Parameter Design of a Self-Generated Power Current Transformer of an Intelligent Miniature Circuit Breaker Based on COMSOL

Abstract

With the deep penetration of renewable energy and power electronic equipment, the overcurrent protection of an intelligent miniature circuit breaker faces new challenges. The electronic controller of an intelligent miniature circuit breaker is typically powered by the bus current rather than the phase voltage to ensure a robust overcurrent protection response under all conditions, including severe short-circuit faults. So, the performance of the current transformer serving as an energy harvesting unit and the corresponding direct current to direct current convention circuit is one of the critical issues due to the limited volume of an intelligent miniature circuit breaker. In this research, a finite element model of a current transformer for an intelligent miniature circuit breaker is constructed by COMSOL to evaluate the impact of the core material, the core size, and the number of coil turns on the energy harvesting capability of the current transformer. Meanwhile, the relationship between the output of the power supply and its design parameters is investigated by circuit simulation. As a result, a novel type of current transformer is proposed based on well-designed parameters. Finally, experimental tests have been conducted to verify the hysteresis characteristics, output characteristics, and energy harvesting effect. The results demonstrate that the hysteresis properties of the transformer align with the simulation results. The power supply can work with a minimum current of 8 amperes, which is 23.08% better than before.

1. Introduction

Distribution switch cabinets are generally used to install miniature circuit breakers to protect power grid terminals. Due to the limited installation area, noncontact current transformers (CTs) are commonly used to power these cabinets [1]. This approach provides a cost-effective solution, substantial power production, isolation from the primary circuit, and improved security. The power-acquisition approach mentioned is widely utilized [2]. Nevertheless, there are several issues associated with the utilization of CTs. The magnitude of the line current influences the energy harvesting effect. Insufficient line current results in a dead zone occurring at the lower boundary of energy harvesting [3,4]. Nevertheless, the restricted capacity of miniature circuit breakers poses a difficulty in implementing a conventional backup power source. Additionally, when the current flowing through the line exceeds a certain threshold, the magnetic core rapidly reaches a condition of deep saturation, leading to an uncontrollable output voltage [5,6]. When the energy obtained by the current transformer is insufficient, the reliability of the overcurrent protection of the small circuit breaker will drop sharply, causing huge safety hazards and even causing fire [7,8].

The following enhancement strategies are suggested to minimize the dead zone at the lower threshold of energy harvesting. Ning Jie et al. [9] proposed an energy acquisition control method for impedance-controlled current transformers. The power is increased by adjusting the secondary side of the CT as a capacitive impedance to excite the core. Cheng Zhiyuan et al. [10] A resonant compensation CT energy extraction method that uses a compensation capacitor to generate a parallel resonance with the excitation branch, thereby increasing its equivalent impedance and thereby increasing the energy extraction power, was used to solve the problem of insufficient energy extraction at low current. Nevertheless, additional circuit elements, such as coil winding, drive control circuit, and battery, present a significant obstacle to the design’s downsizing. Article [11] proposed a design method for an intelligent circuit breaker using a battery power supply, which realizes the continuous operation of the RTC clock after the external power supply of the circuit breaker is interrupted (or other functions are realized). Due to the limitation of the volume of the intelligent miniature circuit breaker, it is impossible to use a larger battery or supercapacitor, and a smaller battery or capacitor cannot guarantee that it can provide a stable current-driven release action. In addition, using batteries and supercapacitors requires regular replacement or charging, and complex power management schemes are required to ensure the reliability of the circuit breaker protection function, increasing the scheme’s difficulty. In addition, long delay overload protection takes a long time, which is also a test for the capacity of batteries or supercapacitors. The self-generating power supply scheme can meet the long-term power supply demand without charging or replacing components, which is a more direct solution.

When the current flowing down the line goes over a specific limit, the core of the CT enters a state of saturation. This causes distortion in the output voltage waveform of the coil’s secondary side and dramatically reduces or eliminates the output power [12]. The following enhancement strategies are suggested to address the core saturation issue. Lin Jie et al. [13] modified the magnetic core by increasing the air gap, which resulted in the separation of flux lines and a decrease in the effective cross-sectional area of the core. This modification improved the reluctance, delayed the magnetization process, and increased the average magnetic circuit length of the core. When the current changed widely, the core’s saturation degree decreased. Jinhua Wang et al. [14] harvested energy and desaturated cores with two secondary coils. When the magnetic core’s current hits its maximum, the supplementary coil starts current flow, reducing saturation and increasing the line’s maximum current. By studying how air gap size affected magnetic core material initial permeability, Chi et al. [15] chose magnetic core materials and air gap architectures with a more extensive linear range. The discharge circuit no longer oversaturated the CT when the primary current was high. The above study is practical; however, pursuing a high saturation current level makes small current-level energy harvesting harder.

CT modeling uses two main methods: numerical and finite element simulation. Model accuracy depends on hysteresis description accuracy. Hysteresis underpins the numerical model. Based on the Preisach principle, Zhao Xiaojun et al. [16,17,18] simulated the nonlinear response of the system by constructing a combination of multiple binary oscillation elements. They built a hysteresis model based on Preisach. The model uses control parameters to control the threshold and weight of each Preisach element and the interaction strength between them. This model shows the system’s nonlinear response with multiple binary oscillation parts. The control parameters determined the threshold, weight, and interaction strength of each Preisach element, ensuring great simulation accuracy. Model parameter identification and simulation computations are complicated. Liu R. and Chen Hao created the energetic hysteresis model using energy conservation and electromagnetics [19,20]. Although this basic model is computationally efficient, it cannot account for nonlinear processes. To produce accurate simulation results, models must work together. Based on the simplified Landau-Lifshitz-Gilbert equation, Tanaka H and Yan Peng et al. [21,22] obtained the hysteresis model of the LLG equation describing the magnetization dynamics. The model has a clear physical meaning, few parameters, and simple identification. However, it needs to be solved by numerical analytical method, which has a large amount of calculation, and the description of the hysteresis loop of low magnetic density is not accurate enough. However, the numerical analytical method needs complex computations and cannot adequately describe the hysteresis loop with low magnetic density.

The usage of finite element simulation software is prevalent in scientific research and practical engineering due to its accurate solution function and ability to perform multi-physics coupling calculations [23,24]. Tianwei Gao et al. [25] used the finite element method to simulate and evaluate the CT in order to address the issues of magnetic core saturation in the CT’s online energy supply and the challenge of measuring the output power of the magnetic core. A. Torkamani et al. [26] analyzed partial saturation occurrence in a core balance current transformer using the finite element method. The finite element simulation model offers significant advantages over the numerical model regarding spatial resolution, material nonlinearity, boundary condition processing, visualization, and post-processing.

The main work and contributions of this paper are as follows: (1) The working characteristics of the self-generating power current transformer are analyzed, and the theoretical relationship between the output characteristics and the design parameters is established. (2) The finite element model of the transformer based on COMSOL is built to study the influence of iron core material, iron core size, and coil turns on the energy extraction ability of the current transformer, and the optimal parameter combination is determined. (3) The prototype is made, and the energy extraction experiment is carried out to verify the model’s validity.

2. Analysis of Working Characteristics of Self-Generating Power Supply CT

2.1. Working Principle and Equivalent Circuit

The self-generating power supply CT is a unique transformer that utilizes the principle of electromagnetic induction to turn current into energy [27]. Figure 1 depicts the fundamental operational concept. The primary side winding is connected to the AC power supply I_ac, generating an alternating magnetic field in the magnetic core, an induced electromotive force e₂ on the secondary side, and an induced current in the secondary circuit.

During regular operation, the excitation of the primary side winding can be considered an ideal current source, while the impedance of the primary winding can be effectively disregarded. Similarly, the leakage reactance of the secondary side is a constant minimum value that can also be approximately ignored [28]. As stated in Equation (1), the voltage u₁ is equivalent to the induced electromotive force e₁ of the primary winding. Likewise, the secondary induced electromotive force e₂ is equivalent to the multiplication of the current on the secondary side and the overall impedance of the secondary side.

$$\left\{\begin{array}{l}{e}_1=u_1\hfill \\ e_2=I_2{Z}_0=I_2\left(R_{\mathsf{\Sigma }}+j\omega L_0\right)\hfill \end{array}\right.$$

(1)

where u₁ and u₂ are the primary and secondary side terminal voltages, respectively, R_Σ is the total equivalent resistance of the secondary side, L₀ is the total equivalent inductance of the secondary side, $\omega$ is the angular frequency, and e₁ and e₂ are the induced electromotive force generated by the main flux on the primary and secondary side windings, respectively. Figure 2 illustrates the equivalent circuit of the CT. I_ac is the primary side constant current source, and L_δ and R_h are the equivalent hysteresis loss and eddy current loss branches.

2.2. Self-Generated Power CT Output Characteristics

The output power represents the immediate manifestation of the energy harvesting phenomenon. When examining the output characteristics of the CT, the primary focus is on the elements that influence the output power. Hence, the vector relationship of the CT is simplified by disregarding the iron loss and leakage inductance of the secondary coil [29]. Figure 3 illustrates both the original and simplified vector relationships.

According to the electromagnetic induction law and the simplified vector relationship of the current transformer, when the primary side input is a sine wave, the secondary side terminal voltage U2 of the self-generating power supply current transformer is shown in Equation (2).

$$U_2=E_2=\sqrt{2}\pi f{N}_2{\varphi }_m=\frac{2\pi f\mu S{I}_e{N}_2\eta }{l}$$

(2)

where E₂ is the induced electromotive force of the secondary side, I_e is the excitation current, μ is the permeability, f is the power frequency, and l is the average magnetic circuit length. ϕ_m is the maximum flux, and l is the average magnetic circuit length. η is the lamination factor of the iron core. N₂ is the number of turns of the secondary side coil, and S is the cross-sectional area of the core.

When the current transformer of the self-generating power supply is determined, the parameter permeability μ, the power frequency f, the average magnetic circuit length l, and the lamination coefficient η of the iron core are all specific values. The coefficient k is used to simplify the calculation, and the simplified Equation (3) is shown.

$$U_2=E_2=k{I}_e{N}_2$$

(3)

According to Ohm’s law, the output power P_out of the self-generating power supply current transformer can be obtained, as shown in Equation (4):

$$P_{\mathrm{out}}=\frac{U_2^2}{R_0}=\frac{{\left(k{I}_{\mathrm{e}}{N}_2\right)}^2}{R_0}=\frac{I_1^2{R}_0{k}^2{N}_2^2}{R_0^2+k^2{N}_2^4}$$

(4)

For the limit of the above equation, Equation (5):

$$P_{\mathrm{out}}\le \frac{k{I}_1^2}{2}=\frac{\pi \mu fS\eta I_1^2}{l}=P_{\max }$$

(5)

The output power P_out reaches its maximum value P_max only when R₀ = kI₁₂. From Equation (5) of the self-generating power supply CT, we can draw the following conclusions:

The output power of the self-generating power supply reaches its maximum value, P_max, when the CT’s primary side current and the load impedance remain unsaturated. When the primary side current is determined and the grid frequency is constant, increasing the permeability μ (using high-permeability materials), the lamination coefficient η of the magnetic core, the cross-sectional area S of the magnetic core, and reducing the average magnetic circuit length l can increase the output power of the self-generating power supply CT. The line’s working condition determines the size and frequency of the primary side current excitation, making artificial regulation impossible. So, the next step in designing the self-generating power supply CT’s parameters only looks at the core material, the average length of the magnetic circuit, the number of turns in the coil, the core’s cross-sectional area, and the core lamination coefficient. It is optimized to increase output power.

3. Construction of Finite Element Model of Self-Generated Power CT of Miniature Circuit Breaker

3.1. Geometric Model Creation

In order to facilitate modification of the geometric modeling structure of the simulation model at a later stage, it is necessary to designate specific geometric parameters of the model as variables.

Table 1. Geometric model parameters of self-generated power CTs.

Variable Name	Expression	Unit	Description
lout	lout [mm]	mm	Iron core outer diameter length
lin	lout-4.4	mm	Core inner diameter length
Wout	Wout	mm	Core outer diameter width
Win	Wout-4.4	mm	Core inner diameter width
H	0.35∙η	mm	Core thickness
NP	NP	turn	Primary side coil turns
NS	NS	turn	Secondary side coil turns
H	H	piece	Number of iron core laminations
r	KN∙NS	$\Omega$	Coil resistance

gives the precise characteristics, with N_S representing the number of coil turns and K_N indicating the matching coefficient of internal resistance and coil turns.

Figure 4 depicts the geometric model using the variable parameters specified in Table 1. The geometric characteristics of the magnetic core can be altered by adjusting variables such as the inner diameter, outer diameter length, inner diameter, outer diameter breadth, thickness, and other factors. In order to enhance the spatial configuration of the self-generating power supply, the design utilizes a back-shaped core structure by encasing the CT on a conductive sheet to induce electrical power. The coil domain replicates the multi-turn coil structure by uniformly dispersing the wire based on the spatial volume within the coil domain. The wire’s radius is uniform. The software’s intrinsic material attributes encompass the wire’s resistivity and relative dielectric constant. The wire is composed of copper material.

To simulate the natural environment accurately and improve the compatibility and accuracy of the model, an air domain is included around the geometric model of the self-generating power supply CT, as depicted in Figure 5. This addition ensures a more precise simulation of the magnetic field distribution.

3.2. Construction of Circuit Outside the Model and Setting of Boundary Conditions

The COMSOL finite element model lacks the power supply stimulation from the external circuit and the equivalent connection load on the secondary side. Thus, it is imperative to construct the external circuit of the model in order to establish a comprehensive circuit connection link before conducting the model simulation and calculation analysis. The equivalent circuit reveals the internal circuit relationship between the excitation current branch and the primary and secondary windings of the CT, indicating the coupling between them. Furthermore, the circuit serves as the primary external connection for a similar model. Figure 6 depicts the external circuitry of the finite element model for the self-generating power CT. In the figure, I_ac represents the power frequency sinusoidal current source. R₁ represents the resistance on the primary side, with a value of zero ohms (just the circuit connection is shown). R₀ represents the equivalent load on the secondary side.

The node number, denoted as P (0) in the diagram, indicates the circuit’s connection relationship and the direction of the current entering and exiting the component. The precise numerical value indicates the presence of a circuit connection relationship. The symbol “P” denotes that the electrical current enters the component from this particular node, while the letter “N” signifies that the current exits the node.

To enhance the precision of the simulation, the model employs the secondary curl unit to discretize the magnetic vector potential and applies Ampere’s law constraint throughout the whole model domain. The self-generating power supply CT simulation incorporates the Jiles–Atherton model for the hysteresis module. The constitutive connection includes the conduction model, defined by the ‘conductivity’, and the dielectric model, which is determined by the ‘relative dielectric constant’. The mathematical representation is presented in Equation (6), where the conductivity σ and the relative dielectric constant ε_r are obtained from the material.

$$\left\{\begin{array}{l}{J}_c=\sigma E\\ D={\epsilon }_r{\epsilon }_{0}E\end{array}\right.$$

(6)

The coil module chooses the specific coil domain within the magnetic field interface. The coil wire type determines the uniform multi-turn configuration. The coil type determines its value. The coil excitation involves selecting the circuit (current) and connecting it to the external coupling interface. In this model, we designate the number of coil turns as a variable, allowing for straightforward adjustments in later simulations. The A-field specification is constant throughout all domain spaces, and the control equation is in equilibrium. An ideal magnetic conductor is utilized on the anti-symmetric section, and the boundary condition of zero tangential magnetic fields is imposed. The appropriate boundary condition for the symmetric section border is the default magnetic insulation, corresponding to a zero standard magnetic field.

The model initially conducts self-subdivisions of the physical field to regulate the subdivision process. It then proceeds to do mesh subdivisions by adjusting the local area as required. Figure 7 displays the meshing outcomes of the model. The losses in the CT are primarily caused by the magnetic core, which significantly impacts the output power. The coil is designed to ensure that the current and magnetic field are uniformly spread throughout. As a result, the magnetic core is meticulously aligned during the design process, whereas the winding section of the transformer and its surrounding air space are intentionally made less detailed.

4. Parameter Design of Self-Generated Power CT of Miniature Circuit Breaker

4.1. Analysis of Model Core Material Simulation Results

Equation (10) demonstrates that the core permeability μ directly impacts the transformer’s output power, and the core material is responsible for determining the core permeability. To achieve a CT with output power that satisfies the desired usage requirements, choosing a sophisticated electrical and magnetic material as the core is essential. This material should possess characteristics such as high frequency, high magnetic density, and low loss [29].

Table 2. Parameter comparison of three soft magnetic materials.

Compare Items	Silicon Steel Sheet	Permalloy	Cobalt-Based Amorphous Alloy
Saturation magnetic flux density (T)	1.5	1	1.6
Initial magnetic permeability (H/m)	1	>100	125
Core loss	8.15	13.5	5.2
(W/kg)	0.96	0.91	0.93
Lamination coefficient (/)	10	140	18

displays the data for three magnetic core materials that exhibit exceptional performance. An analysis evaluates and assesses the saturation magnetic flux density, initial permeability, lamination coefficient, and pricing. The initial permeability of permalloy and cobalt-based amorphous alloy is significantly high, resulting in a decreased limit for the energy harvesting dead zone when the self-generating power CT is operational. Nevertheless, permalloy has a low saturation flux density [30], making it prone to entering the saturation zone quickly. Additionally, it is relatively expensive. Cobalt-based amorphous alloy materials possess notable advantages in terms of initial permeability and pricing. Furthermore, their saturation magnetic flux density and lamination coefficient are similar to silicon steel sheets and superior to permalloy materials.

To enhance the study’s accuracy mentioned above, the magnetic cores of three soft magnetic materials, namely silicon steel sheet, permalloy, and cobalt-based amorphous alloy, are simulated using the finite element model. The coil’s turns ratio is configured as 1:1000 while keeping other parameters, such as the magnetic core size, unchanged. Figure 8a–c depict the B-H curves of silicon steel sheet, permalloy, and cobalt-based amorphous alloy, respectively. Figure 9, Figure 10 and Figure 11 illustrates the magnetic flux density and loss density distribution in three core samples.

The simulation results of the three soft magnetic materials demonstrate that the magnetic flux is uniformly distributed within the core. Most of the loss is concentrated at the inner corner of the core, where the magnetic flux is dense. Assuming that the input current, coil turns, and core size parameters remain constant, the saturated magnetic flux density (B) of the CT core varies among three materials: cobalt-based amorphous alloy, permalloy, and silicon steel sheet. Additionally, the loss size varies in the following order: permalloy, silicon steel sheet, and cobalt-based amorphous alloy. Simultaneously, the peak value of the B-H curve of the soft magnetic material indicates the magnitude of the saturated magnetic flux density. At the same time, the area represents the magnitude of the core loss. The relationship between the area and the loss is directly proportional, as the simulation results indicate.

Furthermore, the simulated output current of the secondary side of the self-generating power CT, which is constructed using three core materials, is analyzed. The core has a cross-sectional area of 43.56 mm², the magnetic circuit has a length of 35.5 mm, and there are one turn and 1000 turns in the coil, respectively. All parameters, excluding the core substance, remain unchanged. The simulation seeks to accurately represent the performance of different magnetic core materials when subjected to low levels of electrical current. It specifically focuses on the conditions of modest current excitation. Figure 12 displays the results.

Figure 12 demonstrates that the cobalt-based amorphous alloy core and the permalloy core exhibit a significant initial permeability. Additionally, the magnitude and rate of increase in the secondary side output current are superior to those of the silicon steel sheet material when subjected to low current excitation. The device can fulfill operational needs in less favorable settings, and its energy dead zone is more minor. The simulation results align with the theoretical analysis.

To summarize, examining the simulation outcomes of the finite element model of the self-generating power supply CT reveals that the core loss of the cobalt-based amorphous alloy material is minimal. Additionally, it possesses a smaller energy dead zone and is resistant to reaching saturation. The selection of the core material for the self-generating power supply CT considers considerations such as pricing, and the preferred choice is a cobalt-based amorphous alloy.

4.2. Analysis of Model Core Size Simulation Results

To examine the impact of the core size on the output voltage of the self-generating power supply CT, the primary side input current of the model is adjusted to 30 A, while the number of turns in the primary and secondary coils is set to 1 and 1000, respectively. The simulation is used to determine the output voltage of the self-generating power supply CT on the secondary side, considering different core cross-sectional sizes S and average magnetic circuit lengths l. The results are presented in

Table 3. Output voltage under different iron core sizes.

Condition	Parameter	Parameter Value
S = 43.56 mm2	l/(mm)	25	28	31	34	37	40
	Output voltage U2/(mV)	285	281	278	276	273	271
l = 35.5 mm	S/(mm2)	30	35	40	45	50	55
	Output voltage U2/(mV)	270	272	274	278	280	283

.

Assuming all other factors remain the same, the voltage produced on the secondary side of the self-generating power supply CT will rise as the cross-sectional area of the magnetic core grows. The output power of the secondary side can be determined due to the constant resistance of the secondary side load. Moreover, the output power of the secondary side decreases as the average magnetic circuit length of the self-generating power CT becomes shorter. The simulation results shown here align with the theoretical analysis discussed in Section 2.2.

In order to analyze the influence of the number of magnetic core laminations on the CT of the self-generating power supply, the primary side input current of the model is set to 30 A, the number of turns of the primary and secondary coils is set to 1 turn and 1000 turns, respectively, and the total thickness of the magnetic core is 6 mm. Other conditions are consistent. The simulation model’s output under different numbers of magnetic core laminations is obtained by simulation. The results are shown in

Table 4. Output voltage under different number of laminations.

Condition	Parameter	Parameter Value
S = 43.56 mm2	Number of laminations	14	16	18	20	22	24
l = 35.5 mm	Output voltage U2/(mV)	273	276	278	281	283	286

. With the increase in the number of laminations of the self-generating power supply CT core, the output voltage of the secondary side will increase, which is consistent with the results of the theoretical analysis of the second chapter.

To optimize the transmission properties of the self-generating power CT’s core, the average length l and cross-sectional area S of the magnetic circuit are computed quantitatively. The Ampere loop theorem allows for the derivation of the following:

$$Hl=\sqrt{2}{N}_1{I}_e=\sqrt{2}\sqrt{{\left(N_1{I}_1\right)}^2-{\left(N_2{I}_2\right)}^2}$$

(7)

According to Ohm’s law, Equations (2) and (3), we can obtain:

$$l=\frac{\sqrt{2}}{H}\sqrt{{I_1}^2-{\left(\frac{P_{\mathrm{out}}}{\sqrt{2}\pi fBS\eta }\right)}^2}$$

(8)

The magnetic core is a back-type design. Therefore, the average magnetic circuit length of the core is:

$$l=(L_{\mathrm{out}}+L_{\mathrm{in}}+W_{\mathrm{out}}+W_{\mathrm{in}})/2$$

(9)

where L_out, L_in, W_out, and W_in represent the length of the outer and inner diameters of the core and the width of the outer and inner diameters, respectively. When the length and width of the inner and outer diameters are equal, the magnetic circuit is the shortest. At this time, the cross-sectional area S of the core can be expressed as Equation (10), where h represents the thickness of the core.

$$S=h(L_{\mathrm{out}}-L_{\mathrm{in}})/2$$

(10)

The thickness of the magnetic core can be expressed as:

$$h=\frac{\sqrt{2}{P}_{\mathrm{out}}}{\pi fB\eta (L_{\mathrm{out}}-L_{\mathrm{in}})\sqrt{{I_1}^2-0.5H^2{(L_{\mathrm{out}}+L_{\mathrm{in}})}^2}}$$

(11)

The length and width of the inner diameter of the magnetic core are 11.3 mm, considering the thickness of the winding, the fixed structure, the clamping structure between the conductive copper sheet and the coil inside the miniature circuit breaker, and the magnetic core protective box. The dimensions of the outer diameter are 23.9 mm in length and width. The calculation takes into account various factors such as the space limitations of the comprehensive circuit breaker mechanism, the size of the output power, the volume factor of the magnetic core, the size of the cross-sectional area, and the characteristics of the magnetization curve. The final result indicates that the thickness of the magnetic core h is 6.3 mm and the average length of the magnetic circuit l for the self-generating power supply CT is 35.2 mm. The magnetic core has a cross-sectional size of 39.69 mm². Based on the prior studies, increasing the number of magnetic core laminations under identical conditions leads to an enhanced energy harvesting effect. Given the magnetic core lamination technique and cost, we have decided to use 18 laminations for the magnetic core, with each component having a thickness of 0.35 mm.

4.3. Simulation Design of Coil Turns of Self-Generated Power CT

To examine the impact of the core coil’s number of turns and the load resistance on the output voltage of the self-generating power supply CT, we vary the coil’s turns and the load resistance while keeping the primary side input current at 5 A. The other conditions remain unchanged, as indicated in

Table 5. Output voltage under different coil turns and load resistance.

Condition	Parameter	Parameter Value
R0 = 10 $\Omega$	N2/(turn)	450	600	750	900	1150	1300
	Output voltage U2/(mV)	287	282	280	278	275	271
N2 = 800	R0/$\Omega$	5	10	15	20	25	30
	Output voltage U2/(mV)	264	266	269	272	276	278

.

Table 5 demonstrates that the output voltage on the secondary side of the self-generating power supply CT is minimally influenced by the number of turns on the secondary side coil. The relationship between the two variables is not a simple straight line; instead, it follows a nonmonotonic pattern. An optimal number of rotations exists that maximizes the output voltage. Suppose the number of turns in the coil of a self-generating power CT is excessively high. In that case, it leads to a diminutive secondary side current, causing a reduction in the output voltage. Conversely, if the number of turns in the coil is deficient, the induced voltage on the secondary side decreases, decreasing the output voltage. When the primary current and the number of turns of the secondary coil are provided, the voltage on the secondary side grows progressively as the load resistance increases. The output voltage remains constant when the resistance value reaches a specified threshold.

The test results mentioned above align with the theoretical analysis presented in the second chapter. Hence, the output power of the self-generating power supply CT is determined by the primary side current, the number of turns in the secondary side coil, and the load impedance. The self-generating power CT is designed to provide power to the over-current protection circuit of a miniature circuit breaker with a maximum current level of 63 A. Due to the fixed size of the secondary load, there is an optimal number of coil turns on the secondary side, ensuring the effectiveness of the CT. The power output is optimized. After conducting many simulation tests, it has been determined that a secondary side analog load of 15.1 Ω is the most effective in simulating the secondary side overcurrent safety circuit, given a rated current level of 63 A. Figure 13 illustrates the correlation between the number of spins on the secondary side and the output voltage. The most significant output voltage can be achieved when the number of turns in the secondary coil ranges from 1000 to 1100 turns. The number of turns in the circuit breaker is 1050, considering its core construction and internal space.

4.4. Test Verification of Self-Generated Power CT of Miniature Circuit Breaker

The magnetic core is manufactured based on the specified parameters. It is used to construct the electrodeless adjustable tiny circuit breaker, which has a rated current range of 10 A to 63 A. To ensure the accuracy of the simulation results for the CT and validate the model, various tests are conducted. These include measuring the B-H curve of the transformer, analyzing the output waveform of the secondary side voltage and current under different operating situations, and evaluating the impact of energy harvesting.

4.4.1. Hysteresis Loop Test of Self-Generated Power CT

The core’s B-H curve directly impacts the transformer’s performance and is crucial for its operation [31]. To validate the B-H curve’s accuracy in the transformer’s finite element model, the hysteresis loop automatic tester is used to measure the actual B-H curve. Next, the simulation model’s vector hysteresis module assigns values to the associated model parameters. The model’s output results are compared with the measured results of the hysteresis loop automatic tester to validate the model’s accuracy.

This article employs a distinct vector hysteresis module to simulate the B-H curve and provide a realistic depiction of the hysteresis features of the self-generating power supply CT core. Due to the Jiles–Atherton model’s well-defined physical characteristics and ability to effectively replicate the link between magnetic induction and magnetic field intensity [32], it was chosen to simulate the self-generated power CT model. The particle swarm algorithm is employed to determine the parameters of the Jiles–Atherton model and the ideal solution for the model parameters is presented in

Table 6. Jiles–Atherton model parameters.

Parameter Name	Numerical Value	Unit	Description
MS	6.15 × 105	A/m	Saturation magnetization
a	15.3	A/m	Domain wall density
α	6.9 × 10−5	/	Mean field parameters
c	0.71	/	Magnetization coefficient
k	4.2	A/m	Irreversible loss coefficient

.

The procedure entails inputting the parameter values into the finite element model vector hysteresis module and subsequently conducting a simulation of the transformer’s B-H curve using model simulation. Next, a comparison is conducted between the simulated results and the measured findings produced by utilizing the hysteresis loop automatic tester. The B-H curves of the two, as shown in Figure 14, exhibit a strong correlation, suggesting that the finite element model of the self-generating power supply CT accurately represents the magnetic relationship of the transformer.

4.4.2. Test of Output Characteristics of Self-Generated Power CT

The primary side of the self-generating power CT applies excitation currents at varying levels. The process of validating the simulation model entails comparing the simulated current and voltage on the secondary side of the model with the actual output current and voltage of the self-generating power CT under matching operational conditions.

The test circuit consists mainly of a current test bench, digital oscilloscope, load resistance, voltage probe, and current probe, as depicted in Figure 15. The existing test bench can produce various levels of current excitation necessary for the experiment. The system can replicate the fault current in various operational scenarios, including overload and short-circuit transient currents.

Experiments validate the accuracy of the finite element model of the self-generating power CT. When the resistance R₀ is adjusted to 5 Ω, sinusoidal currents of 5 A, 32 A, and 63 A are sequentially applied to the test circuit. The excitation and load resistance remain constant during the experiment. The simulation model’s output current is compared to the output current of the test circuit.

When a small amplitude sinusoidal current of 5 A is applied, the core of the self-generating power supply CT does not become saturated. The output current of the simulation model and the test output current exhibit typical sine waveforms, and their waveforms are highly similar, as depicted in Figure 16a. When a sinusoidal current with an amplitude of 32 A is applied to the primary side of the self-generating power supply CT, the core is not saturated. However, the relationship between the current on the primary and secondary sides is no longer utterly proportional to the turn ratio due to the increasing excitation current. The output current of the simulation model remains undistorted compared to the test output current. The simulated output voltage and current accurately represent the actual output voltage and current, as depicted in Figure 16b. Figure 16c displays the waveform of the output generated by the self-generating power supply CT when subjected to a current of 63 A. The iron core has reached saturation, resulting in a distorted output current waveform. Nevertheless, the finite element model of the self-generating power supply CT can accurately simulate the actual output waveform and the saturation trend of voltage and current.

To measure the similarity between the simulated results of the self-generating power supply CT model and the actual output, the Pearson correlation coefficient method is employed. This method analyzes the similarity of the output voltage and output current waveforms under three different excitation current conditions. The calculation equation is represented by Equation (12), and the corresponding calculation results may be found in

Table 7. Output waveform similarity.

Excitation Current	Output Voltage Similarity	Output Current Similarity
5 A	97.75%	97.96%
32 A	95.52%	95.13%
63 A	95.13%	93.65%

.

$$r_{xy}=\frac{{\displaystyle \sum _{i=1}^n\left(X_i-\overline{X}\right)}\left(Y_i-\overline{Y}\right)}{\sqrt{{{\displaystyle \sum _{i=1}^n\left(X_i-\overline{X}\right)}}^2}\sqrt{{\displaystyle \sum _{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}}$$

(12)

where n represents the total number of samples; $\overline{X}$ and $\overline{Y}$ represent the average value of the model simulation output results and the average value of the measured output results; X_i and Y_i represent the model simulation output value and the measured output value, respectively.

Based on the findings of the similarity analysis of the output waveform, it can be concluded that the waveform similarity exceeds 95% when the transformer is not saturated, indicating a high level of waveform consistency. When the transformer reaches saturation, the waveform’s similarity degree is 93%. Although the similarity degree decreases slightly, it still closely follows the trend of transformer saturation. The empirical findings align with the computational results. The finite element model of the self-generating power supply CT accurately represents the actual output voltage and output current of the device, and its validity has been demonstrated.

4.4.3. The Energy Harvesting Effect Test

Typically, the miniature circuit breaker supplies energy to the load through the power conversion circuit using the self-generating power supply CT output. The load comprises the primary control board and the tripping mechanism of the circuit breaker. Figure 17 demonstrates the principle.

(1)

Experimental verification of small current energy harvesting

This paper uses a Buck DC-DC circuit to stabilize the line voltage. Compared with the linear regulator, it has higher efficiency and is more beneficial to low power consumption. As seen in Figure 18, the output voltage of the optimized prototype begins to increase when the line current increases to 5 A. When the line current is 9 A, the output voltage remains stable after reaching 3.3 V and does not continue to increase with the line current. The prototype with a linear regulator chip generates a voltage output when the line current is 7 A, and a stable output voltage can be established at about 12 A. In the Buck DC-DC voltage regulator circuit, compared with the power conversion circuit of the traditional linear regulator, the stable output voltage is obtained under a lower line current level, which is more conducive to overcurrent protection when the small line current takes energy.

In GB/T 14048.2-2020 Low-voltage switchgear and control gear-Part 2: Circuit-breakers [33], the overload long delay current setting I_R range is 0.4 I_n − I_n, which can be selected according to the protection scenario, usually 0.8 I_n. When the rated current is less than 63 A, the circuit breaker should be able to trip within 1 h when the actual current reaches the 1.3 I_R current threshold. As a result, the energy transformer prototype’s lower limit of stable energy harvesting should be 1.3 I_R = 10.4 A.

The prototype is designed to increment the input current by 4–13 A for each 1 A increase, and ten tests are conducted for each current level. The power conversion circuit’s mean output voltage is monitored, and the protective measures are documented.

Table 8. Small current energy harvesting experimental results.

Line Current (A)	Output Voltage (V)	Success Rate of Trip (%)
4	0	0
5	2.51	0
6	2.85	80
7	3.01	90
8	3.15	100
9	3.29	100
10	3.30	100
11	3.30	100
12	3.29	100
13	3.30	100

displays the test results. According to Table 8, the miniature circuit breaker equipped with the designed prototype can activate the release mechanism when the line current reaches 6 A. When the line current reaches 8 A, it can consistently and effectively activate the release mechanism to ensure the completion of the release protection action. This fulfils the requirement for protection action when the current reaches a maximum of 10.4 A. The current is decreased by 23.08%, and the voltage output remains constant till it reaches the desired voltage of 3.3 V.

(2)

Experimental verification of large current energy harvesting

GB/T 22710-2008 Electronic controller for low-voltage circuit breaker stipulates that the current setting value of the instantaneous protection is in the range of 2I_n–15I_n [34]. To confirm the energy harvesting capability at high input current levels, the design prototype must successfully extract energy under the specified condition of 15 I_n, which corresponds to a range of 150 A–945 A. The current delay characteristic test bench is utilized to incrementally raise the input current from 100 A to 1400 A, with 10 tests conducted at each current level. The power conversion circuit’s average output voltage is monitored, and the release’s protection action is recorded. The test results are displayed in

Table 9. High current energy harvesting experimental results.

Line Current (A)	Output Voltage (V)	Success Rate of Trip (%)
100	3.29	100
200	3.30	100
300	3.31	100
400	3.31	100
500	3.28	100
600	3.29	100
800	3.31	100
900	3.32	100
1000	3.31	100
1100	3.30	100
1200	3.31	100
1300	3.31	100

. Table 9 demonstrates that the developed prototype remains steady in energy harvesting and reliable in protection action, even under high input current conditions. Furthermore, there are no issues of protection rejection due to energy saturation.

5. Conclusions

With the implementation of the new low-voltage distribution network architecture, classic mechanical circuit breakers are inadequate to satisfy the evolving demands and are being progressively substituted with intelligent miniature circuit breakers. The reliable functioning of the intelligent miniature circuit breaker’s overcurrent protection feature is highly dependent on the stability of the power supply, making it an essential safeguard for terminals. When the external power supply is no longer available, its ability to provide protection will be completely lost. The self-generating power supply faces a major issue of energy dead zone and energy saturation in the CT, which is caused by the limited volume of the miniature circuit breaker. Researching the crucial technology behind the self-generating power supply of the intelligent miniature circuit breaker is of utmost importance. This article specifically examines the parameter design of the self-generating power supply CT in the intelligent miniature circuit breaker. The initial step involves analyzing the operational characteristics of the self-generating power supply CT. Subsequently, an equivalent circuit for the CT is constructed, and a theoretical relationship between the output characteristics and the design parameters is established. This theoretical guidance serves to provide a foundation for the construction of the model. Furthermore, utilizing COMSOL, a finite element model is constructed to replicate the process of choosing the core material, core size parameters, and coil turns for the CT. The simulation results are then analyzed to determine the ideal combination of parameters. Experiments ultimately confirm the hysteresis characteristics, output characteristics, and energy harvesting effect by accurately reproducing the real-life working conditions. The main research results include:

(1)

Based on theoretical analysis, it is determined that increasing the core permeability, lamination coefficient, core cross-sectional area, and reducing the average magnetic circuit length of the core can increase the output power of the self-generating power supply CT when determining the primary side current size and frequency.

(2)

A self-generating power supply CT, specifically built for step-less adjustable miniature circuit breakers with a rated current level ranging from 10 A to 63 A, is developed using finite element model simulation design. The choice is made to use a core composed of an amorphous alloy based on cobalt. The thickness h is 6.3 mm, the average magnetic circuit length l is 35.2 mm, the cross-sectional area of the core is 39.69 mm², the number of core laminations is 18, and the number of coil turns is 1050 turns.

(3)

The empirical results demonstrate that the observed hysteresis properties align with the conclusions obtained from the simulated model. Under typical operating conditions, the observed output voltage and current waveforms exhibit a similarity of over 93% to the model simulation results. A current of 8 A is a dependable method for achieving protection against excessive current flow, and the minimum threshold for energy harvesting is decreased by 23.08%.

While the method proposed in this paper has a good energy harvesting effect, related challenges remain. The forthcoming research agenda is outlined as follows: This work focuses on designing the model parameters of the self-generating power CT just for intelligent miniature circuit breakers. The subsequent phase involves contemplating the optimization of the energy harvesting device and expanding the spectrum of current protection; There is no distinct heat dissipation design implemented during the simulation design process. Next, we need to analyze the thermal simulation of various current levels using multi-physical field coupling software in order to enhance the heat dissipation design.