Modern power system has entered the high-voltage large power grid and large-scale power system interconnection and the emergence of many high-tech components, making the safety and stability of power systems increasingly prominent in order to establish a set of efficient power system online monitoring, forecasting and prevention System, it is necessary to find a power system with its own open dynamic characteristics, introducing a universally applicable state variable. The entropy function has this characteristic and points out an important fact. This is the several probability distribution functions commonly found in probability theory. The different principles of entropy maximization are used to solve different constraints and the power system reliability theory is based on probability theory. Therefore, the power system reliability theory closely related to the life, state and probability theory of power components must be intrinsically linked with the entropy principle reflecting the chaos of things. It can be predicted that the entropy principle must have a place in the research of power system reliability theory. 2 The principle of entropy 2.1 The origin of entropy and the theory of entropy is one of the great achievements in the development of natural science in the 19th century. The concept of entropy was first applied to thermodynamics by R. Clausius in the second law of thermodynamics. Entropy (S) is a universal state function, 0 indicates that in an isolated system, the irreversible process entropy is added, and the reversible process entropy is unchanged. It reveals that all the irreversible processes within the system spontaneously proceed in the direction of entropy plus, ie, the entropy is maximum. principle.
At the beginning of the 20th century, some famous laws in physics were derived from the maximal principle of entropy, such as Maxwell's molecular velocity distribution law, mass action law Planck blackbody radiation law, etc. So some people called the entropy principle as the cultivation of scientific laws.
The first step in the concept of quantitative expression of entropy is presented. In 1948, Shan Shannon introduced the concept of entropy into information theory, and entropy as a source of information to measure the amount of information, enriching the meaning of entropy, that is, entropy has become a concept to describe the degree of system state chaos. Shannon and the probability / (X) is a probability density function, and there are 1 (4) from the equations (1) and (2), the value of the entropy H is obviously the value of / (x) and P (x) Related, that is, the probability distribution is different, and the corresponding entropy value is also different, which in turn produces an inverse problem, that is, if the probability distribution /(x) is not known in advance, and the entropy value H is known, can the function /( x) This question is the key to the problem, and its derivation process can be characterized by the following figure.
Entropy is a universally applicable concept and state quantity, which is often bound and restricted by certain conditions, but its constraints can not fundamentally change the basic characteristics of the entropy function. Therefore, the theory of wide entropy under constraints is still a superior study. The theory of natural body structure and orderly change of natural processes. However, how to construct a wide entropy function usually, the mathematical expectation of the amplitude of the signal and its energy are limited by a certain potential well. To find the probability density distribution of x when the entropy is maximum under the condition of the well constraint, we use the functional. The extremum method is assumed to be a constrained general formula: distribution, a and b are respectively the upper and lower limits of x, and Lagrangian 1, 2, ..., n), and the structure augmented entropy function is: 3 Power system saliability overview power system Reliability refers to the ability of one or more components in a system, or even the entire system, to perform a defined function or task under specified constraints for a predetermined period of time. It includes power supply reliability, transmission line reliability, electrical main wiring reliability, distribution system. From a reliability point of view, power components are divided into repairable components and non-repairable components. If the components fail after a period of use, they are repaired. It can be restored to its original working state, which is called a repairable component. If the component fails after a period of repair, it cannot be repaired or it can be repaired but it is uneconomical, it is called an unrepairable component. From this we can see that the non-repairable elements only have some of the characteristics of the repairable elements, and they can also be called the inclusion and inclusion relationship. Therefore, we will regard the power components as repairable components, and discuss their reliability indicators as follows: Reliability R(t) refers to the probability that the component will not recover in the time interval under the normal conditions of the starting time. The reliability of the component, the focus is mainly on the time from the start time to the first fault; the unreliability F(t) refers to the probability that the repairable component will fail for the first time in the time interval under the condition that the repairable component is in good condition; The rate h(t) refers to the probability that a component will fail within a unit time after the time t from the start time to the time instant t; the repair probability G(t) refers to the component repaired at time under the fault condition at the initial time. Probability; repair rate m(t) refers to the probability of repairing the unit time after time t under the condition that the component is faulty from the start time to the time t; 4 Solving the reliability index of the power system with the entropy maximum principle 4.1 Solution Form We first analyze the form of the solution of the reliability index of the power component. For this reason, there are N power components that will fail in the first time, then what is the number of failures in the component? In the case of a set of components, it is obvious that when N and t are constant, An is proportional to At, and when t and At are unchanged, it is obvious that equations (13) and (14) are negative in probability theory. It means that without losing the generality, it is assumed that the above-mentioned proportional coefficient will be different due to t, so that according to the definition of the probability density distribution, it can be seen that the above-mentioned f(x) has exactly the meaning of the probability distribution, and once the function is solved, The meaning of the probability density distribution can be solved by the principle of maximum entropy.
4.2 Using the entropy maximum principle to solve the probability distribution function f(t) with the entropy maximum principle, we must introduce the wide entropy function. To do this, we must first determine the constraints in the problem. For this problem, we can know that the two constraints are as follows: f(t) has the property of probability density distribution, so it must be normalized, that is, the number, that is, after the constraint, according to the principle of entropy, it can be constructed widely The entropy function solves the extremum of the above formula and assumes that the failure rate h(t) is constant, that is, h(t)=X. Using two constraint equations and substituting T with infinity, the same reason, assuming repair rate m(t) is a constant, that is, m(t) = a probability density distribution function using a number type. Since the above algorithm only indicates that the extreme value is reached, but whether it is a maximal or a minimum value, the public cannot reflect the use of the previous calculation to obtain jIl. This indicates that the obtained negative exponential solution just makes L reach the maximum value, that is, the negative exponential function. Under the known constraints, the entropy will be maximized, and the application of the entropy maximum principle in the reliability of power system will be realized. 5 Conclusions and prospects Through the analysis and calculation of the principle of entropy and the reliability principle of power system, it is highlighted. The applicability of the principle of entropy maximization in power systems is expected to attract the attention of the majority of power system researchers. The power system itself is an open dynamic system, and the flow of electrical energy is one-way and irreversible. It can be seen that the power system is The concept of chaos, in line with the principle of entropy plus principle entropy, reveals the direction of the development of things, and has been widely used in many fields, such as signal processing earthquake prediction, market management, etc. It can therefore be predicted as uncertainty and disorder of material systems. The entropy of the measure of interest is based on data difference entropy and minimum entropy feature extraction for power system data processing; based on information fusion entropy, Reliability Analysis, Prediction and Evaluation of Power System Based on Holkov Entropy and Fault Tree Entropy; Reliability Optimization Based on Maximum and Minimal Entropy Method for Processing Inequality Constraints; Based on Super Entropy Principle and Hierarchical Neural Network Entropy Algorithm (PSHNN) Research on safe and reliable control of power system
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