CN115792374A - Sine wave frequency measurement calculation method, system, storage medium and calculation equipment - Google Patents
Sine wave frequency measurement calculation method, system, storage medium and calculation equipment Download PDFInfo
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Abstract
The invention discloses a sine wave frequency measurement and calculation method, a sine wave frequency measurement and calculation system, a storage medium and calculation equipment in the technical field of power system relay protection, and aims to solve the problems of low calculation precision and large calculation amount when sine wave frequency is measured in the prior art. The method comprises the steps of collecting instantaneous values of sine waveforms according to a fixed sampling period to form an instantaneous value discrete sequence table; selecting instantaneous value sequences which are positioned near two adjacent zero-crossing points in the same direction in the instantaneous value discrete sequence table; calculating the separation time of two zero-crossing points according to the two sections of instantaneous value sequences and the fixed sampling period; and calculating the frequency of the sine waveform according to the separation time of the two zero-crossing points. The invention can use the sampling value near the zero crossing point to predict the zero crossing point time, thereby solving the measurement error caused by the sampling point not being the zero crossing point, realizing high-precision frequency calculation under the condition of lower sampling rate, effectively reducing the calculated amount and improving the operation efficiency.
Description
Technical Field
The invention relates to the technical field of power system relay protection, in particular to a sine wave frequency measurement and calculation method, a sine wave frequency measurement and calculation system, a storage medium and calculation equipment.
Background
In the protection of large and medium-sized generators, phase modulators or pumped storage machines in an electric power system, frequency abnormality protection and frequency difference protection are necessary protection for preventing metal fatigue of the generators and ensuring the stability of the system, wherein the precision of voltage frequency calculation directly determines the precision of protection, and the protection is generally realized by the following method: voltage is introduced through a voltage transformer, a voltage signal is sampled to obtain a voltage instantaneous value, time between zero crossing points is measured to obtain a period, and the reciprocal of the period is further calculated to obtain a frequency magnitude value.
However, when using the above algorithm, since the sampling point usually cannot fall on the zero crossing point, there are the following problems:
(1) When the sampling rate is not integral multiple of the voltage frequency, the time of the sampling point near the zero crossing point is used for replacing the time of the zero crossing point, so that the time measurement between the zero crossing points has errors, and the frequency calculation has errors;
(2) Although the purpose of increasing the calculation accuracy can be achieved by increasing the sampling rate and reducing the gap between the sampling point time and the zero crossing point time, the calculation resource consumption and the power consumption are increased, and the running efficiency of the CPU is reduced.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a sine wave frequency measurement and calculation method, a sine wave frequency measurement and calculation system, a storage medium and calculation equipment, and solves the problems of low calculation precision and large calculation amount of the current sine wave frequency measurement.
In order to solve the technical problems, the invention is realized by adopting the following technical scheme:
in a first aspect, the present invention provides a sine wave frequency measurement and calculation method, which is characterized by comprising the following steps:
acquiring instantaneous values of sine waveforms according to a fixed sampling period to form an instantaneous value discrete sequence table;
selecting instantaneous value sequences which are respectively positioned near two adjacent zero-crossing points in the same direction in an instantaneous value discrete sequence table;
calculating to obtain the interval time between two adjacent zero-crossing points in the same direction according to the two sections of instantaneous value sequences and the fixed sampling period;
and calculating the frequency of the sine waveform according to the interval time between two adjacent zero-crossing points in the same direction.
Further, before calculating the separation time between two adjacent zero-crossing points in the same direction according to the two instantaneous value sequences and the fixed sampling period, the method further includes:
respectively calculating effective values of two sine waveforms according to the two sections of instantaneous value sequences;
and respectively compensating and correcting the sampling values in the corresponding instantaneous value sequences according to the effective values of the two sine waveforms.
Further, the calculation formula of the compensation correction is as follows:
in the formula, U represents an effective value of a sine waveform, U (x) represents a sampling value in an instantaneous value sequence, and U' (x) represents a corrected sampling value obtained by compensating and correcting U (x).
Further, the two instantaneous value sequences are respectively expressed as { u (n), u (n + 1), u (n + 2),. }, { u (m), u (m + 1), u (m + 2),. };
the sampling values in the two instantaneous value sequences meet the following conditions:
u (n) × u (n + 1) ≦ 0 and u (m) × u (m + 1) ≦ 0 and u (n) × u (m) > 0
In the formula, u (n) represents the nth sample value in the instantaneous value discrete sequence table, u (n + 1) represents the (n + 1) th sample value in the instantaneous value discrete sequence table, u (n + 2) represents the (n + 2) th sample value in the instantaneous value discrete sequence table, u (m) represents the mth sample value in the instantaneous value discrete sequence table, u (m + 1) represents the (m + 1) th sample value in the instantaneous value discrete sequence table, and u (m + 2) represents the (m + 2) th sample value in the instantaneous value discrete sequence table.
Furthermore, the sampling values in the two instantaneous value sequences also satisfy the following conditions:
u (n) > 0 and u (n + 1) ≦ 0 and u (m) > 0 and u (m + 1) ≦ 0.
Further, the calculation formula for calculating the separation time between two adjacent zero-crossing points in the same direction is as follows:
in the formula: t is a unit of 0 Representing a fixed sampling period and T representing the separation time between two adjacent and co-directional zero-crossings.
Further, the calculation formula for calculating the separation time between two adjacent zero-crossing points in the same direction is as follows:
in the formula: t is a unit of 0 Representing a fixed sampling period and T representing the separation time between two adjacent and co-directional zero-crossings.
Further, the formula for calculating the frequency of the sine waveform is as follows:
in the formula: t denotes the separation time between two adjacent zero-crossings in the same direction, and f denotes the frequency of the sinusoidal waveform.
In a second aspect, the present invention provides a sine wave frequency measurement calculation system comprising:
the acquisition module acquires instantaneous values of sine waveforms according to a fixed sampling period to form an instantaneous value discrete sequence table;
the sequence selection module is used for selecting instantaneous value sequences which are respectively positioned near two adjacent zero-crossing points in the same direction in the instantaneous value discrete sequence list;
the time calculation module is used for calculating the interval time between two adjacent zero-crossing points in the same direction according to the two sections of instantaneous value sequences and the fixed sampling period;
and the frequency calculation module is used for calculating the frequency of the sine waveform according to the interval time between two adjacent zero-crossing points in the same direction.
In a third aspect, the invention provides a computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform any of the methods according to the first aspect.
In a fourth aspect, the present invention provides a computing device comprising:
one or more processors, one or more memories, and one or more programs stored in the one or more memories and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods according to the first aspect.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, the instantaneous value of the sine waveform is collected to form an instantaneous value discrete sequence table, then the instantaneous value sequences respectively positioned near two adjacent zero-crossing points in the same direction are selected, and accordingly, the sampling values near the zero-crossing points can be used for predicting the zero-crossing point time, so that the measurement error caused by the fact that the sampling points are not the zero-crossing points can be solved, thus the high-precision frequency calculation is realized under the condition of lower sampling rate, the calculated amount is effectively reduced, and the operation efficiency is improved;
2. according to the invention, the sampling value can be corrected through compensation correction, so that the sampling value is closer to the actual conversion proportion, a new compensated fit line and a sine waveform are enabled to pass zero at the same point, the measurement error caused by the nonlinearity of the sine waveform is reduced, the effect of reducing the error is achieved, and the frequency calculation precision is further improved;
3. according to the embodiment of the invention, the sine function is fitted to be the parabolic function near the zero crossing point, and the moments of the two zero crossing points are predicted according to the two sections of instantaneous value sequences, so that a more accurate prediction result can be obtained on the premise of properly increasing the calculated amount and increasing the operation load, the requirements of all aspects can be considered, and the effect is excellent.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of a sine wave frequency measurement calculation method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the sine wave frequency measurement calculation method of FIG. 1 for calculating the separation time between two zero crossings;
FIG. 3 is a schematic diagram illustrating compensation correction in a sinusoidal wave frequency measurement calculation method according to a second embodiment of the present invention;
FIG. 4 is a schematic diagram of the calculation of the separation time between two zero crossings using the corrected sample values in the sine wave frequency measurement calculation method shown in FIG. 3.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The first embodiment is as follows:
as shown in fig. 1, an embodiment of the present invention provides a sine wave frequency measurement and calculation method, including the following steps:
step 2, selecting instantaneous value sequences which are respectively positioned near two adjacent zero-crossing points in the same direction in the instantaneous value discrete sequence table;
step 3, calculating to obtain the interval time between two adjacent zero-crossing points in the same direction according to the two sections of instantaneous value sequences and the fixed sampling period;
and 4, calculating to obtain the frequency of the sine waveform according to the interval time between two adjacent zero-crossing points in the same direction.
Specifically, the above-mentioned discrete sequence table of instantaneous values can be expressed as:
{u(0),u(1),u(2),u(3),......,u(n),u(n+1),u(n+2),......,u(m),u(m+1),u(m+2),......}
the two sequences of instantaneous values selected can be expressed as:
{u(n),u(n+1),u(n+2),......}，{u(m),u(m+1),u(m+2),......}
the sampling values in the two instantaneous value sequences meet the following conditions:
u (n) × u (n + 1) ≦ 0 and u (m) × u (m + 1) ≦ 0 and u (n) × u (m) > 0
In the formula, u (n) represents the nth sample value in the instantaneous value discrete sequence table, u (n + 1) represents the (n + 1) th sample value in the instantaneous value discrete sequence table, u (n + 2) represents the (n + 2) th sample value in the instantaneous value discrete sequence table, u (m) represents the mth sample value in the instantaneous value discrete sequence table, u (m + 1) represents the (m + 1) th sample value in the instantaneous value discrete sequence table, and u (m + 2) represents the (m + 2) th sample value in the instantaneous value discrete sequence table.
It should be noted that, by limiting the above conditions, u (n) and u (n + 1), u (m) and u (m + 1) are sampling values respectively located at two nearest sides of two zero-crossing points, and the requirements of two adjacent zero-crossing points in the same direction are met; and the two zero-crossing points are adjacent and in the same direction, so that the two zero-crossing points are limited to be positioned at the head and the tail of a complete cycle of the sine wave, and the subsequent time interval of the two zero-crossing points is ensured to be the time of the complete cycle of the sine wave.
In this embodiment, the sampling values in the two instantaneous value sequences further satisfy the following condition:
u (n) > 0 and u (n + 1) ≦ 0 and u (m) > 0 and u (m + 1) ≦ 0.
It should be noted that, by the above definition, two zero-crossing points are further limited to be zero-crossing points at which the sine wave changes from a positive value to a negative value, so that when the method of the present embodiment is used to continuously calculate the sine wave frequency, half of the calculation amount can be reduced, thereby improving the operation efficiency and reducing the load of the device.
As shown in fig. 2, in this embodiment, the calculation formula for calculating the separation time between two adjacent zero-crossing points in the same direction is as follows:
in the formula: t is 0 Representing a fixed sampling period and T representing the separation time between two adjacent and co-directional zero-crossings.
Specifically, the specific derivation process of the above calculation formula is as follows:
predicting the first zero crossing point time T n Comprises the following steps:
predicting the second zero crossing point time T m Comprises the following steps:
the time between two zero crossings is:
in this embodiment, the formula for calculating the frequency of the sine waveform is:
in the formula: t denotes the separation time between two adjacent and co-directional zero crossings, and f denotes the frequency of the sinusoidal waveform.
It should be noted that, according to the present invention, by using the characteristic that the sine function is similar to a linear function near the zero crossing point, the time of the two zero crossing points is predicted according to the two sections of instantaneous value sequences, and compared with the conventional method, the present invention can solve the measurement error caused by the fact that the sampling point is not the zero crossing point, thereby realizing high precision frequency calculation under the condition of lower sampling rate, effectively reducing the calculation amount, and improving the operation efficiency.
Example two:
the embodiment of the invention provides a sine wave frequency measurement and calculation method, which is different from the first embodiment in that before the interval time between two adjacent zero-crossing points in the same direction is calculated according to two sections of instantaneous value sequences and a fixed sampling period, the method further comprises the following steps:
respectively calculating effective values of two sine waveforms according to the two sections of instantaneous value sequences;
and respectively compensating and correcting the sampling values in the corresponding instantaneous value sequences according to the effective values of the two sine waveforms.
In this embodiment, the calculation formula of the compensation correction is:
in the formula, U represents an effective value of a sine waveform, U (x) represents a sampling value in an instantaneous value sequence, and U' (x) represents a corrected sampling value obtained by compensating and correcting U (x).
Specifically, the corrected sampling values obtained after the compensation correction of the above calculation formula on the sampling values in the two instantaneous value sequences are respectively:
in the formula, U '(n) represents a corrected sample value obtained by compensation correction of U (n), U' (n + 1) represents a corrected sample value obtained by compensation correction of U (n + 1), U '(n + 2) represents a corrected sample value obtained by compensation correction of U (n + 2), and U' (n + 2) represents a corrected sample value obtained by compensation correction of U (n + 2) n Represents an effective value of a sine waveform calculated from the instantaneous value sequence { U (n), U (n + 1), U (n + 2),...... }, U '(m) represents a corrected sampling value obtained by compensation correction of U (m), U' (m + 1) represents a corrected sampling value obtained by compensation correction of U (m + 1), U '(m + 2) represents a corrected sampling value obtained by compensation correction of U (m + 2), and U' (m + 2) represents a corrected sampling value obtained by compensation correction of U (m + 2) m Represents the effective value of the sinusoidal waveform calculated from the instantaneous value sequence { u (m), u (m + 1), u (m + 2) }.
It should be noted that, the specific derivation process of the compensation correction formula is as follows:
expanding the Taylor polynomial of the sine waveform, and removing the remainder to obtain:
wherein, theta x Is an angle value of the abscissa and a value range
U sin(θ x ) Is the sampled value, when Usin (theta) x ) In the vicinity of the zero crossing point, θ x Tends to 0, theta x 3 ≈sin 3 (θ x ),
The above formula can thus be transformed into:
it can be seen that with u (x) = Usin (θ) x ) When performing interpolation calculation, there is
Compensating the deviation, a compensation formula can be obtained as follows:
as shown in fig. 3, since the angle is proportional to the time, the zero-crossing point time can be calculated by angle conversion, and the sine wave zero-crossing point interpolation uses the sine wave value u (x) = Usin (θ) of the ordinate x ) Approximate alternative abscissa angle value theta x The zero-crossing point time is predicted by scaling, but the zero-crossing point directly interpolated by the sampling value has an error with the actual value due to the nonlinearity of the sine function, and the sampling value can be corrected by compensation correction so that U' (x) = f (usin (theta)) x ) The new fitting line after compensation and the sine waveform are enabled to zero at the same point, the measurement error caused by the nonlinearity of the sine waveform is reduced, the effect of reducing the error is achieved, and the frequency calculation precision is further improved.
In order to visually compare the frequency accuracy obtained by calculation by the conventional method, the first embodiment method and the second embodiment method, simulation calculation is respectively performed according to the sampling rate of 600Hz, and the conclusion is as follows:
through simulation calculation, under the condition of 600Hz sampling rate, the maximum error (the frequency range of the sine waveform to be measured is 40-60 Hz) of the frequency is calculated to be 5Hz by directly using the traditional sampling point; as shown in fig. 2, the maximum error (frequency range of the sine waveform to be measured 40-60 Hz) of the calculated frequency by using the frequency calculation method of the first embodiment is 0.07Hz; as shown in fig. 4, the maximum error of the calculated frequency (the frequency range of the sine waveform to be measured is 40 to 60 Hz) is 0.015Hz by using the sine wave frequency measurement and calculation method of the second embodiment, and the calculation accuracy is greatly improved.
Example three:
the embodiment of the invention provides a sine wave frequency measurement calculation method, which is different from the first embodiment and the second embodiment in that the calculation formula for calculating the separation time between two adjacent zero-crossing points in the same direction is as follows:
in the formula: t is 0 Representing a fixed sampling period and T representing the separation time between two adjacent and co-directional zero-crossings.
Specifically, the specific derivation process of the above calculation formula is as follows:
predicting the first zero crossing point time T n Comprises the following steps:
predicting the second zero crossing point time T m Comprises the following steps:
the time between two zero crossings is:
it should be noted that, in the implementation of the present invention, a sinusoidal function is fitted to a parabolic function near a zero-crossing point of the sinusoidal function, and then two zero-crossing points are predicted according to two sections of instantaneous value sequences, in comparison with the method for simulating a linear function in the embodiment, although one more sampling value is adopted compared to the embodiment, and three sampling values are used to predict the zero-crossing point, which increases the amount of calculation and increases the operation load, the obtained prediction result is relatively more accurate, so that the selection can be performed according to different practical application requirements, and various requirements can be considered.
Example four:
the embodiment of the invention provides a sine wave frequency measurement and calculation system, which comprises:
the acquisition module acquires instantaneous values of sine waveforms according to a fixed sampling period to form an instantaneous value discrete sequence table;
the sequence selection module is used for selecting instantaneous value sequences which are respectively positioned near two adjacent zero-crossing points in the same direction in the instantaneous value discrete sequence list;
the time calculation module is used for calculating the interval time between two adjacent zero-crossing points in the same direction according to the two sections of instantaneous value sequences and the fixed sampling period;
and the frequency calculation module is used for calculating the frequency of the sine waveform according to the interval time between two adjacent zero-crossing points in the same direction.
Example five:
the present invention provides a computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform any of the methods according to the first aspect.
Example six:
the invention provides a computing device comprising:
one or more processors, one or more memories, and one or more programs stored in the one or more memories and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods of claims 1-8.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (11)
1. The sine wave frequency measurement and calculation method is characterized by comprising the following steps of:
acquiring instantaneous values of sine waveforms according to a fixed sampling period to form an instantaneous value discrete sequence table;
selecting instantaneous value sequences which are respectively positioned near two adjacent zero-crossing points in the same direction in an instantaneous value discrete sequence table;
calculating to obtain the interval time between two adjacent zero-crossing points in the same direction according to the two sections of instantaneous value sequences and the fixed sampling period;
and calculating the frequency of the sine waveform according to the interval time between two adjacent zero-crossing points in the same direction.
2. The sine wave frequency measurement and calculation method according to claim 1, wherein before calculating the separation time between two adjacent zero-crossing points in the same direction according to two instantaneous value sequences and a fixed sampling period, further comprising:
respectively calculating effective values of two sine waveforms according to the two sections of instantaneous value sequences;
and respectively compensating and correcting the sampling values in the corresponding instantaneous value sequences according to the effective values of the two sine waveforms.
3. The sine wave frequency measurement calculation method of claim 2, wherein the compensation correction is calculated by the formula:
in the formula, U represents an effective value of a sine waveform, U (x) represents a sampling value in an instantaneous value sequence, and U' (x) represents a corrected sampling value obtained by compensating and correcting U (x).
4. A sine wave frequency measurement calculation method according to claim 1, characterized in that two sequences of instantaneous values are denoted { u (n), u (n + 1), u (n + 2),. ·. }, { u (m), u (m + 1), u (m + 2),. ·. };
the sampling values in the two instantaneous value sequences meet the following conditions:
u (n) × u (n + 1) ≦ 0 and u (m) × u (m + 1) ≦ 0 and u (n) × u (m) > 0
In the formula, u (n) represents the nth sample value in the instantaneous value discrete sequence table, u (n + 1) represents the (n + 1) th sample value in the instantaneous value discrete sequence table, u (n + 2) represents the (n + 2) th sample value in the instantaneous value discrete sequence table, u (m) represents the mth sample value in the instantaneous value discrete sequence table, u (m + 1) represents the (m + 1) th sample value in the instantaneous value discrete sequence table, and u (m + 2) represents the (m + 2) th sample value in the instantaneous value discrete sequence table.
5. Sine wave frequency measurement calculation method according to claim 4, characterized in that the sample values in the two instantaneous value sequences also satisfy the following condition:
u (n) > 0 and u (n + 1) ≦ 0 and u (m) > 0 and u (m + 1) ≦ 0.
6. The sine wave frequency measurement calculation method according to claim 4 or 5, wherein the calculation formula for calculating the separation time between two adjacent zero-crossing points in the same direction is:
in the formula: t is 0 Representing a fixed sampling period and T representing the separation time between two adjacent and co-directional zero-crossings.
7. The sine wave frequency measurement calculation method according to claim 4 or 5, wherein the calculation formula for calculating the separation time between two adjacent zero-crossing points in the same direction is:
in the formula: t is 0 Representing a fixed sampling period and T representing the separation time between two adjacent and co-directional zero-crossings.
8. The sine wave frequency measurement calculation method of claim 1, wherein the frequency of the sine wave is calculated by the formula:
in the formula: t denotes the separation time between two adjacent and co-directional zero crossings, and f denotes the frequency of the sinusoidal waveform.
9. A sine wave frequency measurement computing system, comprising:
the acquisition module acquires instantaneous values of sine waveforms according to a fixed sampling period to form an instantaneous value discrete sequence table;
the sequence selection module is used for selecting instantaneous value sequences which are respectively positioned near two adjacent zero-crossing points in the same direction in the instantaneous value discrete sequence list;
the time calculation module is used for calculating the interval time between two adjacent zero-crossing points in the same direction according to the two sections of instantaneous value sequences and the fixed sampling period;
and the frequency calculation module is used for calculating the frequency of the sine waveform according to the interval time between two adjacent zero-crossing points in the same direction.
10. A computer readable storage medium storing one or more programs, the one or more programs comprising instructions, which when executed by a computing device, cause the computing device to perform any of the methods of claims 1-8.
11. A computing device, comprising:
one or more processors, one or more memories, and one or more programs stored in the one or more memories and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods of claims 1-8.
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