RU2585966C1 - Method for determining value and time of thermal effect of short circuit current - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: invention relates to electrical engineering, particularly to electric equipment installed on power plants and substations in systems for production, transmission and power consumption, and can be used in all electrical installations using digital data processing. Method includes measuring, recording and digitising N times during period T and in every current moment in time t_j current instantaneous value of short-circuit current x_sc(t_i) in each phase. Method includes determining value of thermal effect B_ter in each phase using following expression:

where B_ter is value of thermal effect of short circuit current in one phase, A²s; Δt = T/N is time-sampling step of signal, s, summation is carried out on j from j = 1, which corresponds to moment t₁ is time of occurrence of short-circuit current, to moment of time t_apv - time completion of automatic repeated turning on, when j = f(t_apv+1)N; x_sc(t_i) is instantaneous value of short-circuit current in given phase at current time t_j, A; x_sc(t_i+1) is instantaneous value of short-circuit current in given phase in next time t_j+1, A; f is industrial frequency, Hz; N is number of sampling intervals. Thermal exposure time t_sc at each j-th measurement of cumulative monotonously increases with value t_sc = 0 for value of time sampling pitch Δt, provided that x_sc(t_j) is current instantaneous value of short-circuit current in this phase is not equal to zero and is determined in accordance with following expression:

.

EFFECT: technical result is fast and accurate determination of magnitude and time of thermal effect on conductors and electric devices of short circuit current by fixation of instantaneous values and calculating using mathematical expressions given in claim.

1 cl

Description

The invention relates to electrical engineering, in particular to technologies using electrical equipment installed in power plants and substations in power generation, transmission and consumption systems, and can be used in all electrical installations using digital data processing.

The invention relates to the field of electrical engineering, in particular to methods for processing instantaneous values of measurement results of variable electrical signals, for example, low-frequency currents up to 1000 Hz, obtained using digital devices.

The claimed invention relates to a priority area of development of science and technology "Technologies for creating energy-saving systems for transportation, distribution and consumption of heat and electricity" [Alphabetical index to the International Patent Classification in priority areas of science and technology / Yu.G. Smirnov, E.V. Skidanova, S.A. Krasnov. - M.: PATENT, 2008 .-- p. 97], because it can be used on all electrical installations equipped with digital ammeters to obtain digitized instantaneous current values, and allows you to determine the magnitude of the thermal effect on the conductors and electrical apparatus from the short circuit current, which is necessary both to determine the degree of a specific thermal effect, and to determine their current and residual thermal stability in future short circuits.

The determination of the magnitude and time of the thermal effect on conductors and electrical devices from the short circuit current, given in the extensive technical literature, is based on GOST 30323-95 Short circuits in electrical installations. Methods for calculating the electrodynamic and thermal effects of short circuit current. Reissue. August 2004, paragraphs 3.1.1-3.1.8. " Therefore, it is selected as an analogue. A sign of an analogue that coincides with the essential features of the variants of the proposed method is only the purpose.

The disadvantage of the analogue, from the point of view of the technical result, is, firstly, low accuracy, since to calculate the magnitude and time of the thermal effect it is necessary to use not specific exact values of the short circuit current and its duration, but some calculated estimated values of the short circuit current in in accordance with the instructions for using various “initial design circuits” and “design short circuit duration in an electrical installation”.

Secondly, the disadvantage of the analogue is the low speed. Considering that a short circuit can practically occur at any point in an electric circuit having a configuration of any complexity, it is possible to select a suitable initial calculation circuit for determining the short circuit current, that is, a circuit that provides the greatest accuracy, only if there is an infinite bank of initial calculation circuits, which will require infinite calculation time. But even with the original calculation circuit available, the mathematical expressions with numbers from (35) to (49) given in GOST 30323-95 require a large number of unknown (and therefore estimated) parameters to determine the periodic and aperiodic components of the short-circuit current by difficult expressions. All these calculations are time consuming.

Thirdly, the disadvantage of the analogue is the high complexity of the calculations, as can be seen from the mathematical expressions (35-49) given in GOST 30323-95.

Fourth, GOST 30323-95 does not take into account the DC component of the short circuit current, which, like the periodic and aperiodic components, are present in the electrical signal during emergency conditions.

Finally, in § 1.1.5. we read: “The estimated duration of a short circuit when checking conductors and electrical apparatuses for thermal stability should be determined by adding up the duration of the main relay protection, in the zone of which the tested conductors and electrical apparatuses are included, and the total time that the corresponding circuit breaker trips, and when checking cables for fire safety - by adding up the operating time of the backup relay protection and the total time of tripping the circuit breaker closest to the place of short circuit. According to GOST R 52565-2006 AC circuit breakers for voltages from 3 to 750 kV. General technical conditions »total shutdown time - the time from the moment the command for shutdown is issued until the arc goes out in all phases. However, it is known, for example, “Chunikhin A.A. Electric devices: General course. Textbook for high schools. - 3rd ed., Revised. and add. - M: Energoatomizdat, 1988, p. 137-143. ”, That after extinction the arc may catch fire again. And this can be repeated several times depending on the nature of the chain. Thus, the calculated short circuit time may not correspond to the exact actual short circuit time, which can easily be obtained from digital measurements.

It does not seem possible to choose a prototype for the proposed method, because among the existing methods for determining the magnitude and time of the thermal effect from the short circuit current, it was not possible to find a method that uses the digitized instantaneous current value x (t _j ) at time t _j = t ₁ , t ₂ , ..., t _N , where N is the number of measurements during the period T, with t _j + 1 = t _j + Δt, where Δt = T / N is the time step of the signal sampling.

The objective of the invention is to develop a simple, fast and accurate method for determining the magnitude and time of the thermal effect of a short circuit current based on the measurement of both the instantaneous values of this current and its duration. The method is focused on obtaining data from conventional digital measuring instruments of the current current value and / or digital recorders of emergency processes, without the use of additional energy-consuming and expensive equipment. This allows the operation to obtain the following results:

- reduce the time spent on determining the magnitude and time of the thermal effect from the short circuit current in operation;

- use the exact values of the magnitude of the thermal effect of the short circuit current and the exact time of its operation for monitoring and predicting the state of insulation;

- use the exact values of the magnitude of the thermal effect of the short circuit current and the exact time of its action to assess the state of contacts of electrical switching devices;

- increase the accuracy of the calculation of the current value of the value and time of the thermal effect from the short circuit current.

Achievable technical result of the claimed invention, when determining the magnitude and time of the thermal effect from the short circuit current, in the following:

- the ability to continuously monitor the magnitude of the thermal effect of the short circuit current and the exact time of its operation for all electrical devices in order to control their thermal stability;

- an increase in speed, since all the necessary and accurate data for calculating the magnitude of the thermal effect of the short circuit current and the exact time of its action are already available in digital form, and the mathematical expressions for calculating these parameters according to the formula of the invention contain only the operations of addition and multiplication of measurement results ;

- improving the accuracy of determining the magnitude and time of the thermal effect from the short circuit current and, as a result, improving the quality of control of the electric power facility;

- the absence of the need to calculate the constant, periodic and aperiodic components of the short circuit current, since they are all already present in the digitized instantaneous value of the current.

The technical result is achieved by the fact that in the claims the technical essence of the method for determining the magnitude and time of the thermal effect from the short circuit current that occurred at time t ₁ , including measuring, fixing and digitizing N times during the period T and at each current time t _j , j = 1, 2, ..., N, and

where t _{j + 1} - the next moment in time, s;

t _j - current time, s;

Δt = T / N is the signal discretization time step, s,

the current instantaneous value of the short circuit current x _kz (t _i ) in each phase, determine the magnitude of the thermal effect B _mer in each phase according to the following mathematical expression:

where B _mer - the magnitude of the thermal effect of the short circuit current in one of the phases, And ² s;

Δt = T / N is the signal discretization time step, s,

the summation is carried out over j from j = 1, which corresponds to the moment t ₁ - the time of occurrence of the short circuit current, up to the time t _up - the time for completion of automatic restart when j = f (t _up + 1) N;

x _KZ (t _i ) is the instantaneous value of the short circuit current in this phase at the current time t _j , A;

x _KZ (t _{i + 1} ) is the instantaneous value of the short circuit current in this phase at a subsequent time t _{j + 1} , A;

f is the industrial frequency, Hz;

N is the number of sampling intervals,

and the thermal exposure time t _KZ at each jth measurement on a cumulative basis increases monotonically from the value of t _KZ = 0, for j = 1, by the value of the sampling step of the signal in time Δt, provided that x _KZ (t _j ) is the current instantaneous value the short circuit current in this phase is not equal to zero, and the thermal exposure time t _kz remains unchanged if x _kz (t _j ) is the current instantaneous value of the short circuit current in this phase is zero, thus, the thermal exposure time t _kz for each of phases is determined by the following mat cal expression:

для всех j=1, 2, 3, …, f(t_апв+1)N,

for all j = 1, 2, 3, ..., f (t _apr +1) N,

where t _KZ - time of thermal exposure, s;

x _KZ (t _i ) is the instantaneous value of the short circuit current in this phase at the current time t _j , A;

Δt is the signal discretization time step, s;

f is the industrial frequency, Hz;

N is the number of sampling intervals.

The proposed method for determining the value of B _ter and time t _{cz of the} thermal effect from the short circuit current is based on measuring the digitized instantaneous values of the current t _cz (t _j ) at time t _j , where j = 1, 2, ..., N, N is the number of partitions on the period T, Δt = T / N is the time discretization step of the signal.

The degree of thermal effect of short circuit current on conductors and electrical apparatuses in accordance with GOST 30323-95. Short circuits in electrical installations. Methods for calculating the electrodynamic and thermal effects of short circuit current. Reissue. August 2004 3.1.1 "is determined by the value of the Joule integral (B _mer ) in amperes squared per second, that is, the following mathematical expression

- квадрат мгновенного значения тока короткого замыкания в произвольный момент времени t в течение диапазона интегрирования, А;Where $$x_{\mathrm{to}s}^2\left(t\right)$$

- the square of the instantaneous value of the short circuit current at an arbitrary time t during the integration range, A;

integration is carried out from the time t ₁ - time of occurrence of the fault current, until _none t - the time the tripping time, i.e., until the calculated duration fault in the installation, p.

In the general case, the current instantaneous value of the short circuit current x _kz (t _i ) at time t _i can be analytically represented by one of the following six mathematical expressions:

- in stationary mode with a symmetric phase-phase load is described by the well-known equality

- in the presence of X _P - constant component, the harmonic electric signal moves parallel to the abscissa axis up or down depending on the sign and value of X _P , and the expression for this signal has the form

- in the presence of a rapidly proceeding transient process due to switching or critical modes (short circuits, phase breaks), either an additive aperiodic component appears, which can be either decreasing

- or increasing

or a multiplicative aperiodic component, which can also be either decreasing

- or increasing

where for all six formulas describing the mathematical form of the measurement results of the digitized instantaneous values of the short circuit current in digital data processing, the following notation is used:

x _KZ (t _j ) is the result of measuring the digitized instantaneous current values at time t _i , A,

X _m is the amplitude value of the current, A,

ω = 2πf, - circular frequency, rad / s,

f is the signal frequency, Hz,

X _P - constant current component, A,

A _{a ↓ ·} is the initial value of the decreasing additive aperiodic current component, A,

τ _{a ↓} is the decay time constant of the decreasing additive aperiodic current component, s ^-1 ,

A _{a ↑ ·} is the initial value of the increasing additive aperiodic current component, A,

τ _{a ↑} is the decay time constant of the increasing additive aperiodic current component, s ^-1 ,

A _{M ↓ ·} is the initial value of the decreasing multiplicative aperiodic current component, A,

τ _{M ↓} is the decay time constant of the decreasing multiplicative aperiodic current component, s ^-1 ,

A _{M ↑ ·} is the initial value of the increasing multiplicative aperiodic current component, A,

τ _{M ↑} is the decay time constant of the increasing multiplicative aperiodic current component, s ^-1 ,

t _i = t ₁ , t ₂ , ..., t _N - times in which the signal is measured, t _{i + 1} = t _i + Δt, c,

Δt = T / N is the sampling step of the signal x (t _i ) in time, that is, in seconds, the value of the sampling step in radians is 2π / N,

T is the duration of the period, s,

N is the number of current measurements during the period.

Thus, the current instantaneous value of the current x _kz (t _i ) at time t _i by its nature contains all components (constant, periodic, aperiodic), if they occur in this circuit. This is a property of the instantaneous current value and it is not necessary to specifically determine these components.

Substituting the current instantaneous value of current x _kz (t _i ) into expression (1) written for calculating the integral for discrete measurements with step Δt (the trapezoid formula for calculating the integral, which provides sufficient accuracy for the calculations with the relative simplicity of the final expressions), we obtain a mathematical expression, given in the formula of the invention for determining the magnitude of the thermal effect of current

where B _mer - the magnitude of the thermal effect of the short circuit current in one of the phases, And ² s;

Δt = T / N is the signal discretization time step, s,

the summation is carried out over j from j = 1, that is, from the moment t ₁ - the time of occurrence of the short circuit current, to the time t _anv - the time of completion of the automatic restart, that is, to j = f (t _anv +1) N;

x _KZ (t _i ) is the instantaneous value of the short circuit current in this phase at the current time t _j , A;

x _KZ (t _{i + 1} ) is the instantaneous value of the short circuit current in this phase at a subsequent time t _{j + 1} , A;

f is the industrial frequency, Hz;

N is the number of sampling intervals.

The difficulty is the definition of real time t _KZ thermal effects from the short circuit current, since according to the research “A. Chunikhin Electric devices: General course. Textbook for high schools. - 3rd ed., Revised. and add. - M .: Energoatomizdat, 1988, p. 137-143. ”When switching the arc can go out and light up several times depending on the nature of the circuit. At a time when the arc does not burn and the short circuit current does not flow, there is not any thermal effect on the conductors and electrical apparatus from the short circuit current. Therefore, this time does not need to be taken into account, and it is not taken into account in the claims of the invention.

In this case, one more requirement of GOST 30323-95, clause 1.1.5, which reads as follows: “If there are devices for automatically re-connecting the circuit, the total thermal effect of the short circuit current must be taken into account. The time during which the circuit can automatically turn on again depends on the nature of the circuit and is set by relay services. Therefore, to calculate the degree of thermal effect of the short circuit current on conductors and electrical apparatuses, the calculation time must be increased by one second, to complete all transients, that is, to make t _tv +1. To convert this time from seconds to the number of measurements of the digitized instantaneous current values, it is necessary to multiply the time by the industrial frequency f, thereby obtaining the number of periods, and then multiplying by the number of measurements in period N - the number of sampling intervals. Thus, the number of measurements of instantaneous current values will be f (t _apv +1) N.

The algorithm for calculating the thermal exposure time t _KZ can be described as follows:

the thermal exposure time t _KZ at each jth measurement on a cumulative basis increases monotonically from the value of t _KZ = 0, for j = 1, by the value of the sampling step of the signal over time Δt, provided that x _KZ (t _j ) is the current instantaneous current value the short circuit in this phase is not equal to zero, and the thermal exposure time t _kz remains unchanged if x _kz (t _j ) is the current instantaneous value of the short circuit current in this phase is zero, so the thermal exposure time t _kz for each phase determined by the following math another expression:

для всех j=1, 2, 3, …, f(t_апв+1)N,

for all j = 1, 2, 3, ..., f (t _apr +1) N,

where t _KZ - time of thermal exposure, s;

x _KZ (t _i ) is the instantaneous value of the short circuit current in this phase at the current time t _j A;

Δt is the signal discretization time step, s;

f is the industrial frequency, Hz;

N is the number of sampling intervals.

Claims (1)

The method of determining the magnitude and time of the thermal effect from the short circuit current that occurred at time t ₁ , including measuring, fixing and digitizing N times during the period T and at each current time t _j , j = 1, 2, ..., N, and
t _{j + 1} = t _j + Δt,
where t _{j + 1} - the next moment in time, s;
t _j - current time, s;
Δt = T / N is the sampling step of the signal in time, s, of the current instantaneous value of the short circuit current x _kz (t _i ) in each phase, the magnitude of the thermal effect is determined In _mer in each phase according to the following mathematical expression:

where In _mer - the magnitude of the thermal effect of the short circuit current in one of the phases, And ² s;
Δt = T / N is the signal discretization time step, s,
the summation is over j from j = 1, which corresponds to the time t ₁ - the time of occurrence of the short circuit current, up to the time t _anв - the time of completion of the automatic restart when j = f (t _anв +1) N;
x _KZ (t _i ) is the instantaneous value of the short circuit current in this phase at the current time t _j , A;
x _KZ (t _{i + 1} ) is the instantaneous value of the short circuit current in this phase at a subsequent time t _{j + 1} , A;
f is the industrial frequency, Hz;
N is the number of sampling intervals,
and the thermal exposure time t _KZ at each jth measurement on a cumulative basis increases monotonically from the value of t _KZ = 0 by the value of the sampling step of the signal in time Δt, provided that x _KZ (t _j ) is the current instantaneous value of the short circuit current in this phase is not equal to zero, and the thermal exposure time t _KZ remains unchanged if x _KZ (t _j ) - the current instantaneous value of the short-circuit current in this phase is zero, thus, the thermal exposure time for each phase is determined by the following mathematical expression:

where t _KZ - time of thermal exposure, s;
x _KZ (t _i ) is the instantaneous value of the short circuit current in this phase at the current time t _j , A;
Δt is the signal discretization time step, s;
f is the industrial frequency, Hz;
N is the number of sampling intervals.