Power system sample generation method based on physical information generative adversarial network

Abstract

The invention discloses a power system sample generation method based on a physical information generative adversarial network, and the method comprises the steps: 1), obtaining a large number of training samples through PSD-BPA simulation, extracting the characteristic quantity of each generator, and taking the stability result of the samples as original data; 2) training an original SSAE (Stacked Sparse Autoencoder) by using the original data, and screening out a critical sample according to a predicted value of the sample; 3) training a generative adversarial neural network fused with physical information according to the screened critical samples to obtain a critical sample generation model; 4) generating a critical sample set by using the trained critical sample generation model, and constructing an enhanced critical sample set based on the original sample set and the critical sample set; and 5) training a transient stability evaluation model based on data driving by using the enhanced critical sample set. According to the method, the data conforming to the dynamic equation of the power system can be generated, and the evaluation accuracy of the model can be effectively improved by training the model through the training set after critical sample enhancement.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and specifically to a method for generating power system samples based on physical information generation and adversarial neural networks. Background Art

[0002] Data-driven research in the field of power systems is currently a hot topic. Data-driven machine learning models offer fast computational speed and high accuracy, enabling them to fit the classification boundaries of many classification problems in the power system field. The performance of data-driven transient stability assessment models depends heavily on the samples used for training.

[0003] With the widespread deployment of PMUs and the rapid development of WAMS, the actual operating data of various system components is transmitted to the control center through PMU collection and communication lines. The system data collected by PMUs lays a solid foundation for data-driven power system transient stability assessment. However, due to the robustness of power systems, the number of critical samples on the stability boundary in the training set used for training is far less than that of samples at other locations. Assigning larger training weights to samples at the stability boundary does not effectively improve the ability to fit the stability boundary, so the model's fit to the stability boundary remains insufficient.

[0004] By using a generative adversarial neural network, a dynamic process sample generation model for power systems can be constructed. Furthermore, by introducing physical loss constraints, the physical conformity of the samples generated by the generative adversarial neural network can be improved. Therefore, the present invention constructs a power system sample generation method based on a physical information generative adversarial network, capable of generating critical transient stability samples that conform to physical constraints. Summary of the Invention

[0005] The performance of the data-driven transient stability assessment (TSA) model is affected by the quality of the sample set. However, the lack of critical samples on the stability boundary in the sample set will lead to an inaccurate fitting of the model to the stability boundary. The present invention provides a method for generating power system samples based on a physical information-generated adversarial neural network, which can strengthen the critical samples on the stability boundary and make the generated samples conform to the dynamic process of the power system by introducing physical information constraints. The method can generate data that conforms to the dynamic equations of the power system, and the training model with the training set enhanced by critical samples can effectively improve the evaluation accuracy of the model.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is: a method for generating power system samples based on physical information generative adversarial networks, comprising:

[0007] 1) Obtain a large number of training samples through PSD-BPA simulation, extract the characteristic quantities of each generator, and the stability results of the samples as raw data;

[0008] 2) Use the original data to train the original stacked sparse autoencoder SSAE and screen out critical samples based on the predicted values ​​of the samples;

[0009] 3) Based on the selected critical samples, a generative adversarial neural network integrating physical information is trained to obtain a critical sample generation model;

[0010] 4) Generate a critical sample set using the trained critical sample generation model, and construct an enhanced critical sample set based on the original sample set and the critical sample set;

[0011] 5) Use enhanced critical sample sets to train data-driven transient stability assessment models.

[0012] As a possible implementation, further, step 1) is specifically as follows:

[0013] Set different power system fault conditions and obtain a large number of training samples through PSD-BPA software simulation;

[0014] The power angle, speed deviation, unbalanced power and moment of inertia of each generator in the system are extracted as feature quantities, and the fault clearing moment and the subsequent 9 cycles as well as the stability of the sample are used as raw data.

[0015] As a possible implementation manner, further, the power system fault condition includes a power system load level, a fault location, a fault duration, and a fault type.

[0016] As a possible implementation, further, step 2) is specifically as follows:

[0017] The stacked sparse autoencoder (SSAE) is trained using the original dataset to obtain the initial TSA model. The samples whose output prediction values ​​are between (0.1, 0.9) in the original samples are then screened as critical samples using the initial TSA model.

[0018] As a possible implementation, further, step 3) specifically includes:

[0019] Using the selected boundary samples, a generative adversarial neural network based on a conditional generative adversarial neural network that integrates physical information is trained, so that the generated samples not only conform to the rotor motion equation of the generator, but also contain conditional information on stability.

[0020] Among them, the generator rotor motion equation that the power system transient process conforms to is shown in the following formula (1):

[0021]

[0022] Where, δ represents the power angle of the generator; is the first-order derivative of the power angle with respect to time; is the second-order derivative of the power angle with respect to time; ω is the angular velocity of the generator rotor; ω0 is the synchronous speed of the system, M is the moment of inertia of the generator; D is the damping coefficient of the generator; P m and P e are the mechanical power and electromagnetic power of the generator respectively, where the generator is in an undamped form;

[0023] Since the generator's power angle, rotor angular velocity and unbalanced power are constrained by the rotor motion equation during the system disturbance, the goal of generating samples that conform to the rotor motion equation is achieved by introducing physical penalty terms in the training process of the generative adversarial neural network.

[0024] The physical information generative adversarial neural network is based on the structure of the conditional generative network CGAN. The training objective function of the conditional generative adversarial neural network is shown in the following formula (2):

[0025]

[0026] Where x is the real sample; P r(x) is the probability distribution of the real sample; z is random noise; P z(x) is the probability distribution of random noise; y is the conditional information, where the conditional information y = 1 for stable samples and y = 0 for unstable samples; D(·|y) is the discriminator; G(·|y) is the generator; E represents the mathematical expectation;

[0027] The Wasserstein GAN with gradient penalty is introduced to improve the loss function of CGAN. The improved training objective function is shown in the following formula (3):

[0028]

[0029] Where λ is the weight of the gradient penalty; is a random interpolation between the real sample x and the generated sample G(z|y); For the discriminator pair Derivative; ||·||2 is the 2-norm;

[0030] The RMSE between the sample power angle derivative and the speed deviation and between the speed deviation derivative and the unbalanced power is calculated to reflect the degree of fit of the sample to the rotor motion equation, as shown in the following formulas (4) and (5):

[0031]

[0032] Where n is the number of features of the sample, is the first-order derivative of the rotor angular velocity with respect to time;

[0033] The physical loss term of the physical information generation adversarial network is shown in the following formula (6):

[0034]

[0035] Where, γ phy The physical constraint coefficient is a hyperparameter;

[0036] The physical loss term is introduced into the training loss function of the generator of the physical information generative adversarial network of the model, as shown in the following formula (7):

[0037]

[0038] Where λ phy is the physical loss weight;

[0039] The loss function of the discriminator of the physical information generation adversarial network is shown in the following formula (8):

[0040]

[0041] After constructing the generator neural network and the discriminator neural network, the generator and the discriminator are alternately trained according to the above loss function to realize the training of the physical information generation adversarial network.

[0042] As a possible implementation, further, step 4) is specifically as follows:

[0043] Random noise of 10% of the size of the original sample set is input into the generator part of the trained physical information generative adversarial network to generate a critical sample set of 10% of the size of the original sample set and merge it with the original sample set to construct an enhanced critical sample set.

[0044] As a possible implementation manner, further, the method for generating power system samples based on physical information generative adversarial networks also includes: 6) using a transient stability assessment model to perform stability assessment on the power system state.

[0045] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art:

[0046] 1. By introducing the degree of fit of the generated samples to the generator rotor motion equation as the physical loss term of the loss function of the generative adversarial neural network, the present invention can effectively improve the degree of fit of the generated samples to the rotor motion equation and generate samples that are more in line with real physical laws.

[0047] 2. When generating samples that are more in line with real physical laws, the present invention can improve the distribution similarity between the generated samples and the original critical samples. That is, after introducing physical constraints, the samples generated by the generative adversarial network can be closer to real samples.

[0048] 3. The present invention effectively enhances the evaluation accuracy of the TSA model by only strengthening the critical samples close to the stability boundary, while placing less burden on TSA model training. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0050] Figure 1 It is a simplified flow chart of the present invention;

[0051] Figure 2 This is the wiring diagram of the IEEE 39-node system. DETAILED DESCRIPTION

[0052] The present invention will be described in further detail below with reference to the accompanying drawings and examples. It is particularly noted that the following examples are intended only to illustrate the present invention and are not intended to limit the scope of the present invention. Similarly, the following examples are only some embodiments of the present invention and are not intended to be exhaustive. All other embodiments obtained by those of ordinary skill in the art without creative effort are intended to fall within the scope of protection of the present invention.

[0053] Refer to the attached Figure 1 As shown, the present invention provides a method for generating power system samples based on a physical information generative adversarial network, comprising:

[0054] 1) Obtain a large number of training samples through PSD-BPA simulation, extract the characteristic quantities of each generator, and the stability results of the samples as raw data;

[0055] 2) Use the original data to train the original stacked sparse autoencoder SSAE and screen out critical samples based on the predicted values ​​of the samples;

[0056] 3) Based on the selected critical samples, a generative adversarial neural network integrating physical information is trained to obtain a critical sample generation model;

[0057] 4) Generate a critical sample set using the trained critical sample generation model, and construct an enhanced critical sample set based on the original sample set and the critical sample set;

[0058] 5) Using enhanced critical sample sets to train data-driven transient stability assessment models;

[0059] 6) Use the transient stability assessment model to conduct stability assessment on the power system status.

[0060] The power system sample generation method based on physical information generation adversarial neural network provided by the present invention can strengthen the critical samples at the stability boundary and make the generated samples conform to the dynamic process of the power system by introducing physical information constraints; this method can generate data that conforms to the dynamic equations of the power system, and the training model with the training set enhanced by critical samples can effectively improve the evaluation accuracy of the model.

[0061] Example 1

[0062] This embodiment provides a method for generating power system samples based on a physical information generative adversarial network, which specifically includes the following steps:

[0063] 1) A large number of training samples were obtained through PSD-BPA software simulation according to different power system load levels, fault locations, fault durations, and fault types. The power angle, speed deviation, unbalanced power, and moment of inertia of each generator in the system were extracted as feature quantities. The fault clearing moment and the subsequent nine cycles, as well as the stability of the samples, were used as raw data.

[0064] 2) The stacked sparse autoencoder (SSAE) is trained using the original dataset to obtain the initial TSA model. The samples whose output prediction values ​​are between (0.1, 0.9) in the original samples are then screened as critical samples using the initial TSA model.

[0065] 3) Using the screened boundary samples, a generative adversarial neural network based on a conditional generative adversarial neural network that integrates physical information is trained, so that the generated samples not only conform to the rotor motion equation of the generator, but also carry conditional information on stability.

[0066] Among them, the generator rotor motion equation that the power system transient process conforms to is shown in the following formula (1):

[0067]

[0068] Where, δ represents the power angle of the generator; is the first-order derivative of the power angle with respect to time; is the second-order derivative of the power angle with respect to time; ω is the angular velocity of the generator rotor; ω0 is the synchronous speed of the system, M is the moment of inertia of the generator; D is the damping coefficient of the generator; P m and P eare the mechanical power and electromagnetic power of the generator respectively. In order to simplify the calculation, the generator is assumed to be undamped in this paper.

[0069] Since the generator's power angle, rotor angular velocity and unbalanced power are constrained by the rotor motion equation during the system disturbance, the goal of generating samples that conform to the rotor motion equation is achieved by introducing physical penalty terms in the training process of the generative adversarial neural network.

[0070] The physical information generative adversarial neural network is based on the structure of the conditional generative network (CGAN). The training objective function of the conditional generative adversarial neural network is shown in the following formula (2):

[0071]

[0072] Where x is the real sample; P r(x) is the probability distribution of the real sample; z is random noise; P z(x) is the probability distribution of random noise; y is the conditional information, where the conditional information y=1 for stable samples and y=0 for unstable samples; D(·|y) is the discriminator; G(·|y) is the generator; E represents the mathematical expectation.

[0073] The original CGAN has problems with gradient vanishing and mode collapse, so the WassersteinGAN with gradient penalty is introduced to improve the loss function of CGAN. The improved training objective function is shown in the following formula (3):

[0074]

[0075] Where λ is the weight of the gradient penalty; is a random interpolation between the real sample x and the generated sample G(z|y); For the discriminator pair Derivative; ||·||2 is the 2-norm.

[0076] The root mean square error (RMSE) between the sample power angle derivative and the speed deviation and between the speed deviation derivative and the unbalanced power is calculated to reflect the degree of fit of the sample to the rotor motion equation, as shown in the following formulas (4) and (5):

[0077]

[0078] Where n is the number of features of the sample, is the first derivative of the rotor angular velocity with respect to time.

[0079] The physical loss term of the physical information generation adversarial network is shown in the following formula (6):

[0080]

[0081] Where, γ phy The physical constraint coefficient is a hyperparameter.

[0082] The training loss function of the generator of the physical information generative adversarial network that introduces the physical loss term into the model is shown in the following formula (7):

[0083]

[0084] Where λ phy is the physical loss weight.

[0085] The loss function of the discriminator of the physical information generation adversarial network is shown in the following formula (8):

[0086]

[0087] After constructing the generator neural network and the discriminator neural network, the generator and the discriminator are alternately trained according to the above loss function to realize the training of the physical information generation adversarial network.

[0088] 4) Random noise of 10% of the size of the original sample set is input into the generator part of the trained physical information generative adversarial network to generate a critical sample set of 10% of the size of the original sample set and merge it with the original sample set to construct an enhanced critical sample set.

[0089] 5) Use the enhanced critical sample set to train a data-driven transient stability assessment (TSA) model.

[0090] 6) Use the transient stability assessment model to conduct stability assessment on the power system status.

[0091] The following provides a specific application example:

[0092] The PSD-BPA simulation software is used to simulate the IEEE39 node system (such as the attached Figure 2 33 lines (shown in Figure 2) were selected as fault lines, with three-phase short-circuit faults set at 10%, 50%, and 90% of the line length. The system load level increased from 85% to 115% in steps of 5%. The fault duration increased from 6 to 20 cycles in steps of 0.5 cycles. 20,115 samples were generated through simulation, of which 10,230 were stable samples and 9,885 were unstable samples. The power angle, angular velocity, and unbalanced power of each generator were selected as the original features for 9 cycles after the fault was cleared. The sample set was used to train the SSAE model and extract the critical samples from the original sample set.

[0093] To validate the effectiveness of the proposed criticality enhancement method, we focused on the similarity of the generated samples' distributions to the original samples and their fit to the rotor's equations of motion. We used the Fréchet distance (FID) and Wasserstein distance (WD) as metrics for sample distribution similarity. We also used the symmetric mean absolute percentage error (sMAPE) as a metric to assess the physical consistency of the generated samples.

[0094] The proposed physics-informed generative adversarial network (PIGAN) was compared with existing commonly used data augmentation techniques. The algorithms included GAN, CGAN, DCGAN, WGAN, and WGAN-GP. Five-fold cross-validation was performed to determine the optimal hyperparameters. The results of enhancing critical samples using different generator models were compared, as shown in Table 1.

[0095] Table 1 Feature data recovery effects of different models

[0096]

[0097] As can be seen in Table 1, the sample augmentation performance of the PIGAN algorithm is significantly improved compared to other sample augmentation algorithms. The proposed PIGAN achieves the best FID and WD metrics. This demonstrates that introducing physical loss during model training can enhance the ability of generated samples to fit real data to a certain extent. Furthermore, the average sMAPE of the generated samples is minimal, indicating that the generated samples better fit physical laws and are more consistent with the rotor motion equations of the generator in the power system.

[0098] The above descriptions are only some embodiments of the present invention and do not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for generating power system samples based on physical information generative adversarial networks, characterized in that: include: 1) Obtain a large number of training samples through PSD-BPA simulation, extract the characteristic quantities of each generator, and the stability results of the samples as raw data; 2) Use the original data to train the original stacked sparse autoencoder SSAE and screen out critical samples based on the predicted values ​​of the samples; 3) Based on the selected critical samples, a generative adversarial neural network integrating physical information is trained to obtain a critical sample generation model; 4) Generate a critical sample set using the trained critical sample generation model, and construct an enhanced critical sample set based on the original sample set and the critical sample set; 5) Use enhanced critical sample sets to train data-driven transient stability assessment models.

2. The method for generating power system samples based on physical information generative adversarial networks according to claim 1, characterized in that: Step 1) is as follows: Set different power system fault conditions and obtain a large number of training samples through PSD-BPA software simulation; The power angle, speed deviation, unbalanced power and moment of inertia of each generator in the system are extracted as feature quantities, and the fault clearing moment and the subsequent 9 cycles as well as the stability of the sample are used as raw data.

3. The method for generating power system samples based on physical information generative adversarial networks according to claim 2, characterized in that: The power system fault conditions include power system load level, fault location, fault duration, and fault type.

4. The method for generating power system samples based on physical information generative adversarial networks according to claim 1, characterized in that: Step 2) is as follows: The stacked sparse autoencoder (SSAE) is trained using the original dataset to obtain the initial TSA model. The samples whose output prediction values ​​are between (0.1, 0.9) in the original samples are then screened as critical samples using the initial TSA model.

5. The method for generating power system samples based on physical information generative adversarial networks according to claim 1, characterized in that: Step 3) specifically includes: Using the selected boundary samples, a generative adversarial neural network based on a conditional generative adversarial neural network that integrates physical information is trained, so that the generated samples not only conform to the rotor motion equation of the generator, but also contain conditional information on stability. Among them, the generator rotor motion equation that the power system transient process conforms to is shown in the following formula (1): Where, δ represents the power angle of the generator; is the first-order derivative of the power angle with respect to time; is the second-order derivative of the power angle with respect to time; ω is the angular velocity of the generator rotor; ω0 is the synchronous speed of the system, M is the moment of inertia of the generator; D is the damping coefficient of the generator; P m and P e are the mechanical power and electromagnetic power of the generator respectively, where the generator is in an undamped form; The physical information generative adversarial neural network is based on the structure of the conditional generative network CGAN. The training objective function of the conditional generative adversarial neural network is shown in the following formula (2): Where x is the real sample; P r(x) is the probability distribution of the real sample; z is random noise; P z(x) is the probability distribution of random noise; y is the conditional information, where the conditional information y = 1 for stable samples and y = 0 for unstable samples; D(·|y) is the discriminator; G(·|y) is the generator; E represents the mathematical expectation; The Wasserstein GAN with gradient penalty is introduced to improve the loss function of CGAN. The improved training objective function is shown in the following formula (3): Where λ is the weight of the gradient penalty; is a random interpolation between the real sample x and the generated sample G(z|y); For the discriminator pair Derivative; ||·||2 is the 2-norm; The RMSE between the sample power angle derivative and the speed deviation and between the speed deviation derivative and the unbalanced power is calculated to reflect the degree of fit of the sample to the rotor motion equation, as shown in the following formulas (4) and (5): Where n is the number of features of the sample, is the first-order derivative of the rotor angular velocity with respect to time; The physical loss term of the physical information generation adversarial network is shown in the following formula (6): Where, γ phy The physical constraint coefficient is a hyperparameter; The physical loss term is introduced into the training loss function of the generator of the physical information generative adversarial network of the model, as shown in the following formula (7): Where λ phy is the physical loss weight; The loss function of the discriminator of the physical information generation adversarial network is shown in the following formula (8): After constructing the generator neural network and the discriminator neural network, the generator and the discriminator are alternately trained according to the above loss function to realize the training of the physical information generation adversarial network.

6. The method for generating power system samples based on physical information generative adversarial networks according to claim 1, characterized in that: Step 4) is as follows: Random noise of 10% of the size of the original sample set is input into the generator part of the trained physical information generative adversarial network to generate a critical sample set of 10% of the size of the original sample set and merge it with the original sample set to construct an enhanced critical sample set.

7. The method for generating power system samples based on a physical information generative adversarial network according to any one of claims 1 to 6, characterized in that: Also includes: 6) Use the transient stability assessment model to conduct stability assessment on the power system status.

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