CN117318037B - Power distribution network state analysis method containing large-scale distributed new energy access - Google Patents
Power distribution network state analysis method containing large-scale distributed new energy access Download PDFInfo
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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
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- H—ELECTRICITY
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- 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
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
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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
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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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
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Abstract
The invention discloses a power distribution network state analysis method comprising large-scale distributed new energy access, which comprises the steps of firstly constructing a new energy power change matrix based on the power of a new energy access node acquired by a power distribution network state detection device; then analyzing the state of the power distribution network under the access of new energy based on the circular law and M-P law construction indexes; and finally, combining the second-class indexes to construct a comprehensive power distribution network state analysis index. The invention fully utilizes the big data collected by the power distribution network state detection device, can carry out real-time state analysis on the power distribution network with large-scale distributed access, and is suitable for application in engineering practice.
Description
Technical Field
The invention belongs to a power grid state analysis method, and particularly relates to a power distribution network state analysis method with large-scale distributed new energy access.
Background
The current globalization of petroleum energy is increasingly scarce, and the problem of serious carbon emission is increasingly serious. Under the background, new energy sources such as wind power, photovoltaic and the like are built and accessed on a large scale, and the method has great significance for adjusting energy structure, saving energy and reducing emission. However, the new energy is intensively connected in a large scale, so that the possibility of occurrence of a blackout accident of the power grid is increased, and therefore, the inventor considers that the power distribution network state detection device is based on the power distribution network state quantity acquisition and analysis of the power distribution network state is of great significance. At present, for a power distribution network without new energy access, a power grid state evaluation method based on entropy theory considering load rate and network structure exists, but the load rate partition is greatly influenced by human factors, and the evaluation result has uncertainty. Aiming at a power grid accessed by distributed new energy, some documents construct a mapping relation between key physical quantity indexes and power grid states through a neural network, but the demand of the documents on training samples is large, and the generalization of a machine learning method is poor, so that the application of the documents in practice is limited.
Disclosure of Invention
The invention aims to provide a power distribution network state analysis method with large-scale distributed new energy access, which solves the problem of power distribution network state analysis with large-scale distributed new energy access, respectively constructs power change matrixes based on collected new energy power and branch power, and provides corresponding power distribution network state analysis indexes to analyze the power distribution network state from different angles.
The method comprises the steps of firstly collecting power of a new energy access node based on a power distribution network state detection device, and constructing a new energy power matrix; then analyzing the state of the power distribution network under the access of new energy based on the circular law and M-P law construction indexes; and finally, combining the second-class indexes to construct a comprehensive power distribution network state analysis index. The invention fully utilizes the big data collected by the power distribution network state detection device, can carry out real-time state analysis on the power distribution network with large-scale distributed access, and is suitable for engineering practical application.
The technical scheme of the invention is as follows: a power distribution network state analysis method with scale distributed new energy access comprises the following steps:
1) Constructing a new energy power change matrix based on the collected new energy power;
2) Preprocessing a new energy power change matrix:
3) Constructing a power distribution network state index MSR based on a circular law:
4) Constructing a power distribution network state index V based on an M-P law;
5) And constructing a power distribution network state analysis index based on the power distribution network state index MSR and the power distribution network state index V.
The specific operation of the step 1) is as follows:
Constructing a new energy power change matrix shown in a formula (2) for the collected new energy power:
Wherein p is the number of nodes with new energy power access, n is the sampling number, each row of X is the same measuring point, and each column is the same sampling time.
The new energy power in the step 1) is collected by a power distribution network state detection device arranged at a new energy access node;
the power distribution network state detection device comprises:
the energy taking module is used for sensing and obtaining energy from a power distribution network line to supply power for the device;
The voltage and current sensor is used for collecting the voltage and current of the lead;
And the data acquisition and processing system acquires information acquired by the voltage and current sensors, calculates the power of each node, and uploads the acquired information to the background monitoring terminal through the communication network.
The specific operation of the step 2) is as follows:
step 2.1) normalization treatment:
Normalizing the new energy power change matrix X according to the formula (3) to obtain a normalized matrix
Wherein μ (X i) and σ (X i) represent the mean and variance, respectively, of X i, X i is row i of X;
step 2.2) calculating a covariance matrix:
The calculation mode of the covariance matrix comprises the following steps:
Wherein X * is the complex conjugate transpose of X.
The specific operation of the step 3) is as follows:
Firstly, singular value decomposition S=W ΣU is carried out on a covariance matrix M, a square matrix sigma corresponding to singular values is taken, and M u=Y1×∑×Y2 is used for obtaining a singular value equivalent matrix, wherein Y 1 and Y 2 are random-generated Haar unitary matrices;
The following treatment is carried out on M u,
Wherein, The ith row of M u is characterized;
Carrying out eigenvalue solution on M u as shown in a formula (6), and carrying out average value solution on the eigenvalue as shown in a formula 7);
Mu=W'∑'U' (6)
Wherein W 'and U' are left and right eigenvectors, respectively, Σ 'is a singular value matrix, and the diagonal position Σ' is the characteristic value of M u; at this time, the M u eigenvalues are averaged on a complex domain, and the state index MSR of the power distribution network can be obtained;
Wherein λ i is the i-th eigenvalue.
The specific operation of the step 4) is as follows: constructing a power distribution network state index V based on an M-P law, as shown in a formula (12):
Wherein k= (d-c)/N; wherein f 1 and f 2 are respectively spectrum distribution functions corresponding to the M-P law and the new energy power matrix, and specifically shown in the formulas (10) and (9);
Where c=p/n, σ 2 is the variance,
F M (x) is an empirical spectrum distribution function; p is the number of the characteristic values; is the ith eigenvalue of matrix M; i {.cndot. } is an indirection function.
The power distribution network state analysis index in the step 5) is as shown in a formula (13):
W=MSR+c/V (13)
Wherein c is a constant; when the new energy power in the power grid is not obviously changed, the spectrum distribution obtained based on the new energy power is similar to the M-P law, and the V is smaller, so that the comprehensive index W of the new energy power change rate is larger; conversely, a larger new energy output change rate can cause the singular value corresponding to the new energy power matrix to drop towards the circle center, so that MSR is smaller; the spectrum distribution obtained based on the new energy power has larger deviation from the M-P law, and the V is larger, and the W is smaller.
The invention collects big data representing the state of the power distribution network based on the power distribution network state detection device, then constructs a new energy power change matrix, and provides corresponding state analysis indexes to analyze the state of the power distribution network containing large-scale distributed new energy access. The method has high sensitivity, can analyze the state of the power distribution network containing large-scale distributed new energy access in real time, and has engineering application value.
Drawings
Fig. 1 is a schematic diagram of a power distribution network state detection device.
FIG. 2 is a graph of the ring rate.
Fig. 3 is a schematic diagram of an improved IEEE 33 node power distribution system.
FIG. 4 is a schematic diagram of wind speed variation during simulation.
Fig. 5 is a graph of a trend of power grid state evaluation index based on a wind power matrix.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
According to the distribution network state analysis method with the large-scale distributed new energy access, new energy power and branch power are collected through the distribution network state monitoring device, and the distribution network state monitoring device mainly comprises an energy taking module, a voltage sensing module, a current sensing module and a data collecting and processing system. The energy taking module mainly senses energy from a power distribution network line to supply power for the device; the voltage and current sensor respectively collects the voltage and current of the lead; the data acquisition and processing system realizes the synchronous acquisition, storage and transmission functions of voltage and current signals. And installing the power distribution network state detection device at a new energy access node, calculating new energy power based on voltage and current acquisition, and taking the new energy power as a data base for power distribution network state analysis.
The invention constructs a power change matrix and corresponding power grid state analysis indexes based on the collected new energy power, and performs state analysis on a power distribution network containing large-scale distributed new energy access, and mainly comprises the following steps:
step 1, constructing a new energy power change matrix based on new energy power;
Step 2, preprocessing a new energy power change matrix;
step 3, calculating a power distribution network state index based on a circular law;
step 4, calculating a power distribution network state index based on an M-P law;
and 5, calculating comprehensive state indexes of the power distribution network based on the step 3 and the step 4.
The specific operation of the step 1 of the power distribution network state analysis method containing the large-scale distributed new energy access is as follows:
Assuming that p new energy access nodes exist in the power distribution network, each measuring point has a power value at a sampling time t i, the power values of all measuring points can form a time vector x (t i), as shown in formula (1):
for n sampling results, all time vectors are combined to form a high-dimensional data matrix X with the size of p multiplied by n,
As can be seen from equation (2), each row of X is the same measurement point, and each column is the same sampling time.
The specific operation of the step 2 of the power distribution network state analysis method containing the large-scale distributed new energy access is that the step 2.1 is performed with normalization treatment,
Normalizing X according to formula (3) to obtain normalized matrix with mean value of 0 and variance of 1
Wherein μ (X i) and σ (X i) represent the mean and variance, respectively, of X i, X i is row i of X.
Step 2.2, calculating a covariance matrix,
Wherein X * is the complex conjugate transpose of X. In large-dimension data analysis, the analysis amount in many multivariate statistics can be expressed as a function of the empirical spectral distribution of the sample covariance, so the sample covariance matrix is very widely used in random matrices.
The specific operation of the step 3 is that step 3.1, the singular treatment is carried out on the covariance matrix M, the specific operation is that,
First, performing singular value decomposition s=wΣu on M, taking a square matrix Σ of the corresponding singular value, and using M u=Y1×∑×Y2 to obtain a singular value equivalent matrix, wherein Y 1 and Y 2 are randomly generated Haar unitary matrices.
The following treatment is carried out on M u,
Wherein, The ith row of M u is characterized.
Next, the eigenvalue solution is performed on M u as shown in the formula (6), and the average value solution of the eigenvalues is performed as shown in the formula (7)
Mu=W'∑'U' (6)
Wherein W 'and U' are left and right eigenvectors, respectively, sigma 'is a singular value matrix, and the diagonal position of Sigma' is M u eigenvalues. At this time, the M u eigenvalues are averaged on the complex domain, and the power distribution network state index MSR can be obtained.
Wherein λ i is the i-th eigenvalue.
The specific operation of the step 4 is to construct a power distribution network state analysis index based on an M-P law.
If each element in the matrix X satisfies the independent equal distribution (iid.) and the mean is 0 and the variance is 1, the empirical spectrum distribution of M u almost certainly converges to the single-loop theorem, and the probability density is:
This is the circular law, which states that if each element of X satisfies the independent same distribution, the eigenvalues of M u will be distributed in a circle with an outer circle radius of 1 and an inner circle radius of (1-c) 1/2, as shown in FIG. 2; otherwise, if the relevance appears in the system, part of characteristic values gather towards the center of the circular ring, and the stronger the relevance is, the stronger the degree of gathering towards the center is.
The circular law indicates that when the system only has white noise, small disturbance and measurement error, the data distribution of the system presents a statistical random characteristic, the data satisfy independent identical distribution, and the singular eigenvalues of the state matrix of the system are distributed in a circular ring with the inner ring radius of (1-c) 1/2 and the outer ring radius of 1 on a complex plane; on the contrary, when a signal source (event) exists in the system, the randomness is broken, the data are no longer in accordance with the independent identical distribution condition, the singular eigenvalue falls down to the inner ring, and the higher the degree of element deviation from the independent identical distribution in the matrix is, the higher the degree of the eigenvalue gathering towards the circle center is.
Under large-scale new energy access, the output change of the new energy can influence the state of the power grid. In particular, a change in the power of the new energy source will cause a change in the power flow distribution of the power grid, and thus a change in the state of the power grid.
Therefore, for new energy power matrixThe singular eigenvalue analysis is carried out, when the power change of the new energy which is accessed in a large scale in the power grid is not big,The singular values of the corresponding covariance matrix will be distributed between the inner and outer rings, with an average spectral radius (MSR) between the inner ring radius and 1; on the contrary, when the new energy source generates the integral power change, whether the integral is increased or reduced, the characteristic value of M u falls into the inner ring, and the larger the power change degree is, the larger the degree that the singular value gathers towards the circle center is, and the smaller the MSR value is. Therefore, MSR can be used for constructing and representing the power change level index of the new energy.
The specific operation of the step 4 is to construct the state characteristics of the power distribution network based on the M-P law.
If each element of the matrix X satisfies the independent co-distribution, the spectrum distribution function (as shown in formula (9)) corresponding to the eigenvalue of the covariance matrix M will converge to the M-P law (as shown in formula (10)).
F M (x) is an empirical spectrum distribution function; p is the number of the characteristic values; is the ith eigenvalue of matrix M; i {.cndot. } is an indirection function.
Where c=p/n, σ 2 is the variance,This is the M-P law for parameters c and σ 2.
The M-P law indicates that when elements in the matrix meet independent co-distribution conditions, the spectral distribution corresponding to the covariance matrix will converge to the M-P law, and when elements in the matrix deviate from independent co-distribution conditions, the spectral distribution corresponding to the covariance matrix will deviate from the M-P law. For new energy power matrixAnd (3) performing spectrum analysis, wherein the degree of deviation of the spectrum distribution from the M-P law represents the degree of the power change level of the new energy.
The invention sets the spectrum distribution function of the standard M-P law as f 1(x),x∈[c1,d1, the spectrum distribution function corresponding to the wind power matrix as f 2(x),x∈[c2,d2, and defines the difference degree v of the two functions as
Where c=min (c 1,c2)d=max(d1,d2), and n is the order. For the limited-maintenance new energy power matrix, the discrete form of the formula (11) is shown as the formula (12).
Where k= (d-c)/N.
The smaller V and V, the closer f 1 (x) and f 2 (x) are, the smaller the change in new energy power is; conversely, the larger the difference between f 1 (x) and f 2 (x), the larger the change in new energy power.
According to the method for analyzing the state of the power distribution network with the large-scale distributed new energy access, the specific operation of the step 5 is that comprehensive indexes for analyzing the state of the power distribution network are constructed based on indexes of the step 3 and the step 4, and the comprehensive indexes are shown as a formula (13).
W=MSR+c/V (13)
Where c is a constant. When the new energy power in the power grid is not changed obviously, the singular values corresponding to the new energy power matrix are distributed between the inner ring and the outer ring, the MSR is also positioned between the radiuses of the inner ring and the outer ring, and the value is relatively larger; meanwhile, the spectrum distribution obtained based on the new energy power is similar to the M-P law, and if V is smaller, the new energy power change rate comprehensive index W is larger. Conversely, a larger new energy output change rate can cause the singular value corresponding to the new energy power matrix to drop towards the circle center, so that MSR is smaller; the spectrum distribution obtained based on the new energy power has larger deviation from the M-P law, and the V is larger, and the W is smaller.
The following example analyzes the status of a power distribution network to which a wind turbine is connected. A 33 node power distribution system was modified to verify the effectiveness of the proposed method. The original system line parameters are kept unchanged, the upper limit of the active output of the wind turbine generator is 0.6MW, the range of the reactive output is-0.02-0.06 Mvar, 10 groups of fans are installed at the node 10, and 10 groups of fans are installed at the node 24. In the simulation verification process, the invention builds a model based on PSASP, and analyzes the extracted index when the wind speed is increased and single-phase grounding occurs at the node 6, wherein the simulation sampling frequency is 100Hz, and the simulation time is 5s.
The change of wind speed can cause the change of the output of the wind turbine, and the change of the output of the wind turbine can influence the change of the tide distribution in the power grid, so that the change of the power grid state is caused. The example assumes that the wind speed increases slowly from 6m/s to 10m/s, the wind speed changing during the simulation is shown in FIG. 4. Namely, the wind speed is kept at about 6m/s within 0-1 s; at 1-3s, the wind speed is increased to 10m/s linearly; and at 3-5s, keeping the wind speed at 10m/s, respectively acquiring corresponding wind power output data and branch power data based on the simulation, constructing a corresponding wind power matrix and a corresponding branch power matrix, and analyzing the state of the power distribution network.
In the example, a wind power matrix with the dimension of 20 is constructed by using power data of 10 wind turbines at the node 10 and 10 wind turbines at the node 24 in a simulation stage, and the width of a sliding time window is made to be n=50 based on c=p/n epsilon (0, 1) (the width of the sliding time window in the branch power matrix is also made to be 50). Fig. 5 is a graph of a wind power change level index based on a circular law, a wind power change level index based on an M-P law, and a wind power change rate comprehensive index, where c=1 in the wind power change rate comprehensive index (may be selected according to the actual weight preference of MSR and V). Since the sliding window width takes n=50, the values of the various indices start from the bar t=0.5.
As shown in fig. 5 (a), the MSR can accurately reflect the wind power variation level. At t=0-1 s, the MSR is kept at about 0.9, and the process is stable, so that the condition of small wind power change degree is correctly projected; when t=1.01 s, the MSR drops significantly, and in the phase t=1.01-4 s, the MSR is in an oscillating state, which corresponds to the wind speed gradually increasing in this phase. It is worth noting that the wind speed is maintained at 10m/s from t=3s, but the MSR does not start to recover to a more stable state until t=4s, which means that the wind speed change at this stage has a larger influence on the wind power output, and the wind speed change is continued until t=4s, although the wind speed has been maintained at around 10/s at the stage t=3-4s, due to the change of the grid power flow and the change of the wind power.
The index V describes the wind power change level of the power grid from the perspective of the deviation degree of the spectrum distribution and the M-P law. As shown in fig. 5 (b), when t=0.5-1, the value of V is kept around 0.01, because the wind speed is kept at 6M/s and the wind power is kept at a level where a certain change is not large, the value and distribution of the wind power matrix constructed are not large, and the corresponding spectral distribution is close to the M-P law, so the V value is small. Starting from t=1.07 s, the V value suddenly increases and oscillates, accurately reflecting the wind power level.
The foregoing is merely illustrative embodiments of the present invention, and the present invention is not limited thereto, and any changes or substitutions that may be easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (2)
1. A power distribution network state analysis method containing scale distributed new energy access is characterized in that: the method comprises the following steps:
1) Constructing a new energy power change matrix based on the collected new energy power;
2) Preprocessing a new energy power change matrix;
3) Constructing a power distribution network state index MSR based on a circular law;
4) Constructing a power distribution network state index V based on an M-P law;
5) Constructing a power distribution network state analysis index based on the power distribution network state index MSR and the power distribution network state index V;
The specific operation of the step 1) is as follows:
Constructing a new energy power change matrix shown in a formula (2) for the collected new energy power:
wherein p is the number of nodes with new energy power access, n is the sampling number, each row of X is the same measuring point, and each column is the same sampling moment;
the specific operation of the step 2) is as follows:
step 2.1) normalization treatment:
Normalizing the new energy power change matrix X according to the formula (3) to obtain a normalized matrix
Wherein μ (X i) and σ (X i) represent the mean and variance, respectively, of X i, X i is row i of X;
step 2.2) calculating a covariance matrix:
The calculation mode of the covariance matrix comprises the following steps:
Wherein X * is the complex conjugate transpose of X;
The specific operation of the step 3) is as follows:
Firstly, singular value decomposition S=W ΣU is carried out on a covariance matrix M, a square matrix sigma corresponding to singular values is taken, and M u=Y1×∑×Y2 is used for obtaining a singular value equivalent matrix, wherein Y 1 and Y 2 are random-generated Haar unitary matrices;
The following treatment is carried out on M u,
Wherein, The ith row of M u is characterized;
Carrying out eigenvalue solution on M u as shown in a formula (6), and carrying out average value solution on the eigenvalue as shown in a formula 7);
wherein W 'and U' are left and right eigenvectors respectively, sigma 'is a singular value matrix, and the diagonal position of Sigma' is M u eigenvalues; at this time, the M u eigenvalues are averaged on a complex domain, and the state index MSR of the power distribution network can be obtained;
Wherein lambda i is the i-th eigenvalue;
the specific operation of the step 4) is as follows: constructing a power distribution network state index V based on an M-P law, as shown in a formula (12):
Wherein k= (d-c)/N; wherein f 1 and f 2 are respectively spectrum distribution functions corresponding to the M-P law and the new energy power matrix, and specifically shown in the formulas (10) and (9); the value range of the independent variable in f 1 is x epsilon [ c 1,d1],f2 ] and the value range of the independent variable in f epsilon [ c 2,d2];c=min(c1,c2),d=max(d1,d2);
Where c=p/n, σ 2 is the variance,
F M (x) is an empirical spectrum distribution function; p is the number of the characteristic values; is the ith eigenvalue of matrix M; i {. Cndot. Is an indirection function;
the power distribution network state analysis index in the step 5) is as shown in a formula (13):
W=MSR+c/V (13)
Wherein c is a constant; when the new energy power in the power grid is not obviously changed, the spectrum distribution obtained based on the new energy power is similar to the M-P law, and the V is smaller, so that the comprehensive index W of the new energy power change rate is larger; conversely, a larger new energy output change rate can cause the singular value corresponding to the new energy power matrix to drop towards the circle center, so that MSR is smaller; the spectrum distribution obtained based on the new energy power has larger deviation from the M-P law, and the V is larger, and the W is smaller.
2. The method for analyzing the state of the power distribution network with the large-scale distributed new energy access according to claim 1, wherein the method comprises the following steps: the new energy power in the step 1) is collected by a power distribution network state detection device arranged at a new energy access node;
the power distribution network state detection device comprises:
the energy taking module is used for sensing and obtaining energy from a power distribution network line to supply power for the device;
The voltage and current sensor is used for collecting the voltage and current of the lead;
and the data acquisition and processing system acquires information acquired by the voltage and current sensors and calculates the power of each node.
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