A harmonic series-parallel resonance amplification analysis method for offshore wind farms

Abstract

A harmonic series-parallel resonance amplification analysis method suitable for offshore wind farms. This application proposes a general modeling method for offshore wind farms, which realizes the rapid establishment of a full-order state space model of the offshore wind farm. By solving its dominant poles, the potential resonant frequency of the offshore wind farm is discovered; then the Laplace transform is introduced to convert the high-order differential relationship of the offshore wind farm in the time domain into a product relationship in the complex frequency domain; on this basis, a rapid calculation method for the harmonic amplification factor and harmonic content of the offshore wind farm is proposed. The analysis results show that the harmonic resonance analysis method proposed in this application can realize 2~50 harmonic resonance analysis, and the operation process is simple and easy. There is no need to perform frequency scanning on each node in the system to obtain the potential resonant frequency of the offshore wind power system, and then analyze the possible harmonic resonance phenomenon, and at the same time can effectively evaluate the harmonic amplification factor and harmonic content rate of key nodes.

Description

Technical Field

[0001] The present invention relates to the technical field of harmonic analysis of power systems, and in particular to a harmonic series-parallel resonance amplification analysis method suitable for offshore wind farms. Background Art

[0002] Offshore wind power has developed rapidly due to its rich resources and proximity to load centers. In addition, most offshore wind farms are usually connected to the onshore power grid through long-distance AC submarine cables. Considering that the distributed capacitance of AC cables under the same transmission distance and voltage level is usually 20 to 40 times that of overhead lines, while the line impedance is 50% to 100% of that of overhead lines, it is highly likely that offshore wind power systems will experience harmonic resonance and harmonic amplification phenomena that are not common in onshore wind farms, which will seriously endanger the safe and stable operation of the power system.

[0003] At present, the research on the analysis of harmonic resonance amplification phenomenon in offshore wind farms mainly focuses on finding potential series-parallel resonance points based on system grid information. The analysis method provided is only applicable to series resonance of harmonic voltage source or parallel resonance of harmonic current source, and it is difficult to analyze the harmonic resonance and harmonic amplification phenomena generated by the simultaneous action of series and parallel resonance in the system. In addition, the common harmonic analysis method currently requires scanning all nodes or node admittance matrices in the offshore wind farm, which is cumbersome and has limited scalability. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a harmonic series-parallel resonance amplification analysis method suitable for offshore wind farms. By establishing a state space model of all dynamic elements inside the offshore wind farm, the dominant poles of the state space model are calculated, the potential resonant frequency of the offshore wind farm is discovered, and then the possible harmonic phenomena in the offshore wind farm are analyzed. The Laplace final theorem is introduced to quickly calculate the resonance amplification factor and harmonic content of the offshore wind farm.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A harmonic series-parallel resonance amplification analysis method applicable to an offshore wind farm comprises the following steps:

[0007] S1: According to the characteristics of the offshore wind farm structure, extract the basic unit modules that can characterize the offshore wind farm;

[0008] S2: connecting the basic unit modules formed in step S1 in series and parallel to establish a state space model of the offshore wind farm to be analyzed;

[0009] S3: Establish a complex frequency domain model of harmonic sources in offshore wind farms;

[0010] S4: applying Laplace transform to obtain a complex frequency domain model of the offshore wind farm according to the state space model of the offshore wind farm established in step S2, and calculating the dominant poles of the offshore wind farm;

[0011] S5: Based on the dominant poles obtained in S4 and combined with the complex frequency domain model of the harmonic source in the offshore wind farm in S3, the data information of the risk of beat frequency oscillation in the offshore wind farm and the data information of the risk of harmonic resonance in the offshore wind farm are analyzed;

[0012] S6: Send the analysis results obtained in S5 to the wind farm control center for reference and adjustment by the operation personnel.

[0013] To optimize the above technical solutions, the specific measures taken also include:

[0014] Furthermore, the specific content of step S1 is:

[0015] In order to characterize the structural characteristics of the offshore wind farm and not be affected by objective factors of the operation mode, the basic unit module is composed of a resistor, an inductor and a capacitor in series; therefore, the model of the basic unit module is expressed as:

[0016]

[0017] Where: subscript N represents the Nth basic unit module of the offshore wind farm. There are three basic unit modules, namely j, k and m, that is, N is j, k and m; i represents the inductor current or branch current; u represents the capacitor voltage or node voltage; u s with i s They respectively represent the harmonic voltage source excitation and harmonic current source excitation on the corresponding basic unit module; R and L represent the equivalent resistance and inductance of the transmission line and transformer equipment; C represents the equivalent capacitance to ground of the AC cable and reactive compensation device, among which, if the corresponding basic unit module is a short-distance overhead line or transformer branch, the equivalent capacitance C is set to zero.

[0018] Furthermore, the specific content of step S2 is:

[0019] For the three basic unit modules j, k and m, determine the state space model of the offshore wind farm in the series-parallel relationship between them;

[0020] 1) If the jth, kth and mth basic unit modules are connected in series, the corresponding state space model of the offshore wind farm is:

[0021]

[0022] 2) If the kth basic unit is connected in parallel with the mth basic unit module and then connected in series with the jth module, the corresponding state space model of the offshore wind farm is:

[0023]

[0024] 3) If the jth, kth and mth basic unit modules are in parallel, the corresponding offshore wind farm state space model is:

[0025]

[0026] Where: B is a diagonal matrix, indicating whether the corresponding basic unit module has a harmonic voltage source or a harmonic current source;

[0027] In summary, the obtained state space model of the offshore wind farm is generally expressed as:

[0028]

[0029] Where: subscripts j and k represent the jth and kth basic unit modules in the offshore wind farm, respectively, and the matrix T and matrix A are and W jk With L jk is the relationship between the jth and kth basic unit modules, and the relationship under different connection modes is shown in equations (2) to (4); B is a diagonal matrix Indicates whether there is a harmonic source on the basic unit. If there is a harmonic voltage source, then B su Take 1; if there is a harmonic current source, then B si Take 1; x is the state variable of the basic unit module, taking the inductor current and capacitor voltage; d is a 2D column matrix Where: d su represents the harmonic voltage source, d si represents harmonic current source;

[0030] For the convenience of description, the state space model of the offshore wind farm represented by formula (5) is rewritten as:

[0031]

[0032] Where: T′ corresponds to the matrix A′ corresponds to the matrix B′ corresponds to the matrix x′ corresponds to the vector d′ corresponds to the vector

[0033] Furthermore, the complex frequency domain model of the harmonic source in the offshore wind farm established in step S3 is as follows:

[0034]

[0035] D(s) represents the harmonic voltage source Dsu (s) or harmonic current source D si (s);ω n is the harmonic frequency; A n is the amplitude of the nth harmonic source; θ n is the initial phase of the nth harmonic source, and s is the complex frequency.

[0036] Furthermore, the specific content of step S4 is:

[0037] S4.1: Apply Laplace transformation to transform the state space model of the offshore wind farm into the complex frequency domain, that is, transform formula (6) to obtain the complex frequency domain model x′(s) of the harmonic source in the offshore wind farm:

[0038] x′(s)=(sT′-A′) -1 B′D(s) (8)

[0039] Where: (·) -1 represents the matrix inversion operation, and extracts the system characteristic matrix sT′-A′ part in formula (8), and sets f(s)=(sT′-A′);

[0040] S4.2: Use the Newton-Raphson method to solve the dominant poles of the complex frequency domain model of the harmonic source in the offshore wind farm, that is, to solve the poles of formula (8).

[0041] Furthermore, the specific content of step S4.2 is:

[0042] S4.2.1: Determine the initial value s(0) of the complex frequency s, the error precision e, and the range of the dominant pole modulus |s| as follows:

[0043]

[0044] In the formula, 1i represents a complex number;

[0045] S4.2.2: Calculate f(s(n)) and the corresponding derivative f′(s(n)) of the nth s(n) according to the formula f(s)=(sT′-A′), and determine whether f′(s(n)) is equal to zero. If not, proceed to S4.2.3; otherwise, output an alarm signal to prompt the replacement of the initial value of the complex frequency variable s;

[0046] S4.2.3: Use formula (10) to calculate the value of s corresponding to n+1, s(n+1), as follows:

[0047]

[0048] S4.2.4: Determine whether the Newton-Raphson algorithm has converged according to formula (11). If formula (11) does not hold, it means that the algorithm has not converged. Combined with the s value obtained by formula (10), return to step S4.2.2 to continue iterating; where formula (11) is:

[0049] max{|s(n+1)-s(n)|} <e (11)

[0050] S4.2.5: When the Newton-Raphson algorithm in step S4.2.4 converges, the final s(n+1) value is output, which is the dominant pole of the dominant pole existing in the offshore wind farm.

[0051] Furthermore, the specific content of step S5 is:

[0052] S5.1: According to the dominant pole judgment obtained in S4, set the standard damping value; if the damping of the dominant pole is greater than the standard damping value, there is no harmonic resonance risk in the offshore wind farm; if the damping of the dominant pole is less than the standard damping value, and the natural frequency of the dominant pole is r and harmonic frequency ω n If the phase difference is less than 100π(rad / s), the offshore wind farm will experience beat frequency oscillation; if the natural frequency of the dominant pole ω r Equal to the harmonic frequency ω n , then harmonic resonance occurs in offshore wind farms (beat frequency oscillation is a special form of harmonic resonance, but harmonic resonance has a greater impact on the system);

[0053] S5.2: If it is determined according to S5.1 that there is a risk of beat frequency oscillation in the offshore wind farm, the oscillation amplitude u of the key node p is analyzed and calculated. p (∞)′;

[0054] S5.3: If it is determined according to S5.1 that there is a risk of harmonic resonance in the offshore wind farm, the complex frequency domain model of the harmonic source in the offshore wind farm established in step S3 and the complex frequency domain model x(s) of the harmonic source in the offshore wind farm established in step S4 are combined; and the Laplace terminal value theorem is applied to obtain the index at the key node p.

[0055] Furthermore, in step S5.2, if the offshore wind farm has a beat frequency oscillation phenomenon, the oscillation amplitude u of the key node p p The calculation of (∞)′ is shown in formula (12):

[0056]

[0057] Where ξ is the damping ratio corresponding to the dominant pole of the offshore wind farm.

[0058] Furthermore, in step S5.3, if the offshore wind farm has a harmonic resonance risk, the specific content of the index at the key node p is obtained as follows:

[0059] Combining formula (8) with the modified formula, the offshore wind farm harmonic resonance amplification evaluation matrix G(s) is defined as shown in formula (13):

[0060] G(s)=E(sT′-A′) -1 B′ (13)

[0061] Where: E is the observation matrix of the system;

[0062] Obtaining the indicators at the key node p includes:

[0063] (1) Based on the evaluation matrix G(s), use formula (14) to identify the node BusN where the background harmonic voltage is seriously amplified and its amplification factor Val;

[0064] [BusN,Val]=max(G (：,1) (1i×ω n )) (14)

[0065] In the formula, G (:,1) (s) represents the first column vector in the evaluation matrix G(s); max(·) represents the maximum value of the vector and the corresponding position;

[0066] (2) Based on the evaluation matrix G(s), the steady-state voltage amplitude u of any node p in the offshore wind farm under the background harmonic voltage source is p (∞), the harmonic resonance voltage amplification factor α corresponding to node p v From formulas (15) to (16), we get:

[0067]

[0068] In the formula, α v Indicates the harmonic voltage amplification factor, Represents the phase shift of the voltage waveform, G (2p，1) (s) represents the element at position 2p,1 in the matrix G(s);

[0069] (3) Based on the evaluation matrix G(s), the steady-state current amplitude i of any branch q under the action of the total harmonic current of the offshore wind farm under the Norton equivalent is q (∞), the harmonic resonant current amplification factor α corresponding to branch q i From formulas (17) to (18), we get:

[0070]

[0071] Where c is the number of the offshore wind farm grid connection point, α i Indicates the current harmonic amplification factor, Represents the phase shift of the current waveform, G (2c,2q-1) (s) represents the element at position 2c,2q-1 in the matrix G(s);

[0072] (4) The steady-state current amplitude i injected into the system by the mth wind turbine mq (∞) is obtained from formula (19):

[0073]

[0074] Where, the subscript mbus is the node number corresponding to the mth wind turbine, G (2mbus,2q-1) (s) represents the element at position 2mbus,2q-1 in the matrix G(s);

[0075] (5) The harmonic content β of the offshore wind farm grid connection point is calculated by formula (20):

[0076]

[0077] Where: A1 represents the fundamental amplitude of the equivalent power grid; A mn With θ mn They represent the harmonic current amplitude and phase angle output by the mth wind turbine respectively; t represents the total number of offshore wind turbines; G mi (s) represents the element corresponding to the basic unit of the mth wind turbine; |G mi (s)|、angle(G mi (s)) respectively indicate that s approaches the harmonic frequency 1i×ω n Time function G i (s) The corresponding amplitude and phase angle.

[0078] Furthermore, the specific content of step S6 is:

[0079] If beat frequency oscillation occurs in an offshore wind farm, the oscillation amplitude u of the key node p calculated according to formula (12) is p (∞)′ is sent to the wind farm control center for reference and adjustment by the operators;

[0080] If the offshore wind farm has a harmonic resonance risk, the background harmonic voltage calculated by formula (14) will be amplified to the node BusN and its amplification factor Val, and the steady-state voltage amplitude u of the key node calculated by formulas (15)-(16) will be p (∞) and the corresponding harmonic resonance voltage amplification factor α v , the steady-state current amplitude i of any branch q calculated by formulas (17)-(18) q(∞) and the corresponding harmonic resonant current amplification factor α i , the steady-state current amplitude i injected into the system by the mth wind turbine calculated by formula (19) mq (∞) and the harmonic content β of the offshore wind farm grid connection point calculated by formula (20) are sent to the wind farm control center for reference and adjustment by the operating personnel.

[0081] The beneficial effects of the present invention are:

[0082] 1. The present invention is applicable to the harmonic series-parallel resonance amplification analysis method of offshore wind power systems, which effectively reduces the complexity of offshore wind power system modeling and lays a model foundation for analyzing the harmonic resonance amplification of large-scale offshore wind farms.

[0083] 2. The present invention is applicable to the harmonic series-parallel resonance amplification analysis method of offshore wind power systems. It can detect potential harmonic resonance risks in offshore wind farms without node scanning, has low economic cost and high engineering practicability.

[0084] 3. The present invention proposes a harmonic series-parallel resonance amplification analysis method suitable for offshore wind farms, which can reveal phenomena such as harmonic resonance and beat frequency oscillation in offshore wind farms, and can quickly and effectively evaluate the harmonic amplification factor and maximum harmonic content of key nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a schematic diagram of the overall solution flow in an embodiment of the present invention.

[0086] Figure 2 Schematic diagram of the harmonic impedance and basic unit model of an offshore wind farm in an embodiment of the present invention; Figure 2 a is the model of the harmonic impedance of an offshore wind farm in a certain place, Figure 2 b is the basic unit model of a local offshore wind farm.

[0087] Figure 3 It is a schematic diagram of the structure of a local offshore wind farm in an embodiment of the present invention.

[0088] Figure 4 Schematic diagram of simulation waveform in an embodiment of the present invention; Figure 4 a is the simulated waveform of phase A voltage at the grid connection point under the action of fundamental wave, Figure 4 b is the simulated waveform of phase A voltage at the grid connection point under the action of the fifth harmonic. Figure 4 c is the simulated waveform of phase A voltage at the grid connection point under the action of 4.5th interharmonic. Figure 4 d is the simulated waveform of phase A voltage at the grid connection point under the action of the 15th harmonic.

[0089] Figure 51 is a schematic diagram of the frequency spectrum of the A-phase voltage at the grid connection point under the combined action of the harmonic voltage source and the harmonic current source in an embodiment of the present invention. DETAILED DESCRIPTION

[0090] The present invention will now be described in further detail with reference to the accompanying drawings.

[0091] The overall technical solution of the present invention is as follows:

[0092] This specific embodiment discloses a harmonic series-parallel resonance amplification analysis method applicable to an offshore wind power system. The specific flow chart of the method is as follows: Figure 1 As shown, the following steps are included:

[0093] S1: According to the structural characteristics of offshore wind farms, extract the basic unit modules that can characterize offshore wind farms;

[0094] S2: connect the basic units formed in S1 in series and parallel to establish the state space model of the offshore wind farm to be analyzed;

[0095] S3: Establish a complex frequency domain model of harmonic sources in offshore wind farms;

[0096] S4: Apply Laplace transform to obtain the complex frequency domain model of the offshore wind farm according to the state space model established in S2, and calculate the dominant poles existing in the offshore wind farm;

[0097] S5: Based on the dominant poles obtained in S4 and the harmonic source model in S3, the harmonic resonance vibration mode existing in the offshore wind farm is analyzed, and the harmonic resonance amplification factor and harmonic content at the key nodes in the offshore wind farm (such as the wind farm grid connection point) are evaluated;

[0098] S6: Send the evaluation results obtained in S5 to the wind farm control center for reference by the operation personnel.

[0099] Furthermore, in step S1, in order to characterize the structural characteristics of the offshore wind farm and not be affected by objective factors of the operation mode, the basic unit module is composed of a resistor, an inductor and a capacitor in series; Figure 2 a and Figure 2 As shown in b, the model of the basic unit module is expressed as:

[0100]

[0101] Where: subscript N represents the Nth basic unit module of the offshore wind farm. There are three basic unit modules, namely j, k and m, that is, N is j, k and m; i represents the inductor current or branch current; u represents the capacitor voltage or node voltage; u s with i sThey respectively represent the harmonic voltage source excitation and harmonic current source excitation on the corresponding basic unit module; R and L represent the equivalent resistance and inductance of the transmission line and transformer equipment; C represents the equivalent capacitance to ground of the AC cable and reactive compensation device, among which, if the corresponding basic unit module is a short-distance overhead line or transformer branch, the equivalent capacitance C is set to zero.

[0102] Furthermore, in step S2, multiple basic units are connected in series and parallel to form an offshore wind farm that requires harmonic analysis. The basic unit connection rules are as follows:

[0103] In order not to lose generality, the three basic modules j, k, and m are taken as examples for analysis;

[0104] 1) If the jth, kth and mth basic unit modules are connected in series, the corresponding state space model of the offshore wind farm is:

[0105]

[0106] 2) If the kth basic unit is connected in parallel with the mth basic unit module and then connected in series with the jth module, the corresponding state space model of the offshore wind farm is:

[0107]

[0108] 3) If the jth, kth and mth basic unit modules are in parallel, the corresponding offshore wind farm state space model is:

[0109]

[0110] Where: B is a 6-dimensional diagonal matrix, indicating whether the corresponding basic unit module has a harmonic voltage source or a harmonic current source. Taking the kth module as an example, if there is a harmonic voltage source, the element B(3,3) is equal to 1; if there is a harmonic current source, then B(4,4) is equal to 1; otherwise it is equal to 0. In addition, if it is case 2, then u sk Equal to u sm ; If it is case 3, then u sj 、u sk with u sm All three are equal;

[0111] Moreover, by modifying the corresponding elements in equations (2) to (4), the wind farm operation conditions, topology changes, etc. can be flexibly reflected. If a certain wind turbine (or power collection cable) is out of operation, it is only necessary to set the resistance and inductance corresponding to the basic unit of the wind turbine (or power collection cable) to a larger value (the present invention takes 10 8 ), the capacitor is set to a smaller value (the present invention takes 10 -12); If the high-voltage cable is switched from single-circuit operation to double-circuit operation, it is only necessary to divide the resistance and inductance values ​​set by the high-voltage cable basic unit by 2, and multiply the capacitance value by 2. In addition, if a new wind turbine is added to a node, the basic connection rules provided by equations (2) to (4) can still be used to realize the later expansion of the offshore wind farm;

[0112] In summary, the obtained state space model of the offshore wind farm is generally expressed as:

[0113]

[0114] Where: subscripts j and k represent the jth and kth basic unit modules in the offshore wind farm, respectively, and the matrix T and matrix A are and W jk With L jk is the relationship between the jth and kth basic unit modules, and the relationship under different connection modes is shown in equations (2) to (4); B is a diagonal matrix Indicates whether there is a harmonic source on the basic unit. If there is a harmonic voltage source, then B su Take 1; if there is a harmonic current source, then B si Take 1; x is the state variable of the basic unit module, taking the inductor current and capacitor voltage; d is a 2D column matrix Where: d su represents the harmonic voltage source, d si represents harmonic current source;

[0115] For the convenience of description, the state space model of the offshore wind farm represented by formula (5) is rewritten as:

[0116]

[0117] Where: T′ corresponds to the matrix A′ corresponds to the matrix B′ corresponds to the matrix x′ corresponds to the vector d′ corresponds to the vector

[0118] Furthermore, in step S3, a complex frequency domain model of a harmonic source with a high harmonic content is established based on the offshore wind farm operation data:

[0119]

[0120] D(s) represents the harmonic voltage source D su (s) or harmonic current source D si (s);ω n is the harmonic frequency; A n is the amplitude of the nth harmonic source; θn is the initial phase of the nth harmonic source, and s is the complex frequency.

[0121] Furthermore, in step S4, the state space model of the offshore wind farm is converted to the complex frequency domain by applying Laplace transformation. To this end, based on formula (6), the offshore wind farm model in the complex frequency domain can be obtained as follows:

[0122] x′(s)=(sT′-A′) -1 B′D(s)=(f(s)) -1 B′D(s) (8)

[0123] Where: (·) -1 Denotes the matrix inversion operation, and extracts the system characteristic matrix sT′-A′ part in formula (8), and sets f(s)=(sT′-A′).

[0124] Furthermore, in step S4, the Newton-Raphson method is used to solve the dominant poles of the complex frequency domain model of the harmonic source in the offshore wind farm, that is, to solve the poles of formula (8);

[0125] S4.1: Determine the initial value s(0) of the complex frequency s, the error accuracy e, and the range of the dominant pole modulus |s| as follows:

[0126]

[0127] In the formula, 1i represents a complex number;

[0128] S4.2: Calculate f(s(n)) and the corresponding derivative f′(s(n)) of the nth s(n) according to the formula f(s)=(sT′-A′), and determine whether f′(s(n)) is equal to zero. If not, proceed to S4.2.3; otherwise, output an alarm signal to prompt the replacement of the initial value of the complex frequency variable s;

[0129] S4.3: Use formula (10) to calculate the value s(n+1) corresponding to n+1, as follows:

[0130]

[0131] S4.4: Determine whether the Newton-Raphson algorithm has converged according to formula (11). If formula (11) does not hold, it means that the algorithm has not converged. Combined with the s value obtained by formula (10), return to step S4.2.2 to continue iterating; where formula (11) is:

[0132] max{|s(n+1)-s(n)|}<e (11)

[0133] S4.5: When the Newton-Raphson algorithm in step S4.2.4 converges, the final s(n+1) value is output, which is the dominant pole of the dominant pole existing in the offshore wind farm.

[0134] Further, in step S5, if the resonant frequency ω corresponding to the dominant pole obtained in step S4 is r Harmonic sources of offshore wind farms n If the frequencies are inconsistent, the offshore wind farm will have obvious beat frequency oscillations. The oscillation amplitude of node p is shown in formula (12):

[0135] Where ξ is the damping ratio corresponding to the dominant pole of the offshore wind farm.

[0136] Further, in step S5, if the resonant frequency ω corresponding to the dominant pole is r The harmonic source frequency of offshore wind farm ω n When they are consistent, offshore wind farms will produce harmonic resonance.

[0137] Furthermore, in step S5, in combination with formula (8), the offshore wind farm harmonic resonance amplification evaluation matrix G(s) is defined as shown in formula (13):

[0138] G(s)=E(sT′-A′) -1 B′ (13)

[0139] Where: E is the observation matrix of the system.

[0140] Further, in step S5, based on the evaluation matrix G(s), the node BusN where the background harmonic voltage is most amplified and its amplification factor Val can be identified using formula (14);

[0141] [BusN,Val]=max(G (：,1) (1i×ω n )) (14)

[0142] In the formula, G (:,1) (s) represents the first column vector in the evaluation matrix G(s); max(·) represents the maximum value of the vector and the corresponding position.

[0143] Further, in step S5, based on the evaluation matrix G(s), the steady-state voltage amplitude u of any node p in the offshore wind farm under the background harmonic voltage source is p (∞), the harmonic resonance voltage amplification factor α corresponding to node p v From formulas (15) to (16), we get:

[0144]

[0145] In the formula, α v Indicates the harmonic voltage amplification factor, Represents the phase shift of the voltage waveform, G (2p，1) (s) represents the element at the 2p,1th position in the matrix G(s).

[0146] Further, in step S5, based on the evaluation matrix G(s), the steady-state current amplitude i of any branch q under the action of the total harmonic current of the offshore wind farm under the Norton equivalent is q (∞), the harmonic resonant current amplification factor α corresponding to branch q i From formulas (17) to (18), we get:

[0147]

[0148] Where c is the number of the offshore wind farm grid connection point, α i Indicates the current harmonic amplification factor, Represents the phase shift of the current waveform, G (2c,2q-1) (s) represents the element at the 2c,2q-1th position in the matrix G(s).

[0149] Further, in step S5, the steady-state current amplitude i injected into the system by the mth wind turbine is mq (∞) is obtained from formula (19):

[0150]

[0151] Where, the subscript mbus is the node number corresponding to the mth wind turbine, G (2mbus,2q-1) (s) represents the element at the 2mbus,2q-1th position in the matrix G(s).

[0152] Further, in step S5, the harmonic content β of the offshore wind farm grid connection point is calculated by formula (20):

[0153]

[0154] Where: A1 represents the fundamental amplitude of the equivalent power grid; A mn With θ mn They represent the harmonic current amplitude and phase angle output by the mth wind turbine respectively; t represents the total number of offshore wind turbines; G mi (s) represents the element corresponding to the basic unit of the mth wind turbine; |G mi (s)|、angle(G mi (s)) respectively indicate that s approaches the harmonic frequency 1i×ω n Time function G i (s) The corresponding amplitude and phase angle.

[0155] Furthermore, according to formula (15), taking the background harmonic voltage source phase angle as a reference, when the harmonic current phase of all wind turbines satisfies When the corresponding system harmonic content rate is the maximum value |β| max , according to |β| max It can realize the rapid assessment of the harmonic content of offshore wind farms and avoid the harmonic resonance amplification phenomenon in offshore wind farms.

[0156] Two embodiments of the present invention are described below.

[0157] Embodiment 1:

[0158] The verification example used in the present invention is that a certain offshore wind farm in Jiangsu is connected to the power grid via an AC submarine cable. The system structure diagram is shown in FIG. Figure 3 As shown. The offshore wind farm is connected to the onshore 220kV system through a three-stage boosting method. The specific structure is: the offshore wind farm is connected to the same 35kV busbar through a collecting submarine cable, and the voltage is boosted to 110kV through an offshore booster station. After that, it is connected to the onshore substation through a double-circuit 110kV AC submarine cable, and the voltage is boosted to 220kV through a 35 / 110 / 220kV three-winding transformer and connected to the onshore power grid through overhead lines. According to the measured data, when the system undergoes harmonic amplification, the harmonic voltage content of the system is about 0.88%, and the harmonic current content injected into point F by the wind farm is about 6.7A. Figure 1 The method of the present invention shown in the figure performs harmonic resonance analysis and calculates that the dominant pole of the offshore wind farm is -8.6±j1407, and the corresponding natural frequency is 224 Hz.

[0159] In order to verify that the present invention can analyze the harmonic resonance amplification phenomenon in different frequency bands, the following Figure 3 The transient simulation model is shown. The operating conditions are set as follows: 1. The onshore power grid adds a fundamental wave with an amplitude of 1p.u., a frequency of 50Hz, and a phase of 0°; 2. The onshore power grid adds a fifth harmonic with an amplitude of 0.0088pu, a frequency of 250Hz, and a phase of 0°; 3. The onshore power grid adds an interharmonic with an amplitude of 0.001pu, a frequency of 225Hz, and a phase of 0°; 4. The onshore power grid adds a 15th harmonic with an amplitude of 0.001pu, a frequency of 750Hz, and a phase of 0°. The voltage simulation waveforms of the offshore wind farm grid connection point under different operating conditions are shown in the figure below. Figure 4 a, 4b, 4c and 4d.

[0160] According to 4a, when the excitation source of the offshore wind power system is the fundamental wave, after a short transient process, the grid-connected point voltage amplitude u(∞) finally stabilizes at 1.0536pu, which is consistent with the 1.054pu calculated by the present invention. After the offshore wind farm injects the fifth harmonic, the harmonic frequency differs from the natural frequency of the dominant pole by 52 (rad / s). According to the present invention, the system will experience beat frequency oscillation. According to 5b, the grid-connected point voltage will experience beat frequency oscillation during the transient process, and the frequency The rate is about 25.95Hz, and the voltage amplitude is finally stabilized at 0.0373pu, which is consistent with 0.0371pu calculated by the present invention. When the offshore wind farm is injected with 4.5 interharmonics, it can be seen from the present invention that the harmonic frequency is basically equal to the natural frequency corresponding to the dominant pole, and the offshore wind farm will have serious harmonic resonance. It can be further seen from 5c that the grid connection point voltage is 0.073pu, which is consistent with 0.0737pu calculated by the present invention. When the offshore wind farm is injected with high-frequency harmonics, according to Figure 4 d It can be seen that the grid connection point voltage is finally stabilized at 0.00135pu, which is consistent with the 0.001366pu calculated by the present invention. Therefore, it is shown that the harmonic resonance amplification calculation method proposed by the present invention is effective and feasible, and can be adapted to broadband harmonic resonance calculation.

[0161] Embodiment 2:

[0162] In order to further verify the effectiveness of the proposed method in harmonic evaluation, the operating conditions are set as follows: the equivalent grid side adds a fundamental wave with an amplitude of 1 p.u., a frequency of 50 Hz, and a phase of 0°, and a 5th harmonic voltage with an amplitude of 0.0088 pu, a frequency of 250 Hz, and a phase of 0°, and at the same time, the wind farm side injects a 5th harmonic current with an amplitude of 6.7 A, a frequency of 250 Hz, and a phase of 0° into the system.

[0163] The simulation results show that the 5th harmonic voltage distortion rate THD at the PCC point reaches 3.71%, which is basically consistent with the 5th harmonic content rate of about 3.7% calculated by the present invention. In addition, according to the present invention, when the phase angle of the harmonic current source satisfies The harmonic phenomenon of offshore wind farms is most serious when the harmonic current source voltage is -89.4°. The present invention calculates that when the harmonic current source voltage is -89.4°, the 5th harmonic content of the grid connection point is about 4.852%. Therefore, under the premise of the above parameter settings, the phase of the harmonic current source is modified to -89.4°. The simulation results are as follows Figure 5 As shown, the harmonic distortion rate THD is 4.66%, which shows the effectiveness and correctness of the present invention in terms of harmonic content evaluation.

[0164] It should be noted that the terms such as "upper", "lower", "left", "right", "front", "back", etc. cited in the invention are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments in their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0165] The above are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A harmonic series-parallel resonance amplification analysis method suitable for offshore wind farms, characterized in that: The following steps are involved: S1: According to the characteristics of the offshore wind farm structure, extract the basic unit modules that can characterize the offshore wind farm; The basic unit module is composed of a resistor, an inductor and a capacitor in series; therefore, the model of the basic unit module is expressed as: Where: subscript N represents the Nth basic unit module of the offshore wind farm. There are three basic unit modules, namely j, k and m, that is, N is j, k and m; i represents the inductor current or branch current; u represents the capacitor voltage or node voltage; u s with i s They represent the harmonic voltage source excitation and harmonic current source excitation on the corresponding basic unit module respectively; R and L represent the equivalent resistance and inductance of the transmission line and transformer equipment; C represents the equivalent capacitance to ground of the AC cable and reactive power compensation device, where if the corresponding basic unit module is a short-distance overhead line or transformer branch, the equivalent capacitance C is set to zero; S2: connecting the basic unit modules formed in step S1 in series and parallel to establish a state space model of the offshore wind farm to be analyzed; S3: Establish a complex frequency domain model of the harmonic source in the offshore wind farm, the complex frequency domain model is as follows: D(s) represents the harmonic voltage source D su (s) or harmonic current source D si (s);ω n is the harmonic frequency; A n is the amplitude of the nth harmonic source; θ n is the initial phase of the nth harmonic source, s is the complex frequency; S4: applying Laplace transform to obtain a complex frequency domain model of the offshore wind farm according to the state space model of the offshore wind farm established in step S2, and calculating the dominant poles of the offshore wind farm; S5: Based on the dominant poles obtained in S4 and combined with the complex frequency domain model of the harmonic source in the offshore wind farm in S3, the data information of the risk of beat frequency oscillation in the offshore wind farm and the data information of the risk of harmonic resonance in the offshore wind farm are analyzed; S6: Send the analysis results obtained in S5 to the wind farm control center for reference and adjustment by the operation personnel.

2. The harmonic series-parallel resonance amplification analysis method applicable to an offshore wind farm according to claim 1, characterized in that: The specific content of step S2 is: For the three basic unit modules j, k and m, determine the state space model of the offshore wind farm in the series-parallel relationship between them; 1) If the jth, kth and mth basic unit modules are connected in series, the corresponding state space model of the offshore wind farm is: 2) If the kth basic unit is connected in parallel with the mth basic unit module and then connected in series with the jth module, the corresponding state space model of the offshore wind farm is: 3) If the jth, kth and mth basic unit modules are in parallel, the corresponding offshore wind farm state space model is: Where: B is a diagonal matrix, indicating whether the corresponding basic unit module has a harmonic voltage source or a harmonic current source; In summary, the obtained state space model of the offshore wind farm is generally expressed as: Where: subscripts j and k represent the jth and kth basic unit modules in the offshore wind farm, respectively, and the matrix T and matrix A are and W jk With L jk is the relationship between the jth and kth basic unit modules, and the relationship under different connection modes is shown in equations (2) to (4); B is a diagonal matrix Indicates whether there is a harmonic source on the basic unit. If there is a harmonic voltage source, then B su Take 1; if there is a harmonic current source, then B si Take 1; x is the state variable of the basic unit module, taking the inductor current and capacitor voltage; d is a 2D column matrix Where: d su represents the harmonic voltage source, d si represents harmonic current source; For the convenience of description, the state space model of the offshore wind farm represented by formula (5) is rewritten as: Where: T′ corresponds to the matrix A′ corresponds to the matrix B′ corresponds to the matrix x′ corresponds to the vector d′ corresponds to the vector 3. The harmonic series-parallel resonance amplification analysis method applicable to an offshore wind farm according to claim 1, characterized in that: The specific content of step S4 is: S4.1: Apply Laplace transformation to transform the state space model of the offshore wind farm into the complex frequency domain, that is, transform formula (6) to obtain the complex frequency domain model x′(s) of the harmonic source in the offshore wind farm: x′(s)=(sT′-A′) -1 B′D(s) (8) Where: (·) -1 represents the matrix inversion operation, and extracts the system characteristic matrix sT′-A′ part in formula (8), and sets f(s)=(sT′-A′); S4.2: Use the Newton-Raphson method to solve the dominant poles of the complex frequency domain model of the harmonic source in the offshore wind farm, that is, to solve the poles of formula (8).

4. The harmonic series-parallel resonance amplification analysis method applicable to an offshore wind farm according to claim 3, characterized in that: The specific content of step S4.2 is: S4.2.1: Determine the initial value s(0) of the complex frequency s, the error precision e, and the range of the dominant pole modulus |s| as follows: In the formula, 1i represents a complex number; S4.2.2: Calculate f(s(n)) and the corresponding derivative f′(s(n)) of the nth s(n) according to the formula f(s)=(sT′-A′), and determine whether f′(s(n)) is equal to zero. If not, proceed to S4.2.3; otherwise, output an alarm signal to prompt the replacement of the initial value of the complex frequency variable s; S4.2.3: Use formula (10) to calculate the value of s corresponding to n+1, s(n+1), as follows: S4.2.4: Determine whether the Newton-Raphson algorithm has converged according to formula (11). If formula (11) does not hold, it means that the algorithm has not converged. Combined with the s value obtained by formula (10), return to step S4.2.2 to continue iterating; where formula (11) is: max{|s(n+1)-s(n)|}<e(11) S4.2.5: When the Newton-Raphson algorithm in step S4.2.4 converges, the final s(n+1) value is output, which is the dominant pole of the offshore wind farm.

5. The harmonic series-parallel resonance amplification analysis method applicable to an offshore wind farm according to claim 4, characterized in that: The specific content of step S5 is: S5.1: According to the dominant pole judgment obtained in S4, set the standard damping value; if the damping of the dominant pole is greater than the standard damping value, there is no harmonic resonance risk in the offshore wind farm; if the damping of the dominant pole is less than the standard damping value, and the natural frequency of the dominant pole is r and harmonic frequency ω n If the phase difference is less than 100π(rad / s), the offshore wind farm will experience beat frequency oscillation; if the natural frequency of the dominant pole ω r Equal to the harmonic frequency ω n , then harmonic resonance occurs in offshore wind farms; S5.2: If it is determined according to S5.1 that there is a risk of beat frequency oscillation in the offshore wind farm, the oscillation amplitude u of the key node p is analyzed and calculated. p (∞)′; S5.3: If it is determined according to S5.1 that there is a risk of harmonic resonance in the offshore wind farm, the complex frequency domain model of the harmonic source in the offshore wind farm established in step S3 and the complex frequency domain model x(s) of the harmonic source in the offshore wind farm established in step S4 are combined; and the Laplace terminal value theorem is applied to obtain the index at the key node p.

6. A harmonic series-parallel resonance amplification analysis method applicable to an offshore wind farm according to claim 5, characterized in that: In step S5.2, if the offshore wind farm has a beat frequency oscillation, the oscillation amplitude u of the key node p p The calculation of (∞)′ is shown in formula (12): Where ξ is the damping ratio corresponding to the dominant pole of the offshore wind farm.

7. A harmonic series-parallel resonance amplification analysis method applicable to an offshore wind farm according to claim 6, characterized in that: In step S5.3, if the offshore wind farm has a harmonic resonance risk, the specific content of the index at the key node p is obtained as follows: Combining formula (8) with the modified formula, the offshore wind farm harmonic resonance amplification evaluation matrix G(s) is defined as shown in formula (13): G(s)=E(sT′-A′) -1 B′ (13) Where: E is the observation matrix of the system; Obtaining the indicators at the key node p includes: (1) Based on the evaluation matrix G(s), use formula (14) to identify the node BusN where the background harmonic voltage is seriously amplified and its amplification factor Val; [BusN,Val]=max(G (：,1) (1i×ω n )) (14) In the formula, G (:,1) (s) represents the first column vector in the evaluation matrix G(s); max(·) represents the maximum value of the vector and the corresponding position; (2) Based on the evaluation matrix G(s), the steady-state voltage amplitude u of any node p in the offshore wind farm under the background harmonic voltage source is p (∞), the harmonic resonance voltage amplification factor α corresponding to node p v From formulas (15) to (16), we get: In the formula, α v Indicates the harmonic voltage amplification factor, Represents the phase shift of the voltage waveform, G (2p，1) (s) represents the element at position 2p,1 in the matrix G(s); (3) Based on the evaluation matrix G(s), the steady-state current amplitude i of any branch q under the action of the total harmonic current of the offshore wind farm under the Norton equivalent is q (∞), the harmonic resonant current amplification factor α corresponding to branch q i From formulas (17) to (18), we get: Where c is the number of the offshore wind farm grid connection point, α i Indicates the current harmonic amplification factor, Represents the phase shift of the current waveform, G (2c,2q-1) (s) represents the element at position 2c,2q-1 in the matrix G(s); (4) The steady-state current amplitude i injected into the system by the mth wind turbine mq (∞) is obtained from formula (19): Where, the subscript mbus is the node number corresponding to the mth wind turbine, G (2mbus,2q-1) (s) represents the element at position 2mbus,2q-1 in the matrix G(s); (5) The harmonic content β of the offshore wind farm grid connection point is calculated by formula (20): Where: A1 represents the fundamental amplitude of the equivalent power grid; A mn With θ mn They represent the harmonic current amplitude and phase angle output by the mth wind turbine respectively; t represents the total number of offshore wind turbines; G mi (s) represents the element corresponding to the basic unit of the mth wind turbine; |G mi (s)|、angle(G mi (s)) respectively indicate that s approaches the harmonic frequency 1i×ω n Time function G i (s) The corresponding amplitude and phase angle.

8. A harmonic series-parallel resonance amplification analysis method applicable to offshore wind farms according to claim 7, characterized in that: The specific content of step S6 is: If beat frequency oscillation occurs in an offshore wind farm, the oscillation amplitude u of the key node p calculated according to formula (12) is p (∞)′ is sent to the wind farm control center for reference and adjustment by the operators; If the offshore wind farm has a harmonic resonance risk, the background harmonic voltage calculated by formula (14) will be amplified to the node BusN and its amplification factor Val, and the steady-state voltage amplitude u of the key node calculated by formulas (15)-(16) will be p (∞) and the corresponding harmonic resonance voltage amplification factor α v , the steady-state current amplitude i of any branch q calculated by formulas (17)-(18) q (∞) and the corresponding harmonic resonant current amplification factor α i , the steady-state current amplitude i injected into the system by the mth wind turbine calculated by formula (19) mq (∞) and the harmonic content β of the offshore wind farm grid connection point calculated by formula (20) are sent to the wind farm control center for reference and adjustment by the operating personnel.

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