Probabilistic Analysis of an RL Circuit Transient Response under Inductor Failure Conditions

Abstract

We apply probability theory for the analysis of the exponentially decaying transient response of a resistor inductor electric circuit with partially known value of the inductance due to its failure. The inductance is known to be within a continuous interval, and the exact value is unknown, which may happen as a result of inductor faults due to a variety of factors—for example, when the circuit is deployed in an unusually harsh environment. We consider the inductance as a continuous uniform random variable for our analysis, and the transient voltage is treated as a derived random variable which is a function of the inductance random variable. Using this approach, a probability model of the transient voltage at the output terminals of the circuit is derived in terms of its cumulative distribution function and the probability density function. In our work, we further elaborate that the probability model of any other circuit parameter can also be obtained in a similar manner, or it can be derived from the transient voltage probability model. This is demonstrated by getting the model of a branch current from the probability distribution of the transient voltage. Usage of the probability model is demonstrated with the help of examples. The probability of the transient voltage falling in a certain interval at a given instant of time is evaluated. Similarly, the probability values of the branch current in different intervals are determined and analyzed. The derived probability model is checked for its validity and correctness as well. The model is found to be useful for probabilistic analysis of the circuit.

An Investigation of the Transient Response of an RC Circuit with an Unknown Capacitance Value Using Probability Theory

“…The random variable I o is a derived random variable that depends on the random variable C. From (19)…”

“…The capacitance of the capacitor is treated as a random variable and the probability model of the exponentially rising transient response current of the circuit is then developed as a derived random variable. An RL circuit is investigated using the probability methods in [19]. The probability model of the transient response of the circuit is developed, treating the inductor as a random variable.…”

“…Probability theory is a valuable mathematical tool that is used for the analysis and exploration of solutions to a number of engineering problems [20][21][22][23][24]. In this paper, we extend the work in [18,19] and utilize probability theory to analyze the exponentially decreasing transient current response of an RC electric circuit, where the precise value of the capacitance is unknown and is only known to exist within a specific interval of values. First, an expression for the decaying response of the circuit is derived using conventional circuit analysis techniques.…”