RU2608854C1 - Method of harmonic signals distortion parameters determining (versions) - Google Patents

Abstract

FIELD: electrical engineering.

SUBSTANCE: invention relates to electrical engineering, in particular, to technologies, using electric equipment, installed on electric power plants and substations in systems of production, transmission and consumption of power, and can be used in all electrical installations using digital data processing. Method of harmonic signals distortion parameters determining, in which establishing additive aperiodic component harmonic signals distortion decreasing type and calculating constant component value in signals. To determine signal A_a additive aperiodic component initial value and signal τ_a aperiodic component damping time constant continuously N times during period T and in each current moment in time t_i, i=1, 2, …, N, measuring and recording signal x(t_i) instantaneous values, and calculating signal A_a additive aperiodic component values, signal τ_a aperiodic component damping time constant by signal instantaneous values two consecutive measurements x(t_i) and x(t_i-1) according to following mathematical expressions:

where A_a is additive aperiodic component initial value, signal unit: for voltage are volts, V, for current are amperes, A; τ_a is signal additive aperiodic component damping time, s, x(t_i) is measured signal current value at moment of time t_(i), signal measurement unit; x(t_i-1) is same signal previous value at moment of time t_i-1, signal measurement unit; X_INT is signal constant component, signal measurement unit; k_i=X_m⋅sin(ωt_i) – harmonic signal value at moment of time t_(i), signal measurement unit; k_i-1=X_msin(ωt_i-1) – harmonic signal value at moment of time t_i-1, signal measurement unit; X_m is harmonic signal amplitude value, signal measurement unit, V or A.

EFFECT: technical result consists in simplification of currents and/or voltages measuring method.

2 cl, 2 dwg, 1 tbl

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 the processing of instantaneous values of measurement results of variable electrical signals, such as voltages and currents obtained using digital instruments.

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], since it allows for the distortion of the sinusoidal signal caused by switching in normal or emergency modes to determine the parameters of the aperiodic component necessary for assessing the state and control of the electric power system.

There are various methods and devices for identifying and determining the parameters of the aperiodic component of a rapidly occurring transient caused by switching in an alternating current electric circuit, and / or a constant component in an electric signal, due to both non-sinusoidal signal and non-symmetry of the phase load. Typically, these methods and devices are either associated with the costs of acquiring and installing special equipment, and then with the constant costs of its subsequent maintenance and maintenance, or require knowledge of additional parameters of the electrical circuit, such as active, capacitive and inductive resistances, or determine only the fact the presence of an aperiodic component, without solving the very problem of determining the parameters.

The known method described in GOST 28249-93 "Short circuits in electrical installations. Calculation methods in electrical installations of alternating current voltage up to 1 kV "section" 4. Calculation of the aperiodic component of the short circuit current. "

A sign of an analogue that coincides with the essential features of the proposed method is the ability to determine the parameters of the aperiodic component of the short circuit current.

The disadvantage of the analogue, from the point of view of the technical result, is that “in the general case, the largest initial value of the aperiodic component of the short circuit current is always prescribed to be equal to the amplitude X _{m of the} periodic component of the current” [GOST 28249-93]. In fact, this value belongs to the interval from -X _m to X _m and will be the same as the instantaneous current value at the time of the short circuit.

The second disadvantage of the analogue is the use of inductive and active resistances of the circuit, which, as a rule, are not known and can be, according to the complicated technology given in GOST, calculated only for the subsequent determination of the decay time constant of the aperiodic current component.

The third drawback is that only the additive aperiodic component of the current is determined, which is the algebraic sum of the aperiodic and harmonic components. However, as can be seen on the oscillograms of real transients, including those caused by short circuits, the change in currents most often has a multiplicative character, that is, in the form of a product of aperiodic and harmonic components.

Finally, the constant component, which may also be in the electrical signal, is not determined or even mentioned.

A known method of identifying an aperiodic or constant component according to the patent of the Russian Federation No. 2379823, IPC H03D 1/00. A method for identifying an aperiodic or constant component in an electric signal / Mamaev V.A., publ. 01/20/2010.

A sign of the analogue, which coincides with the essential features of the proposed method, is the possibility, based on the analysis of envelopes of amplitudes, to identify the fact of the presence of aperiodic or constant components in the electrical signal.

The disadvantage of the prototype analogue, from the point of view of the technical result, is that the method only allows to identify the fact of the presence of an aperiodic or constant component, but does not determine the parameters of the aperiodic component, namely the initial value of the aperiodic component and the value of the decay time constant of the aperiodic component of the electric signal.

A known method for identifying constant and / or aperiodic components with the determination of their parameters according to the patent of the Russian Federation No. 2543934, IPC H03D 1/00, G01R 31/327 (2006.01). A method for identifying the type of distortion of harmonic signals and determining the parameters of distortion under the multiplicative effect (Options) / Mussonov G.P., publ. 03/10/2015. The method described in paragraph 1 of the claims of the patent of the Russian Federation No. 2543934, is used as a prototype for a variant of the proposed method, characterized in paragraph 2 of the claims.

Signs of the prototype, coinciding with the essential features of the proposed method, are the ability to identify the nature of the distortion based on the processing of instantaneous values of the measurement results of changing electrical signals, to establish the presence of aperiodic and / or constant components in the electrical signal, as well as to determine their current values.

The disadvantage of the prototype is the low speed, since to determine the parameters of the aperiodic component, namely the initial value of the aperiodic component and the value of the decay time constant of the aperiodic component of the signal, instantaneous signal values obtained over a half period, that is, within 0.01 second, are required.

A known method of identifying a constant component with the determination of its parameters, given in the monograph: L. Bessonov Theoretical foundations of electrical engineering. Electric circuits / Ninth edition, revised and supplemented / M .: Higher School, 1996. The method uses the fact that the integral of the harmonic function is equal to zero, taken for one period. In the presence of a constant component in the signal, the value of this integral is equal to the constant component. The method is used as a prototype for a variant of the proposed method, characterized in paragraph 1 of the claims. However, the method does not determine the parameters of the aperiodic component of the signal.

The objective of the invention is the creation of a high-speed method for determining the parameters of the aperiodic component from the measurement results of two adjacent instantaneous signal values, which allows in operation to obtain complete information about the parameters of a fast-moving transient, the duration of which does not exceed the period.

The technical result of the invention is to reduce the measurement time, to increase the accuracy of the measurement, as well as to ensure that the fast-moving transient with a duration of less than one period of the possibility of determining the parameters in order to further study the characteristics of the electrical circuit.

The technical essence of the method for determining the distortion parameters of harmonic signals, described in paragraph 1 of the claims and used in the case of additive effects, is that they establish a decreasing type of distortion of the harmonic signals of the additive aperiodic component and calculate the value of the constant component in the signals, and differs in that for determining an initial value of the aperiodic signal component additive _{A a} constant and the decay time of the aperiodic component Sig la τ _and continuously N times during a period T and at each current instant of time t _{i, i} = 1, 2, ..., N, measure and record the instantaneous values x (t _i) signal and the calculated values of the additive aperiodic signal component A _and , the decay time constant of the aperiodic component of the signal τ, _and only by two successive measurements of the instantaneous values of the signal x (t _i ) and x (t _i-1 ) according to the following mathematical expressions:

And _a = (x (t _i ) -X _P -k _i ) / exp (t _i / τ _a ),

τ _a = (t _i -t _i-1 ) / ln ((x (t _i-1 ) -X _П -k _i-1 ) / ((x (t _i ) -Х _П -k _i )),

where A _a is the initial value of the additive aperiodic component, signal units: for voltage - volts, V, for current - amperes, A;

τ _a is the decay time constant of the additive aperiodic component of the signal, s;

x (t _i ) is the current value of the measured signal at time t _i , the unit of measurement of the signal;

x (t _i-1 ) is the previous value of the same signal at time t _i-1 , the unit of measurement of the signal;

X _P - the constant component of the signal, the unit of measurement of the signal;

k _i = X _m sin (ωt _i ) is the value of the harmonic signal at time t _i , the unit of measurement of the signal;

k _i-1 = X _m sin (ωt _i-1 ) is the value of the harmonic signal at time

t _i-1 , signal units;

X _m - the amplitude value of the harmonic signal, the signal units, V or A.

In the second independent claim, the technical essence of the method for determining the parameters of distortion of harmonic signals used in a multiplicative effect is disclosed, which consists in setting a decreasing type of distortion of harmonic signals in a multiplicative aperiodic component and calculating the magnitude of the constant component in the signals, and differs in that for determining the initial value of the multiplicative aperiodic component of the signal A _m and the attenuation time constant the aperiodic component of the signal τ _m constantly N times during the period T and at each current point in time t _i , i = 1, 2, ..., N, measure and record the instantaneous values of the signal x (t _i ), and calculate the values of the decreasing multiplicative aperiodic the signal component A _m and the decay time constant of the aperiodic signal component τ _m only by two consecutive measurements of the instantaneous values of the signal x (t _i ) and x (t _i-1 ) according to the following mathematical expressions:

A _m = (x (t _i ) -X _P ) ⋅exp (t _i / τ _m ) / k _i ,

τ _m = (t _i -t _i-1 ) / ln ((x (t _i-1 ) -Х _П ) k _i / ((x (t _i ) -Х _П ) k _i-1 )),

where A _m is the initial value of the multiplicative aperiodic component, signal units: for voltage - volts, V, for current - amperes, A;

τ _m is the decay time constant of the multiplicative aperiodic component of the signal, s;

x (t _i ) is the current value of the measured signal at time t _i , the unit of measurement of the signal;

x (t _i-1 ) is the previous value of the same signal at time t _i-1 , the unit of measurement of the signal;

X _P - the constant component of the signal, the unit of measurement of the signal;

k _i = sin (ωt _i ) is the value of the harmonic signal at time t _i , the unit of measurement of the signal;

k _i-1 = sin (ωt _i-1 ) is the value of the harmonic signal at time t _i-1 , the unit of measurement of the signal.

Differences from the prototype prove the novelty of the technical solutions described in paragraph 1 and paragraph 2 of the claims.

The new approach allows providing for a fast-moving transient with a duration of less than one period the possibility of determining the parameters in order to further study the characteristics of the electric circuit, as well as reduce the measurement time and increase the accuracy of measurement, which confirms the compliance of the claimed technical solutions with the patentability condition “industrial applicability”.

From the prior art, the distinctive essential features of the proposed method, described in the claims, are unknown, which confirms their compliance with the condition of patentability "inventive step".

The invention is illustrated by drawings, where

in FIG. 1 is a graph of a decreasing additive aperiodic and constant components of harmonic signal distortion;

in FIG. 2 is a graph of a decreasing multiplicative aperiodic and constant components of harmonic signal distortion.

The method is as follows.

In the presence of a rapidly proceeding transient process due to disconnection or discharge of the load, as well as the critical mode (phase wire breaks), distortion of harmonic signals appears. This is a decreasing or additive aperiodic component described by the expression

or the multiplicative aperiodic component described by the expression

where in both mathematical expressions (1) and (2) the following notation is used:

x (t _i ) is the result of measuring an electrical signal (current and / or voltage, i (t), u (t) with a frequency ƒ) at time t _i , the signal unit, V or A;

X _P - constant component, which moves the electrical signal parallel to the abscissa axis up or down depending on the sign and value of X _P , the constant component is always additive;

X _m - the amplitude value of the harmonic signal, the signal unit, V or A;

ω = 2πƒ - circular frequency, rad / s;

ƒ - harmonic signal frequency, Hz;

ϕ is the phase of the harmonic signal, rad;

A _a is the initial value of the additive aperiodic component, the signal unit, B or A;

τ _a is the decay time constant of the additive aperiodic component, s;

And _m is the initial value of the multiplicative aperiodic component, the signal unit, B or A;

τ _m is the decay time constant of the multiplicative aperiodic component, s.

The value of the phase of the harmonic signal ϕ for solving the problem of determining the parameters of the aperiodic component in the electric signal does not play a role.

The value of the frequency of the harmonic signal неизмен remains unchanged for any switching, phase-wire breakage and transient.

The indices “ a ” and “m” in the designation of the initial value of A and the decay time constant τ mean “additive” and “multiplicative”, respectively.

The graphs of the additive and multiplicative aperiodic processes differ in that in the additive process shown in FIG. 1, a harmonic signal (sinusoid) curve with a constant amplitude equal to three signal units is “strung” onto an aperiodic curve with parameters A _a = 5 signal units and τ _a = 0.01 s and decreases with it. These two connected curves move parallel to the abscissa axis up or down depending on the sign and magnitude of the constant component. In FIG. 1 constant component X _P = 2 units of signal measurement.

In the graph of the multiplicative aperiodic process shown in FIG. 2, it can be seen that the axis of the curve of the harmonic signal (sinusoid) either coincides with the abscissa axis when there is no constant component, or moves parallel to the abscissa axis up or down depending on the sign and value of the constant component (in this case, the constant component X _П = 2 units signal measurement), and all aperiodic changes are associated only with a change in the amplitude value of the harmonic signal. The parameter values are similar to FIG. 1 and have the following meanings: A _m = 5 units of signal measurement, τ _m = 0.01 s, X _P = 2 units of signal measurement.

Under the multiplicative action of the aperiodic component, according to expression (2), the amplitude value of the harmonic signal follows the initial value of the aperiodic component and is equal to it at each moment of time, as can be seen in FIG. 2.

The following circumstances allow to accelerate the process of determining the parameters of the aperiodic component of the signal.

The constant component, which moves the electric signal parallel to the abscissa axis up or down depending on the sign and value of X _P , is caused either by the conversion of an alternating electric signal, for example, by its rectification, or by an asymmetric phase load. The value of the constant component is constantly updated in various ways and algorithms during the operation of the power system. For example, by the method of the prototype or by the zero sequence during the decomposition of the signal, finally, by direct measurement of the signals and the subsequent calculation (Bessonov L.A.). Therefore, the value of the constant component is predetermined and can be used as a known value for calculating the distortion parameters of harmonic signals, that is, the initial value and the decay time constant of the additive aperiodic component.

With the additive action of the aperiodic component, it is assumed that the amplitude value of the harmonic signal does not change during the rapidly proceeding transient process. This is because, firstly, all changes associated with the transient are enclosed in a term describing the aperiodic component of the signal. Secondly, the measurement and calculation of the parameters of the aperiodic component of the signal, which comes in the form of the term expression (1), is carried out during the first half period when the relay protection has not yet worked and the load parameters have remained unchanged, including the amplitude value of the harmonic signal. Normative documents of relay protection prescribe the time of its operation equal to half the period, that is, 0.01 s.

The amplitude value of the harmonic signal X _m can be determined from the actual value X _∂ , which is always measured and controlled by dispatch services, according to the well-known expression

.

.

Therefore, the amplitude value of the harmonic signal under the additive action of the aperiodic component can be used as a known quantity for calculating the distortion parameters of harmonic signals.

Finally, the last circumstance concerns the calculation of the values of the harmonic function sin (ωt _i ). The International Standard IEEE Std С37.111-1999 “General Transitional Data Exchange Format in Power Systems (COMTRADE)”, taking into account the requirements of which all digital measuring instruments are built, precisely prescribes N - the number of measurements of the instantaneous signal values over a period. The standard contains a number of N values that can be used. The number of measurements determines the accuracy of the device, the more measurements, the more accurate the device. Thus, the angular values of ωt _i , i = 1, 2, ..., N, for each device are fixed, since t _i = Δt⋅i, i = 1, 2, ..., N, where Δt = T / N is the step discretization of the signal x (t _i ) in time, T is the period of the harmonic signal. And this means that for each particular device the values of the harmonic function sin (ωt _i ) are fixed and can be calculated in advance.

Given these circumstances, mathematical expressions (1) and (2) can be written in the following form:

where the measurement results and known quantities are collected to the left of the equal sign of expressions (3) and (4), and unknown parameters of the aperiodic component are to the right of the equal sign. Using the results of the previous measurement at time t _i-1 , we obtain expressions similar to (3) and (4), dividing them into each other, respectively, for the identical type of distortion of harmonic signals, we obtain the mathematical expressions:

,

,

,

,

in which there is no one unknown parameter - the initial value of the aperiodic component. Having logarithm the obtained expressions and solving them with respect to another unknown parameter, we find it, that is, the time constant of the aperiodic component. It is these expressions that are given in two independent claims, respectively, for the additive and multiplicative aperiodic component.

Substituting the obtained value of the time constant of the aperiodic component in expressions (3) and (4), we find mathematical expressions for determining the initial value of the aperiodic component, which are given in two independent claims, respectively, for the additive and multiplicative aperiodic component of distortion of harmonic signals.

Another component influences the accuracy of calculating the parameters of the aperiodic component of the electric signal - this is the stochastic component due to the random nature of the moments of switching on and off the load. The use of two adjacent instantaneous signal values x (t _i ) and x (t _i-1 ) to determine the parameters of the aperiodic component of the signal allows to increase the number of measurements up to N / 2 times during one half period, while according to the established rules the relay protection has not yet worked. This allows you to significantly improve the accuracy of calculations, since the averaging of the calculated value of some parameter S _j , j = 1, ..., n, by the expression

where the summation is over j = 1, ..., n,

S is the average value of some parameter, for example, the decay time constant,

n is the number of calculations of this parameter over which averaging is performed, and in our case n = N / 2,

allows you to increase the accuracy of the calculation results of all parameters, reducing the variance (scatter) of the values of each parameter in N / 2 times.

As an example, the table shows a fragment of a transient process containing 0.001 seconds from its beginning. Only 8 first measurements from N = 128 per period. This time is enough to determine eight times all the parameters of the additive aperiodic component and seven times for the multiplicative aperiodic component, since division by zero is a forbidden operation.

For N = 128 we get: the sampling step Δt = T / N = 0.02 / 128 = 0.00015625.

The data in the table are given for the additive, according to expression (1), and for the multiplicative, according to expression (2), aperiodic components of the distortion of harmonic signals in the presence of a constant component. Data was obtained with the following parameter values (in arbitrary units of signal measurement):

constant component X _P = 2,

the initial value of the aperiodic component A = 5,

the value of the decay time constant of the aperiodic component τ = 0.01 s,

the amplitude value of the harmonic signal X _m = 3 for the additive model, according to expression (1).

Substituting the data from the table into the expressions for determining the distortion parameters of harmonic signals with the additive aperiodic component, for example, for the third and second dimensions, that is, for i = 3, we obtain

,

,

.

.

Similarly, we can calculate the value of the distortion parameters for the increasing multiplicative aperiodic component, that is, for the last column of the table. Having performed the calculations using mathematical expressions given in paragraph 2 of the claims,

,

,

,

,

we obtain the following results: τ _m = 0.01, A _m = 5.

The calculated values of the parameters of both the additive and multiplicative aperiodic components of the harmonic signal distortion according to the mathematical expressions given in two independent claims of the proposed method give an absolutely accurate result. The reason for this is the absence of a stochastic component due to the random nature of the moments of switching on and off the load. However, given the fact of a huge number of consumers of electric energy, it can be considered that the stochastic component has the character of “white noise”, that is, its mathematical expectation is zero. And, with a large number n of calculating the parameter values, the calculation results will tend to the exact value. Using expression (5) allows to increase the accuracy of the calculation results of all parameters, reducing the variance (scatter) of the values of each parameter n times.

The graphs shown in FIG. 1 and FIG. 2, are built on the database of the table, if it is continued for a half period. The curve drawn by the solid bold line shows the aperiodic component, the curve drawn by the dashed line shows the harmonic signal. A straight line parallel to the abscissa axis and drawn by a solid thin line shows the constant component.

Claims (22)

1. The method of determining the parameters of distortion of harmonic signals, which establish a decreasing type of distortion of harmonic signals of the additive aperiodic component and calculate the value of the constant component in the signals, characterized in that to determine the initial value of the additive aperiodic component of the signal A _a and the decay time constant of the aperiodic component of the signal τ _and constantly N times during the period T and at each current moment of time t _i , i = 1, 2, ..., N, instantaneous values are measured and recorded signal x (t _i), and calculated values of the additive aperiodic signal component _Aa, the instantaneous values x (t _i) and x (t _i-1) signal the time constant of attenuation of the aperiodic component τ signal _and two consecutive measurements according to the following mathematical expressions :

where A _a is the initial value of the additive aperiodic component, signal units: for voltage - volts, V, for current - amperes, A; τ _a is the decay time constant of the additive aperiodic signal component, s; x (t _i ) is the current value of the measured signal at time t _i , the unit of measurement of the signal; x (t _i-1 ) is the previous value of the same signal at time t _i-1 , the unit of measurement of the signal; X _P - the constant component of the signal, the unit of measurement of the signal; k _i = X _m ⋅sin (ωt _i ) is the value of the harmonic signal at time t _i , the unit of measurement of the signal; k _i-1 = X _m sin (ωt _i-1 ) is the value of the harmonic signal at time t _i-1 , signal units; X _m - the amplitude value of the harmonic signal, the units of the signal, V or A. 2. A method for determining the distortion parameters of harmonic signals, in which a decreasing type of distortion of harmonic signals of the multiplicative aperiodic component is established and a constant component in the signals is calculated, characterized in that for determining the initial value of the multiplicative aperiodic component of the signal A _m and the decay time constant of the aperiodic component of the signal τ _m constantly N times during the period T and at each current time moment U, i = 1, 2, ..., N, measure and record instantly the signal values x (t _i ), and the values of the decreasing multiplicative aperiodic component of the signal A _m and the decay time constant of the aperiodic component of the signal τ _m are calculated from two successive measurements of the instantaneous values of the signal x (t _i ) and x (t _i-1 ) from the following mathematical expressions:

where A _m is the initial value of the multiplicative aperiodic component, signal units: for voltage - volts, V, for current - amperes, A; τ _m is the decay time constant of the multiplicative aperiodic component of the signal, s; x (t _i ) is the current value of the measured signal at time t _i , the unit of measurement of the signal; x (t _i-1 ) is the previous value of the same signal at time t _i-1 , the unit of measurement of the signal; X _P - the constant component of the signal, the unit of measurement of the signal; k _i = sin (ωt _i ) is the value of the harmonic signal at time t _i , the unit of measurement of the signal; k _i-1 = sin (ωt _i-1 ) is the value of the harmonic signal at time t _i-1 , the unit of measurement of the signal.

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