2023 ieee 16th international conference of actual problems of electronic instrument engineering (apeie)

III.System Modes

System Modes - is its state at any time or interval of time. The mode of the system is determined by the parameters of the mode - indicators that depend on the change of the mode. Mode parameters include voltages at different points of the mode, currents in its elements, divergence angles of EMF and voltage vectors, active and reactive powers, etc.
In Fig. 1, there are three main modes of electrical systems when analyzing and constructing a mathematical description:

Fig. 1. Analysis of mathematical description.

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  A steady state in which the normal electrical system is designed and its technical and economic characteristics are determined;
  
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  A steady state that occurs after an emergency shutdown of any element or a number of elements of the system after an accident. The parameters of these modes do not change over time, and the connections between them are represented by algebraic equations;
  
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  Transition is a mode in which the system changes from one state to another. It is characterized by the change of all its parameters over time and its description by differential equations.
  

Any mode consists of many different processes. The mode parameters of the electrical system connect interconnected paths with certain relationships that include some proportionality coefficients depending on the characteristics of the system elements and the method. For example, the current in a cross section of a transmission line,
_{ }, (1)
In this, _{ } mode parameters, _{ }–resistance of this part of the line.
The simplest form of flow in the network of a complex system in a current.
_{ } , (2)
here, _{ }mode parameters, _{ }called constant coefficients and system parameters.
System parameters can be affected by changes in its mode. In this case, the system is called non-linear. The parameters of all real electrical systems are nonlinear to some extent.
But the mathematical apparatus for their study has not yet been sufficiently developed. In this regard, in many practical problems, the parameters of the system should be considered constant, this system is linear in some field of study. Here, the engineer's art is clearly manifested in choosing a certain linearization range and highlighting the cases where nonlinearity should be taken into account in order to avoid significant errors.
However, in the mathematical interpretation of the mode of the energy system, there is always another type of nonlinearity - it is a nonlinearity that depends on the nature of the relationship between the parameters of the mode. For example,
_{ } (3)
these types of nonlinearities cannot be eliminated, so they must be taken into account.
One of the features of engineering calculation is the ability to simplify it depending on the task. Another feature is that an engineer must deal with complex electrical circuits and, in connection with this, develop special methods for calculating and analyzing electrical circuits that are equivalent circuits for complex electrical networks. To analyze the steady state of the electrical system, it is necessary to construct algebraic communication equations.
The main challenges in this article,

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  first of all, the need to take into account the nonlinearity or, if possible, get rid of it;
  
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  secondly, to formulate and solve a large number of equations of a network with a complex configuration and many quantities to be determined.
  

In this case, you can use matrix methods that allow you to concisely write the problem and develop its solution.
Transition modes are divided into normal (operational) and emergency.
The current operation of the system is accompanied by simple transient processes. They are related to changes in the system load and the reaction of devices responding to them. During normal operational operations, normal processes occur:

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  switching on and off transformers, as well as separate power lines; normal operating changes in the system switching scheme;
  
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  switching individual generators and loads on and off or changing their capacity. In simple transient processes, the deviations of the mode parameters from their steady-state values are often so small that linear differential equations can be used to describe the system.
  

Emergency transitions in the electrical system can also occur due to any sudden emergency changes in the regime: short circuits in the system and their subsequent shutdown, changes in the connection scheme of the system. These changes, which are called large disturbances or effects in the mathematical theory of electrical systems, lead to significant deviations of the mode parameters from the initial state.
To study the behavior of a system, it is necessary to write and solve the complete equations of motion of the system. At the same time, simplifying assumptions are introduced, based mainly on practical considerations, that indicate what methods should be used to solve the problem accurately.