RU2479085C2 - Method to produce values of orthogonal projections of one vector to direction of another vector of two single-frequency electric signals - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: method consists in production of values of orthogonal projections of one vector to direction of another vector of two single-frequency electric signals on the basis of using an operation of multiplication of three factors, every of which is an electric signal, at the same time a certain non-sinusoidal electric signal is generated, containing a permanent component, which is identified by the available method. The value of the identified permanent component is definitely related to one of the projections of one vector to the direction specified by the vector of another one of two single-frequency harmonic electric signals. Depending on which projections are identified and for which of two vectors, in the method there are requirements specified to each of three factors.

EFFECT: increased accuracy and performance.

3 cl, 7 dwg

Description

и второго

, например, напряжения f₁(t)=u(t) и тока f₂(t)=i(t). При этом получение ортогональных проекций выполняет входящий в структуру устройства релейной защиты, противоаварийной автоматики и измерения (УРЗАИ) вычислительно-логический модуль (ВЛМ), который на своем выходе в виде цифрового или аналогового сигнала формирует информацию о значениях ортогональных проекций. Эту информацию используют в логике принятия УРЗАИ действия, вытекающего из конкретно возникшей ситуации в системе электроснабжения промышленной частоты f.The invention relates to electrical engineering, and in particular to methods and devices based on them, which, in the steady state operating mode of a three-phase power supply system of industrial frequency f, identify the values of the orthogonal projections of the complex vector of one of two single-frequency harmonic electrical signals, to the direction of the complex vector of another harmonic electrical signal, which considered as a reference, and by which the direction for orthogonal projections is set, each of two single-frequency harmonic electric signals generally as harmonics may be part of the spectrum of harmonics corresponding to their non-sinusoidal periodic electrical signals, namely the first

and second

, for example, the voltage f ₁ (t) = u (t) and the current f ₂ (t) = i (t). At the same time, the production of orthogonal projections is performed by the computational logic module (VLM), which is included in the structure of the relay protection, emergency automation and measurement device (URIAI), which generates information about the values of the orthogonal projections at its output in the form of a digital or analog signal. This information is used in the logic of the adoption of the URZAI action arising from the specific situation in the power supply system of industrial frequency f.

For example, one of the methods for determining the distance of a probable short circuit location on a high-voltage power line of a three-phase power supply system uses information about the magnitude of the projection of the voltage vector of the short circuit loop on the direction of the vector of the short circuit current flowing in this loop [Dyakov A.F. Microprocessor automation and relay protection of electric power systems: textbook. manual for universities / A.F. Dyakov, N.I. Ovcharenko. - M .: Publishing house MPEI, 2008, p.259-261]; to ensure that the automatic adjustment system for synchronous generator requires information about I _gr reactive and active components of the vector I _GA current generator I _d, the currents I _gr and I _GA determined projections current vector I _g respectively perpendicular and coincident direction specified by the corresponding reference voltage vector U _{g of the} generator [Ovcharenko NI Automation of energy systems: a textbook for universities. - 2nd ed., Revised. and add. N.I. Ovcharenko: under the editorship of Corr. RAS, doc. tech. sciences, prof. A.F. Dyakov. Publishing House MPEI, 2007. S.154-156, 164-166]. The proposed method can also be used in devices for determining the components of the total power that is consumed by an element of the power supply system at the frequency of single-frequency electrical signals.

In some cases, the voltages u (t) and currents i (t) in the AC power supply system can vary according to periodic non-sinusoidal laws with a repetition period T = 1 / f. This may cause incorrect operation of the URZAI. Under these conditions, information on the operating mode of the power supply system component controlled by the device is obtained by appropriate technical and software solutions using the parameters of the damaged power supply system element for the main harmonics of voltage u (t) and current i (t) with frequency f, which are part of periodic non-sinusoidal, respectively voltage and current.

Closest to the final task to be solved, but not having common features with the invention, however, the invention according to [Application No. 2009110871 (RU) IPC Н03В 28/00 (2006.01) is accepted as a close prototype. A method of obtaining an analog electrical signal of a module of the orthogonal component of a vector of one of two single-frequency harmonic electrical signals [Text] / Mamaev V.A. (RU): applicant and patent holder of the State Educational Institution of Higher Professional Education “North Caucasus State Technical University” (RU). - publ. 09/27/2010. Bull. No. 27].

The method according to the adopted prototype can be used for two single-frequency harmonic electrical signals under conditions of slight sinusoidal distortion of two periodic electrical signals with the same repetition period T = 1 / f, for example voltage and current, and the difference in time when their instantaneous values are zero, it is practically determined by the difference in the moments of passage through the zero value of their main harmonics entering the first electric signal and the second electric signal with a frequency th f. In addition, in determining the orthogonal component, the effective value of the corresponding instantaneous electrical signal is used, the value of which is affected by the harmonics present in the electrical signal that are multiples of the frequency f. The noted features of the method adopted as a prototype limit the scope of its application mainly only for harmonic single-frequency electrical signals.

The method of obtaining the values of the orthogonal projections of one vector on the direction of the other vector of two single-frequency electrical signals according to the invention consists in the ability to obtain the parameters of the orthogonal projections of one vector, for example, the complex harmonic amplitude, in particular the harmonic of the fundamental frequency f, which is included in the harmonic spectrum, for example, periodic non-sinusoidal electric signal f ₁ (t), in the direction determined by the vector of the complex amplitude of the other harmonic of the main frequency f, but included in the structure of the second periodic non-sinusoidal electric signal f ₂ (t) having the same repetition period T, while the vector of the complex harmonic amplitude, which determines the orthogonal directions, is considered to be reference.

основной гармоники

напряжения, входящей в состав гармоник периодического несинусоидального напряжения

, и комплексный опорный вектор

основной гармоники

тока, входящей в состав гармоник периодического несинусоидального тока

, причем k и n - номера гармоник.Proposed in the invention method, it is advisable to use in digital URASA. In this case, the VLM module included in the structure of the URZAI operates on the basis of methods and means of linear (LP) and nonlinear (NP) conversion of electrical signals [Shneerson E.M. Digital relay protection. - M .: Energoatomizdat. 2007. P.39-43], while the LP converts the analog non-sinusoidal periodic electrical signals arriving at the VLM input into their digital images, moreover, according to the processing sequences of the information received from the LP according to the information proposed at the input, the latter generates at its outputs digital or analog forms of the final information about the values of the orthogonal projections of one vector on the direction of the other vector of two single-frequency electrical signals, while, in the General case, VLM consists of d of submodules, namely, the SMVF submodule for calculating the phases of single-frequency harmonics and the SMVP submodule for calculating vector projections, the method of the invention is used as the basis for the functioning of the SMVP submodule, while signals are generated at the output of the SMVP submodule that are functionally connected with the modules of the sine and cosine components of the projections of the complex vector the amplitude of the first single-frequency harmonic electrical signal, in the direction of the reference vector of the complex amplitude of the second single-frequency with the first monic electric signal, for example, as these vectors can be a complex vector

fundamental harmonics

voltage, which is part of the harmonics of the periodic non-sinusoidal voltage

, and complex reference vector

fundamental harmonics

current, which is part of the harmonics of a periodic non-sinusoidal current

, and k and n are harmonic numbers.

In comparison with the prototype, the achieved technical result when using the method according to the invention in the VLM module of the corresponding technical device consists in increasing the accuracy and speed of the obtained information about the values of the orthogonal projections of one vector on the direction of the other vector of two single-frequency electrical signals, for example, in the case when each of these single-frequency electrical signals, as a harmonic, is included in the structure of the corresponding nesin a periodic periodic electrical signal, for example, voltage u (t) and current i (t), which, ultimately, increases the metrological and other operational characteristics of a technical device, for example, URESA, whose task is to monitor the state of an element of the power supply system, in particular at the fundamental frequency f.

The theoretical basis for achieving this result is that according to the proposed method for obtaining the values of the orthogonal projections of one vector on the direction of the other vector of two single-frequency electrical signals, each of the single-frequency harmonic electrical signals, in the general case, is a harmonic included in the harmonic spectrum of its periodic non-sinusoidal electrical signal f ₁ (t) and f ₂ (t) with the same repetition period t = 1 / f, form a new non-sinusoidal electrical Sig l, which are multiplied three electrical signal, depending upon the particular problem being solved as one of the factors are used either the first f ₁ (t), or the second f ₂ (t) a non-sinusoidal periodic electrical signal, and as the other two factors according to the present The invention uses two electrical signals, which form in the form of two additional sinusoidally varying electrical signals, isolate the constant component from the generated new non-sinusoidal signal and this the constant component is used to identify the values of the orthogonal projections of the vector of the complex amplitude of the single-frequency harmonic that is part of the harmonics, for example, the first non-sinusoidal periodic electric signal f ₁ (t) in the direction specified by the reference vector of the complex amplitude of the single-frequency harmonic, which is included in the spectrum of harmonics of the second non-sinusoidal periodic electrical signal f ₂ (t).

является суммой изменяющихся по синусоидальному закону k гармоник

и имеет структуруThe theoretical rationale for the proposed method according to the invention is as follows. In the general case, the first periodic non-sinusoidal electrical signal

is the sum of k harmonics varying according to the sinusoidal law

and has a structure

- амплитуда входящей в структуру первого электрического периодического несинусоидального сигнала f₁(t) k-той гармоники; ω=2π/Т=2πf - угловая частота колебаний основной гармоники

электрического сигнала

;

- начальная фаза колебаний k-той гармоники, при этом математическое выражение мгновенного значения основной гармоники (k=1) с частотой f следующееWhere

- the amplitude of the structure of the first electric periodic non-sinusoidal signal f ₁ (t) of the k-th harmonic; ω = 2π / Т = 2πf is the angular frequency of oscillations of the fundamental

electrical signal

;

is the initial phase of oscillations of the k-th harmonic, and the mathematical expression of the instantaneous value of the fundamental harmonic (k = 1) with a frequency f is as follows

The instantaneous harmonic value according to (2) corresponds to the complex amplitude

и имеет структуруIn the general case, the second periodic non-sinusoidal electric signal f ₂ (t) (4) is the sum of n harmonics

and has a structure

и

- соответственно амплитуда n-той гармоники и ее начальная фаза колебаний; при этом основная гармоника (n=1) с частотой f, входящая в структуру периодического несинусоидального электрического сигнала

, имеет следующее математическое выражениеWhere

and

- accordingly, the amplitude of the nth harmonic and its initial phase of oscillation; the fundamental harmonic (n = 1) with a frequency f, which is part of the structure of a periodic non-sinusoidal electric signal

has the following mathematical expression

The instantaneous harmonic value according to (5) corresponds to the complex amplitude

и

, т.е. имеющим частоту f, входящих соответственно в первый периодический несинусоидальный электрический сигнал

и во второй периодический несинусоидальный электрический сигнал

. Для получения значений ортогональных проекций одного вектора, например вектора

на направление другого вектора

, который в данном случае считают опорным, формируют третий несинусоидальный электрический сигнал f₃(t), причем применительно к рассматриваемому случаю этот электрический сигнал определяют через произведение трех электрических сигналов f₁(t), f_доп.1(t) и f_доп.2(t):The essence of the proposed method is shown by the example of an algorithm for its application to two single-frequency, fundamental harmonics

and

, i.e. having a frequency f included respectively in the first periodic non-sinusoidal electrical signal

and in the second periodic non-sinusoidal electrical signal

. To obtain the values of the orthogonal projections of a single vector, for example a vector

to the direction of another vector

, which in this case is considered to be reference, form the third non-sinusoidal electrical signal f ₃ (t), and in relation to the case under consideration, this electrical signal is determined through the product of three electrical signals f ₁ (t), f _{add. 1} (t) and f _{add. 2} (t):

в своей структуре содержит постоянную составляющую.the third non-sinusoidal electrical signal

in its structure contains a constant component.

In the expression (7) the following notation is used:

f ₁ (t) is the first periodic non-sinusoidal electrical signal (1);

f _{add 1} (t) and f _{add 2} (t) - introduced according to the invention, the first and second additional harmonic electrical signals.

The first additional harmonic electric signal f _{add. 1} (t) in (7) has a unit amplitude, changes, in particular, according to a sinusoidal law, while the argument of the trigonometric function consists of two terms, and the first term is determined by the product of the fundamental angular frequency ω = 2πf at time t, the second term is introduced according to the invention and determines the initial angle of oscillations α of the harmonic electric signal, while the value of the angle of oscillations α depends on which vector of the complex amplitude of the main harmonics adopted for reference:

основной гармоники (5), входящей в структуру второго периодического несинусоидального электрического сигнала (4), т.е. выражение (8) в этом случае имеет структуруFor example, when using the proposed method for determining the values of the orthogonal projections of the complex vector (3) of the fundamental harmonic (2), the initial phase of oscillations α in (8) should be equal to the initial phase of the oscillation

fundamental harmonic (5), which is part of the structure of the second periodic non-sinusoidal electric signal (4), i.e. expression (8) in this case has the structure

, т.е. вводимый второй дополнительный гармонический сигнал изменяется по законуThe second additional harmonic electric signal f _{additional 2} (t) introduced in accordance with the invention, in (7) has a unit amplitude, varies according to a sinusoidal law, while the argument of the trigonometric sine function is twice as large as the argument of the trigonometric function of the first additional harmonic signal

, i.e. the introduced second additional harmonic signal changes according to the law

from which it follows that the introduced second additional harmonic signal has a frequency and an initial phase angle of oscillation, twice the frequency and the initial phase angle of oscillation of the first input additional signal (8).

, содержащего постоянную составляющую, например, с использованием операции интегрирования на интервале времени от t₀ до t₀+T, где t₀ момент подачи команды на выполнение операции интегрирования, выделяют эту постоянную составляющую в виде напряжения U₀ постоянного тока, которую согласно изобретению считают четвертым электрическим сигналом f₄, т.е.According to the proposed method from the generated third non-sinusoidal electrical signal

containing a constant component, for example, using an integration operation on a time interval from t ₀ to t ₀ + T, where t _{0 is the} moment a command is issued to perform an integration operation, this constant component is isolated in the form of a DC voltage U ₀ , which is considered according to the invention the fourth electrical signal f ₄ , i.e.

третьей гармоники, при условии, что в (8) и (10) угол

, величина напряжения F₀ постоянного тока по (11), однозначно идентифицирует значение проекции вектора комплексной амплитуды

основной гармоники (2) первого несинусоидального периодического сигнала (1) на направление, перпендикулярное направлению, задаваемому опорным вектором комплексной амплитуды

основной гармоники (5) второго несинусоидального периодического электрического сигнала (4), т.е. применительно к основным гармоникам, входящим в несинусоидальные сигналы

и

, четвертый электрический сигнал

определяется выражениемIn the absence in the first periodic non-sinusoidal electrical signal

third harmonic, provided that in (8) and (10) the angle

, the DC voltage value F ₀ according to (11) uniquely identifies the projection value of the complex amplitude vector

fundamental harmonic (2) of the first non-sinusoidal periodic signal (1) in the direction perpendicular to the direction specified by the reference vector of complex amplitude

fundamental harmonic (5) of the second non-sinusoidal periodic electrical signal (4), i.e. as applied to the fundamental harmonics included in non-sinusoidal signals

and

fourth electrical signal

defined by the expression

, или только второго дополнительного электрического сигнала

в аргумент функции синуса дополнительно вводят угол, соответственно равный либо +π/2, либо -π/2, т.е., например, в этом случае только первый дополнительный электрический сигнал f_доп.1(f) должен иметь структуруTo determine the value of the orthogonal projection of the complex vector (3), which coincides with the direction of the reference complex vector (6), when generating or only the first additional electrical signal

, or only the second additional electrical signal

in the argument of the sine function, an angle is additionally introduced, respectively, equal to either + π / 2 or -π / 2, i.e., for example, in this case, only the first additional electrical signal f _{additional 1} (f) should have the structure

those. in this case, the first additional electrical signal is formed varying according to the law of cosine.

определяется выражениемThen the fourth electrical signal

defined by the expression

основных гармоник (2) и (5) определяет угол сдвига по фазе

между этими гармониками, то выражения (12) и (14) имеют структуру:Given that the difference between the initial phases of the oscillations

fundamental harmonics (2) and (5) determines the phase angle

between these harmonics, then expressions (12) and (14) have the structure:

и

and

проекции вектора комплексной амплитуды (3) на перпендикулярное направление, задаваемое опорным вектором комплексной амплитуды (6), а конечный результат по выражению (16) определяет значение

проекции вектора комплексной амплитуды (3) на направление, совпадающее с направлением, задаваемым опорным вектором комплексной амплитуды (6).in this case, the final result by expression (15) determines the value

the projection of the vector of complex amplitude (3) on the perpendicular direction defined by the reference vector of complex amplitude (6), and the final result from expression (16) determines the value

the projection of the complex amplitude vector (3) on the direction coinciding with the direction specified by the complex amplitude reference vector (6).

дополнительно ввести угол, равный -π/2, т.е. в этом случае только второй дополнительный электрический сигнал f_доп,2(t) должен иметь структуруThe final result, similar to that calculated by expression (16), can be obtained if only in the argument of the sine function of the second additional electric signal

additionally enter an angle equal to -π / 2, i.e. in this case, only the second additional electric signal f _{add, 2} (t) must have the structure

those. in this case, the second additional electrical signal is generated changing according to the law, an inverse change in the cosine.

Thus, the proposed method according to the invention provides for the production of electrical signals, which for two single-frequency harmonics, each included in its own non-sinusoidal electrical signal, identifies the modules of the orthogonal projections of the first complex amplitude vector (3) of the main harmonic of the first non-sinusoidal electric signal (1) in the direction determined the second vector of the complex amplitude (6) of the fundamental harmonic of the second non-sinusoidal electrical signal (4), and the harmonics frequencies are equal.

напряжения основной гармоники несинусоидального периодического напряжения

на соответственно перпендикулярное и совпадающее направления, задаваемое направлением опорного вектора комплексной амплитуды

тока основной гармоники несинусоидального периодического тока

, напряжение

идентифицирует значение синусной составляющей, а напряжение

идентифицирует значение косинусной составляющей вектора комплексной амплитуды

напряжения основной гармоники

напряжения

.If in expressions (15) and (16) the DC voltages F _{0, s} and F _{0, c} are associated with the values of the projections of the complex amplitude vector

harmonic voltage of non-sinusoidal periodic voltage

perpendicular and coincident directions, respectively, defined by the direction of the reference vector of complex amplitude

harmonic current of a non-sinusoidal periodic current

voltage

identifies the value of the sine component, and the voltage

identifies the value of the cosine component of the complex amplitude vector

fundamental voltage

voltage

.

в качестве опорного вектора, с направлением которого связывают направления ортогональных проекций, принимают вектор

при этом в качестве угла α в выражениях (8) и (10) используют угол

начальной фазы колебаний основной гармоники

, входящей в состав первого периодического несинусоидального электрического сигнала

, а для формирования третьего несинусоидального электрического сигнала f₃(t) используют выражениеWhen determining the values of orthogonal projections of the vector of complex amplitude

as a reference vector, with the direction of which the directions of the orthogonal projections are associated, take the vector

in this case, as the angle α in the expressions (8) and (10) use the angle

initial phase of fundamental harmonic oscillations

included in the first periodic non-sinusoidal electrical signal

, and for the formation of the third non-sinusoidal electric signal f ₃ (t) use the expression

основной гармоники

, входящих в структуру первого периодического несинусоидального электрического сигнала

, или

основной гармоники

, входящих в структуру второго периодического несинусоидального электрического сигнала

, по одному из известных методов предварительно определяют начальную фазу колебаний k-той гармоники, например, на основе применения последовательности действий, используемых при вычислении начальных фаз колебаний гармоник ряда Фурье [Бессонов Л.А. Теоретические основы электротехники. Электрические цепи: Учебник. - 10-е изд. - М.: Гардарник, 2001. С.205-206].The initial phases of the oscillations necessary for implementing the method of obtaining the values of the orthogonal projections of one vector on the direction of the other vector of two single-frequency electrical signals, namely, or

fundamental harmonics

included in the structure of the first periodic non-sinusoidal electric signal

, or

fundamental harmonics

included in the structure of the second periodic non-sinusoidal electric signal

, according to one of the known methods, the initial phase of oscillations of the k-th harmonic is preliminarily determined, for example, based on the application of the sequence of actions used in calculating the initial phases of the oscillations of harmonics of the Fourier series [L. Bessonov Theoretical foundations of electrical engineering. Electric Circuits: A Textbook. - 10th ed. - M .: Gardarnik, 2001. S.205-206].

In the presence of a third harmonic with a cyclic frequency of 3ω in the corresponding periodic non-sinusoidal electric signal and its unacceptable influence on the result of determining the values of the orthogonal projections of the fundamental harmonic, one of the known methods preliminarily generates an electric signal without a third harmonic with a cyclic frequency of 3ω and thus formed an electrical signal is used in the method of the invention.

и

, т.е. у которых равны номера гармоник n=k, следовательно, равны угловые частоты колебаний kω=nω, где ω=2π/Т=2πf является частотой основной гармоники (n=k=1) и определяется только периодом повторения Т как первого

, так и второго

периодических несинусоидальных электрических сигналов, при этом первая гармоника

входит в состав первого периодического несинусоидального электрического сигнала f₁(t), а вторая гармоника

, одночастотная с первой гармоникой, входит в состав второго периодического несинусоидального электрического сигнала f₂(t), и отличается способом получения электрических сигналов, идентифицирующих у одной из двух одночастотных гармоник

с комплексной амплитудой

или

с комплексной амплитудой

значений ортогональных проекций его вектора комплексной амплитуды на направление, определяемое опорным вектором комплексной амплитуды другой гармоники, и в зависимости от конкретно решаемой задачи по определению значений ортогональных проекций вектора конкретной одночастотной гармоники используют или начальную фазу колебаний

k-ой гармоники

первого периодического несинусоидального электрического сигнала f₁(t) или начальную фазу колебаний

n-ой гармоники

, у которой n=k, второго периодического несинусоидального электрического сигнала f₂(t).In general, the proposed method is applicable to two single-frequency harmonics

and

, i.e. for which the harmonic numbers n = k are equal, therefore, the angular oscillation frequencies kω = nω are equal, where ω = 2π / Т = 2πf is the fundamental frequency (n = k = 1) and is determined only by the repetition period T as the first

and second

periodic non-sinusoidal electrical signals, with the first harmonic

is part of the first periodic non-sinusoidal electric signal f ₁ (t), and the second harmonic

, single-frequency with the first harmonic, is part of the second periodic non-sinusoidal electric signal f ₂ (t), and differs in the method of obtaining electrical signals identifying one of the two single-frequency harmonics

with complex amplitude

or

with complex amplitude

the values of the orthogonal projections of its vector of complex amplitude in the direction determined by the reference vector of the complex amplitude of the other harmonic, and depending on the specific task to determine the values of the orthogonal projections of the vector of a specific single-frequency harmonic, use either the initial phase of the oscillations

kth harmonic

the first periodic non-sinusoidal electric signal f ₁ (t) or the initial phase of the oscillations

n-th harmonic

, for which n = k, of the second periodic non-sinusoidal electric signal f ₂ (t).

; формируют изменяющийся по синусоидальному закону второй дополнительный гармонический электрический сигнал f_доп.2(t) с постоянной амплитудой, с удвоенной частотой одночастотных электрических гармоник, т.е. с частотой 2kω=2nω_; и вводимой дополнительной начальной фазой колебаний, равной 2α; получают третий несинусоидальный электрический сигнал f₃(t), для чего перемножают три электрических сигнала, причем первый сомножитель является либо первым периодическим несинусоидальным электрическим сигналом f₁(t), либо вторым периодическим несинусоидальным электрическим сигналом f₂(t), второй сомножитель является изменяющимся по закону синуса первым дополнительным гармоническим электрическим сигналом f_доп.1(t), третий сомножитель является изменяющимся по закону синуса вторым дополнительным гармоническим электрическим сигналом f_доп.2(t), при этом выбор из двух периодических несинусоидальных электрических сигналов, т.е. либо f₁(t), либо f₂(t), определяет ту конечную информацию о значениях проекций того вектора комплексной амплитуды соответствующей гармоники, которую необходимо получить для решения конкретной задачи, причем полученный третий несинусоидальный сигнал f₃(t) в своей структуре содержит постоянную составляющую; формируют четвертый электрический сигнал f₄(t) посредством выполнения операции определенного интегрирования, при этом четвертый электрический сигнал f₄(t) является входящей в состав третьего несинусоидального электрического сигнала f₃(t) постоянной составляющей, причем в зависимости от принятого у первого дополнительного синусоидального электрического сигнала f_1доп(t) значения начальной фазы колебаний либо α, либо

четвертый электрический сигнал f₄(t) однозначно идентифицирует либо синусную, либо косинусную проекцию, т.е. значение одной из проекций вектора комплексной амплитуды электрического сигнала одного из одночастотных гармоник на соответствующее направление опорного вектора комплексной амплитуды электрического сигнала другой одночастотной гармоники, при этом, при определении значения проекции вектора комплексной амплитуды гармоники

на направление, перпендикулярное направлению, задаваемому опорным вектором комплексной амплитуды гармоники

при формировании третьего несинусоидального сигнала f₃(t) в качестве первого сомножителя используют первый периодический несинусоидальный электрический сигнал f₁(t), а во втором f_доп.1(t) и в третьем f_доп.2(t) изменяющихся по закону синуса сомножителях дополнительных гармонических электрических сигналов, в качестве вводимой дополнительной начальной фазы α колебаний используют начальную фазу колебаний

n-ой гармоники

второго периодического несинусоидального электрического сигнала f₂(t), при этом при определении значения проекции вектора комплексной амплитуды

гармоники

на направление, совпадающее с направлением, задаваемым опорным вектором комплексной амплитуды

гармоники

, во втором сомножителе f_доп.1(t) в качестве начальной фазы колебании используют сумму углов

; при этом при определении значения проекции вектора комплексной амплитуды

гармоники

на направление, перпендикулярное направлению, задаваемому опорным вектором комплексной амплитуды

гармоники

, при формировании третьего несинусоидального электрического сигнала f₃(t) в качестве первого сомножителя используют второй периодический несинусоидальный электрический сигнал f₂(t), а во втором f_доп.1(t) и в третьем f_доп.2(t) изменяющихся по закону синуса сомножителях, задаваемых дополнительными гармоническими электрическими сигналами f_доп.1(t) и f_доп.2(t), в качестве вводимой в тригонометрическую функцию дополнительной начальной фазы α колебаний используют начальную фазу колебаний

одночастотной гармоники

первого периодического несинусоидального электрического сигнала f₁(t), при этом при определении значения проекции вектора комплексной амплитуды

гармоники

на направление, совпадающее с направлением, задаваемым опорным вектором комплексной амплитуды

гармоники

, во втором сомножителе f_доп.1(t) в качестве начальной фазы колебаний в тригонометрической функции используют сумму углов

, т.е. второй сомножитель f_доп.1(t) формируют изменяющимся по косинусоидальному закону.The method proposed in the invention for obtaining the final result in the form of projection values of the first vector of complex amplitude, which varies according to the sine law of the corresponding harmonic, in the direction specified by the reference vector of the second complex amplitude, changes according to the sine law of the other single-frequency harmonic, each of which is included in the single-frequency harmonics the harmonic spectrum of its periodic non-sinusoidal electric signal f ₁ (t) and f ₂ (t), is the sequence of processing corresponding to in the case of non-sinusoidal periodic electrical signals, in which according to the invention a first additional harmonic electrical signal f _{ext. 1} (t) with a constant amplitude, with a frequency kω = nω of single-frequency electric harmonics and an additional initial oscillation phase of either α or

; form a second additional harmonic electric signal f _{additional 2} (t) with a constant amplitude, with a doubled frequency of single-frequency electric harmonics, that changes according to a sinusoidal law, i.e. with a frequency of 2kω = 2nω _; and introduced an additional initial phase of oscillations equal to 2α; receive a third non-sinusoidal electric signal f ₃ (t), for which three electrical signals are multiplied, the first factor being either the first periodic non-sinusoidal electric signal f ₁ (t) or the second periodic non-sinusoidal electric signal f ₂ (t), the second factor is variable legally first additional harmonic sine electrical signal _dop.1 f (t), the third factor is varying according to the law second additional harmonic sine electrical signal f _op.2 (t), with a choice of two periodic non-sinusoidal electrical signals, i.e. either f ₁ (t) or f ₂ (t) determines that final information about the projection values of that complex vector of the corresponding harmonic amplitude that must be obtained to solve a specific problem, and the resulting third non-sinusoidal signal f ₃ (t) in its structure contains constant component; form a fourth electrical signal f ₄ (t) by performing a certain integration operation, while the fourth electrical signal f ₄ (t) is a constant component of the third non-sinusoidal electric signal f ₃ (t), and depending on the received from the first additional sinusoidal electrical signal f _1dop (t) values of the initial phase of the oscillations of either α or

the fourth electrical signal f ₄ (t) uniquely identifies either a sine or cosine projection, i.e. the value of one of the projections of the complex amplitude vector of the electric signal of one of the single-frequency harmonics on the corresponding direction of the reference vector of the complex amplitude of the electrical signal of the other single-frequency harmonic, while determining the projection value of the complex harmonic amplitude vector

to the direction perpendicular to the direction specified by the reference vector of the complex harmonic amplitude

when forming the third non-sinusoidal signal f ₃ (t), the first periodic non-sinusoidal electric signal f ₁ (t) is used as the first factor, and in the second f _{add 1} (t) and in the third f _{add 2} (t) changing according to the sine law factors of additional harmonic electrical signals, as an input additional initial phase α of oscillations use the initial phase of oscillations

n-th harmonic

the second periodic non-sinusoidal electric signal f ₂ (t), while determining the projection value of the vector of complex amplitude

harmonics

in the direction coinciding with the direction specified by the reference vector of complex amplitude

harmonics

, in the second factor f _{add. 1} (t), as the initial phase of the oscillation, use the sum of the angles

; while determining the projection value of the vector of complex amplitude

harmonics

in the direction perpendicular to the direction specified by the reference vector of complex amplitude

harmonics

, when forming the third non-sinusoidal electric signal f ₃ (t), the second periodic non-sinusoidal electric signal f ₂ (t) is used as the first factor, and in the second f _{additional 1} (t) and in the third f _{additional 2} (t) the sine law of the factors specified by additional harmonic electric signals f _{add. 1} (t) and f _{add. 2} (t), as the input initial phase of oscillations α introduced into the trigonometric function, use the initial phase of oscillations

single frequency harmonics

the first periodic non-sinusoidal electric signal f ₁ (t), while determining the projection value of the complex amplitude vector

harmonics

in the direction coinciding with the direction specified by the reference vector of complex amplitude

harmonics

, in the second factor f _{add. 1} (t), as the initial phase of the oscillations in the trigonometric function, use the sum of the angles

, i.e. the second factor f _{add. 1} (t) is formed varying according to the cosine law.

и

, например k-ые гармоники (kω), которые входят в структуру соответствующих двух периодических несинусоидальных электрических сигналов, а именно первого

и второго

, с одинаковым периодом повторения Т=1/f, в устройстве релейной защиты, автоматики и измерения (УРЗАИ) определяет функционирование программной части ВЛМ, состоящего из двух субмодулей, а именно, субмодуля вычисления фаз гармоник (СМВФ) и субмодуля вычисления ортогональных проекций вектора (СМВП), каждый с двумя входами, причем на первый и второй входы подают соответственно первый

и второй

периодические несинусоидальные электрические сигналы, при этом одночастотные k-ые гармоники

и

характеризуются своими векторами комплексных амплитуд

и

причем, например, k-ая гармоника

и вектор ее комплексной амплитуды

на ортогональные направления которого проектируют вектор комплексной амплитуды

другой одночастотной гармоники

, считаются опорными, а гармонику

и ее комплексную амплитуду

считают не опорными, при этом первый субмодуль (СМВФ) выделяет начальную фазу колебаний

опорной гармоники

, отличается тем, что согласно изобретению выделенное значение начальной фазы колебаний

подают на один из двух информационных входов второго субмодуля (СМВП), который формирует первый

и второй

дополнительные гармонические сигналы с постоянной амплитудой, причем аргумент тригонометрической функции первого дополнительного гармонического сигнала f_доп.1(t) состоит из суммы двух слагаемых, при этом первое слагаемое определяется произведением циклической частоты kω одночастотных электрических сигналов и времени t, а вторым слагаемым по изобретению задают дополнительной начальной фазой колебаний α, причем в качестве этой фазы используют выделенное значение начальной фазы колебаний опорной гармоники; формируют изменяющийся по закону синуса второй дополнительный гармонический электрический сигнал

с постоянной амплитудой, у которого аргумент в два раза больше аргумента тригонометрической функции первого дополнительного гармонического электрического сигнала f_доп.1(t); получают третий несинусоидальный электрический сигнал

в результате перемножения трех электрических сигналов, при этом в зависимости от конкретно решаемой задачи в качестве первого сомножителя используют либо первый

, либо второй

из периодических несинусоидальных электрических сигналов, в качестве двух других сомножителей используют сформированные два дополнительных гармонических электрических сигнала f_доп.1(t) и f_доп.2(t); из третьего несинусоидального электрического сигнала f₃(t) посредством операции интегрирования на заданном интервале времени получают четвертый электрический сигнал

, который определяет входящую в структуру третьего несинусоидального электрического сигнала f₃(t) постоянную составляющую F₀, причем численное значение этой постоянной составляющей однозначно идентифицирует значение одной из проекций вектора комплексной амплитуды, а именно проекции либо синусную

, либо косинусную

не опорной гармоники на направление, задаваемое вектором комплексной амплитуды опорной гармоники, одночастотной с не опорной гармоникой, например, вектора комплексной амплитуды

не опорной гармоники

на ортогональные направления, задаваемые направлением опорного вектора комплексной амплитуды

опорной гармоники

; при этом для получения значений модулей проекций вектора комплексной амплитуды

не опорной гармоники

, в качестве вводимой дополнительной начальной фазы колебаний в первом

и втором

дополнительных гармонических электрических сигналах используют начальную фазу колебаний

электрического сигнала опорной гармоники

, причем для получения перпендикулярного направлению опорного вектора комплексной амплитуды

значения модуля проекции не опорного вектора комплексной амплитуды

не опорной гармоники

, первый дополнительный электрический сигнал f_доп.1(t) делают изменяющимся по закону синуса (8), при этом для получения совпадающего с направлением опорного вектора комплексной амплитуды значения

модуля проекции не опорного вектора комплексной амплитуды

первый дополнительный электрический сигнал f_доп.1(t) делают изменяющимся по закону косинуса (13).The essence of the invention lies in the fact that the method of obtaining the values of the orthogonal projections of one vector on the direction of the other vector of two single-frequency electrical signals

and

, for example, the kth harmonics (kω), which are included in the structure of the corresponding two periodic non-sinusoidal electrical signals, namely the first

and second

, with the same repetition period T = 1 / f, in the relay protection, automation and measurement device (URIAI) determines the functioning of the VLM software part, which consists of two submodules, namely, a submodule for calculating the phases of harmonics (SMVF) and a submodule for calculating orthogonal projections of the vector ( AGM), each with two inputs, and the first and second inputs respectively serve the first

and second

periodic non-sinusoidal electrical signals, with single-frequency kth harmonics

and

characterized by their complex amplitude vectors

and

where, for example, the kth harmonic

and the vector of its complex amplitude

onto the orthogonal directions of which the complex amplitude vector is projected

other single frequency harmonics

are considered reference, while the harmonics

and its complex amplitude

considered non-supportive, while the first submodule (SMVF) identifies the initial phase of oscillation

reference harmonics

, characterized in that according to the invention, the selected value of the initial phase of the oscillations

served on one of two information inputs of the second submodule (AGN), which forms the first

and second

additional harmonic signals with constant amplitude, and the argument of the trigonometric function of the first additional harmonic signal f _{ext. 1} (t) consists of the sum of two terms, the first term is determined by the product of the cyclic frequency kω of single-frequency electrical signals and time t, and the second term according to the invention is defined additional initial phase of the oscillations α, and as this phase, use the selected value of the initial phase of the oscillations of the reference harmonic; form a second additional harmonic electric signal that varies according to the law of sine

with a constant amplitude, in which the argument is twice as large as the argument of the trigonometric function of the first additional harmonic electric signal f _{add. 1} (t); receive a third non-sinusoidal electrical signal

as a result of the multiplication of three electrical signals, while depending on the particular problem being solved, either the first one is used as the first factor

or second

from periodic non-sinusoidal electrical signals, two additional harmonic electrical signals f _{add. 1} (t) and f _{add. 2} (t) are used as two other factors; from the third non-sinusoidal electric signal f ₃ (t) through the integration operation at a given time interval, the fourth electric signal is obtained

, which determines the constant component F ₀ included in the structure of the third non-sinusoidal electric signal f ₃ (t), and the numerical value of this constant component uniquely identifies the value of one of the projections of the complex amplitude vector, namely, the projection or sinus

or cosine

non-reference harmonic in the direction specified by the vector of the complex amplitude of the reference harmonic, single-frequency with a non-reference harmonic, for example, a vector of complex amplitude

no reference harmonic

into orthogonal directions specified by the direction of the reference vector of complex amplitude

reference harmonics

; in this case, to obtain the values of the projection moduli of the vector of complex amplitude

no reference harmonic

, as the introduced additional initial phase of the oscillations in the first

and second

additional harmonic electrical signals use the initial phase of the oscillations

electrical reference signal

and moreover, to obtain a reference amplitude complex vector perpendicular to the direction

values of the projection modulus of a non-reference vector of complex amplitude

no reference harmonic

, the first additional electric signal f _{add. 1} (t) is made to vary according to the law of sine (8), while in order to obtain the value

projection module of a non-reference vector of complex amplitude

the first additional electrical signal f _{ext. 1} (t) is made variable according to the law of cosine (13).

Figure 1-7 explain the essence of the algorithm of the functioning of the device operating according to the method according to the invention, while figure 1 shows a diagram of the supply of analog periodic non-sinusoidal electrical voltage values u (t) and current i (t) to VLM, which, in General case, it may be included in the structure of some relay protection device, emergency control equipment, and URIAI measurement.

с частотой f, входящей в спектр гармоник несинусоидального периодического напряжения u(t), на направление вектора основной гармоники тока

тока, входящей в спектр гармоник несинусоидального периодического тока i(t). В этом случае на выходе субмодуля СМВП получают информацию о значениях ортогональных проекций вектора амплитуды основной гармоники

напряжения, а именно синусной U_o,s и косинусной U_o,c проекциях. Пунктиром показаны направления сигналов, которые обеспечивают на выходе субмодуля СМВП получение информации о значениях ортогональных проекций вектора амплитуды основной гармоники

тока, а именно синусной I_o,s и косинусной I_o,c проекциях.In Fig. 1, solid lines indicate the directions of information transfer from the TV voltage and current sensors to the SMVF and SMVP modules, information from the SMVF submodule to the SMVP submodule and the information generated on its output about the values of the orthogonal components U _{o, s} and U _{o, c} projection of the vector of the fundamental harmonic voltage

with a frequency f included in the spectrum of harmonics of a non-sinusoidal periodic voltage u (t), in the direction of the main harmonic vector of the current

current entering the harmonic spectrum of a non-sinusoidal periodic current i (t). In this case, information on the values of the orthogonal projections of the amplitude vector of the fundamental harmonic is obtained at the output of the submodule of the AGN

voltage, namely sine U _{o, s} and cosine U _{o, c} projections. The dashed line shows the directions of the signals that provide the output of the AGN submodule with information on the values of the orthogonal projections of the amplitude vector of the fundamental

current, namely sine I _{o, s} and cosine I _{o, c} projections.

и

основных гармоник, входящих соответственно в несинусоидальные напряжение u(t) и ток i(t). Полученные значения начальных фаз колебаний

и

субмодуля СМВФ передает в субмодуль СМВП, в основе функционирования которого используют НП, вытекающий из изложенных теоретических положений согласно предложенным в данном изобретении алгоритмам, в которых конечными программируемыми выражениями являются выражения (15) и (16). В результате на выходе субмодуля СМВП формируется информация о начальных фазах колебаний

и

соответствующих гармоник, причем в зависимости от решаемой УРЗАИ задачи она может быть представлена либо в цифровой, либо в аналоговой формах.Figure 1, the VLM module is shown conditionally consisting of two submodules SMVF and SMVP, the computational and logical functions of which are launched by the "Start" command URZAI. In particular, the SMVF submodule carries out the operations of linear transformation of the LP arriving at its input, analog electrical signals i (t) and u (t) into their digital image and through non-linear transformations of the NP, based on which are known algorithms corresponding to non-linear mathematical operations on with these images, the values of the initial phases of oscillations of single-frequency harmonics are obtained, for example

and

fundamental harmonics included respectively in non-sinusoidal voltage u (t) and current i (t). The obtained values of the initial phases of the oscillations

and

The SMVF submodule transfers to the AGN submodule, the operation of which is based on the NP, which follows from the stated theoretical positions according to the algorithms proposed in this invention, in which the expressions (15) and (16) are the final programmed expressions. As a result, information on the initial phases of oscillations is generated at the output of the submodule of the AGN

and

corresponding harmonics, and depending on the problem being solved by URESA, it can be represented either in digital or in analog forms.

. Протекающий через элемент Э электрический ток i(t) имеет несинусоидальную форму и содержит основную гармонику i⁽¹⁾(t) (n=1) с частотой f=50 Гц, пятую и седьмую гармоники, т.е. основные гармоники u⁽¹⁾(t) и i⁽¹⁾(t) являются одночастотными электрическими сигналами. Параметры R и L элемента Э схемы на фиг.1 выбраны такими, что начальная фаза колебаний первой гармоники тока i⁽¹⁾(t) равна

. Необходимые для использования в субмодуле СМВП значения начальных фаз колебаний

и

гармонике с основной частотой f=50 Гц определяют одним из указанных в описании данного изобретения известных способов.The essence of the proposed method is illustrated by the example of modeling in a computer circuit simulation environment for determining the parameters of the orthogonal projections of the fundamental harmonic of a non-sinusoidal periodic voltage u (t) applied to the passive element E (Fig. 1), consisting of linearly connected linear resistance R and inductance L. Periodic non-sinusoidal voltage u (t) with a repetition period T equal to 20 ms contains the fundamental harmonic u ⁽¹⁾ (t) (k = 1) with an oscillation frequency f = 50 Hz, the fifth and seventh harmonics, and the initial phase of the oscillations of the fundamental harmonic u ⁽¹⁾ (t) of the voltage u (t) is set equal to

. The electric current i (t) flowing through the element E has a non-sinusoidal shape and contains the fundamental harmonic i ⁽¹⁾ (t) (n = 1) with a frequency f = 50 Hz, the fifth and seventh harmonics, i.e. the fundamental harmonics u ⁽¹⁾ (t) and i ⁽¹⁾ (t) are single-frequency electrical signals. The parameters R and L of the element E of the circuit in figure 1 are selected such that the initial phase of the oscillations of the first harmonic of the current i ⁽¹⁾ (t) is

. The values of the initial oscillation phases required for use in the AGN submodule

and

harmonics with a fundamental frequency f = 50 Hz are determined by one of the known methods specified in the description of the present invention.

основной гармоники несинусоидального периодического напряжения u(t) на ортогональные направления, задаваемые направлением вектора комплексной амплитуды

основной гармоники несинусоидального периодического тока i(t).Figure 2 shows the front panel of the oscilloscope, the screen of which displays the waveforms of the instantaneous values of the periodic non-sinusoidal voltage u (t) and current i (t) supplied to the SMVF and SMVP submodules (Fig. 1). The electrical signals U _{0, s,} and U _{0, c} shown on the oscilloscope screen after time t ₀ + T in analog form are functionally related to the values of the sine (15) and cosine (16) projections of the complex amplitude vector

of the fundamental harmonic of a non-sinusoidal periodic voltage u (t) to the orthogonal directions specified by the direction of the complex amplitude vector

fundamental harmonic of non-sinusoidal periodic current i (t).

Figure 3-7, the instantaneous values are given in relative units (marked with an asterisk), while the basic values are associated with the amplitudes of the main harmonics of the voltage u (t) and current i (t).

и

и графические пояснения формирования ортогональных проекций вектора

а именно синусной U_0,s и косинусной U_0,c.Figure 3 shows the waveforms of the instantaneous values of voltage u (t) and current i (t). Figure 4 shows the main harmonic u ⁽¹⁾ (t) of the voltage u (t) and the main harmonic i ⁽¹⁾ (t) of the current i (t), which are part of the indicated instantaneous values, respectively. Figure 5 shows the relative positions of the vectors

and

and graphical explanations of the formation of orthogonal projections of the vector

namely sine U _{0, s} and cosine U _{0, c} .

, что согласуется по основной гармонике f=50 Гц с параметрами элемента Э (фиг.1), контролируемого модулем ВЛМ (фиг.1), и косвенно свидетельствует о функциональной связи фиксируемых на выходе субмодуля СМВП значений U_0,s и U_0,c истинными значениями модулей ортогональных проекций вектора

амплитуды основной гармоники u⁽¹⁾(t), входящей в состав несинусоидального периодического напряжения u(t).Figure 6 shows the instantaneous values of the electric signal u _{3, s} (t) generated according to the invention, a certain integral from which (15) is uniquely associated with the magnitude of the sine component of the fundamental voltage harmonic U _{0, s} u (t); Fig. 7 shows the instantaneous values of the electric signal u _{3, c} (t) generated according to the invention, the definite integral (16) from which is uniquely related to the magnitude of the cosine component U _{0, c of the} fundamental voltage harmonic u (t) (Fig. 2). 6 and 7, the integration areas are highlighted. The integration operation is started in the AGN submodule according to the “Start” command generated by the URIAI and completed after time T (FIG. 2). From the waveforms shown in Fig. 2, it follows that after the integration process is completed by the submodule of the AGN, the following values of certain integrals are obtained, namely U _{0, s} = 25.154 mV and U _{0, c} = 43.567 mV. These values correspond to a phase shift φ ⁽¹⁾ between the main harmonics of the voltage u ⁽¹⁾ (t) and current i ⁽¹⁾ (t) and the vectors of their complex amplitudes (Figs. 4, 5), equal to

, which is consistent in the fundamental harmonic f = 50 Hz with the parameters of the element E (Fig. 1), controlled by the VLM module (Fig. 1), and indirectly indicates the functional relationship of the values U _{0, s} and U _{0, c} fixed at the output of the submodule of the AGN true values of the modules of the orthogonal projections of the vector

the amplitude of the fundamental harmonic u ⁽¹⁾ (t), which is part of the non-sinusoidal periodic voltage u (t).

The proposed method for obtaining the values of the orthogonal projections of one vector on the direction of another vector of two single-frequency electrical signals can be implemented both on the basis of methods and means of digital processing of electrical signals (preferred option), and methods and means of analog processing of electrical signals.

Claims (3)

1. A method of obtaining the values of the orthogonal projections of one vector onto the direction of another vector of two single-frequency electrical signals, which determines the functioning of the software part of the computational-logical module of the relay protection, automation and measurement device, consisting of two submodules, namely, a submodule for determining the initial phases of oscillations of two single-frequency electrical signals , which are considered as single-frequency harmonics, each of which is included in the first and second periodic nonsinus, respectively ideal electrical signals with the same repetition period, while one of the harmonics is considered reference and the other harmonic is not reference, and a submodule for calculating orthogonal projections, while both submodules have two inputs, the first and second inputs of the submodules respectively supply the first and second periodic non-sinusoidal electrical signals, and the submodule for determining the initial phases of oscillations of single-frequency harmonics selects the value of the initial phase of oscillations of the reference single-frequency harmonics, the value of which lead to one of two information outputs of this submodule, characterized in that the extracted value of the initial phase of the oscillations is fed to one of two information inputs of the second submodule, which generates the first and second additional harmonic signals with constant amplitude, and the argument of the trigonometric function of the first additional harmonic signal consists from the sum of two terms, the first term being determined by the product of the cyclic frequency of single-frequency electrical signals and time t, the second term is administered more initial phase of oscillation, and in this phase is used as the selected value of the initial phase of a reference harmonic oscillations; forming a second additional harmonic electric signal with a constant amplitude that varies according to the law of sine, in which the argument is twice as large as the argument of the trigonometric function of the first additional harmonic electric signal; a third non-sinusoidal electrical signal is obtained as a result of the multiplication of three electrical signals, while either the first or second of the changing periodic non-sinusoidal electrical signals are used as the first factor, the generated two additional harmonic electrical signals are used as the other two factors, from the third non-sinusoidal electrical signal by integration operations on a given time interval receive the fourth electric signal al, which defines part of the structure of the third non-sinusoidal electrical signal is a DC component, and the magnitude of the fourth electrical signal uniquely identifies the value of one of the projections of the vector complex amplitude harmonics not support in the direction defined by the vector complex amplitude of the reference harmonic, a single frequency with no harmonic of the reference. 2. The method according to claim 1, characterized in that to obtain the projection values of the vector of the complex amplitude included in the first non-sinusoidal periodic electric harmonic signal, characterized as non-reference, in the orthogonal direction specified by the direction of the reference vector of the complex amplitude of the reference harmonic included in the second non-sinusoidal periodic electrical signal, the first additional signal is formed varying according to a sinusoidal law, to obtain the projection value of the set vector xn of the amplitude of the non-reference harmonic that coincides with the direction of the reference vector of the complex amplitude of the reference harmonic, the first additional electric signal is made to vary according to the law of cosine, while the initial phase of the oscillations of the electric signal is used as the input additional initial phase of the oscillations in the arguments of the first and second additional harmonic electric signals reference harmonics included in the structure of the second non-sinusoidal periodic electrical signal. 3. The method according to claim 1, characterized in that to obtain the projection values of the vector of complex amplitude included in the second non-sinusoidal periodic electric harmonic signal, characterized as non-reference, in the orthogonal direction specified by the direction of the reference vector of the complex amplitude of the reference harmonic included in the first non-sinusoidal periodic electrical signal, the first additional signal is formed changing according to a sinusoidal law, to obtain the projection value of the vector of the comp If the second amplitude of the non-reference harmonic coincides with the direction of the reference vector of the complex amplitude of the reference harmonic, the first additional electrical signal is made to vary according to the law of cosine, while the initial phase of the oscillations of the electric signal is used as the input additional initial phase of the oscillations in the arguments of the first and second additional harmonic electric signals reference harmonics included in the structure of the first non-sinusoidal periodic electrical signal.

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