CN110829434B - Method for improving expansibility of deep neural network tidal current model - Google Patents

Method for improving expansibility of deep neural network tidal current model Download PDF

Info

Publication number
CN110829434B
CN110829434B CN201910938908.XA CN201910938908A CN110829434B CN 110829434 B CN110829434 B CN 110829434B CN 201910938908 A CN201910938908 A CN 201910938908A CN 110829434 B CN110829434 B CN 110829434B
Authority
CN
China
Prior art keywords
dnn
power flow
layer
flow model
power
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910938908.XA
Other languages
Chinese (zh)
Other versions
CN110829434A (en
Inventor
余娟
向明旭
杨知方
代伟
杨燕
余红欣
何燕
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chongqing University
Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd
State Grid Corp of China SGCC
Original Assignee
Chongqing University
Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd
State Grid Corp of China SGCC
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chongqing University, Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd, State Grid Corp of China SGCC filed Critical Chongqing University
Priority to CN201910938908.XA priority Critical patent/CN110829434B/en
Publication of CN110829434A publication Critical patent/CN110829434A/en
Application granted granted Critical
Publication of CN110829434B publication Critical patent/CN110829434B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods

Abstract

The invention discloses a method for improving the expansibility of a deep neural network tidal current model, which mainly comprises the following steps: 1) acquiring basic data of a power system; 2) determining a feature vector; 3) establishing an original DNN power flow model; 4) training the original DNN power flow model to obtain a trained original DNN power flow model; 5) the method comprises the steps of expanding an original DNN power flow model to obtain an expanded DNN power flow model; 6) and resolving the probability load flow of the extension system to obtain a probability load flow result. The method can be widely applied to solving the probability load flow of the power system, and is particularly suitable for the condition that the DNN of the original system cannot be applied due to system extension.

Description

Method for improving expansibility of deep neural network tidal current model
Technical Field
The invention relates to the field of power systems and automation thereof, in particular to a method for improving the expansibility of a deep neural network tidal current model.
Background
In recent years, with the vigorous development of renewable energy sources, power systems face more and more uncertainties. These uncertainties have a significant impact on the operation, planning and control of the power system. The probability power flow can comprehensively consider the influence of various uncertainties on the system power flow, so that valuable information is provided for power system analysis.
However, the relationship between each uncertainty factor and the corresponding trend result is very complex, which makes the solution of the probability trend very difficult. The traditional probabilistic power flow calculation method can be divided into the following two methods: analytical methods and simulation methods. The solution idea of the above two methods is shown in fig. 2 and 3.
The core idea of the analytical method is to construct a representative sample from a probability density function of random variables. By calculating the power flow of the typical sample, a calculation result of the probability power flow can be obtained. The method does not need to solve the load flow results of a large number of samples in an iterative mode, and the calculation burden of probability load flow is effectively reduced. However, the flow equation is simplified in the calculation process by the analytical method, and the calculation accuracy of the flow equation cannot be guaranteed in a complex system.
The simulation first generates a probability density function with a large number of samples representing random variables. Then, the trend results of the samples are solved iteratively. And finally, carrying out statistical analysis on the load flow results of the samples so as to obtain a probability load flow calculation result. Compared with an analytical method, the simulation method is more accurate. However, the solution process of the simulation method is time-consuming because of the need to iteratively solve the trend results of a large number of samples. In order to increase the computation speed of the simulation method, researchers have proposed a method based on a linear power flow model and a method based on parallel computation. The linear power flow model converts the nonlinear power flow equation into a linear equation, so that the calculation speed of the probability power flow can be effectively increased. However, due to errors of the linear equation, the calculation accuracy of the probability load flow is reduced by using the linear equation. The method adopts parallel computation to realize the rapid and accurate computation of the probability load flow, but the requirement of the parallel computation on computing resources is higher. It is impractical to use this parallel computing method at every utility company. In conclusion, the computational burden of the probability trend is the bottleneck of the practical application of the probability trend in engineering.
With the continuous development of artificial intelligence technology, some researchers propose to solve probability load flow by using DNN, so that high-precision and fast calculation of the probability load flow is realized. The method comprises the steps of firstly training DNN to obtain a DNN power flow model which can approach a power flow equation with high precision. And then, directly mapping the load flow calculation results of all samples by using the trained DNN load flow model. Therefore, the probability load flow is calculated quickly and accurately. However, this method is difficult to solve the situation of system scale change (when the system scale changes, the DNN of the original system that has been trained will not be directly applied to the new system). With the continuous development of load requirements and new energy, the scale of the power grid is continuously increased (newly added nodes or branches). The structure of the DNN model should correspond to the scale of the system being solved, and thus the DNN of the original system cannot be used to solve the probabilistic power flow of the new system. For this reason, a new DNN needs to be trained to solve the probabilistic power flow of the new system. However, training the DNN from scratch is a very time consuming process. Therefore, it is necessary to improve the training efficiency of the extension system DNN, so as to improve the extensibility of the DNN in the extension system.
Disclosure of Invention
The present invention is directed to solving the problems of the prior art.
The technical scheme adopted for achieving the purpose of the invention is that the method for improving the expansibility of the deep neural network tidal current model mainly comprises the following steps:
1) and acquiring basic data of the power system.
2) Determining a feature vector, mainly comprising the following steps:
2.1) setting uncertain factors including new energy uncertainty and load uncertainty. And setting a power flow result, wherein the power flow result comprises the voltage amplitude and the voltage phase angle of each node, and the active power and the reactive power of each branch circuit.
2.2) calculating the active injection power P of the node iinj,iReactive injection power Q of node iinj,iVoltage amplitude v of node iiAnd voltage phase angle thetaiActive power P of branches i to jijAnd reactive power PijNamely:
Pinj,i＝Pg,i+Pw,i+Pv,i-Pd,i。 (1)
Qinj,i＝Qg,i-Qd,i。 (2)
Figure BDA0002222341060000021
Figure BDA0002222341060000022
Figure BDA0002222341060000031
Figure BDA0002222341060000032
where i and j are the node numbers. n isbIndicating the number of nodes. Pg,iAnd Qg,iAnd representing the active output and the reactive output of the generator of the node i. Pw,iRepresenting the active output of the wind farm at node i. Pv,iAnd representing the active power output of the photovoltaic power station at the node i. Pd,iAnd Qd,iRepresenting the active and reactive loads of node i. v. ofiIs the voltage magnitude at node i. v. ofjIs the voltage magnitude at node j. ThetaijIs the voltage phase angle difference between node i and node j. GijAre elements of the conductance matrix. B isijAre elements of the susceptance matrix. gijAnd bijAre the conductance and susceptance parameters of the transmission line.
2.3) determining an input feature vector of the power flow sample, namely the node injection power x. The input feature vector is as follows:
x＝[Pinj,Qinj]。 (7)
2.4) determining the output characteristic vector of the power flow sample, namely the power flow calculation result y0. The output feature vector is as follows:
yo＝[v,θ,Pij,Qij]。 (8)
where v is the voltage amplitude. And theta is a voltage phase angle.
3) And establishing an original DNN power flow model.
Further, the main steps of establishing the original DNN power flow model are as follows:
3.1) taking active injection power and reactive injection power of each node in the power system as original input x of the DNN power flow model, and taking a calculation result of each power flow sample as original output y of the DNN power flow modelo. And the calculation result of each load flow sample comprises the voltage amplitude of each node, the voltage phase angle of each node, the active power and the reactive power of each branch.
3.2) the original DNN power flow model adopts SDAE as a basic model.
The original SDAE power flow model consists of a plurality of noise reduction automatic encoders DAE. The main steps for establishing the original SDAE power flow model are as follows:
3.2.1) establishing a noise reduction automatic encoder DAE, which mainly comprises the following steps:
3.2.1.1) corrupting the original input x in a randomly mapped manner, resulting in a locally corrupted input
Figure BDA0002222341060000041
The corrosion formula is shown below:
Figure BDA0002222341060000042
in the formula, qDThe method is an etching process by means of random mapping, namely, a plurality of original input x are randomly selected and set to zero. x is the input of the original DNN power flow model.
3.2.1.2) according to the coding function fθCompute hidden layer y, i.e.:
Figure BDA0002222341060000043
in the formula, W is the weight of the encoder. W is a number dy×dxMatrix of dimensions. b is the bias of the encoder. b is a number dyA vector of dimensions. dxIs the dimension of the input layer vector. dyThe dimension of the intermediate layer vector. f. ofθIs a coding function. s (x) is the activation function in the encoding process.
3.2.1.3) decoding function g of the intermediate layer output y by the decoderθ′And obtaining the output of the output layer z, thereby establishing the DAE model.
The output of output layer z is as follows:
z＝gθ′(y)＝s(W′y+b′)。 (11)
wherein, W' is the decoder weight. W' is a number dx×dyA matrix of dimensions. b' is the decoder bias. b' is a number dxA vector of dimensions. dxIs the dimension of the input layer vector. dyThe dimension of the intermediate layer vector.
3.2.2) stacking the n DAE models layer by layer. And the middle layer of the lower DAE model is used as an input layer of the upper DAE model, so that an original SDAE power flow model, namely an original DNN power flow model, is obtained.
Output of original SDAE power flow model
Figure BDA0002222341060000044
As follows:
Figure BDA0002222341060000045
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000046
is the coding function of the l-th layer DAE. 1,2, … n. n is the number of DAE in the original SDAE. l is the number of DAE.
Figure BDA0002222341060000047
Is the coding function at the top layer of the original SDAE power flow model.
4) The main steps for training the original DNN power flow model, namely the original SDAE power flow model, are as follows:
4.1) carrying out unsupervised pre-training on the original SDAE power flow model, and mainly comprising the following steps:
4.1.1) establish the mean square error loss function, i.e.:
Figure BDA0002222341060000048
in the formula, xlIs the input of the l-th layer DAE, i.e., the intermediate layer output y of the l-1-th layer DAEl-1。zlIs the output of the l-th layer DAE.
4.1.2) training the parameters of the DAEs of each layer by using a root mean square propagation algorithm, wherein the updating formulas of the parameters of the DAEs of each layer in the training process are shown as a formula (14) to a formula (23).
After the T +1 th parameter is updated, the weight values of the jth neuron in the l-1 th DAE intermediate layer to the ith neuron in the l-1 th DAE intermediate layer are obtained
Figure BDA0002222341060000051
As follows:
Figure BDA0002222341060000052
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000053
is the weight value from the jth neuron in the intermediate layer of the layer l-1 DAE to the ith neuron in the intermediate layer of the layer l DAE after the T +1 times of parameter updating.
Figure BDA0002222341060000054
Is the weight value from the jth neuron in the intermediate layer of the layer l-1 DAE to the ith neuron in the intermediate layer of the layer l DAE after the Tth parameter updating.
Bias of ith neuron in ith DAE middle layer after T +1 th parameter update
Figure BDA0002222341060000055
As follows:
Figure BDA0002222341060000056
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000057
is the bias of the ith neuron in the middle layer of the ith DAE after the Tth parameter update.
Wherein, after the Tth parameter is updated for the first time, the weight values of the jth neuron of the l-1 th DAE middle layer to the ith neuron of the l-1 th DAE middle layer
Figure BDA0002222341060000058
Weight change in update process
Figure BDA0002222341060000059
As follows:
Figure BDA00022223410600000510
Figure BDA00022223410600000511
Figure BDA0002222341060000061
wherein, after the Tth parameter updating, the bias of the ith neuron of the ith DAE middle layer
Figure BDA0002222341060000062
Bias change in update procedure
Figure BDA0002222341060000063
As follows:
Figure BDA0002222341060000064
Figure BDA0002222341060000065
Figure BDA0002222341060000066
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000067
representing the Hadamard product. η is the learning rate. ρ is a gradient accumulation index. k is an arbitrary sample.
Figure BDA0002222341060000068
Is the weight value from the jth neuron in the intermediate layer l-1 DAE to the ith neuron in the intermediate layer l-1 DAE after the T-1 parameter updating.
Figure BDA0002222341060000069
Is the weight value from the jth neuron in the intermediate layer of the layer l-1 DAE to the ith neuron in the intermediate layer of the layer l DAE after the Tth parameter updating.
Figure BDA00022223410600000610
And iterating the accumulated gradients for the previous T times of weights.
Figure BDA00022223410600000611
The accumulated gradient is iterated for the first T-1 times of weights. Δ is the incremental sign. d is the differential sign. σ is a constant.
Figure BDA00022223410600000612
Are the partial derivative symbols.
Figure BDA00022223410600000613
According to the output of the top layer
Figure BDA00022223410600000614
And the training sample output y constructs a mean square error loss function. k is an arbitrary sample.
Figure BDA00022223410600000615
Is the bias of the ith neuron in the middle layer of the ith DAE after the Tth parameter update.
Figure BDA00022223410600000616
Is the bias of the ith neuron in the ith DAE middle layer after the T-1 parameter update.
Figure BDA00022223410600000617
The gradient accumulated for the previous T bias iterations.
Figure BDA00022223410600000618
The first T-1 bias iterations accumulate gradients. m is the number of samples.
4.1.3) introducing momentum learning rate as an additional item, updating the formula (16) to the formula (19) to obtain the weight value change quantity shown in the formula (22) and the formula (23)
Figure BDA00022223410600000619
And amount of change in bias
Figure BDA00022223410600000620
Namely:
Figure BDA0002222341060000071
Figure BDA0002222341060000072
in the formula, p is a momentum learning rate.
4.1.4) calculating the optimal coding parameter theta of each layer of DAE according to an unsupervised pre-training parameter updating formula, and taking the optimal coding parameter theta as the initial coding parameter with supervised fine tuning.
4.2) carrying out supervised fine tuning on the original SDAE power flow model, and mainly comprising the following steps:
4.2.1) output from the Top layer
Figure BDA0002222341060000073
Constructing a mean square error loss function L with the training sample output y to obtain an optimized objective function argθminJ(W,b)。
argθminJ(W,b)＝argθmin L。 (24)
4.2) according to the optimization objective function argθminJ (W, b), and performing fine adjustment on the optimal coding parameter theta of the original SDAE power flow model by adopting expressions (14) to (23) to obtain the trained SDAE power flow model.
5) And expanding the original DNN power flow model to obtain an expanded DNN power flow model.
Further, the main steps of expanding the original DNN power flow model by using the transfer learning method are as follows:
and 5.1) determining parameters needing initialization in the extension of the DNN power flow model, wherein the parameters comprise hidden layer parameters, input layer parameters and output layer parameters.
5.2) transferring hidden layer parameters in the original DNN power flow model to the extension DNN power flow model.
5.3) initializing input layer parameters and output layer parameters in the extension DNN power flow model, and mainly comprising the following steps:
5.3.1) determining variables connected with the input layer parameters and the output layer parameters of the original DNN power flow model, wherein the variables comprise active injection power, reactive injection power, voltage amplitude, voltage phase angle, branch active power and branch reactive power.
And respectively migrating parameters connected with the variables in the original DNN power flow model to the extension DNN power flow model so as to initialize and extend partial parameters of the DNN power flow model.
5.3.2) initializing and expanding the residual parameters of the input layer and the output layer in the DNN power flow model by using a method for fitting the parameter distribution of the original DNN power flow model.
And 5.4) fine-tuning the extension DNN power flow model by using the power flow sample of the extension system.
6) And resolving the probability load flow of the extension system by using the extension DNN load flow model to obtain a probability load flow result.
Further, the main steps of resolving the extension system probability load flow are as follows:
6.1) collecting training samples and training an extension DNN power flow model.
6.2) sampling the state of the extension system by adopting a Monte Carlo method.
And 6.3) calculating the probability load flow result of the extension system by using the extension DNN load flow model, wherein the probability load flow result comprises the average value and the standard deviation of the variables and the probability density function of all output variables.
It is worth to be noted that, the present invention first directly migrates the parameters of the hidden layer of the DNN of the original system to the DNN of the new system; then, according to random variables connected with the parameters of the input layer and the output layer, migrating the parameters of the input layer and the output layer of the original system DNN to a new system DNN; and finally, fitting parameter distribution connected to each variable in the input layer and the output layer of the original system DNN by adopting non-parameter estimation, and initializing the un-initialized parameters in the new system DNN by sampling the parameter distribution. Simulation results on an IEEE39 node system and an IEEE118 node system show that the knowledge migration method provided by the invention can greatly improve the training efficiency of DNN of a new system and verify the effectiveness of the method.
The technical effect of the present invention is undoubted. The invention provides a knowledge migration method for improving the training efficiency of a DNN of an extension system. The method mainly comprises the following four characteristics:
1) the parameters of the original system DNN are migrated according to the variables to which the parameters are connected. The inputs and outputs of the DNN include various random variables in the power system. The input layer and output layer parameters of the original system DNN have learned the trend characteristics of the variables connected to them, which can provide valuable trend characteristic knowledge for the parameters connected to the corresponding variables in the new system DNN. Based on this, the present invention proposes to migrate the input layer and output layer parameters of the original system DNN to the new DNN according to the random variables to which the parameters are connected.
2) Parameters of the remaining portions of the input layer and the output layer are initialized based on the non-parametric estimates. Since the new system is larger in scale than the original system, the dimensions of the input layer and the output layer of the DNN of the new system are larger than those of the DNN of the original system. Therefore, the parameters of the original system DNN cannot completely cover the parameters of the new DNN, and some of the parameters still need to be initialized. For this part of the parameters, the invention proposes to first obtain the parameter distribution of the original system DNN by non-parametric estimation, and then initialize the remaining part of the parameters by sampling from the parameter distribution.
3) The knowledge migration method provided by the invention can migrate the DNN parameters trained by the original system to the extension system DNN, help the extension system DNN to learn, enable the extension system DNN to converge faster in the training process, and improve the training efficiency, thereby improving the expansibility of the DNN in the extension system.
4) The knowledge migration method provided by the invention can provide a good initial value for the DNN of the extension system by utilizing the DNN parameters trained by the original system. The good initial value reduces the dependence of the extension system DNN on the number of training samples in the training process, and further improves the expansibility of the DNN in the extension system.
The method can be widely applied to solving the probability load flow of the power system, and is particularly suitable for the condition that the DNN of the original system cannot be applied due to system extension. Through the method provided by the invention, the learned trend feature knowledge of the original system DNN can be migrated to the new system DNN, so that the training efficiency of the new system DNN is greatly improved, and the requirement of the training process on the number of samples is effectively reduced.
Drawings
FIG. 1 is a process framework for analytical and simulation;
FIG. 2 is the structure of a DAE;
FIG. 3 is the structure of SDAE;
FIG. 4 is a block diagram of extension system DNN training based on transfer learning;
fig. 5 is a basic block diagram for solving a probabilistic power flow by applying DNN.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1 to 5, a method for improving the expansibility of a deep neural network tidal current model mainly includes the following steps:
1) and acquiring basic data of the power system.
2) A feature vector is determined. DNN is a model that extracts features between sample inputs and outputs. In order to enable the DNN to effectively extract the features of the probabilistic power flow, the input feature vector should include features related to new energy and load. The output feature vector should contain the load flow calculation result of interest.
Further, the main steps of determining the feature vector are as follows:
2.1) setting uncertain factors including new energy uncertainty and load uncertainty. And setting a power flow result, wherein the power flow result comprises the voltage amplitude and the voltage phase angle of each node, and the active power and the reactive power of each branch circuit.
2.2) calculating the active injection power P of the node iinj,iReactive injection power Q of node iinj,iVoltage amplitude v of node iiAnd voltage phase angle thetaiActive power P of branches i to jijAnd reactive power PijNamely:
Pinj,i＝Pg,i+Pw,i+Pv,i-Pd,i。 (1)
Qinj,i＝Qg,i-Qd,i。 (2)
Figure BDA0002222341060000101
Figure BDA0002222341060000102
Figure BDA0002222341060000103
Figure BDA0002222341060000104
where i and j are the node numbers. 1,2, …, nb。j＝1，2，…，nb。nbIndicating the number of nodes. Pg,iAnd Qg,iAnd representing the active output and the reactive output of the generator of the node i. Pw,iRepresenting the active output of the wind farm at node i. Pv,iAnd representing the active power output of the photovoltaic power station at the node i. Pd,iAnd Qd,iRepresenting the active and reactive loads of node i. v. ofiIs the voltage magnitude at node i. v. ofjIs the voltage magnitude at node j. ThetaijIs the voltage phase angle difference between node i and node j. GijAre elements of the conductance matrix. B isijAre elements of the susceptance matrix. gijAnd bijAre the conductance and susceptance parameters of the transmission line.
2.3) determining an input feature vector of the power flow sample, namely the node injection power x. The input feature vector is as follows:
x＝[Pinj,Qinj]。 (7)
2.4) determining the output characteristic vector of the power flow sample, namely the power flow calculation result y0. The output feature vector is as follows:
yo＝[v,θ,Pij,Qij]。 (8)
where v is the voltage amplitude. And theta is a voltage phase angle.
3) And establishing an original DNN power flow model.
The basic model selected by the invention is a Stacked Denoising Auto-Encoder (SDAE), which is a special type of DNN. The SDAE is composed of a plurality of noise reduction Auto-encoders (DAE). DAE is similar to the common three-layer neural network. The main difference is that the DAE contains a corrosion process and the training goal of the DAE is to reconstruct its inputs. The erosion process may force the DAE to extract more robust features. Reconstructing the input may extract potential features of the input, facilitating training of the DNN.
Further, the main steps of establishing the original DNN power flow model are as follows:
3.1) taking active injection power and reactive injection power of each node in the power system as original input x of the DNN power flow model. The calculation result of each power flow sample (namely the voltage amplitude and the voltage phase angle of each node, the active power and the reactive power of each branch) is used as the original output y of the DNN power flow modelo。
The structure of DAE is shown in FIG. 2, and the calculation process is as follows:
eroding the original input x in a random mapping manner to obtain locally eroded input
Figure BDA0002222341060000111
The corrosion formula is shown below:
Figure BDA0002222341060000112
in the formula, qDThe method is an etching process by means of random mapping, namely, a plurality of original input x are randomly selected and set to zero. x is the original input of the original DNN power flow model.
3.2) according to the coding function fθCompute hidden layer y, i.e.:
Figure BDA0002222341060000113
in the formula, W is the weight of the encoder. W is a number dy×dxA matrix of dimensions. b is the bias of the encoder. b is a number dyA vector of dimensions. dxIs the dimension of the input layer vector. dyThe dimension of the intermediate layer vector. f. ofθIs a coding function. s (x) is the activation function in the encoding process.
3.3) decoding function g of the intermediate layer output y by the decoderθ′And obtaining the output of the output layer z, thereby establishing the DAE model.
The output of output layer z is as follows:
z＝gθ′(y)＝s(W′y+b′)。 (11)
wherein, W' is the decoder weight. W' is a number dx×dyA matrix of dimensions. b' is the decoder bias. b' is a number dxA vector of dimensions. dxIs the dimension of the input layer vector. dyThe dimension of the intermediate layer vector.
3.4) stacking the n DAE models layer by layer. The middle layer of the lower DAE model serves as an input layer of the upper DAE model, so as to obtain an SDAE flow model (i.e. the original DNN flow model), as shown in fig. 3.
Output of original SDAE power flow model
Figure BDA0002222341060000121
As follows:
Figure BDA0002222341060000122
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000123
is the coding function of the l-th layer DAE. 1,2, … n. n is the number of DAE in the original SDAE. l is the number of DAE.
Figure BDA0002222341060000124
Is the coding function at the top layer of the original SDAE power flow model.
4) And training the original SDAE power flow model to obtain the trained original SDAE power flow model (namely the original DNN power flow model).
Further, the main steps for training the original SDAE flow model are as follows:
4.1) carrying out unsupervised pre-training on the original SDAE power flow model, and mainly comprising the following steps:
4.1.1) establishing a mean square error loss function LH(xl,zl) Namely:
Figure BDA0002222341060000125
in the formula, xlIs the input of the l-th layer DAE, i.e., the intermediate layer output y of the l-1-th layer DAEl-1。zlIs the output of the l-th layer DAE.
Figure BDA0002222341060000126
Is an objective function.
Figure BDA0002222341060000127
The minimum value is expressed.
Shown below the mean square error loss function.
Figure BDA0002222341060000128
Wherein m is the number of samples,
Figure BDA0002222341060000129
is the output value of SDAE, and y is the actual output of the training sample. L is LH(xl,zl) Is a simplified expression of.
4.1.2) training each layer of DAE by using a root mean square propagation algorithm, wherein the parameter updating formulas of each layer of DAE in the training process are shown as a formula (6) to a formula (16).
After the T +1 th parameter is updated, the weight values of the jth neuron in the l-1 th DAE intermediate layer to the ith neuron in the l-1 th DAE intermediate layer are obtained
Figure BDA0002222341060000131
As follows:
Figure BDA0002222341060000132
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000133
is the weight value from the jth neuron in the intermediate layer of the layer l-1 DAE to the ith neuron in the intermediate layer of the layer l DAE after the T +1 times of parameter updating.
Figure BDA0002222341060000134
Is the weight value from the jth neuron in the intermediate layer of the layer l-1 DAE to the ith neuron in the intermediate layer of the layer l DAE after the Tth parameter updating.
Bias of ith neuron in ith DAE middle layer after T +1 th parameter update
Figure BDA0002222341060000135
As follows:
Figure BDA0002222341060000136
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000137
is the bias of the ith neuron in the middle layer of the ith DAE after the Tth parameter update.
Wherein, after the Tth parameter is updated for the first time, the weight values of the jth neuron of the l-1 th DAE middle layer to the ith neuron of the l-1 th DAE middle layer
Figure BDA0002222341060000138
Weight change in update process
Figure BDA0002222341060000139
As follows:
Figure BDA00022223410600001310
Figure BDA00022223410600001311
Figure BDA00022223410600001312
wherein, after the Tth parameter updating, the bias of the ith neuron of the ith DAE middle layer
Figure BDA00022223410600001313
Bias change in update procedure
Figure BDA00022223410600001314
As follows:
Figure BDA00022223410600001315
Figure BDA0002222341060000141
Figure BDA0002222341060000142
in the formula (I), the compound is shown in the specification,
Figure BDA0002222341060000143
representing the Hadamard product. η is the learning rate, and is 0.001. ρ is the gradient cumulative index, equal to 0.99. ε is constant, take 10-8. k is an arbitrary sample.
Figure BDA0002222341060000144
Is the weight value from the jth neuron in the intermediate layer l-1 DAE to the ith neuron in the intermediate layer l-1 DAE after the T-1 parameter updating.
Figure BDA0002222341060000145
Is the weight value from the jth neuron in the intermediate layer of the layer l-1 DAE to the ith neuron in the intermediate layer of the layer l DAE after the Tth parameter updating.
Figure BDA0002222341060000146
And iterating the accumulated gradients for the previous T times of weights.
Figure BDA0002222341060000147
The accumulated gradient is iterated for the first T-1 times of weights. Δ is the incremental sign. d is the sign of the differential of the signal,
Figure BDA0002222341060000148
is a weight value
Figure BDA0002222341060000149
The differential of (a) is determined,
Figure BDA00022223410600001410
is offset by
Figure BDA00022223410600001411
Differentiation of (2). σ is a constant.
Figure BDA00022223410600001412
Are the partial derivative symbols.
Figure BDA00022223410600001413
Is a weight value
Figure BDA00022223410600001414
The partial derivatives of (a) are,
Figure BDA00022223410600001415
is offset by
Figure BDA00022223410600001416
The partial derivatives of (1).
Figure BDA00022223410600001417
According to the output of the top layer
Figure BDA00022223410600001418
And the training sample output y constructs a mean square error loss function. k is an arbitrary sample.
Figure BDA00022223410600001419
Is the bias of the ith neuron in the middle layer of the ith DAE after the Tth parameter update.
Figure BDA00022223410600001420
Is the bias of the ith neuron in the ith DAE middle layer after the T-1 parameter update.
Figure BDA00022223410600001421
The gradient accumulated for the previous T bias iterations.
Figure BDA00022223410600001422
The first T-1 bias iterations accumulate gradients. m is the number of samples.
4.1.3) introducing momentum learning rate as an additional item, updating the formula (17) to the formula (20) to obtain the weight value change quantity shown in the formula (23) and the formula (24)
Figure BDA00022223410600001423
And amount of change in bias
Figure BDA00022223410600001424
Namely:
Figure BDA00022223410600001425
Figure BDA00022223410600001426
in the formula, p is a momentum learning rate and has a value of 0.9.
4.1.4) calculating the optimal coding parameter theta of each layer of DAE according to an unsupervised pre-training parameter updating formula, and taking the optimal coding parameter theta as the initial coding parameter with supervised fine tuning.
4.2) carrying out supervised fine tuning on the original SDAE power flow model, and mainly comprising the following steps:
4.2.1) output from the Top layer
Figure BDA0002222341060000151
Constructing a mean square error loss function L with the training sample output y to obtain an optimized objective function argθminJ(W,b)。
argθminJ(W,b)＝argθmin L。 (25)
4.2.2) according to an optimized objective function argθmin J (W, b), and thus, fine-tuning the optimal coding parameter θ ═ { W, b } of the original SDAE power flow model to obtain a final SDAE power flow model (i.e., the original DNN power flow model).
5) And expanding the original DNN power flow model to obtain an expanded DNN power flow model.
In a real power system, the system will expand as new energy and load demands develop. From equations (22) and (23), it can be seen that the input and output dimensions of DNN are related to the scale of the system. The input and output dimensions of the original system DNN do not match the extension system, and the original system DNN cannot be applied to the extension system. For this reason, a new DNN needs to be trained for the extension system.
In order to improve the training efficiency of the new DNN, the present invention utilizes a transfer learning technique. Transfer learning is a method of applying useful knowledge of the relevant domain to assist in the training of the target domain model. The new system is obtained by the extension of the original system, so the trend characteristics of the new system are very similar to those of the original system. Therefore, the original system DNN parameters that can reflect the original system flow characteristics are useful knowledge for extending the system DNN. Based on this, the invention migrates the parameters learned by the original system DNN to the new DNN, so as to improve the training efficiency of the new DNN.
The traditional migration learning method directly migrates the trained DNN parameters to the new DNN to initialize the parameters of the new DNN, and then fine-tunes the parameters of the new DNN by using the new samples. However, for the build-out system, since the structure of the new DNN is larger than that of the original system DNN, directly migrating the parameters of the original system DNN cannot cover all the parameters of the new DNN.
Further, the method for expanding the original DNN power flow model by using the transfer learning method mainly comprises the following steps:
and 5.1) determining parameters needing initialization in the extension of the DNN power flow model, wherein the parameters comprise hidden layer parameters, input layer parameters and output layer parameters.
5.2) transferring hidden layer parameters in the original DNN power flow model to the extension DNN power flow model.
5.3) initializing input layer parameters and output layer parameters in the extension DNN power flow model, and mainly comprising the following steps:
5.3.1) determining variables connected with the input layer parameters and the output layer parameters of the original DNN power flow model, wherein the variables comprise active injection power, reactive injection power, voltage amplitude, voltage phase angle, branch active power and branch reactive power.
And respectively migrating parameters connected with the variables in the original DNN power flow model to the extension DNN power flow model so as to initialize and extend partial parameters of the DNN power flow model.
As shown in fig. 4, the parameters of the input layer and the output layer are connected with different variables, including active injection power, reactive injection power, voltage amplitude, voltage phase angle, branch active power and branch reactive power. The parameters connected to each variable in the original system DNN have learned the trend knowledge associated with the variable. The invention therefore proposes to migrate the parameters of the input and output layers according to the variables to which they are connected. Taking the active injection power as an example, in the parameter migration process, the present invention migrates the parameter connected to the active injection power in the original system DNN to the new DNN to initialize a part of the parameter connected to the active injection power in the new DNN, as shown by the light blue line in fig. 4.
5.3.2) initializing and expanding the residual parameters of the input layer and the output layer in the DNN power flow model by using a method for fitting the parameter distribution of the original DNN power flow model.
Taking the active injection power as an example, because the number of nodes of the extension system is greater than that of the original system, in the new system DNN, some parameters connected to the active injection power are not initialized yet, as shown by the light blue solid circles in fig. 4. Since knowledge of the power flow associated with the active injection power is contained in the distribution of the parameters connected to it, the invention first fits the distribution of the parameters connected to the active injection power in the original system DNN and then initializes the remaining parameters connected to the active injection power of the new system DNN by sampling from the fitted distribution. Common distribution fitting methods include parametric estimation and non-parametric estimation. Since there is no prior knowledge of the parameter distribution, the present invention chooses non-parametric estimation to fit the distribution of the parameters.
For the parameters connected to the active injection power, the probability density function can be estimated by equation (26).
Figure BDA0002222341060000161
In the formula, K (x) is a kernel function, and the invention adopts a Gaussian kernel function:
Figure BDA0002222341060000171
wPinj,irepresenting the parameters connected to the active injection power in the original system DNN. h represents the bandwidth factor, and h is 1.8 in the invention. N is a radical ofwIs the number of parameters connected to the active injected power.
By estimated probability density functions
Figure BDA0002222341060000172
The remaining parameters of the new DNN connected to the active injection power may be initialized.
And 5.4) fine-tuning the extension DNN power flow model by using the power flow sample of the extension system.
By the method, the trend knowledge learned in the original system DNN is transferred to the new DNN, and good initial parameters can be provided for the new DNN. And then, fine-tuning the new DNN by using the trend sample of the extension system. Since the output of the DNN is the effect of all parameter interactions in the DNN, the present invention will adjust all parameters in the new DNN. Compared with zero learning, the method can complete the training process of the extension system DNN more quickly. Because the method provided by the invention does not need to execute an unsupervised pre-training stage, and the original system DNN provides a good initial value for the extension system DNN. Furthermore, the proposed method may also reduce the dependency of the training process on the number of training samples.
6) And resolving the probability load flow of the extension system by using the extension DNN load flow model to obtain a probability load flow result.
Further, the main steps of resolving the extension system probability load flow are as follows:
6.1) collecting training samples and training an extension DNN power flow model.
6.2) sampling the state of the extension system by adopting a Monte Carlo method.
And 6.3) calculating a probability power flow result of the extension system by using the extension DNN power flow model, wherein the probability power flow result comprises the average value and the standard deviation of the variables and the probability density function of all output variables.
Example 2:
an experiment for verifying and improving the expansibility of a deep neural network tidal current model mainly comprises the following steps:
1) tidal current sample acquisition
In the present embodiment, an IEEE39 node system and an IEEE118 node system are used for simulation. Original system: in an IEEE39 node system, a wind power plant is introduced to buses 23, 24 and 25, the maximum output of the wind power plant is 260MW, photovoltaic power stations are introduced to buses 17, 18 and 19, and the maximum output of the photovoltaic power stations is 200 MW. In an IEEE118 node system, the invention introduces a wind power plant on buses 59, 80 and 90, the maximum output of the wind power plant is 260MW, and introduces photovoltaic power stations on buses 13, 14, 16 and 23, the maximum output of the photovoltaic power stations is 200 MW. An extension system: in the IEEE39 node system, a bus 40 and branches 26-40 are added on the basis of the original system. In the IEEE118 node system, a bus 119, a branch 118 and branches 75-119 are additionally arranged on the basis of the original system, and a wind power plant is introduced on the bus 119, wherein the maximum output of the wind power plant is 200 MW. Wherein, the wind speed is assumed to follow two parameters Weibull distribution, the scale parameter is 2.016, and the shape parameter is 5.089. The illumination intensity follows Beta distribution, and the shape parameters of the photovoltaic power station and the cut-in wind speed, the rated wind speed and the cut-out wind speed of the wind power plant are shown in table 1. Further, it is assumed that the random characteristic of the load of each node follows a normal distribution with a standard deviation of 10% of the expected value of the load of each node.
TABLE 1 photovoltaic power plant and wind farm related parameters
Figure BDA0002222341060000181
Then, the random variable is sampled for 5 ten thousand times by a Monte Carlo method, and the power flow of each sampling state is solved by a Newton method. The active injection power and the reactive injection power of all sampling states are taken as training sample input x. And (3) taking the load flow calculation results (namely the voltage amplitude and phase angle of each node of the power system, the active power and the reactive power of each branch) of all sampling states obtained by the Newton method as the output y of the training sample.
2) DNN power flow model initialization
Including data preprocessing and determination of DNN model structure. The input and output data of the training samples are normalized by equation (26). Then, the layer structure of the DNN power flow model is set according to the scale and complexity of the power system to be solved, as shown in table 2.
Figure BDA0002222341060000182
In the formula, x is a normalized sample value, x is a sample value to be normalized, μ is a sample mean value, and σ is a sample standard deviation.
TABLE 2 model structures of different systems
System scale IEEE39 node system IEEE118 node system
Implicit layer number 4 4
Number of hidden layer neurons 200 300
3) Original system DNN power flow model training
For the original system, the DNN needs to be trained from scratch, i.e. a two-stage training method with unsupervised pre-training and supervised fine-tuning is used. In the training process, the formula shown in formula (13) -formula (23) is adopted, and the DNN parameters are iteratively adjusted according to the training samples until the testing precision meets the requirement or the iteration times reach 500 times.
4) Extension system DNN power flow model training
For the extension system, the knowledge migration method provided by the invention is adopted to migrate the parameters of the original system DNN to the extension system DNN, and then the extension system DNN is trained. In the training process, the formula shown in the formula (5) -formula (15) is adopted, and the DNN parameters are iteratively adjusted according to the extension system flow sample until the testing precision meets the requirement or the iteration times reach 500 times.
The specific simulation results are as follows:
1) concrete examples and training method comparison
The example information used for the simulation is as follows:
example 1: the improved IEEE39 node system has the load standard deviation of 10% and the new energy permeability of 20%.
Example 2: the improved IEEE118 node system has the load standard deviation of 10% and the new energy permeability of 20%.
Example 3: the improved IEEE39 node system has the load standard deviation of 10% and the new energy permeability of 25%.
Example 4: the improved IEEE118 node system has the load standard deviation of 10% and the new energy permeability of 25%.
Example 5: the extension system based on the example 1 is additionally provided with the bus 40 and the branches 26-40.
Example 6: in the extension system based on the embodiment 2, a bus 119, a branch 118 and a branch 75-119 are additionally arranged, and a wind power plant with the maximum output of 200MW is introduced on the bus 119.
Examples 5 and 6 are extension systems based on examples 1 and 2, respectively. The effectiveness of the knowledge migration method provided by the invention is verified by adopting the following steps of example 5 and example 6.
The DNN power flow model training method compared by the invention is M1-M3:
m1: the DNN is trained from zero.
M2: the knowledge migration method provided by the invention is adopted to train DNN.
M3: as M2, but employs a random initialization method to initialize the remaining parameters in the input and output layers.
The accuracy of the DNN power flow model is evaluated by adopting the following indexes:
PV,β: the probability that the absolute error of the voltage amplitude exceeds β p.u.
Pθ,β: the absolute error of the voltage phase angle exceeds the probability of beta rad.
PP,β: the probability that the absolute error of the active power of the branch exceeds beta MW.
PQ,β: the probability that the absolute error of branch reactive power exceeds beta MVar.
2) Precision analysis of DNN power flow model of original system
The section tests the accuracy of the DNN power flow model of the original system. The DNN power flow model of the original system needs to be trained to solveSolving the probability trend of the original system, and providing useful trend knowledge for the extension system DNN. Table 3 lists the following accuracy indicators: pV,0.0002,Pθ,0.002,PP,2,PQ,2。
TABLE 3 accuracy of DNN Power flow model trained by M1
Examples of the design Method PV,0.0002 Pθ,0.002 PP,2 PQ,2
EXAMPLE 1 M1 0.05％ 0.88％ 1.06％ 0.01％
EXAMPLE 2 M1 1.42％ 1.02％ 0.57％ 0.02％
As can be seen from table 3, the accuracy index of both example 1 and example 2 is less than 1.5%, indicating that the original system DNN can approximate the power flow equation with high accuracy.
To verify the generalization ability of the DNN of the original system, the DNN trained in examples 1 and 2 was used directly herein to solve the examples with higher new energy penetration (examples 3 and 4). The test results are shown in table 4.
TABLE 4 solving the accuracies of example 3 and 4 directly using the trained DNN
Figure BDA0002222341060000201
As can be seen from table 4, all indexes are still less than 2% for examples 3 and 4, thus verifying the generalization capability of the original system DNN.
3) Performance analysis of the proposed knowledge migration method
The section verifies the effectiveness of the knowledge migration method provided by the invention. The dimensions of the input and output of the examples 5 and 6 are different from those of the examples 1 and 2 due to the difference in the scale of the system. Therefore, the DNNs trained in examples 1 and 2 cannot be directly applied to solving the probability flows of examples 5 and 6. To this end, a new DNN suitable for the extension system needs to be trained. For examples 5 and 6, table 5 lists the training results for three methods, M1 (training from scratch), M2 (training using the proposed knowledge migration method), M3 (same as M2, but using the random initialization method to initialize the remaining parameters). The training stop criteria are that all the indicators shown in table 3 are less than 5% or that the number of iterations reaches 500.
TABLE 5 comparison of training results for the extension System from M1-M3
Figure BDA0002222341060000211
As can be seen from table 5, M1 cannot achieve satisfactory accuracy when the number of samples is small. In contrast, in the case of sufficient samples, M1 can meet the accuracy requirement, but the training burden is increased accordingly. In contrast, M2 is able to meet the accuracy requirements faster and with less sample size requirements thanks to the absence of the need to perform unsupervised pre-training and better initial values of the parameters provided by the original system DNN. Among them, the advantage of M2 is well shown in example 6. For examples 5 and 6, the training speed of M2 was improved by 9.92 times and 61.62 times, respectively, compared to M1. Similar to M2, training efficiency is greatly improved by using M3. In contrast, however, M2 was more efficient in training than M3, demonstrating the effectiveness of initializing the remaining parameters by fitting a distribution of parameters. But the advantage of M2 is not obvious due to the small number of remaining parameters. Furthermore, another advantage of M2 over M3 is that M2 is not affected by the random initialization method.
From the experimental results, it can be seen that: the knowledge migration method (M2) provided by the invention can greatly reduce the training time and the requirement on the number of training samples.
In summary, the present invention provides a knowledge migration method. Firstly, migrating parameters of an implicit layer in an original system DNN to a new DNN; then, transferring parameters of input and output layers in the original system DNN according to variables connected with the parameters; finally, the remaining parameters of the input and output layers in the new DNN are initialized according to the fitted parameter distribution of the original system DNN. Therefore, the fact that the trend knowledge learned by the original system DNN is transferred to the extension system DNN is achieved, and therefore training efficiency of the extension system DNN is improved. The example simulation analysis shows that the knowledge migration method provided by the invention can greatly improve the training efficiency of the extension system DNN and reduce the requirement of the training process on the number of samples. In addition, simulation analysis also demonstrates the effectiveness of initializing the remaining parameters from the fitted parameter distribution. Therefore, the invention can greatly improve the expansibility of DNN in the extension system.

Claims (5)

1. A method for improving the expansibility of a deep neural network tidal current model is characterized by mainly comprising the following steps:
1) acquiring basic data of a power system;
2) determining a feature vector;
3) establishing an original DNN power flow model;
4) training the original DNN power flow model to obtain a trained original DNN power flow model;
5) expanding the trained original DNN power flow model to obtain an expanded DNN power flow model;
the main steps of utilizing the transfer learning method to expand the trained original DNN power flow model are as follows:
5.1) determining parameters needing initialization in the extension DNN power flow model, wherein the parameters comprise hidden layer parameters, input layer parameters and output layer parameters;
5.2) transferring hidden layer parameters in the original DNN power flow model to an extension DNN power flow model;
5.3) initializing input layer parameters and output layer parameters in the extension DNN power flow model, and mainly comprising the following steps:
5.3.1) determining variables connected with input layer parameters and output layer parameters of the original DNN power flow model, wherein the variables comprise active injection power, reactive injection power, voltage amplitude, voltage phase angle, branch active power and branch reactive power;
respectively migrating parameters connected with the variables in the original DNN power flow model to an extension DNN power flow model so as to initialize and extend partial parameters of the DNN power flow model;
5.3.2) initializing and expanding the residual parameters of an input layer and an output layer in the DNN power flow model by using a method for fitting the parameter distribution of the original DNN power flow model;
5.4) utilizing the power flow sample of the extension system to finely adjust the extension DNN power flow model:
6) and resolving the probability load flow of the extension system by using the extension DNN load flow model to obtain a probability load flow result.
2. The method for improving the expansibility of the deep neural network tidal flow model according to claim 1, wherein the main steps for determining the eigenvectors are as follows:
1) setting uncertain factors including new energy uncertainty and load uncertainty; setting a power flow result, wherein the power flow result comprises a voltage amplitude value and a voltage phase angle of each node, and active power and reactive power of each branch circuit;
2) calculating active injection power P of node iinj,iReactive injection power Q of node iinj,iVoltage amplitude v of node iiPhase angle theta of voltage at node iiActive power P of branches i to jijAnd reactive power QijNamely:
Pinj,i＝Pg,i+Pw,i+Pv,i-Pd,i； (1)
Qinj,i＝Qg,i-Qd,i； (2)
Figure FDA0002855678260000021
Figure FDA0002855678260000022
Figure FDA0002855678260000023
Figure FDA0002855678260000024
where i and j are node numbers; n isbRepresenting the number of nodes; pg,iAnd Qg,iRepresenting the active output and the reactive output of the generator of the node i; pw,iRepresenting the active output of the wind power plant at the node i; pv,iRepresenting the active power output of the photovoltaic power station at the node i; pd,iAnd Qd,iRepresenting the active load and the reactive load of the node i; v. ofiIs the voltage amplitude of node i; v. ofjIs the voltage amplitude of node j; thetaijIs the voltage phase angle difference between node i and node j; gijIs an element of the conductance matrix; b isijIs an element of a susceptance matrix; gijAnd bijIs the conductance and susceptance parameters of the transmission line;
3) determining an input feature vector of the power flow sample, namely node injection power x; the input feature vector is as follows:
x＝[Pinj,Qinj]； (7)
4) determining output characteristic vector of power flow sample, namely power flow calculation result y0(ii) a The output feature vector is as follows:
yo＝[v,θ,Pij,Qij]； (8)
wherein v is the voltage amplitude; and theta is a voltage phase angle.
3. The method for improving the expansibility of the deep neural network power flow model according to claim 2, wherein the step of establishing the original DNN power flow model comprises the following steps:
1) taking active injection power and reactive injection power of each node in the power system as original input x of the DNN power flow model, and taking a calculation result of each power flow sample as original output y of the DNN power flow modelo(ii) a The calculation result of each load flow sample comprises the voltage amplitude of each node, the voltage phase angle of each node, the active power and the reactive power of each branch;
2) the original DNN power flow model selects SDAE as a basic model;
the SDAE consists of a plurality of noise reduction automatic encoders DAE; the main steps for establishing the original SDAE power flow model are as follows:
2.1) establishing a noise reduction automatic encoder DAE, which mainly comprises the following steps:
2.1.1) corrupting the original input x in a randomly mapped manner, resulting in a locally corrupted input
Figure FDA0002855678260000033
The corrosion formula is shown below：
Figure FDA0002855678260000031
In the formula, qDSelecting a plurality of original input x randomly and setting the x to zero in the corrosion process of a random mapping mode; x is the input of the original DNN power flow model;
2.1.2) according to the coding function fθCompute hidden layer y, i.e.:
Figure FDA0002855678260000032
in the formula, W is the weight of the encoder; w is a number dy×dxA matrix of dimensions; b is the bias of the encoder; b is a number dyA vector of dimensions; dxIs the dimension of the input layer vector; dyDimension of intermediate layer vector; f. ofθIs a coding function; s (x) is an activation function in the encoding process;
2.1.3) decoding function g of the intermediate layer output y by the decoderθ′Obtaining the output of the output layer z, and establishing a DAE model;
the output of output layer z is as follows:
z＝gθ′(y)＝s(W′y+b′)； (11)
wherein, W' is the weight of the decoder; w' is a number dx×dyA matrix of dimensions; b' is decoder bias; b' is a number dxA vector of dimensions; dxIs the dimension of the input layer vector; dyDimension of intermediate layer vector;
2.2) stacking n layers of DAE models layer by layer; the middle layer of the lower DAE model is used as an input layer of the upper DAE model, so that an original SDAE power flow model, namely an original DNN power flow model, is obtained;
output of original SDAE power flow model
Figure FDA0002855678260000041
As follows:
Figure FDA0002855678260000042
in the formula (I), the compound is shown in the specification,
Figure FDA0002855678260000043
an encoding function for layer l DAE; 1,2, … n; n is the number of DAEs in the original SDAE; l is the number of DAE;
Figure FDA0002855678260000044
is the coding function at the top layer of the original SDAE power flow model.
4. The method for improving the expansibility of the deep neural network power flow model according to claim 3, wherein the training of the original DNN power flow model, that is, the original SDAE power flow model, comprises the following steps:
1) the method comprises the following steps of carrying out unsupervised pre-training on an original SDAE power flow model, and mainly comprising the following steps:
1.1) establishing a mean square error loss function, namely:
Figure FDA0002855678260000045
in the formula, xlIs the input of the l-th layer DAE, i.e., the intermediate layer output y of the l-1-th layer DAEl-1；zlIs the output of the l-th layer DAE;
Figure FDA0002855678260000046
to optimize the objective function;
1.2) training parameters of DAEs of each layer by using a root mean square propagation algorithm, wherein the parameter updating formulas of DAEs of each layer in the training process are shown as a formula (6) to a formula (15);
after the T +1 th parameter is updated, the jth neuron of the first-1 DAE middle layer to the ith neuron of the first DAE middle layerWeight of each neuron
Figure FDA0002855678260000047
As follows:
Figure FDA0002855678260000048
in the formula (I), the compound is shown in the specification,
Figure FDA0002855678260000049
the weight value from the jth neuron in the middle layer of the (l-1) th DAE to the ith neuron in the middle layer of the l-1 th DAE after the T +1 th parameter updating;
Figure FDA00028556782600000410
the weight value from the jth neuron in the middle layer of the (l-1) th DAE to the ith neuron in the middle layer of the l-1 th DAE after the Tth parameter updating;
bias of ith neuron in ith DAE middle layer after T +1 th parameter update
Figure FDA0002855678260000051
As follows:
Figure FDA0002855678260000052
in the formula (I), the compound is shown in the specification,
Figure FDA0002855678260000053
is the bias of the ith neuron in the middle layer of the first-layer DAE after the Tth parameter is updated;
wherein, after the Tth parameter is updated for the first time, the weight values of the jth neuron of the l-1 th DAE middle layer to the ith neuron of the l-1 th DAE middle layer
Figure FDA0002855678260000054
Weight change in update process
Figure FDA0002855678260000055
As follows:
Figure FDA0002855678260000056
Figure FDA0002855678260000057
Figure FDA0002855678260000058
wherein, after the Tth parameter updating, the bias of the ith neuron of the ith DAE middle layer
Figure FDA0002855678260000059
Bias change in update procedure
Figure FDA00028556782600000510
As follows:
Figure FDA00028556782600000511
Figure FDA00028556782600000512
Figure FDA00028556782600000513
in the formula (I), the compound is shown in the specification,
Figure FDA00028556782600000514
represents the Hadamard product; η is the learning rate; ρ is a gradient accumulation index; k is an arbitrary sample;
Figure FDA00028556782600000515
the weight value from the jth neuron in the middle layer of the first-1 DAE layer to the ith neuron in the middle layer of the first DAE layer after the T-1 time of parameter updating;
Figure FDA00028556782600000516
the weight value from the jth neuron in the middle layer of the (l-1) th DAE to the ith neuron in the middle layer of the l-1 th DAE after the Tth parameter updating;
Figure FDA0002855678260000061
the gradient accumulated for the previous T times of weight iteration;
Figure FDA0002855678260000062
the gradient accumulated by the first T-1 times of weight iteration; Δ is the incremental sign; d is a differential sign; σ is a constant;
Figure FDA0002855678260000063
is a partial derivative symbol;
Figure FDA0002855678260000064
according to the output of the top layer
Figure FDA0002855678260000065
Constructing a mean square error loss function with the training sample output y; k is an arbitrary sample;
Figure FDA0002855678260000066
is the bias of the ith neuron in the middle layer of the first-layer DAE after the Tth parameter is updated;
Figure FDA0002855678260000067
is the bias of the ith neuron in the middle layer of the first-layer DAE after the T-1 parameter updating;
Figure FDA0002855678260000068
gradients accumulated for the previous T bias iterations;
Figure FDA0002855678260000069
the gradient accumulated by the first T-1 times of bias iteration; m is the number of samples;
1.3) introducing momentum learning rate as an additional item, and updating the formula (16) to the formula (19) to obtain the weight value change quantity shown in the formula (22) and the formula (23)
Figure FDA00028556782600000610
And amount of change in bias
Figure FDA00028556782600000611
Namely:
Figure FDA00028556782600000612
Figure FDA00028556782600000613
wherein p is a momentum learning rate;
1.4) calculating the optimal coding parameter theta of each layer of DAE according to an unsupervised pre-training parameter updating formula, and taking the optimal coding parameter theta as an initial coding parameter with supervision and fine adjustment;
2) carrying out supervised fine tuning on an original SDAE power flow model, and mainly comprising the following steps:
2.1) output according to the top layer
Figure FDA00028556782600000614
And training sample output y constructMaking a mean square error loss function L to obtain an optimized objective function argθminJ(W,b)；
argθminJ(W,b)＝argθminL； (24)
2.2) according to the optimization objective function argθminJ (W, b), and performing fine adjustment on the optimal coding parameter theta of the original SDAE power flow model by adopting expressions (14) to (23) to obtain the trained SDAE power flow model.
5. The method for improving the expansibility of the deep neural network power flow model according to claim 1, wherein the main steps for solving the probabilistic power flow of the augmentation system are as follows:
1) collecting training samples and training and expanding a DNN power flow model;
2) sampling the state of the extension system by adopting a Monte Carlo method;
3) and calculating the probability load flow result of the extension system by using the extension DNN load flow model, wherein the probability load flow result comprises the average value and the standard deviation of the variables and the probability density function of all output variables.
CN201910938908.XA 2019-09-30 2019-09-30 Method for improving expansibility of deep neural network tidal current model Active CN110829434B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910938908.XA CN110829434B (en) 2019-09-30 2019-09-30 Method for improving expansibility of deep neural network tidal current model

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910938908.XA CN110829434B (en) 2019-09-30 2019-09-30 Method for improving expansibility of deep neural network tidal current model

Publications (2)

Publication Number Publication Date
CN110829434A CN110829434A (en) 2020-02-21
CN110829434B true CN110829434B (en) 2021-04-06

Family

ID=69548499

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910938908.XA Active CN110829434B (en) 2019-09-30 2019-09-30 Method for improving expansibility of deep neural network tidal current model

Country Status (1)

Country Link
CN (1) CN110829434B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116451085A (en) * 2023-06-19 2023-07-18 中铁电气化勘测设计研究院有限公司 Power supply flow real-time calculation method based on rail transit power monitoring platform

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104503235A (en) * 2014-12-09 2015-04-08 中国石油大学(华东) Condition monitoring method based on improved BP neural network for power plant equipment
CN106651766A (en) * 2016-12-30 2017-05-10 深圳市唯特视科技有限公司 Image style migration method based on deep convolutional neural network
CN110110434A (en) * 2019-05-05 2019-08-09 重庆大学 A kind of initial method that Probabilistic Load Flow deep neural network calculates

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5469528A (en) * 1992-09-16 1995-11-21 Syseca, Inc. Neural load disturbance analyzer
CN109873425B (en) * 2017-12-01 2023-10-20 中国电力科学研究院有限公司 Power system power flow adjustment method and system based on deep learning and user behavior
CN109117951B (en) * 2018-01-15 2021-11-16 重庆大学 BP neural network-based probability load flow online calculation method
CN108304623B (en) * 2018-01-15 2021-05-04 重庆大学 Probability load flow online calculation method based on stack noise reduction automatic encoder
CN108599172B (en) * 2018-05-18 2021-07-30 广东电网有限责任公司佛山供电局 Transmission and distribution network global load flow calculation method based on artificial neural network
CN109599872B (en) * 2018-12-29 2022-11-08 重庆大学 Power system probability load flow calculation method based on stack noise reduction automatic encoder
CN109902854B (en) * 2019-01-11 2020-11-27 重庆大学 Method for constructing optimal power flow full-linear model of electric-gas interconnection system
CN110163540B (en) * 2019-06-28 2021-06-15 清华大学 Power system transient stability prevention control method and system

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104503235A (en) * 2014-12-09 2015-04-08 中国石油大学(华东) Condition monitoring method based on improved BP neural network for power plant equipment
CN106651766A (en) * 2016-12-30 2017-05-10 深圳市唯特视科技有限公司 Image style migration method based on deep convolutional neural network
CN110110434A (en) * 2019-05-05 2019-08-09 重庆大学 A kind of initial method that Probabilistic Load Flow deep neural network calculates

Also Published As

Publication number Publication date
CN110829434A (en) 2020-02-21

Similar Documents

Publication Publication Date Title
Gao et al. Day-ahead power forecasting in a large-scale photovoltaic plant based on weather classification using LSTM
CN109117951B (en) BP neural network-based probability load flow online calculation method
CN108304623B (en) Probability load flow online calculation method based on stack noise reduction automatic encoder
Aly An intelligent hybrid model of neuro Wavelet, time series and Recurrent Kalman Filter for wind speed forecasting
Gensler et al. Deep Learning for solar power forecasting—An approach using AutoEncoder and LSTM Neural Networks
CN111860982A (en) Wind power plant short-term wind power prediction method based on VMD-FCM-GRU
CN108734391B (en) Method for calculating probability energy flux of electricity-gas integrated energy system based on stack noise reduction automatic encoder
Huang et al. Prediction of wind power by chaos and BP artificial neural networks approach based on genetic algorithm
CN106022521B (en) Short-term load prediction method of distributed BP neural network based on Hadoop architecture
CN109599872B (en) Power system probability load flow calculation method based on stack noise reduction automatic encoder
CN109711617B (en) Medium-and-long-term runoff prediction method based on BLSTM deep learning
CN110580543A (en) Power load prediction method and system based on deep belief network
CN110942194A (en) Wind power prediction error interval evaluation method based on TCN
CN109088407B (en) Power distribution network state estimation method based on deep belief network pseudo-measurement modeling
CN104636985A (en) Method for predicting radio disturbance of electric transmission line by using improved BP (back propagation) neural network
CN109412161B (en) Power system probability load flow calculation method and system
CN110443724B (en) Electric power system rapid state estimation method based on deep learning
CN112116130B (en) Short-term scheduling rule extraction method based on variable structure deep learning framework
CN113553755B (en) Power system state estimation method, device and equipment
CN112016736A (en) Photovoltaic power generation power control method based on gate control convolution and attention mechanism
CN111415010A (en) Bayesian neural network-based wind turbine generator parameter identification method
Li et al. Short-term prediction of the power of a new wind turbine based on IAO-LSTM
CN110829434B (en) Method for improving expansibility of deep neural network tidal current model
CN109408896B (en) Multi-element intelligent real-time monitoring method for anaerobic sewage treatment gas production
CN114861874A (en) Model-driven graph convolution neural network load flow calculation method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant