CN117408129A - Power distribution network state estimation method based on CNN-LSTM pseudo measurement model - Google Patents

Power distribution network state estimation method based on CNN-LSTM pseudo measurement model Download PDF

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CN117408129A
CN117408129A CN202310918500.2A CN202310918500A CN117408129A CN 117408129 A CN117408129 A CN 117408129A CN 202310918500 A CN202310918500 A CN 202310918500A CN 117408129 A CN117408129 A CN 117408129A
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李春
钟伟东
刘维亮
范明
刘伟
褚明华
沈浚
吴方舟
王晨
王大健
高倩
张代红
胡程平
朱晶亮
许超
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Jiaxing Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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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
    • 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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Abstract

The invention discloses a power distribution network state estimation method based on a CNN-LSTM pseudo measurement model, which comprises the following steps: collecting measurement data including power data in a power distribution network; respectively extracting different time scale characteristics of the historical measurement data by utilizing the parallel structures of the LSTM network and the CNN network, establishing a pseudo measurement model, and predicting to obtain pseudo measurement data; simulating error distribution between the pseudo measurement data and the true value based on the Gaussian mixture model, and determining pseudo measurement weight; the real-time measurement data, the pseudo measurement data and the pseudo measurement weight are input into a weighted minimum absolute value estimator for state estimation. According to the invention, a CNN-LSTM pseudo measurement model is established to provide accurate pseudo measurement data, thereby being beneficial to improving the observability of a system and the redundancy of state estimation, and the Gaussian mixture model is utilized to determine the pseudo measurement weight to carry out the state estimation of the power distribution network, so that the precision of the state estimation of the power distribution network is improved.

Description

Power distribution network state estimation method based on CNN-LSTM pseudo measurement model
Technical Field
The invention relates to the technical field of power distribution networks, in particular to a power distribution network state estimation method based on a CNN-LSTM pseudo measurement model.
Background
In recent years, the permeability of intermittent distributed energy sources in a power distribution network is gradually increased, and various types of energy storage equipment, electric vehicles, interruptible loads and intelligent measurement terminals are increasingly put into service, so that the fluctuation of the running state of the power distribution network is more frequent due to the complex multi-direction of the change of power flow. Meanwhile, unlike a transmission network, the system measurement redundancy of the power distribution network is low, the network structure is more complex and the change speed is faster, so that the dynamic state estimation of the power distribution network faces a plurality of brand new challenges in the aspects of calculation precision, efficiency and the like; meanwhile, in the actual situation, the novel power distribution network has the problems that the real-time measurement configuration is insufficient and the measurement error distribution cannot be determined, so that the real-time measurement data is insufficient and is missing, and the final estimation result of the power distribution network state is inaccurate.
The method and the terminal for evaluating the state of the power distribution network based on the LSTM are disclosed in Chinese patent literature, the publication number is CN115759859A, the publication date is 2023-03-07, and a power distribution network state evaluation index system is established; acquiring historical operation data of a power distribution network, and carrying out state evaluation on the historical operation data according to the power distribution network state evaluation index system and by combining a analytic hierarchy process and a CRITIC method to obtain a historical evaluation result of the historical operation data; training an LSTM neural network model according to the historical operation data and the historical evaluation result to obtain a trained LSTM neural network model; acquiring real-time operation data of a power distribution network, and inputting the real-time operation data into the trained LSTM neural network model to obtain a real-time evaluation result; the method can realize automatic real-time assessment of the state of the power distribution network and ensure the effectiveness of the assessment. However, the technology is based on the acquired operation data of the power distribution network, and when the real-time measurement data of the power distribution network is insufficient in actual conditions but is actually problematic, the result of power distribution network state estimation is affected, and the assessment is inaccurate.
Disclosure of Invention
The invention provides a power distribution network state estimation method based on a CNN-LSTM pseudo measurement model, which aims to overcome the defects that in the prior art, the novel power distribution network has insufficient real-time measurement configuration and the measurement error distribution cannot be determined, so that the problem that the state estimation result of the power distribution network is inaccurate due to the insufficient real-time measurement data, and establishes the CNN-LSTM pseudo measurement model to provide accurate pseudo measurement data, thereby being beneficial to improving the observability of a system and the redundancy of state estimation, and further improving the precision of the state estimation of the power distribution network.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a power distribution network state estimation method based on a CNN-LSTM pseudo-measurement model comprises the following steps:
collecting measurement data including power data in a power distribution network;
respectively extracting different time scale characteristics of the historical measurement data by utilizing the parallel structures of the LSTM network and the CNN network, establishing a pseudo measurement model, and predicting to obtain pseudo measurement data;
simulating error distribution between the pseudo measurement data and the true value based on the Gaussian mixture model, and determining pseudo measurement weight;
the real-time measurement data, the pseudo measurement data and the pseudo measurement weight are input into a weighted minimum absolute value estimator for state estimation.
In the invention, partial measurement data are missing because of the problem of insufficient real-time measurement configuration in the actual acquisition process, under the more common condition, the equipment on the two sides of the node where the power supply equipment is located in the power distribution network is more complete, the complete measurement data are acquired, and the power measurement data are easily missing at the node load, so that the real-time load node power is predicted to be used as the pseudo measurement data according to the missing power measurement data through a pseudo measurement model, the observability of the system and the redundancy of state estimation are improved, then the accurate pseudo measurement weight of the pseudo measurement data is given through a Gaussian mixture model, and then the pseudo measurement data and the real-time measurement data are applied together to carry out the state estimation of the power distribution network, thereby improving the precision of the state estimation of the power distribution network.
Preferably, the measurement data includes node voltage amplitude, branch current, branch active and reactive power, and part of the nodes injecting active and reactive power, the sampling time interval is the time length of one day divided by M, and samples of different time scales are constructed based on a sliding pane manner. The sampling time intervals are set at equal intervals of M times per day, and each interval represents one time pane.
Preferably, the process of establishing the pseudo metrology model includes:
selecting a time pane with the length of M to construct an input sample of an LSTM network, and acquiring a daily periodic characteristic through learning and training;
selecting a time pane with the length of 7M to construct an input sample of the CNN network, and acquiring periodic characteristics through learning training;
and (3) inputting the two characteristics into a full-connection layer after characteristic splicing, and constructing a mapping relation between the historical measurement data and the missing load power to obtain a pseudo measurement model.
The CNN-LSTM model aims at utilizing branch power measurement which is strongly related near a node where load power measurement is missing, extracting the characteristic of historical power through a deep learning method, constructing a mapping relation between the historical branch power and the missing load power, and finally establishing a relatively high-precision pseudo measurement model; and splicing the features extracted by the LSTM and the CNN through a splicing function Concate in the Python, and inputting a splicing result into a subsequent full-connection layer so that the model can learn the features extracted by the LSTM and the CNN at the same time, thereby fully learning the information contained in the data of different time scales and improving the prediction precision of the pseudo-measurement model.
Preferably, the optimization objective function in the weighted minimum absolute value estimator is:
minJ(x)＝w T |z-h(x)|
wherein z is m-dimensional total measurements, including real-time measurement data and pseudo-measurement data; w is a measurement weight, including a real-time measurement weight and a pseudo measurement weight; h (x) is a power distribution network measurement function, x is a power distribution network state variable, and is node voltage amplitude and phase angle respectively.
The weighted minimum absolute value estimator is an algorithm capable of enhancing the robustness of a state estimation result, and the iterative process of the algorithm is continued until a specific termination condition is met; the real-time measurement data comprise node voltage amplitude, branch current, branch power, part of node injection active power and part of node injection reactive power; the pseudo measurement data is the predicted value of the CNN-LSTM pseudo measurement model; the real-time measurement weight is generally taken as the reciprocal of the measurement noise variance, and the pseudo measurement weight is replaced according to the calculation result of the Gaussian mixture model.
Preferably, the gaussian mixture model is a probability model of an equivalent probability density function simulating a pseudo-measurement error distribution by combining a plurality of gaussian mixture equations:
wherein the method comprises the steps ofIs pseudo measurement data; m is M e Is the number of gaussian mixture equations; w (w) i Represents the weight of the ith equation, an μ i And->The mean and variance of the ith equation; χ is a parameter of the gaussian mixture model, belonging to the ith Gaussian mixture equation of normal distribution.
In the invention, a certain error exists between the node load power value predicted by the pseudo-measurement model and the true value, and the probability density function of the prediction error cannot be directly expressed by adopting a normal distribution function; in the state estimation, the variance of the measurement error directly affects the measurement weight and is closely related to the state estimation filtering effect; in order to improve the state tracking effect of the power distribution network, a Gaussian mixture model GMM is needed to describe the error probability distribution of the CNN-LSTM pseudo-measurement model approximately.
Preferably, the mean and variance of the equivalent probability density function of the pseudo metrology error distribution is calculated:
wherein mu pre Andmean and variance of equivalent probability density functions of pseudo measurement errors are respectively represented; and the inverse of the variance of the equivalent probability density function of the pseudo measurement error is used as the pseudo measurement weight.
The true value in the invention is a load power flow simulation actual value corresponding to the moment to be predicted, the error distribution is determined according to a Monte Carlo simulation experiment, namely, the load prediction experiment is repeated and error data is counted; taking the inverse of the variance of the equivalent probability density function of the pseudo-measurement error as the pseudo-measurement weight, the accuracy of the pseudo-measurement weight will affect the optimization solving process of the state estimation.
Preferably, for the optimization objective function in the weighted minimum absolute value estimator, the relaxation factors l and u are introduced to translate it into an optimization problem with equality and inequality constraints:
and solving by an interior point method to obtain a final state estimation result.
According to the invention, aiming at the optimization objective function with the absolute value, scaling is firstly carried out according to the definition of the absolute value, then a relaxation factor is introduced to establish an equation, the optimization objective function is converted into an optimization problem with constraint conditions of the equation and the inequality, and the optimization objective function is solved by an interior point method, so that a final power distribution network state evaluation result can be obtained quickly and accurately.
Preferably, the CNN network sequentially includes a convolution layer, a max-pooling layer, and a full-connection layer, where the formula of the convolution operation is:
L＝σ(X*W+b)
wherein X is data input, W is weight of convolution kernel, b is corresponding bias term, sigma (·) is activation function, and L is output characteristic after convolution operation.
In the invention, a CNN network is adopted to extract the features of long time scale, and an LSTM network is adopted to extract the features of short time scale; meanwhile, the CNN network can select a required network layer according to actual demands, a convolution layer, a maximum pooling layer and a full connection layer are selected as topology structures of the CNN network under the condition of extracting periodic characteristics, the history branch active power and real-time branch active power which are strongly related near nodes without load active power measurement are input (load node injection reactive power), and load node injection active power values (load node injection reactive power) after load flow simulation are output.
The invention has the following beneficial effects: the CNN-LSTM pseudo measurement model is established to provide accurate pseudo measurement data, so that the observability of the system and the redundancy of state estimation are improved, and the precision of the state estimation of the power distribution network is improved; extracting data features of different time scales through CNN and LSTM, and then splicing, so that information contained in the data of the different time scales is fully learned, and the prediction accuracy of the pseudo measurement data is improved; and the error probability distribution of the CNN-LSTM pseudo measurement model is approximately described by adopting a Gaussian mixture model, so that more accurate pseudo measurement weight is determined to improve the state tracking effect of the power distribution network.
Drawings
FIG. 1 is a flow chart of power distribution network state estimation based on a CNN-LSTM pseudo-metrology model in the present invention;
FIG. 2 is an overall framework of a CNN-LSTM pseudo metrology model in accordance with the present invention;
FIG. 3 is a schematic diagram of an LSTM memory cell according to the present invention;
FIG. 4 is a block diagram of an IEEE57 node system in accordance with an embodiment of the invention;
FIG. 5 is a pseudo measurement modeling comparison of CNN-LSTM and BP neural network in an embodiment of the invention;
fig. 6 is a diagram of a multi-period state estimation error for three algorithms in an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and detailed description.
As shown in fig. 1, a power distribution network state estimation method based on a CNN-LSTM pseudo measurement model includes:
collecting measurement data including power data in a power distribution network;
respectively extracting different time scale characteristics of the historical measurement data by utilizing the parallel structures of the LSTM network and the CNN network, establishing a pseudo measurement model, and predicting to obtain pseudo measurement data;
simulating error distribution between the pseudo measurement data and the true value based on the Gaussian mixture model, and determining pseudo measurement weight;
the real-time measurement data, the pseudo measurement data and the pseudo measurement weight are input into a weighted minimum absolute value estimator for state estimation.
The measurement data comprises node voltage amplitude, branch current, branch active power and reactive power, and part of the nodes are injected with the active power and the reactive power, the sampling time interval is the time length of one day divided by M, and samples of different time scales are constructed based on a sliding pane mode. The sampling time intervals are set at equal intervals of M times per day, and each interval represents one time pane. The sampling time interval can be set to 15min, 96 times a day, and 35040 historical sections are accumulated for one year.
The process of establishing the pseudo metrology model includes:
selecting a time pane with the length of M to construct an input sample of an LSTM network, and acquiring a daily periodic characteristic through learning and training;
selecting a time pane with the length of 7M to construct an input sample of the CNN network, and acquiring periodic characteristics through learning training;
and (3) inputting the two characteristics into a full-connection layer after characteristic splicing, and constructing a mapping relation between the historical measurement data and the missing load power to obtain a pseudo measurement model.
As shown in fig. 2, the CNN network sequentially includes a convolution layer, a max-pooling layer, and a full-connection layer, where the formula of the convolution operation is:
L＝σ(X*W+b)
wherein X is data input, W is weight of convolution kernel, b is corresponding bias term, sigma (·) is activation function, and L is output characteristic after convolution operation.
As shown in fig. 3, the LSTM is mainly formed by stacking long-short-term memory units, where the basic calculation formula of the long-short-term memory units is as follows:
I t ＝σ(X t ω xi +H t-1 ω hi +b i )
F t ＝σ(X t ω xf +H t-1 ω hf +b f )
O t ＝σ(X t ω xo +H t-1 ω ho +b o )
H t ＝O t e tanh(C t )
wherein F is t ，I t ，O t Forgetting gate, input gate and output gate at time t respectively, C t The state of the memory cell at time t is indicated,to be candidate memory cell state, H t Omega is a hidden state in the forward propagation process xi 、ω xf 、ω xo Omega, omega xc Omega is the weight between the corresponding gate and input hi 、ω hf 、ω ho And omega hc B is the weight between the corresponding gate and gate i 、b f 、b o And b c Then the bias of the corresponding gate.
Selecting a time pane with the length of 7 multiplied by 96 and equal to 672 to construct an input sample of CNN, namely t-672, t-671, wherein the time pane is provided with a strong correlation of historical branch active power and real-time branch active power near a node where load active power measurement is not configured at the moment of t-1, and outputting the sample to inject an active power value into a load node after load flow simulation at the moment of t (the same as the moment of predicting the node to inject reactive power), wherein the aim is to enable a model to learn the periodic characteristics of the historical power; and selecting a time pane with the length of 96 to construct an input sample of the LSTM, namely, a history branch active power and a real-time branch active power which are strongly related near a node where active power measurement of the load is not configured at the time of t-1, wherein the output sample is a load node injection active power value (the same as when the active power is injected by a prediction node) after load flow simulation at the time of t, and the aim is to enable a model to learn the daily periodic characteristic of the history power. In addition, the features extracted by the LSTM and the CNN are spliced through a splicing function Concate in the Python, and the spliced result is input into a subsequent full-connection layer so that the model can learn the features extracted by the LSTM and the CNN at the same time, so that the information contained in different time scale data is fully learned, and the prediction precision is improved.
The Gaussian mixture model is a probability model of an equivalent probability density function simulating pseudo-measurement error distribution by combining a plurality of Gaussian mixture equations:
wherein the method comprises the steps ofIs pseudo measurement data; m is M e Is the number of gaussian mixture equations; w (w) i Represents the weight of the ith equation, an μ i And->The mean and variance of the ith equation; χ is a parameter of the gaussian mixture model,the parameter is typically solved using a maximum expected algorithm; />Belonging to the ith Gaussian mixture equation of normal distribution.
Calculating the mean and variance of the equivalent probability density function of the pseudo-metrology error distribution:
wherein mu pre Andmean and variance of equivalent probability density functions of pseudo measurement errors are respectively represented; and the inverse of the variance of the equivalent probability density function of the pseudo measurement error is used as the pseudo measurement weight.
The optimization objective function in the weighted minimum absolute value estimator is:
minJ(x)＝w T |z-h(x)|
wherein z is m-dimensional total measurement, including real-time measurement data and pseudo measurement data, wherein the real-time measurement includes node voltage amplitude, branch current, branch power, active power injected by partial nodes and reactive power injected by partial nodes, and the pseudo measurement is a CNN-LSTM pseudo measurement model predicted value; w is a measurement weight including a real-time measurement weight and a pseudo measurement weight, the real-time measurement weight is generally taken as the inverse w=1/σ of the measurement noise variance 2 The pseudo-measurement weight is obtained according to a Gaussian mixture modelPerforming replacement; h (x) is a power distribution network measurement function, x is a power distribution network state variable, and is node voltage amplitude and phase angle respectively.
For the optimization objective function in the weighted minimum absolute value estimator,
from the mathematical definition of absolute values, one can derive:
introducing the relaxation factors l.gtoreq.0 and u.gtoreq.0 can lead to:
the variable substitution can be derived by:
converting it into an optimization problem with equality and inequality constraints:
and solving by an interior point method to obtain a final state estimation result.
The Lagrangian multipliers lambda, alpha and beta are introduced to obtain the following components:
J＝w T (l+u)-λ T (z-h(x)+l-u)-α T l-β T u
deriving the above and making the derivative function equal to 0, equation (1) can be derived:
wherein H is a jacobian matrix of the measurement function H (x), α, β, l and u are all column vectors, which are represented by multiplication of two matrix-corresponding elements,/represents division of two matrix-corresponding elements, wherein "" represents mathematical operation of matrix-corresponding elements, and is different from conventional matrix multiplication and matrix division, and the two column vectors are obtained after dot operation or are a column vector.
From the last two equations of the above equation can be derived:
because the iteration convergence of the estimation algorithm is poor when the parameter mu is valued according to the above formula, in order to ensure that the algorithm has better convergence, the following steps are generally set:
wherein: sigma epsilon (0, 1) is the central parameter, which is generally taken as 0.1.
Taylor expansion of formula (1) can give formula (2):
according to J l ＝J u Formula (3) can be obtained:
substituting formula (3) into formula (2) can give formula (4):
from equation (2), equation (5) can be derived:
substituting formula (4) into formula (5) can give formula (6):
the above formula is listed as a matrix:
solving the above formula can obtain Δx and Δλ, and combining formula (3) and formula (4) can obtain Δα, Δβ, Δl and Δu, so as to obtain the final iteration equation of the weighted minimum absolute value algorithm as follows:
wherein θ is p And theta d The step factor is recorded, and the step factor is set for ensuring that the iteration value strictly meets the condition that l is more than or equal to 0 and u is more than or equal to 0. The value is set as follows:
when (when)And (5) considering the algorithm to converge, and stopping iteration.
In the invention, partial measurement data are missing because of the problem of insufficient real-time measurement configuration in the actual acquisition process, under the more common condition, the equipment on the two sides of the node where the power supply equipment is located in the power distribution network is more complete, the complete measurement data are acquired, and the power measurement data are easily missing at the node load, so that the real-time load node power is predicted to be used as the pseudo measurement data according to the missing power measurement data through a pseudo measurement model, the observability of the system and the redundancy of state estimation are improved, then the accurate pseudo measurement weight of the pseudo measurement data is given through a Gaussian mixture model, and then the pseudo measurement data and the real-time measurement data are applied together to carry out the state estimation of the power distribution network, thereby improving the precision of the state estimation of the power distribution network.
The CNN-LSTM model aims at utilizing branch power measurement which is strongly related near a node where load power measurement is missing, extracting the characteristic of historical power through a deep learning method, constructing a mapping relation between the historical branch power and the missing load power, and finally establishing a relatively high-precision pseudo measurement model; and splicing the features extracted by the LSTM and the CNN through a splicing function Concate in the Python, and inputting a splicing result into a subsequent full-connection layer so that the model can learn the features extracted by the LSTM and the CNN at the same time, thereby fully learning the information contained in the data of different time scales and improving the prediction precision of the pseudo-measurement model.
The weighted minimum absolute value estimator is an algorithm capable of enhancing the robustness of a state estimation result, and the iterative process of the algorithm is continued until a specific termination condition is met; the real-time measurement data comprise node voltage amplitude, branch current, branch power, part of node injection active power and part of node injection reactive power; the pseudo measurement data is the predicted value of the CNN-LSTM pseudo measurement model; the real-time measurement weight is generally taken as the reciprocal of the measurement noise variance, and the pseudo measurement weight is replaced according to the calculation result of the Gaussian mixture model.
In the invention, a certain error exists between the node load power value predicted by the pseudo-measurement model and the true value, and the probability density function of the prediction error cannot be directly expressed by adopting a normal distribution function; in the state estimation, the variance of the measurement error directly affects the measurement weight and is closely related to the state estimation filtering effect; in order to improve the state tracking effect of the power distribution network, a Gaussian mixture model GMM is needed to describe the error probability distribution of the CNN-LSTM pseudo-measurement model approximately.
The true value in the invention is a load power flow simulation actual value corresponding to the moment to be predicted, the error distribution is determined according to a Monte Carlo simulation experiment, namely, the load prediction experiment is repeated and error data is counted; taking the inverse of the variance of the equivalent probability density function of the pseudo-measurement error as the pseudo-measurement weight, the accuracy of the pseudo-measurement weight will affect the optimization solving process of the state estimation.
According to the invention, aiming at the optimization objective function with the absolute value, scaling is firstly carried out according to the definition of the absolute value, then a relaxation factor is introduced to establish an equation, the optimization objective function is converted into an optimization problem with constraint conditions of the equation and the inequality, and the optimization objective function is solved by an interior point method, so that a final power distribution network state evaluation result can be obtained quickly and accurately.
In the invention, a CNN network is adopted to extract the features of long time scale, and an LSTM network is adopted to extract the features of short time scale; meanwhile, the CNN network can select a required network layer according to actual demands, a convolution layer, a maximum pooling layer and a full connection layer are selected as topology structures of the CNN network under the condition of extracting periodic characteristics, the history branch active power and real-time branch active power which are strongly related near nodes without load active power measurement are input (load node injection reactive power), and load node injection active power values (load node injection reactive power) after load flow simulation are output.
In the embodiment of the invention, a 57-node novel power distribution network system of a real ground city in China is taken as an example, and the method and the beneficial effects of the invention in practical application are further described. The wiring diagram of the 57-node novel power distribution network is shown in fig. 4, wherein the nodes 9, 12 and 20 are provided with photovoltaic equipment, the node 39 is provided with a wind generating set, and the four nodes are provided with complete measuring equipment, so that real-time measuring information can be collected. Aiming at the load node of the missing power measurement, the history and real-time branch power data which are strongly related are constructed into long-time scale load data with the length of 672 and short-time scale data with the length of 96 according to sliding window lattices with different lengths, the long-time scale data and the short-time scale data are respectively input into CNN and LSTM, the multi-scale time characteristics of the history power are extracted, then the two characteristics are fused by utilizing a merging function and then are input into a full-connection layer for further prediction, and the predicted value is the real-time load node power pseudo-measurement data. And fitting the Gaussian distribution obeyed by the error by adopting a Gaussian mixture model aiming at the error of the pseudo-measurement data and the true value, thereby taking the inverse of the variance of the Gaussian distribution as the pseudo-measurement weight. And finally, inputting the real-time measurement data of the new energy nodes, the pseudo measurement data of the load nodes and the weights thereof into a weighted minimum absolute value state estimator to realize the robust state estimation of the current novel power distribution network.
In order to verify the accuracy of the pseudo measurement data provided by the method, the embodiment sets a BP neural network pseudo measurement model as a comparison test, adopts an average relative error as an evaluation index, and has the following calculation formula:
wherein e p 、e Q Respectively representing the active average relative error and the reactive average relative error, wherein the smaller the value is, the accurate pseudo measurement data is indicated
The higher the degree; n represents the number of samples; p (P) t Is the actual value of the active power at the time t,the active predicted value is the t moment; q (Q) t For the reactive actual value at time t +.>And the reactive power predicted value at the time t.
Pseudo measurement modeling comparison of CNN-LSTM and BP neural network:
in order to illustrate the superiority of the CNN-LSTM pseudo-measurement model, the same input samples are constructed based on a sliding pane mode and are respectively input into two pseudo-measurement models, wherein aiming at CNN with the capability of extracting long-time scale data, the time pane length is 672, aiming at the characteristic that LSTM has stronger capability of processing short-time scale data, the time pane length is 96, the optimal super-parameter multi-training average error is adjusted to carry out comparison analysis, and the error results of 8 nodes are randomly selected to be visually displayed.
As shown in fig. 5, the comparison between the CNN-LSTM pseudo measurement model and the BP neural network pseudo measurement model shows that the CNN-LSTM pseudo measurement model can obtain more accurate pseudo measurement results for both the active power average relative error and the reactive power average relative error with respect to the BP neural network. As can be seen from the active average relative error comparison graph, the node 45 with the minimum precision improvement still has 13.76 percent improvement; as can be seen from the reactive average relative error comparison graph, the node No. 25 with the minimum precision improvement still has 31.35 percent improvement
State estimation test based on two types of neural network pseudo measurement models:
in order to further illustrate the beneficial effect of the model of the invention on the power distribution network state estimation, the power distribution network state estimation results based on the two types of neural network pseudo-measurement models are compared. The average absolute error and the maximum absolute error are selected as evaluation indexes, and the calculation formula is as follows:
where J is the number of system nodes;is the estimated value of node voltage, V i Node voltage true value; />Is the node voltage phase angle estimation value, delta i Is the true value of the node voltage phase angle.
The error results of the CNN-LSTM pseudo-metrology model and the BP neural network pseudo-metrology model are given in Table 1, respectively. As can be seen from table 1, the CNN-LSTM model shows excellent performance in terms of both the average absolute error and the maximum absolute error, wherein the voltage estimation accuracy is improved by 38.89% and 60%, respectively; the phase angle estimation precision is respectively improved by 40.23 percent and 40 percent
Table 1 comparison of two methods of state estimation results for power distribution networks
Model e v e δ |ΔV| max |Δδ| max
CNN--LSTM 0.0011 0.0052 0.0014 0.0015
BP 0.0018 0.0087 0.0035 0.0025
As fig. 6 shows the state estimation error of multiple time periods combined with two pseudo metrology models and using only the weighted least squares total three algorithms, it can be seen that the state estimation method (histogram) of the CNN-LSTM pseudo metrology model has smaller estimation error at each node than the other algorithms, which is sufficient to illustrate its superiority.
In summary, the method of the invention aims at the problems of insufficient measured data, difficulty in ensuring the observability of the system and the like in the power distribution network, establishes a pseudo measurement model based on deep learning, can provide a large amount of accurate pseudo measurement data, and provides preconditions and guarantees for effective application of state estimation.
The foregoing embodiments are further illustrative and explanatory of the invention, as is not restrictive of the invention, and any modifications, equivalents, and improvements made within the spirit and principles of the invention are intended to be included within the scope of the invention.

Claims (8)

1. The power distribution network state estimation method based on the CNN-LSTM pseudo-measurement model is characterized by comprising the following steps of:
collecting measurement data including power data in a power distribution network;
respectively extracting different time scale characteristics of the historical measurement data by utilizing the parallel structures of the LSTM network and the CNN network, establishing a pseudo measurement model, and predicting to obtain pseudo measurement data;
simulating error distribution between the pseudo measurement data and the true value based on the Gaussian mixture model, and determining pseudo measurement weight;
the real-time measurement data, the pseudo measurement data and the pseudo measurement weight are input into a weighted minimum absolute value estimator for state estimation.
2. The method of claim 1, wherein the measurement data includes node voltage amplitude, branch current, branch active and reactive power, and partial node injection of active and reactive power, the sampling time interval is a time length of day divided by M, and samples of different time scales are constructed based on sliding panes.
3. A method for estimating a state of a power distribution network based on a CNN-LSTM pseudo-metrology model according to claim 1 or 2, wherein the process of establishing the pseudo-metrology model comprises:
selecting a time pane with the length of M to construct an input sample of an LSTM network, and acquiring a daily periodic characteristic through learning and training;
selecting a time pane with the length of 7M to construct an input sample of the CNN network, and acquiring periodic characteristics through learning training;
and (3) inputting the two characteristics into a full-connection layer after characteristic splicing, and constructing a mapping relation between the historical measurement data and the missing load power to obtain a pseudo measurement model.
4. The method for estimating a state of a power distribution network based on a CNN-LSTM pseudo-metrology model according to claim 1, wherein the optimization objective function in the weighted minimum absolute value estimator is:
minJ(x)＝w T |z-h(x)|
wherein z is m-dimensional total measurements, including real-time measurement data and pseudo-measurement data; w is a measurement weight, including a real-time measurement weight and a pseudo measurement weight; h (x) is a power distribution network measurement function, and x is a power distribution network state variable.
5. The method for estimating a state of a power distribution network based on a CNN-LSTM pseudo-measurement model according to claim 1 or 4, wherein the gaussian mixture model is a probability model of an equivalent probability density function simulating a pseudo-measurement error distribution by combining a plurality of gaussian mixture equations:
wherein the method comprises the steps ofIs pseudo measurement data; m is M e Is the Gaussian mixture equation numberAn amount of; w (w) i Represents the weight of the ith equation, and w i ＞0，μ i And->The mean and variance of the ith equation; χ is a parameter of the gaussian mixture model, belonging to the ith Gaussian mixture equation of normal distribution.
6. The method for estimating a power distribution network state based on a CNN-LSTM pseudo-metrology model according to claim 5, wherein the mean and variance of the equivalent probability density function of the pseudo-metrology error distribution are calculated:
wherein mu pre Andmean and variance of equivalent probability density functions of pseudo measurement errors are respectively represented; and the inverse of the variance of the equivalent probability density function of the pseudo measurement error is used as the pseudo measurement weight.
7. The method for estimating a state of a power distribution network based on a pseudo-metrology model of CNN-LSTM according to claim 4, wherein for the optimization objective function in the weighted minimum absolute value estimator, the relaxation factors l and u are introduced to transform it into an optimization problem with equality and inequality constraints:
and solving by an interior point method to obtain a final state estimation result.
8. The method for estimating a state of a power distribution network based on a CNN-LSTM pseudo-measurement model according to claim 3, wherein the CNN network sequentially includes a convolution layer, a max-pooling layer and a full-connection layer, and the formula of the convolution operation is:
L＝σ(X*W+b)
wherein X is data input, W is weight of convolution kernel, b is corresponding bias term, sigma (·) is activation function, and L is output characteristic after convolution operation.
CN202310918500.2A 2023-07-25 2023-07-25 Power distribution network state estimation method based on CNN-LSTM pseudo measurement model Pending CN117408129A (en)

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