CN114414885A - Improved calculation method for phase difference measurement of power system - Google Patents
Improved calculation method for phase difference measurement of power system Download PDFInfo
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Abstract
The invention discloses an improved calculation method for phase difference measurement of a power system, which comprises the steps of respectively installing a voltage sensor or a current sensor on each phase of the power system to monitor load current iL (t) and system voltage us (t) of each phase, wherein L represents a load, S represents a system, variable t is time, periodic non-sinusoidal load current iL (t) and an active reference signal x of fundamental current of the load current1，x1Sin (ω t), reactive reference signal x2，x2The synchronous sampling is performed so as to obtain a discrete value il (n) of the load current at the current sampling time n and a fundamental wave active discrete value x of the reference signal1(n) and the fundamental reactive discrete value x2(n) wherein x1Is a standard fundamental voltage, x2The value of the phase-shifted signal is 90 degrees, and omega is the fundamental crossover frequency. Has the advantages that: the algorithm reduces the interference among the harmonics and is suitable for the frequency deviation of a wide range of signals; better noise and interferenceInterference suppression capability.
Description
Technical Field
The invention relates to the technical field of power systems, in particular to an improved calculation method for phase difference measurement of a power system.
Background
With the grid connection of large-capacity units such as wind power and photovoltaic units under new conditions, the ratio of new energy power generation in a power system is improved, and the frequency fluctuation of a power grid is influenced by the characteristics of randomness, intermittence and the like of the new energy power generation such as wind power and photovoltaic.
Due to the existence of frequency deviation of the power system, the frequency of a measured signal cannot be guaranteed to be always integral multiple of the sampling frequency, and strict synchronous sampling cannot be achieved; this produces a fence effect and short range leakage, which results in incorrect signal parameters (frequency, amplitude and phase) from the DFT.
Due to various problems caused by harmonic wave and frequency shift even frequency fluctuation in the power system, in order to solve the problem that the traditional power harmonic wave detection algorithm cannot meet the requirement of harmonic wave detection precision, the situation that the fundamental wave frequency of a power grid is greatly shifted even fluctuates in a wide range is faced, and therefore the traditional power harmonic wave estimation algorithm needs to be corrected and improved.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides an improved calculation method for phase difference measurement of a power system.
In order to achieve the purpose, the invention adopts the following technical scheme: a method for improving and calculating phase difference measurement of a power system comprises the following steps:
s1: respectively installing a voltage sensor or a current sensor on each phase of the power system to monitor the load current iL (t) and the system voltage us (t) of each phase, wherein L represents a load, S represents a system, and a variable t is time;
s2: active reference signal x for periodic non-sinusoidal load current iL (t) and its fundamental current1，x1Sin (ω t), reactive reference signal x2，x2The synchronous sampling is performed so as to obtain a discrete value il (n) of the load current at the current sampling time n and a fundamental wave active discrete value x of the reference signal1(n) and the fundamental reactive discrete value x2(n) wherein x1Is a standard fundamental voltage, x2The value of the phase-shifted signal is 90 degrees, and omega is the fundamental wave alternating frequency;
s3: the fundamental wave active discrete value x at the current sampling moment is obtained1(n) and the fundamental reactive discrete value x2(n) a fundamental discrete value matrix x (n) where x is the current sampling time1(n)，x2(n)]；
Taking the fundamental wave reactive discrete value as a target curve to perform curve fitting,obtaining a phase compensation curve f (x) which is most approximate to the target curve, and determining a phase compensation transfer function according to the phase compensation curve f (x); then curve fitting is carried out, n is a natural number, n and b0、b1、…、bn、a1、a2、…、anAs fitting parameters, the laplace transform factor s is a complex variable;
s4: measuring current discrete value iα(n)、iβ(n) and a discrete value u of a reference voltageα(n)、uβ(n) and according to the discrete value i of the fundamental currentα(n)、iβ(n) and a discrete value u of a reference voltageα(n)、uβ(n) calculating the equivalent conductance Gp (n) of the fundamental current
Gp(n)＝iα(n)uα(n)+iβ(n)uβ(n)；
S5: taking a direct current signal with a current value of1 as a reference input signal, and obtaining a linear equivalent conductance G (n) by an adaptive filter of a least mean square algorithm, wherein G (n) is w (n) 1, w (n) is a weight coefficient of the adaptive filter at the current time n, and the initial value of the weight coefficient is zero;
s6: calculating the fundamental wave active current i of the discrete value of the fundamental wave current according to the linear equivalent conductance G (n) obtained in the step 5p1α(n)，ip1β(n)，
ip1α(n)＝G(n)uα(n)
ip1β(n)＝G(n)uβ(n)；
S7: obtaining harmonic currents
Dispersing the current by a value iα(n)、iβ(n) subtracting the fundamental wave active current i respectivelyp1α(n)，ip1 beta (n) to obtain a current discrete value generalized harmonic current icα(n)、icβ(n)；
icα(n)＝iα(n)-ip1α(n)
icβ(n)＝iβ(n)-ip1β(n)
S8: calculating step size factor of adaptive filter
Will make the equivalent conductance Gp(n) subtracting the linear equivalent conductance G (n) of step C to obtain a residual signal e (n) of the adaptive filter at the current time n, where e (n) is Gp(n)-G(n)；
Normalizing residual signals e (n) by using the absolute value of equivalent conductance Gp (n) to obtain normalized residual signals s (n) of the current time n, wherein s (n) e (n)/| Gp (n) |;
iteratively calculating an autocorrelation estimate p (n) of the normalized residual signal s (n) at the current time n and the normalized residual signal s (n-1) at the previous time n-1,
p(n)＝βp(n-1)+(1-β)s(n)s(n-1)；
calculating a reference phase difference (theta) from the phase difference of the fundamental reactive dispersion values1) (ii) a Calculating a second receiving signal for the signal wave of the voltage discrete value; according to equivalent conductance Gp(n) determining apparent phase difference (. theta.) from phase difference2') to a host; will represent the upper phase difference (theta)2') through an upper phase difference (theta)2') the product of the number n of revolutions of the reference point of an angle value within the variation range and 360 DEG plus the apparent phase difference (theta)2') to obtain a true phase difference (theta)2)。
In the above improved calculation method for measuring the phase difference of the power system, it is assumed that the fundamental frequency f1 of the active reference signal x (t) of the fundamental current changes at the rate of df 1/dt; and correcting the normalized frequency correction value based on the frequency change rate, and substituting the corrected normalized frequency correction value into a frequency correction formula, an amplitude correction formula and a phase correction formula to obtain the frequency, the amplitude and the phase of the K-th harmonic.
In the above improved calculation method for measuring phase difference of power system, if the rate of x (t) changes to ROCOF1 ═ df1/dt, the frequency change rate of k-th harmonic is ROCOFk ═ dfk/dt ═ k · df1/dt, the frequencies of the first stage signal and the second stage signal are fk and f' k, respectively, the frequency offset of the two stage signals is dfk, that is:
f′k＝fk+dfk
the frequency offset is considered herein to be equal to the product of the frequency rate of change of the signal and time, so that:
dfk＝ROCOFk·t0＝kt0·df1/dt
time length for shifting the second segment signal: t0 is L/fs, wherein fs is the sampling frequency, L is the number of points of the second section of signal delayed from the first section of signal, and the above formula is substituted to obtain:
dfk＝(kL/fs)·df1/dt
because the frequency of the second section of signal changes, the initial phase should be corrected to the phase of the signal after translation, and the phase difference of the two sections of signals is deduced to be:
wherein, the initial phase angle of k harmonics, T is the length of a sampling window, and phi is the phase of the harmonic signal after window addition and truncation;
the corrected frequency correction amount is:
when the discrete spectrum correction is carried out, the time length of the second section of signal translation is as follows: t0 ═ L/fs, frequency correction amount:
peak frequency corresponding to this subharmonic: substituting the frequency correction amount with f-mk Δ f can obtain a corrected normalized frequency correction amount:
wherein, Δ f is frequency resolution, mk is a peak spectral line number corresponding to k-th harmonic, and N is the length of the sampling sequence; in practical calculation, the value range of the phase is (-pi, pi), the period is 2 pi, and the delta may exceed the interval, so the following processing is required: let δ' ═ mod (δ,2 π), and let δ "be in the range of (- π, π);
similarly to the processing of δ, the calculation result of the phase correction formula may not be within the range of (- π, π), and therefore it is necessary to make the obtained result within the range of (- π, π) as the final correction result.
In the above-mentioned method for improving the measurement and calculation of the phase difference of the power system, the apparent phase difference (θ)2') the direction of increase or decrease is detected continuously; if an apparent phase difference (theta) is detected2') changing the number of revolutions n to n +1 when the reference point is passed while increasing; if an apparent phase difference (theta) is detected2') changing the number of revolutions n to n-1 when the reference point is passed while decreasing; according to the true phase difference (theta)2) Phase difference from reference (theta)1) Determining the state measurement information of the object to be measured based on the angle difference (Delta theta); upper phase difference (theta)2') ranges from 0 to 360 DEG, with a reference point of 0 deg.
Compared with the prior art, the invention has the advantages that: the phase difference measurement improvement algorithm is provided on the basis of a DFT detection algorithm, and has the following three advantages: polynomial transformation is carried out on the frequency spectrum expression of the signal, so that the side lobe attenuation speed is accelerated, the interference among subharmonics is reduced, and the method is suitable for wide-range frequency offset of the signal; meanwhile, the frequency change rate is introduced to improve the traditional phase difference, so that the asynchronous error caused by frequency change is reduced, and the phase difference measurement result with higher precision is obtained; in addition, the frequency spectrum leakage caused by asynchronous sampling is further reduced by adopting a cubic phase difference method, and the noise and interference suppression capability is better.
Detailed Description
The following examples are for illustrative purposes only and are not intended to limit the scope of the present invention.
Examples
A method for improving and calculating phase difference measurement of a power system comprises the following steps:
s1: respectively installing a voltage sensor or a current sensor on each phase of the power system to monitor the load current iL (t) and the system voltage us (t) of each phase, wherein L represents a load, S represents a system, and a variable t is time;
s2: active reference signal x for periodic non-sinusoidal load current iL (t) and its fundamental current1，x1Sin (ω t), reactive reference signal x2，x2The synchronous sampling is performed so as to obtain a discrete value il (n) of the load current at the current sampling time n and a fundamental wave active discrete value x of the reference signal1(n) and the fundamental reactive discrete value x2(n) wherein x1Is a standard fundamental voltage, x2The value of the phase-shifted signal is 90 degrees, and omega is the fundamental wave alternating frequency;
s3: the fundamental wave active discrete value x at the current sampling moment is obtained1(n) and the fundamental reactive discrete value x2(n) a fundamental discrete value matrix x (n) where x is the current sampling time1(n)，x2(n)]；
Taking the fundamental wave reactive discrete value as a target curve to perform curve fitting to obtain a phase compensation curve f (x) most approximate to the target curve, and determining a phase compensation transfer function according to the phase compensation curve f (x); then curve fitting is carried out, n is a natural number, n and b0、b1、…、bn、a1、a2、…、anAs fitting parameters, the laplace transform factor s is a complex variable;
s4: measuring current discrete value iα(n)、iβ(n) and a discrete value u of a reference voltageα(n)、uβ(n) and according to the discrete value i of the fundamental currentα(n)、iβ(n) and a discrete value u of a reference voltageα(n)、uβ(n) calculating the equivalent conductance Gp (n) of the fundamental current
Gp(n)＝iα(n)uα(n)+iβ(n)uβ(n)；
S5: taking a direct current signal with a current value of1 as a reference input signal, and obtaining a linear equivalent conductance G (n) by an adaptive filter of a least mean square algorithm, wherein G (n) is w (n) 1, w (n) is a weight coefficient of the adaptive filter at the current time n, and the initial value of the weight coefficient is zero;
s6: calculating the fundamental wave active current i of the discrete value of the fundamental wave current according to the linear equivalent conductance G (n) obtained in the step 5p1α(n)，ip1β(n)，
ip1α(n)＝G(n)uα(n)
ip1β(n)＝G(n)uβ(n)；
S7: obtaining harmonic currents
Dispersing the current by a value iα(n)、iβ(n) subtracting the fundamental wave active current i respectivelyp1α(n)，ip1 beta (n) to obtain a current discrete value generalized harmonic current icα(n)、icβ(n)；
icα(n)＝iα(n)-ip1α(n)
icβ(n)＝iβ(n)-ip1β(n)
S8: calculating step size factor of adaptive filter
Will make the equivalent conductance Gp(n) subtracting the linear equivalent conductance G (n) of step C to obtain a residual signal e (n) of the adaptive filter at the current time n, where e (n) is Gp(n)-G(n)；
Normalizing residual signals e (n) by using the absolute value of equivalent conductance Gp (n) to obtain normalized residual signals s (n) of the current time n, wherein s (n) e (n)/| Gp (n) |;
iteratively calculating an autocorrelation estimate p (n) of the normalized residual signal s (n) at the current time n and the normalized residual signal s (n-1) at the previous time n-1,
p(n)＝βp(n-1)+(1-β)s(n)s(n-1)；
calculating a reference phase difference (theta) from the phase difference of the fundamental reactive dispersion values1) (ii) a Calculating a second receiving signal for the signal wave of the voltage discrete value; according to equivalent conductance Gp(n) determining apparent phase difference (. theta.) from phase difference2') to a host; will represent the upper phase difference (theta)2') through an upper phase difference (theta)2') the product of the number n of revolutions of the reference point of an angle value within the variation range and 360 DEG plus the apparent phase difference (theta)2') to obtain a true phase difference (theta)2)。
The fundamental frequency f1 of the active reference signal x (t) of the fundamental current is assumed to change at the rate of df 1/dt; and correcting the normalized frequency correction value based on the frequency change rate, and substituting the corrected normalized frequency correction value into a frequency correction formula, an amplitude correction formula and a phase correction formula to obtain the frequency, the amplitude and the phase of the K-th harmonic.
If the rate of x (t) changes to ROCOF1 ═ df1/dt, the frequency change rate of the k-th harmonic is ROCOFk ═ dfk/dt ═ k · df1/dt, the frequencies of the first stage signal and the second stage signal are fk and f' k, respectively, the frequency offset of the two stage signals is dfk, that is:
f′k＝fk+dfk
the frequency offset is considered herein to be equal to the product of the frequency rate of change of the signal and time, so that:
dfk＝ROCOFk·t0＝kt0·df1/dt
time length for shifting the second segment signal: t0 is L/fs, wherein fs is the sampling frequency, L is the number of points of the second section of signal delayed from the first section of signal, and the above formula is substituted to obtain:
dfk＝(kL/fs)·df1/dt
because the frequency of the second section of signal changes, the initial phase should be corrected to the phase of the signal after translation, and the phase difference of the two sections of signals is deduced to be:
wherein, the initial phase angle of k harmonics, T is the length of a sampling window, and phi is the phase of the harmonic signal after window addition and truncation;
the corrected frequency correction amount is:
when the discrete spectrum correction is carried out, the time length of the second section of signal translation is as follows: t0 ═ L/fs, frequency correction amount:
peak frequency corresponding to this subharmonic: substituting the frequency correction amount with f-mk Δ f can obtain a corrected normalized frequency correction amount:
wherein, Δ f is frequency resolution, mk is a peak spectral line number corresponding to k-th harmonic, and N is the length of the sampling sequence; in practical calculation, the value range of the phase is (-pi, pi), the period is 2 pi, and the delta may exceed the interval, so the following processing is required: let δ' ═ mod (δ,2 π), and let δ "be in the range of (- π, π);
similarly to the processing of δ, the calculation result of the phase correction formula may not be within the range of (- π, π), and therefore it is necessary to make the obtained result within the range of (- π, π) as the final correction result.
Apparent phase difference of pair (theta)2') the direction of increase or decrease is detected continuously; if an apparent phase difference (theta) is detected2') changing the number of revolutions n to n +1 when the reference point is passed while increasing; if an apparent phase difference (theta) is detected2') changing the number of revolutions n to n-1 when the reference point is passed while decreasing; according to the true phase difference (theta)2) Phase difference from reference (theta)1) Determining the state measurement information of the object to be measured based on the angle difference (Delta theta); upper phase difference (theta)2') ranges from 0 to 360 DEG, with a reference point of 0 deg.
Claims (4)
1. A method for improving and calculating phase difference measurement of a power system is characterized by comprising the following steps:
s1: respectively installing a voltage sensor or a current sensor on each phase of the power system to monitor the load current iL (t) and the system voltage us (t) of each phase, wherein L represents a load, S represents a system, and a variable t is time;
s2: active reference signal x for periodic non-sinusoidal load current iL (t) and its fundamental current1，x1Sin (ω t), reactive reference signal x2，x2The synchronous sampling is performed so as to obtain a discrete value il (n) of the load current at the current sampling time n and a fundamental wave active discrete value x of the reference signal1(n) and the fundamental reactive discrete value x2(n) wherein x1Is a standard fundamental voltage, x2The value of the phase-shifted signal is 90 degrees, and omega is the fundamental wave alternating frequency;
s3: the fundamental wave active discrete value x at the current sampling moment is obtained1(n) and the fundamental reactive discrete value x2(n) a fundamental discrete value matrix x (n) where x is the current sampling time1(n)，x2(n)]；
Taking the fundamental wave reactive discrete value as a target curve to perform curve fitting to obtain a phase compensation curve f (x) most approximate to the target curve, and determining a phase compensation transfer function according to the phase compensation curve f (x); then curve fitting is carried out, n is a natural number, n and b0、b1、…、bn、a1、a2、…、anAs fitting parameters, the laplace transform factor s is a complex variable;
s4: measuring current discrete value iα(n)、iβ(n) and a discrete value u of a reference voltageα(n)、uβ(n) and according to the discrete value i of the fundamental currentα(n)、iβ(n) and a discrete value u of a reference voltageα(n)、uβ(n) calculating the equivalent conductance Gp (n) of the fundamental current
Gp(n)＝iα(n)uα(n)+iβ(n)uβ(n)；
S5: taking a direct current signal with a current value of1 as a reference input signal, and obtaining a linear equivalent conductance G (n) by an adaptive filter of a least mean square algorithm, wherein G (n) is w (n) 1, w (n) is a weight coefficient of the adaptive filter at the current time n, and the initial value of the weight coefficient is zero;
s6: calculating the fundamental wave active current i of the discrete value of the fundamental wave current according to the linear equivalent conductance G (n) obtained in the step 5p1α(n)，ip1β(n)，
ip1α(n)＝G(n)uα(n)
ip1β(n)＝G(n)uβ(n)；
S7: obtaining harmonic currents
Dispersing the current by a value iα(n)、iβ(n) subtracting the fundamental wave active current i respectivelyp1α(n)，ip1 beta (n) to obtain a current discrete value generalized harmonic current icα(n)、icβ(n)；
icα(n)＝iα(n)-ip1α(n)
icβ(n)＝iβ(n)-ip1β(n)
S8: calculating step size factor of adaptive filter
Will make the equivalent conductance Gp(n) subtracting the linear equivalent conductance G (n) of step C to obtain a residual signal e (n) of the adaptive filter at the current time n, where e (n) is Gp(n)-G(n)；
Normalizing residual signals e (n) by using the absolute value of equivalent conductance Gp (n) to obtain normalized residual signals s (n) of the current time n, wherein s (n) e (n)/| Gp (n) |;
iteratively calculating an autocorrelation estimate p (n) of the normalized residual signal s (n) at the current time n and the normalized residual signal s (n-1) at the previous time n-1,
p(n)＝βp(n-1)+(1-β)s(n)s(n-1)；
calculating a reference phase difference (theta) from the phase difference of the fundamental reactive dispersion values1) (ii) a Calculating a second receiving signal for the signal wave of the voltage discrete value; according to equivalent conductance Gp(n) determining apparent phase difference (. theta.) from phase difference2') to a host; will represent the upper phase difference (theta)2') through an upper phase difference (theta)2') the product of the number n of revolutions of the reference point of an angle value within the variation range and 360 DEG plus the apparent phase difference (theta)2') to obtain a true phase difference (theta)2)。
2. The improved calculation method for measuring the phase difference of the power system as claimed in claim 1, wherein the fundamental frequency f1 of the active reference signal x (t) of the fundamental current is assumed to change at the rate of df 1/dt; and correcting the normalized frequency correction value based on the frequency change rate, and substituting the corrected normalized frequency correction value into a frequency correction formula, an amplitude correction formula and a phase correction formula to obtain the frequency, the amplitude and the phase of the K-th harmonic.
3. The method of claim 1, wherein the rate of x (t) changes to ROOF 1 ═ df1/dt, the frequency change rate of k-th harmonic is ROCOFk ═ dfk/dt ═ k · df1/dt, the frequencies of the first stage signal and the second stage signal are fk and f' k, respectively, the frequency offset of the two stage signals is dfk, that is:
f′k＝fk+dfk
the frequency offset is considered herein to be equal to the product of the frequency rate of change of the signal and time, so that:
dfk＝ROCOFk·t0＝kt0·df1/dt
time length for shifting the second segment signal: t0 is L/fs, wherein fs is the sampling frequency, L is the number of points of the second section of signal delayed from the first section of signal, and the above formula is substituted to obtain:
dfk＝(kL/fs)·df1/dt
because the frequency of the second section of signal changes, the initial phase should be corrected to the phase of the signal after translation, and the phase difference of the two sections of signals is deduced to be:
wherein, the initial phase angle of k harmonics, T is the length of a sampling window, and phi is the phase of the harmonic signal after window addition and truncation;
the corrected frequency correction amount is:
when the discrete spectrum correction is carried out, the time length of the second section of signal translation is as follows: t0 ═ L/fs, frequency correction amount:
peak frequency corresponding to this subharmonic: substituting the frequency correction amount with f-mk Δ f can obtain a corrected normalized frequency correction amount:
wherein, Δ f is frequency resolution, mk is a peak spectral line number corresponding to k-th harmonic, and N is the length of the sampling sequence; in practical calculation, the value range of the phase is (-pi, pi), the period is 2 pi, and the delta may exceed the interval, so the following processing is required: let δ' ═ mod (δ,2 π), and let δ "be in the range of (- π, π);
similarly to the processing of δ, the calculation result of the phase correction formula may not be within the range of (- π, π), and therefore it is necessary to make the obtained result within the range of (- π, π) as the final correction result.
4. The method of claim 1 wherein the apparent phase difference (θ) is calculated2') the direction of increase or decrease is detected continuously; if an apparent phase difference (theta) is detected2') changing the number of revolutions n to n +1 when the reference point is passed while increasing; if an apparent phase difference (theta) is detected2') changing the number of revolutions n to n-1 when the reference point is passed while decreasing; according to the true phase difference (theta)2) Phase difference from reference (theta)1) Determining the state measurement information of the object to be measured based on the angle difference (Delta theta); upper phase difference (theta)2') ranges from 0 to 360 DEG, with a reference point of 0 deg.
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| CN115695104A (en) * | 2023-01-03 | 2023-02-03 | 成都登临科技有限公司 | Method, device, electronic equipment and medium for compensating differential line |
| CN115695104B (en) * | 2023-01-03 | 2023-07-21 | 成都登临科技有限公司 | Differential line compensation method, device, electronic equipment and medium |
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