RU2527491C2 - Method of filtering industrial frequency signals - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: invention can be used in electrical engineering. According to the invention, measured current or voltage values are converted to vector values consisting of quadrature component on an observation interval which is equal to or is a multiple of the period of industrial frequency, and conversion of the measured current (voltage) values is carried out with a set of N multipliers, N adders and N delay elements, where N is a given bit capacity of the digital filter, connected to enable realisation of one of real transformations: Hartley, sine and cosine, performed with subsequent conversion of the real transformation result into quadrature components of vector values.

EFFECT: simple method of filtering industrial frequency signals.

2 tbl, 8 dwg

Description

The invention relates to electrical engineering and can be used in measuring relay protection bodies, electric meters, telemechanics devices, emergency control devices, etc., where estimates of the complex amplitudes of currents and voltages of industrial frequency are necessary.

To describe sinusoidal values in the electric power industry, the method of complex amplitudes is used [for example, Electrotechnical Encyclopedia: T1, ed. A.F. Dyakova - M .: MEI Publishing House, 2005, p. 34], for example, when calculating short circuits, selecting settings and characteristics of relay protection, etc. In this case, a vector display of sinusoidally changing electrical quantities of currents and voltages is specified, at which

x (t) = Asin (2πf ₀ t + φ)

matches vector

,

,

. При этом любому из синусоидальных сигналов Asin(2πf₀t+φ) соответствует неизменный во времени векторuniformly rotating with an angular frequency ω ₀ = 2πf ₀ counterclockwise, where f ₀ is the industrial frequency. For convenience of consideration and calculations, the rotating vector is “stopped”, multiplying it by

. Moreover, any of the sinusoidal signals Asin (2πf ₀ t + φ) corresponds to a time-invariant vector

.

.

Using a vector mapping, it is convenient to consider the amplitude and phase relationships (parameters A, φ) between the sinusoidal AC signals, since the basic operations with these signals (addition, multiplication, etc.) are quite simply described by the same operations with the vectors corresponding to these signals.

The complex amplitude method is applicable to discretized digital signals, which are digital samples u (nT), i (nT) of analog sinusoidal AC signals u (t), i (t)

u (nT) = Usin (2nf ₀ nT + φ _u ); i (nT) = Isin (2πf ₀ nT + φ _i ).

Thus, the sampled sinusoidal signals of industrial frequency can be represented by rotating vectors of the form

;

;

,

,

where U _x (nT) and U _y (nT); I _x (nT) and I _y (nT) are the quadrature components of the complex vectors of voltage and current [for example, Schneerson E.M. Digital relay protection - M .: Energoatomizdat, 2007].

Quadrature (orthogonal) components of current and voltage signals are widely used in electrical practice. For example, the method of obtaining them underlies the construction of digital measuring relay protection bodies and is based on various filtering methods.

Known, for example, are methods of filtering industrial frequency signals, which consist in obtaining quadrature components based on instantaneous values of quantities and their derivatives; algorithms of two, three samples; quarter-period sampling, etc. [for example, Schneerson E.M. Digital relay protection - M .: Energoatomizdat, 2007. p. 50-52; Kulikov A.L., Misrikhanov M.Sh. Introduction to the methods of digital relay protection of high voltage power lines: Textbook. allowance. - M .: Energoatomizdat, 2007, p. 105-121].

The closest technical solution to the proposed invention is a method of filtering industrial frequency signals [Ziegler G. Digital distance protection: principles and application / Transl. from English under the editorship of AF Dyakova - M .: Energoatomizdat, 2005, p. 305], according to which the measured current (voltage) values are converted into vector quantities consisting of quadrature components, using orthogonal filters based on the complex Fourier transform on the observation interval equal to or a multiple of the industrial frequency period. For example, in the practice of digital relay protection [Schneerson E.M. Digital relay protection - M .: Energoatomizdat, 2007, p.56-60] use the half-period discrete Fourier transform (DFT), full-period DFT, etc.

The structure of the device that implements the known method can be performed according to the scheme (figure 1) [Schneerson E.M. Digital relay protection - M .: Energoatomizdat, 2007. p. 59] and consists of two filters, respectively, using the sine and cosine coefficients of complex exponentials. Thus, to obtain the orthogonal components, two separate filters (sine and cosine) with real coefficients are used. To preserve the unity of designations with figure 2-7, figure 1 introduced the following numbering: delay elements 2, adders 3, multipliers 5.

However, the fact of double redundancy of the Fourier transform associated with the Hermitian property of this transformation is known [Bracewell R. Hartley Transformation: Trans. from English - M.: Mir, 1990, p.]. For example, a DFT of dimension N has N degrees of freedom, despite the fact that it includes 2N real coefficients. The specified redundancy indicates the irrationality of the organization of processing operations using the Fourier transform. For example, for the DFT, a more rational organization of the calculations allows to halve the number of filtering operations of industrial frequency signals.

Let’s explain an example involving the use of the discrete Hartley transform (DPC), as well as the “short window” filters (algorithms for two, three samples, quarter-period sampling, etc.), which make it possible to implement rational calculations, while reducing the number of processing operations by almost half and ensuring in some cases, obtaining a result similar to the DFT. Note that the filtering properties of the industrial frequency signal processing device are preserved.

DPC of the sequence x _(i) = {x ₍₀₎ , x ₍₁₎ , ..., x _(N-1) } of the samples of the sinusoidal signal, taking into account the notation adopted in [Schneerson E.M. Digital relay protection - M .: Energoatomizdat, 2007], are determined by the ratio [Bracewell R. Hartley Transformation: Trans. from English - M.: Mir, 1990].

, n-N+1≤i≤n,

, n-N + 1≤i≤n,

where cas (α) = cos (α) + sin (α). The connection between the DFT (F _(n) ) and the DPH (X _(n) ), defined by the formulas

,

,

X _(n) = Re (F _(n) ) -Im (F _(n) ),

where X _(-n) = X _(Nn) .

To implement quadrature filters in combination with DPH, we use the property:

cas (α + β) = cos (β) · cas (α) + sin (β) · cas (-α).

, тогдаWe choose, for example,

then

.

.

Taking into account the filtering of the industrial frequency harmonics and the previously accepted designations, the DPC of the sequence delayed by N / 4 samples has the form

Taking the values cos (π / 2) = 0 and sin (π / 2) = 1, we obtain

.

.

Thus, for the formation of quadrature components according to the quarter-period sampling algorithm, the implementation of the expressions

;

;

.

.

When this filtering device has the form (figure 2).

The operations of dividing into two in the scheme (figure 2) are implemented by a simple shift of the bits, are conditional in nature and do not require hardware and time costs.

(где t_д - интервал дискретизации сигнала) по сравнению с фильтрацией посредством N-точечного ДПФ (ДПХ). Дополнительная задержка может оказаться неприемлемой при реализации быстродействующих цифровых устройств, например, релейной защиты.Despite the simplicity of the circuit (Fig. 2) and significant computational savings, such filtering has a significant drawback - an additional increase in the delay in the filter structure

(where t _d is the sampling interval of the signal) compared to filtering by N-point DFT (DPC). The additional delay may not be acceptable when implementing high-speed digital devices, such as relay protection.

Under these conditions, it is advisable to obtain, although somewhat complicated, but more rapid technical solutions using DPH. The methods for constructing “quick” procedures can be realized using two- and three-sample methods.

The two-sample algorithm uses two consecutive samples and exists in two versions. In relation to the problem being solved, we take into account that

,

,

from here

.

.

Then, for example, a quadrature filter can be implemented according to the expressions:

In this case, the possible structure of the devices are of the form (Figs. Obviously, the structures of FIG. 3a and FIG. 3b differ slightly in speed and hardware costs. So, for example, for the variant of FIG. 3a, only two multiplications are required instead of three of FIG. 3b, but this is offset by additional additions.

We note an important special case of the two-sample algorithm, when the delay in the structure of the quadrature filter is N / S samples of the signal. Wherein

.

.

Then the quadrature filter equations take the form

;

;

;

;

and its structure (figure 4) is greatly simplified.

Three sample algorithms use three consecutive samples to obtain quadrature components.

To form the most efficient three-sample algorithm (with fewer computational operations), we use the following relations

;

;

;

;

then

.

.

Thus, the result of subtracting X _{(n + 1)} -X _(n-1) can be used to obtain the sequence X _(-n) necessary for the formation of quadrature components.

The simplest structure of the filtering device is as shown in FIG.

Note that the option of constructing a quadrature filter (Fig. 5) for the algorithm of three samples is not the only one; possible technical solutions can be implemented taking into account [Kulikov A.L., Misrikhanov M.Sh. Introduction to the methods of digital relay protection of high voltage power lines: Textbook. allowance. - M .: Energoatomizdat, 2007]. However, the presented structure (figure 5) has the least computational cost.

The considered simplified structures of digital filters are not the only ones. Similar structures can be synthesized using real sine or cosine transforms. For example, for the sine transform, quadrature components can be calculated using the equalities

sin (α-β) = sin (α) cos (β) -sin (β) cos (α).

and end result

;

;

.

.

The structure of the digital quadrature filter for the obtained expressions corresponds to Fig.6.

Digital quadrature filtering using three consecutive samples (three-sample algorithm) and sine transform can be implemented, for example, in two ways.

Option 1. We use the equality

From here

;

;

.

.

Option 2. Based on the ratios

,

,

then the mathematical description of the quadrature filter

;

;

.

.

The block diagram of the filter, for example, according to option 2 is presented in Fig.7.

As indicated earlier, instead of a sine transform with simplified filtering, it is possible to use a cosine transform with the synthesis of the corresponding quadrature filters.

The objective of the invention is to simplify the method of filtering industrial frequency signals.

The task is achieved by a method of filtering industrial frequency, according to which the measured current or voltage values are converted into vector quantities consisting of quadrature components, on the observation interval equal to or a multiple of the industrial frequency period. According to the proposed method, the conversion of the measured current or voltage values is carried out on the basis of one of the actual transformations: Hartley, sine transform, cosine transform, followed by recalculation of the results of the actual transform into quadrature components of vector quantities.

Technical implementation of the proposed method for filtering industrial frequency signals can be carried out by digital filters, the structures of which are presented in Fig.2-7.

Digital quadrature filters contain one of the blocks 1 of the actual Hartley transform, sine or cosine transform, delay elements 2, adders 3, dividers 4 by two and multipliers 5.

Digital quadrature filters work as follows.

The operation of the devices of Fig.2-7 is similar. The digital digital quadrature filters receive the actual digital samples x (nN) of the current (voltage). As a result of their processing by the actual conversion unit 1, the corresponding Hartley transform samples X (n) are obtained (for the devices of FIGS. 2-5), the sine transform samples y _⊥ (n) (FIGS. 6, 7), or the cosine transform samples. To obtain the final result in the form of quadrature components of the complex vector of current (voltage), the results of the actual conversion by block 1 are recalculated using the previously given mathematical expressions. Depending on the accepted filtering option, a mathematical expression is selected for recalculation using delay elements 2, adders 3, dividers 4 by two, multipliers 5. The output of digital quadrature filtering (Fig.2-7) are the components y (n), y _⊥ (n) of the complex current vectors a (voltage).

To justify the advantages of the proposed method for filtering industrial frequency signals, we will compare the computational costs for the known digital filtering device (Fig. 1) and new digital filters (Fig. 2-7). So, to implement a digital filter (Fig. 1) with a given dimension N, it is required:

- 2 (N-1) addition operations;

- 2N multiplication operations.

On the contrary, for digital filters (Fig.2-7) requires a smaller number of similar operations (table 1). It should be noted that the dividers 4 into two do not require hardware costs and additional processing time, because the operation of dividing into two is achieved by simple switching of wires (shift of discharges).

Table 1 Computational cost of algorithms with simplified digital filtering Digital Filter Option Number of operations additions multiplications figure 2 N + 1 N figa N + 1 N + 4 figb N + 1 N + 3 figure 4 N N + 1 figure 5 N + 1 N + 2 Fig.6 N N + 2 Fig.7 N + 1 N + 2

The results of calculating the gain in the number of operations depending on the dimension N due to the application of the proposed method for digital filtering of industrial frequency signals are shown in table 2.

table 2 The gain in computational cost of digital filtering algorithms compared to the existing DFT algorithm Digital Filter Option Win in number of operations additions multiplications N = 8 N = 16 N = 32 N = 8 N = 16 N = 32 figure 2 5 13 29th 8 16 32 figa 5 13 29th four 12 28 figb 5 13 29th 5 13 29th figure 4 6 fourteen thirty 7 fifteen 31 figure 5 5 13 29th 6 fourteen thirty 6 6 fourteen thirty 6 fourteen thirty Fig.7 5 13 29th 6 fourteen thirty

An analysis of Table 2 shows that with increasing dimension N, the gain in the number of operations for the proposed method for filtering industrial frequency signals increases.

Thus, the proposed method is an effective means of filtering industrial frequency signals. It can be extended to signals of other frequencies and will also find wide application in the problems of digital processing of communication signals, radio engineering, control, etc.

Claims (1)

A method for filtering industrial frequency signals, according to which the measured current or voltage values are converted into vector quantities consisting of quadrature components, on an observation interval equal to or a multiple of the industrial frequency period, characterized in that the conversion of the measured current (voltage) values is carried out by a set of N multipliers, N adders and N delay elements, where N is the given dimension of the digital filter, connected with the possibility of implementing one of the real transformations: Hartley, usnogo transform, cosine transform performed, followed by transfer of the actual conversion result in quadrature components of vector quantities.

Images