Two-stage transient voltage evaluation method suitable for direct current receiving end system

Abstract

The invention discloses a two-stage transient voltage evaluation method suitable for a direct current receiving end system. Firstly, a typical voltage instability scene containing a direct current power transmission system is built, and different fault types are set to generate a transient voltage sample set. Secondly, segmenting the transient voltage recovery process, dividing the transient voltage recovery process into two stages according to the voltage recovery speed in the transient voltage recovery process of the direct current system, and solving the duration of the transient voltage stage I; carrying out dimension reduction processing by utilizing a principal component analysis method, selecting a transient voltage stability key influence factor, and carrying out nonlinear fitting on the key influence factor and the transient voltage stability margin by utilizing a least square method; and finally, transient simulation verification is carried out in the built IEEE 3-machine 9-node system and the double-infeed direct-current power transmission system. According to the method, the judgment missing phenomenon of a traditional multi-binary table method in the direct current power transmission system is improved, the evaluation speed is high, and certain practicability and engineering reference value are achieved.

Description

Technical Field

[0001] The invention belongs to the field of transient voltage stability of AC and DC receiving ends, and in particular relates to a two-stage transient voltage evaluation method suitable for a DC receiving end system. Background Art

[0002] In order to achieve power transmission in heavy-load energy areas, high voltage direct current (HVDC) has become the mainstream long-distance, large-capacity regional power transmission method. With the increasing proportion of DC transmission equipment and new energy systems, the reactive power reserve capacity of the DC system has further decreased. In addition, the DC converter also needs to absorb a large amount of reactive power, making the transient voltage stability problem of the AC / DC system increasingly severe. Therefore, a transient voltage assessment method suitable for DC systems is urgently needed.

[0003] Most of the existing transient voltage assessment indicators are defined based on the transient voltage drop acceptability indicators established based on engineering experience. For example, after a power system failure, the duration of the bus voltage below 0.75pu does not exceed 1s, and the duration below 0.8pu does not exceed 10s. The multi-binary table indicator further refines its interval and the voltage drop interval, which can more accurately measure the transient voltage stability. However, this method can only perform qualitative analysis on the voltage and cannot be applied in real time, so it needs to be improved.

[0004] At the same time, existing voltage assessment methods are often based on the stability and practical criteria of the entire system, and few focus on transient voltage assessment methods for DC systems. Due to the complex transient characteristics of DC systems, their voltage recovery process presents an obvious segmented process, and the traditional multi-binary meter may misjudge the assessment results in DC systems.

[0005] To this end, based on the existing multi-binary table criteria and the transient recovery characteristics of the DC system, a two-stage transient voltage assessment method suitable for the DC receiving system is proposed. First, a typical voltage instability scenario involving a DC transmission system is built, and different fault types are set to generate a transient voltage sample set. Secondly, the transient voltage recovery process is segmented, and it is divided into two stages according to the voltage recovery speed during the transient voltage recovery process of the DC system, and the duration of transient voltage stage I is solved. Then, the principal component analysis method is used for dimensionality reduction, and the key influencing factors of transient voltage stability are selected. The least squares method is used to perform nonlinear fitting of the key influencing factors and the transient voltage stability margin. Finally, transient simulation verification is carried out in the constructed IEEE 3-machine 9-bus system and the doubly fed DC transmission system. Summary of the invention

[0006] In view of the shortcomings of the existing evaluation methods, the purpose of the present invention is to propose a two-stage transient voltage evaluation method suitable for a DC receiving-end system.

[0007] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows.

[0008] A two-stage transient voltage assessment method for DC receiving systems. First, a typical voltage instability scenario involving a DC transmission system is constructed, and different fault types are set to generate transient voltage sample sets. Secondly, the transient voltage recovery process is segmented, and it is divided into two stages according to the voltage recovery speed during the transient voltage recovery process of the DC system, and the duration of transient voltage stage I is solved. Then, the principal component analysis method is used for dimensionality reduction, the key influencing factors of transient voltage stability are selected, and the least squares method is used to perform nonlinear fitting of the key influencing factors and the transient voltage stability margin. Finally, transient simulation verification is carried out in the constructed IEEE 3-machine 9-bus system and the doubly fed DC transmission system.

[0009] As a preferred embodiment of the present invention, the scheme comprises the following steps:

[0010] S1: Establish typical voltage instability scenarios involving DC transmission systems and generate sample sets

[0011] S2: Dimensionality reduction based on principal component analysis

[0012] S3: Least squares method for fitting key voltage influencing factors and transient voltage stability margin

[0013] S4: Model evaluation and validation

[0014] Step S1 establishes a typical voltage instability scenario involving a DC transmission system and generates a sample set. The specific strategy is as follows:

[0015] Appropriate modifications are made to the IEEE 3-machine 9-node system, a DC transmission system is added, and the load model is modified to a comprehensive load model consisting of an induction motor load and a constant impedance load. By setting a three-phase short-circuit fault in the transient simulation model, the fault time varies randomly between 0.06s and 0.2s, and different transient voltage stability samples are generated. The bus active and reactive power, branch active and reactive power, DC trigger angle, delay angle, DC voltage, current and other information in the transient stage are recorded as a transient sample set.

[0016] Step S2 is based on principal component analysis for dimensionality reduction. The specific strategy is:

[0017] S21: Calculate the correlation coefficient matrix R, and use the Pearson correlation coefficient to calculate the correlation coefficients between the indicators, that is, the correlation coefficients between the columns;

[0018] S22: Calculate the eigenvalues ​​and eigenvectors of R: Calculate the eigenvalues ​​and arrange them in order from large to small, and the corresponding eigenvectors are also arranged accordingly. The eigenvalues ​​are: λ1≥λ2≥…≥λ n ≥0; its corresponding eigenvector is: e j =(l1,l2,…l n ).

[0019] S23: Calculate the principal component contribution rate and cumulative contribution rate, assuming that the contribution rate of the jth index is a j , assuming that the cumulative contribution rate of the first p indicators is a si :

[0020]

[0021] If the cumulative contribution rate of the first p indicators is greater than 85%, it can be considered that these p principal components can comprehensively reflect the indicators.

[0022] Step S3 uses the least square method to fit the key voltage influencing factors and the transient voltage stability margin. The specific strategy is:

[0023] S31: Calculate the sample transient voltage stability margin and use the drop area during the voltage fault to distinguish different stability margins. The larger the drop area, the lower the transient voltage stability.

[0024] S32: The least square method is used to perform regression fitting on the key voltage influencing factors and transient voltage stability margin to guide the selection of weights for improvement indicators.

[0025] Step S4: Model evaluation and verification. The specific strategy is:

[0026] S41: In the verification system, a large number of simulations are set up to set up training sets and verification sets

[0027] S42: Calculate the transient voltage evaluation index η value and evaluate the evaluation result, wherein the index η is calculated as shown in formula (2):

[0028]

[0029] Where U N is the rated voltage of the DC system, t0-t1 is the transient voltage stage I, t1-t2 is the transient voltage stage II, K is the weight coefficient, when η is less than 1, the voltage is stable, and when it is greater than 1, the voltage is unstable. The weight K can be assigned according to the function fitted in step S32, as shown in the following formula:

[0030]

[0031] In the formula, S is a continuous function composed of multiple parameters, which is used to measure the transient voltage stability margin index. The larger the S, the worse the stability level, and a larger value is assigned to K; when S is less than 1, a smaller value is assigned to K.

[0032] S43: Solve the duration of transient voltage recovery stage I:

[0033] By analyzing the transient recovery process of the DC transmission system, it is divided into two stages according to the voltage recovery speed during the transient voltage recovery process. The voltage recovery speed in transient stage I is fast, but the duration is short, while the recovery speed in transient stage II is fast, but the duration is long. Through simulation analysis and mechanism analysis, the key factors affecting the two recovery stages are studied, and the duration of transient stage I is calculated. The calculation formula is as follows:

[0034] t I =0.16f dc 3 +0.00002f dc 2 -0.02f dc +0.04435 (4)

[0035] where f dc is the DC system access ratio, which is obtained by the following formula:

[0036]

[0037] In the formula, S dc is the DC system capacity connected to the system, S ac is the total capacity of the AC system generators in the AC power grid.

[0038] S44: Evaluation of model evaluation results

[0039] To verify the model evaluation effect, define the model evaluation accuracy A CC , missed detection rate L A and the false positive rate F A as follows:

[0040]

[0041] Where T and F are the number of samples predicted correctly and incorrectly, respectively; the subscripts s and us represent the samples predicted to be stable and unstable, respectively. A Indicates the probability of evaluating an unstable sample as stable, and the misjudgment rate F A Represents the probability of evaluating a stable sample as unstable.

[0042] Compared with the existing technology, this technology has the following beneficial effects:

[0043] First, a typical voltage instability scenario involving a DC transmission system is constructed, and different fault types are set to generate a transient voltage sample set. Secondly, the transient voltage recovery process is segmented, and it is divided into two stages according to the voltage recovery speed during the transient voltage recovery process of the DC system, and the duration of transient voltage stage I is solved. Then, the PCA principal component analysis is used to select the influencing factors of transient voltage stability, and the least squares method is used to fit the key influencing factors and the transient voltage stability margin. Finally, transient simulation verification is carried out in the constructed IEEE 3-machine 9-node system and two-circuit DC transmission system. Compared with traditional methods, the research object of this method focuses on the DC receiving system network. Secondly, the traditional multi-binary table will have misjudgment phenomenon when evaluating the DC system. The present invention can significantly reduce the probability of misjudgment when evaluating the DC system, which has certain reference significance for the transient voltage evaluation of the DC system. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solution and practical examples of the present invention, the used drawings are briefly introduced below.

[0045] Figure 1 Schematic diagram of the evaluation process of the present invention

[0046] Figure 2 A transient voltage instability scenario involving a DC system is constructed.

[0047] Figure 3 Schematic diagram of two-stage transient voltage recovery.

[0048] Figure 4 Schematic diagram of analysis of influencing factors in transient voltage recovery stage I.

[0049] Figure 5 Schematic diagram of analysis of influencing factors in transient voltage recovery stage II.

[0050] Figure 6 Schematic diagram for comparing model evaluation results under different induction motor load ratios.

[0051] Figure 7 Schematic diagram of the comparison of model evaluation results under the IEEE 3-machine 9-node model. DETAILED DESCRIPTION

[0052] The present invention provides a two-stage transient voltage evaluation method applicable to a receiving end of a DC system. To make the purpose, technical solution and effect of the present invention clearer, the specific implementation scheme of the present invention is described in detail below in conjunction with the accompanying drawings and examples. The specific examples described in the present invention are only used to explain the present invention and are not used to limit the present invention.

[0053] 1. Introduction to the specific embodiments of the invention

[0054] Figure 1 A two-stage transient voltage evaluation method for a receiving end of a DC system provided by the present invention is shown in FIG. Figure 1 The specific steps of the transient voltage evaluation method described in the present invention are as follows:

[0055] S1: Establish typical voltage instability scenarios involving DC transmission systems and generate sample sets

[0056] S2: Dimensionality reduction based on principal component analysis

[0057] S3: Least squares method for fitting key voltage influencing factors and transient voltage stability margin

[0058] S4: Model evaluation and validation

[0059] Further, the method comprises the following specific steps:

[0060] Step S1 establishes a typical voltage instability scenario involving a DC transmission system and generates a sample set. The specific strategy is as follows:

[0061] Appropriate modifications are made to the IEEE 3-machine 9-node system, a DC transmission system is added, and the load model is modified to a comprehensive load model consisting of an induction motor load and a constant impedance load. By setting a three-phase short-circuit fault in the transient simulation model, the fault time varies randomly between 0.06s and 0.2s, and different transient voltage stability samples are generated. The bus active and reactive power, branch active and reactive power, DC trigger angle, delay angle, DC voltage, current and other information in the transient stage are recorded as a transient sample set.

[0062] Step S2 is based on principal component analysis for dimensionality reduction. The specific strategy is:

[0063] S21: Calculate the correlation coefficient matrix R, and use the Pearson correlation coefficient to calculate the correlation coefficients between the indicators, that is, the correlation coefficients between the columns;

[0064] S22: Calculate the eigenvalues ​​and eigenvectors of R: Calculate the eigenvalues ​​and arrange them in order from large to small, and the corresponding eigenvectors are also arranged accordingly. The eigenvalues ​​are: λ1≥λ2≥…≥λ n ≥0; its corresponding eigenvector is: e j =(l1,l2,…l n ).

[0065] S23: Calculate the principal component contribution rate and cumulative contribution rate, assuming that the contribution rate of the jth index is a j , assuming that the cumulative contribution rate of the first p indicators is a si :

[0066]

[0067] If the cumulative contribution rate of the first p indicators is greater than 85%, it can be considered that these p principal components can comprehensively reflect the indicators.

[0068] Step S3 uses the least square method to fit the key voltage influencing factors and the transient voltage stability margin. The specific strategy is:

[0069] S31: Calculate the sample transient voltage stability margin, and use the drop area during the voltage fault to distinguish different stability margins. The larger the drop area, the lower the transient voltage stability. The transient voltage stability margin calculation formula is shown in formula (8):

[0070]

[0071] Where U N is the rated DC voltage, U(t) is the voltage value during the fault, D is the penalty factor, which is 0 when the practical criterion is met, otherwise it is p (p>0, which can be adjusted appropriately to clearly distinguish between stable and unstable scenarios); t is the fault start time, Δt1 is the time when U(t) is lower than U N The duration of the voltage instability is η>p, and p is generally greater than 1.

[0072] S32: The least square method is used to perform regression fitting on the key influencing factors of voltage and the transient voltage stability margin, which is used to guide the weight selection of the two-stage multi-binary table indicators in this paper. The function form after fitting is as follows:

[0073]

[0074] In the formula, the value range of i, j, k, l, and m is 0, 1, 2, 3, and 4. There are 126 undetermined coefficients (including the constant term b) in formula (9), where x1, x2, x3, x4, and x5 represent the key influencing factors obtained by principal component analysis.

[0075] Step S4: Model evaluation and verification. The specific strategy is:

[0076] S41: In the verification system, a large number of simulations are set up to set up training sets and verification sets

[0077] S42: Calculate the transient voltage evaluation index η value and evaluate the evaluation result, wherein the index η is calculated as follows:

[0078]

[0079] Where U Nis the rated voltage of the DC system, t0-t1 is the transient voltage stage I, t1-t2 is the transient voltage stage II, K is the weight coefficient, when η is less than 1, the voltage is stable, and when it is greater than 1, the voltage is unstable. The weight K can be assigned according to the function fitted in step S32, as shown below:

[0080]

[0081] In the formula, S is a continuous function composed of multiple parameters, which is used to measure the transient voltage stability margin index. The larger the S, the worse the stability level, and a larger value is assigned to K; when S is less than 1, a smaller value is assigned to K.

[0082] S43: Solve the duration of transient voltage recovery stage I:

[0083] By analyzing the transient recovery process of the DC transmission system, it is divided into two stages according to the voltage recovery speed during the transient voltage recovery process. The voltage recovery speed in transient stage I is fast, but the duration is short, while the recovery speed in transient stage II is fast, but the duration is long. Through simulation analysis and mechanism analysis, the key factors affecting the two recovery stages are studied, and the duration of transient stage I is calculated. The calculation formula is as follows:

[0084] t I =0.16f dc 3 +0.00002f dc 2 -0.02f dc +0.04435 (12)

[0085] where f dc is the DC system access ratio, which is obtained by the following formula:

[0086]

[0087] In the formula, S dc is the DC system capacity connected to the system, S ac is the total capacity of the AC system generators in the AC power grid.

[0088] S44: Evaluation of model evaluation results

[0089] To verify the model evaluation effect, define the model evaluation accuracy A CC , missed rate L A and the false positive rate F A as follows:

[0090]

[0091] Where T and F are the number of samples predicted correctly and incorrectly, respectively; the subscripts s and us represent the samples predicted to be stable and unstable, respectively. A Indicates the probability of evaluating an unstable sample as stable, and the misjudgment rate F A Represents the probability of evaluating a stable sample as unstable.

[0092] 2. Technical feasibility verification of the present invention

[0093] Adopt this article Figure 2 In the network structure shown, the proportion of induction motors in the load is set to 50%, 65% and 80% respectively, and the transient voltage evaluation effects of the two methods are compared when a three-phase short circuit fault occurs in the system. Figure 3 Schematic diagram of transient voltage segmented recovery in DC system. Figure 4 As the key influencing factors affecting transient stage I, it can be found that the appropriate increase in VDCOL control I dmin , reduce U dL and U dH This will deteriorate the transient voltage stability.

[0094] Figure 5 As the key influencing factors affecting transient stage II, it is found that the access capacity of the DC system has a greater impact on transient voltage recovery stage II, while the VDCOL parameters have a smaller impact on it.

[0095] Figure 6 Shown in Figure 2 (a) Comparison of the evaluation results of the two methods when the ratio of induction motor load is changed in the system shown in Table 1. Table 1 shows the values ​​of the index η of the two methods in the two transient stages, where η Ⅰ , η Ⅱ They represent the index values ​​corresponding to the transient stages I and II, respectively, η=η Ⅰ +η Ⅱ . η Ⅰ / η is the ratio of the integral value of transient stage I to the total index η.

[0096] Table 1 Calculation value of the integral of the transient index η in two stages

[0097]

[0098]

[0099] Depend on Figure 6 (a) It can be seen that the recovery speed of transient voltage is different under different proportions of induction motor load. The lower the voltage, the greater the reactive power that the induction motor needs to absorb during the fault period. Therefore, a large number of induction motor loads will affect the transient voltage stability of the system. Figure 6In (b), the induction motor load ratio is 50%, and the voltage returns to stability in a short time after the fault. The evaluation indicators of the two methods are accurate. However, the evaluation value of the multi-binary table method reaches the maximum value during the transient stage I. As shown in Table 1, the integral value during the transient stage I accounts for η Ⅰ The transient voltage stability is 62.84% of the total η, which is at risk of misjudgment. Transient stage II can well characterize transient voltage stability. Poor transient voltage stability and insufficient reactive power reserve will lead to slow voltage recovery in stage II. Therefore, the greater the proportion of the integral value of transient stage II to the total η, the higher the stability discrimination of transient voltage assessment of this indicator. Compared with the multi-binary table method, the two-stage evaluation method described in this paper is more reasonable. Figure 6 In (c), the proportion of induction motors is 65%, and the voltage recovery is slower than when the proportion of induction motors is 50%, but it can eventually return to stability. The multi-binary table method makes a wrong judgment in this case, while the method described in the present invention accurately assesses that the voltage is stable. Figure 6 (d) The proportion of induction motors further increases. Excessive induction motor loads cause a sharp increase in reactive power demand during the fault period, resulting in voltage instability. At this time, both methods are accurate in evaluation, and the indicator evaluation value of the method described in the present invention is slightly larger, indicating that for more serious faults, the two-stage transient voltage evaluation method described in the present invention has a strong discrimination.

[0100] Depend on Figure 7 For Figure 2 (b) Comparison of evaluation results when the system shown in Figure 2 is used as the research object. Figure 7 It can be seen that the two-stage transient voltage assessment method proposed in the present invention has a lower misjudgment rate than the multi-binary method. In the evaluation of stable samples, the multi-binary table method has a large number of misjudgment samples because the multi-binary table assigns a larger weight to transient stage I. In unstable samples, the evaluation value of the method of the present invention is slightly lower than that of the multi-binary table method in samples with relatively poor transient stability levels, but the evaluation value of the method of the present invention is greater than that of the multi-binary table method in samples with extremely poor stability levels. And in terms of judgment time, Figure 7 (a) It can be seen that the two-stage transient voltage evaluation method proposed in the present invention can make a faster judgment on the instability situation with extremely poor fault degree. The evaluation effects of the two methods are compared, as shown in Table 2.

[0101] Table 2 Comparison of evaluation indicators of the two methods

[0102]

[0103] It can be seen from Table 2 that when the traditional multi-binary table method is applied to the DC system, due to the delayed recovery phenomenon of the DC system during the voltage recovery process, its accuracy is low and the misjudgment rate is high; after optimizing the weights during transient stage I, the evaluation results are significantly improved. The two-stage transient voltage evaluation method proposed in the present invention can improve the evaluation accuracy while ensuring the missed judgment rate is 0 after a reasonable selection of the threshold. The smaller the threshold is, the smaller the missed judgment rate is. When the threshold is 0.82, the missed judgment rate is 0, but its accuracy is not as high as when the threshold is 1. In practical applications, appropriate thresholds should be selected as needed to ensure that the accuracy and missed judgment rate are within an acceptable range.

[0104] In summary, the transient voltage evaluation method for a DC receiving system described in the present invention has good applicability and accuracy in different DC receiving systems. The method of the present invention improves the under-judgment phenomenon of the traditional multi-binary table method in the DC transmission system, and has a faster evaluation speed, and has certain practicality and engineering reference value.

[0105] Finally, it should be noted that the above examples of the present invention are merely examples for illustrating the present invention, and are not intended to limit the embodiments of the present invention. Although the applicant has described the present invention in detail with reference to the preferred embodiments, for those of ordinary skill in the art, other different forms of changes and modifications can be made based on the above description. It is impossible to list all the embodiments here. Any obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A two-stage transient voltage assessment method applicable to a receiving end of a DC system, characterized in that: The following steps are involved: S1: Establish typical voltage instability scenarios involving DC transmission systems and generate sample sets S2: Solve the duration of transient voltage recovery stage I S3: Least squares method for fitting key voltage influencing factors and transient voltage stability margin S4: Model evaluation and validation.

2. A two-stage transient voltage assessment method applicable to a receiving end of a DC system according to claim 1, characterized in that: Step S2 solves the duration of transient voltage recovery phase I. The specific strategy is: By analyzing the transient recovery process of the DC transmission system, the voltage recovery speed is divided into two stages according to the transient voltage recovery process. The voltage recovery speed in transient stage I is fast but the duration is short, while the voltage recovery speed in transient stage II is fast but the duration is long. Through simulation analysis and mechanism analysis, the key factors affecting the two recovery stages are studied, and the duration of transient stage I is calculated. The calculation formula is shown in formula (1): t I =0.16f dc 3 +0.00002f dc 2 -0.02f dc +0.04435 (1) where f dc is the DC system access ratio, which can be obtained by formula (2): In the formula, S dc is the DC system capacity connected to the system, S ac is the total capacity of the AC system generators in the AC power grid.

3. A two-stage transient voltage assessment method applicable to a receiving end of a DC system according to claim 1, characterized in that: Step S4: Model evaluation and verification. The specific strategy is: S41: In the verification system, a large number of simulations are set up to set up training sets and verification sets S42: Calculate the transient voltage evaluation index η value and evaluate the evaluation result, wherein the index η is calculated as shown in formula (3): Where U N is the rated voltage of the DC system, t0-t1 is the transient voltage stage I, t1-t2 is the transient voltage stage II, K is the weight coefficient, when η is less than 1, the voltage is stable, and when it is greater than 1, the voltage is unstable. The weight K can be assigned according to the function fitted in step S34, as shown in formula (4): In formula (4), S is a continuous function composed of multiple parameters, which is used to measure the transient voltage stability margin index. The larger the S is, the worse the stability level is, and a larger value is assigned to K; when S is less than 1, a smaller value is assigned to K. To verify the model evaluation effect, define the model evaluation accuracy A CC , missed detection rate L A and the false positive rate F A as follows: Where T and F are the number of samples predicted correctly and incorrectly, respectively; the subscripts s and us represent the samples predicted to be stable and unstable, respectively. A Indicates the probability of evaluating an unstable sample as stable, and the misjudgment rate F A Represents the probability of evaluating a stable sample as unstable.

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