Energy system stability. General information. Ways to improve sustainability. Dynamic stability of the power system

STATIC STABILITY

power system - ability electric power system restore the initial state (mode) after its small perturbations. Violation of S. at. can occur during the transmission of large powers through power lines (usually extended), with a decrease in voltage at load nodes due to a shortage of reactive power, when generators of power plants operate in the underexcitation mode. Main measures to ensure S. at .: increase in nominal. voltage of power transmission lines and reduction of their inductive resistance; automatic excitation control large synchronous machines, application synchronous compensators, synchronous motors and static. reactive power compensators in load nodes. S. at. can also be increased when using generators in power systems with excitation control in the longitudinal and transverse windings of the rotor.

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static stability of the electrical system- static stability of the electrical system; static stability The ability of an electrical system to return to its original mode (or very close to it) after small perturbations of the mode ... Polytechnic terminological explanatory dictionary

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English: Energetic system static (resistance) stability The ability of the power system to return to the steady state after its small disturbances (according to GOST 21027 75) Source: Terms and definitions in the electric power industry. Directory … Construction dictionary

Books

• , V. Pyshnov. Aircraft aerodynamics. Part two. Equilibrium in straight flight and static stability
• Aircraft aerodynamics. Part two. Equilibrium in rectilinear flight and static stability, Pyshnov V.S. This book will be produced in accordance with your order using Print-on-Demand technology. Aircraft aerodynamics. Part two. Balance in straight flight and static stability…

Energy System Sustainability- this is its ability to return to its original state with small or significant perturbations. By analogy with a mechanical system, the steady state of the power system can be interpreted as its equilibrium position.

Parallel operation of generators of power plants included in the power system differs from the operation of generators at one station by the presence of power lines connecting these stations. The resistance of power lines reduces the synchronization power of generators and makes it difficult for them to work in parallel. In addition, deviations from the normal operation of the system, which occur during shutdowns, short circuits, sudden load shedding or surge, can also lead to a violation of stability, which is one of the most severe: accidents leading to a power outage consumers Therefore, the study of the problem of stability is very important, especially in relation to power lines with alternating current. There are two types of stability: static and dynamic.

Static stability is called the ability of the system to independently restore the original mode under small and slowly occurring perturbations, for example, with a gradual slight increase or decrease in load.

Dynamic energy system sustainability characterizes the system's ability to maintain synchronism after sudden and abrupt changes in mode parameters or in case of accidents in the system (short circuits, frequent outages of generators, lines or transformers). After such sudden disruptions in normal operation, a transient process occurs in the system, after which the established post-emergency mode of operation should again occur.

Ways to improve resilience

The main way to increase stability is to increase the limit of the transmitted power. This can be achieved by increasing the emf. generators, voltage on the load buses or a decrease in the inductive resistance of the line. The main means of increasing stability are the following:

The use of high-speed automatic voltage regulators that increase e. d.s. generators when the load increases. To improve dynamic stability at short circuit. of particular importance is the excitation forcing, in which the contacts of a special relay shunt the excitation rheostats; as a result, the largest possible current is supplied to the exciter winding (“ceiling” excitation). In modern generators, the "ceiling" excitation current is 1.8-2.0 of its nominal value;

Increasing the voltage of existing lines, for example, from 110 to 150 or IA 220 kV;

Reducing the inductive resistance of lines, achieved by splitting the wires of powerful lines into two or three, or by using longitudinal capacitive compensation with a series connection of a capacitor bank in the line;

The use of high-speed switches, protections and automatic re-closing of lines.

The state of a system at any point in time or over a period of time is called regime systems. The mode is characterized by indicators that quantitatively determine the operating conditions of the system. These indicators are called mode parameters . These include the values ​​of power, voltage, frequency, shift angles of EMF vectors, voltages, currents.

The electrical system mode can be established or transitional .

In any transient processes, regular sequential changes in the mode parameters occur due to any reasons. These reasons are called disturbing influences . They create initial deviations of the mode parameters − mode perturbations .

Under normal operating conditions, there are always small load changes. Therefore, there is no strictly unchanging regime in the system, and when speaking of the steady regime, one always means the regime of small perturbations.

Small perturbations should not cause a violation of the stability of the system, that is, they should not lead to a progressively increasing change in the parameters of the initial mode of the system.

Static stability - this is the ability of the system to restore the original (or close to the original) mode after a small perturbation.

Under certain conditions, the steady state can be unstable. This occurs when the system is operating in limiting modes (too much or too little transmitted power, voltage drop at load nodes, etc.). In these cases, small perturbations lead to a progressively increasing change in the regime parameters, which at first occur very slowly, manifesting itself in the form of a spontaneous change, sometimes called creep (fluidity) parameters of the normal mode of the system.

When studying static stability, it is assumed in advance that it is impossible to establish the absolute values ​​of changes in the mode parameters when they deviate from the steady-state values. The cause and place of their occurrence are not fixed. These are some free perturbations having a probabilistic character.

The task of studying static stability is reduced, therefore, only to determining the nature of the change in the regime parameters without determining the magnitude of disturbances. In this case, the analysis is limited to a small region e, given in the region of the steady value of the parameters.

The static stability of an electrical system can be assessed in different ways:

1. With the help of practical criteria based on simplifying assumptions. In this case, the answer is obtained only in the form of "yes - no", "will leave - will not leave" the mode from its initial state with a small perturbation of the system.

2. Using the method of small oscillations based on the study of the equations of motion. In this case, the physical nature of the occurring phenomena is clarified more fully: not only the stability of the regime is established, but also the nature of the movement (aperiodic or oscillatory, increasing or fading).

Emergency modes in the electrical system occur during short circuits, emergency shutdowns of loaded units or lines, etc. Under the action of large perturbations, abrupt changes in the regime occur.

Large disturbances can also occur in normal modes: turning off and on generators, lines, starting powerful engines, etc.

In relation to large perturbations, the concept of dynamic stability is introduced.

Dynamic Stability is the ability of the system to restore its original state after a large disturbance.

The concepts of “small” and “large” perturbations introduced above are conditional. A small perturbation in this case is understood as a perturbation, the influence of which on the nature of the system behavior manifests itself practically regardless of the location of the appearance of the perturbing effect and its magnitude. In this regard, in the range of regimes close to the initial one, the system is considered as linear.

A large perturbation is a perturbation, the influence of which on the nature of the behavior of the system depends on the time of existence, magnitude and place of occurrence of the perturbing effect.

In this regard, in the study of dynamic stability, the system in the entire range of the study should be considered as non-linear.

The main method for studying the dynamic stability of electrical systems at the present stage is numerical integration differential equations describing the behavior of the system.

These calculations are carried out on computers that work according to programs that control the accuracy of calculations by reducing the integration step until the modulus of the difference between the calculated values ​​of the function is less than some given positive number e.

Depending on the purpose of the calculations, in practice, simplified methods are often used that do not claim high accuracy. These methods are used when it is possible to confine ourselves to the general characteristics of the process. Among the simplified methods, the method of successive intervals, the essence of which lies in the approximate calculation of the integral, is most widely used.

But there is a simpler and more illustrative method based on the energy approach to the analysis of dynamic stability, which is called the area method. With this method, the kinetic energy of the system is determined by the area of ​​the graph of the transient process. The task of the study is to compare the areas of acceleration and deceleration, that is, to compare the kinetic energy obtained in the process of accelerating the generator rotor with the energy that is consumed in the process of rotor deceleration.

The stability of the electrical system, the stability of the electrical power system, the ability of the electrical system (ES) to restore the original (or almost close to it) state (mode) after any of its perturbations, manifested in the deviation of the values ​​of the parameters of the ES mode from the initial (initial) values. In ES, the sources of electrical energy are usually synchronous generators, electrically interconnected by a common network, and the rotors of all generators rotate synchronously; such a regime, called normal, steady, must be stable, i.e., the ES must return to its original (or almost close to it) state every time after deviations from the steady state. Deviations can be associated, for example, with a change in load power, short circuits, outages of power lines, etc. The stability of the system, as a rule, decreases with an increase in the load (the power supplied by the generators) and a decrease in voltage (an increase in the power of consumers, a decrease in the excitation of generators); for each ES, some limiting (critical) values ​​of these or related quantities characterizing the stability limit can be determined. Reliable operation of the ES is possible if a certain margin of stability of the ES is provided, i.e. if the parameters of the operating mode and the parameters of the ES itself differ sufficiently from the critical ones. To ensure U. e. with. provide for a number of measures, such as ensuring an adequate margin of stability in the design of ES, the use of automatic control of the excitation of generators, the use of emergency automation, etc.

At the analysis U. e. with. Distinguish between static, dynamic and resulting stability. Static stability characterizes U. e. with. for small perturbations, i.e. such perturbations for which the investigated ES can be considered as linear. The study of static stability is carried out on the basis of general methods developed by A. M. Lyapunov for solving stability problems. In engineering practice, the study of U. e. with. sometimes they are carried out in a simplified way, focusing on practical stability criteria that determine its presence or absence under certain assumptions arising from practice (for example, about the impossibility of the so-called self-rocking of the system, about the invariance of the frequency of the electric current in the system, etc.). In the study of static stability, digital and analog computers are used.

Dynamic stability determines the behavior of the ES after strong disturbances arising from short circuits, disconnection of power lines, etc. In the analysis of dynamic stability (the system is usually considered as non-linear), it becomes necessary to integrate high-order non-linear transcendental equations. For this, analog computers, etc. are used. calculation models of alternating current; most often create special algorithms and programs that allow you to make calculations on a digital computer. The consistency of the compiled programs is checked by comparing the results of calculations with the results of experiments on a real ES or on a physical (dynamic) model of an ES.

The resulting stability characterizes U. e. with. in case of violation of the synchronism of a part of the operating generators. The subsequent restoration of the normal mode of operation occurs without turning off the main elements of the ES. Calculations of the resulting stability are made very approximately (due to their complexity) and aim to identify unacceptable effects on equipment, as well as to find a set of measures leading to the elimination of the asynchronous operation of the ES.

Static W. e. with. can be increased mainly by using strong regulation, dynamic - by forcing the excitation of generators, quick shutdown of emergency sections, the use of special devices for braking generators, disconnecting part of the generators and part of the load. An increase in the resulting stability, usually considered as an increase in the survivability of the ES, is achieved primarily by regulating the power generated by generators that have fallen out of synchronism and by automatically turning off some of the consumers (automatic unloading of the ES).

Dynamic stability is understood as the ability of the power system to maintain synchronous parallel operation of generators in case of significant sudden disturbances that occur in the power system (short circuit, emergency shutdown of generators, transformer line).

The area method is used to evaluate dynamic stability. As an example, consider the mode of operation of a double-circuit power transmission that connects the power plant with the power system, with a short circuit on one of the lines with the damaged line disconnected and its successful auto-reclosing (Fig. 10.3, a).

The initial power transmission mode is characterized by point 1 located on the angular characteristic I, which corresponds to the original power transmission scheme (Fig. 10.3, b).

Rice. 10.3. Qualitative analysis of dynamic stability at K3 on a power line: a - power transmission scheme; b - angular characteristics of power transmission; c - change of angle in time

At K3 at point K1 on line W2, the angular characteristic of the power transmission takes position II. The decrease in the amplitude of characteristic II is caused by a significant increase in the resulting resistance between the points of application. At the moment K3, the electric power is discharged by a value due to a decrease in the voltage on the station buses (point 2 in Fig. 10.3, b). The discharge of electrical power depends on the type of K3 and its location. In the limiting case, with a three-phase K3, the power is reset to zero on the busbars of the station. Under the influence of the excess mechanical power of the turbines over the electrical power, the rotors of the station's generators begin to accelerate, and the angle increases. The process of power change goes according to characteristic II. Point 3 corresponds to the moment of disconnection of the damaged line from both sides by relay protection devices РЗ. After the line is disconnected, the power transmission mode is characterized by point 4 located on the characteristic , which corresponds to the power transmission scheme with one disconnected line. During the change of the angle from to the rotors of the generators of the station acquire additional kinetic energy. This energy is proportional to the area bounded by the line, the characteristic II and the ordinates at points 1 and 3. This area is called the acceleration platform. At point 4, the process of braking the rotors begins, since the electric power is greater than the power of the turbines. But the braking process occurs with an increase in the angle. The increase in the angle will continue until all the stored kinetic energy is converted into potential.

The potential energy is proportional to the area bounded by the line and the angular characteristics of the post-emergency mode. This area was called the braking area. At point 5, after a certain pause after the W2 line is disconnected, the automatic reclosure device is triggered (it is assumed to use a three-phase high-speed automatic reclosure with a small pause). With a successful AR, the process of increasing the angle will continue according to the characteristic (point 6) corresponding to the original power transmission scheme. The increase in the angle will stop at point 7, which is characterized by the equality of the areas. At point 7, the transient process does not stop: due to the fact that the electric power exceeds the power of the turbines, the braking process will continue according to the characteristic , but only with a decrease in the angle. The process will be established at point 1 after several oscillations around this point. The nature of the change in angle 5 with time is shown in Fig. 10.3, c.

In order to simplify the analysis, the power of the turbines during the transient process is taken unchanged. In reality, it changes somewhat due to the action of the turbine speed controllers.

Thus, the analysis showed that under the conditions of this example, the stability of parallel operation is preserved. A necessary condition for dynamic stability is the fulfillment of the conditions for static stability in the post-accident mode. In the considered example, this condition is met, since the power of the turbines does not exceed the limit of static stability.

The stability of parallel operation would be violated if, in the transient process, the angle passed the value corresponding to point 8. Point 8 limits the maximum braking area on the right. The angle corresponding to point 8 is called critical. When crossing this boundary, an avalanche increase in the angle is observed, i.e. loss of generators out of synchronism.

The dynamic stability margin is estimated by a coefficient equal to the ratio of the maximum possible braking area to the acceleration area:

At , the regime is stable, at , stability is violated.

In case of unsuccessful AR (switching on the line to failed K3), the process from point 5 will switch to characteristic II. It is easy to see that, under the conditions of this example, stability is not preserved after repeated K3 and subsequent disconnection of the line.