, which will have a significant effect on the measurement. Considering that the number of turns of the primary side winding is relatively limited, its influence can be ignored. Based on the power frequency equivalent circuit, the inter-layer capacitance is added to characterize the inter-winding capacitance effect, and the high-frequency equivalent model shown in Figure 2 is constructed.

Considering the small number of turns and thick wire diameter of the CT primary side coil, its distributed capacitance is ignored [16]. The simplified CT harmonic equivalent circuit is converted to the primary side, and the converted broadband equivalent circuit is shown in Figure 3.

In Figure 3, ${L_1}^{\prime }$ and ${R_1}^{\prime }$ are the primary winding leakage inductance and DC resistance (converted to the secondary side), $L_2$ and $R_2$ are the secondary winding leakage inductance and DC resistance, $R_m$ and $L_m$ are the excitation resistance and magnetizing inductance of CT, C is the secondary side stray capacitance, and R is the equivalent load of the current transformer.

In the designed electromagnetic current transformer, $L_1$, $L_2$, $R_1$, and $R_2$ are all fixed constants. However, the equivalent resistance $R_m$, which is related to the core loss, and the magnetizing inductance $L_m$, which is affected by the excitation characteristics of the ferromagnetic material, are not constant but fluctuate with the change in the saturation degree of the core [17]. Therefore, the key to obtaining the component parameters of the broadband equivalent circuit of the current transformer is to obtain the broadband parameters of the excitation impedance.

3. Study on the Frequency Characteristics of Complex Permeability of Ferromagnetic Materials

When analyzing the broadband response characteristics of current transformers, researchers often focus on the influence of distributed capacitance but pay less attention to the dynamic characteristics of excitation impedance changing with frequency. In fact, in broadband high-precision measurement applications, the frequency dependence of the excitation impedance is a key factor that cannot be ignored. This nonlinear characteristic is essentially derived from the inherent properties of the excitation process of ferromagnetic materials. The analysis of the broadband characteristics of the current transformer needs to focus on two key parameters. One is that the permeability μ is a key parameter to measure the magnetic properties of ferromagnetic materials, which reflects the magnetization ability and magnetic flux conduction efficiency of the material under the action of the magnetic field. The second is the core loss angle θ, which refers to the phase delay of the magnetic induction intensity B relative to the magnetic field intensity H due to the hysteresis effect and eddy current effect of the ferromagnetic material during the alternating magnetization process. This angle reflects the energy loss characteristics of the core. Both H and B can be described by Formulas (1) and (2).

$$H=H_{\mathrm{m}}\sin \omega t=H_{\mathrm{m}}{\mathrm{e}}^{\mathrm{j}\omega t}$$

(1)

$$B=B_{\mathrm{m}}\sin (\omega t-\theta )=B_{\mathrm{m}}{\mathrm{e}}^{\mathrm{j}(\omega t-\theta )}$$

(2)

In the formula, $\omega$ is the angular frequency, $H_m$ is the magnetic field intensity amplitude, and $B_m$ is the magnetic flux density amplitude.

The complex permeability of ferromagnetic materials in a period can be expressed as follows:

$$\mu ={\displaystyle \frac{B}{H}}={\displaystyle \frac{B_{\mathrm{m}}}{H_{\mathrm{m}}}}{\mathrm{e}}^{-\mathrm{j}\theta }={\mu }^{\prime }-\mathrm{j}{\mu }^{″}$$

(3)

In the formula, the real and imaginary parts of the complex permeability are, respectively,

$${\mu }^{\prime }={\displaystyle \frac{B_m\cos \theta }{H_m}}$$

(4)

$${\mu }^{″}={\displaystyle \frac{B_m\sin \theta }{H_m}}$$

(5)

The tangent of the core loss angle is

$$\mathrm{tg}\theta ={\displaystyle \frac{{\mu }^{″}}{{\mu }^{\prime }}}$$

(6)

At present, the core of the electromagnetic transformer is a laminated structure, and its thickness is far less than the width and length, so only the one-dimensional flow of the current is considered, and the following equation can be obtained:

$${\displaystyle \frac{{\partial }^2{H}_Z}{\partial x^2}}=j\omega {\mu }_0{\mu }_r(\sigma +j\omega \epsilon )H_z=k^2{H}_Z$$

(7)

where ω is the angular frequency of the excitation signal ${\mathrm{\mu }}_{\mathrm{r}}$; is the relative permeability; ε is the complex permittivity; σ is the core conductivity; ${\mathrm{H}}_{\mathrm{Z}}$ is the component of the magnetic field intensity in the z direction; ${\mathrm{\mu }}_0$ is the vacuum permeability; and k is the propagation constant, and its calculation formula is

$$k=(1+j)\sqrt{{\displaystyle \frac{\omega \sigma {\mu }_0{\mu }_r}{2}}}$$

(8)

In the formula, $\sigma$ is the core conductivity.

The calculation formula of the magnetic field intensity on the core surface is

$$H={\displaystyle \frac{k\mathrm{\Phi }\cosh (k\frac{b}{2})}{2{\mu }_0{\mu }_{r}h\sinh (k\frac{b}{2})}}$$

(9)

In the formula, b represents the thickness of the silicon steel sheet; H represents the magnetic field intensity on the surface of the iron core; h is the width of the lamination; and $\mathrm{\varnothing }$ denotes the magnetic flux with a cross-sectional area of bh. Therefore, the spatial average magnetic flux density B in the z direction is related to the magnetic flux passing through the cross-sectional area, and the relationship is

$$\mu ={\displaystyle \frac{\overline{B}}{H}}=k_{Fe}{\mu }_r{\displaystyle \frac{\tanh (\frac{kb}{2})}{\frac{kb}{2}}}$$

(10)

In the formula, ${\mathrm{k}}_{\mathrm{F}\mathrm{e}}$ is the core lamination coefficient, ${\mathrm{k}}_{\mathrm{F}\mathrm{e}}=\mathrm{b}/(\mathrm{b}+∆)$; Δ is the thickness of the insulating layer. The relative permeability ${\mathrm{\mu }}_{\mathrm{r}}$ is close to the initial permeability ${\mathrm{\mu }}_{\mathrm{i}}$ of the iron core, and ${\mathrm{\mu }}_{\mathrm{i}}$ is defined as the relative permeability at zero magnetic field strength, which is

$${\mu }_r\approx {\mu }_i={\displaystyle \frac{1}{{\mu }_0}}\underset{H\to 0}{\lim }{\displaystyle \frac{B}{H}}$$

(11)

There are

$$\mu ={\displaystyle \frac{\overline{B}}{H}}=k_{Fe}{\mu }_i{\displaystyle \frac{\tanh (\frac{kb}{2})}{\frac{kb}{2}}}$$

(12)

Based on the simulation model, the real part ${\mathrm{\mu }}^{\prime }$ imaginary part ${\mathrm{\mu }}^{″}$, and its amplitude $\left|\mathrm{\mu }\right|$ of the relative complex permeability of the core and the curve of the relationship between the loss angle of the core and the frequency change are shown in Figure 4, Figure 5 and Figure 6, and the specific parameters used in the simulation model are shown in

Table 1. Core parameters.

Parameter Name and Symbol	Numerical Value
Core thickness b/m	0.0634
Insulation layer thickness ∆/mm	1.7
Core resistivity  $\mathrm{\rho }/\left(\mathrm{\Omega }·\mathrm{m}\right)$	$1.72 \times {10}^{-7}$
Conductivity of iron core  $\mathrm{\sigma }/(\mathrm{S}·{\mathrm{m}}^{-1})$	$5.6 \times {10}^7$
The relative permeability of iron core  ${\mathrm{\mu }}_{\mathrm{i}}/(\mathrm{H}·\mathrm{m})$	0.03212
Magnetic flux path length L/M	0.78
Primary side winding thickness  ${\mathrm{d}}_1/\mathrm{m}\mathrm{m}$	0.62
Secondary winding thickness  ${\mathrm{d}}_2/\mathrm{m}\mathrm{m}$	12.58
Winding height h/mm	620
The average winding turn length p/mm	100
Vacuum permeability  ${\mathrm{\mu }}_0/(\mathrm{H}·{\mathrm{m}}^{-1})$	$1.26 \times {10}^{-6}$

.

From the simulation results of Figure 4, Figure 5 and Figure 6, it can be seen that the real part and amplitude of the relative permeability decrease with the increase in frequency. The imaginary part of the relative permeability increases with the increase in frequency in the range of 0~1000 Hz and decreases with the increase in frequency when it exceeds 1000 Hz.

4. Frequency Characteristic Analysis of Current Transformer

4.1. Mathematical Model of the Frequency Characteristics of Current Transformers

Usually, the error of the current transformer mainly covers the ratio difference and the phase difference. The following will elaborate on the definition of these two types of errors.

The so-called ratio difference refers to the error caused by the difference between the actual current ratio and the rated current ratio in the measurement process of the current transformer. The so-called phase difference refers to the phase difference between the primary and secondary current phasors of the current transformer [18].

Ratio error GB1208-87: The definition of the ratio error is as follows [19]:

$$e\%={\displaystyle \frac{K{I}_s-I_p}{I_p}}\times 100$$

(13)

In the formula, $I_s$ and $I_p$ are the primary and secondary side currents, respectively, and the rated ratio $K=N_s/N_p$; $N_{\mathrm{p}}$ and $N_s$ are the number of turns of the primary and secondary windings, respectively.

The definition of the phase error in GB1208-87 is as follows:

$$\epsilon ={\alpha }_s-{\alpha }_p[\mathrm{deg}]$$

(14)

In the formula, ${\alpha }_s$ is the secondary current phase angle, and ${\alpha }_p$ is the primary current phase angle.

According to the CT broadband equivalent circuit established above (as shown in Figure 3), the transfer function expression of CT can be derived:

$$G(s)={\displaystyle \frac{I_2(s)}{I_1(s)}}={\displaystyle \frac{Z_m}{Z_m+Z_{2L}}}\cdot {\displaystyle \frac{1/sC}{1/sC+R}}$$

(15)

In the formula, $Z_{2L} = \left({\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$sC$}\right.}// R\right)+\left(R_2 + s{L}_2\right)$ is substituted into Equation (15) and simplified to obtain the transfer function of CT:

$$G(s)={\displaystyle \frac{R_m+s{L}_m}{(RCs+1)[(L_m+L_2)s+(R_m+R_2)]+R}}$$

(16)

When the CT material and winding mode are unchanged, the stray capacitance of the primary and secondary sides and the capacitance of the secondary side winding to the ground are fixed in the frequency range of the research current [19]. Therefore, as long as the excitation impedance parameters of the transformer are obtained, the amplitude–frequency characteristic curve can be obtained by bringing them into Equation (18). According to the amplitude–frequency curve, the ratio difference and angle difference in the transformer can be obtained.

In the calculation of transformer parameters, the value of excitation impedance is related to the real and imaginary parts of complex permeability [20], and the corresponding relationship is shown in Equations (17) and (18):

$$Lm={\displaystyle \frac{N^2{\mu }^{\prime }S}{l}}$$

(17)

$$Rm={\displaystyle \frac{\omega N^2{\mu }^{″}S}{l}}$$

(18)

According to the simulation model, the frequency response curve of the excitation impedance is drawn as shown in Figure 7 and Figure 8.

As the frequency increases, the eddy current effect will increase, resulting in a decrease in the excitation inductance in the transformer coil. At the same time, at high frequencies, the imaginary part of the complex permeability decreases faster than the frequency increase rate, resulting in a decrease in the excitation resistance as the frequency increases. The equivalent circuit parameters of the current transformer are shown in

Table 2. Parameters of current transformer equivalent circuit.

Parameter	Values
Transformer ratio	1:300
Secondary distributed capacitance C/pF	60
Secondary leakage inductance  $L_2/H$	0.73
Secondary leakage resistance  $R_2/\Omega$	0.08
Accuracy level	0.2
Rated load	20

.

According to the corresponding calculation formulas of Equations $R_m$ and $L_m$, the broadband response curve of the transformer at 50–3000 Hz can be obtained by introducing the transfer function Equation (16) derived from the broadband equivalent circuit, as shown in Model 1.

The accuracy level of the current transformer in this study is 0.2, which, according to the standard (GB 1208-2006), means its maximum permissible ratio error is ±0.2% at the rated current and burden. From the above analysis, it can be seen that when the frequency is in the range of 50–650 Hz, the ratio difference is controlled within −0.2%, which meets the accuracy level requirements. In the frequency band of more than 1000 Hz, the error increases significantly. When the frequency reaches 3000 Hz, the ratio difference has reached −0.61%, and the angle difference has reached −5.3°, which is much larger than the error level under the working condition. At this time, the ratio difference and angle difference cannot meet the accuracy requirements, indicating that the current transformer is difficult to accurately measure the high-frequency current.

4.2. Comparative Analysis of the Experiment

Based on the above theoretical analysis, in order to study the variation law of the current transformer ratio difference and phase angle under different frequency signals, the electromagnetic current transformer, which is the same as the simulation model, is selected as the test object, and the programmable power supply was used to apply a primary current signal, the amplitude and frequency of which could be accurately adjusted (current resolution: 0.1%, frequency resolution: 0.1 Hz). In order to obtain accurate reference datum, the standard inductive voltage divider (ratio error <±2 × 10⁻⁶, calibration uncertainty: 5 × 10⁻⁶, and k = 2) and the electromagnetic current transformer to be tested are connected in parallel to the test circuit. In the process of experimental data acquisition, a high-precision digital lock-in amplifier is used to record the output characteristics of the measured transformer under different working conditions in real time so as to calculate the ratio difference and angle difference in the CT to be tested (the specific test results are shown in

Table 3. Measured test data of ratio error and phase error at different frequencies.

Current Frequency/Hz	Ratio Difference/(%)	Angle Difference/(°)
50	−0.1785	−0.1457
100	−0.1786	−0.1693
150	−0.1744	−0.2085
200	−0.1684	−0.2556
250	−0.1639	−0.2948
300	−0.1577	−0.3576
350	−0.1487	−0.4361
400	−0.1438	−0.5145
450	−0.1475	−0.5694
500	−0.1568	−0.6479
550	−0.1683	−0.7028
600	−0.1775	−0.7891
700	−0.1879	−0.9225
800	−0.1909	−1.0716
900	−0.1954	−1.1814
1000	−0.2022	−1.2991
2000	−0.4107	−2.3584
3000	−0.6032	−3.5432

). To quantitatively assess the reliability of the measurement results, we conducted five repeated measurements at each test frequency point. Based on the dispersion of the measured values, the experimental standard deviation was calculated using the Class A evaluation method. The lengths of the error bars in Model 1 correspond to the measurement standard deviations at each frequency point, reflecting the repeatability of the measurement results, the field experiment diagram is shown in Figure 9.

When analyzing the broadband characteristics of current transformers, the existing models often ignore the variation in excitation impedance with frequency [21]. However, for high-precision current transformers with broadband characteristics, the frequency characteristics of the excitation impedance need to be taken into account.

The derived error frequency curve (Model 1) and the existing model error curve (Model 2) are compared with the measured data, as shown in Figure 10 and Figure 11. The results show that, in the low frequency range of 50–300 Hz, the trend of the three curves is basically consistent. In the low frequency range of 50–300 Hz, the maximum deviation of the ratio difference between Model 1 and the measured value is 0.03%, and the angle difference deviation is 0.3°, which is better than 0.06% and 0.5° of Model 2, which verifies the accuracy of the complex permeability modeling. When the frequency exceeds 300 Hz, the deviation between Model 2 and the measured value increases significantly, while the deviation between Model 1 and the measured data is still controlled within 0.05% because of the broadband characteristics of the core hysteresis loss. This shows that the existing model does not take into account the complex characteristics of permeability at high frequencies, resulting in the insufficient prediction accuracy of high-frequency error, while this model is closer to the actual operating conditions.

5. Frequency Characteristic Improvement and Frequency Band Broadening

In actual operating conditions, some parameters change due to the influence of the current transformer manufacturing process, winding process, and material selection difference [22,23,24,25]. Through the transfer function expression of the current transformer, it can be seen that its frequency characteristics are closely related to the excitation impedance and the secondary side coil parameters. These influencing factors are reflected in the above relationship, and the measurement error of the circuit transformer can be compensated by adjusting the relevant parameters so as to optimize its performance.

The influence of changing the excitation impedance value on the frequency characteristics of the current transformer is shown in Figure 12 and Figure 13. Through in-depth analysis of the experimental data of Figure 12 and Figure 13, it is found that reducing the excitation impedance parameter value can significantly expand the amplitude–frequency characteristic bandwidth and effectively improve the amplitude–frequency response performance. However, this same adjustment yields only a marginal improvement in the phase–frequency characteristic. Consequently, while the amplitude error is greatly reduced across a broader band, the phase error remains largely unchanged and becomes the dominant factor limiting the overall measurement accuracy at high frequencies.

Figure 14 and Figure 15 show the influence of the secondary winding parameter $Z_2$ on the frequency characteristics and working frequency band of the current transformer. The analysis results show that reducing the excitation impedance value has a significant effect on expanding the frequency band of amplitude–frequency characteristics and optimizing the amplitude–frequency characteristics but has a slight effect on the phase–frequency characteristics.

Affected by differences in the CT manufacturing process, winding process, and material properties in actual production, some parameters may change [26]. Through the analysis of the simplified high-frequency equivalent circuit of CT, it is found that the capacitance C of the secondary winding to the ground is the key factor affecting the accuracy of the CT measurement. In order to explore the influence of stray capacitance change on the CT ratio difference and angle difference, the simulation calculation is carried out. The results are shown in Figure 16 and Figure 17. The research shows that the influence of the secondary side winding on the ground capacitance change contrast difference and angle difference is consistent. With the increase in the capacitance parameter, the CT ratio difference and angle difference will increase accordingly. In addition, the higher the current frequency, the more significant the impact on the measurement error.

Through the above analysis, we can improve the frequency response performance of the current transformer and extend its effective working frequency band from many aspects. At the material and structural level, high permeability materials are selected to reduce the excitation impedance. By optimizing the parameters of the secondary side coil, the coil impedance is reduced. At the same time, the appropriate winding process is adopted to reduce the ground capacitance of the secondary side winding. In engineering application practice, the accurate adjustment of parameters can be realized by means of optimized design scheme. For example, the use of iron-based nanocrystalline alloy as the core material has the advantage of high initial permeability and is the ideal core material; optimizing the parameters of the secondary side coil can improve the winding process and adjust the wire diameter [27,28,29,30]. In addition, it can also consider building a compensation network, using hardware compensation, and using algorithm compensation to further improve its frequency characteristic performance.

6. Conclusions

Based on an in-depth analysis, the broadband equivalent circuit of the electromagnetic current transformer was established and effectively simplified. Utilizing this simplified model, the mechanisms governing the generation of ratio and phase errors in CT were thoroughly investigated, leading to the development of an accurate simulation model for analyzing its wide-frequency behavior.

The core of the proposed model lies in the precise representation of the excitation impedance, which is intrinsically linked to the complex permeability of the core material. The frequency-dependent values of the excitation impedance were calculated analytically, and their response curves were obtained via simulation, forming the basis for determining the CT’s error characteristics across the 50–3000 Hz frequency range.

Simulation results demonstrate that the CT maintains its specified 0.2 accuracy class within the 50–650 Hz range, with the ratio error effectively contained within −0.2%. However, beyond 1000 Hz, both the ratio and phase errors exhibit a pronounced increasing trend. At 3000 Hz, the ratio error deteriorates to −0.61% and the phase error reaches −5.3′, values that significantly exceed the permissible limits for accurate measurement, thereby highlighting the CT’s inherent limitation in measuring high-frequency currents.

The validity and advantage of the proposed model were unequivocally confirmed through experimental measurements. A direct comparison between the simulated error trends and the measured data revealed close agreement, proving that the model more accurately reflects actual operating conditions, particularly for high-order harmonics where conventional CTs exhibit substantial errors.

Furthermore, the parameter sensitivity analysis conducted with the simulation model provided critical insights for performance improvement. It was found that, while reducing the excitation impedance effectively broadens the amplitude–frequency bandwidth, its effect on improving the phase–frequency characteristic is limited. Consequently, a comprehensive optimization strategy—simultaneously reducing the secondary winding impedance and stray capacitance—is identified as essential for mitigating the dominant phase error and achieving optimal broadband performance. This systematic analysis offers valuable guidance for the error compensation and structural design of future wide-band CT.