Impedance analysis method for forced subsynchronous oscillation of doubly-fed wind power plant grid-connected system

Abstract

The invention discloses an impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind power plant grid-connected system, which is used for evaluating the risk of forced subsynchronous oscillation and belongs to the technical field of doubly-fed wind power plants. The method comprises the following steps: step 1, determining an inter-harmonic frequency output by a doubly-fed fan, and judging whether forced subsynchronous oscillation of a doubly-fed wind power plant grid-connected system can be excited or not; step 2, establishing a small signal impedance model of the doubly-fed wind power plant and the power grid; step 3, calculating the amplitude ratio and phase difference of the double-fed wind power plant and the power grid impedance under the inter-harmonic frequency; step 4, calculating a proportion A (sih) of an inter-harmonic current amplitude to a fundamental current amplitude based on a system steady-state equivalent circuit; and step 5, judging the severity of the forced subsynchronous oscillation according to the calculated A (sih). The forced subsynchronous oscillation mechanism and physical significance can be clearly disclosed, and the forced subsynchronous oscillation characteristic can be comprehensively analyzed.

Description

Technical Field

[0001] The present invention belongs to the technical field of doubly-fed wind farms, and particularly relates to an impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system. Background Art

[0002] The problem of subsynchronous oscillation in a doubly-fed wind farm grid-connected system frequently occurs worldwide and has become one of the focuses of attention. According to the causes, the subsynchronous oscillation in a doubly-fed wind farm grid-connected system can be divided into negative-damping subsynchronous oscillation and forced subsynchronous oscillation. The converter-connected wind turbines generate interharmonics at subsynchronous frequencies, which easily excite the subsynchronous modes with similar frequencies in the doubly-fed wind farm grid-connected system to produce forced subsynchronous oscillation, threatening the safe operation of the system.

[0003] The impedance analysis method based on the Nyquist criterion is an important tool for analyzing the negative-damping subsynchronous oscillation caused by the interaction between a doubly-fed wind farm and the power grid. The impedance analysis method based on the Nyquist criterion respectively establishes the impedance models of the doubly-fed wind farm subsystem and the power grid subsystem, and then analyzes the small-signal stability of the system based on the Nyquist criterion. At the same time, the risk of negative-damping subsynchronous oscillation of the system can be quantitatively evaluated by calculating the phase margin and amplitude margin. However, different from the negative-damping subsynchronous oscillation, the forced subsynchronous oscillation is generated by the excitation of weak-damping modes by interharmonics in the system. When the forced subsynchronous oscillation occurs, both the system damping and the phase margin are positive. The risk index of negative-damping subsynchronous oscillation cannot be used to evaluate the risk of forced subsynchronous oscillation, and the impedance analysis method based on the Nyquist criterion is not applicable to the analysis of forced subsynchronous oscillation. Summary of the Invention

[0004] The purpose of the present invention is to provide an impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system to evaluate the risk of forced subsynchronous oscillation.

[0005] The present invention is implemented by the following technical solutions:

[0006] An impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system includes the following steps:

[0007] Step 1: Determine the interharmonic frequency f ih of the output of the doubly-fed wind turbine, and judge whether it will excite the forced subsynchronous oscillation of the doubly-fed wind farm grid-connected system;

[0008] Step 2: Establish the small-signal impedance models of the doubly-fed wind farm and the power grid;

[0009] Step 3: Calculate the amplitude ratio and phase difference of the impedances of the doubly-fed wind farm and the power grid at the interharmonic frequency;

[0010] Step 4: Calculate the ratio A(s ih ) of the interharmonic current amplitude to the fundamental current amplitude based on the steady-state equivalent circuit of the system

[0011] The output current of the DFIG wind farm in the steady state contains both the fundamental current with the grid fundamental frequency f0 and the interharmonic current with the interharmonic frequency f ih . According to the different current frequencies, the DFIG wind farm is equivalent to a Norton equivalent circuit in parallel with a fundamental current source i cr0 and an impedance Z dfig0 ; the power grid is equivalent to a Thevenin equivalent circuit in series with a fundamental voltage source u g0 and an impedance Z g0 ; the DFIG wind farm is equivalent to a Norton equivalent circuit in parallel with an interharmonic current source i ih (s ih = j2πf ih ) and an impedance Z dfig (s ih ). The equivalent interharmonic voltage source of the power grid is 0 and is regarded as a short circuit, and the power grid is only equivalent to an impedance Z g (s ih ); according to the established steady-state interharmonic circuit model of the system, the interharmonic current i g.ih (s ih ) in the system current can be obtained, and the expression is as follows:

[0012]

[0013] In the formula, i ih (s ih ) is the interharmonic current output by the DFIG wind farm.

[0014] Define the ratio of the interharmonic current amplitude to the fundamental current amplitude in the system as the severity index A ( s ih) of the forced subsynchronous oscillation, as follows:

[0015]

[0016] In the formula, i g0 is the fundamental current in the system current output by the DFIG wind farm, and its amplitude |i g0 | can be calculated by ; where n is the number of DFIGs in the DFIG wind farm; U pcc is the effective value of the grid-connected point voltage; P DFIG is the output power of the DFIG.

[0017] Step 5: Judge the severity of the forced subsynchronous oscillation according to the calculated A(s ih )

[0018] According to the Chinese standard GBT / 24337, the percentage of sub / super-synchronous frequency harmonics in the system caused by the grid connection of a doubly-fed wind farm shall not exceed 0.2%. When A(s ih ) ≤ 0.2%, it is considered that the severity of the system's forced sub-synchronous oscillation is relatively low; when A(s ih ) > 0.2%, it is considered that the severity of the system's forced sub-synchronous oscillation is relatively high, and the higher the value, the higher the severity.

[0019] The present invention first analyzes the modulation process of interharmonics generated by a doubly-fed wind turbine, determines the interharmonic frequency, and judges whether it will trigger forced sub-synchronous oscillation in the grid-connected system of the doubly-fed wind farm; then respectively establishes small-signal impedance models of the doubly-fed wind farm and the power grid, and calculates the amplitude ratio and phase difference of the impedances of the doubly-fed wind farm and the power grid at the interharmonic frequency; finally, based on the steady-state equivalent circuit of the system, calculates the ratio of the interharmonic current amplitude to the fundamental current amplitude, and uses this as an index to evaluate the severity of the forced sub-synchronous oscillation in the system. The present invention is applicable to analyzing the forced sub-synchronous oscillation of the grid-connected system of a doubly-fed wind farm, which is beneficial to comprehensively analyzing the characteristics of forced sub-synchronous oscillation and provides a reference for the proposed method of suppressing forced sub-synchronous oscillation. The calculation results of the impedance analysis method proposed by the present invention correspond well with the spectrum analysis results obtained by simulation in PSCAD / EMTDC, indicating that the method proposed by the present invention can accurately describe the characteristics of the system's forced sub-synchronous oscillation.

[0020] The present invention has the following beneficial effects:

[0021] 1. The present invention establishes an impedance analysis model for the forced sub-synchronous oscillation of the grid-connected system of a doubly-fed wind farm based on the steady-state equivalent circuit of the system, which can clearly reveal the mechanism and physical meaning of the forced sub-synchronous oscillation and is beneficial to comprehensively analyzing the characteristics of the forced sub-synchronous oscillation.

[0022] 2. Based on the established impedance analysis model, the present invention derives an expression for the ratio of the interharmonic current amplitude to the fundamental current amplitude, which can quantitatively evaluate the severity of the forced sub-synchronous oscillation. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The drawings here are incorporated into the specification and form a part of this specification, showing embodiments consistent with the present invention and used together with the specification to explain the principles of the present invention.

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0025] Figure 1 It is a schematic diagram of the topological structure of the doubly-fed wind turbine of the present invention.

[0026] Figure 2 is the impedance-based small-signal equivalent circuit diagram of the grid-connected system of the present invention's grid-type doubly-fed wind farm.

[0027] Figure 3 is the fundamental wave equivalent circuit diagram of the system of the present invention under steady state.

[0028] Figure 4 is the interharmonic equivalent circuit diagram of the system of the present invention under steady state.

[0029] Figure 5 is the flow chart of the impedance analysis method for forced subsynchronous oscillation of the doubly-fed wind farm of the present invention.

[0030] Figure 6 is the structure diagram of the doubly-fed wind farm of the present invention.

[0031] Figure 7 is the Bode plot of the positive sequence impedance of the doubly-fed wind farm and the power grid of the present invention.

[0032] Figure 8 is the simulation waveform diagram of the output power of the doubly-fed wind farm of the present invention under three wind speeds.

[0033] Figure 9 is the simulation waveform diagram of the output current of the doubly-fed wind farm of the present invention from 5 seconds to 6 seconds.

[0034] Figure 10 is the simulation waveform diagram of the output current of the doubly-fed wind farm of the present invention from 8 seconds to 9 seconds.

[0035] Figure 11 is the frequency spectrum diagram of the output current of the doubly-fed wind farm of the present invention from 5 seconds to 6 seconds and from 8 seconds to 9 seconds. Detailed implementation manners

[0036] In order to be able to more clearly understand the above-mentioned objects, features and advantages of the present invention, the solution of the present invention will be further described below. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0037] In the description, it should be noted that the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance. It should be noted that unless otherwise clearly defined and limited, the terms "installed", "connected" and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal communication of two components. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific situations.

[0038] In the following description, many specific details are set forth in order to provide a thorough understanding of the present invention. However, the present invention may be practiced in other ways than those described herein. Obviously, the embodiments in the specification are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0039] The following specifically describes the embodiments of the present invention with reference to the accompanying drawings.

[0040] Embodiment 1, an impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system, as shown in the accompanying Figure 5 figure, includes the following steps:

[0041] Step 1: Determine the interharmonic frequency f ih of the output of the doubly-fed wind turbine, and determine whether it will excite the forced subsynchronous oscillation of the doubly-fed wind farm grid-connected system;

[0042] Step 2: Establish a small-signal impedance model of the doubly-fed wind farm and the power grid;

[0043] Step 3: Calculate the amplitude ratio and phase difference of the impedances of the doubly-fed wind farm and the power grid at the interharmonic frequency;

[0044] Step 4: Calculate the ratio A(s ih ) of the interharmonic current amplitude to the fundamental current amplitude based on the system steady-state equivalent circuit.

[0045] The output current of the doubly-fed wind farm in the steady state contains both the fundamental current with a frequency of the power grid fundamental frequency f0 and the interharmonic current with a frequency of the interharmonic frequency f ih . According to the different current frequencies, the doubly-fed wind farm is equivalent to a Norton equivalent circuit in parallel with a fundamental current source i cr0 and an impedance Z dfig0 ; the power grid is equivalent to a Thevenin equivalent circuit in series with a fundamental voltage source u g0 and an impedance Z g0 ; the doubly-fed wind farm is equivalent to a Norton equivalent circuit in parallel with an interharmonic current source i ih (s ih = j2πf ih ) and an impedance Z dfig (s ih ). The equivalent interharmonic voltage source of the power grid is 0 and is regarded as a short circuit. The power grid is only equivalent to an impedance Z g (s ih ); according to the established system steady-state interharmonic circuit model, the expression of the interharmonic current i g.ih (s ih ) in the system current can be obtained as follows:

[0046]

[0047] where \(i\) ih (s ih ) is the interharmonic current output by the doubly-fed wind farm.

[0048] Define the ratio of the interharmonic current amplitude to the fundamental current amplitude in the system as the severity index \(A\) of the forced subsynchronous oscillation ( s ih) , as follows:

[0049]

[0050] where \(i\) g0 is the fundamental current in the system current output by the doubly-fed wind farm, and its amplitude \(|i\) g0 | can be calculated by ; where \(n\) is the number of doubly-fed induction generators in the doubly-fed wind farm; \(U\) pcc is the effective value of the grid connection point voltage; \(P\) DFIG is the output power of the doubly-fed induction generator.

[0051] Step 5. Judge the severity of the forced subsynchronous oscillation according to the calculated \(A(s\) ih );

[0052] According to the Chinese standard GBT / 24337, the percentage of sub / supersynchronous frequency harmonics in the system caused by the grid connection of the doubly-fed wind farm shall not exceed 0.2%. When \(A(s\) ih ) ≤ 0.2%, it is considered that the severity of the forced subsynchronous oscillation in the system is low; when \(A(s\) ih ) > 0.2%, it is considered that the severity of the forced subsynchronous oscillation in the system is high, and the higher the value, the higher the severity.

[0053] Embodiment 2. The present invention takes the grid-connected system of the doubly-fed wind farm as the research object, and the structure of the doubly-fed induction generator is as shown in the appendix Figure 1 . The doubly-fed induction generator mainly consists of three parts: an asynchronous motor, a rotor-side converter, and a grid-side converter. The control structure of the rotor-side converter includes an active power outer loop, a reactive power outer loop, a current inner loop, and a phase-locked loop. The control structure of the grid-side converter includes a DC voltage outer loop, a reactive power outer loop, a current inner loop, and a phase-locked loop. The rotor-side converter and the grid-side converter adopt fully controlled switching devices, and the control method is sinusoidal pulse width modulation.

[0054] Figure 1 In, \(u\) s and \(i\) s respectively represent the stator-side voltage and current of the doubly-fed induction generator; \(u\) r and \(i\) r respectively represent the rotor-side voltage and current of the doubly-fed induction generator; \(u\) c and \(i\) c respectively represent the output voltage and current of the grid-side converter; \(u\) dc and \(i\)dc denote DC voltage and current; θ pll denote the output angle of the phase-locked loop; θ r denote the rotor position angle; S rscx and S gscx respectively denote the switching functions of the rotor-side converter and the grid-side converter; L c denote the filter inductance on the AC side of the grid-side converter. The symbols with subscripts abc and dq respectively correspond to the components of each electrical quantity in the abc and dq coordinate systems; the subscript with ref is the reference value of this electrical quantity.

[0055] The fundamental electrical frequency f of the rotor side of the doubly-fed wind turbine rsc is related to the speed of the asynchronous motor and has time-varying characteristics. Under the influence of the dead-time effect, the modulation of the rotor-side converter will cause harmonic components with a frequency of 6kf rsc (k = 1, 2, 3,...) to appear on the DC side. The DC current i dc can be expressed as:

[0056]

[0057] In the formula, i dc0 is the DC component of the DC current; i dch is the harmonic component of concern in the DC current; i dck is the amplitude of the harmonic component of the kth order in the DC current, which decreases with the increase of the harmonic order; ω rsc = 2πf rsc is the fundamental angular frequency of the rotor side of the doubly-fed wind turbine; φ k is the phase of the harmonic component of the kth order.

[0058] The modulation of the rotor-side converter will not only introduce the fundamental component on the AC side into the DC side to generate harmonic components of each order, but also output the harmonic components generated on the DC side back to the AC side to generate new harmonic components, that is, inter-harmonics. The harmonic components i rhx (x = a, b, c) contained in the rotor-side current of the doubly-fed wind turbine and the harmonic component i dch of the DC current have the following relationship:

[0059] i rhx = i dch S rscx (t) (2)

[0060] In the formula, S rscx(t)(x = a, b, c) is the switching function of the rotor-side converter. Since the present invention mainly studies the subsynchronous oscillation occurring in the doubly-fed wind turbine grid-connected system, the supersynchronous oscillation frequency coupled in the AC system will not be higher than twice the grid fundamental frequency 2f0, and the carrier frequency of the PWM converter is usually much greater than 2f0. Therefore, the sideband harmonic terms near the carrier frequency are ignored to simplify S rscx (t).

[0061] The simplified S rscx (t) is as follows:

[0062]

[0063] In the formula, S r0 is the amplitude of the switching function of the rotor-side converter; φ r +p2π / 3 is the phase angle of the switching function of the rotor-side converter, and p takes values of 0, -1, and 1, corresponding to phases a, b, and c respectively.

[0064] Substituting (1) and (3) into (2) can obtain the expression of the low-frequency harmonic components contained in the rotor-side current of the doubly-fed wind turbine, as follows:

[0065]

[0066] It can be seen from (1) and (4) that when there is a harmonic component with a frequency of 6kf rsc on the DC side, interharmonic components with a frequency of (6k±1)f rsc will be generated in the rotor-side current of the doubly-fed wind turbine. The interharmonic with a frequency of (6k + 1)f rsc has a positive sequence; the interharmonic with a frequency of (6k - 1)f rsc has a negative sequence.

[0067] Similarly, the modulation effect of the grid-side converter will also cause low-frequency interharmonic components i chx (x = a, b, c) to be generated in the AC-side current of the grid-side converter. The relationship between i chx and i dch is as shown in (5):

[0068]

[0069] The expression of i chx derived is as shown in (6):

[0070]

[0071] In the formula, S gscx (t)(x = a, b, c) is the switching function of the grid-side converter; S c0 is the amplitude of the switching function of the grid-side converter; φc +p2π / 3 is the phase angle of the grid-side converter switching function; ω0 = 2πf0 is the grid fundamental angular frequency.

[0072] It can be seen from (6) that when there is a harmonic component with a frequency of 6kf on the DC side rsc harmonic components with frequencies of 6kf ± f0 will be generated in the AC side current of the grid-side converter. Since the frequency of this harmonic component is not an integer multiple of the fundamental frequency, this harmonic component is an interharmonic. The phase sequence of the interharmonic with a frequency of 6kf rsc +f0 is the positive sequence; the phase sequence of the interharmonic with a frequency of 6kf rsc -f0 is the negative sequence. rsc

[0073] The stator side of the doubly-fed wind turbine is connected to the grid, and the fundamental frequency of the stator winding is the grid fundamental frequency f0. The fundamental frequency of the stator winding of the doubly-fed wind turbine and the fundamental frequency f rsc of the rotor side have the following relationship:

[0074] f rsc = f0 - f r (7)

[0075] where f r is the rotational frequency of the asynchronous motor rotor.

[0076] According to the operating principle of the doubly-fed wind turbine asynchronous motor, it is known that the interharmonics in the rotor current will induce interharmonics in the stator current. The frequency relationship between the positive-sequence interharmonics in the rotor current and the positive-sequence interharmonics in the stator current can be expressed by (7). Due to the modulation effect of the rotor-side converter, there are positive-sequence interharmonics with a frequency of (6k + 1)f rsc and negative-sequence interharmonics with a frequency of (6k - 1)f rsc in the rotor winding. The positive-sequence component with a frequency of f is equivalent to the negative-sequence component with a frequency of -f. Therefore, the negative-sequence interharmonic component with a frequency of (6k - 1)f rsc in the rotor side is equivalent to the positive-sequence interharmonic component with a frequency of (1 - 6k)f rsc . Therefore, substituting the frequencies of the two positive-sequence interharmonics in the rotor current into (7), the frequencies of the two positive-sequence interharmonics induced in the stator current can be deduced, as shown in (8) and (9) respectively:

[0077] f sh1 = (6k + 1)f rsc + f r = 6kf rsc + f0 (8)

[0078] f sh2 = (1 - 6k)f rsc + f r = f0 - 6kfrsc (9)

[0079] It can be seen from Equations (8) and (9) that when there are inter-harmonic components with a frequency of (6k±1)f rsc in the rotor-side current of the doubly-fed wind turbine, positive-sequence inter-harmonic components with frequencies of 6kf rsc +f0 and f0-6kf rsc will be induced in the stator winding. It should be noted that the positive-sequence inter-harmonic component with a frequency of f0-6kf rsc is equivalent to the negative-sequence inter-harmonic component with a frequency of 6kf rsc -f0. Analyzing Equations (6), (8), and (9), it can be known that the inter-harmonic current frequencies on the AC side of the grid-side converter of the doubly-fed wind turbine are the same as those output by the stator winding. The inter-harmonics input by the doubly-fed wind turbine into the power grid are the superposition of the inter-harmonics output by the grid-side converter and the stator winding. The expression of the inter-harmonic component frequency f ih in the output current of the doubly-fed wind turbine is shown in Equation (10).

[0080] f ih =|6kf rsc ±f0|

[0081] =|(6k±1)f0-6kf r |, k = 1, 2, 3, … (10)

[0082] In the formula, the inter-harmonic component with a frequency of f ih1 =(6k+1)f0-6kf r is positive-sequence, and the inter-harmonic component with a frequency of f ih2 =(6k-1)f0-6kf r is negative-sequence, which is equivalent to the positive-sequence inter-harmonic component with a frequency of f ih3 =-f ih2 .

[0083] The inter-harmonics that can excite forced subsynchronous oscillation are the positive-sequence inter-harmonics with frequencies between 0 and 2f0. It can be calculated that f ih1 +f ih3 =2f0. Therefore, when both f ih1 >0 and f ih3 =-f ih2 >0 are satisfied, the inter-harmonics generated by the doubly-fed wind turbine can excite forced subsynchronous oscillation. It can be seen from (10) that different values of k may cause multiple pairs of positive-sequence inter-harmonics with complementary frequencies to exist in the output current of the doubly-fed wind turbine. Since the amplitude of the inter-harmonics with k = 1 is much larger than that of the other inter-harmonics, only the forced subsynchronous oscillation excited by the inter-harmonics with k = 1 is considered. When the wind speed is determined, the corresponding f rSubstitute into Equation (10) to determine whether the output interharmonic frequency of the doubly-fed wind turbine is two positive-sequence interharmonic frequencies with complementary frequencies. If not, the interharmonics output by the doubly-fed wind turbine at this wind speed will not excite the forced subsynchronous oscillation of the doubly-fed wind farm grid-connected system, and the following steps do not need to be executed; if so, the interharmonics output by the doubly-fed wind turbine at this wind speed can excite the forced subsynchronous oscillation of the doubly-fed wind farm grid-connected system, and the following steps are executed to perform impedance analysis on it.

[0084] Embodiment 3. The small-signal equivalent circuit based on impedance of the grid-connected system of the grid-following doubly-fed wind farm is as shown in the appendix Figure 2 The grid-following controlled doubly-fed wind farm is equivalent to a Norton equivalent circuit in parallel with a small-signal current source Δi cr (s) and a small-signal impedance Z dfig (s); the power grid is equivalent to a Thevenin equivalent circuit in series with a small-signal voltage source Δu g (s) and a small-signal impedance Z g (s); x and y are the common connection points of the doubly-fed wind farm and the power grid.

[0085] Embodiment 4. Substitute the positive-sequence interharmonic frequencies f ih1 and f ih3 with complementary frequencies and the system parameters into Z dfig (s) and Z g (s) to calculate the amplitude ratio and phase difference of the impedances of the doubly-fed wind farm and the power grid at two different interharmonic frequencies, that is, the amplitude ratio D1 and phase difference δ1 of Z g (s ih1 ) and Z dfig (s ih1 ), and the amplitude ratio D3 and phase difference δ3 of Z g (s ih3 ) and Z dfig (s ih3 ).

[0086] Embodiment 5. The output current of the doubly-fed wind farm in the steady state contains both the fundamental current with a frequency of the grid fundamental frequency f0 and the interharmonic current with a frequency of the interharmonic frequency f ih . According to the different current frequencies, the equivalent circuit of the system in the steady state is divided into the fundamental wave circuit shown in the appendix Figure 3 and the interharmonic circuit shown in the appendix Figure 4 . The frequencies of all electrical quantities in the appendix Figure 3 are all f0. The doubly-fed wind farm is equivalent to a Norton equivalent circuit in parallel with a fundamental current source i cr0 and an impedance Z dfig0 . The power grid is equivalent to a Thevenin equivalent circuit in series with a fundamental voltage source u g0 and an impedance Z g0 . The appendix Figure 4The frequency of all electrical quantities in is f ih . The doubly-fed wind farm is equivalent to an interharmonic current source i ih (s ih = j2πf ih ) and an impedance Z dfig (s ih ) in parallel Norton equivalent circuit. The equivalent interharmonic voltage source of the power grid is 0 and is regarded as a short circuit, and the power grid is only equivalent to an impedance Z g (s ih ).

[0087] According to Figure 4 The interharmonic current i g.ih (s ih ) in the system current can be obtained, and the expression is as follows:

[0088]

[0089] From the appendix Figure 3 It can be seen that i g0 is the fundamental current in the system current output by the doubly-fed wind farm. The fundamental current amplitude |i g0 | at different wind speeds can be calculated through . Among them, n is the number of doubly-fed wind turbines in the doubly-fed wind farm; U pcc is the effective value of the voltage at the point of common coupling. Each wind speed can correspond to a calculated fixed value |i g0 |. By calculating the ratio of |i g.ih (s ih )| to |i g0 |, that is, the ratio A(s ih ) of the interharmonic current amplitude to the fundamental current amplitude, as an index to evaluate the severity of forced subsynchronous oscillation:

[0090]

[0091] |1 + Z g (s ih ) / Z dfig (s ih )| The calculation formula is as shown in the following formula:

[0092]

[0093] From f ih1 =(6k + 1)f0 - 6kf r > 0 and f ih3 =-f ih2 =-[(6k - 1)f0 - 6kf r > 0, the range of f r that can excite forced subsynchronous oscillation can be deduced as follows:

[0094] [1 - 1 / (6k)]f0 < f r <[1 + 1 / (6k)]f0 (14)

[0095] Substitute k = 1 into Equation (14) to obtain the range of f that can excite forced subsynchronous oscillation as follows: r as follows:

[0096] 5 / 6f0 < f r <7 / 6f0 (15)

[0097] The amplitude of the interharmonic current |i ih (s ih )| output by the doubly-fed wind farm also has a time-varying characteristic that changes with the wind speed. However, the range of f that can excite forced subsynchronous oscillation is small, and the corresponding wind speed interval is also small. The change of |i r in this wind speed interval is small. On the other hand, |i ih (s ih )| in practice is very small, and the occurrence of forced subsynchronous oscillation mainly depends on whether |1 + Z ih (s ih ) / Z g (s ih )| is small enough. For the above reasons, when calculating A(s dfig (s ih ) at different wind speeds, |i ih (s ih )| can be set as a small constant. Substitute |i ih (s ih )|, |i ih |, and the two sets of sample values D1 / δ1 and D3 / δ3 described above into Equation (12) to obtain the proportion of the interharmonic current amplitude A(s g0 ) and A(s ih1 ) corresponding to the two interharmonic frequencies. ih3 )

[0098] The principle of this method is as follows:

[0099] First, based on the modulation mechanism of the doubly-fed wind turbine converter, the formula for the interharmonic frequency output by the doubly-fed wind turbine is derived, and the interharmonic frequency of the doubly-fed wind farm at a given wind speed is calculated to determine whether it will excite the forced subsynchronous oscillation of the doubly-fed wind farm grid-connected system. If it will not be excited, impedance analysis is not performed on it; if it will be excited, establish as in Appendix Figures 2-4The small signal impedance model of the doubly fed wind farm and the power grid and the equivalent circuit of the steady-state doubly fed wind farm grid-connected system shown in the figure are used to calculate the amplitude ratio and phase difference of the impedance of the doubly fed wind farm and the power grid at the interharmonic frequency through the small signal impedance model, and the ratio of the interharmonic current amplitude to the fundamental current amplitude A (s ih Finally, according to the calculated A(s ih ) to judge the severity of forced subsynchronous oscillation. ih )≤0.2%, the severity of the forced subsynchronous oscillation of the system is considered to be low; when A(s ih )>0.2%, it is considered that the severity of the system forced subsynchronous oscillation is high, and the larger the value, the higher the severity.

[0100] Embodiment 6, as attached Figure 6 The double-fed wind farm grid-connected system shown has 300 identical 2MW double-fed induction generators. The power generated by the double-fed wind farm grid-connected system is first stepped up from 35kV to 220kV. The power is then stepped up to 750kV and transmitted to the main grid. The parameters are shown in Table 1.

[0101] Table 1 Case system parameters

[0102]

[0103] Select three wind speeds of v = 7.25, 7.76, and 8.05 m / s, and the Bode plots of the positive sequence impedance of the double-fed wind farm and the power grid are shown in the attached figure. Figure 7 The calculation results of the forced subsynchronous oscillation judgment index are shown in Table 2.

[0104] Table 2 Calculation results of forced subsynchronous oscillation determination index

[0105]

[0106] In Table 2, the first column is the wind speed; the second column is the f calculated by formula (10) ih ; The third column is |i ih (s ih )|; the 4th column is |i g0 |; Columns 5 and 6 are through Z g (s ih ) / Z dfig (s ih ) calculated; the seventh column is A(s) calculated by equation (12) ih ). From Table 2 we can see that:

[0107] 1) For speed v = 7.76 m / s, severity index A (s ih= j2π×59.6 Hz) is the largest. This indicates that among the three wind speeds, the impact of forced subsynchronous oscillation on the normal system operation is also the highest when v = 7.76 m / s.

[0108] 2) For v = 7.25 m / s, the severity index A(s ih = j2π×60.8 Hz) is the second largest. This indicates that among the three wind speeds, the impact of forced subsynchronous oscillation on the normal system operation is also the second highest when v = 7.25 m / s.

[0109] 3) For v = 8.05 m / s, both A(s ih ) are very small. This indicates that among the three wind speeds, the impact of forced subsynchronous oscillation on the normal system operation is the smallest when v = 8.05 m / s.

[0110] The simulation waveforms of the output power of the doubly-fed wind farm grid-connected system at three wind speeds are shown in the appendix. Figure 8 As shown. From Figure 8 it can be seen that when the wind speed v = 7.25 m / s, the power waveform has a slight oscillation. The impact of this oscillation on the normal system operation is relatively small, and the severity of the forced subsynchronous oscillation is also relatively small. When the wind speed v increases to 7.76 m / s at 6 s, the power waveform diverges and oscillates violently, and at this time the subsynchronous oscillation is the most severe. When the wind speed v increases to 8.05 m / s at 9 s, the power waveform gradually converges and returns to the stable state. After the switch transient ends, the forced subsynchronous oscillation can be ignored, so the severity of the forced subsynchronous oscillation is the smallest. The simulation results are consistent with the analysis results of the impedance-based method. The above results verify the correctness of the forced subsynchronous oscillation impedance analysis method proposed in the present invention.

[0111] Figure 9 and Figure 10 respectively show the simulation waveforms of the output current of the doubly-fed wind farm from 5 s to 6 s and from 8 s to 9 s. Figure 11 shows the frequency spectra of the current waveforms in these two time periods. From Figure 11 it can be seen that the oscillation frequencies in these two time periods are 39.2 / 60.8 Hz and 40.4 / 59.6 Hz respectively. They are consistent with the interharmonic current frequencies when the wind speeds are 7.25 and 7.76 m / s respectively. Among the 39.2 Hz and 60.8 Hz components at v = 7.25 m / s, the amplitude ratio of the 60.8 Hz component to the fundamental component is 0.47%. This is consistent with A(s ih = j2π×60.8 Hz) in Table 2. The amplitude ratio of the 39.2 Hz component to the fundamental component is 0.28%, which is much larger than A(s ih= j2π×39.2 Hz). Among the 40.4 Hz and 59.6 Hz components at a speed v = 7.7 m / s, the amplitude ratio of the 59.6 Hz component to the fundamental wave component is relatively large, which is 2.16%. This is consistent with A(s in Table 2 ih = j2π×59.6 Hz). The amplitude ratio of the 40.4 Hz component to the fundamental wave component is 0.90%, which is much larger than A(s in Table 2 ih = j2π×40.4 Hz). It should be noted that there are calculation errors in A(s of the 39.2 Hz and 40.4 Hz components ih ). These calculation errors are caused by the mirror frequency effect. The significantly increased 60.8 Hz and 59.6 Hz components in the system will serve as excitation sources, and through the mirror frequency effect, 39.2 Hz and 40.4 Hz components are generated. This results in the amplitude ratio of the 39.2 Hz and 40.4 Hz components obtained through simulation being greater than A(s calculated in Table 2 ih ). However, for each wind speed, only the larger one of A(s ih1 ) and A(s ih3 ) is selected as the evaluation index for the severity of forced subsynchronous oscillation. Therefore, the calculation errors of the smaller one of A(s ih1 ) and A(s ih3 ) will not affect the evaluation of the severity of forced subsynchronous oscillation. In summary, the simulation results are consistent with the calculation results of the larger one of A(s ih1 ) and A(s ih3 ) at each wind speed, which is the key to the evaluation of the severity of forced subsynchronous oscillation.

[0112] The present invention can clearly reveal the mechanism and physical meaning of forced subsynchronous oscillation in a doubly-fed wind farm grid-connected system, quantitatively evaluate the severity of forced subsynchronous oscillation, facilitate a comprehensive analysis of the characteristics of forced subsynchronous oscillation, and provide a reference for the proposal of methods for suppressing forced subsynchronous oscillation.

[0113] The above are only specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Although the foregoing embodiments have been described in detail, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments, and they should all be covered by the protection scope of the claims.

Claims

1. An impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system, characterized in that: Including the following steps: Step 1. Determine the output interharmonic frequency f of the doubly-fed wind turbine, and judge whether it will excite the forced sub-synchronous oscillation of the doubly-fed wind farm grid-connected system; ih ​ Step 2: Establish a small-signal impedance model of the doubly-fed wind farm and the power grid; Step 3: Calculate the amplitude ratio and phase difference of the impedances of the doubly-fed wind farm and the power grid at the interharmonic frequency; Step 4: Calculate the ratio A(s ih ) of the inter-harmonic current amplitude to the fundamental current amplitude based on the steady-state equivalent circuit of the system; The output current of a doubly-fed wind farm in steady state contains both fundamental current with a frequency of the grid fundamental frequency f0 and interharmonic current with a frequency of the interharmonic frequency f ih ; according to the different current frequencies, the doubly-fed wind farm is equivalent to a fundamental current source i cr0 and an impedance Z dfig0 in parallel Norton equivalent circuit; the grid is equivalent to a fundamental voltage source u g0 and an impedance Z g0 in series Thevenin equivalent circuit; the doubly-fed wind farm is equivalent to an interharmonic current source i ih (s ih = j2πf ih ) and an impedance Z dfig (s ih ) in parallel Norton equivalent circuit, the equivalent interharmonic voltage source of the grid is 0 and is regarded as a short circuit, and the grid is only equivalent to an impedance Z g (s ih ); according to the established system steady-state interharmonic circuit model, the interharmonic current i g.ih (s ih ) in the system current can be obtained, and the expression is as follows: where i ih (s ih ) is the interharmonic current output by the doubly-fed wind farm; Define the ratio of the interharmonic current amplitude to the fundamental current amplitude in the system as the severity index A of forced subsynchronous oscillation ( s ih) , as follows: Where, i g0 is the fundamental wave current in the system current output by the doubly-fed wind farm, and its amplitude |i g0 | can be calculated through ; where, n is the number of doubly-fed wind turbines in the doubly-fed wind farm; U pcc is the effective value of the grid connection point voltage; P DFIG is the output power of the doubly-fed wind turbine; Step 5. Determine the severity of forced sub-synchronous oscillation based on the calculated A(s ih ). The percentage of sub- / supra-synchronous frequency harmonics in the system caused by the grid connection of the doubly-fed wind farm shall not exceed 0.2%; when A(s ih ) ≤ 0.2%, it is considered that the severity of the system's forced sub-synchronous oscillation is relatively low; when A(s ih ) > 0.2%, it is considered that the severity of the system's forced sub-synchronous oscillation is relatively high, and the higher the value, the higher the severity.

2. The impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 1, characterized in that: The doubly-fed wind turbine includes three parts: an asynchronous motor, a rotor-side converter, and a grid-side converter; the control structure of the rotor-side converter includes an active power outer loop, a reactive power outer loop, a current inner loop, and a phase-locked loop; the control structure of the grid-side converter includes a DC voltage outer loop, a reactive power outer loop, a current inner loop, and a phase-locked loop; the rotor-side converter and the grid-side converter adopt fully-controlled switching devices, and the control method is sinusoidal pulse width modulation.

3. The impedance analysis method for forced sub-synchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 2, wherein: Step 1 is implemented with the following steps: The fundamental electrical frequency f of the rotor side of the doubly-fed fan rsc is related to the rotational speed of the asynchronous motor and has time-varying characteristics; under the influence of the dead-time effect, the rotor-side converter of the doubly-fed fan will modulate on the DC side to generate harmonic components with a frequency of 6kf rsc (k = 1, 2, 3,...); DC current i dc is expressed as: where, i dc0 is the DC component of the DC current; i dch is the harmonic component of interest in the DC current; i dck is the amplitude of the harmonic component of the k-th order in the DC current, which decreases as the harmonic order increases; ω rsc = 2πf rsc is the fundamental angular frequency of the rotor side of the doubly-fed wind turbine; φ k is the phase of the harmonic component of the k-th order; The modulation effect of the rotor-side converter will also output the harmonic components generated on the DC side back to the AC side to generate new harmonic components, namely interharmonics. Therefore, the switching function S of the rotor-side converter is introduced. rscx (t)(x = a, b, c) is used to represent the relationship between the harmonic components of the rotor-side current and the harmonic components of the DC-side current. The harmonic components i rhx (x = a, b, c) contained in the rotor-side current of the doubly-fed wind turbine and the harmonic components i dch of the DC current have the following relationship: i rhx = i dch S rscx (t) (2) After simplifying the switching function of the rotor-side converter, the following expression is obtained: where S r0 is the amplitude of the rotor-side converter switching function; φ r + p2π / 3 is the phase angle of the rotor-side converter switching function, where p takes values of 0, -1, and 1, corresponding to phases a, b, and c respectively; Substituting (1) and (3) into (2) can obtain the expression of the low-frequency harmonic component contained in the rotor-side current of the doubly-fed wind turbine: It can be seen from (1) and (4) that when there are harmonic components with a frequency of 6kf on the DC side, rsc interharmonic components with a frequency of (6k±1)f will be generated in the rotor-side current of the doubly-fed wind turbine; rsc the interharmonic components with a frequency of (6k+1)f rsc have a positive sequence; the interharmonic components with a frequency of (6k-1)f rsc have a negative sequence; Similarly, the modulation effect of the grid-side converter will also cause low-frequency interharmonic components i chx (x = a, b, c); i chx and i dch The relationship of is as shown in (5): where S gscx (t)(x = a, b, c) is the switching function of the grid-side converter.

4. The impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 3, wherein: Derive i chx The expression of is shown in (6) as follows: where S c0 is the amplitude of the grid-side converter switching function; φ c + p2π / 3 is the phase angle of the grid-side converter switching function; ω0 = 2πf0 is the grid fundamental angular frequency; According to the relationship between the fundamental frequency of the stator winding of the doubly-fed wind turbine and the fundamental frequency on the rotor side, the positive and negative sequence inter-harmonic component frequencies generated in the stator winding can be deduced; it can be analyzed that the inter-harmonic current frequencies on the AC side of the grid-side converter of the doubly-fed wind turbine are the same as those of the stator winding output. The inter-harmonics input to the power grid by the doubly-fed wind turbine are the superposition of the inter-harmonics of the grid-side converter and the stator winding output, and the expression of the inter-harmonic frequency f ih is obtained as follows: f ih = |6kf rsc ± f0| = |(6k ± 1)f0 - 6kf r |, k = 1, 2, 3, … (10) where f0 is the power grid fundamental frequency; f r is the rotor frequency of the doubly-fed wind turbine, and the frequency f ih1 =(6k + 1)f0 - 6kf r interharmonic is positive sequence; the frequency f ih2 =(6k - 1)f0 - 6kf r interharmonic is negative sequence.

5. The impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 4, characterized in that: The interharmonics that can excite forced subsynchronous oscillation are positive-sequence interharmonics with frequencies between 0 and 2f0; the negative-sequence interharmonics with a frequency of f ih2 are equivalent to positive-sequence interharmonics with a frequency of f ih3 =-f ih2 The positive-sequence interharmonics can be calculated to obtain f ih1 +f ih3 =2f0; therefore, when both f ih1 >0 and f ih3 =-f ih2 >0 are satisfied, the interharmonics generated by the doubly-fed wind turbine can excite forced subsynchronous oscillation.

6. The impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 5, characterized in that: Since the amplitude of the interharmonic with k = 1 is much larger than that of the other interharmonics, only the forced subsynchronous oscillation excited by the interharmonic with k = 1 is considered; when the wind speed is determined, the corresponding f r is substituted into Equation (10) to determine whether the interharmonic frequencies output by the doubly-fed wind turbine are two positive-sequence interharmonic frequencies with complementary frequencies; if not, the interharmonics output by the doubly-fed wind turbine at this wind speed will not excite the forced subsynchronous oscillation of the doubly-fed wind farm grid-connected system, and the following steps do not need to be executed; if so, the interharmonics output by the doubly-fed wind turbine at this wind speed can excite the forced subsynchronous oscillation of the doubly-fed wind farm grid-connected system, and the following steps are executed.

7. The impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 4, wherein: In step 2, the doubly-fed wind farm with grid-following control is equivalent to a small-signal current source Δi cr (s) and a Norton equivalent circuit in parallel with a small-signal impedance Z dfig (s); the power grid is equivalent to a small-signal voltage source Δu g (s) and a Thevenin equivalent circuit in series with a small-signal impedance Z g (s).

8. The impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 7, characterized in that: In step 3, substitute the positive - sequence inter - harmonic frequencies \(f\) ih1 and \(f\) ih3 with complementary frequencies, as well as the system parameters into \(Z\) dfig (s) and \(Z\) g (s). Calculate the amplitude ratios and phase differences of the grid - side impedance and the DFIG - based wind farm impedance at two different inter - harmonic frequencies, namely the amplitude ratio \(D1\) and phase difference \(\delta1\) of \(Z\) g (s ih1 ) and \(Z\) dfig (s ih1 ), and the amplitude ratio \(D3\) and phase difference \(\delta3\) of \(Z\) g (s ih3 ) and \(Z\) dfig (s ih3 ).

9. The impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to claim 1, characterized in that: |1 + Z g (s ih ) / Z dfig (s ih ) | The calculation formula is as follows:

10. An impedance analysis method for forced subsynchronous oscillation of a doubly-fed wind farm grid-connected system according to any one of claims 4-8, characterized in that: From f ih1 =(6k + 1)f0 - 6kf r > 0 and f ih3 =-f ih2 =-[(6k - 1)f0 - 6kf r > 0, it can be deduced that the range of f that can excite subsynchronous oscillation is as follows: r as follows: [1 - 1 / (6k)]f0 < f r <[1 + 1 / (6k)]f0 (14) Substitute \(k = 1\) into Equation (14) to obtain the range of \(f\) that can excite forced subsynchronous oscillation as follows: r as follows: 5 / 6f0 < f r <7 / 6f0 (15).

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