## 3 Results
The algorithm for analyzing the current state of the technological process and the dynamics of power consumption (Figure 4) takes into account the emergence of new initial data. This allows for the accumulation of retrospective information for managing the technological process and power consumption modes, as well as forecasting. Let us analyze the fluctuations of a system parameter, which can be effectively used in automatic power consumption management systems [68; 69]. Increasing the frequency of analyzing power flow parameters (voltage, current, power, frequency) within the power supply system enables effective real-time management of power consumption [70]. This is important because deviations in the power flow parameters can increase the probability of the power consumption value going beyond the permissible limits of the planned one (the mathematical expectation of a random process). If the value of power consumption \(W_{1}\) changes by \(\Delta W_{1}\), which is recorded during a control measurement at moment \(t_{1}\), then it is essential to assess the probability of power consumption going beyond the permissible limits in subsequent time intervals. Consequently, it is necessary to forecast level-crossings of random processes. The need to use the characteristics of level-crossings of random processes originates from the limiting conditions of technological processes because manufacturers do not envisage redundancy in their process lines. The requirements for safety, reliability, and efficiency of the technological process must be met regardless of power consumption levels (maximum and minimum) and under all permissible operational conditions [71; 72]. This is important because the technological process needs to operate under critical and extreme conditions, which can be achieved through an in-depth analysis of the probabilistic structure of random processes. The graph of possible fluctuations in the system parameter is shown in Figure 5.  
Figure 5: Graph of possible fluctuations in the system parameter \(X\). Since the question of the probabilities of rare random events in scientific and technical literature, due to the lack and uncertainty of factual information, was discussed mainly only in theoretical terms, this study uses the methodological approaches outlined in [73; 74]. The range of permissible variations in the system parameter \(X\), corresponding to the values of power consumption (voltage, current, power, frequency) lies within the interval \(\{\alpha,\beta\}\). As long as its value does not go beyond \(\alpha<X<\beta\), the technological process retains its integrative property, including integrity (the unity of the interrelations and interactions of components) and emergence (irreducibility of the system's properties to the properties of individual components). When \(X\) goes beyond the interval \(\{\alpha,\beta\}\), it is impossible to maintain the dynamic equilibrium of the technological process through coordinated control. When intergativeness is lost at \(t>t_{5}\) (Figure 5), the technological process is disrupted due to the activation of protection devices that prevent damage to the process line [75; 76; 77; 78]. The partial components of the system parameter \(X\) can take values \(\{\gamma>\alpha,\ \delta<\beta\}\), which defines the area of partial homeostasis \(\{\gamma<X<\delta\}\). At \(\{\gamma<X<\alpha\}\) or \(\{\delta<X<\beta\}\), the technological process normally shifts to a new qualitative state, while maintaining its functionality. This occurs in the time ranges \(\{t_{1},\ t_{2}\}\) and \(\{t_{3},\ t_{4}\}\). The approach of the system parameter to the maximum permissible values (areas \(A\) and \(B\) in Figure 5) can lead to a disruption of the technological process. It is worth noting that when the technological process enters the bifurcation zone, predicting its further state becomes impossible. Let us consider additionally the conditions specifying the behavior and parameters of power consumption.