Static voltage stability boundary calculation method and system based on deep neural network

Abstract

The application discloses a static voltage stability boundary calculation method and system based on a deep neural network. The static voltage stability boundary point sample set is obtained by calling the continuation power flow method to detect the PV curve nose point for multiple times; the static voltage stability boundary model of a complex high-dimensional power system is established by taking the power growth mode as input features and taking the maximum power growth as an output variable; since the uniformity of the sample has a great influence on the model, the "baffle method" which can uniformly generate feature sets in the sample space is proposed; the static voltage stability boundary sample is generated based on the "baffle method" in the IEEE9 and IEEE39 node systems, and compared with the Monte Carlo random sample, the uniformity and efficiency of the sample generated by the "baffle method" are higher; the static voltage stability boundary model of the system is constructed based on the deep neural network, and compared with the boundary detected by the continuation power flow method, the accuracy of the model is verified, and compared with the time domain simulation boundary, the effectiveness of the model is verified.

Description

Technical Field

[0001] This invention belongs to the field of static voltage stability analysis of power systems, and specifically relates to a method and system for calculating static voltage stability boundaries based on deep neural networks. Background Technology

[0002] In recent years, with the increasing prominence of fossil fuel shortages, environmental pollution, and climate change issues... [1] Traditional power systems are transforming towards green and low-carbon development. [2-3] With the extensive integration of new energy sources on the power supply side, the randomness of system power fluctuations is greatly enhanced. [4] .

[0003] Common continuous power flow methods assume, based on experience, a power growth pattern and use the power limit under this growth pattern as the static voltage stability limit of the system. [5-6] In power systems where a large number of new energy sources are integrated and the randomness of power changes is enhanced, the error of the stability margin index based on the continuous power flow method will increase significantly, making it difficult to meet the requirements.

[0004] The static voltage stability domain method can provide power limit information under all growth modes, becoming an effective means to address the randomness of power variation. [7] The key lies in constructing the static voltage stability boundary. The static voltage stability boundary is a complex nonlinear surface in the nodal injected power space. [8] Currently, there is no analytical expression for the static voltage stability boundary of complex power systems; it can only be approximated by algorithms. Existing methods are broadly classified into point-by-point methods. [9] Boundary fitting method [10-15] Parameter tracking method [16-18] There are three categories. All three methods for obtaining SVSRB have certain limitations. The pointwise method has high accuracy, but the computational cost is large and it is difficult to guarantee real-time performance. The boundary fitting method and the parameter tracking method have fast computation speed. Existing boundary fitting methods usually take a certain boundary point as the reference and perform high-order expansion to obtain an approximate stable boundary expression. It has high accuracy near the expansion point, but the global accuracy is limited. The parameter tracking method has the problem that the tracking difficulty increases when the stable boundary is not smooth.

[0005] With the development of deep learning technology, deep learning has been applied in various industries. Many scholars have studied the application of deep learning in static voltage stability assessment. The literature mainly focuses on how to improve the accuracy and generalization ability of deep learning models, and the difference between different documents mainly lies in the input feature extraction method and the selection of the model. Literature

[19] proposes to use a radial basis neural network to estimate the system static voltage stability margin, taking the node voltage, system reactive power reserve, and reactive power loss as input features, and taking the load margin index as the output variable, to construct the mapping relationship between system state and stability margin. Literature

[20] is based on parallel self-organizing hierarchical neural network, taking the active and reactive power of the node as the input feature, and taking the load margin as the output variable, and using entropy-based feature selection to reduce the dimension of the feature variable, greatly reducing the number of artificial neural networks, and finally realizing the online emergency ordering of system node voltage. Literature

[21] is based on transfer learning and generative adversarial network, and proposes a static voltage critical sample generation method with voltage as sample feature variable of non-connected node, which can avoid the convergence problem of power flow sample and the non-zero power problem of tie node, and can more effectively generate high-quality samples. Literature

[22] is based on convolutional neural network, taking the power flow Jacobian matrix as the feature input, and taking the static voltage stability margin of the system as the variable output, which maintains high prediction accuracy and strong generalization ability when the system network topology changes. Literature

[23] is based on Tri-Training-LASSO-BP network, taking the power of the power flow section as the feature input, dividing the samples into two categories: labeled and unlabeled, and through the Tri-Training method, the least absolute shrinkage and selection method, and the error back propagation neural network, the requirement for the amount of training set data of the model is reduced.

[0006] Applying deep learning to the construction of static voltage stability boundary can help to realize the accurate and fast construction of the static voltage stability boundary of complex power systems. Considering that deep neural networks have strong fitting ability, as long as the network depth and size are large enough, theoretically, they can fit any complex nonlinear mapping relationship. The static voltage stability boundary of complex power systems is a complex nonlinear surface in high-dimensional space, and the invention proposes to use deep neural networks to construct the static voltage stability boundary of any complex power system.

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[23] Tang Y Q, Dong S F, Zhu C Z, Wu J C, Song Y H. Static voltage stability margin online prediction method based on Tri-Training-LASSO-BP network[J]. Proceedings of the CSEE, 2020, 40(12): 3824-3835. SUMMARY

[0031] The application provides a static voltage stability boundary construction method and system based on a deep neural network, and can realize high-dimensional static voltage stability boundary construction of an arbitrary complex power system.

[0032] According to a first aspect of an embodiment of the application, a static voltage stability boundary calculation method based on a deep neural network is provided.

[0033] A general mathematical model of the static voltage stability boundary is determined,

[0034] u i =u b +b i F(b i )

[0035] F represents a mapping relationship between b i and λ imax :

[0036] λ max =F(b)

[0037] u i is an arbitrary point on the static voltage stability boundary, u b is an initial operating base state, b i is a power change mode of the initial operating base state u b to the static voltage stability boundary point u i , λ imax is a maximum power increment in the power change mode, u i and u b are high-dimensional column vectors, and the components of the column vectors are active power and reactive power in an injection power space.

[0038] A point in an R-dimensional injection power space is selected as an initial operating base state u b .

[0039] A baffle method is used to generate M power growth modes required for constructing the static voltage stability boundary, and a power growth mode sample set is established.

[0040] A continuous power flow method is used to calculate maximum power increments corresponding to the M power growth modes generated by the baffle method at the initial operating base state u b , and a maximum power increment sample set is constructed.

[0041] The power growth mode sample set and the maximum power increment sample set are one-to-one corresponding to form a complete sample set.

[0042] The complete sample set is used to train a deep neural network, and a mapping relationship F is fitted, wherein the power growth mode sample set is an input variable set of the deep neural network, and the maximum power increment sample set is an output variable set of the deep neural network.

[0043] Substitute the mapping relation F obtained by fitting into the above two formulas to obtain a static voltage stability boundary model.

[0044] According to a second aspect of the embodiment of the present application, a static voltage stability boundary calculation system based on a deep neural network is provided, comprising: a processor; a memory for storing instructions executable by the processor; wherein the processor is configured to execute all or part of the steps of the method.

[0045] According to a second aspect of the embodiment of the present application, a non-transitory computer-readable storage medium having a computer program stored thereon is provided, wherein the computer program is executed by a processor to implement all or part of the steps of the method.

[0046] Compared with the existing boundary fitting method, the global fitting accuracy of the present application is greatly improved; compared with the point-by-point detection of the continuous power flow method, the speed of calculating the boundary after the model training of the present application is greatly improved, and the accuracy and efficiency of constructing a complex power system are significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings of the embodiments will be briefly introduced below.

[0048] Figure 1 A flowchart of a static voltage stability boundary calculation method based on a deep neural network provided by an embodiment of the present application.

[0049] Figure 2 A schematic diagram of detecting a static voltage stability boundary by a continuous power flow method provided by an embodiment of the present application.

[0050] Figure 3 A schematic diagram of a "baffle method" provided by an embodiment of the present application.

[0051] Figure 4 An IEEE9 node example diagram provided by an embodiment of the present application.

[0052] Figure 5 An IEEE39 node example diagram provided by an embodiment of the present application.

[0053] Figure 6 A comparison diagram of the baffle method and Monte Carlo sample generation provided by an embodiment of the present application.

[0054] Figure 7 An iteration process schematic diagram of constructing an IEEE9 static voltage stability boundary provided by an embodiment of the present application.

[0055] Figure 8 A comparison diagram of an IEEE9 node system stability boundary provided by an embodiment of the present application.

[0056] Figure 9 An IEEE39 static voltage stability boundary construction iterative process schematic diagram is provided for an embodiment of the present application.

[0057] Figure 10 An IEEE39 node system maximum power growth limit schematic diagram is provided for an embodiment of the present application. DETAILED DESCRIPTION

[0058] Figure 1 A static voltage stability boundary calculation method based on a deep neural network is shown, which fully utilizes the global information of the static voltage stability boundary and improves the construction precision and efficiency. The method shown in the following will be described in detail. Figure 1

[0059] Step 1, determine the general mathematical model of the static voltage stability boundary.

[0060] (1) Based on the idea of detecting the boundary by the continuation power flow method, as shown in the following formula, the mathematical model of the static voltage stability boundary point can be expressed as: Figure 2

[0061] u i =u b +Δu i =u b +b i λ imax (1)

[0062] In the formula, u i is any point on the static voltage stability boundary, u b is the initial operating base state, b i is the power change mode from the initial operating base state u b to the static voltage stability boundary point u i , and λ imax is the maximum power increment under the power change mode. u i and u b are both high-dimensional column vectors, and the components of the column vectors are the active and reactive power in the injected power space.

[0063] (2) Considering that when the initial state u b is fixed, the power growth mode and the maximum power growth amount exist one-to-one correspondence, therefore the general mathematical model of the static voltage stability boundary point is:

[0064] u i =u b +b i F(b i ) (2)

[0065] Where F represents the mapping relationship between b i and λ imax :​​

[0066] λ max = F(b) (3)

[0067] The mapping relationship F is a complex nonlinear function of a high-dimensional space, and it is difficult to derive an analytical expression, and the application trains the mapping relationship by using a deep neural network.

[0068] Step 2, determining an initial ground state for constructing a static voltage stability boundary.

[0069] (1) determining an injection power space, the full-dimensional full injection power space of the system is:

[0070] u = [P1, P2...P n-1 , Q1, Q2...Q m ] (4)

[0071] The above formula represents an n+m-1 dimensional injection power space, wherein n is the number of system nodes, and m is the number of PQ nodes.

[0072] In an actual system, only power nodes with relatively large power variation randomness need to be considered, and therefore the injection power space is simplified as:

[0073] u = [u1, u2...u R ] (5)

[0074] The above formula represents an R-dimensional injection power space determined according to a specific research system, and R≤n+m-1.

[0075] (2) determining an initial operation ground state, since the initial operation ground state u b is contained in the general model of the static voltage stability boundary, and the mapping relationship F will be different when the initial operation ground state is selected differently, therefore a fixed initial operation ground state needs to be determined, which can be selected as the origin of the injection power space, that is:

[0076] u b = 0 (6)

[0077] Step 3, generating a power growth mode sample set required for constructing a static voltage stability boundary by using a baffle method.

[0078] (1) in the R-dimensional injection power space, an arbitrary power growth mode can be expressed as:

[0079]

[0080] In the formula, k i is a proportional coefficient, e i is a unit vector base. When the proportional coefficient k i takes different combinations, different power growth directions are represented, and when k iWhen the combination of the R-dimensional sample space covers the entire R-dimensional sample space, the corresponding power growth mode b will be evenly distributed in the entire R-dimensional sample space.

[0081] (2) Based on the principle of permutation and combination, as shown in the formula (2), R-1 baffles are used to separate D small balls to obtain the proportion coefficient, and the separation rule is as follows: Figure 3

[0082] 1) All small balls and all baffles are exactly the same, but there is a label order, which increases from left to right;

[0083] 2) The baffles can be placed in any one of the D+1 gaps;

[0084] 3) The same gap can place multiple baffles.

[0085] The R parts of small balls are separated by the above rules, and the number of small balls is represented as Num=[n1,n2…n R ] T .

[0086] The proportion coefficient is represented by the normalized number of small balls as:

[0087]

[0088] (3) Exhaust all ways of separating small balls with baffles, that is, each direction power growth mode can be generated uniformly in the sample space, according to the principle of permutation and combination, M power growth modes can be generated:

[0089]

[0090] (4) M power growth modes constitute a set, denoted as:

[0091] B={b1,b2,…b M},b i ∈R R×1 and ||b i ||2=1 (10)

[0092] Step 4, call the continuous flow method to calculate the maximum power growth corresponding to the power growth mode, and construct the maximum power growth sample set.

[0093] Call the continuous flow method program to calculate the maximum power growth corresponding to the M power growth modes generated by the baffle method under the base state u b , and construct a set denoted as:

[0094] Λ={λ 1max ,λ 2max …λ Mmax} (11)

[0095] ​Step 5, the power growth mode sample set and the large power growth sample set are one-to-one corresponding to form a complete sample set, wherein the former is the input variable set of the deep neural network, and the latter is the output variable set of the deep neural network.

[0096] Sample set:

[0097] P = {B, Λ} = {(b1, λ1), (b2, λ2)…(b M ,λ M )} (12)

[0098] Step 6, sample set data initialization, the sample set is divided into a training set and a test set according to a certain proportion, and the data in the sample set is normalized.

[0099] (1) The sample set data is divided into a training set and a test set according to a certain proportion:

[0100]

[0101] (2) Normalization processing of sample data:

[0102]

[0103] In the formula, μ is the mean of the characteristic variable, σ is the variance of the characteristic variable, and both are R-dimensional vectors:

[0104]

[0105] Step 7, initialization of the size and hyperparameters of the deep neural network.

[0106] (1) Constructing a deep neural network model: mainly including setting the depth (number of layers) of the deep neural network, setting the number of neurons of each layer of the deep neural network, setting the activation function of each layer of the neural network, setting the learning rate and the maximum number of iterations, and other hyperparameters.

[0107] (2) Initialization of the parameters of the deep neural network, mainly including the weight coefficient and the bias coefficient.

[0108] Step 8, training the deep neural network through the training set data, including three steps of forward propagation, backward propagation and model parameter updating, and the finally trained mapping relationship can be represented as:

[0109] Λ = g {L} (W {L} g {L-1} (…g {1} (W {1} B+Bios {1} ))+Bios {L} ) (16)

[0110] where L is the number of layers of the model, W and Bios are the trained weight and bias coefficients, g {l} represents the activation function of the l-th layer of neurons.

[0111] Step 9, detecting the fitting performance of the deep neural network, including the model fitting ability and the generalization ability detection, wherein the fitting ability is embodied by detecting the training set error, and the generalization ability is embodied by detecting the test set error.

[0112] Step 10, giving a static voltage stability boundary model based on the deep neural network, combining equations (2)-(3) and equation (16), the static voltage stability boundary model is expressed as:

[0113] u=u b +bg {L} (W {L} g {L-1} (…g {1} (W {1} b+Bios {1} ))+Bios {L} ) (17)

[0114] In an exemplary embodiment, a static voltage stability boundary construction system based on a deep neural network is also provided, the system comprising: a processor; a memory for storing instructions executable by the processor; wherein the processor is configured to perform all or part of the steps of the above method.

[0115] In an exemplary embodiment, a non-transitory computer readable storage medium having stored thereon a computer program is also provided, the computer program being executed by a processor to implement all or part of the steps of the above method. For example, the non-transitory computer readable storage medium can be a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device, etc.

[0116] The following takes IEEE9 and IEEE39 node systems as examples to verify the accuracy of the static voltage stability boundary construction based on the deep neural network. The IEEE9 node test system is as shown in Figure 4 , and the IEEE39 node test system is as shown in Figure 5 .

[0117] The IEEE9 node system selects nodes 5, 6 and 8 as key nodes, and the active power of nodes 5, 6 and 8 as the injection power space, and the power growth mode variable is selected as the increment of the active power of nodes 5, 6 and 8:

[0118] b=[b P5 ,b P6 ,b P8 ] (18)

[0119] The parameters of the baffle method are set as D = 60, and 1891 power growth modes are generated by the proposed baffle method, which is compared with the way of randomly generating samples by Monte Carlo method, as shown in Figure 6 It can be seen that the samples generated by the baffle method are more evenly distributed in the entire sample space, and the generation efficiency is higher.

[0120] The continuous power flow method is called to calculate the stable boundary points corresponding to the 1891 power growth modes, which is completed on a computer equipped with Intel Core i5-8400 2.8GHz CPU and 8GB RAM, and the total time consumption is 1003s, and part of the data is shown in Table 1.

[0121] Table 1. Part of the boundary point data of IEEE9 calculated by the continuous power flow method

[0122]

[0123] A 10-layer deep neural network is built based on python, and the configuration of each layer network is shown in Table 2:

[0124] Table 2. Deep neural network construction parameters

[0125]

[0126] The model parameters are randomly initialized, and the gradient descent training parameters are trained, and the learning rate is set to 0.0075. The model iteration training process is shown in Figure 7 The horizontal axis of the figure is the logarithmic value of the iteration number, and the vertical axis is the loss function value of the model training. After 10000 iterations, the time consumption is 180s. The loss function error of the training set has been reduced to 0.7x10 -5 , and at this time the error of the model parameters in the test set is 1.0x10 -5 .

[0127] The 3D static voltage stability boundary model constructed by the deep neural network is used to calculate the stable boundary under the 1891 power growth modes generated by the baffle method, which is still completed on a computer equipped with Intel Core i5-8400 2.8GHz CPU and 8GB RAM, and the total time consumption is 0.128s, which is 7836 times faster than the continuous power flow method. The static voltage stability boundary constructed by the deep neural network model is compared with the static voltage stability boundary detected by the continuous power flow method, as shown in Figure 8 The two are basically coincident. The absolute value of the difference in three variable dimensions is only 9.4967x10 -4 p.u., and the maximum error is only 1.8x10 -3 p.u., which shows that the static voltage stability boundary model based on deep neural network can accurately construct the static voltage stability boundary considering the randomness of load in the global range.

[0128] The IEEE 39-node system selects nodes 3, 23, 30, and 32 as critical nodes, using the active power of nodes 3, 23, 30, and 32 as the injected power space. The power growth method variable is selected as the increment of the active power of nodes 3, 23, 30, and 32.

[0129] b = [b P3 ,b P23 ,b P30 ,b P32 (19)

[0130] With the baffle method parameter D=29, 4960 power growth patterns were generated using the proposed baffle method. The continuous power flow method was then used to calculate the stable boundary points corresponding to these 4960 power growth patterns. This was completed on a computer equipped with an Intel Core i5-8400 2.8GHz CPU and 8GB RAM, taking a total of 100965 seconds. Some data are shown in Table 3.

[0131] Table 3 Boundary point data for some IEEE 99 examples calculated using the continuous power flow method.

[0132]

[0133] The model is randomly initialized, and gradient descent is used to train the parameters with a learning rate of 0.0075. The iterative training process of the model is as follows: Figure 9 As shown in the figure. The horizontal axis represents the logarithm of the number of iterations, and the vertical axis represents the loss function value during model training. After 10,000 iterations, the training time was 677 seconds. The training set loss function error was reduced to 1.5 × 10⁻⁶. -5 At this point, the error of the model parameters on the test set is 1.7 × 10⁻⁶. -5 .

[0134] Using a static voltage stability boundary model based on a deep neural network, the stability boundary was calculated for 4890 power growth patterns generated by the baffle method. This was completed on a computer equipped with an Intel Core i5-8400 2.8GHz CPU and 8GB of RAM, taking a total of 0.174 seconds. Compared to the continuous power flow method, this represents a 580,259-fold speed improvement. A comparison was made between the maximum power growth detected by the CPF and the maximum power growth output by the DNN model, such as... Figure 10 As shown, among 4960 growth methods, the average error of the absolute difference between the static voltage stability boundaries obtained by CPF and DNN across four variable dimensions is only 2.1 × 10⁻⁶. - 3 The maximum error of PU is only 3.2×10. -3 pu

[0135] The application provides a static voltage stability boundary construction method based on a deep neural network, which can be used for constructing a static voltage stability boundary of an arbitrary complex power system. According to the result, the method realizes accurate construction of the static voltage stability boundary in a global range.

Claims

1. A method for calculating the static voltage stability boundary based on a deep neural network, characterized in that, include: Determine the general mathematical model for the static voltage stability boundary. (1) F express b i and λ imax Mapping relationship: (2) u i Let be any point on the static voltage stability boundary. u b This is the initial operating ground state. b i The initial operating ground state u b To the static voltage stability boundary point u i The power change mode, λ imax This represents the maximum power increment under this power change pattern. u i and u b All are high-dimensional column vectors, and the components of the column vectors are the active and reactive power injected into the power space; Select a point in the R-dimensional injected power space as the initial operating ground state. u b ; The baffle method is used to generate the necessary parameters for constructing the static voltage stability boundary. M Identify different power growth methods and establish a sample set of power growth methods. Using the continuous power flow method, calculate the initial operating ground state. u b baffle method M Find the maximum power increase corresponding to each power increase method and construct a sample set of maximum power increase. By matching the power growth method sample set with the maximum power growth amount sample set one by one, a complete sample set is formed; A deep neural network is trained using the complete sample set to fit the mapping relationship. F The power growth method sample set is the input variable set of the deep neural network, and the maximum power growth amount sample set is the output variable set of the deep neural network. The fitted mapping relationship F Substituting into equations (1) and (2), we obtain the static voltage stability boundary model; Among them, R Injecting power space, any power growth method can be expressed as: (3) In the formula k i e is the proportionality coefficient. i As a unit vector basis, when the scaling factor k i Different combinations represent different directions of power growth. k i The combination methods cover the entire R When considering a 3D sample space, the corresponding power growth method... b It will be evenly distributed throughout R 3D sample space; Based on the principles of permutations and combinations, using R -1 baffle separation D We have a set of balls and a proportional coefficient. The separation rules are as follows: all balls and all barriers are exactly the same, but they are numbered sequentially from left to right; the barriers are placed... D +1 position within the gaps; there is no limit to the number of baffles that can be placed in the same gap; Separated by the above rules R The number of balls is represented as Num = [ n 1, n 2… n R ] T The proportionality coefficient is represented by the normalized number of balls: (4) Exhaustively enumerate all ways to separate the balls with baffles, uniformly generate power growth patterns in all directions in the sample space, and generate power growth patterns according to the principle of permutation and combination. M Power growth methods: (5) M The power growth methods constitute a power growth method sample set, denoted as: (6)。 2. The method according to claim 1, characterized in that, Select R The origin of the dimensional injection power space is used as the initial operating ground state. u b .

3. The method according to claim 1, characterized in that, The sample set of maximum power growth is denoted as: (7)。 4. The method according to claim 3, characterized in that, The complete sample set is denoted as: (8)。 5. The method according to claim 4, characterized in that, The mapping relationship obtained through training is represented as follows: (9) In the formula, L represents the number of model layers, and W and Bios are the trained weight and bias coefficients, respectively. Indicates the first Activation functions of layer neurons.

6. The method according to claim 5, characterized in that, Static voltage stability boundary model expression: (10)。 7. A static voltage stability boundary calculation system based on a deep neural network, characterized in that, include: processor; Memory used to store the processor's executable instructions; The processor is configured to perform the steps of the method according to any one of claims 1-6.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 6.

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