CN110569476A - Method for estimating harmonic parameters of power system - Google Patents
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Abstract
the invention discloses a method for estimating harmonic parameters of an electric power system, which comprises the following steps: acquiring a current signal d (t) with noise in a power system, wherein t represents time; discretizing the current signal d (t) into a converted current signal d (n) and using d (n) as a desired signal in an adaptive filter; establishing an adaptive filter model according to a harmonic signal y (n) in the power system, and determining an input vector X (n) and a weight vector W in the adaptive filter modelm(n) and output vectorAdopting minimum logarithm absolute deviation algorithm to pair weight vector W in modelmand (n) estimating to obtain the amplitude and the phase angle of the harmonic signal.
Description
Technical Field
The invention belongs to the technical field of parameter estimation methods, and relates to an estimation method of harmonic parameters of an electric power system.
Background
with the development of scientific technology in the present generation, a large amount of harmonics are generated in a power system due to the use of more and more power electronic devices and nonlinear loads, so that the harmonic problem in the power system becomes a more serious problem at present. The quality of electric energy is concerned with the production efficiency and the electricity utilization safety in daily life, and along with the introduction of a large amount of harmonic pollution, the quality of electric energy not only influences the efficiency of electric energy production, transmission and use, but also aggravates the aging of electric appliances, influences communication and seriously leads to the damage of devices. Therefore, the solution of harmonic pollution becomes urgent. The prerequisite for solving the problem of harmonic pollution is to find a harmonic source and know the parameters and the positions of the harmonics.
The traditional adaptive filtering method only considers the gaussian noise of the system when estimating the harmonic parameters of the power system, such as the least mean square error-based adaptive filtering algorithm (LMS) and the recursive least square estimation algorithm (RLS), and the method has larger deviation on the estimation accuracy of the amplitude and the phase angle in the non-gaussian noise interference environment. In an actual power system, non-gaussian noise often exists, so that the research on a robust power system harmonic parameter estimation method has important practical significance.
Disclosure of Invention
the invention aims to provide an estimation method of harmonic parameters of a power system, which can effectively reduce the influence of non-Gaussian noise on the estimation of the harmonic parameters.
The technical scheme adopted by the invention is that the method for estimating the harmonic parameters of the power system comprises the following steps:
Step 1, collecting a current signal d (t) with noise in a power system, wherein t represents time;
step 2, discretizing the current signal d (t) into a converted current signal d (n), and taking d (n) as an expected signal in the adaptive filter;
Step 3, establishing an adaptive filter model according to a harmonic signal y (n) in the power system, and determining an input vector X (n) and a weight vector W in the adaptive filter modelm(n) and output vector
Step 4, adopting a minimum logarithm absolute deviation algorithm to carry out comparison on weight vector W in the modelm(n) estimating to obtain the amplitude and phase of the harmonic signalAnd (4) an angle.
The invention is also characterized in that:
the current signal d (t) in step 1 is:
In the above formula, vdcIs a direct current component; a. thekIs the amplitude of the kth harmonic, fkAt the frequency of the k-th harmonic,Is the phase of the kth harmonic, M is the highest harmonic order, n0(t) is the noise in the true harmonic signal, n0(t)＝n1(t)+n2(t)，n1(t) is Gaussian noise; n is2(t) is non-Gaussian noise.
the discretized transition current signal d (n) of the step 2 is:
in the above formula, Ts＝1/fs，fsis the sampling frequency, TsIs the sampling period and n is the number of iterations.
the step 3 specifically comprises the following steps:
Step 3.1, analyzing the harmonic signal to be estimated, and establishing an adaptive filter model:
step 3.2, determining input vectors X (n) and W by formula (5)m(n) and output vector
inputting a vector:
X(n)＝[vdc，x1，x2，…，x2M-1，x2M]T (5)；
＝[1，cos(ω1n)，sin(ω1n)…，cos(ωMn)，sin(ωMn)]T
In the above formula, ωkBeing angular frequency, omega, of the signalk＝2πfk；
weight vector:
Wm(n)＝[wdc，w1，w2，…，w2M-1，w2M]T
＝[d0，a1，b1，…，aM，bM]T (6)；
whereink takes the value 1, 2 … … M; m is the weight vector length;
Based on input vectors X (n), Wm(n) calculating to obtain an output vector
the step 4 specifically comprises the following steps:
Step 4.1, according to the output vectorAnd the desired signal d (n) to obtain an error signal e (n):
Step 4.2, the error signal e (n) is substituted into the cost function, and the expression of the cost function is as follows:
In the above formula, a is a design parameter of the cost function;
and 4.3, constructing a weight vector iterative formula by adopting a gradient method according to the cost function:
in the above formula, mu is a step length parameter;
step 4.4, carrying out iterative calculation on the formula (12) until the error signal e (n) is converged and approaches zero, and processing the weight vector to obtain the amplitude A of the harmonic signalkangle of sum
the invention has the beneficial effects that: according to the estimation method, the self-adaptive filter constructed by the method can effectively reduce the influence of non-Gaussian noise (especially impact noise) on harmonic parameter estimation, and ensure the effectiveness of parameter estimation precision; the algorithm is stable, the calculation complexity is low, and the steady state convergence accuracy under the non-Gaussian noise condition is higher than that of other similar traditional algorithms.
Drawings
FIG. 1 is a schematic diagram of a method for estimating harmonic parameters of an electrical power system according to the present invention;
FIG. 2 is a comparison graph of step size parameters versus mean square error of performance of estimated values for the method of estimating harmonic parameters of an electrical power system according to the present invention;
FIG. 3 is a comparison graph of step size parameter versus amplitude of 5 th harmonic in the method for estimating harmonic parameters of an electric power system according to the present invention;
FIG. 4 is a comparison graph of step size parameter versus phase angle of 5 harmonics for a method of estimating harmonic parameters of an electrical power system in accordance with the present invention;
FIG. 5 is a comparison graph of mean square error of parameter a versus estimated value performance for an estimation method of harmonic parameters of an electric power system according to the present invention;
FIG. 6 is a comparison graph of parameter a versus 5 th harmonic amplitude for a method of estimating harmonic parameters of an electrical power system according to the present invention;
FIG. 7 is a comparison of parameter a versus phase angle of 5 th harmonic for a method of estimating harmonic parameters of an electrical power system according to the present invention;
FIG. 8 is a diagram showing a comparison of mean square error between LLAD algorithm under Gaussian noise and LMS and RLS algorithm according to the estimation method of harmonic parameters of the power system;
FIG. 9 is a comparison graph of the amplitude of 5 th harmonic of the LLAD, LMS, RLS algorithms under the condition of mixed noise according to the estimation method of the harmonic parameters of the power system of the present invention;
FIG. 10 is a phase angle comparison diagram of 5 harmonics of LLAD, LMS, RLS algorithms under the condition of mixed noise according to the estimation method of harmonic parameters of the power system of the present invention;
fig. 11 is a tracking diagram of the dynamic signal by the LLAD algorithm under the condition of mixed noise according to the method for estimating harmonic parameters of the power system of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
A method for estimating harmonic parameters of an electric power system, as shown in fig. 1, includes the following steps:
Step 1, collecting a current signal d (t) with noise in a power system, wherein t represents time;
d(t)＝y(t)+n0(t) (1)；
Wherein n is0(t) is a noise signal, y (t) is a harmonic signal without noise, then:
In the above formula, vdcis a direct current component; a. thekIs the amplitude of the kth harmonic, fkAt the frequency of the k-th harmonic,is the phase of the kth harmonic, M is the highest harmonic order, n0(t) is the noise in the true harmonic signal, n0(t)＝n1(t)+n2(t)，n1(t) is Gaussian noise; n is2(t) is non-Gaussian noise.
Step 2, discretizing the current signal d (t) into a converted current signal d (N), and taking d (N) as a desired signal in an adaptive filter, wherein N is 0, 1, 2 … … N-1, and N is the maximum iteration number;
in the above formula, Tsis the sampling period, Ts＝1/fs，fsIs the sampling frequency and n is the number of iterations.
step 3, establishing an adaptive filter model according to a harmonic signal y (n) in the power system, and determining an input vector X (n) and a weight vector W in the adaptive filter modelm(n) and output vector
Step 3.1, analyzing the harmonic signal y (n) in the power system, and establishing an adaptive filter model:
Step 3.2, determining input vectors X (n) and W by formula (5)m(n) and output vector
inputting a vector:
X(n)＝[vdc，x1，x2，…，x2M-1，x2M]T
＝[1，cos(ω1nTs)，sin(ω1nTs)…，cos(ωMnTs)，sin(ωMnTs)]T (5)；
in the above formula, ωkBeing angular frequency, omega, of the signalk＝2πfk；
Weight vector:
Wm(n)＝[wdc，w1，w2，…，w2M-1，w2M]T
＝[d0，a1，b1，…，aM，bM]T (6)；
Whereink takes the value 1, 2 … … M; m is the weight vector length;
Based on input vectors X (n), Wm(n) calculating to obtain an output vector
Step 4, adopting a least-logarithm absolute deviation algorithm (LLAD) to carry out weighting on a weight vector W in the modelmAnd (n) estimating to obtain the amplitude and the phase angle of the harmonic signal.
step 4.1, according to the output vectorAnd the desired signal d (n) to obtain an error signal e (n):
Step 4.2, the invention adopts the cost function of the minimum logarithm absolute deviation algorithm, and the error signal e (n) is brought into the cost function, and the expression of the cost function is as follows:
In the above formula, a is a design parameter of the cost function, affects the performance of the algorithm, and determines the constraint range of the error;
And 4.3, constructing a weight vector iterative formula by adopting a gradient method according to the cost function:
Formula (9) is first substituted into formula (10), which is then derived to obtain the gradient update:
The updated weight vector is:
In the above formula, mu is a step length parameter, and determines the performance of the algorithm;
Step 4.4, carrying out iterative calculation on the formula (12) until the error signal e (n) is converged and approaches zero, and processing the weight vector to obtain the amplitude A of the harmonic signalkangle of sumThe method comprises the following specific steps:
According to the constitution of the weight vector:
Wm(n)＝[wdc，w1，w2，…，w2M-1，w2M]T
＝[d0，a1，b1，…，aM，bM]T (6)；
Then:
Through the mode, the self-adaptive filter constructed by the estimation method can effectively reduce the influence of non-Gaussian noise (especially impact noise) on the harmonic parameter estimation, and ensure the effectiveness of the parameter estimation precision; the algorithm is stable, the calculation complexity is low, and the steady state convergence accuracy under the non-Gaussian noise condition is higher than that of other similar traditional algorithms.
The performance of the algorithm of the invention is tested, and the results are as follows:
Before the experiment, the harmonic signal y (n) was defined as:
y(n)＝50*cos(2*pi*f*t-pi/6)+25*cos(2*pi*f*3*t-pi/3)
+10*cos(2*pi*f*5*t-pi/4)+5*cos(2*pi*f*9*t
-pi/3)+8；
the signal duration is 0.3s, the sampling frequency is 10KHz, the fundamental wave frequency f is 50Hz, and the signal contains fundamental wave, 3-order harmonic wave, 5-order harmonic wave, 9-order harmonic wave and direct current component; the mean value of Gaussian noise is 0, the variance is 1, and the signal-to-noise ratio is 30 dB.
the following simulations all use the magnitude and phase angle of the fifth harmonic as a performance reference.
example 1
The harmonic signal definition performs performance analysis on the design parameters of the LLAD algorithm under the condition that only Gaussian noise exists in the signal, as shown in FIGS. 2, 3 and 4, the parameter a is fixed, the step length is changed to probe the step length parameter, and the convergence speed is higher when the step length is larger, but the steady-state precision is lower and the steady-state fluctuation amplitude is larger; fig. 5, 6, and 7, the step size parameter is fixed, and the performance of the parameter a is explored, it can be seen that the parameter a has a characteristic similar to the step size, and the larger the parameter a is, the faster the convergence speed is, and the lower the accuracy is.
Example 2
When the harmonic noise is gaussian noise, as shown in fig. 8, the LLAD algorithm of the present invention is compared with the LMS and RLS algorithms, and it can be seen that the LLAD algorithm has no advantages in the gaussian noise environment, the performance of the algorithm is similar to that of the LMS, but the convergence rate is lower than that of the RLS; table 1 shows that the LLAD, LMS and RLS algorithms are compared by 20 monte carlo experiments, and it is verified that the LLAD algorithm has robustness under gaussian noise condition and has very high accuracy.
example 3
when the harmonic noise is a mixed noise environment of the impulse noise and the gaussian noise, as shown in fig. 9 and 10, comparing the LLAD with the LMS and RLS algorithms, it can be seen that the LLAD algorithm can obviously inhibit the abrupt non-gaussian noise in the non-gaussian noise environment, and the accuracy is higher than that of the traditional algorithm; as shown in fig. 11, under the condition of non-gaussian noise, the dynamic signal tracking performance of the algorithm can obtain a good tracking performance of the LLAD algorithm, and the harmonic signal can be well fitted during the pulse spike; table 2 shows that the LLAD, LMS and RLS algorithms are compared by 20 monte carlo experiments, and it is verified that the LLAD algorithm has robustness under the non-gaussian noise condition and has higher accuracy, while the traditional algorithm has larger deviation.
TABLE 1
TABLE 2
Claims (5)
1. a method for estimating harmonic parameters of an electric power system is characterized by comprising the following steps:
step 1, collecting a current signal d (t) with noise in a power system, wherein t represents time;
Step 2, discretizing the current signal d (t) into a converted current signal d (n), and taking d (n) as an expected signal in an adaptive filter;
step 3, establishing an adaptive filter model according to a harmonic signal y (n) in the power system, and determining an input vector X (n) and a weight vector W in the adaptive filter modelm(n) and output vector
Step 4, adopting a minimum logarithm absolute deviation algorithm to carry out comparison on weight vector W in the modelmAnd (n) estimating to obtain the amplitude and the phase angle of the harmonic signal.
2. The method for estimating harmonic parameters of an electric power system according to claim 1, wherein the current signal d (t) in step 1 is:
in the above formula, vdcIs a direct current component; a. thekis the amplitude of the kth harmonic, fkAt the frequency of the k-th harmonic,Is the phase of the kth harmonic, M is the highest harmonic order, n0(t) is the noise in the true harmonic signal, n0(t)＝n1(t)+n2(t)，n1(t) is Gaussian noise; n is2(t) is non-Gaussian noise.
3. the method according to claim 2, wherein the discretized transition current signal d (n) in step 2 is:
In the above formula, Ts＝1/fs，fsIs the sampling frequency, TsIs the sampling period and n is the number of iterations.
4. the method for estimating harmonic parameters of an electric power system according to claim 1, wherein step 3 specifically comprises:
Step 3.1, analyzing the harmonic signal to be estimated, and establishing an adaptive filter model:
Step 3.2, determining input vectors X (n) and W by formula (5)m(n) and output vector
inputting a vector:
X(n)＝[vdc，x1，x2，…，x2M-1，x2M]T
＝[1，cos(ω1n)，sin(ω1n)…，cos(ωMn)，sin(ωMn)]T (5)；
In the above formula, ωkBeing angular frequency, omega, of the signalk＝2πfk；
weight vector:
Wm(n)＝[wdc，w1，w2，…，w2M-1，w2M]T
＝[d0，a1，b1，…，aM，bM]T (6)；
whereink takes the value 1, 2 … … M; m is the weight vector length;
Based on input vectors X (n), Wm(n) calculating to obtain an output vector
5. The method for estimating harmonic parameters of an electric power system according to claim 1, wherein step 4 specifically comprises:
step 4.1, according to the output vectorand the desired signal d (n) to obtain an error signal e (n):
Step 4.2, the error signal e (n) is substituted into the cost function, and the expression of the cost function is as follows:
In the above formula, a is a design parameter of the cost function;
and 4.3, constructing a weight vector iterative formula by adopting a gradient method according to the cost function:
in the above formula, mu is a step length parameter;
step 4.4, carrying out iterative calculation on the formula (12) until the error signal e (n) is converged and approaches zero, and processing the weight vector to obtain the amplitude A of the harmonic signalkAngle of sum
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