Optimization design method of second-order high-pass filter and C-type damping filter for power system

Abstract

The invention discloses an optimal design method of a second-order high-pass filter and a C-type damping filter for a power system. The method comprises the following steps: inputting parameters required for designing the second-order high-pass filter and the C-type damping filter; calculating a main capacitance parameter and a resistance lower limit value; calculating an m parameter of fundamental wave power loss and power frequency loss characteristics of medium resistors R and R'of the second-order high-pass filter and the C-type damping filter and a harmonic amplification coefficient of characteristic harmonic voltage of the AC filter of the converter station; judging whether the parameter selection calculation process is terminated or not. According to the method, a filtering effect and a harmonic amplification effect are combined with a circuit principle, and the optimization design process of the second-order high-pass filter and the C-type damping filter is analyzed in detail, so that the filtering effect and the economical efficiency of the second-order high-pass filter and the C-type damping filter are improved.

Description

Technical Field

[0001] The invention relates to the technical field of passive filter design, and in particular to an optimization design method for a second-order high-pass filter and a C-type damping filter for an electric power system. Background Art

[0002] In recent years, conventional high voltage direct current (HVDC) has become an important form of long-distance power grid interconnection due to its advantages such as large transmission capacity and low transmission loss. However, grid-commutated HVDC, or LCC-HVDC, uses half-controlled thyristors to achieve AC-DC-AC conversion, which has strong nonlinear characteristics and generates a large number of harmonics during operation. For example, the most widely used 12-pulse converter will inject 12p±1 harmonics (p is an arbitrary positive integer) into the power grid under ideal operating conditions. These harmonics are defined as characteristic harmonics, and the remaining harmonics are non-characteristic harmonics.

[0003] A lot of research has been conducted at home and abroad on the harmonic control problem in HVDC projects, and the filtering schemes can be divided into four categories: passive, active, hybrid and inductive filtering. Among them, the C-type damping filter in the passive filter has been applied in most actual LCC-HVDC projects due to its simple structure, low power frequency loss, low cost and convenient operation and maintenance. However, the existing second-order high-pass filter and C-type damping filter design schemes only aim to filter out characteristic subharmonics, and do not fully consider the impact of non-characteristic subharmonics, resulting in the risk of resonance in the system. Therefore, it is necessary to optimize the design of the second-order high-pass filter and C-type damping filter.

[0004] The existing passive filter design scheme for converter stations only aims to filter out characteristic subharmonics, but does not fully consider the impact of non-characteristic subharmonics, resulting in the risk of resonance in the system. In order to suppress a single characteristic harmonic, second-order high-pass filters and C-type damping filters are often used in actual converter stations. Summary of the invention

[0005] Aiming at the problem that the design theories of the existing second-order high-pass filter and C-type damping filter are unclear and the filter circuit design parameters have a large optimization space, the present invention provides an optimization design method for a second-order high-pass filter and a C-type damping filter for a power system, optimizes the calculation of resistance and inductance component parameters of the second-order high-pass filter and the C-type damping filter, and adjusts the m parameter of the power frequency loss characteristic of the second-order high-pass filter and the C-type damping filter and the harmonic amplification coefficient H (ω) of the characteristic harmonic voltage, which reflects the loss characteristics and harmonic amplification effect of the second-order high-pass filter and the C-type damping filter, so as to improve the filtering effect and economy of the second-order high-pass filter and the C-type damping filter.

[0006] The technical solution adopted by the present invention is:

[0007] As the existing second-order high-pass filter design theory is unclear and the design parameters have a lot of room for optimization, the design is optimized by combining circuit principles.

[0008] An optimization design method for a second-order high-pass filter for a power system includes the following steps: Taking Case 1 as an example:

[0009] Step 1: Input the parameters Q required for the second-order high-pass filter design n ,ω0,U n Among them, Q n The reactive power required to compensate for the system; U n is the bus voltage of the AC system; ω0 is the system angular frequency at the operating frequency.

[0010] Step 2: Calculate the main capacitor parameters and the lower limit of the resistance:

[0011] In the second-order high-pass filter circuit, according to the reactive power requirements of the system, the value of the main capacitor C1 is determined according to the following formula, namely:

[0012]

[0013] make A lower limit value R of the resistance R is obtained as follows:

[0014]

[0015] Among them, △1 determines whether the equation has a root; R is the resistance in the second-order high-pass filter.

[0016] Step 3: Let R = R, k = 1;

[0017] If R ≥ R max , output the result; if R <R max , according to the LC series resonance condition, the formula for calculating L1 is as follows:

[0018]

[0019] Where k represents the number of cycles; R max Represents the maximum value of the resistance of the second-order high-pass filter; L1 represents the inductance in the second-order high-pass filter.

[0020] The fundamental power loss of the resistor R in the second-order high-pass filter, the m parameter of the power frequency loss characteristic, and the harmonic amplification factor H(ω0) of the characteristic harmonic voltage of the converter station AC filter are calculated according to the following equations (4) to (6):

[0021]

[0022] Among them, P R(ω) represents the fundamental power loss of the resistor R in the second-order high-pass filter; U(ω) n represents the bus voltage of the AC system; Z(ω) represents the impedance function of the second-order high-pass filter; ω represents the different angular frequencies of the second-order high-pass filter; L1 represents the inductance in the second-order high-pass filter.

[0023]

[0024] In formula (5), m represents the power frequency loss characteristic of the second-order high-pass filter; Q represents the quality factor of the second-order high-pass filter.

[0025]

[0026] In formula (6), H(ω0) represents the harmonic amplification factor of the characteristic harmonic voltage of the second-order high-pass filter of the converter station; Z F (ω0) represents the impedance value of the second-order high-pass filter at the angular frequency ω; Z S (ω0) 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 second-order high-pass filter at the tuning point.

[0027] Step 4: Parameter selection to determine whether the calculation process is terminated:

[0028] If H(ω0)≤μ,m≤θ, then output the result, μ represents the voltage harmonic amplification factor limit value of the filter at the tuning point, θ represents the power frequency loss factor limit value of the filter; otherwise, let R=R+△R, k=k+1, △R represents the increase of resistance R, k represents the number of cycles in the judgment process. Go to step 3.

[0029] As the existing C-type damping filter design theory is unclear and the design parameters have a lot of room for optimization, the design is optimized in combination with circuit principles.

[0030] An optimization design method for a C-type damping filter for a power system. The flowchart of the design scheme of the C-type damping filter proposed by the present invention is shown in FIG5 , and includes the following steps in detail, taking Case 1 as an example;

[0031] Step 1: Input the parameters Q required for C-type damped filter design n ',ω0',U n ', Q n ' represents the reactive power required to be compensated by the C-type damping filter; ω0' represents the system angular frequency of the C-type damping filter at the working frequency; U n ' represents the bus voltage of the AC system of the C-type damping filter.

[0032] Step 2: Calculate the main capacitor parameters and the lower limit of the resistance:

[0033] According to the reactive power requirement of the system, the value of the main capacitor C1' in the C-type damping filter is determined according to the following formula, namely:

[0034]

[0035] make

[0036] Among them: △1' determines whether the C-type damping filter equation has a root; R' represents the resistance in the C-type damping filter; C2 represents the additional capacitance in the C-type damping filter.

[0037] A lower limit value R' of the resistance R' is obtained as follows:

[0038]

[0039] Step 3: Let R' = R ', k = 1. If R' ≥ R max , output the result; if R' <R max ,

[0040] For the specified tuning point ω0', the resistance value R' of the given resistor is taken into account, the equipment cost is taken into account, the capacitance of the actual auxiliary capacitor C2 single capacitor and the insulation coordination problem of the auxiliary capacitor C2 are considered, and the symbolic operation in MATLAB is used to calculate the following equation (9) to obtain the capacitance of C2, and the larger solution is usually taken.

[0041]

[0042] In formula (9), η, k1, k2 represent intermediate variables, where

[0043] The C-type damping filter reduces the base frequency loss by adding an additional capacitor C2, and the auxiliary capacitor C2 resonates with L1 at the base frequency, and the calculation formula of the reactor L1' can be obtained:

[0044]

[0045] According to the following equations (11) to (13), the fundamental power loss of the middle resistor R' of the C-type damping filter, the m parameter of the power frequency loss characteristic, and the harmonic amplification factor H(ω0)' of the characteristic harmonic voltage of the converter station AC filter are calculated:

[0046]

[0047] In formula (11), P R (ω)' represents the fundamental power loss of the resistor R in the C-type damping filter; U(ω) n' represents the bus voltage of the AC system; Z(ω)' represents the impedance function of the C-type damping filter.

[0048]

[0049] In formula (12), Q' represents the quality factor of the C-type damping filter.

[0050]

[0051] In formula (13), H(ω0)' represents the harmonic amplification factor of the characteristic harmonic voltage of the C-type damping filter in the converter station; Z F (ω0)' represents the impedance value of the C-type damping filter at the angular frequency ω; Z S (ω0)' represents the impedance value of the equivalent system at the angular frequency ω; Step 4: Parameter selection calculation process to determine whether to terminate. If H(ω0)'≤μ', m≤θ', then output the result; μ' represents the voltage harmonic amplification factor limit value of the C-type damping filter at the tuning point, and θ' represents the power frequency loss factor limit value of the C-type damping filter; otherwise, let R=R+△R, k=k+1, △R represents the increase in resistance R in the C-type damping filter, and go to step 3.

[0052] The present invention discloses an optimization design method for a second-order high-pass filter and a C-type damping filter for an electric power system, and the technical effects are as follows: 1) The present invention considers the filtering effect and the harmonic amplification effect in combination with the circuit principle, and conducts a detailed analysis of the optimization design process of the second-order high-pass filter and the C-type damping filter, thereby improving the filtering effect and economy of the second-order high-pass filter and the C-type damping filter.

[0053] 2) The present invention considers modifying the filter parameters from the perspective of cost saving, and the proposed optimization scheme can filter out characteristic subharmonics and suppress non-characteristic subharmonic resonances.

[0054] 3) The m parameter introduced in the present invention can further reflect the power frequency loss characteristics of the high-pass filter and better control the power loss of the high-pass filter.

[0055] 4) The simulation results of the PSCAD / EMTDC platform show that the optimization scheme of the present invention can effectively reduce the power loss of the filter and improve the filtering effect, and has good engineering development prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0057] Figure 1 This is the topological diagram of the second-order high-pass filter.

[0058] Figure 2 This is the topological structure diagram of the C-type damping filter.

[0059] Figure 3 The curve of the change of inductance L1 with resistance R at the specified tuning point ω0 for the second-order high-pass filter.

[0060] Figure 4 The frequency characteristic curves of the second-order high-pass filter under two design schemes.

[0061] FIG5(a) is a filter frequency characteristic curve of a second-order high-pass filter under different resistances R (Case 1);

[0062] FIG5( b ) is a filter frequency characteristic curve of a second-order high-pass filter under different resistances R (Case 2);

[0063] FIG5(c) is a filter frequency characteristic curve of a second-order high-pass filter under different resistances R (Case 3).

[0064] Figure 6 The filter frequency characteristic curves under two design schemes of C-type damping filter.

[0065] Figure 7(a) is a curve showing the impedance characteristics of a C-type damped filter changing with resistance R (Case 1);

[0066] Figure 7(b) is a curve showing the impedance characteristics of the C-type damped filter changing with the resistance R (Case 2);

[0067] Among them: the larger the R value, the smaller the lowest value of the curve.

[0068] Figure 8 This is the curve showing how the loss of the high-pass filter (HP3) changes with the resistance R.

[0069] Fig. 9 This is the curve showing how the m parameter of the high-pass filter (HP3) changes with the resistance R.

[0070] Fig.10 This is the schematic diagram of the equivalent circuit at the parallel bus of the AC filter.

[0071] Fig.11 This is the flow chart of the design solution for the second-order high-pass filter Case 1.

[0072] Fig.12 This is the flow chart of the design solution for Case 1 of C-type damping filter.

[0073] Fig.13 Topology diagram of the second-order high-pass filter verification circuit.

[0074] Fig.14 Topology diagram of the C-type damping filter verification circuit.

[0075] Fig.15 These are the resistor active power curves for two design schemes of second-order high-pass filters.

[0076] Fig.16 The effective value curve of the third harmonic current of the main capacitor under two design schemes of the second-order high-pass filter.

[0077] Fig.17 The effective value curve of the third harmonic current of the main capacitor under two design schemes of C-type damping filter. DETAILED DESCRIPTION

[0078] The present invention will be further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0079] An optimization design method for a second-order high-pass filter and a C-type damping filter for a power system is provided, and the selection and calculation of relevant circuit parameters are performed according to the following principles:

[0080] (I) Second-order high-pass filter:

[0081] Without considering the resistance value of the dry-type reactor, the topology of the second-order high-pass filter is as follows: Figure 1 As shown, according to the reactive power requirement of the system, the value of the main capacitor C1 is determined according to the following formula, namely:

[0082]

[0083] In the formula, Q n Indicates the reactive power required to compensate for the system, U n represents the bus voltage of the AC system; ω1=2πf1 represents the system angular frequency at the power frequency. Figure 1 , the impedance function of the second-order high-pass filter can be written as follows:

[0084]

[0085] According to the conditions for resonance of the second-order circuit, the resonance equation can be obtained as follows:

[0086]

[0087] Therefore, the tuning corner frequency of the second-order high-pass filter is:

[0088]

[0089] From the above formula, we can see that when R→∞, the tuning angular frequency That is, the angular frequency of the LC series resonance. For the specified tuning frequency, if the tuning frequency is still calculated according to the literature [1] (Liu Ke, et al. Analysis of intrinsic characteristics and optimal application scenarios of C-type damping filters. "China Electric Power". 2023, Vol. 56 (Issue 7)), the actual high-pass filter tuning point will shift to the right, that is, the tuning frequency will be too large. According to the definition of the quality factor of the RLC series resonant circuit, that is, the ratio of the effective value of the terminal voltage of the dynamic element under the resonant condition to the effective value of the voltage source, the quality factor of the second-order high-pass filter can be obtained by the same token:

[0090]

[0091] From the above formula (17), it can be seen that this formula is different from the formula for the quality factor of the second-order high-pass filter given in most textbooks, but it can be seen that the quality factor of the second-order high-pass filter is proportional to the resistance R. In other words, the larger the resistance R, the better the filtering effect of the second-order high-pass filter. However, in practical applications, the cost of equipment must also be considered. For the specified quality factor, if Q is still calculated according to the literature [2] (Zhao Yanru. Design of Passive Filter Based on MATLAB [J]. Electronic World, 2013, (13): 160-161.), the actual high-pass filter quality factor will be too small.

[0092] According to the resonance condition, we can get the quadratic equation about the inductance L1, namely:

[0093]

[0094] make A lower limit value R of the resistance R is obtained as follows:

[0095]

[0096] For a specified tuning point, taking into account the equipment cost, the calculation formula for inductance L1 is as follows:

[0097]

[0098] (II) C-type damping filter:

[0099] Without considering the resistance value of the reactor, the topology of the C-type damping filter is as follows: Figure 2 As shown, according to the system reactive power C1

[0100] Power requirements, the main capacitor value is determined according to the following formula, namely:

[0101]

[0102] In the formula, Q n ' represents the reactive power required for compensation of the system, U n' represents the bus voltage of the AC system; ω1=2πf1 represents the system angular frequency at the power frequency. Figure 1 , the impedance function of the C-type damping filter can be written as follows:

[0103]

[0104] According to the conditions for the circuit to resonate, the resonance equation can be obtained as follows:

[0105]

[0106] The C-type damping filter reduces the fundamental frequency loss by adding auxiliary capacitor C2. C2 resonates with L1' at the fundamental frequency, and the calculation formula of the reactor L1' can be obtained:

[0107]

[0108] Therefore, the tuning corner frequency of the C-type damped filter is:

[0109]

[0110] From the above formula, we can see that when R'→∞, the tuning angular frequency That is, it is several times the angular frequency of the power frequency. Usually, C2>C1' is required. For a specified tuning frequency, if the tuning frequency is still calculated according to the reference [1], the actual tuning point of the C-type damped filter will shift to the right, that is, the tuning frequency will be too large. According to the definition of the quality factor of the RLC series resonant circuit, that is, the ratio of the effective value of the terminal voltage of the dynamic element to the effective value of the voltage source under the resonant condition, the quality factor of the C-type damped filter can be obtained by the same logic:

[0111]

[0112] It can be seen from formula (21) that this formula is different from the formula for the quality factor of the C-type damping filter given in most textbooks and papers.

[0113] R'R'

[0114] The same, but it can be seen that the quality factor of the C-type damping filter is inversely proportional to the resistance. In other words, the larger the resistance, the worse the filtering effect of the C-type damping filter. However, in practical applications, the cost of the equipment must also be considered.

[0115] Q'

[0116] If the quality factor is still calculated according to reference [2], the quality factor of the actual C-type damping filter will be too large.

[0117] η

[0118] According to Figure 2The resonance condition of the circuit shown can be obtained by a quadratic equation about the unknown variable, namely:

[0119] η 2 (k1-1)+η(k1-k2)-k2=0 (22);

[0120] In the formula,

[0121] make A lower limit value R' of the resistance R' is obtained as follows:

[0122]

[0123] The calculation formula of variable η is as follows:

[0124]

[0125] ω0'R'

[0126] For a specified tuning point, the resistance value of the resistor in the C-type damping filter is given, the equipment cost is taken into account, and the capacitance of the actual auxiliary capacitor C2 and the insulation coordination of the auxiliary capacitor C2 are considered.

[0127]

[0128] An optimization design method for a second-order high-pass filter and a C-type damping filter for a power system, wherein the calculation and selection of the inductor L1 are as follows.

[0129] Second-order high-pass filter:

[0130] Taking the third harmonic tuning point as an example, according to Figure 3 It can be seen that in actual engineering, when the value of L1 is designed according to formula (3), it is larger than the value of L1 calculated according to the LC series resonance condition, and as the resistance R increases, the two gradually become equal. The formula for calculating L1 according to the LC series resonance condition is as follows:

[0131]

[0132] The scheme of calculating L1 according to formula (3) is recorded as Case 1, and the scheme of calculating L1 according to formula (23) is recorded as Case 2, and the frequency characteristics of the second-order high-pass filter are studied respectively. Obviously, Case 1 has restrictions on the resistor R in the design, while Case 2 has no restrictions on the resistor R.

[0133] from Figure 4 It can be seen that the filter frequency characteristics designed according to Case 2 ( Figure 4 The dashed line in the middle shows that the entire case is slightly offset to the right compared to Case 1. Figure 5(a) to Figure 5(c)It can be seen that the larger the resistance R value, the smaller the value of the lowest point of the impedance curve of the second-order high-pass filter, and the better the filter effect at this time.

[0134] C-type damping filter:

[0135] In actual engineering, when the value of L1 is designed according to formula (3), it is larger than the value of L1 calculated according to the LC series resonance condition, and as the resistance R increases, the two gradually become equal. The formula for calculating L1 according to the LC series resonance condition is as follows:

[0136]

[0137] The scheme of calculating L1' according to formula (23) is recorded as Case 2, and the scheme of calculating L1 according to formulas (9) and (22) is recorded as Case 1, and the frequency characteristics of the C-type damping filter are studied respectively. Obviously, Case 1 has restrictions on the resistor R in the design, while Case 2 has no restrictions on the resistor R. It can be seen from Figure 7(a) and Figure 7(b) that the frequency characteristics of the filter designed according to Case 2 are partially offset to the right relative to Case 1 as shown by the dotted lines in Figure 7(a) and Figure 7(b).

[0138] An optimization design method for a second-order high-pass filter and a C-type damping filter for a power system, considering the loss problem of the second-order high-pass filter and the C-type damping filter:

[0139] Second-order high-pass filter:

[0140] The power loss P of the middle resistor R of the second-order high-pass filter at different angular frequencies ω R The formula is as follows:

[0141]

[0142] Among them, |Z(ω)| is the modulus of the impedance function of the second-order high-pass filter; U(ω) n It represents the effective value of the AC filter bus voltage at different angular frequencies ω.

[0143] from Figure 8 It can be seen that, taking the third harmonic tuning point as an example, the power frequency loss of the second-order high-pass filter (HP3) is Before, as the resistance R decreases, the power frequency loss increases rapidly (the rate of increase is very large); After that, as R increases, the power frequency loss slowly decreases (the rate of decrease is very small). For the loss of the second-order high-pass filter at the resonant frequency, its value is approximately proportional to the size of the resistor R, but its value is actually very small, so the focus is on the power frequency loss of the second-order high-pass filter. Therefore, theoretically, the larger the value of R, the smaller the power frequency loss, so the m parameter that reflects the power frequency loss characteristics of the second-order high-pass filter is defined as follows:

[0144]

[0145] Obviously, the smaller the value of the m parameter is, the smaller the loss of the second-order high-pass filter is. In actual power engineering, considering the cost of electrical equipment, m is usually less than 0.5.

[0146] from Fig. 9 It can be seen that the change law of the m parameter of the second-order high-pass filter with the resistance R is basically consistent with the change law of the power frequency loss of the high-pass filter with the resistance R. Therefore, by controlling the size of the m value of the second-order high-pass filter within an appropriate range, its loss can be controlled not to exceed the specified value.

[0147] The equivalent circuit diagram of the AC filter parallel bus is as follows: Fig.10 As shown in the figure, in order to qualitatively measure the filtering performance of the converter station AC filter for characteristic subharmonics, the harmonic amplification factor of the characteristic harmonic voltage of the converter station AC filter is defined as:

[0148]

[0149] In the above formula, lg[] represents the logarithm with base 10. 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.

[0150] In summary, the flowchart of the design scheme of the second-order high-pass power filter proposed by the present invention is as follows: Fig.11 shown.

[0151] C-type damping filter:

[0152] The power loss P of the middle resistor R' of the C-type damping filter at different angular frequencies ω R 'The formula is as follows:

[0153]

[0154] Among them, |Z(ω)|' is the modulus of the impedance function of the C-type damping filter; U(ω) n ' represents the effective value of the AC filter bus voltage at different angular frequencies ω.

[0155] Similarly, the m parameter reflecting the power frequency loss characteristics of the C-type damping filter is defined as follows:

[0156]

[0157] Obviously, the smaller the value of the m parameter is, the smaller the loss of the C-type damping filter is. In engineering, considering the cost of equipment, m is usually taken to be less than 0.5.

[0158] Through simulation, it is found that the variation law of the m parameter of the C-type damping filter with the resistance R is basically consistent with the variation law of the power frequency loss of the C-type damping filter with the resistance R. Therefore, by controlling the m value of the C-type damping filter within an appropriate range, its loss can be controlled to not exceed the specified value. The equivalent circuit diagram of the AC filter parallel bus is shown in the attached figure. Fig.10 As shown in the figure, in order to qualitatively measure the filtering performance of the converter station AC filter for characteristic subharmonics, the harmonic amplification factor of the characteristic harmonic voltage of the converter station AC filter is defined as:

[0159]

[0160] In summary, the flow chart of the design scheme of the C-type damping filter proposed by the present invention is as follows: Fig.12 shown.

[0161] To verify the correctness of the solution (Case 1) of the C-type damping filter proposed in the present invention, as Fig.10 As shown, u s represents the bus voltage source of the AC filter in the converter station, i r Represents the harmonic current source generated by the converter. It is known that the rated voltage of the AC bus is 775kV, the reactive compensation capacity of the filter is 300Mvar, and the parameters of the C-type damping filter (HP3) are designed according to Case 1 and Case 2. The parameters of the C-type damping filter are shown in Table 3. The simulation analysis is completed by PSCAD software, and the simulation parameter settings are shown in Table 4.

[0162] According to the above simulation results Fig.17 It can be seen that the resistance R value plays a decisive role in the filtering performance of the C-type damping filter. It is recommended to design the resistance value according to formula (2) when designing the C-type damping filter according to Case 2. And through comparison, the simulation results show that the design scheme of Case 1 has obvious advantages over Case 2 in characteristic harmonic suppression.

[0163] Table 1 Parameters of second-order high-pass filter

[0164] Design <![CDATA[C1 / μF]]> <![CDATA[L1 / mH]]> R / Ω Q Case 1 1.58999 728.9 4000 5.8224 Case 2 1.58999 708.0 3000 4.4956

[0165] Table 2 Second-order high-pass filter simulation parameter settings

[0166] Parameter name Internal impedance Voltage / kV Harmonic Sources Internal resistance 10Ω Harmonic voltage source effective value 50 Grid-side voltage source Impedance (1Ω+1Ω / / 0.1H) The effective value of the grid-side voltage source is 447.4465

[0167] Table 3 Parameters of C-type damping filter

[0168] Design <![CDATA[C1 / μF]]> <![CDATA[L1 / mH]]> R / Ω <![CDATA[C2 / μF]]> Case 1 1.58999 820.049 4000 12.3555 Case 2 1.58999 708.0 3500 14.31

[0169] Table 4 Simulation parameter settings of C-type damping filter

[0170] Parameter name Internal impedance Voltage / kV Harmonic Sources Internal resistance 10Ω Harmonic voltage source effective value 50 Grid-side voltage source Impedance (1Ω+1Ω / / 0.1H) The effective value of the grid-side voltage source is 447.4465

Claims

1. An optimization design method for a second-order high-pass filter for a power system, characterized in that The following steps are involved: Step 1: Input the parameters Q required for the second-order high-pass filter design n ,ω0,U n ; Among them, Q n The reactive power required to compensate for the system; U n is the bus voltage of the AC system; ω0 is the system angular frequency at the power frequency; Step 2: Calculate the main capacitor parameters and the lower limit of the resistance: In the second-order high-pass filter circuit, according to the reactive power requirements of the system, the value of the main capacitor C1 is determined according to the following formula, namely: make A lower limit value R of the resistance R is obtained as follows: Among them, △1 determines whether the equation has roots; R is the resistance in the second-order high-pass filter; Step 3: Let R = R, k = 1; If R ≥ R max , output the result; if R <R max , according to the LC series resonance condition, the formula for calculating L1 is as follows: Where k represents the number of cycles; R max represents the maximum value of the resistance of the second-order high-pass filter; L1 represents the inductance in the second-order high-pass filter; The fundamental power loss of the resistor R in the second-order high-pass filter, the m parameter of the power frequency loss characteristic, and the harmonic amplification factor H(ω0) of the characteristic harmonic voltage of the converter station AC filter are calculated according to the following equations (4) to (6): Among them, P R (ω) represents the fundamental power loss of the resistor R in the second-order high-pass filter; U(ω) n represents the bus voltage of the AC system; Z(ω) represents the impedance function of the second-order high-pass filter; ω represents the different angular frequencies of the second-order high-pass filter; L1 represents the inductance in the second-order high-pass filter; In formula (5), m represents the power frequency loss characteristic of the second-order high-pass filter; Q represents the quality factor of the second-order high-pass filter; In formula (6), H(ω0) represents the harmonic amplification factor of the characteristic harmonic voltage of the second-order high-pass filter of the converter station; Z F (ω0) represents the impedance value of the second-order high-pass filter at the angular frequency ω; Z S (ω0) 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 second-order high-pass filter at the tuning point; Step 4: Parameter selection to determine whether the calculation process is terminated: If H(ω0)≤μ,m≤θ, then output the result, μ represents the voltage harmonic amplification factor limit value of the filter at the tuning point, θ represents the power frequency loss factor limit value of the filter; otherwise, let R=R+△R, k=k+1, △R represents the increase of resistance R, k represents the number of cycles in the judgment process; go to step three.

2. An optimization design method for a C-type damping filter for a power system, characterized in that The steps include: Step 1: Input the parameters Q required for C-type damped filter design n ',ω0',U n ', Q n ' represents the reactive power required to be compensated by the C-type damping filter; ω0' represents the system angular frequency of the C-type damping filter at the working frequency; U n ' represents the bus voltage of the AC system of the C-type damping filter; Step 2: Calculate the main capacitor parameters and the lower limit of the resistance: According to the reactive power requirement of the system, the value of the main capacitor C1' in the C-type damping filter is determined according to the following formula, namely: make Among them: △1' determines whether the C-type damping filter equation has a root; R' represents the resistance in the C-type damping filter; C2 represents the additional capacitance in the C-type damping filter; A lower limit value R' of the resistance R' is obtained as follows: Step 3: Let R' = R ', k = 1; if R' ≥ R max , output the result; if R' <R max , For the specified tuning point ω0', the resistance value R' of the given resistor is taken into account, the equipment cost is taken into account, the capacitance of the actual auxiliary capacitor C2 and the insulation coordination of the auxiliary capacitor C2 are considered, and the capacitance of C2 is calculated by the following equation (9); In formula (9), η, k1, k2 represent intermediate variables, where The C-type damping filter reduces the base frequency loss by adding an additional capacitor C2, and the auxiliary capacitor C2 resonates with L1 at the base frequency, and the calculation formula of the reactor L1' can be obtained: According to the following equations (11) to (13), the fundamental power loss of the middle resistor R' of the C-type damping filter, the m parameter of the power frequency loss characteristic, and the harmonic amplification factor H(ω0)' of the characteristic harmonic voltage of the converter station AC filter are calculated: In formula (11), P R (ω)' represents the fundamental power loss of the resistor R in the C-type damping filter; U(ω) n ' represents the bus voltage of the AC system; Z(ω)' represents the impedance function of the C-type damping filter; In formula (12), Q' represents the quality factor of the C-type damping filter; In formula (13), H(ω0)' represents the harmonic amplification factor of the characteristic harmonic voltage of the C-type damping filter in the converter station; Z F (ω0)' represents the impedance value of the C-type damping filter at the angular frequency ω; Z S (ω0)' represents the impedance value of the equivalent system at the angular frequency ω; Step 4: Parameter selection to determine whether the calculation process is terminated; if H(ω0)'≤μ', m≤θ', then output the result; μ' represents the voltage harmonic amplification factor limit value of the C-type damping filter at the tuning point, and θ' represents the power frequency loss factor limit value of the C-type damping filter; otherwise, let R=R+△R, k=k+1, △R represents the increase in resistance R in the C-type damping filter, and go to step 3.

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