## 2 Circuit Breaker Overload Protection Working Principle and Its Service Status  
### Working Principle of Circuit Breaker Overload Protection and Its Failure Analysis  
Thermal release is the core component of the overload protection function of low-voltage circuit breakers, which is mainly composed of a heating element and a thermal bimetal. In this paper, overload experiments are carried out using a company's molded-case circuit breakers that were produced in the same batch; the type of circuit breaker shell current rating \(I_{e}=125\) A and the rated voltage is 380 V. The structure of the composite heated thermal release is shown in Figure 1.  
According to the law of conservation of energy, the differential equation of heat balance for a bimetal sheet is [31]:  
\[Pdt=cmd\tau+K_{T}A\tau dt \tag{1}\]  
where \(P\) is the total heating power, \(c\) is the specific heat capacity of the material, \(m\) is the mass of the heat generator, \(K_{T}\) is the comprehensive heat dissipation coefficient, \(A\) is the effective heat dissipation area, \(\tau\) is the temperature rise, \(Pdt\) is the total heat generation, \(cmd\tau\) is the heat storage, and \(K_{T}A\tau dt\) is the heat dissipation.  
Considering the heat generation along with the heat dissipation to the surrounding medium, the solution to this differential equation is:  
\[\tau=\tau_{w}\Big{(}1-e^{-t/T}\Big{)}+\tau_{0}e^{-t/T} \tag{2}\]  
where \(\tau_{w}\) is the stabilized temperature rise, \(\tau_{0}\) is the initial temperature rise, and \(T\) is the thermal time constant.  
Figure 1: Composite heating thermal release structure. (1. Wire terminals. 2. Heating elements. 3. Hot bimetals. 4. Electromagnetic coils.).  
A hot bimetal is fixed at one end and bent at the free end when heated, producing a deformation of:  
\[f=\frac{KL^{2}\tau}{\delta} \tag{3}\]  
where \(K\) is the specific bending ratio, \(L\) is the length, and \(\delta\) is the thickness.  
Thrust formula [32]:  
\[F=\frac{KEb\delta^{2}}{4L}\tau \tag{4}\]  
where \(E\) is the modulus of elasticity and \(b\) is the height.  
In practice, as shown in Figure 2 the thermal bimetal has a certain distance from the linkage mechanism and the bending displacement of the thermal bimetal is the empty stroke before encountering the obstruction, at which time the resulting thrust is calculated by the formula:  
\[F=\frac{KEb\delta^{2}}{4L}\tau-\frac{Eb\delta^{3}}{4L^{3}}f^{\prime} \tag{5}\]  
where \(f^{\prime}\) is the free-end air travel.  
After the heating element is energized, the heat increases the temperature of the thermal bimetal through heat conduction, heat convection, and heat radiation, which leads to the deformation of the thermal bimetal. Furthermore, when the deformation distance reaches the decoupling distance, the thermal bimetal pushes the decoupling shaft of the circuit breaker to make the circuit breaker disconnect to realize the overload protection.  
With an increase in the service time of the product, the overload protection action characteristics of low-voltage circuit breakers are gradually changed by the working environment and the degradation of its own performance and other factors. On the one hand, the dispersion of the action time becomes larger, on the other hand, the action time curve is gradually shifted, resulting in the action characteristics of the product no longer meeting the requirements of the national standards and ultimately manifesting in two failure modes, i.e., (1) when overloading of the power supply line or the power-using equipment occurs, the circuit breaker cannot act quickly and reliably and it cannot cut off the faulty line and does not act and (2) when there is no overloading of the power supply line or the power-using equipment, the circuit breaker breaks off the normally operating line, and the circuit breaker malfunctions.