Optimization design method of double-tuned filter for converter station

Abstract

An optimization design method of a double-tuned filter for a converter station comprises the following steps: calculating a total impedance function Z (omega) of the double-tuned filter; representing two tuning points of the filter through a full impedance function Z (omega) of the double-tuned filter, and defining an intermediate angular frequency of the double-tuned filter; the value of a high-voltage side capacitor C1 is determined according to the fundamental wave reactive compensation quantity QS1, and the values of L1, L2 and C2 are solved; and calculating the fundamental wave power loss of the medium resistor R of the double-tuned filter and the harmonic amplification coefficient H (omega) of the characteristic harmonic voltage of the AC filter of the converter station. And with the filtering performance, the resonance-free risk and the equipment investment cost as constraint conditions, the values of L1, L2 and C2 are optimized by adopting an optimization algorithm. According to the method, the optimal design process of an existing double-tuned filter topological structure for the converter station is analyzed in detail by considering the filtering effect and the harmonic amplification effect and combining the circuit principle, the filtering effect of the double-tuned filter for the converter station can be improved, and the harmonic resonance or harmonic amplification risk is avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of double-tuned filter optimization design, and in particular to an optimization design method for a double-tuned filter used in a converter station. Background Art

[0002] In the power system, the most widely used means of reducing harmonics is passive filters, which can not only suppress harmonics but also compensate for reactive power. AC / DC filters are important components of HVDC transmission converter stations, usually accounting for a considerable portion of conventional HVDC converter stations. Together with the required switchgear, AC filters account for about a quarter of the total area of ​​the HVDC solution. In addition, the scope of filter design research is wide and the design process is complex, requiring repeated calculations, which will affect other aspects of the converter station design and the entire project progress. Quickly and accurately configuring the filters required for different projects is very important for the design of HVDC converter stations.

[0003] There are various circuit types of passive filters, mainly single-tuned filters, double-tuned filters, high-pass filters, C-type filters and other forms. Among them, the double-tuned filter can filter out the harmonics of two frequency bands, which is more technically economical than two independent single-tuned filters. There is only one capacitor at a high potential, which is convenient for solving the filtering problem at low transmission power. The types of filters are reduced, the equipment and spare parts are less, and it is easy to maintain. It is the most commonly used filter form in high-voltage DC engineering. Therefore, it is very important to carry out parameter optimization design for double-tuned filters. The electrical design scheme of the existing double-tuned filter for converter stations only aims to filter out characteristic subharmonics, and does not fully consider the influence of non-characteristic subharmonics, resulting in the risk of resonance between the filter group and the AC / DC system. The electrical parameters of the existing double-tuned filter for converter stations follow the empirical design formula, the theoretical basis is not sufficient, and the system has the risk of resonance, so it is necessary to optimize the design of its electrical parameters. Summary of the invention

[0004] The present invention aims at the problem that the design theory of electrical parameters of double-tuned filters in existing converter stations is unclear and the design of AC / DC filter circuit parameters has a large optimization space. The present invention provides an optimization design method for double-tuned filters for converter stations. The method adopts an optimization algorithm to optimize the design of capacitance and inductance component parameters of the double-tuned filters and optimizes the harmonic amplification factor H(ω) of the characteristic harmonic voltage of the double-tuned filters reflecting their harmonic amplification effect and the filter loss for improving the filtering effect of the double-tuned filters for converter stations.

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

[0006] An optimization design method for a double-tuned filter for a converter station comprises the following steps:

[0007] Step 1: Calculate the total impedance function Z(ω) of the double tuned filter;

[0008] Step 2: The two tuning points of the filter are expressed by the total impedance function Z(ω) of the double-tuned filter, and the intermediate angular frequency of the double-tuned filter is defined;

[0009] Step 3: According to the fundamental wave reactive power compensation Q S1 Determine the high voltage side capacitor C 1 The value of L 1 , L 2 and C 2 The value of

[0010] Step 4: Calculate the fundamental power loss of the resistor R in the double-tuned filter and the harmonic amplification factor H(ω) of the characteristic harmonic voltage of the converter station AC filter.

[0011] Step 5: Using the filtering performance, no resonance risk and equipment investment cost as constraints, an optimization algorithm is used to optimize L 1 , L 2 and C 2 Optimize the value of .

[0012] In the step 1: calculate the total impedance function Z(ω) of the double tuned filter:

[0013]

[0014] In formula (1), R represents the damping resistance of the double-tuned filter; ω represents the angular frequency of the AC system under different harmonics; j represents the imaginary unit; L 1 Represents the series branch inductance of the double tuned filter; L 2 represents the parallel branch inductance of the double tuned filter; C 1 Represents the series branch capacitance of the double tuned filter; C 2 Represents the parallel branch capacitance of the double tuned filter.

[0015] In the step 2: according to the circuit resonance principle, the two tuning points of the filter are represented by the total impedance function Z(ω) of the double tuned filter, and the intermediate angular frequency of the double tuned filter is defined, that is:

[0016] ω 00 =λω 01 +(1-λ)ω 02 ,λ∈(0,1);

[0017] In the above formula, ω 00 represents the intermediate angular frequency; ω 01represents the first resonant angular frequency of the double-tuned filter; ω 02 represents the second resonant angular frequency of the double-tuned filter; λ represents the parameter to be optimized.

[0018] And there are:

[0019]

[0020] In the above formula,

[0021] In step 3: for the AC filter, according to the actual fundamental reactive power compensation amount Q required by the converter station S1 , determine the high-voltage side capacitor C according to the following formula 1 Values:

[0022]

[0023] In formula (2), U s Indicates the rated voltage of the AC bus; ω 1 is the fundamental angular frequency; h 00 =ω 00 / ω 1 Indicates the intermediate tuning times.

[0024] Because ω 01 ,ω 02 These are all known parameters, and the parameter λ can be adjusted and optimized according to the filtering effect of the filter and the risk of system resonance.

[0025] To this end, according to the known parameters λ, resistor R, capacitor C 1 and tuning point ω 01 ,ω 02 , solve the nonlinear algebraic equations to obtain L 1 , L 2 and C 2 The specific expression is as follows:

[0026] According to formula (1), the circuit series resonance condition is:

[0027]

[0028] make have to:

[0029]

[0030] Substituting formula (4) into formula (3), we get:

[0031] R 2 C 1 η(η-L 1 -L 2 )=R2 L 2 C 2 (η-L 1 )+(η-L 1 -L 2 )η 2 (5);

[0032] η 3 -(L 1 +L 2 +R 2 C 1 )η 2 +R 2 (L 2 C 2 +L 1 C 1 +L 2 C 1 )η-R 2 L 1 L 2 C 2 =0(6);

[0033] According to Cardano's formula, the three real roots of equation (6) are as follows:

[0034] The discriminant of its root is: The expressions of the three real roots of equation (6) are as follows:

[0035]

[0036] Where: η 1 represents the first root of the cubic equation (6); η 2 represents the second root of the cubic equation (6); η 3 represents the third root of the cubic equation (6);

[0037]

[0038] constant j represents an imaginary unit. And η 2 <η 1 <η 3 .

[0039] According to the circuit resonance principle, the two tuning points of the filter are expressed by the total impedance function Z(ω) of the double-tuned filter, and the intermediate angular frequency of the double-tuned filter is defined, that is:

[0040] The two tuning corner frequencies of the double tuned filter In addition, the intermediate tuning angle frequency ω of the double-tuned filter is defined as 00 =λω 01 +(1-λ)ω02 ,λ∈(0,1);

[0041] And there are:

[0042] Using Vieta's theorem, we can get:

[0043]

[0044] Definition 00 =h 00 ω 1 ,ω 1 is the fundamental angular frequency. According to the actual required fundamental reactive power compensation amount Q S1 , determine the high-voltage side capacitor C according to the following formula 1 Values:

[0045]

[0046] Where U s Indicates the rated voltage of the AC bus.

[0047] When designing AC / DC filters, ω 01 ,ω 02 These are all known parameters. Parameter λ can be adjusted and optimized according to the filtering effect of the filter and the risk of system resonance. In practice, the value of the resistor R can be adjusted according to engineering experience, and its value varies within 150 to 350Ω.

[0048] To this end, according to the known parameters λ, resistor R, capacitor C 1 and tuning point ω 01 ,ω 02 , solve the nonlinear algebraic equations (7) to obtain L 1 , L 2 and C 2 The numerical value of .

[0049] In the step 4, the power loss of the resistor R in the double tuned filter, the losses of the reactor and capacitor, and the harmonic amplification factor H(ω) of the characteristic harmonic voltage of the converter station AC filter are calculated according to the following equations (9), (10), (11), and (12):

[0050]

[0051] In the above formula, P R (ω h ) represents the power frequency loss of the double tuned filter damping resistor R; Represents the AC filter busbar hth harmonic voltage phasor; Z(ω h ) represents the hth harmonic impedance function of the double tuned filter; ωh is the angular frequency of the hth harmonic; U h,Li Indicates the reactor L i The hth harmonic voltage effective value; X h,Li Indicates the reactor L i The hth harmonic reactance value; m = 2; k Lp Indicates the loss factor of the reactor; Represents capacitor C i The effective value of the hth harmonic voltage, tanδ represents the dielectric loss coefficient; H(ω) represents the voltage harmonic amplification factor of the AC filter bus voltage under each harmonic; Z F (ω) represents the impedance function of the AC filter under each harmonic; Z S (ω 0 ) represents the impedance function of the AC equivalent system under each harmonic; μ represents the voltage harmonic amplification factor limit value of the filter at the tuning point.

[0052] In step 5: taking filtering performance, no resonance risk and equipment investment cost as constraints, select an optimization algorithm to optimize L 1 , L 2 and C 2 The value of is optimized to meet the filter performance requirements. At the same time, there is no risk of resonance between the filter group and the AC system and the power frequency loss of the resistor is reduced.

[0053] The present invention provides an optimization design method for a double-tuned filter for a converter station, and the technical effects are as follows:

[0054] 1) Step 1 of the present invention provides a theoretical basis for step 3 to adopt an AC / DC filter electrical design based on the circuit resonance principle;

[0055] 2) Step 2 of the present invention proposes for the first time to use the intermediate angular frequency to design the circuit parameters of the double tuned filter, thereby ensuring that the impedance characteristic curve of the double tuned filter has two minimum points;

[0056] 3) Step 3 of the present invention firstly uses the root theory of cubic equations to solve the circuit parameter calculation problem of the double-tuned filter, and finally transforms the problem into solving the problem containing L under the premise of known parameters. 1 , L 2 and C 2 Variable nonlinear equations problem; 4) Step 4 of the present invention further performs L in step 3 1 , L 2 , C 2 The values ​​of and R are optimized to avoid resonance between the double tuned filter and the AC system at the tuning point, while also taking into account that its power frequency loss meets the requirements;

[0057] 5) Step 5 of the present invention further treats L in step 4 1, L 2 , C 2 The values ​​of L and R are optimized to avoid the total equipment cost of the double-tuned filter exceeding the budget and improve its economy. Secondly, the optimization algorithm is selected to optimize the L and R values ​​based on the filtering performance, no resonance risk and equipment investment cost. 1 , L 2 and C 2 The value of is optimized to meet the filter performance requirements, while eliminating the risk of resonance between the filter group and the AC system, reducing the power frequency loss of the resistor and lowering the design cost.

[0058] 6) This method analyzes the optimization design process in detail for the existing double-tuned AC / DC filter topology used in converter stations, considering the filtering effect and harmonic amplification effect combined with circuit principles. It can improve the filtering effect of the double-tuned filter used in converter stations and avoid the risk of harmonic resonance or harmonic amplification, thereby improving the filtering effect and economy of the double-tuned filter. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0060] Figure 1 The topological structure diagram of the double tuned filter.

[0061] Figure 2 This is the schematic diagram of the equivalent circuit at the parallel bus of the AC filter.

[0062] Figure 3 The filter impedance-harmonic order variation curve at different intermediate tuning angular frequencies (R = 300Ω).

[0063] Figure 4 Impedance curves under original design parameters and optimized parameters.

[0064] Figure 5 The phase curves are the original design parameters (λ=0.55) and the optimized parameters.

[0065] Figure 6 Topology diagram for the double-tuned high-pass filter verification circuit.

[0066] Figure 7 The figure is a comparison chart of the original design parameters (λ=0.55) and the optimized 24th harmonic filtering effect.

[0067] Figure 8 The figure is a comparison chart of the original design parameters (λ=0.55) and the optimized 36th harmonic filtering effect.

[0068] Fig. 9 This is a comparison chart of the original design parameters (λ=0.55) and the optimized loss. DETAILED DESCRIPTION

[0069] An optimization design method for a double-tuned filter for a converter station comprises the following steps:

[0070] Step 1: Figure 1 As shown, without considering the arrester, the full impedance function of the double tuned filter is written as follows:

[0071]

[0072] in: ω is the fundamental or harmonic angular frequency of the system.

[0073] According to the circuit series resonance conditions:

[0074]

[0075] make have to:

[0076]

[0077] Substituting formula (4) into formula (3), we get:

[0078] R 2 C 1 η(η-L 1 -L 2 )=R 2 L 2 C 2 (η-L 1 )+(η-L 1 -L 2 )η 2 (5);

[0079] η 3 -(L 1 +L 2 +R 2 C 1 )η 2 +R 2 (L 2 C 2 +L 1 C 1 +L 2 C 1 )η-R 2 L 1 L 2 C 2 =0(6);

[0080] According to Cardano's formula, the three real roots of equation (6) are as follows:

[0081] The discriminant of its root is: The expressions of the three real roots of equation (6) are as follows:

[0082]

[0083] Where: η 1 represents the first root of the cubic equation (6); η 2 represents the second root of the cubic equation (6); η 3 represents the third root of the cubic equation (6);

[0084]

[0085] constant j represents an imaginary unit. And η 2 <η 1 <η 3 .

[0086] Step 2: According to the circuit resonance principle, the two tuning points of the filter are expressed by the total impedance function Z(ω) of the double-tuned filter, and the intermediate angular frequency of the double-tuned filter is defined, that is:

[0087] The two tuning corner frequencies of the double tuned filter In addition, the intermediate tuning angle frequency ω of the double-tuned filter is defined as 00 =λω 01 +(1-λ)ω 02 ,λ∈(0,1);

[0088] And there are:

[0089]

[0090] Using Vieta's theorem, we can get:

[0091]

[0092] Step 3: Define ω 00 =h 00 ω 1 ,ω 1 is the fundamental angular frequency. According to the actual required fundamental reactive power compensation amount Q S1 , determine the high-voltage side capacitor C according to the following formula 1 Values:

[0093]

[0094] Where U s Indicates the rated voltage of the AC bus.

[0095] When designing AC / DC filters, ω 01,ω 02 These are all known parameters. Parameter λ can be adjusted and optimized according to the filtering effect of the filter and the risk of system resonance. In practice, the value of the resistor R can be adjusted according to engineering experience, and its value varies within 150 to 350Ω.

[0096] To this end, according to the known parameters λ, resistor R, capacitor C 1 and tuning point ω 01 ,ω 02 , solve the nonlinear algebraic equations (7) to obtain L 1 , L 2 and C 2 The numerical value of .

[0097] Step 4: Considering the risk of resonance between the double-tuned filter and the system and its own loss, the power loss calculation formula of the capacitor, reactor and resistor R in the double-tuned filter at different angular frequencies ω is as follows:

[0098]

[0099] Where P R (ω h ) represents the power frequency loss of the double tuned filter damping resistor R; Represents the AC filter busbar hth harmonic voltage phasor; Z(ω h ) represents the hth harmonic impedance function of the double tuned filter; ω h is the angular frequency of the hth harmonic; U h,Li Indicates the reactor L i The hth harmonic voltage effective value; X h,Li Indicates the reactor L i The hth harmonic reactance value; m = 2; k Lp Indicates the loss factor of the reactor; Represents capacitor C i The hth harmonic voltage effective value, tanδ represents the dielectric loss coefficient.

[0100] The equivalent circuit diagram of the AC filter parallel bus is as follows: Figure 2 As shown in the figure, in order to qualitatively measure the filtering performance of the AC / DC filter of the converter station for characteristic subharmonics, the harmonic amplification factor of the characteristic harmonic voltage of the AC / DC filter of the converter station is defined as:

[0101]

[0102] In the above formula, lg[] represents the logarithm with base 10; Z F (ω) represents the impedance value of the filter at the angular frequency ω; Z S (ω) represents the impedance value of the equivalent system at the angular frequency ω; ω0 represents the system angular frequency at the power frequency; μ represents the voltage harmonic amplification factor limit value of the double-tuned filter at the tuning point.

[0103] Step 5: Use an optimization algorithm, such as a multi-objective particle swarm optimization algorithm, to solve the optimization model of the AC / DC filter based on the basic resonance principle, using filtering performance, no resonance risk, and equipment investment cost as constraints. The optimization object is parameter L 1 , L 2 and C 2 The optimization goal is to meet the filter performance requirements while having no resonance risk with the AC / DC system and reducing the power frequency loss of the resistor.

[0104] Multi-objective particle swarm optimization algorithm is used to solve the optimal design model of AC / DC filters based on the basic resonance principle;

[0105] The specific optimization model includes objective function and constraints, where the objective function includes:

[0106] (1) Target 1: Double tuned filter has good filtering performance, denoted as F 1 ;

[0107] The total harmonic distortion rate of the AC side system voltage is the smallest, that is, And T u ≤T u_max ;

[0108] The total harmonic distortion rate of the AC side system current is the smallest, that is, And T I ≤T I_max ;

[0109] Among them, U 1 Indicates the effective value of the AC bus fundamental voltage; I 1 Indicates the effective value of the fundamental current injected into the AC system; T u_max , T I_max It indicates the upper limit of the total distortion rate of the voltage and current in the AC system, which is generally given according to national standards.

[0110] (2) Objective 2: Design of a double-tuned filter without resonance risk, denoted as F 2 ;

[0111] And H(ω)≤μ.

[0112] (3) Objective 3: Minimize the engineering cost of the double-tuned filter, denoted as F 3 ;

[0113]

[0114] Where: k c1, k c2 , k l The unit capacity prices of high-voltage capacitors, low-voltage capacitors and reactors of double-tuned filters are respectively, k R is the unit capacity price of the damping resistor, S c1 , S c2 , S l1 and S l2 They are the capacities of the high-voltage capacitor, low-voltage capacitor, and low-voltage reactor of the double-tuned filter, in kVar; G R They are the capacity of the damping resistor respectively, unit: kW.

[0115] (4) Objective 4: Minimize the loss of the double-tuned filter, denoted as F 4 ;

[0116] min△p=P R +P L +P C

[0117] Among them, P R , P L and P C They represent the total losses of the resistor, reactor and capacitor of the double tuned filter respectively.

[0118] The constraints include:

[0119] a: Equality constraint:

[0120] ①、Intermediate angular frequency equation constraint: ω 00 =λω 01 +(1-λ)ω 02 ,λ∈(0,1);

[0121] ②, Capacitance C 1 Equality constraint (7):

[0122] ③、The values ​​of the reactor and capacitor are subject to the nonlinear equation constraint formula (6): F(L 1 ,L 2 ,C 2 )=0.

[0123] b: Inequality constraints:

[0124] 1)T u ≤T u_max , T I ≤T I_max ;

[0125] 2) H(ω)≤μ;

[0126] 3) Discriminant of equation (5)

[0127] 4) The value of resistor R satisfies the inequality: 150≤R≤350Ω;

[0128] 5) Telephone harmonic waveform coefficient inequality constraint: The telephone harmonic waveform coefficient THFF should not be greater than 1.0%.

[0129] The multi-objective particle swarm optimization algorithm is used to solve the above optimization model. The solution steps are as follows:

[0130] Step 1: Input known parameters, including system AC voltage level, fundamental reactive power compensation of double tuned filter, etc., initialize the optimization program, and determine the optimization decision variable as X=[λ,L 1 ,L 2 ,C 2 ], the proportional weighting method is used to achieve the coordination among the multi-objective functions. Since the magnitudes of the various objectives are not uniform, the four indicators are first normalized. That is, F i ′=(F i -F i min ) / (F i max -F i min ), i = 1, 2, 3, 4; the total objective function weighted by the four objective functions is: Among them, φ i is the weight of the i-th objective function, φ i =rd i / (rd 1 +rd 4 ),i=1,2,3,4,rd i Represents a non-negative random real number or a non-negative random integer.

[0131] Step 2: Set X as the particle position; V as the particle velocity; F(x) as the objective function value; L(x) as the constraint function value; rep as the storage repository for non-dominated particles; P best is the individual extreme value of the particle; G best is the leading particle; W is the inertia weight. The speed and position changes of a single particle in each iteration are:

[0132] Speed ​​Update: c 1 、c 2 are the learning coefficients of individual particles and populations respectively; r 1 、r 2 It is a random number in the range of [0,1]; the inertia weight W decreases exponentially with the increase of the number of iterations m.

[0133] Location Updates: Inertia weight update: W0 and W1 are the maximum and minimum values ​​of the set inertia weight respectively. 0 is 0.9, W 1 is 0.2; m and M are the current iteration number and the set maximum iteration number respectively. The processing principle for the above constraints is: when comparing two particles, their constraints need to be checked. If both are feasible, the Pareto dominance property is directly applied to judge the quality of their objective function values ​​to determine the better one; if one is feasible and the other is not feasible, the former is better; if both are not feasible, the particle with the least number of constraint violations is better. The constraint processing mechanism is referenced in the comparison before and after the mutation of particles, the update of individual extreme values, and the update of the repository.

[0134] After several iterations, the optimization results of this round are output.

[0135] Example:

[0136] Taking the electrical parameter optimization design of the HP24 / 36 double-tuned filter of a UHV converter station as an example, its original design parameters are shown in Table 1.

[0137] Table 1 Original design parameters of double tuned filter

[0138]

[0139] The rated voltage of the converter station AC system is 775kV, and the three-phase reactive power compensation capacity of the HP24 / 36 double-tuned filter is 300Mvar. Figure 3 The following is the filter impedance-harmonic order variation curve at different intermediate tuning angle frequencies (R = 300Ω). It can be seen that when λ = 0.5, the impedance value of the impedance characteristic curve near the tuning point is relatively balanced. Figure 6 To verify the topology of the double-tuned high-pass filter circuit, its electromagnetic transient simulation model was established in PSCAD software, and the transient characteristics test of the filter before and after the optimization design was completed. The simulation results are shown in Figure 2. Figure 7 to Figure 9 shown.

[0140] The parameters optimized by the above method are shown in Table 2. From Table 2, it can be seen that the capacitor C 1 The value of R is increased by 50Ω; L 1 The value of L 2 The value of C increases; 2 The value is reduced by about 2μF.

[0141] Table 2 Design parameters of double tuned filter after optimization

[0142]

[0143] from Figure 4 It can be seen that the impedance value of the optimized impedance curve near the tuning point is smaller; Figure 5 It can be seen that the phase of the impedance curves after optimization near the tuning point is similar; in general, Figure 4 , Figure 5 It can be seen that the impedance characteristics of the optimized filter are better. Figure 7 It can be seen that the ability of the filter to pass the 24th harmonic does not change much before and after the optimization design; Figure 8 It can be seen that the ability of the filter to pass the 36th harmonic after optimization is greatly improved compared with before optimization; Fig. 9 It can be seen that the loss of the resistor R after the filter optimization is reduced. Figure 7 to Figure 9 It can be seen that the filtering effect and loss of the optimized filter are better than those of the original filter.

Claims

1. An optimization design method for a double-tuned filter for a converter station, characterized in that The following steps are involved: Step 1: Calculate the total impedance function Z(ω) of the double tuned filter; Step 2: The two tuning points of the filter are expressed by the total impedance function Z(ω) of the double-tuned filter, and the intermediate angular frequency of the double-tuned filter is defined; Step 3: According to the fundamental wave reactive power compensation Q S1 Determine the value of the high-voltage side capacitor C1 and solve for the values ​​of L1, L2, and C2; Step 4: Calculate the fundamental power loss of the resistor R in the double-tuned filter and the harmonic amplification factor H(ω) of the characteristic harmonic voltage of the AC filter in the converter station; Step 5: Taking filtering performance, no resonance risk and equipment investment cost as constraints, use the optimization algorithm to optimize the values ​​of L1, L2 and C2.

2. The optimization design method of a double tuned filter for a converter station according to claim 1, characterized in that: In the step 1: calculate the total impedance function Z(ω) of the double tuned filter: In formula (1), R represents the damping resistance of the double tuned filter; ω represents the angular frequency of the AC system under different harmonics; j represents the imaginary unit; L1 represents the series branch inductance of the double tuned filter; L2 represents the parallel branch inductance of the double tuned filter; C1 represents the series branch capacitance of the double tuned filter; C2 represents the parallel branch capacitance of the double tuned filter.

3. The optimization design method of a double tuned filter for a converter station according to claim 1, characterized in that: In the step 2, the two tuning points of the filter are represented by the full impedance function Z(ω) of the double-tuned filter, and the intermediate angular frequency of the double-tuned filter is defined, that is: oh 00 =I am 01 +(1-λ)ω 02 ,λ∈(0,1); In the above formula, ω 00 represents the intermediate angular frequency; ω 01 represents the first resonant angular frequency of the double-tuned filter; ω 02 represents the second resonant angular frequency of the double-tuned filter; λ represents the parameter to be optimized; And there are:

4. The optimization design method of a double tuned filter for a converter station according to claim 1, characterized in that: In the step 3: for the AC filter, according to the fundamental wave reactive compensation amount Q S1 , determine the value of the high-voltage side capacitor C1 according to the following formula: In formula (2), U s represents the rated voltage of the AC bus; ω1 is the fundamental angular frequency; h 00 =ω 00 / ω1 indicates the intermediate tuning number; Because ω 01 ,ω 02 These are all known parameters, and the parameter λ can be adjusted and optimized according to the filtering effect of the filter and the risk of system resonance; According to the known parameters λ, resistor R, capacitor C1 and tuning point ω 01 ,ω 02 , solve the nonlinear algebraic equations to obtain the values ​​of L1, L2 and C2, which are specifically expressed as follows: According to formula (1), the circuit series resonance condition is: make have to: Substituting formula (4) into formula (3), we get: R 2 C1η(η-L1-L2)=R 2 L2C2(η-L1)+(η-L1-L2)η 2 (5); η 3 -(L1+L2+R 2 C1)η 2 +R 2 (L2C2+L1C1+L2C1)η-R 2 L1L2C2=0(6); According to Cardano's formula, the three real roots of equation (6) are as follows: The discriminant of its root is: The expressions of the three real roots of equation (6) are as follows: Wherein: η1 represents the first root of the cubic equation (6); η2 represents the second root of the cubic equation (6); η3 represents the third root of the cubic equation (6); constant j represents an imaginary unit; and η2<η1<η3.

5. The optimization design method of a double tuned filter for a converter station according to claim 4, characterized in that: According to the circuit resonance principle, the two tuning points of the filter are expressed by the total impedance function Z(ω) of the double-tuned filter, and the intermediate angular frequency of the double-tuned filter is defined, that is: The two tuning corner frequencies of the double tuned filter In addition, the intermediate tuning angle frequency ω of the double-tuned filter is defined as 00 =λω 01 +(1-λ)ω 02 ,λ∈(0,1); And there are: Using Vieta's theorem, we can get: Definition 00 =h 00 ω1, ω1 is the fundamental angular frequency; according to the actual required fundamental reactive power compensation amount Q S1 , determine the value of the high-voltage side capacitor C1 according to the following formula: Where U s Indicates the rated voltage of the AC bus; When designing AC / DC filters, ω 01 ,ω 02 These are all known parameters. The parameter λ can be adjusted and optimized according to the filtering effect of the filter and the risk of system resonance. To this end, according to the known parameters λ, resistor R, capacitor C1 and tuning point ω 01 ,ω 02 , solve the nonlinear algebraic equation system (7) to obtain the values ​​of L1, L2 and C2.

6. The optimization design method of a double tuned filter for a converter station according to claim 5, characterized in that: In the step 4, the power loss of the resistor R in the double tuned filter, the losses of the reactor and capacitor, and the harmonic amplification factor H(ω) of the characteristic harmonic voltage of the converter station AC filter are calculated according to the following equations (9), (10), (11), and (12): In the above formula, P R (ω h ) represents the power frequency loss of the double tuned filter damping resistor R; Represents the AC filter busbar hth harmonic voltage phasor; Z(ω h ) represents the hth harmonic impedance function of the double tuned filter; ω h is the angular frequency of the hth harmonic; U h,Li Indicates the reactor L i The hth harmonic voltage effective value; X h,Li Indicates the reactor L i The hth harmonic reactance value; m = 2; k Lp Indicates the loss factor of the reactor; Represents capacitor C i The effective value of the hth harmonic voltage, tanδ represents the dielectric loss coefficient; H(ω) represents the voltage harmonic amplification factor of the AC filter bus voltage under each harmonic; Z F (ω) represents the impedance function of the AC filter under each harmonic; Z S (ω0) represents the impedance function of the AC equivalent system under each harmonic; μ represents the voltage harmonic amplification factor limit value of the filter at the tuning point.

7. The optimization design method of a double tuned filter for a converter station according to claim 6, characterized in that: In the step 5, a multi-objective particle swarm optimization algorithm is used to solve the optimization model of the AC / DC filter, and the filtering performance, no resonance risk and equipment investment cost are used as constraints. The optimization objects are parameters L1, L2 and C2. The optimization goal is to meet the filter performance requirements while having no resonance risk with the AC / DC system and reducing the power frequency loss of the resistor; The multi-objective particle swarm optimization algorithm solves the optimization model of the DC filter. The optimization model includes objective functions and constraints, where the objective function includes: (1) Target 1: The double-tuned filter has good filtering performance, denoted as F1; The total harmonic distortion rate of the AC side system voltage is the smallest, that is, And T u ≤T u_max ; The total harmonic distortion rate of the AC side system current is the smallest, that is, And T I ≤T I_max ; Among them, U1 represents the effective value of the AC bus fundamental voltage; I1 represents the effective value of the fundamental current injected into the AC system; T u_max , T I_max Indicates the upper limit of the total distortion rate of the AC system voltage and current, which is generally given according to national standards; (2) Objective 2: Design of a double-tuned filter without resonance risk, denoted as F2; And H(ω)≤μ; (3) Objective 3: The engineering cost of the double-tuned filter is minimized, denoted as F3; Where: k c1 , k c2 , k l The unit capacity prices of high-voltage capacitors, low-voltage capacitors and reactors of double-tuned filters are respectively, k R is the unit capacity price of the damping resistor, S c1 , S c2 , S l1 and S l2 They are the capacities of the high-voltage capacitor, low-voltage capacitor, and low-voltage reactor of the double-tuned filter, in kVar; G R They are the capacity of the damping resistor, in kW; (4) Objective 4: The loss of the double-tuned filter is minimized, denoted as F4; min△p=P R +P L +P C Among them, P R , P L and P C They represent the total losses of the resistor, reactor and capacitor of the double tuned filter respectively.

8. The optimization design method of a double tuned filter for a converter station according to claim 7, characterized in that: The constraints of the optimization model of the DC filter include: a: Equality constraint: ①、Intermediate angular frequency equation constraint: ω 00 =λω 01 +(1-λ)ω 02 ,λ∈(0,1); ②、Capacitance C1 equation constraint (7): ③ The values ​​of the reactor and capacitor are subject to the nonlinear equation constraint (6): F(L1, L2, C2) = 0; b: Inequality constraints: 1)T u ≤T u_max ,T I ≤T I_max ; 2) H(ω)≤μ; 3) Discriminant of equation (5) 4) The value of the resistor R satisfies the inequality: 150≤R≤350Ω; 5) Telephone harmonic waveform coefficient inequality constraint: The telephone harmonic waveform coefficient THFF should not be greater than 1.0%.

9. The optimization design method of a double tuned filter for a converter station according to claim 8, characterized in that: The multi-objective particle swarm optimization algorithm is used to solve the optimization model. The solution steps are as follows: Step 1: Input known parameters, including the system AC voltage level, the fundamental reactive power compensation of the double-tuned filter, etc., initialize the optimization program, determine the optimization decision variable as X = [λ, L1, L2, C2], and use the proportional weighting method to achieve coordination among multi-objective functions; since the order of magnitude of each objective is not uniform, the four indicators are first normalized; that is, F i ′=(F i -F i min ) / (F i max -F i min ), i = 1, 2, 3, 4; the total objective function weighted by the four objective functions is: Among them, φ i is the weight of the i-th objective function, φ i =rd i / (rd1+rd4),i=1,2,3,4,rd i Represents a non-negative random real number or a non-negative random integer; Step 2: Set X as the particle position; V as the particle velocity; F(x) as the objective function value; L(x) as the constraint function value; rep as the storage repository for non-dominated particles; P best is the individual extreme value of the particle; G best is the leading particle; W is the inertia weight; The speed and position changes of a single particle in each iteration are: Speed ​​Update: c1 and c2 are the learning coefficients of individual particles and populations respectively; r1 and r2 are random numbers in the range [0,1]; the inertia weight W decreases exponentially with the increase of the number of iterations m; Location Updates: Inertia weight update: W0 and W1 are the maximum and minimum values ​​of the set inertia weight respectively; m and M are the current number of iterations and the set maximum number of iterations respectively.

10. The optimization design method of a double tuned filter for a converter station according to claim 9, characterized in that: The method for handling constraints is as follows: when comparing two particles, their constraints need to be checked. If both are feasible, the Pareto dominance property is directly applied to judge the quality of their objective function values ​​to determine the better one; if one is feasible and the other is not feasible, the former is better; if both are not feasible, the particle with the least number of constraint violations is better; the constraint handling mechanism is referenced in the comparison before and after the mutation of particles, the update of individual extreme values, and the update of the repository; after several iterations, the optimization results of this round are output.

Images