Wind turbine equivalent inertia estimation method based on frequency dynamic response equivalence

Abstract

The application discloses a wind turbine equivalent inertia estimation method based on frequency dynamic response equivalence, which dynamically equivalent the frequency change of a system supported by a wind turbine to the frequency change of a system with equivalent inertia increased, and the equivalent inertia of the wind turbine is the inertia of the system after equivalence minus the inertia of the synchronous machine before equivalence. Compared with the traditional equivalent inertia evaluation of the power system, the method provided by the application can quantify the equivalent inertia of the wind turbine under different active support methods, and provides an auxiliary decision for the dispatching operation of the power grid.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of equivalent inertia evaluation of power systems, and particularly relates to a wind turbine equivalent inertia estimation method based on frequency dynamic response equivalence. BACKGROUND

[0002] With the increasing of large-scale wind power grid connection and penetration rate, the equivalent inertia of power systems gradually decreases, and low inertia systems are prone to lose frequency stability due to insufficient disturbance resistance. In recent years, there have been several power outages in new energy high proportion power grids, such as the "8.9" blackout in the UK, the Texas 2021 blackout in the United States, etc. The reason is that the system imbalance power leads to a large drop in frequency, and the protection switch acts correctly and then causes power outage. Therefore, wind turbines need to provide active support when the system is disturbed, effectively suppressing the change of grid frequency by reducing the system imbalance power. In order to ensure the stable operation of power systems in the scenario of high proportion of new energy, the equivalent inertia of the system needs to be accurately evaluated. At the same time, the inertia estimation result can provide a reference for reasonable allocation of virtual inertia and assist in determining the reasonable proportion of new energy access in nodes or regions.

[0003] The existing inertia evaluation methods of power systems mainly include inertia evaluation based on large disturbance events, inertia evaluation based on small disturbance events and inertia evaluation based on quasi-steady state operation. For the first method, the load shedding event of the generator can be experimented, and the generator inertia can be calculated according to the load change and the frequency change rate. The regional inertia can also be estimated according to the inter-regional tie-line power and the dominant generator frequency after the disturbance. The second method can estimate the generator inertia based on dynamic mode decomposition method by collecting the generator speed and power after the disturbance. The system inertia can also be identified by using small amplitude probe signal excitation system, combined with input-output identification algorithm and ORT subspace method. For the third method, the generator inertia can be identified based on ARMAX model and output error model.

[0004] In the traditional power system, the system load and the synchronous machine power generation achieve active balance. When the load fluctuation causes the change of grid frequency, the synchronous machine releases the kinetic energy stored in the rotor to provide active support for the grid, and under the condition of ignoring the mechanical power, the change of electromagnetic power of the synchronous machine is proportional to the frequency change rate of the grid. While the wind turbine is mostly connected to the grid through a converter, and its electromagnetic power is controlled by the converter, which is no longer affected by the load disturbance and the change of grid frequency, resulting in that the original equivalent inertia evaluation method of power system is no longer applicable.

[0005] When the grid frequency deviates due to unbalanced power in the system, the wind turbine suppresses the grid frequency change through various active support methods to provide different levels of equivalent inertia for the grid. Considering that the wind turbine has limited rotor kinetic energy, it needs to return to the maximum power point tracking operation mode after active support, and the speed is restored to the balance point before active support by reducing electromagnetic power. During the active support stage of the wind turbine, the grid frequency change is mainly suppressed through virtual inertia control, droop control, step inertia control and ramp control. The virtual inertia control of the wind turbine simulates the inertia response characteristics of the traditional synchronous machine, the active support power is proportional to the grid frequency change rate, and the proportional coefficient is called the virtual inertia coefficient. The active support power of the droop control is the product of the grid frequency deviation and the droop coefficient, so that the wind turbine has the primary frequency response characteristics of the synchronous machine. The step inertia control provides constant power support for the grid during the initial frequency disturbance, and the power support is called incremental power. The ramp control instantaneously increases the output when the frequency event occurs, and then the active support power decreases with the decrease of the speed, and the active support power is a linear function of the speed. The wind turbine suppresses the grid frequency change through the above active support methods, which actually increases the equivalent inertia of the grid. However, the existing equivalent inertia estimation method lacks a quantitative means to estimate the equivalent inertia provided by the wind turbine under active support. In view of this defect, the present application provides a wind turbine equivalent inertia estimation method based on frequency dynamic response equivalence. SUMMARY

[0006] The purpose of the present application is to provide a wind turbine equivalent inertia estimation method based on frequency dynamic response equivalence, thereby solving the problem that the traditional power system equivalent inertia evaluation method cannot accurately evaluate the equivalent inertia of the wind turbine under different active support methods.

[0007] Technical scheme: The wind turbine equivalent inertia estimation method based on frequency dynamic response equivalence of the present application comprises the following steps:

[0008] (1) Estimate the inertia and damping of the synchronous machine under normal operation of the grid;

[0009] (2) Obtain the related parameters of the synchronous machine governor, and establish a power system frequency response model combined with the estimated inertia and damping of the synchronous machine in step (1);

[0010] (3) Obtain the load power and grid frequency data under the active support of the wind turbine;

[0011] (4) In the perspective of frequency dynamic response equivalence, the active support of the wind turbine is equivalent to the increase of the system inertia or damping, and the equivalent inertia and damping of the system after the active support of the wind turbine are estimated through the data in step (3);

[0012] (5) Calculate the equivalent inertia and damping of the wind turbine.

[0013] In step (1), when estimating the inertia and damping of the synchronous machine, the whole network synchronous machine is equivalent to an equivalent synchronous machine, which includes the following steps:

[0014] (1.1) Obtain the electromagnetic power at the terminal of the synchronous machine and the bus frequency in T seconds under normal operation of the power grid, and divide T seconds into n segments with a length of l seconds and a sliding time of Δt;

[0015] (1.2) Fit a first-order transfer function with the electromagnetic power of each segment of the synchronous machine as the input and the bus frequency as the output, as follows:

[0016]

[0017] Where a i and b i are the polynomial coefficients of the numerator and denominator of the transfer function, respectively, and s represents the differential operator.

[0018] (1.3) Calculate the estimated values of the inertia and damping of the synchronous machine in each time segment, as follows:

[0019]

[0020]

[0021] Where H i and D i are the estimated values of the inertia and damping of the synchronous machine in the i-th time segment.

[0022] (1.4) Process the estimated values H i and D i (i = 1, 2,..., n) by the percentile method to remove discrete values, set the lower percentile threshold and the upper percentile threshold; if the estimated value is between the data corresponding to the lower and upper percentile thresholds, it is saved; if the estimated value is outside the data corresponding to the lower and upper percentile thresholds, the average of the data corresponding to the lower and upper percentile thresholds is taken; and the processed data is averaged to obtain the estimated values of the inertia and damping of the synchronous machine.

[0023] In step (2), the synchronous machine governor-related parameters are obtained, including the mechanical power gain coefficient K m , the high-pressure turbine power coefficient F H , the reheating time constant T R , and the governor coefficient R, the governor transfer function is obtained according to the obtained parameters, and the power system frequency response model is established in combination with the estimated inertia and damping of the synchronous machine in step (1); wherein the governor transfer function is:

[0024]

[0025] In step (3), the load power and grid frequency data under active wind turbine support are obtained, wherein the load power is obtained by adding the synchronous machine and the electromagnetic power of the wind turbine.

[0026] In step (4), estimating the equivalent inertia and damping of the system after active support of the wind turbine includes the following steps:

[0027] (4.1) From the perspective of frequency dynamic response equivalence, the wind turbine's participation in the active support of the system is equivalent to an increase in the system's inertia or damping; the system equations under the active support of the wind turbine are:

[0028]

[0029] Where, ΔP wt ΔP is the active support power of the wind turbine. m H represents the primary frequency modulation power increment of the synchronous machine. sg D is the estimated value of the synchronizing machine inertia in step 1; L This is the estimated damping value from step 1;

[0030] After equipping the active support of the wind turbine, the equivalent system equations are as follows:

[0031]

[0032] Among them, H eq D represents the system inertia after active support of the wind turbine; eq The system damping is the equivalent of the active support of the wind turbine;

[0033] (4.2) Equivalent transfer function The following is a summary:

[0034]

[0035] Write G(s) in the form of state equations:

[0036]

[0037] Among them, state variables Output y = x1 + h0u;

[0038] Matrix in the state equation C = [1 0], D = 0;

[0039] (4.3) Based on the load power and grid frequency data in step (3), identify the gray box model of the system; where the governor parameters are known parameters, and the equivalent system inertia H eq and damping D eq These are the parameters to be identified.

[0040] In step (5), the equivalent inertia and damping of the fan are calculated according to the estimated inertia and damping of the synchronous machine in step (1) and the equivalent system inertia and damping in step (4), respectively as follows:

[0041] H wt = H eq -H sg (9)

[0042] D wt = D eq -D L (10)

[0043] Advantages: Compared with the prior art, the technical scheme of the present application has the following advantages: (1) the fan active support in the system is equivalent to the increase of the system inertia or damping from the equivalent perspective of frequency dynamic response, and then the equivalent inertia and damping under the fan active support are quantified; (2) the frequency variation dynamic of the system under the wind turbine active support is equivalent to the frequency variation dynamic of the system with the equivalent inertia increased, and the equivalent inertia of the wind turbine is the equivalent system inertia minus the inertia of the synchronous machine; compared with the traditional equivalent inertia evaluation of the power system, the present scheme can quantify the equivalent inertia of the wind turbine under different active support methods, and provide auxiliary decision for the grid dispatching operation. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is the flowchart of the present application;

[0045] Figure 2 is the frequency response model of the power system containing wind power in the present application;

[0046] Figure 3 is the load fluctuation curve under the normal operation state of the power grid in the present application;

[0047] Figure 4 is the frequency deviation curve under the normal operation state of the power grid in the present application;

[0048] Figure 5 is the comparison curve of the power grid frequency before and after the equivalent of the virtual inertia control of the fan in the present application;

[0049] Figure 6 is the comparison curve of the power grid frequency before and after the equivalent of the droop control of the fan in the present application;

[0050] Figure 7 is the comparison curve of the power grid frequency before and after the equivalent of the step inertia control of the fan in the present application;

[0051] Figure 8 is the comparison curve of the power grid frequency before and after the equivalent of the ramp control of the fan in the present application. DETAILED DESCRIPTION

[0052] The technical solutions of the present application will be described in detail below in combination with specific embodiments and the accompanying drawings.

[0053] As shown in the figure, the equivalent inertia estimation method of the wind turbine based on the frequency dynamic response equivalence of the present application comprises the following steps: Figure 1

[0054] (1) Estimate the inertia and damping of the synchronous machine under normal operation of the power grid, specifically:

[0055] (1.1) Obtain the electromagnetic power at the terminal of the synchronous machine and the bus frequency under normal operation of the power grid within T seconds, and divide T seconds into n segments with a length of l seconds and a sliding time of Δt;

[0056] (1.2) Fit a first-order transfer function with the electromagnetic power of each segment of the synchronous machine as the input and the bus frequency as the output, as follows:

[0057]

[0058] Where a i and b i are the polynomial coefficients of the numerator and denominator of the transfer function, respectively, and s represents the differential operator.

[0059] (1.3) Calculate the inertia and damping estimation values of the synchronous machine in each time segment, as follows:

[0060]

[0061]

[0062] Where H i and D i are the inertia and damping estimation values of the synchronous machine in the i-th time segment.

[0063] (1.4) Process the estimation values H i and D i (i=1,2,...,n) by the percentile method to remove discrete values, set the lower percentile threshold to 20 and the upper percentile threshold to 80. The estimation values between the data corresponding to the upper and lower percentile thresholds are saved, and the average of the data corresponding to the upper and lower percentile thresholds is taken outside. Take the average of the processed data to obtain the inertia and damping estimation values of the synchronous machine.

[0064] (2) Obtain the related parameters of the synchronous machine governor, specifically including: the mechanical power gain coefficient K m , the high-pressure turbine power coefficient F H , and the reheating time constant T R ​, the governor coefficient R, obtaining the governor transfer function according to the obtained parameters, and combining the estimated inertia and damping of the synchronous machine in step (1) to establish a frequency response model of the power system; wherein the governor transfer function is:

[0065]

[0066] (3) obtaining the load power and grid frequency data under the active support of the wind turbine; wherein the load power is obtained by adding the electromagnetic power of the synchronous machine and the wind turbine;

[0067] (4) calculating the system inertia and damping after the equivalent of the active support of the wind turbine. The wind turbine suppresses the change of the grid frequency through active support, and the system inertia or damping improvement also has the effect of suppressing the change of the grid frequency, so the active support of the wind turbine can be equivalent to the improvement of the system inertia or damping from the perspective of frequency dynamic response equivalence. The inertia and damping estimation steps of the equivalent system are as follows:

[0068] (4.1) equivalent the active support of the wind turbine to the improvement of the system inertia or damping from the perspective of frequency dynamic response equivalence. The system equation under the active support of the wind turbine is:

[0069]

[0070] Wherein, ΔP wt is the active support power of the wind turbine; ΔP m is the primary frequency regulation power increment of the synchronous machine; H sg is the inertia estimation value of the synchronous machine in step 1; D sg is the damping estimation value in step 1.

[0071] After the equivalent of the active support of the wind turbine, the wind turbine does not provide active support power, and the system inertia or damping is improved. The system equation after the equivalent is:

[0072]

[0073] Wherein, H eq is the system inertia after the equivalent of the active support of the wind turbine; D eq is the system damping after the equivalent of the active support of the wind turbine.

[0074] (4.2) the equivalent transfer function G(s) is arranged as follows:

[0075]

[0076] Write G(s) in the form of state equation:

[0077]

[0078] Wherein, the state variable​ Output y = x1 + h0u.

[0079] Matrix in equation of state C = [1 0], D = 0.

[0080] (4.3) According to the load power and grid frequency data in step (3), identify the system gray box model. Wherein the governor parameter is a known parameter, and the equivalent system inertia H eq and damping D eq are to be identified parameters.

[0081] (5) According to the estimated synchronous machine inertia, damping in step (1), and the equivalent system inertia and damping in step (4), calculate the equivalent inertia and damping of the fan, respectively as follows:

[0082] H wt = H eq -H sg (9)

[0083] D wt = D eq -D L (10)

[0084] The application quantifies the active support capability of the fan by dynamically equivalent the frequency change of the system supported by the fan to the frequency change of the power system with improved equivalent inertia, so as to provide auxiliary decision for grid dispatching operation.

[0085] A computer device comprises a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor implements the following steps when executing the computer program:

[0086] (1) Estimate the inertia and damping of the synchronous machine in the normal operation state of the power grid;

[0087] (2) Obtain the related parameters of the synchronous machine governor, and establish a power system frequency response model in combination with the estimated inertia and damping of the synchronous machine in step (1);

[0088] (3) Obtain the load power and grid frequency data under the active support of the fan;

[0089] (4) In the equivalent perspective of frequency dynamic response, equivalent the active support of the fan to the improvement of the system inertia or damping, and identify the equivalent system inertia and damping after the active support of the fan through the data in step 3;

[0090] (5) Calculate the equivalent inertia and damping of the fan.

[0091] A computer storage medium, which stores a computer program, the computer program is executed by a processor to realize the following steps:

[0092] (1) estimating the inertia and damping of the synchronous machine in the normal operation state of the power grid;

[0093] (2) obtaining the related parameters of the synchronous machine governor, and establishing a power system frequency response model in combination with the inertia and damping of the synchronous machine estimated in step 1;

[0094] (3) obtaining the load power and grid frequency data under the active support of the wind turbine;

[0095] (4) equivalent to the promotion of system inertia or damping in the equivalent perspective of frequency dynamic response, identifying the equivalent inertia and damping of the system after the active support of the wind turbine is equivalent through the data in step (3);

[0096] (5) calculating the equivalent inertia and damping of the wind turbine.

[0097] Embodiment 1

[0098] Based on MATLAB / Simulink, a power system frequency response model containing wind power is built to verify the effectiveness of the method proposed in the application. The power grid model uses a low-order system response model (System Frequency Response, SFR), as shown in Figure 2 .

[0099] The grid parameters are set as follows: K m = 0.95, F H = 0.3, T R = 8, R = 0.0549. The actual inertia of the synchronous machine is 3.2884s, the damping is 1, and the wind power ratio is 20%. The load fluctuation curve and the frequency deviation curve under the normal operation state of the power grid are shown in Figure 3 , Figure 4 . The load fluctuation amplitude is small in this scenario, and the primary frequency regulation of the synchronous machine is not started.

[0100] Divide T = 600 into n = 32 segments with l = 40, Δt = 16, and obtain the inertia and damping estimation values of the synchronous machine by the percentile method to remove discrete values, which are H sg = 3.278s and D L = 1.0018. The relative error of the inertia estimation of the synchronous machine is: The relative error of the damping estimation is:

[0101] To verify that the application can accurately quantify the equivalent inertia and damping under the active support of the wind turbine, set the example: constant wind speed of 10 m / s, virtual inertia parameter of the wind turbine (denoted as kdf ) is set to 6; the droop control parameter (denoted as k pf ) is set to 3; the step inertia control parameter (denoted as ΔP0) is set to 0.02; the slope control parameter (the slope and the intercept of the linear function are denoted as k and b, respectively) are set to 0.3 and 0.03, respectively.

[0102] The estimated values of the equivalent inertia and damping of the system under the virtual inertia control of the fan are 3.8907 s and 1.0034, respectively. Therefore, the virtual inertia control of the fan provides an equivalent inertia of 3.8907-3.278 = 0.6127 s and an equivalent damping of 1.0034-1.0018 = 0.0016 ≈ 0. The comparison curve of the grid frequency before and after the equivalent of the virtual inertia control is shown in Figure 5 .

[0103] The estimated values of the equivalent inertia and damping of the system under the droop control of the fan are 3.2884 s and 1.6, respectively. Therefore, the virtual inertia control of the fan provides an equivalent inertia of 3.2884-3.278 = 0.0104 ≈ 0 s and an equivalent damping of 1.6-1.0018 = 0.5982. The comparison curve of the grid frequency before and after the equivalent of the droop control is shown in Figure 6 .

[0104] The estimated values of the equivalent inertia and damping of the system under the step inertia control of the fan are 3.4489 s and 1.7333, respectively. Therefore, the virtual inertia control of the fan provides an equivalent inertia of 3.4489-3.278 = 0.1709 s and an equivalent damping of 1.7333-1.0018 = 0.7315. The comparison curve of the grid frequency before and after the equivalent of the step inertia control is shown in Figure 7 . The estimated values of the equivalent inertia and damping of the system under the slope control of the fan are 3.6416 s and 1.8462, respectively. Therefore, the virtual inertia control of the fan provides an equivalent inertia of 3.6416-3.278 = 0.3636 s and an equivalent damping of 1.8462-1.0018 = 0.8444. The comparison curve of the grid frequency before and after the equivalent of the slope control is shown in Figure 8 .

Claims

1. A method for estimating the equivalent inertia of a wind turbine based on frequency dynamic response equivalence, characterized in that, Includes the following steps: (1) Estimate the inertia and damping of the synchronous machine under normal grid operation conditions; (2) Obtain relevant parameters of the synchronous speed controller, and establish a power system frequency response model based on the synchronous inertia and damping estimated in step (1). (3) Obtain load power and grid frequency data under active wind turbine support; (4) From the perspective of frequency dynamic response equivalence, the wind turbine's participation in the active support of the system is equivalent to the increase of system inertia or damping. The equivalent inertia and damping of the system after the active support of the wind turbine are estimated by the data in step (3). (5) Calculate the equivalent inertia and damping of the fan; In step (4), estimating the equivalent inertia and damping of the system after active support of the wind turbine includes the following steps: (4.1) From the perspective of frequency dynamic response equivalence, the wind turbine's participation in the active support of the system is equivalent to an increase in the system's inertia or damping; the system equations under the active support of the wind turbine are: Wherein, ΔP wt ΔP is the active support power of the wind turbine. m H represents the primary frequency modulation power increment of the synchronous machine. sg D is the estimated value of the synchronizing machine inertia in step 1; L This is the estimated damping value from step 1; After equipping the active support of the wind turbine, the equivalent system equations are as follows: Among them, H eq D represents the system inertia after active support of the wind turbine; eq The system damping is the equivalent of the active support of the wind turbine; (4.2) Equivalent transfer function The following is a summary: Write G(s) in state equation form: Among them, state variables Output y = x1 + h0u; Matrix in the state equation C = 1, 0; D = 0; (4.3) Based on the load power and grid frequency data in step (3), identify the gray box model of the system; where the governor parameters are known parameters, and the equivalent system inertia H eq and damping D eq The parameters to be identified; In step (5), the equivalent inertia and damping of the fan are calculated based on the synchronous machine inertia and damping estimated in step (1) and the equivalent system inertia and damping in step (4), as shown in the following formulas: H wt =H eq -H sg (9)D wt =D eq -D L (10)。 2. The method for estimating the equivalent inertia of a wind turbine based on frequency dynamic response equivalence as described in claim 1, characterized in that, In step (1), when estimating the inertia and damping of the synchronizing machine, the entire network of synchronizing machines is equivalent to a single equivalent synchronizing machine, specifically including the following steps: (1.1) Obtain the electromagnetic power at the generator terminal and the bus frequency under normal grid operation within T seconds, and divide T seconds into n segments with a length of l seconds and a sliding time of Δt; (1.2) The first-order transfer function is obtained by fitting the electromagnetic power of each synchronous machine segment as the input and the bus frequency as the output, as follows: Among them, a i b i These are the polynomial coefficients in the numerator and denominator of the transfer function, respectively, and the symbol s represents the differential operator; (1.3) Calculate the estimated values ​​of the synchronous machine inertia and damping for each time period, as follows: Among them, H i D i These are the estimated values ​​of the synchronous machine's inertia and damping during the i-th time segment; (1.4) The estimated value H is obtained by removing discrete values ​​using the percentile method. i D i The data (i = 1, 2, ..., n) are processed by setting lower percentile and upper percentile thresholds. If the estimated value is between the data corresponding to the upper and lower percentile thresholds, it is saved. If the estimated value is outside the data corresponding to the upper and lower percentile thresholds, the average value of the data corresponding to the upper and lower percentile thresholds is taken. The average value of the processed data is then used to obtain the estimated values ​​of the synchronous machine inertia and damping.

3. The method for estimating the equivalent inertia of a wind turbine based on frequency dynamic response equivalence as described in claim 1, characterized in that, In step (2), the relevant parameters of the synchronous speed controller are obtained, including the mechanical power gain coefficient K. m High-pressure steam turbine power coefficient F H Reheat time constant T R The governor coefficient R is used to obtain the governor transfer function based on the acquired parameters. A power system frequency response model is then established using the synchronous machine inertia and damping estimated in step (1). The governor transfer function is:

4. The method for estimating the equivalent inertia of a wind turbine based on frequency dynamic response equivalence as described in claim 1, characterized in that, In step (3), the load power and grid frequency data under active wind turbine support are obtained, wherein the load power is obtained by adding the synchronous machine and the electromagnetic power of the wind turbine.

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