## 2 Circuit Breaker Overload Protection Working Principle and Its Service Status
### Overload Protection Service State Considering Safety Margins for Action Characteristics
In order to better utilize the Markov model to describe the state transfer of LV circuit breaker overload protection, the following assumptions are made:  
(1) The initial operating moment of the low-voltage circuit breaker is in a healthy state (state 1) and the degradation of the circuit breaker's thermal disconnectors' performance up to the severe fault state (state 5) is degraded step by step. (2) The currently observed state is the result of the cumulative effect of the operating time and different factors prior to the observation point. (3) The degradation of the low-voltage circuit breaker thermal release performance has a continuous time Markovian nature, where the evolution of the future state of the circuit breaker in the current state does not depend on the previous state, i.e., there is no memory effect. (4) The degradation trend of low-voltage circuit breaker thermal release performance remains monotonic, i.e., if the trend of overload protection action time change is increasing, its action time will keep increasing and eventually exceed the upper limit of the action time, resulting in a refusal failure for the circuit breaker. If the trend of the overload protection action time change is decreasing, its action time will keep decreasing and eventually exceed the lower limit of the action time, resulting in a malfunctioning failure for the circuit breaker. (5) The linear degradation model is utilized to describe the degradation of the performance of the thermal release of the low-voltage circuit breaker, and the degradation model of the overload protection action characteristics is as follows:  
\[t_{d}(U_{t})=t_{d0}+\beta U_{t} \tag{8}\]  
where \(t_{d}(U_{t})\) is the time of the overload protection action time, \(t_{d0}\) is the circuit breaker overload protection action time of the initial value, with a normal distribution to describe its dispersion expressed as \(t_{d0}\sim N(\mu_{d0},\sigma_{d0}^{2})\). The action time degradation rate is expressed as \(\beta\), and also described by a normal distribution, i.e., \(\beta\sim N(\mu_{\beta},\sigma_{\beta}^{2})\); the mean value of \(\mu_{\beta}\) can be positive or negative. When \(\beta<0\) is manifested as a gradual decrease in the overload protection action time, it may cause false faults, and when the opposite is true, it may cause refusal faults. Describing the degradation process using a linear degradation model helps to analyze the effect of thermal release performance degradation on the service state of low-voltage circuit breaker overload protection. When the degradation model adopts other forms, the analytical process in this paper can also be referred to. (6) Circuit breakers that are subject to environmental temperature, altitude, salt spray, humidity, mold, and other factors, the operating conditions of low-voltage circuit breakers are divided into three cases [11]: good operating conditions (such as office or residential premises), general operating conditions (such as commercial or light industrial production and other places), and poor operating conditions (outdoor, agricultural network and heavy industrial production and other places). The degradation rates of the overload protection action times for low-voltage circuit breakers under different operating conditions are different. (7) The upper threshold for a degradation failure of the thermal release of a low-voltage circuit breaker is the overload protection action time \(t_{\text{max}}\), whereas the lower threshold is the action time \(t_{\text{min}}\). The reliability level of a low-voltage circuit breaker affects the dispersion of the initial overload protection action time and the rate of action time degradation \(\beta\). The higher the reliability level of a circuit breaker, the lower the dispersion of the initial overload protection action time \(t_{d0}\); the lower \(\beta\) means that the circuit breaker can work reliably for a longer period of time and there is a higher probability of it being in a healthy operating condition.