A voltage stability assessment method and system for systems with flexible DC transmission based on improved MLE calculation.

Abstract

A method and system for assessing voltage stability in a power system with flexible DC transmission based on improved MLE calculation is proposed. The method first acquires the time-series data of voltage amplitude and voltage phase angle at each AC bus node of the power system under transient conditions. Then, based on the voltage amplitude time-series data, it calculates the maximum Lyapunov exponent of the voltage amplitude and plots the voltage amplitude MLE curve. Similarly, based on the voltage phase angle time-series data, it calculates the maximum Lyapunov exponent of the voltage phase angle and plots the voltage phase angle MLE curve. Next, it determines whether the voltage amplitude MLE curve oscillates. If the voltage amplitude MLE curve does not oscillate, the transient voltage stability is assessed based on the voltage amplitude MLE curve. If the voltage amplitude MLE curve oscillates, the transient voltage stability is assessed based on the voltage phase angle MLE curve. Compared to traditional transient voltage stability assessment methods that rely solely on the voltage amplitude MLE, this invention utilizes the voltage phase angle MLE curve for assessment even when the voltage amplitude MLE curve oscillates, resulting in higher assessment accuracy.

Description

Technical Field

[0001] This invention belongs to the field of transient voltage assessment technology, specifically relating to an improved method, system, device, and medium for assessing voltage stability of systems with flexible DC transmission and dynamic range (MLE) calculation. Background Technology

[0002] With the large-scale integration of inverters into modern power systems, transient voltage stability assessment has become increasingly important. Transient voltage stability assessment methods based on the Maximum Lyapunov Exponent (MLE) have attracted widespread attention due to their high computational efficiency. However, traditional MLE transient voltage stability assessment methods suffer from several technical drawbacks, such as misjudgments of transient voltage stability caused by MLE oscillations and misjudgments due to jumps in PMU sampling data, resulting in low accuracy of the final assessment results. Summary of the Invention

[0003] The purpose of this invention is to address the aforementioned problems in the prior art by providing an improved method, system, device, and medium for evaluating voltage stability of systems with flexible DC transmission and flexible circuitry (MLE) calculations that can improve evaluation accuracy.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows:

[0005] In a first aspect, the present invention provides a voltage stability evaluation method for a system containing flexible DC based on improved MLE calculation, the evaluation method comprising the following steps:

[0006] S1. Obtain the voltage amplitude time series data and voltage phase angle time series data of each AC bus node of the power system under transient conditions;

[0007] S2. Calculate the maximum Lyapunov exponent of voltage amplitude based on voltage amplitude time series data to obtain the voltage amplitude MLE curve; calculate the maximum Lyapunov exponent of voltage phase angle based on voltage phase angle time series data to obtain the voltage phase angle MLE curve.

[0008] S3. Determine whether there is oscillation in the voltage amplitude MLE curve. If there is no oscillation in the voltage amplitude MLE curve, assess whether the transient voltage is stable based on the voltage amplitude MLE curve. If there is oscillation in the voltage amplitude MLE curve, assess whether the transient voltage is stable based on the voltage phase angle MLE curve.

[0009] Before step S2, cubic Hermite interpolation is used to repair data jumps in voltage amplitude timing data and voltage phase angle timing data.

[0010] The specific method for repairing data jumps using cubic Hermitian interpolation is as follows:

[0011] Let F(t0) and F(t1) be two data points in the same time series that do not have a data jump. Calculate the cubic interpolation polynomial G(t) at time t using the following formula, and replace the data points that have a data jump with G(t):

[0012]

[0013] In the above formula, F(t0) represents the data value at time t0, F′(t0) represents the derivative of F(t0); F(t1) represents the data value at time t1, F′(t1) represents the derivative of F(t1); G(t) represents the cubic interpolation polynomial at time t, t0 < t < t1.

[0014] In S2, the calculation of the maximum Lyapunov exponent of the voltage amplitude based on the voltage amplitude time series data is specifically as follows:

[0015] A1. Define the expression for the voltage amplitude time series data V as follows:

[0016]

[0017] In the above formula, V MΔt This represents the voltage amplitude vector at time MΔt; Δt is the sampling time interval; M represents the total number of samples; and n represents the total number of nodes in the power system.

[0018] A2. Select data from the voltage amplitude time series data V that meets the following conditions as steady-state data:

[0019] ε1<|V iΔt -V (i-1)Δt ||<ε2 (i=1, 2,...,N);

[0020] In the above formula, ε1 and ε2 represent arbitrary decimals, ε1 < ε2; N represents the length of the selected steady-state data, N < M; ||·|| represents the L2 norm;

[0021] A3. Calculate the maximum Lyapunov exponent of the voltage amplitude using the following formula:

[0022]

[0023]

[0024] In the above formula, MLE(kΔt) is the maximum Lyapunov exponent value at time kΔt, k = N+1, N+, ..., M-2N; k > N; D(·) represents the Mahalanobis distance calculation formula; V (k+i-1)Δt V (k+i-1)Δt These are the voltage amplitude data vectors at times (k+i)Δt and (k+i-1)Δt, respectively; V iΔt V(i-1)Δt The voltage amplitude data vectors at times iΔt and (i-1)Δt are respectively; the superscript T indicates the inversion of the vector; Cov represents the covariance matrix of the two vectors, and the superscript -1 indicates the inverse of the matrix.

[0025] The voltage amplitude timing data and voltage phase angle timing data are both obtained by the phase measurement unit.

[0026] Secondly, the present invention provides a voltage stability evaluation system for a flexible DC system based on improved MLE calculation, the evaluation system comprising a data acquisition module, an MLE calculation module, and an evaluation module;

[0027] The data acquisition module is used to acquire the voltage amplitude time series data and voltage phase angle time series data of each AC bus node of the power system under transient conditions.

[0028] The MLE calculation module is used to calculate the maximum Lyapunov exponent of the voltage amplitude based on the voltage amplitude time series data to obtain the voltage amplitude MLE curve, and to calculate the maximum Lyapunov exponent of the voltage phase angle based on the voltage phase angle time series data to obtain the voltage phase angle MLE curve.

[0029] The evaluation module is used to determine whether there is oscillation in the voltage amplitude MLE curve. If there is no oscillation in the voltage amplitude MLE curve, the transient voltage is evaluated based on the voltage amplitude MLE curve. If there is oscillation in the voltage amplitude MLE curve, the transient voltage is evaluated based on the voltage phase angle MLE curve.

[0030] The evaluation system also includes a preprocessing module; the preprocessing module is used to repair data jumps in voltage amplitude time series data and voltage phase angle time series data using cubic Hermite interpolation.

[0031] The preprocessing module repairs data abrupt changes according to the following steps:

[0032] Let F(t0) and F(t1) be two data points in the same time series that do not have a data jump. Calculate the cubic interpolation polynomial G(t) at time t using the following formula, and replace the data points that have a data jump with G(t):

[0033]

[0034] In the above formula, F(t0) represents the data value at time t0, F′(t0) represents the derivative of F(t0); F(t1) represents the data value at time t1, F′(t1) represents the derivative of F(t1); G(t) represents the cubic interpolation polynomial at time t, t0 < t < t1.

[0035] The MLE calculation module calculates the maximum Lyapunov exponent of the voltage amplitude according to the following steps:

[0036] A1. Define the expression for the voltage amplitude time series data V as follows:

[0037]

[0038] In the above formula, V MΔt This represents the voltage magnitude vector at time MΔt; Δt is the sampling time interval; M represents the total number of samples; m represents the total number of nodes in the power system.

[0039] A2. Select data from the voltage amplitude time series data V that meets the following conditions as steady-state data:

[0040] ε1<||V iΔt -V (i-1)Δt ||<ε2 (i=1, 2,...,N);

[0041] In the above formula, ε1 and ε2 represent arbitrary decimals, ε1 < ε2; N represents the length of the selected steady-state data, N < M; ||·|| represents the L2 norm;

[0042] A3. Calculate the maximum Lyapunov exponent of the voltage amplitude using the following formula:

[0043]

[0044] In the above formula, MLE(kΔt) is the maximum Lyapunov exponent value at time kΔt, k = N+1, N+2, ..., M-2N; k > N; D(·) represents the Mahalanobis distance calculation formula; V (k+i)Δt V (k+i-1)Δt These are the voltage amplitude data vectors at times (k+i)Δt and (k+i-1)Δt, respectively; V iΔt V (i-1)Δt The voltage amplitude data vectors at times iΔt and (i-1)Δt are respectively; the superscript T indicates the inversion of the vector; Cov represents the covariance matrix of the two vectors, and the superscript -1 indicates the inverse of the matrix.

[0045] The data acquisition module is used to acquire the voltage amplitude time-series data and voltage phase angle time-series data of each AC bus node of the power system under transient conditions using the phase measurement unit.

[0046] Thirdly, the present invention provides a voltage stability evaluation device for a flexible DC system based on improved MLE calculation, the evaluation device including a memory and a processor;

[0047] The memory is used to store computer program code and transmit the computer program code to the processor;

[0048] The processor is configured to execute the aforementioned method according to instructions in the computer program code.

[0049] Fourthly, the present invention provides a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, implements the aforementioned method.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] 1. The present invention discloses a voltage stability assessment method for a flexible DC system based on improved MLE calculation. First, it acquires the voltage amplitude time-series data and voltage phase angle time-series data of each AC bus node in the power system under transient conditions. Then, it calculates the maximum Lyapunov exponent of the voltage amplitude based on the voltage amplitude time-series data to obtain the voltage amplitude MLE curve, and calculates the maximum Lyapunov exponent of the voltage phase angle based on the voltage phase angle time-series data to obtain the voltage phase angle MLE curve. Next, it determines whether the voltage amplitude MLE curve oscillates. If the voltage amplitude MLE curve does not oscillate, it assesses the stability of the transient voltage based on the voltage amplitude MLE curve; if the voltage amplitude MLE curve oscillates, it assesses the stability of the transient voltage based on the voltage phase angle MLE curve. This design uses the voltage phase angle MLE curve for assessment even when the voltage amplitude MLE curve oscillates. Compared to traditional transient voltage stability assessment methods that rely solely on the voltage amplitude MLE, this design offers higher assessment accuracy. Therefore, the present invention can improve assessment accuracy.

[0052] 2. The voltage stability assessment method for systems with flexible DC transmission based on improved MLE calculation described in this invention employs cubic Hermitian interpolation to correct potential PMU data jumps in time-series data, thereby enhancing the robustness and applicability of the proposed method. Therefore, this invention improves the robustness in handling sampling data jumps.

[0053] 3. The voltage stability assessment method for flexible DC systems based on improved MLE calculation described in this invention improves the traditional MLE calculation formula. Compared with the Euclidean distance in the traditional formula, this design uses Mahalanobis distance to more accurately measure the difference between two time series data segments, thereby further improving the accuracy of the assessment results. Therefore, this invention can further improve the assessment accuracy. Attached Figure Description

[0054] Figure 1 This is a flowchart of the evaluation method described in this invention.

[0055] Figure 2 This is a topology diagram of a two-zone, four-machine power system.

[0056] Figure 3 This is the timing data of the voltage amplitude for scenario I.

[0057] Figure 4 This is the voltage phase angle timing data for scenario I.

[0058] Figure 5 The MLE curves for voltage amplitude and phase angle in scenario I are shown.

[0059] Figure 6 This is the timing data of the voltage amplitude for Scenario II.

[0060] Figure 7 This is the voltage phase angle timing data for Scenario II.

[0061] Figure 8 The MLE curves for voltage amplitude and phase angle in scenario II are shown.

[0062] Figure 9 This is a topology diagram of a simulation model of a flexible DC transmission system.

[0063] Figure 10 This is the timing data of the voltage amplitude for scenario a.

[0064] Figure 11 This is the voltage phase angle timing data for scenario a.

[0065] Figure 12 The MLE curves for voltage amplitude and phase angle in scenario a are shown.

[0066] Figure 13 This is the timing data of the voltage amplitude for scenario b.

[0067] Figure 14 This is the voltage phase angle timing data for scenario b.

[0068] Figure 15 The MLE curves for voltage amplitude and phase angle in scenario b are shown.

[0069] Figure 16 This is the timing data of the voltage amplitude for scenario (i).

[0070] Figure 17 The voltage amplitude timing data after repair for scenario (i).

[0071] Figure 18 This is the timing data of the voltage amplitude for scenario (ii).

[0072] Figure 19 The voltage amplitude timing data after repair for scenario (ii).

[0073] Figure 20 This is a schematic diagram of the structure of the evaluation system described in the invention. Detailed Implementation

[0074] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0075] Example 1:

[0076] See Figure 1 A voltage stability assessment method for a system with flexible DC transmission based on improved MLE calculation is performed in the following steps:

[0077] S1. Use the phase measurement unit (PMU) to obtain the voltage amplitude time series data and voltage phase angle time series data of each AC bus node of the power system under transient conditions;

[0078] S2. Identify whether there are data jumps in the voltage amplitude time series data and voltage phase angle time series data. A data jump refers to a discrepancy between the PMU sampled data at a certain moment or time period and the actual value. If the PMU sampled data at a certain moment is incorrect, it is called a single-point data jump; if the PMU sampled data at a certain time period is incorrect, it is called a multi-point data jump. If data jumps exist in the voltage amplitude time series data and voltage phase angle time series data, cubic Hermitian interpolation is used to correct the erroneous data, which can enhance the robustness of the evaluation results. Specifically: Let F(t0) and F(t1) be two data points in the same time series data that do not have data jumps. Calculate the cubic interpolation polynomial G(t) at time t according to the following formula, and replace the data points that have experienced data jumps with G(t).

[0079]

[0080] In the above formula, F(t0) represents the data value at time t0, F′(t0) represents the derivative of F(t0); F(t1) represents the data value at time t1, F′(t1) represents the derivative of F(t1); G(t) represents the cubic interpolation polynomial at time t, t0 < t < t1;

[0081] S3. Calculate the maximum Lyapunov exponent of the voltage amplitude based on the voltage amplitude time-series data to obtain the voltage amplitude MLE curve; specifically:

[0082] A1. Define the expression for the voltage amplitude time series data V as follows:

[0083]

[0084] In the above formula, V MΔT This represents the voltage amplitude vector at time MΔt; Δt is the sampling time interval; M represents the total number of samples; and n represents the total number of nodes in the power system.

[0085] A2. Select data that meets the following conditions from the voltage amplitude time series data V as steady-state data, and denote the obtained steady-state data as [V0, V...].Δt , ..., V NΔt ]:

[0086] ε1<||V iΔt -V (i-1)Δt ||<ε2 (i=1, 2,...,N);

[0087] In the above formula, ε1 and ε2 represent arbitrary decimals, ε1 < ε2; N represents the length of the selected steady-state data, N < M; ||·|| represents the L2 norm;

[0088] A3. Let transient data [V] kΔt V (k+1)Δt , ..., V (k+N)Δt The maximum Lyapunov exponent of the voltage amplitude is calculated according to the improved MLE calculation formula, which is as follows:

[0089]

[0090]

[0091] In the above formula, MLE(kΔt) is the maximum Lyapunov exponent value at time kΔt, k = N+1, N+2, ..., M-2N; k > N; D(·) represents the Mahalanobis distance calculation formula; V (k+i)Δt V (k+i-1)Δt These are the voltage amplitude data vectors at times (k+i)Δt and (k+i-1)Δt, respectively; V iΔt V (i-1)Δt These are the voltage amplitude data vectors at times iΔt and (i-1)Δt, respectively; the superscript T indicates the inversion of the vector; Cov represents the covariance matrix of the two vectors, and the superscript -1 indicates the inverse of the matrix;

[0092] The Mahalanobis distance is introduced into the traditional MLE calculation formula to measure the difference between two time series data. The main reason is that steady-state data and transient data have different mathematical distributions. If the traditional formula uses Euclidean distance for calculation, it may incorrectly measure the difference between the two time series data by ignoring the mathematical distribution. Using Mahalanobis distance helps to make up for this shortcoming.

[0093] The maximum Lyapunov exponent of the voltage phase angle is calculated based on the voltage phase angle time series data to obtain the voltage phase angle MLE curve. The calculation steps for the maximum Lyapunov exponent of the voltage phase angle are the same as those for the maximum Lyapunov exponent of the voltage amplitude. The voltage amplitude data in A1-A3 can be replaced with the voltage phase angle data, which will not be elaborated here.

[0094] S4. Determine whether there is oscillation in the voltage amplitude MLE curve. If there is no oscillation in the voltage amplitude MLE curve, assess whether the transient voltage is stable based on the voltage amplitude MLE curve. If there is oscillation in the voltage amplitude MLE curve, assess whether the transient voltage is stable based on the voltage phase angle MLE curve.

[0095] To verify the effectiveness of the evaluation method described in this invention, three examples were set up, and the evaluation method proposed in this invention was applied for evaluation. The above examples were conducted on a computer with an Intel Core i7-12700 CPU@2.10GHz and 16GB of memory, and the MATLAB software version was 2022a.

[0096] Example 1:

[0097] To verify the effectiveness of the evaluation method described in this invention, a system was built in MATLAB as follows: Figure 2 The two-zone, four-machine power system shown has PMU devices configured at Bus 1 and Bus 2 to collect voltage amplitude and phase angle timing data. This example assumes no data jumps in the PMU sampled data; therefore, cubic Emilt interpolation was not used for data repair. At position f1 in the two-zone, four-machine power system, two scenarios of three-phase short-circuit faults were simulated, with the fault starting at 5 seconds. Other main fault parameters are shown in Table 1.

[0098] Table 1 Main Fault Parameters in the Two-Zone Four-Machine Power System

[0099]

[0100]

[0101] For scenario I, the acquired voltage amplitude time-series data and voltage phase angle time-series data are as follows: Figure 3 , Figure 4 As shown. By Figure 3 , Figure 4 As can be seen, during the 5-5.1s fault period, severe voltage drops occurred on Bus 1 and Bus 2, with their voltage amplitudes dropping to near zero and 0.8 pu, respectively. After the fault was cleared, the amplitudes of Bus 1 and Bus 2 basically returned to the normal level (about 1 pu). It can be determined that the system is in a transient voltage stable state under scenario I.

[0102] The MLE curves of voltage amplitude and phase angle under transient faults obtained by applying the evaluation method proposed in this invention are as follows: Figure 5 As shown. The MLE curve for voltage amplitude will be denoted as M1, and the improved MLE curve of this invention will be denoted as M2. From... Figure 5As can be seen, before the fault occurred, both M1 and M2 were less than 0, indicating that the system was in a transient voltage stable state. At the moment the fault occurred, M1 and M2 suddenly increased and became greater than 0. After the fault was cleared, M2 dropped below 0 in about 5.3 seconds, while M1 oscillated around 0. Since oscillations were detected in M1, it is difficult to accurately assess the transient voltage stability of the system based on M1 alone. In contrast, although M2 also showed a situation of M2>0 at the beginning of the fault, M2 quickly dropped below 0 after the fault was cleared. Therefore, it is feasible to use M2 for transient voltage assessment and it is more accurate than M1.

[0103] For scenario II, the acquired voltage amplitude time-series data and voltage phase angle time-series data are as follows: Figure 6 , Figure 7 As shown. By Figure 6 , Figure 7 As can be seen, after the fault was cleared, the voltage amplitude and phase angle of Bus 1 and Bus 2 did not return to normal levels, but instead oscillated. It can be determined that the system is in a transient voltage instability state.

[0104] The MLE curves of voltage amplitude and phase angle under transient faults obtained by applying the evaluation method proposed in this invention are as follows: Figure 8 As shown. By Figure 8 As can be seen, when a fault occurs, both M1 and M2 increase and change from negative to positive. After the fault is cleared, M1 and M2 remain above 0, indicating that the system is in a transient voltage instability state. However, it should be noted that M1 and M2 suddenly decrease at 5.2s, and M1 falls below 0 between 5.4 and 5.5s, while M2 remains above 0. This shows that the accuracy of transient voltage assessment based on M2 is higher than that based on M1.

[0105] Example 2:

[0106] To verify the application of the present invention in a flexible DC transmission system, a system was built in MATLAB as follows. Figure 9 The simulation model of the flexible DC transmission system shown includes a PMU device at Bus 1 to collect voltage amplitude and phase angle time-series data. This example assumes no data jumps in the PMU sampling data; therefore, cubic Emilt interpolation was not used for data repair. Two three-phase short-circuit fault scenarios were set at position f1 in the flexible DC transmission system simulation model, with the fault starting at 1.5 seconds. Other main fault parameters are shown in Table 2.

[0107] Table 2 Main Fault Parameters of Flexible DC Transmission Systems

[0108]

[0109]

[0110] For scenario a, the acquired voltage amplitude time-series data and voltage phase angle time-series data are as follows: Figure 10 , Figure 11 As shown. By Figure 10 , Figure 11 As can be seen, a voltage dip occurred on Bus 1 during the 1.5-1.7s fault period. After the fault was cleared (1.7-2s), a strong oscillation was detected on Bus 1. Subsequently, the voltage amplitude and phase angle returned to normal levels in about 2s. It can be determined that the flexible DC transmission system is in a transient voltage stable state.

[0111] The MLE curves of voltage amplitude and phase angle under transient faults obtained by applying the evaluation method proposed in this invention are as follows: Figure 12 As shown; by Figure 12 As can be seen, at the initial moment of the fault (1.5s), both M1 and M2 rise but remain less than 0, indicating that the system is in a transient voltage stabilization state. Subsequently, when the fault is cleared, the curves M1 and M2 rise again and cross the zero line. Finally, as the voltage amplitude and phase angle recover, the curves M1 and M2 drop below 0. Although both M1 and M2 show values ​​greater than 0, M2 drops below 0 much faster than M1, demonstrating better assessment accuracy.

[0112] For scenario b, the acquired voltage amplitude time-series data and voltage phase angle time-series data are as follows: Figure 13 , Figure 14 As shown. By Figure 13 , Figure 14 As can be seen, a severe voltage drop occurred on Bus 1, and the phase angle continued to decrease after the initial oscillation. Since the fault continued until the end of the simulation, the system can be considered to be in a transient voltage instability state.

[0113] The MLE curves of voltage amplitude and phase angle under transient faults obtained by applying the evaluation method proposed in this invention are as follows: Figure 15 As shown; by Figure 15 As can be seen, after the fault occurred, M1 and M2 rapidly increased and became greater than 0, and then remained above 0 until the simulation ended. At this point, both M1 and M2 indicate that the system is in a transient voltage instability state. However, the fluctuation amplitude of M2 during the fault period is greater than that of M1. It can be seen that in actual transient voltage stability assessment problems, this behavior of M2 will be more helpful in making system assessments.

[0114] Example 3:

[0115] To verify the robustness of this invention under MLE sampling data jump scenarios, this example, based on Example 1, sets up two scenarios of PMU sampling data jumps; the data jumps occur during... Figure 2 The data transition scenario settings on the PMU device configured at Bus 2 are shown in Table 3:

[0116] Table 3 PMU Sampling Data Jump Scenarios

[0117] Scene type Jump corresponding time (i) Single-point jump 4.95s (ii) Multi-point jump 4.95-5.00s

[0118] For scenario (i), the acquired voltage amplitude time-series data is as follows: Figure 16 As shown; by Figure 16 As can be seen, the voltage amplitude data sampled by the PMU experienced a single-point data jump at 4.95s, changing from 1.00211pu to 0pu. This erroneous data was repaired using the cubic Hermitian interpolation method described in this invention; the repaired value is shown below. Figure 17 ,Depend on Figure 17 The magnified view shows that the cubic Hermitian interpolation method effectively corrected the erroneous data, with the error between the corrected value and the true value being only 0.0017%. If the jump value is used to calculate the MLE, the resulting MLE curve will increase to a value greater than 0 before the fault occurs, which may lead to a misjudgment of the system voltage stability as an unstable state. However, if the corrected value is used to calculate the MLE, the resulting MLE curve is almost identical to the true MLE, indicating that the influence of PMU data jumps has been effectively eliminated.

[0119] For scenario (ii), the acquired voltage amplitude time-series data is as follows: Figure 18 As shown; by Figure 18 As can be seen, the voltage amplitude data sampled by the PMU exhibited multiple data jumps within the range of 4.95-5.00 s. The cubic Hermitian interpolation method described in this invention was used to repair this erroneous data; the repaired values ​​are shown below. Figure 19 ,Depend on Figure 19 The magnified view shows that the erroneous data has been well corrected, with an average error of only 0.0032% between the corrected and true values. This error is slightly larger than the error between the corrected and true values ​​in scenario (i), mainly because the accuracy of cubic Hermitian interpolation decreases when dealing with more data. In summary, this invention corrects erroneous data using cubic Hermitian interpolation, enabling the evaluation results to exhibit good robustness and anti-interference capabilities in both single-point and multi-point data jump scenarios.

[0120] Example 2:

[0121] See Figure 20A voltage stability assessment system for a flexible DC system based on improved MLE calculation is disclosed, comprising a data acquisition module, a preprocessing module, an MLE calculation module, and an assessment module. The data acquisition module uses a phase measurement unit to acquire the voltage amplitude time-series data and voltage phase angle time-series data of each AC bus node in the power system under transient conditions. The preprocessing module uses cubic Hermitian interpolation to repair data jumps in the voltage amplitude time-series data and voltage phase angle time-series data. Specifically, it assumes two data points without data jumps in the same time-series data are F(t0) and F(t1), calculates the cubic interpolation polynomial G(t) at time t according to the following formula, and replaces the data points with data jumps with G(t):

[0122]

[0123] In the above formula, F(t0) represents the data value at time t0, F′(t0) represents the derivative of F(t0); F(t1) represents the data value at time t1, F′(t1) represents the derivative of F(t1); G(t) represents the cubic interpolation polynomial at time t, t0 < t < t1;

[0124] The MLE calculation module is used to calculate the maximum Lyapunov exponent of the voltage amplitude based on the voltage amplitude time series data, obtaining the voltage amplitude MLE curve, and to calculate the maximum Lyapunov exponent of the voltage phase angle based on the voltage phase angle time series data, obtaining the voltage phase angle MLE curve; the MLE calculation module calculates the maximum Lyapunov exponent of the voltage amplitude according to the following steps:

[0125] A1. Define the expression for the voltage amplitude time series data V as follows:

[0126]

[0127] In the above formula, V MΔt This represents the voltage amplitude vector at time MΔt; Δt is the sampling time interval; M represents the total number of samples; and n represents the total number of nodes in the power system.

[0128] A2. Select data from the voltage amplitude time series data V that meets the following conditions as steady-state data:

[0129] ε1<||V iΔt -V (i-1)Δt ||<ε2(i=1, 2,...,N);

[0130] In the above formula, ε1 and ε2 represent arbitrary decimals, ε1 < ε2; N represents the length of the selected steady-state data, N < M; ||·|| represents the L2 norm;

[0131] A3. Calculate the maximum Lyapunov exponent of the voltage amplitude using the following formula:

[0132]

[0133] In the above formula, MLE(kΔt) is the maximum Lyapunov exponent value at time kΔt, k = N+1, N+2, ..., M-2N; k > N; D(·) represents the Mahalanobis distance calculation formula; V (k+i)Δt V (k+i-1)Δt These are the voltage amplitude data vectors at times (k+i)Δt and (k+i-1)Δt, respectively; V iΔt V (i-1)Δt These are the voltage amplitude data vectors at times iΔt and (i-1)Δt, respectively; the superscript T indicates the inversion of the vector; Cov represents the covariance matrix of the two vectors, and the superscript -1 indicates the inverse of the matrix;

[0134] The calculation steps for the maximum Lyapunov exponent of the voltage phase angle are the same as those for the maximum Lyapunov exponent of the voltage amplitude; simply replace the voltage amplitude data in A1-A3 with the voltage phase angle data.

[0135] The evaluation module is used to determine whether there is oscillation in the voltage amplitude MLE curve. If there is no oscillation in the voltage amplitude MLE curve, the transient voltage is evaluated based on the voltage amplitude MLE curve. If there is oscillation in the voltage amplitude MLE curve, the transient voltage is evaluated based on the voltage phase angle MLE curve.

[0136] Example 3:

[0137] An improved MLE calculation voltage stability assessment device for a flexible DC system includes a memory and a processor; the memory is used to store computer program code and transfer the computer program code to the processor; the processor is used to execute the method described in Embodiment 1 according to the instructions in the computer program code.

[0138] Example 4:

[0139] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0140] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0141] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0142] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0143] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0144] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A voltage stability assessment method for systems with flexible DC transmission based on improved MLE calculation, characterized in that: The evaluation method includes the following steps: S1. Obtain the voltage amplitude time series data and voltage phase angle time series data of each AC bus node of the power system under transient conditions; S2. Calculate the maximum Lyapunov exponent of voltage amplitude based on voltage amplitude time series data to obtain the voltage amplitude MLE curve; calculate the maximum Lyapunov exponent of voltage phase angle based on voltage phase angle time series data to obtain the voltage phase angle MLE curve. S3. Determine whether there is oscillation in the voltage amplitude MLE curve. If there is no oscillation in the voltage amplitude MLE curve, assess whether the transient voltage is stable based on the voltage amplitude MLE curve. If there is oscillation in the voltage amplitude MLE curve, assess whether the transient voltage is stable based on the voltage phase angle MLE curve. In S2, the calculation of the maximum Lyapunov exponent of the voltage amplitude based on the voltage amplitude time series data is specifically as follows: A1. Define voltage amplitude timing data The expression is: ； In the above formula, express The voltage magnitude vector at time t; The sampling time interval; Indicates the total number of samples; This represents the total number of nodes in the power system. A2. From voltage amplitude time series data Data that meets the following conditions are selected as steady-state data: ； In the above formula, and Represents any decimal. ; Indicates the length of the selected steady-state data. ; Represents the L2 norm; A3. Calculate the maximum Lyapunov exponent of the voltage amplitude using the following formula: ； ； ； In the above formula, for The maximum Lyapunov exponent value at time t. ; ; This represents the formula for calculating Mahalanobis distance. , They are respectively , Voltage amplitude data vector at time; , They are respectively , Voltage amplitude data vector at time; superscript Indicates the inversion of a vector; Let represent the covariance matrix of two vectors, with the superscript -1 indicating the inverse of the matrix.

2. The voltage stability assessment method for systems with flexible DC transmission based on improved MLE calculation according to claim 1, characterized in that: Before step S2, cubic Hermite interpolation is used to repair data jumps in voltage amplitude timing data and voltage phase angle timing data.

3. The voltage stability assessment method for systems with flexible DC transmission based on improved MLE calculation according to claim 2, characterized in that: The specific method for repairing data jumps using cubic Hermitian interpolation is as follows: Let two data points in the same time series that do not have data jumps be respectively. , Calculate according to the following formula cubic interpolation polynomial at time t Data that has undergone a jump will be used replace: ； In the above formula, express Data values ​​at any given time express The derivative value; express Data values ​​at any given time express The derivative value; express The cubic interpolation polynomial at time t, .

4. The voltage stability assessment method for a system with flexible DC based on improved MLE calculation according to any one of claims 1-3, characterized in that: The voltage amplitude timing data and voltage phase angle timing data are both obtained by the phase measurement unit.

5. A voltage stability evaluation system for systems with flexible DC transmission based on improved MLE calculation, characterized in that: The evaluation system includes a data acquisition module, an MLE calculation module, and an evaluation module; The data acquisition module is used to acquire the voltage amplitude time-series data and voltage phase angle time-series data of each AC bus node of the power system under transient conditions. The MLE calculation module is used to calculate the maximum Lyapunov exponent of the voltage amplitude based on the voltage amplitude time series data to obtain the voltage amplitude MLE curve, and to calculate the maximum Lyapunov exponent of the voltage phase angle based on the voltage phase angle time series data to obtain the voltage phase angle MLE curve. The evaluation module is used to determine whether there is oscillation in the voltage amplitude MLE curve. If there is no oscillation in the voltage amplitude MLE curve, the transient voltage is evaluated based on the voltage amplitude MLE curve. If there is oscillation in the voltage amplitude MLE curve, the transient voltage is evaluated based on the voltage phase angle MLE curve. The MLE calculation module calculates the maximum Lyapunov exponent of the voltage amplitude according to the following steps: A1. Define voltage amplitude timing data The expression is: ； In the above formula, express The voltage magnitude vector at time t; The sampling time interval; Indicates the total number of samples; This represents the total number of nodes in the power system. A2. From voltage amplitude time series data Data that meets the following conditions are selected as steady-state data: ； In the above formula, and Represents any decimal. ; Indicates the length of the selected steady-state data. ; Represents the L2 norm; A3. Calculate the maximum Lyapunov exponent of the voltage amplitude using the following formula: ； ； ； In the above formula, for The maximum Lyapunov exponent value at time t. ; ; This represents the formula for calculating Mahalanobis distance. , They are respectively , Voltage amplitude data vector at time; , They are respectively , Voltage amplitude data vector at time; superscript Indicates the inversion of a vector; Let represent the covariance matrix of two vectors, with the superscript -1 indicating the inverse of the matrix.

6. The voltage stability assessment system for a system with flexible DC transmission based on improved MLE calculation according to claim 5, characterized in that: The evaluation system also includes a preprocessing module; the preprocessing module is used to repair data jumps in voltage amplitude time series data and voltage phase angle time series data using cubic Hermite interpolation.

7. The voltage stability assessment system for flexible DC systems based on improved MLE calculation according to claim 6, characterized in that: The preprocessing module repairs data abrupt changes according to the following steps: Let two data points in the same time series that do not have data jumps be respectively. , Calculate according to the following formula cubic interpolation polynomial at time t Data that has undergone a jump will be used replace: ； In the above formula, express Data values ​​at any given time express The derivative value; express Data values ​​at any given time express The derivative value; express The cubic interpolation polynomial at time t, .

8. The voltage stability assessment system for a flexible DC system based on improved MLE calculation according to any one of claims 5-7, characterized in that: The data acquisition module is used to acquire the voltage amplitude time-series data and voltage phase angle time-series data of each AC bus node of the power system under transient conditions using the phase measurement unit.

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