Virtual Inertia Compensation Control Method for Wind Farms Based on the Responsibility Sharing of Grid Inertia Weakening

Abstract

A virtual inertia compensation control method for a wind farm based on the sharing of responsibilities for weakening grid inertia includes the following steps: Step 1: Detect the frequencies and load powers of each high-voltage bus node in the grid, and identify the inertia of each node by applying the subspace algorithm H b,k , and calculate the aggregated inertia of the grid H eq(1),k ; furthermore, obtain the weakening amount △ H eq,k of the grid-connected inertia of the wind farm; Step 2: According to the weakening amount △ H eq,k of the grid-connected inertia of the wind farm obtained in Step 1, solve the virtual inertia compensation amount of the wind farm implementing SFD inertia control H wf,k ; calculate the real-time control gain of the wind turbine K df ; Step 3: Detect whether a power system frequency accident occurs based on the rate of change of frequency detection and threshold judgment: when it occurs, adopt K df a dynamic setting method to dynamically set K av.df ( t ); if it does not occur, set K df = 0. The method of the present invention is significantly effective for adapting to the frequency safety and stability of a power grid with large-scale and high-penetration wind power grid connection.

Description

Technical Field

[0001] The present invention relates to the field of frequency safety and stability analysis of wind power integrated power grids, and particularly to a virtual inertia compensation control method for wind farms based on the sharing of responsibilities for grid inertia weakening. Background Art

[0002] The large-scale and high-proportion access of wind power continuously reduces the grid inertia, and the dynamic frequency characteristics of the power grid will deteriorate severely. In view of the above situation, wind power virtual inertia control is considered an effective means to solve the above problems. However, the implementation of virtual inertia control has a dual game nature of "being disadvantageous to itself" and "bearing responsibilities" for wind farms. On the one hand, the technical implementation will have several adverse effects on wind farms: 1) The wind turbines deviate from the optimal rotational speed and maximum power tracking state, reducing power generation economy; 2) The greater the inertia support provided and the more kinetic energy released, the longer the rotational speed recovery and disturbance process will be; 3) The rotational speed of the wind turbine rotor changes frequently, causing shaft torque forces and shortening the service life of the unit. The greater the inertia support strength provided by the wind farm and the longer the continuous process, the more prominent the above adverse effects will be. On the other hand, the grid connection of wind farms causes the continuous weakening of the grid equivalent inertia, and the responsibility for compensating the grid inertia should be borne by implementing virtual inertia control. Therefore, a control method lacking a scientific determination of the responsibility for inertia weakening and a matching inertia support strength is difficult to promote and implement in the operation and transformation of wind farms. It is urgent to explore and study an inertia control method that can provide a reliable theoretical basis for the implementation of control technologies and the formulation of standards.

[0003] Considering the fact that the root cause of the deterioration of the grid dynamic frequency characteristics lies in the weakening of the grid inertia caused by the grid connection of new energy sources such as wind power, if the key issues of how much the grid connection of wind farms weakens the grid equivalent inertia and how much inertia support should be borne and compensated by wind farms during the frequency disturbance process can be clarified, the method of sharing the responsibilities of wind farm grid connection determined by the inertia weakening amount can be established, and a reliable theoretical basis can be provided for the implementation of virtual inertia control technologies and the formulation of standards. Summary of the Invention

[0004] In view of this, quantitatively calculate the amount of grid inertia weakening caused by the grid connection of wind farms, determine the virtual inertia compensation target of the wind farm according to the amount of grid inertia weakening, and clarify the functional relationship between the inertia compensation target and the control parameters. The present invention proposes a virtual inertia compensation control method for wind farms based on the sharing of responsibilities for grid inertia weakening. This method first estimates the amount of wind power grid connection inertia weakening, then calculates the inertia compensation amount of the wind farm according to the amount of wind power grid connection inertia weakening, clarifies the functional relationship between the inertia compensation target and the control parameters, and finally executes the control strategy by dynamically adjusting the key control parameters to maintain the frequency safety and stability of the power grid. This method is significantly effective for adapting to the frequency safety and stability of large-scale and high-penetration wind power integrated power grids.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A virtual inertia compensation control method for a wind farm based on the sharing of the responsibility for weakening the grid inertia includes the following steps:

[0007] Step 1, estimating the weakening amount ΔH of the inertia of the wind power grid connection: eq,k Estimate:

[0008] Detect the frequencies and load powers of the high-voltage bus nodes of the power grid, and identify the inertia H of each node by applying the subspace algorithm b,k , and calculate the aggregated inertia H of the power grid eq(1),k ; and then obtain the weakening amount ΔH of the inertia of the wind farm grid connection eq,k ;

[0009] Step 2, calculating the real-time control gain K of the wind turbine generator: df Calculate:

[0010] According to the weakening amount ΔH of the inertia of the wind farm grid connection obtained in Step 1 eq,k , solve the virtual inertia compensation amount H of the wind farm implementing the SFD inertia control wf,k ; calculate the real-time control gain K of the wind turbine generator df ;

[0011] Step 3, detecting whether a power system frequency accident occurs according to the frequency change rate detection and threshold judgment:

[0012] When it occurs, adopt the K df dynamic setting method to dynamically set K av .df(t); if not, set K df = 0.

[0013] In the said Step 1, the weakening amount ΔH of the inertia of the wind power grid connection eq,k refers to the value by which the grid equivalent inertia decreases due to the connection of wind farm k, and its magnitude is equal to the grid equivalent inertia before the connection of wind farm k minus the grid equivalent inertia after the connection of wind farm k.

[0014] In the said Step 1, in a power system with a large-scale wind power, the system equivalent inertia can be expressed as:

[0015]

[0016] In the formula, m is the number of wind farms, and n is the number of synchronous generator units; H wf,i , S wf,i are respectively the equivalent inertia and grid connection capacity of the i-th wind farm; H syn,j , S syn,j are respectively the inertia and grid connection capacity of the j-th synchronous generator unit. In the traditional control mode, the wind turbine generator is decoupled from the grid frequency, and the equivalent inertia of the corresponding wind farm is approximately 0, and there is:

[0017]

[0018] For the k-th wind farm connected to the system, the equivalent grid inertia in its grid-connected and islanded states is respectively:

[0019]

[0020]

[0021] In the formula, the subscripts 1 and 0 represent the grid-connected and islanded states of the wind farm respectively. Then the reduction of the grid inertia caused by the grid connection of the k-th wind farm is:

[0022]

[0023] It can be seen from Equation (5) that when H eq(1),k , S wf,k , and are known, ΔH eq,k can be obtained, where S wf,k , is the unit grid connection information and is easy to obtain. The main problem is how to solve H eq(1),k . In principle, as long as the grid connection information of the grid-connected units mastered by the dispatching center: capacity and inertia are used, H eq(1),k can be calculated through Equation (3). However, in actual operation, there are a large number of scattered non-dispatchable units, and their grid connection information is not mastered by the dispatching center, so Equation (3) cannot be directly used to calculate the accurate grid inertia H eq(1),k . According to the real-time operation state of the grid, using the operation data information to identify H eq(1),k , and then combining with Equation (5) to solve ΔH eq,k is a feasible method.

[0024] The subspace identification algorithm is an algorithm based on input-output data for identification. This algorithm does not need to obtain the system model and its parameters by minimizing a certain objective function, but directly processes the full state space model of the system through various matrix operations without iterative operations. Therefore, there is no convergence problem, and the numerical robustness is good, which can ensure the accuracy of the identification results.

[0025] H eq(1),k is the overall network inertia when the wind farm is grid-connected. When specifically estimating H eq(1),k , the high-voltage bus node can be used as the basic object, and first estimate the inertia H b,k of each node, b = 1, 2... B, where B is the high-voltage bus node with power access in the whole network.

[0026] For any b-th node, it can be equivalent to a synchronous generator set, and the corresponding incremental form of the rotor motion equation is:

[0027]

[0028] In the formula, Δf b , ΔP m,b , ΔP e,b , D b,k are respectively the measured frequency, equivalent mechanical power increment, load power increment, and equivalent damping of node b.

[0029] When the inertia H of each node is estimated b,k , use the following formula to solve for H eq(1),k :

[0030]

[0031] In the formula, b is the high-voltage bus node with power access in the whole network, where b = 1, 2... B; S b,k is the aggregated capacity of the synchronous power sources connected under node b.

[0032] For any high-voltage bus node b and the equivalent unit described by Equation (7), when there is a load power disturbance ΔP e,b , under the dynamic action of the inertia of the equivalent unit, a corresponding node frequency disturbance Δf b will be generated. Considering that the mechanical power acts for a long time and ΔP m,b ≈0 during the dynamic process. Therefore, there is a frequency response system of node b with ΔP e,b as the input and Δf b as the output, and the inertia H b,k of this system can be identified using real-time disturbance data. During the continuous operation of the system, the input / output data are divided into small disturbances and large disturbances according to the amplitude. In the case of small disturbances, only the inertia dynamics exist in the equivalent system. In the case of large disturbances, when the amplitude of the frequency disturbance exceeds the dead zone of the primary frequency regulation of the unit, both inertia and primary frequency regulation dynamic responses exist. However, in both of these cases, the equivalent inertia H b,k can be obtained through the initial impulse response of the calculation model, and the relationship between H b,k and the impulse response of the system is:

[0033]

[0034] In the formula, g1(t) is the impulse response function of the system in the time domain for small disturbances (corresponding to the frequency domain transfer function G1(s)), and G2(s) is the frequency domain transfer function of the system for large disturbances (corresponding to the impulse response function g2(t)) in the time domain. Therefore, regardless of whether it is excited by small disturbance or large disturbance data, the node inertia H b,k can be identified.

[0035] Based on the above analysis, if the node load power ΔP e,b is used as the input and the node Δf b is used as the output, and the node equivalent frequency response system is regarded as the system to be identified, the transfer function of the model has the following general form:

[0036]

[0037] where a0, …, a n-1 , b0, …, b n-1 are the coefficients of the transfer function model. This model is determined by the input and output data, can describe the external characteristics of the node equivalent frequency response system, and the parameters do not have obvious physical meanings. According to the initial value theorem, we can get:

[0038] g(t)| t＝0 = sG(s)| s→∞ = a0 (10);

[0039] According to the corresponding relationship of Equation (8), the equivalent inertia of the identified node can be obtained as:

[0040]

[0041] In the process of solving H b,k above, mainly the model parameters a0, …, a n-1 , b0, …, b n-1 are identified. In the present invention, the subspace method is selected for identification.

[0042] In step 2, the SFD inertia control refers to the supplementary frequency differentiation inertia control. This inertia control is a classical virtual inertia control method for wind turbines. Its principle is that when a frequency disturbance occurs, by triggering the supplementary inertia control module and adjusting the control gain K df , the electromagnetic torque and active power output of the wind turbine are changed, so as to suppress the system frequency change and can externally exhibit virtual inertia.

[0043] In step 2, after considering the implementation of SFD inertia control on wind farm k, its equivalent virtual inertia is H wf,k , then the equivalent inertia of the power grid after this wind farm is connected to the grid should be:

[0044]

[0045] The inertia of the power grid before and after wind farm k is connected to the grid should remain unchanged:

[0046] H′ eq(1),k = H eq(0),k (13);

[0047] Substituting Equation (4) and Equation (12) into Equation (13), we can obtain:

[0048]

[0049] After simplification, we can obtain:

[0050]

[0051] Combining with Equation (3), Equation (5) and Equation (15) again, we get H wf,k and ΔH eq,k relationship:

[0052]

[0053] In the formula, m is the number of wind farms, n is the number of synchronous units; S wf,i is the grid connection capacity of the i-th wind farm; S syn,j is the grid connection capacity of the j-th synchronous unit; S wf,k is the grid connection capacity of wind farm k.

[0054] Equation (16) shows that if the equivalent inertia of wind farm k is H wf,k by implementing the virtual inertia control strategy, it can ensure the effective compensation for ΔH eq,k and ensure that the grid inertia remains unchanged before and after the grid connection of the wind farm.

[0055] In the said step 2, under the action of the SFD inertia control strategy, the virtual rotational inertia of the doubly-fed wind turbine relative to the change of the system synchronous angular frequency can be expressed as:

[0056]

[0057] In the formula, J DFIG , ω r0 , Δω r respectively represent the inherent rotational inertia of the doubly-fed wind turbine, the initial rotor angular frequency and the rotor angular frequency increment; ω s0 , Δω s respectively represent the initial system synchronous angular frequency and the system synchronous angular frequency increment.

[0058] According to Equation (17) and the basic definition of inertia, the equivalent virtual inertia of the doubly-fed wind turbine can be expressed as:

[0059]

[0060] In the formula, S N is the rated capacity of the wind turbine; ω nom is the rated angular frequency of the wind turbine; H DFIG = ω 2 nomJ DFIG / (2P 2 S N ) is the inherent inertia of the wind turbine.

[0061] Referring to the basic derivation process of the system frequency response model (SFR) and combining with Equation (18), the complex frequency domain expression of H can be obtained as: equ The complex frequency domain expression of H is:

[0062]

[0063] In the formula, K df , T f are the virtual inertia control gain and the filter time constant respectively; K pT , K iT are the proportional coefficient and the integral coefficient of the speed controller respectively.

[0064] Rearranging Equation (19) gives:

[0065]

[0066]

[0067]

[0068] Then, according to the discriminant Δ=(K 2 +K pT / (2H DFIG )s+K iT / (2H DFIG ) of the equation s pT / 2H DFIG ) 2 -2K iT / H DFIG in the form of, it is discussed in two cases to convert Equation (20) into the time domain form.

[0069] 1) When Δ≥0

[0070]

[0071]

[0072] Among them, α1, α2, α3 are the three single roots of D(s)=0; K1, K2, K3 are the expansion coefficients of the partial fraction of Equation (21).

[0073]

[0074] Among them, α1' and α2'±jβ are respectively a single root and a pair of conjugate complex roots of D(s)=0; β is the imaginary part of α2'±jβ; θ = ∠K2'; K1' and K2' are the expansion coefficients of the partial fraction of Equation (21).

[0075] Equations (22) and (23) are for the corresponding virtual inertia control gain K df , the initial synchronous angular frequency ω s0 , the initial rotor angular frequency ω r0 , related physical / control parameters (H DFIG , ω nom , K pT , K iT , T f ) of the doubly-fed wind turbine equivalent virtual inertia time-domain value. According to Equations (22) and (23), among the numerous parameters affecting H equ (t), H DFIG , ω nom , K pT , K iT , T f are constant values, the initial synchronous angular frequency ω s0 is the rated value at steady state, and the virtual inertia control gain K df and the initial rotor angular frequency ω r0 jointly determine H equ (t).

[0076] Therefore, if we want to compensate for the grid inertia ΔH eq,k weakened by the grid connection of the wind farm and simulate the virtual inertia H wf,k of the wind farm corresponding to Equation (16), we should allocate H wf,k to each wind turbine in the wind farm to share jointly.

[0077] Since the wind speed difference in the wind farm is very small and usually the same type of units are used, with the same parameters H DFIG , J DFIG , S N ; the speed controller parameters K pT , K pT ; each wind turbine adopts the same virtual inertia control model and control parameters, that is, with the same virtual inertia control gain K df and the filter time constant T f . Then, when the wind farm k contains L wind turbines, the virtual inertia H wf,k of the wind farm k can be expressed as:

[0078]

[0079] In the formula, H wf,klis the virtual inertia of the l-th wind turbine in wind farm k, and numerically equal to the virtual inertia H of wind farm k wf,k , that is, the inertia compensation target of any wind turbine in wind farm k is equal to the virtual inertia of wind farm k.

[0080] Based on the above description, it is necessary to use the H in Eqs. (22) and (23) equ (t) - K df , ω r0 time-domain function relationship, and inversely determine the control gain K according to the wind turbine inertia compensation target in Eq. (24) df :

[0081]

[0082] where H wf,k is the equivalent inertia of wind farm k; ω nom is the rated angular frequency of the wind turbines in wind farm k; ω r0 is the initial rotor angular frequency of the wind turbines in wind farm k; ω s0 is the initial grid synchronization angular frequency; T f is the filtering time constant of the virtual inertia controller of the wind turbines in wind farm k; Δ = (K pT / 2H DFIG ) 2 - 2K iT / H DFIG is the discriminant of the equation s 2 + K pT / (2H DFIG )s + K iT / (2H DFIG ), where: H DFIG ,, K pT and K iT are the inherent inertia time constant, the proportional coefficient of the speed controller, and the integral coefficient of the speed controller of the wind turbines in wind farm k respectively; α1, α2, α3 are the three single roots of D(s) = 0 in Eq. (21) when Δ ≥ 0, and K1, K2, K3 are the expansion coefficients of the partial fraction of Eq. (21) when Δ ≥ 0, where Eq. (21) is:

[0083]

[0084] α1', α2' ± jβ are a single root and a pair of conjugate complex roots of D(s) = 0 in Eq. (21) when Δ ≤ 0 respectively, β is the imaginary part of α2' ± jβ, θ = ∠K2', and K1' and K2' are the expansion coefficients of the partial fraction of Eq. (21) when Δ ≤ 0.

[0085] The grid-connected inertia reduction of the wind farm ΔH eq,kSubstitute into Equation (16) to solve for the virtual inertia compensation amount H of the wind farm implementing SFD inertia control wf,k , and then calculate the real-time control gain K of the wind turbine according to Equation (25) df .

[0086] Each wind turbine, according to the real-time wind speed and the corresponding rotational speed ω r0 , by setting the control gain K of Equation (25) df executes the virtual inertia compensation control strategy, and can then respond to the inertia compensation target in Equation (24). The entire wind farm can also respond to the compensated virtual inertia H wf,k .

[0087] In step 3, the rate of change of frequency RoCoF (Rate of Change of Frequency) is numerically equal to the real-time slope value of the power system frequency dynamic curve.

[0088] In step 3, a power system frequency accident refers to an accident where, when there is a large active power shortage in the power system, the frequency drops significantly, causing a major power outage or other accidents in the power system or a local system.

[0089] In step 3 Figure 1 is the K df curve under different wind speeds, corresponding to the case of Δ ≤ 0 in Equation (25). The K df curve when Δ ≥ 0 can be referred to Figure 2 . If directly setting K Figure 1 according to Equation (25) and df , there are two problems

[0090] ①. The K df curve is continuously time-varying. If setting parameters based on this and frequently changing K df , there will be phenomena such as electromagnetic torque oscillation and unstable output active power

[0091] ②. Since the numerator of K df is always a positive constant and the denominator is a time-varying function, K df may be an infinite value. Setting K df too large will lead to power self-excited oscillation, causing the control system to lose stability. Therefore, when K df is infinite, it should be restricted.

[0092] Therefore, to solve the above two problems, the following dynamic setting method of K df can be adopted

[0093] 1). During the inertial response dynamic process, K df changes once every 0.1 s cycle, and each set value is the integral mean value of the K df curve within the cycle

[0094]

[0095] Among them, u = [10×t] / 10, w = ([10×t] / 10) + 0.1, and the symbol [] represents the rounding operation.

[0096] 2): If K df The left and right limits approach infinity around a certain t0 moment. Let the set value of the period where the t0 moment is located be the K of the previous 1 df Integral mean value.

[0097] 3): When the rate of change of frequency (RoCoF) RoCoF ≤ ε is continuously detected, where ε is the set precision error, indicating that the frequency response tends to be stable, set K df = 0, and the inertial response is cut off.

[0098] The virtual inertia compensation control method for a wind farm based on the responsibility sharing of grid inertia weakening in the present invention has the following technical effects:

[0099] 1) The calculation process of the grid-connected inertia weakening amount of the wind farm is clear, which can be used as a direct basis for evaluating the responsibility sharing of the grid-connected wind farm in weakening the grid inertia.

[0100] 2) The grid connection of the wind farm causes the dynamic characteristics of the system frequency to deteriorate significantly. By implementing the virtual inertia compensation control strategy of the wind farm, the dynamic characteristics of the frequency can be maintained well.

[0101] 3) The virtual inertia compensation control strategy of the wind farm can dynamically adjust the control gain according to the wind speed change, accurately compensate the inertia weakening amount, so as to ensure the frequency support ability under frequency accidents, and the strategy has good adaptability.

[0102] 4) As the wind power penetration rate increases, the control method of the present invention can still be applied to ensure the grid inertia level and effectively avoid the deterioration of the dynamic frequency characteristics of the system. In the process of building a new power system in the future, wind power will be connected to the system on a larger scale and with a higher penetration rate. The present invention may be an effective measure to address the grid frequency safety and stability under this situation. Description of the Drawings

[0103] Figure 1 K at different wind speeds df Curve graph (corresponding to formula (25), Δ ≤ 0).

[0104] Figure 2 K at different wind speeds df Curve graph (corresponding to formula (25), Δ ≥ 0).

[0105] Figure 3 It is the execution flow chart of the virtual inertia compensation control strategy for the wind farm.

[0106] Figure 4 It is the system diagram of the example.

[0107] Figure 5 It is the frequency response curve affected by the virtual inertia compensation control of the wind farm.

[0108] Figure 6 It is the RoCoF curve affected by the virtual inertia compensation control of the wind farm.

[0109] Figure 7 It is the frequency response curve affected by the control under different wind speeds.

[0110] Figure 8 It is the RoCoF curve affected by the control under different wind speeds.

[0111] Figure 9 It is the frequency response curve affected by the control under different wind power penetration rates.

[0112] Figure 10 It is the RoCoF curve affected by the control under different wind power penetration rates. Specific implementation method

[0113] For the virtual inertia compensation control method of the wind farm based on the responsibility sharing of grid inertia weakening, first, the present invention takes network nodes as the basic objects, uses the active power / frequency random disturbance information of the nodes to identify the node inertia and the grid aggregated inertia, and further solves the weakening amount of the grid inertia caused by the grid connection of the wind farm through mathematical derivation; then, according to the idea of responsibility sharing of "weakening - compensation" of inertia, calculates the inertia compensation target of the wind farm, and further establishes the time-domain function relationship between the inertia compensation target and the key control parameters and state parameters of the virtual inertia; then dynamically sets the control parameters according to the inertia compensation target of the fan and executes the virtual inertia compensation control strategy. Finally, the effectiveness and superiority of the theoretical method proposed by the present invention are verified through an example system. The implementation flowchart is as Figure 3 shown, including the following steps:

[0114] Step 1: Inertia weakening amount ΔH of wind power grid connection eq,k Estimation:

[0115] Detect the frequencies and load powers of each high-voltage bus node of the power grid, and apply the subspace algorithm to identify the inertia H of each node b,k ; Substitute H b,k into Equation (7) to calculate the grid aggregated inertia H eq(1),k ; Furthermore, obtain the inertia weakening amount ΔH of the wind farm grid connection through Equation (5) eq,k .

[0116] In a power system with large-scale wind power, the equivalent inertia of the system can be expressed as:

[0117]

[0118] In the formula, m is the number of wind farms, and n is the number of synchronous generator sets; H wf,i , S wf,i are the equivalent inertia and grid connection capacity of the i-th wind farm respectively; H syn,j , S syn,j are the inertia and grid connection capacity of the j-th synchronous generator set respectively. In the traditional control mode, the wind turbine generator is decoupled from the grid frequency, and the equivalent inertia of the corresponding wind farm is approximately 0, and there is:

[0119]

[0120] For the k-th wind farm connected to the system, the equivalent grid inertia in its grid-connected and off-grid states is respectively:

[0121]

[0122]

[0123] In the formula, the subscripts 1 and 0 represent the grid-connected and off-grid states of the wind farm respectively. Then the reduction amount of the grid inertia caused by the grid connection of the k-th wind farm is:

[0124]

[0125] It can be seen from formula (5) that when H eq(1),k , S wf,k , and are known, ΔH eq,k can be obtained. Among them, S wf,k , is the unit grid connection information and is easy to obtain. The main problem is how to solve H eq(1),k . In principle, as long as the grid connection unit information (capacity, inertia) mastered by the dispatching center is used, H eq(1),k can be calculated through formula (3). However, in actual operation, there are a large number of scattered non-dispatchable units, and their grid connection information is not mastered by the dispatching center, so formula (3) cannot be directly used to calculate the accurate grid inertia H eq(1),k . According to the real-time operation state of the power grid, it is a feasible method to identify H eq(1),k using the operation data information and then solve ΔH eq,k in combination with formula (5).

[0126] H eq(1),k is the total grid inertia when the wind farm is grid-connected. When specifically estimating H eq(1),k , the high-voltage bus node can be used as the basic object, and first estimate the inertia H b,k of each node (b = 1, 2... B, which are the high-voltage bus nodes with power sources connected to the whole network).

[0127] For any b-th node, it can be equivalent to a synchronous generator set, and the corresponding incremental form of the rotor motion equation is:

[0128]

[0129] where Δf b , ΔP m,b , ΔP e,b , D b,k are respectively the measured frequency, equivalent mechanical power increment, load power increment, and equivalent damping of node b.

[0130] After estimating the inertia H b,k of each node, the following formula can be further used to solve for H eq(1),k :

[0131]

[0132] where S b,k is the aggregated capacity of the synchronous power sources connected under node b.

[0133] For any high-voltage bus node b and the equivalent unit described by Equation (7), when there is a load power disturbance ΔP e,b , under the dynamic action of the inertia of the equivalent unit, a corresponding node frequency disturbance Δf b will be generated. Considering that the mechanical power acts for a long time, ΔP m,b ≈0 during the dynamic process. Therefore, there is a frequency response system of node b with ΔP e,b as the input and Δf b as the output, and the inertia H b,k of this system can be identified using real-time disturbance data. During the continuous operation of the system, the input / output data are divided into small disturbances and large disturbances according to the amplitude. In the case of small disturbances, only the inertia dynamics exist in the equivalent system. In the case of large disturbances, when the amplitude of the frequency disturbance exceeds the dead zone of the primary frequency regulation of the unit, both the inertia and the primary frequency regulation dynamic responses exist. However, in both of the above cases, the equivalent inertia H b,k can be obtained through the initial impulse response of the calculation model, and the relationship between H b,k and the impulse response of the system is:

[0134]

[0135] where g1(t) is the impulse response function of the system in the time domain for small disturbances (corresponding to the frequency domain transfer function G1(s)), and G2(s) is the frequency domain transfer function of the system for large disturbances (corresponding to the impulse response function g2(t)) in the time domain. Therefore, regardless of whether it is excited by small disturbance or large disturbance data, the node inertia H b,k can be identified.

[0136] Based on the above analysis, if the node load power ΔP e,b is used as the input and the node Δf b is used as the output, and the node equivalent frequency response system is regarded as the system to be identified, the transfer function of the model has the following general form:

[0137]

[0138] where a0, …, a n-1 , b0, …, b n-1 are the coefficients of the transfer function model. This model is determined by the input and output data, can describe the external characteristics of the node equivalent frequency response system, and the parameters do not have obvious physical meanings. According to the initial value theorem, we can get:

[0139] g(t)| t＝0 = sG(s)| s→∞ = a0 (10)

[0140] According to the corresponding relationship of Equation (8), the equivalent inertia of the identified node can be obtained as:

[0141]

[0142] In the process of solving H b,k above, mainly the model parameters a0, …, a n-1 , b0, …, b n-1 are identified. In the present invention, the subspace method is selected for identification.

[0143] Step 2: Calculate the real-time control gain K df of the wind turbine:

[0144] According to the wind farm grid connection inertia reduction amount ΔH eq,k obtained in Step 1, substitute it into Equation (16) to solve the virtual inertia compensation amount H wf,k of the wind farm implementing SFD inertia control; then calculate the real-time control gain K df of the wind turbine according to Equation (25).

[0145] Considering that after implementing SFD inertia control on wind farm k, its equivalent virtual inertia is H wf,k , then the equivalent inertia of the power grid after grid connection of this wind farm should be:

[0146]

[0147] The inertia of the power grid before and after grid connection of wind farm k should remain unchanged:

[0148] H′ eq(1),k = H eq(0),k (13)

[0149] Substituting Equation (4) and Equation (12) into Equation (13), we can obtain:

[0150]

[0151] After simplification, we can obtain:

[0152]

[0153] Combined with Equation (3), Equation (5) and Equation (15) again, we get the relationship between H wf,k and ΔH eq,k :

[0154]

[0155] Equation (16) indicates that if the equivalent inertia of wind farm k is H wf,k by implementing the virtual inertia control strategy, the effective compensation for ΔH eq,k can be guaranteed, ensuring that the grid inertia remains unchanged before and after the grid connection of the wind farm.

[0156] Under the action of the SFD inertia control strategy, the virtual moment of inertia of the doubly-fed wind turbine relative to the change in the system synchronous angular frequency can be expressed as:

[0157]

[0158] where J DFIG , ω r0 , and Δω r represent the inherent moment of inertia, the initial rotor angular frequency, and the rotor angular frequency increment of the doubly-fed wind turbine, respectively; ω s0 , and Δω s represent the initial system synchronous angular frequency and the system synchronous angular frequency increment, respectively.

[0159] According to Equation (17) and the basic definition of inertia, the equivalent virtual inertia of the doubly-fed wind turbine can be expressed as:

[0160]

[0161] where S N is the rated capacity of the wind turbine; ω nom is the rated angular frequency of the wind turbine; H DFIG = ω 2 nom J DFIG / (2P 2 S N ) is the inherent inertia of the wind turbine.

[0162] Referring to the basic derivation process of the system frequency response model (SFR) and combining with Equation (18), we can obtain Hequ The complex frequency domain expression of

[0163]

[0164] is: In the formula, K df , T f are the virtual inertia control gain and the filtering time constant respectively; K pT , K iT are the proportional coefficient and the integral coefficient of the speed controller respectively.

[0165] Arrange Equation (19) as:

[0166]

[0167] where P(s) is:

[0168]

[0169] Then, according to the discriminant Δ=(K 2 +K pT / (2H DFIG )s+K iT / (2H DFIG ) of the equation s pT / 2H DFIG ) 2 -2K iT / H DFIG in the form of, discuss in two cases in order to convert Equation (20) into the time domain form.

[0170] 1) When Δ≥0

[0171]

[0172] where α1, α2, α3 are the three single roots of D(s)=0; K1, K2, K3 are the expansion coefficients of the partial fraction of Equation (21).

[0173] 2) When Δ≤0

[0174]

[0175] where α1', α2'±jβ are a single root and a pair of conjugate complex roots of D(s)=0 respectively; θ=∠K2'; K1' and K2' are the expansion coefficients of the partial fraction of Equation (21).

[0176] Equations (22) and (23) are for the corresponding virtual inertia control gain K df , the initial synchronous angular frequency ω s0 of the system, the initial angular frequency ω r0 of the rotor, and the relevant physical / control parameters (H DFIG , ωnom , K pT , K iT , T f ) of the doubly-fed wind turbine equivalent virtual inertia time-domain value. According to Eqs. (22) and (23), among the many parameters affecting H equ (t), H DFIG , ω nom , K pT , K iT , T f are constant values, the system initial synchronous angular frequency ω s0 is the rated value at steady state, and the virtual inertia control gain K df and the rotor initial angular frequency ω r0 jointly determine H equ (t).

[0177] Therefore, if we want to compensate for the grid inertia ΔH eq,k weakened by the grid connection of the wind farm and simulate the virtual inertia H wf,k of the wind farm corresponding to Eq. (16), H wf,k should be allocated to each wind turbine in the wind farm to jointly bear.

[0178] Since the wind speed difference in the wind farm is very small and usually the same type of units are used, with the same parameters H DFIG , J DFIG , S N ; the speed controller parameters K pT , K pT ; each wind turbine adopts the same virtual inertia control model and control parameters, that is, with the same virtual inertia control gain K df and the filtering time constant T f . Then, when the wind farm k contains L wind turbines, the virtual inertia H wf,k of the wind farm k can be expressed as:

[0179]

[0180] In the formula, H wf,kl is the virtual inertia of the l-th wind turbine in the wind farm k, and numerically it is equal to the virtual inertia H wf,k of the wind farm k, that is, the inertia compensation target of any wind turbine in the wind farm k is equal to the virtual inertia of the wind farm k.

[0181] Based on the above description, it is necessary to use the H equ (t)-K df , ω r0 time-domain function relationship of Eqs. (22) and (23) to inversely determine the control gain K df according to the fan inertia compensation target of Eq. (24):

[0182]

[0183] Each fan, according to the real-time wind speed and the corresponding rotational speed ω r0 , by setting the control gain K in Equation (25) df to execute the virtual inertia compensation control strategy, the inertia compensation target in Equation (24) can be responded to, and the entire wind farm can also respond to the compensated virtual inertia H wf,k .

[0184] Step 3: Dynamic setting of the virtual inertia control gain K df Dynamic setting:

[0185] Based on the RoCoF detection and threshold judgment, determine the occurrence of a power system frequency accident: when it occurs, adopt the K df dynamic setting method to dynamically set K av.df (t); if it does not occur, set K df = 0.

[0186] Figure 1 is the K df curve under different wind speeds, corresponding to the case of Δ≤0 in Equation (25), and the K df curve when Δ≥0 can be referred to Figure 2 . If directly set K Figure 1 according to Equation (25) and df , there are two problems: ① The K df curve changes continuously with time. If the parameters are set accordingly and K df is frequently changed, electromagnetic torque oscillation and unstable output active power will occur; ② Since the numerator of K df is always a positive constant and the denominator is a function that changes with time, K df may be an infinite value. Setting K df too large will cause power self-excitation oscillation and make the control system lose stability. Therefore, when K df is infinite, it should be restricted. Therefore, to solve the above two problems, the following K df dynamic setting method can be adopted:

[0187] 1) During the dynamic process of inertia response, K df changes once every 0.1 s cycle, and each setting value is the integral mean value of the K df curve within the cycle:

[0188]

[0189] where u = [10×t] / 10, w = ([10×t] / 10) + 0.1, and the symbol [] represents the integer operation.

[0190] 2) If K dfAt around a certain moment \(t_0\), the left and right limits approach infinity. Let the set value of the cycle where the moment \(t_0\) is located be \(K\) of the previous cycle. df Integral mean value.

[0191] 3) When the rate of change of frequency (RoCoF) is continuously detected and \(RoCoF\leqslant\varepsilon\) (the set precision error), it indicates that the frequency response tends to be stable, and set \(K\) df = 0, and the inertial response is cut off.

[0192] Step 4: The virtual inertia compensation control method of the wind farm based on the sharing of the responsibility for weakening the power grid inertia established above is verified by using, for example, Figure 4 a numerical example system and based on the Matlab / simulink tool.

[0193] In this numerical example, a large wind farm \(k\) is connected. The detailed parameters of the system and each component are shown in Table 1. Before the simulation calculation, the following settings are made:

[0194] 1) To reflect different wind speed states of the wind farm, three wind conditions are set during the simulation operation: ① Wind condition 1, wind speed = 11 m / s; ② Wind condition 2, wind speed = 10 m / s; ③ Wind condition 3, wind speed = 9 m / s.

[0195] 2) Simulate and set the normal random disturbance of the load during actual operation: Add small-amplitude randomly varying loads to bus 1 and bus 2 respectively to reflect the load disturbance in the system.

[0196] Table 1 Parameter values of the numerical example system

[0197]

[0198] Taking the grid connection capacity of G1 as 400 MW, G2 as 500 MW, G3 as 900 MW, G4 as 900 MW, and the grid connection capacity of the wind farm as 1500 MW as the initial steady state of the numerical example system, and calculating respectively by the subspace method and the actual grid connection capacity of the unit. According to Equation (3), for the power grid inertia under the grid connection of the wind farm, the estimated value of the power grid inertia can be obtained as 4.08 s, and the theoretical value is 4.04 s; further, according to the power grid inertia under the grid connection of the wind farm, applying Equation (5), the estimated value of the inertia weakening amount can be obtained as 2.27 s, and the theoretical value is 2.24 s. The estimated error of the inertia weakening amount is only 1.34%. It can be seen that the accuracy of estimating the inertia weakening amount by the subspace method is relatively high. Therefore, this index can be used as the direct basis for quantitatively evaluating the sharing of the responsibility for weakening the power grid inertia by the grid-connected wind farm.

[0199] (1) Verification of the effect of the virtual inertia compensation control strategy of the wind farm:

[0200] When t = 100 s is set, the sudden increase in load L3 = 160 MW, a frequency accident occurs in the simulated system, the corresponding wind power penetration pene. = 33%, and the wind speed = 10 m / s. According to the above operating conditions, according to Figure 3 The control gain K is dynamically set according to the control flow df , and the virtual inertia compensation control strategy of the fan is executed. The system frequency response curves in three cases of the wind farm being off-grid, the virtual inertia compensation control of the wind farm, and the virtual inertia of the wind farm not being compensated are extracted and compared, as shown in Figure 5 .

[0201] From Figure 5 the comparison, it can be seen that:

[0202] 1) Compared with the off-grid state of the wind farm, the frequency drop speed is much faster and the lowest point of the frequency drop is significantly deeper when the wind farm is connected to the grid. The frequency dynamic characteristics deteriorate significantly, which is caused by the weakening of the grid inertia;

[0203] 2) When the wind farm is connected to the grid, by implementing the virtual inertia compensation control strategy, its frequency response dynamic characteristics can be made close to those when off-grid (both the frequency drop speed and the lowest point of the frequency are relatively close), and the frequency dynamic characteristics are maintained well.

[0204] On the other hand, the rate of change of the system frequency is a key indicator reflecting the frequency dynamic characteristics and also a key factor determining the lowest point of the frequency drop. It can be quantitatively described by RoCoF = ΔP L / 2H eq (ΔP L is the power deficit, and H eq is the system equivalent inertia). Therefore, in order to more intuitively show the accuracy and effect of the virtual inertia compensation control in this paper, the rate of change of frequency curves within 0.5 s after the frequency disturbance occurs under the corresponding Figure 5 three conditions are extracted, as shown in Figure 6 . It can be seen from Figure 6 that within 0.5 s after the frequency disturbance occurs, this period has the most significant impact on the lowest point of the frequency drop. When the wind farm is connected to the grid (without compensation control), RoCoF is significantly larger, and through the virtual inertia compensation control, its RoCoF can be made close to that under the off-grid condition, indicating that the control method can more accurately compensate for the weakening of the grid inertia, which also makes the Figure 5 frequency dynamic response processes of the two more consistent.

[0205] (2) Verification of the effect of the control strategy under different wind speeds:

[0206] According to Equation (25), it can be seen that: it is necessary to dynamically adjust the control gain K r0 according to the real-time wind speed of the wind farm (determining ω df ) to accurately compensate for the weakening of the inertia ΔH when the wind farm is connected to the grideq,k In view of this, Figure 7 and Figure 8 respectively simulated the frequency response characteristic curves and rate of change of frequency curves during frequency accidents under Wind Condition 1 and Wind Condition 3. From Figure 7 and Figure 8 the comparison results: Under the two wind speed conditions, the frequency dynamic response curves and RoCoF curves through the virtual inertia compensation control of wind turbines are both relatively close to the off-grid state, indicating that with the change of wind speed, the control gain K df can be dynamically adjusted to adapt, and still can accurately compensate the reduction of grid inertia and ensure the frequency support ability under frequency accidents.

[0207] (3) Verification of the effect of control strategies under different wind power penetration rates:

[0208] To verify the effect of the inertia compensation control strategy under different wind power penetration rates, the frequency response characteristic curves and rate of change of frequency curves during frequency accidents under wind power penetration rates pene. = 25% and 50% were respectively obtained, as shown in Figure 9 and Figure 10 . According to Figure 9 and Figure 10 the comparison: 1) Under the two wind power penetration levels, the frequency dynamic response curves and RoCoF curves through the implementation of virtual inertia compensation control of wind turbines are both relatively close to the off-grid state, and both can accurately compensate the reduction of grid inertia with good control effects; 2) With the increase of wind power grid connection penetration rate, the method proposed in the present invention can still be applied to ensure the grid inertia level and effectively avoid the deterioration of the system dynamic frequency characteristics.

Claims

1. A virtual inertia compensation control method for a wind farm based on the sharing of the responsibility for weakening the power grid inertia, characterized in that including the following steps: Step 1: Detect the frequencies and load powers of the high-voltage bus nodes of the power grid, and use the subspace algorithm to identify the inertia H of each node, calculate the aggregated inertia H of the power grid b,k , and then obtain the reduction amount △H of the grid-connected inertia of the wind farm eq(1),k ; eq,k ; Step 2: According to the inertia reduction amount △H of the wind farm grid connection obtained in Step 1 eq,k , solve the virtual inertia compensation amount H of the wind farm implementing SFD inertia control wf,k ; calculate the real-time control gain K of the wind turbine df ; Step 3. Detect whether a power system frequency accident occurs based on the frequency change rate and threshold judgment: When it occurs, adopt a K df dynamic setting method to dynamically set K av.df (t); if it does not occur, set K df = 0; In step 1, when the inertia H of each node is estimated b,k after that, solve for H using the following formula eq(1),k : where b is the high-voltage bus node with power source access in the whole network, where b = 1, 2... B, B is the total number of nodes, and S b,k is the aggregated capacity of synchronous power sources connected under node b; The grid inertia weakening amount ΔH caused by the grid connection of wind farm k eq,k is as follows: Where m is the number of wind farms and n is the number of synchronous generators; S wf,i is the grid-connected capacity of the i-th wind farm; H syn,j , S syn,j are the inertia and grid-connected capacity of the j-th synchronous generator respectively; H eq(1),k is the equivalent inertia of the power grid when the k-th wind farm is connected to the grid; H eq(0),k is the equivalent inertia of the power grid when the k-th wind farm is disconnected from the grid; Identify the inertia H of each node using the subspace algorithm b,k , substitute H b,k into Equation (7) to calculate the grid aggregated inertia H eq(1),k ; then obtain the inertia reduction ΔH of the wind farm connected to the grid through Equation (5) eq,k ; In step 2, the amount of grid inertia weakening △H caused by the grid connection of wind farm k eq,k and the virtual inertia compensation amount H of wind farm k wf,k are related as follows: Where m is the number of wind farms and n is the number of synchronous generator sets; S wf,i is the grid connection capacity of the i-th wind farm; S syn,j is the grid connection capacity of the j-th synchronous generator set; S wf,k is the grid connection capacity of wind farm k; Virtual inertia compensation amount H of wind farm k wf,k and real-time control gain K of wind turbine generator set df The relationship between them is as follows: Where, H wf,k is the equivalent inertia of wind farm k; ω nom is the rated angular frequency of the wind turbines in wind farm k; ω r0 is the initial rotor angular frequency of the wind turbines in wind farm k; ω s0 is the initial synchronous angular frequency of the power grid; T f is the filtering time constant of the virtual inertia controller of the wind turbines in wind farm k; Δ=(K pT / 2H DFIG ) 2 -2K iT / H DFIG is the discriminant of the equation s 2 +K pT / (2H DFIG )s+K iT / (2H DFIG ), where: H DFIG , K pT and K iT are respectively the inherent inertia time constant, the proportional coefficient of the speed controller, and the integral coefficient of the speed controller of the wind turbines in wind farm k; α1, α2, α3 are the three single roots of D(s)=0 in Equation (21) when Δ≥0, and K1, K2, K3 are the expansion coefficients of the partial fraction of Equation (21) when Δ≥0, where Equation (21) is: α1', α2'±jβ are respectively a single root and a pair of conjugate complex roots of D(s)=0 in Equation (21) when Δ≤0, β is the imaginary part of α2'±jβ, θ = ∠K2', and K1' and K2' are the expansion coefficients of the partial fraction of Equation (21) when Δ≤0; Wind farm grid connection inertia weakening amount △H eq,k Substitute into Equation (16) to solve for the virtual inertia compensation amount H of the wind farm implementing SFD inertia control wf,k Then calculate the real-time control gain K of the wind turbine according to Equation (25) df ; In step 3, K df The dynamic setting method includes the following steps: 1): During the inertial response dynamic process, K df changes every 0.1 s cycle, and each setting value is the integral mean value of the K df curve within the cycle: where u = [10×t] / 10, w = ([10×t] / 10)+0.1, and the symbol [] represents the rounding operation; 2): If K df has a left and right limit approaching infinity around a certain time t0, let the set value of the period where the time t0 is located be the K of the previous 1 period df Integral mean value; 3): When the rate of change of frequency RoCoF ≤ ε is continuously detected, where ε is the set precision error, indicating that the frequency response tends to a steady state, set K df = 0, and the inertial response is cut off.

2. The virtual inertia compensation control method for a wind farm based on the responsibility sharing of grid inertia weakening according to claim 1, characterized in that: In the above step 1, the inertia reduction amount ΔH of wind power grid connection eq,k refers to the value of the reduction in the equivalent inertia of the power grid caused by the grid connection of wind farm k, and its magnitude is equal to the equivalent inertia of the power grid before the grid connection of wind farm k minus the equivalent inertia of the power grid after the grid connection of wind farm k.

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