CN105790261B - Random harmonic power flow calculation method - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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Abstract
The invention provides a random harmonic power flow calculation method, which comprises the following steps: step 1: establishing a probability distribution model of active power output of the distributed power supply; step 2: establishing a time sequence correlation model of active power output of the distributed power supply; and step 3: randomly generating a plurality of distributed power supply active output time sequences with time sequence correlation; and 4, step 4: calculating a corresponding distributed power supply harmonic current time sequence; and 5: performing first harmonic load flow calculation on the power network, and reserving a calculation result; step 6: and according to the calculation result of each harmonic load flow, statistically calculating relevant harmonic evaluation indexes. The method is mainly applied to power system harmonic power flow simulation and evaluation of the influence level of the distributed power supply harmonic on the power grid. By considering the time sequence correlation of the harmonic emission quantity of the distributed power supply, the result obtained by the method can reflect the actual power grid condition.
Description
Technical Field
The invention relates to the field of analysis and safety evaluation of a power system, in particular to a random harmonic power flow calculation method considering correlation of a distributed power supply harmonic emission time sequence.
Background
With the rapid development of economy and the continuous increase of population, the problem of insufficient reserves of traditional energy sources and the problem of environmental pollution caused by the traditional energy sources are more serious, so that the development and utilization of distributed renewable energy sources such as wind energy and photovoltaic energy are more and more emphasized. The rapid development of the distributed green power supply will become a development trend of the power system in China for decades in the future. Although the distributed power supply has the advantages of unique environmental protection and the like, when the distributed power supply is connected to a power grid, new problems, such as harmonic pollution, are brought to the power grid. The harmonic waves injected into the power grid by the distributed power supply affect the quality of electric energy, and hidden danger is brought to the safe operation of the power grid. The harms of the harmonic waves mainly include damage to power electronic devices and electric equipment, reduction of electric energy utilization efficiency and the like. Therefore, the research on the distribution of the harmonic waves in the power system is an important basis for the harmonic wave management of the power grid, and the harmonic wave power flow calculation is an effective means for researching the distribution characteristics of the harmonic waves in the power grid.
Analysis of the measured harmonic data of the grid-connected point of the distributed power supply shows that the active power output of the distributed power supply is correspondingly in random volatility due to the influence of fluctuating random quantities such as illumination intensity, wind speed and the like, so that the generated harmonic waves are randomly changed. The IEEE 519 harmonic standard, when describing harmonic distortion, suggests extracting a corresponding probability distribution map from field-measured harmonic data to represent the randomness of the actual harmonics. In order to analyze the randomness of the power grid harmonic waves, random harmonic flow calculation is required. The random harmonic current calculation is a statistical calculation method for harmonic distribution characteristics of a power system. The probability distribution of harmonic current in the power grid is obtained through the randomness of harmonic current emission of a harmonic source, and the probability distribution is analyzed and harmonic indexes are calculated. Therefore, compared with deterministic harmonic power flow calculation, random harmonic power flow calculation can reveal the actual characteristics of harmonic distribution when the power system runs better, and harmonic evaluation indexes with higher reference value and statistical significance are provided.
The current random harmonic power flow calculation method mainly comprises a simulation method, an analytic method and an approximation method. The method is characterized in that probability harmonic power flow is obtained by using mathematical modeling and derivation methods in analytic methods such as a semi-invariant method and approximation methods such as a point estimation method, so that the problem of power flow model linearization and the problem of convergence judgment exist, and the method is not suitable for harmonic power flow calculation of a large power network with a complex structure. The simulation method mainly comprises a Monte Carlo simulation method, and can make full use of the computing power of a computer and give a high-precision computing result. According to the Monte Carlo simulation method, a large number of harmonic currents are sampled according to the probability distribution of harmonic emission, then deterministic harmonic power flow calculation is carried out on a determined power grid structure formed by each sample, and finally the distribution conditions of the harmonic power flow of each branch and each node are counted and harmonic evaluation indexes are calculated. At present, the monte carlo simulation method mostly assumes that the harmonic emission meets the standard probability distribution such as normal distribution, however, the actual probability distribution of the harmonic emission is closely related to random variables such as illumination intensity, wind speed and the like, and has strong time sequence correlation. Therefore, in order to objectively reflect the actual harmonic emission characteristics of the distributed power supply, a random harmonic flow calculation method capable of reflecting the correlation of the harmonic emission time sequence of each harmonic source needs to be established, and a basis is provided for system analysis, safety assessment and harmonic treatment of a power grid accessed to the distributed power supply by power grid operators, so that the new energy accepting capability of the power grid is improved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a random harmonic power flow calculation method which can reflect the time sequence correlation of the emission quantity of a distributed power supply harmonic source and is closer to the condition of an actual power grid.
The invention adopts the following technical scheme: a random harmonic power flow calculation method, the calculation method comprising the steps of:
step 1: counting historical time sequence data to obtain a probability distribution model F of active power output of each type of distributed power supply;
step 2: establishing a time sequence correlation model of the active power output of the distributed power supply, and recursively updating the model data according to a time sequence;
and step 3: randomly generating a plurality of distributed power supply active output random samples with time sequence correlation;
and 4, step 4: calculating a time sequence of harmonic emission quantity of the distributed power supply;
and 5: performing first harmonic load flow calculation on the power network, and reserving a calculation result;
step 6: and according to the calculation result of each harmonic load flow, statistically calculating relevant harmonic evaluation indexes.
Preferably, the step (1) comprises the steps of:
1) for various harmonic sources formed by different distributed power supplies, a probability distribution model of active power P of the harmonic sources is described by using quantile probability Q (tau);
Prob(P＜Q(τ))＝τ
(1)
the formula shows that the probability of P value below Q (tau) is tau, tau is equal interval value in [0,1 ];
2) expressing the quantile probability Q (τ) as the argument xiLinear combination of basis functions of, for wind power generation, the argument xiThe values are the wind speed and the availability ratio of the fan which influence the wind power output; for photovoltaic power generation, the independent variable xiThe value is the illumination intensity which influences the photovoltaic power generation capacity;
wherein b (-) represents a basis function α (τ) and θij(τ) is an unknown parameter whose value is estimated using the least squares method; subscript i takes the value of [1, imax]Integer of interval, where i max is the argument xiThe number of (2); subscript j takes the value of [1, jmax]An integer number of intervals, where j max is the number of basis functions b (-);
3) obtaining a probability distribution model F of each type of harmonic source, namely the active power output of each type of distributed power supply, according to the relationship that the quantile probability Q (tau) and the probability distribution model are inverse functions;
F＝Q(τ)-1(3)。
preferably, the step (2) includes the steps of:
1) determining a time sequence length K considering the time sequence correlation, and converting the real sample value of each active power output P into uniformly distributed random variables by using time sequence historical sample data containing M K lengths in total length and a probability distribution function F
2) Random variable is transformed by using Probit function
Conversion to normally distributed random variables
Random vector of length K
Namely, the method obeys multivariate Gaussian distribution;
3) by X(m)The covariance matrix represents the time sequence correlation among the time sequence lengths K, and the covariance matrix is recursively updated according to the total time sequence length;
in the formula, sigmamIs X(m)λ is an update factor, λ ∈ [0,1), representing the rate of update of the covariance matrix, sigmamThe initial value of (a) is a diagonal matrix with diagonal elements of 1 and the remaining elements of 0; m represents the time sequence history sample data of the mth length K, wherein M is 1.
To prevent sigmamAnd (3) carrying out normalization processing on the covariance matrix deviating from the multivariate Gaussian:
in the formula sigmamIs sigmamThe square root of the diagonal elements of (a) is the vector of standard deviations, the Θ notation represents the division between the elements of the matrix.
Preferably, the step (3) includes the steps of:
1) according to the probability distribution function F and the covariance matrix sigmamRandomly generating N time-length M multivariate Gaussian distribution N (0, ∑)m) Random variable of (2), denoted as X(m,n)：
2) Using the anti-Probit function, X is(m,n)Conversion to random variables
3) Given the input data of typical wind speed and illumination intensity independent variables with the duration M, the inverse function F of the probability distribution function F is utilized-1To, for
And (3) transformation:
thus, N random samples of the active power output of the distributed power supply with the duration of M are obtained
Preferably, in the step (4), the output is determined according to the power outputRelation of force P and each harmonic emission quantity, N random samples of active force of distributed power supply with duration of M
Calculating a harmonic emission quantity time sequence with time sequence correlation corresponding to the distributed power source active power output random sample;
when only one harmonic source exists in the system, the harmonic emission phase angle theta is 0 degree;
when a plurality of harmonic sources act together in the system, the value of the phase angle theta of the emission quantity of each harmonic of each type of harmonic source is a sample which is uniformly distributed in a [0 DEG, 180 DEG ] interval.
Preferably, in the step (5), the power network is composed of harmonic emission quantities per time in a time series of harmonic emission quantities of the distributed power supply.
Preferably, in the step (6), the harmonic evaluation index includes: harmonic current of each branch, harmonic voltage of each node, expected value of harmonic distortion rate of each node, variance value and 95% probability value.
Compared with the prior art, the invention has the following beneficial effects:
the random harmonic power flow calculation method provided by the invention can truly reflect the time sequence correlation of the harmonic emission quantity of the distributed power supply, and can be used for harmonic calculation, simulation and evaluation of a power system.
The method takes the data of wind speed, illumination intensity and the like as independent variables, establishes a probability distribution curve of the active power output of the distributed power supply, and utilizes a Gaussian covariance matrix to express the time sequence correlation between the active power output at each time point. According to the empirical relationship between the active output and each harmonic emission, a plurality of harmonic emission time sequences are randomly generated, harmonic load flow calculation is carried out, and a statistical value of a harmonic index is given.
The method can objectively reflect the actual characteristics of the harmonic emission quantity of the distributed power supply, and provides a basis for the power grid operator to perform system analysis, safety assessment and harmonic treatment on the power grid accessed to the distributed power supply, so that the new energy accepting capability of the power grid is improved, and the method has high practical value.
Drawings
Fig. 1 is a flow chart of random harmonic power flow calculation provided by the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved by the embodiments of the present invention clearer, the following detailed description will be given with reference to the accompanying drawings and specific embodiments.
The embodiment provides a random harmonic power flow calculation method considering the time sequence correlation of harmonic emission quantity of a distributed power supply, which comprises the following steps:
step 1: counting to obtain a probability distribution model of active power output of each type of distributed power supply (including wind power generation and photovoltaic power generation) through historical time sequence data;
step 2: obtaining a time sequence correlation model of the active power output of the distributed power supply by establishing a Gaussian covariance matrix, and carrying out recursive updating according to a time sequence;
and step 3: randomly generating a plurality of time sequences with time sequence correlation of the active output of the distributed power supply by the established probability distribution model and the time sequence correlation model;
and 4, step 4: calculating a corresponding distributed power supply harmonic emission quantity time sequence with time sequence correlation according to the relation between the active power output and the harmonic emission quantity obtained from the historical data;
and 5: the harmonic emission quantity at each moment in the distributed power supply harmonic emission quantity time sequence can form a set power network, primary harmonic power flow calculation is carried out on the power network, and the calculation result is reserved;
step 6: and according to the calculation result of each harmonic load flow, statistically calculating relevant harmonic evaluation indexes.
The step (1) specifically comprises the following steps:
1) for various harmonic sources formed by different distributed power supplies, a probability distribution model of active power output P of the harmonic sources is described by using quantile probability Q (tau), and the probability that the value of P is below Q (tau) is represented by Q (tau) and is tau. Tau is taken at equal intervals of 5% in the interval of [0,1], namely
τ＝0.05,0.10,0.15,...0.95,1.0。
Prob(P＜Q(τ))＝τ (1)
2) From the history data, the probability distribution represented by equation (1) is estimated. The system of this example contains two distributed power harmonic sources, one being a wind power generation source and the other being a photovoltaic source.
For wind power generation, the hourly wind speed W data is known and taken as an independent variable, and the quantile probability Q (τ) is expressed as a linear combination of the basis functions of the independent variable W;
for photovoltaic power generation, known data is sunlight average intensity gamma provided by a weather station, and in order to obtain the active output quantile probability Q (tau) of each hour, the sunlight average intensity gamma, the sunlight duration S and the time t in one day are used as independent variables, and an hourly quantile probability Q (tau) model is established.
Wherein B (-) represents a basis function, such as a cubic B-spline basis function, α (τ) and θ·j(τ) is an unknown parameter whose value is estimated using the least squares method; subscript i takes the value of [1, imax]Integer of interval, where i max is the argument xiThe number of (2); subscript j takes the value of [1, j max]And the interval integer is the number of the basis functions b (-) to jmax, and the value of the jmax can be manually adjusted according to the precision requirement.
3) And obtaining the probability distribution function F of the active power output of each type of harmonic source according to the relationship that the quantile probability Q (tau) and the probability distribution function are inverse functions.
F＝Q(τ)-1(4)
The step (2) specifically comprises the following steps:
1) the timing length K considering the timing correlation is set to 24 hours in a day, i.e. K is 24, and the length K is one year, i.e. the total length includes M365K longConverting the real sample value of the active power output P at each moment into uniformly distributed random variables by time sequence historical sample data of the power and the probability distribution function F established in the step 1
2) Using Probit functions, i.e.
(where erf-1As an inverse error function), a random variable is substituted
Conversion to normally distributed random variables
Thus, a random vector of length K
I.e. obey a multivariate gaussian distribution.
3) By X(m)The covariance matrix of (a) represents the timing correlation between timing lengths K. In order to reflect the change of the time sequence correlation in different time periods, the covariance matrix is recursively updated according to the total time sequence length.
In the formula, sigmamIs X(m)λ is the update factor, λ ∈ [0,1), representing the speed of covariance matrix updatemIs a diagonal matrix with diagonal elements of 1 and the remaining elements of 0. To prevent sigmamAnd (3) carrying out normalization processing on the covariance matrix deviating from the multivariate Gaussian:
in the formula sigmamIs sigmamThe square root of the diagonal elements of (a) is the vector of standard deviations, the Θ notation represents the division between the elements of the matrix.
The step (3) specifically comprises the following steps:
1) according to the probability distribution function F established in the step 1) and the covariance matrix sigma established in the step 2)mFirstly, randomly generating N time length M obeying multivariate Gaussian distribution N (0, ∑)m) Random variable of (2), denoted as X(m,n)：
2) Using the anti-Probit function, X is(m,n)Conversion to random variables
3) Giving input data of independent variables such as typical wind speed and illumination intensity with the duration of M, and using a probability distribution function F to carry out the comparison
And (3) transformation:
thus, N random samples of harmonic source active power output with the duration of M are obtained
The step (4) specifically comprises the following steps:
according to the active output P and each harmonic emission quantity (in the content rate I) obtained from historical datah% representation), and N random samples of harmonic source active power output with the duration of M obtained in step 3 by adopting an interval correspondence method
And calculating a corresponding time sequence of harmonic emission quantities.
For each harmonic emission phase angle theta, due to the combined action of two harmonic sources in the system, the randomness of the phase angle needs to be considered, namely, for each harmonic emission phase angle of each type of harmonic source, samples which are uniformly distributed in a [0 degrees and 180 degrees ] interval are randomly generated:
the step (5) specifically comprises the following steps:
because the random harmonic power flow method needs to perform multiple deterministic harmonic power flow calculations on a large number of samples, in order to save the calculation amount, a direct decoupling method is adopted to perform deterministic harmonic power flow calculations. The method can meet the requirement of general engineering in precision. The method comprises the following specific steps:
1) and (4) carrying out fundamental wave solving by adopting a Newton-Raphson method to obtain a power grid fundamental wave load flow calculation result.
2) And determining the mth harmonic emission current component of the power grid according to the fundamental voltage and current calculation result of each node and the harmonic emission current sample of each harmonic source.
3) And establishing a harmonic admittance matrix of the h-th harmonic for each element of the power grid, including a generator, a transformer, a power transmission line and a non-harmonic source load, and forming a node admittance matrix of each node of the power grid. The harmonic node admittance matrix describes the connection condition of the h-th harmonic network and the branch harmonic admittance values.
4) According to
And (4) carrying out harmonic load flow calculation by an equation to obtain the harmonic voltage of each node and the harmonic current of each branch of the h-th harmonic of the power grid.
The step (6) specifically comprises the following steps:
according to the harmonic power flow calculation result obtained in the step 5, the probability distribution curves of the harmonic current of each branch, the harmonic voltage of each node and the harmonic distortion rate of each node are calculated in a statistical manner, and harmonic evaluation indexes are calculated according to the probability distribution curves, wherein the probability distribution curves comprise: each branch harmonic current, each node harmonic voltage, expected value of each node harmonic distortion rate, variance value, and 95% probability value (CP 95).
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present application and not for limiting the scope of protection thereof, and although the present application is described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that after reading the present application, they can make various changes, modifications or equivalents to the specific embodiments of the application, but these changes, modifications or equivalents are all within the scope of protection of the claims to be filed.
Claims (5)
1. A random harmonic power flow calculation method is characterized by comprising the following steps:
step 1: counting historical time sequence data to obtain a probability distribution model F of active power output of each type of distributed power supply;
step 2: establishing a time sequence correlation model of the active power output of the distributed power supply, and recursively updating the model data according to a time sequence;
and step 3: randomly generating a plurality of distributed power supply active output random samples with time sequence correlation;
and 4, step 4: calculating a time sequence of harmonic emission quantity of the distributed power supply;
and 5: performing first harmonic load flow calculation on the power network, and reserving a calculation result;
step 6: according to the calculation result of each harmonic load flow, the relevant harmonic evaluation indexes are calculated in a statistical manner;
in the step 4, N random samples P of the active power output of the distributed power supply with the duration of M are obtained according to the relation between the active power output P and each harmonic emission quantityk (m，n)Calculating a harmonic emission quantity time sequence with time sequence correlation corresponding to the distributed power supply active power output random sample;
when only one harmonic source exists in the system, the harmonic emission phase angle theta is 0 degree;
when a plurality of harmonic sources act together in the system, samples which are uniformly distributed in an interval of [0 degrees and 180 degrees ] are taken as the phase angle theta of the emission quantity of each harmonic of each type of harmonic source;
in the step 5, the power network is composed of harmonic emission quantities at each moment in the distributed power supply harmonic emission quantity time series.
2. The power flow calculation method according to claim 1, wherein the step 1 includes the steps of:
1) for various harmonic sources formed by different distributed power supplies, a probability distribution model of active power P of the harmonic sources is described by using quantile probability Q (tau);
Prob(P＜Q(τ))＝τ (1)
the formula shows that the probability of P value below Q (tau) is tau, tau is equal interval value in [0,1 ];
2) expressing the quantile probability Q (τ) as the argument xiLinear combination of basis functions of, for wind power generation, the argument xiThe values are the wind speed and the availability ratio of the fan which influence the wind power output; for photovoltaic power generation, the independent variable xiThe value is the illumination intensity which influences the photovoltaic power generation capacity;
wherein b (-) represents a basis function α (τ) and θij(τ) is an unknown parameter, and the value is calculated by the least squares methodEstimating; subscript i takes the value of [1, imax]Integer of interval, where imax is the argument xiThe number of (2); subscript j takes the value of [1, jmax]An integer number of intervals, where jmax is the number of basis functions b (·);
3) obtaining a probability distribution model F of each type of harmonic source, namely the active power output of each type of distributed power supply, according to the relationship that the quantile probability Q (tau) and the probability distribution model are inverse functions;
F＝Q(τ)-1(3)。
3. the power flow calculation method according to claim 1, wherein the step 2 includes the steps of:
1) determining a time sequence length K considering the time sequence correlation, and converting the real sample value of each active power output P into uniformly distributed random variables by using time sequence historical sample data containing M K lengths in total length and a probability distribution function F
2) Random variable is transformed by using Probit function
Conversion to normally distributed random variables
Random vector of length K
Namely, the method obeys multivariate Gaussian distribution;
3) by X(m)The covariance matrix represents the time sequence correlation among the time sequence lengths K, and the covariance matrix is recursively updated according to the total time sequence length;
in the formula, sigmamIs X(m)Of the covariance matrix, λ being an updateThe factor λ ∈ [0,1) representing the speed of covariance matrix update ∑mThe initial value of (a) is a diagonal matrix with diagonal elements of 1 and the remaining elements of 0; m represents the time sequence history sample data of the mth length K, wherein M is 1.
To prevent sigmamAnd (3) carrying out normalization processing on the covariance matrix deviating from the multivariate Gaussian:
in the formula sigmamIs sigmamThe square root of the diagonal elements of (a) is the vector of standard deviations, the Θ notation represents the division between the elements of the matrix.
4. The power flow calculation method according to claim 1, wherein the step 3 includes the steps of:
1) according to the probability distribution function F and the covariance matrix sigmamRandomly generating N time-length M multivariate Gaussian distribution N (0, ∑)m) Random variable of (2), denoted as X(m,n)：
2) Using the anti-Probit function, X is(m,n)Conversion to random variables
3) Given the input data of typical wind speed and illumination intensity independent variables with the duration M, the inverse function F of the probability distribution function F is utilized-1To, for
And (3) transformation:
thus, N random samples of the active power output of the distributed power supply with the duration of M are obtained
5. The power flow calculation method according to claim 1, wherein in the step 6, the harmonic evaluation index includes: harmonic current of each branch, harmonic voltage of each node, expected value of harmonic distortion rate of each node, variance value and 95% probability value.
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| CN106651150B (en) * | 2016-12-01 | 2021-02-09 | 全球能源互联网研究院有限公司 | Method and device for evaluating harmonic influence of power grid |
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