Multi-working-condition impedance modeling and stability analysis method for conventional direct-current power transmission system

Abstract

The invention discloses a multi-working-condition impedance modeling and stability analysis method for a conventional direct-current power transmission system. The modeling method comprises the steps of converter modeling, alternating-current system modeling, phase-locked loop modeling, control system modeling and direct-current line modeling. Converter modeling is carried out, and a 12-pulse converter small signal model is established; modeling a phase-locked loop, and obtaining a transfer function of the SRF phase-locked loop according to the structure of the per-unit SRF phase-locked loop; acquiring a transfer function of the MAF phase-locked loop; and control system modeling, including CIGRE model control system modeling and Guizhou II model control system modeling in different control modes under the AC voltage drop working condition. According to the method, small signal modeling is performed on different control modes of an alternating voltage drop working condition, a closed-loop transfer function of the LCC-HVDC is obtained according to an impedance analysis method, and the small interference stability of the system is judged according to the distribution characteristic of a characteristic root of the closed-loop transfer function on an s plane.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-voltage direct current (HVDC) transmission, and in particular relates to a multi-operating-condition impedance modeling and stability analysis method for a conventional HVDC transmission system. Background Art

[0002] With the continuous development and construction of conventional high-voltage direct current (LCC-HVDC) systems, their transmission capacity is also increasing. Conventional HVDC systems are subject to the risk of oscillation. Therefore, analyzing the small-disturbance stability of conventional HVDC systems has theoretical research and engineering application value.

[0003] The first step in studying the oscillation mechanism and stability analysis of conventional HVDC systems is to establish a small-signal model of the LCC-HVDC, including the converter model, phase-locked loop model, control system model, and DC link model. Converter models primarily include quasi-steady-state models, switching function models, dynamic phasor models, and state-space models. Phase-locked loop models mostly use the SRF (synchronous reference frame phase-locked loop) phase-locked loop. Regarding control system modeling, existing technical solutions focus on modeling the control system at a single steady-state operating point under rated operating conditions, such as constant current control on the rectifier side and constant voltage control on the inverter side, without analyzing operating conditions with AC voltage drops. Furthermore, existing technical solutions typically focus on standard test models, with limited research on actual engineering models and a lack of small-signal stability analysis of engineering models under multiple operating conditions. Summary of the Invention

[0004] The main purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and to propose a multi-operating-condition impedance modeling and stability analysis method for a conventional direct current transmission system.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A multi-operating impedance modeling method for conventional DC transmission systems, including converter modeling, AC system modeling, phase-locked loop modeling, control system modeling, and DC line modeling;

[0007] Converter modeling, with the AC voltage, DC current and actual trigger angle of the dq synchronous rotating coordinate system as input, and the AC current, DC voltage, commutation angle and actual turn-off angle of the dq synchronous rotating coordinate system as output, establishes a 12-pulse converter small signal model; Phase-locked loop modeling, according to the structure of the per-unit SRF phase-locked loop, obtains the transfer function of the SRF phase-locked loop; obtains the transfer function of the MAF phase-locked loop; Control system modeling, including CIGRE model control system modeling and Guiguang II model control system modeling under different control modes of AC voltage drop conditions; DC line modeling, the DC line adopts a π-type equivalent line, and a concentrated parameter model of the π-type equivalent line is established.

[0008] The present invention also includes a conventional DC transmission system stability analysis method, based on the modeling method provided by the present invention, the method uses impedance analysis to perform stability analysis, divides the system into two subsystems, and determines the system stability by impedance ratio;

[0009] At the DC side outlet of the inverter side converter, the DC system is divided into two subsystems Z rec and Z inv , where the DC side impedance of the rectifier side and the DC line impedance are combined as Z rec , the DC side impedance of the inverter side is Z inv ;

[0010]

[0011] Where T(s) is the closed-loop transfer function of the system. The stability of the system is determined by the characteristic roots of T(s). It is a necessary and sufficient condition for the stability of the system that all the real parts of the characteristic roots of T(s) lie in the left half plane of s. Conversely, when one or more roots among the characteristic roots have positive real parts, the system is unstable.

[0012] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0013] 1. The present invention derives a small-disturbance formula for the trigger angle of an LCC-HVDC system with different AC voltages and control modes. This formula combines the converter model, the phase-locked loop model, and the AC-side dq-axis impedance to derive the DC impedance of the rectifier and inverter sides. The closed-loop transfer function of the DC system is derived using impedance analysis combined with the DC impedance and DC line impedance. The small-disturbance stability of the DC system is determined based on the characteristic roots of the closed-loop transfer function, thereby mapping the stability domains for different AC voltages and control parameters. Combined with the technical solution of the present invention, the effects of different AC voltages and control modes on the stability of the DC system can be understood, providing a basis for selecting LCC-HVDC control parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a schematic diagram of the modeling method of the present invention;

[0015] Figure 2 This is the structural diagram of LCC-HVDC;

[0016] Figure 3 This is the structure diagram of the per-unit SRF phase-locked loop;

[0017] Figure 4 This is the MAF-SRF phase-locked loop structure diagram;

[0018] Figure 5 It is the control structure diagram of the CIGRE model;

[0019] Figure 6 It is the electrical wiring diagram of the CIGRE model;

[0020] Figure 7 This is the structure diagram of the Guiguang II model control system;

[0021] Figure 8 It is a lumped parameter model of π-type equivalent line;

[0022] Figure 9 This is a schematic diagram considering the DC side impedance of the damping circuit;

[0023] Figure 10 It is a simplified circuit diagram of a high voltage DC system;

[0024] Figure 11 This is the circuit structure diagram of the CIGRE HVDC standard test model;

[0025] Figure 12 This is the schematic diagram of the circuit structure of the Guiguang II model;

[0026] Figure 13 This is the DC side impedance sweep verification result diagram when the AC voltage on the rectifier side of the CIGRE model changes;

[0027] Figure 14 This is a schematic diagram of the frequency sweep verification results when the AC voltage on the rectifier side of the Guiguang II model changes;

[0028] Figure 15a is the DC current control proportional coefficient K of the rectifier side of the CIGRE model pIdc Zero-pole diagram when changing;

[0029] Figure 15b is the DC current control proportional coefficient K of the rectifier side of the CIGRE model pIdc Simulation waveform verification diagram during changes;

[0030] Figure 16 It is the CIGRE model U acr Stability domain under different parameters during changes;

[0031] Figure 17 It is the CIGRE model U aci Stability domain under different parameters during changes;

[0032] Figure 18 is the U under different short circuit ratios of Guiguang II model acr Schematic diagram of the comparison of stable domains during changes;

[0033] Figure 19 is the U under different short circuit ratios of Guiguang II model aci Schematic diagram of the comparison of stable domains during changes. DETAILED DESCRIPTION

[0034] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0035] like Figure 1 and Figure 2 As shown in the present invention, a conventional DC transmission system multi-operating impedance modeling method is based on Figure 2 The structure of LCC-HVDC shown in the figure includes converter modeling, AC system modeling, phase-locked loop modeling, control system modeling, and DC line modeling.

[0036] Converter modeling, specifically: AC voltage U in dq synchronous rotating coordinate system d and U q , DC current I dc , the actual trigger angle α is input, and the AC current I in the dq synchronous rotating coordinate system d and I q , DC voltage U dc , commutation angle μ, and actual turn-off angle γ are output, and a small signal model of a 6-pulse converter is established:

[0037]

[0038] Regarding the K matrix and formula (1), specifically:

[0039] The transfer function of the commutation angle is:

[0040]

[0041] Among them, μ is the commutation angle, ω0 is the angular frequency, α is the trigger angle, δ is the angle at which the commutation ends, i 2d ,i 2q is the intermediate variable of dq axis current, i 2d ,i 2q and the AC side dq axis voltage u d ,u q The relationship is:

[0042]

[0043] Steady state i 2d0 ,i 2q0 The expression is as follows:

[0044]

[0045] In formula (2), L μ1 , L μ2 , L μ3 The expression is as follows:

[0046]

[0047] The transfer function of DC voltage is:

[0048]

[0049] Among them, K 33 Considering the total voltage drop of the rectifier inductor, L eq The expression is:

[0050]

[0051] Among them L c is the commutation inductor.

[0052] AC current I d and I q The transfer function is:

[0053]

[0054] In formula (9), L i1 , L i2 , L i3 , L i4 The expression is:

[0055]

[0056] In formula (9)

[0057]

[0058] The transfer function of the turn-off angle is:

[0059]

[0060] Where γ is the turn-off angle.

[0061] The small signal model of the LCC converter is obtained as follows:

[0062]

[0063] According to formula (3), we can get i 2d ,i 2q About U d , U q The expression of , and the Laplace transform of formula (3) is:

[0064]

[0065] After linearization and sorting, we get:

[0066]

[0067] According to formula (15), we can eliminate the 5th and 6th columns of the K matrix and obtain:

[0068]

[0069] The commutation angle and turn-off angle of the 6-pulse converter are sampled and held every 60° electrical angle. Therefore, the fourth and fifth rows of the K matrix need to be multiplied by the zero-order holder. The transfer function of the zero-order holder is:

[0070]

[0071] Wherein, T is the sampling period, T = 0.02 / 6s, s represents the complex frequency, s = σ + jω, σ is the real part, ω is the imaginary part, ω represents the angular frequency, ω = 2πf, and f is the frequency.

[0072] The DC project uses a 12-pulse converter composed of two 6-pulse converters connected in series. Its DC voltage and AC current are twice that of the 6-pulse converter. The DC voltages on the inverter-side converter and the rectifier-side converter are in opposite directions, so the third row of the K matrix of the inverter-side converter model needs to be multiplied by -1. The expressions for the 12-pulse converter models on the rectifier and inverter sides are as follows:

[0073]

[0074] Where ΔU and ΔY represent the converter input and output, respectively. The subscript rec represents the rectifier side, the subscript inv represents the inverter side, x represents the xth column of the K matrix, and H represents the transfer function of the zero-order holder.

[0075] To achieve dynamic voltage balancing of series-connected thyristors and suppress commutation overshoot, a damping circuit exists in the actual converter. Therefore, this circuit must be considered during modeling. Because the conduction conditions of the converter valves differ between commutation and non-commutation periods, an averaging approach is used to calculate the equivalent impedance of the damping circuit. For a 12-pulse converter, the equivalent impedance on the DC side of the damping circuit is expressed as follows:

[0076]

[0077] Among them, Zeq is the equivalent impedance of the damping circuit, μ0 is the commutation angle, Z RC4 Indicates the damping circuit impedance in the non-commutation stage, Z RC5 Represents the damping circuit impedance during the commutation phase, Z RC4 and Z RC5 The expression is:

[0078]

[0079] Among them, R is the damping loop resistance, and C is the damping loop capacitance.

[0080] Phase-locked loop modeling, specifically: Figure 3 As shown in the figure, it is the structure diagram of the SRF phase-locked loop. a 、u b 、u c is the AC bus voltage, θ S is the actual phase of the AC bus voltage, θ PLL is the phase of the phase-locked loop output. Due to the existence of the phase-locked loop, there are two dq coordinate systems in the system, one is the dq coordinate system on the system side, and the dq axis voltage on the system side is and θ S Synchronous, the other is the dq coordinate system on the controller side, assuming the dq axis voltage on the controller side is and θ PLL Synchronous; set is the normalized q-axis voltage on the controller side, ω0 is the fundamental angular frequency, K pPLL 、T iPLL are the proportional coefficient and integral constant of the phase-locked loop PI link respectively;

[0081] according to Figure 1 、 Figure 3 , the open-loop transfer function of the SRF phase-locked loop is:

[0082]

[0083] The small disturbance transfer function G between the phase of the phase-locked loop output and the q-axis voltage on the system side SRF-PLL for:

[0084]

[0085] The phase-locked loop of the Guiguang II project model is a MAF phase-locked loop, which adds a sliding average filter on the basis of the SRF-PLL. Its structure is as follows: Figure 4 As shown; the transfer function of the MAF phase-locked loop is:

[0086]

[0087] Among them, T dis the sliding window length of MAF, and the transfer function of the MAF phase-locked loop is obtained as follows:

[0088]

[0089] Control system modeling, including CIGRE model control system modeling and Guiguang II model control system modeling under different control modes of AC voltage drop conditions; Figure 5 As shown in Figure 1, the control structure of the CIGRE model includes constant current, constant voltage, constant turn-off angle control, VDCOL control, and current deviation control. The trigger angle transfer function of constant current control is:

[0090]

[0091] Among them, K Idc 、T Idc is the proportional coefficient and integral constant of the first-order inertia link of constant current control; K pIdc 、T iIdc are the proportional coefficient and integral constant of the PI link of constant current control respectively; the trigger angle transfer function of constant voltage control is:

[0092]

[0093] Among them, K Udc 、T Udc is the proportional coefficient and integral constant of the first-order inertia link of constant voltage control, K pUdc 、T iUdc is the proportional coefficient and integral constant of the constant voltage control PI link; the trigger angle transfer function of the fixed turn-off angle control is:

[0094]

[0095] Among them, T G K is the time constant of the first-order inertia link of fixed turn-off angle control, pG 、T iG are the proportional coefficient and integral constant of the PI link of the fixed turn-off angle control; when the current deviation takes effect, the trigger angle transfer function of the fixed turn-off angle control is:

[0096]

[0097] Among them, K CEC is the slope of the current deviation control curve.

[0098] In the CIGRE model, when the rectifier side is in constant current control and VDCOL control is started, the DC voltage disturbance on the inverter side will be transmitted to the DC current command value on the rectifier side through VDCOL. Therefore, it is necessary to obtain the relationship between the DC voltage on the rectifier side and the DC voltage on the inverter side. If there is a voltage disturbance ΔU on the rectifier side,dcr , the voltage disturbance response on the inverter side is ΔU dci , according to the idea of ​​partial pressure, such as Figure 6 As shown, ΔU dcr With ΔU dci The relationship is:

[0099]

[0100] Among them, K ur_ui is the transfer function between the DC voltage on the rectifier side and the DC voltage on the inverter side, Z dci is the DC impedance of the inverter side, R dc , L dc 、C dc are the resistance, inductance, and capacitance on the DC line. When the rectifier side has a constant current and VDCOL control is started, the transfer function of the trigger angle is:

[0101]

[0102] Among them, K VDCOL is the slope of the VDCOL curve; when the inverter side is in constant current control and VDCOL control is enabled, the transfer function of its trigger angle is:

[0103]

[0104] When the inverter side is in fixed turn-off angle control and VDCOL control is enabled, the transfer function of its trigger angle is:

[0105]

[0106] Among them, K pIdc 、T iIdc They are the proportional coefficient and integral constant of the constant current control PI link respectively.

[0107] The specific modeling of Guiguang II control system is as follows: Figure 7 The control structure of the Guiguang II model is shown in Figure 2. There is a VDCOL control link on both the rectifier and inverter sides, while the VDCOL of the CIGRE model only exists on the inverter side. The trigger angle transfer function under constant current control is:

[0108]

[0109] Among them, α ord0 is the trigger angle of steady-state working condition; K m_Idc is the proportional coefficient of the constant current control piecewise function, K m Idc =0.75; G αIdc is the constant DC current controller ΔI dc to Δαord Transfer function; constant current control anti-aliasing filter G AAFI The transfer function of (s) is:

[0110]

[0111] Digital filter G IIR The transfer function of (s) is:

[0112]

[0113] Among them, T c is the execution step length of Guiguang II engineering control system, T c =0.625ms; the input of constant voltage control in the Guiguang II circuit project model is the voltage U after smoothing reactor filtering. dcL , U dcL The DC voltage U at the converter output dc The small perturbation relationship is:

[0114] ΔU dcL =ΔU dc +sLΔI dc (36)

[0115] The firing angle transfer function under DC voltage control is obtained as follows:

[0116]

[0117] Among them, K pUdc 、T iUdc They are the proportional coefficient and integral constant of the constant voltage control PI link; the constant voltage control anti-aliasing filter G AAFU The transfer function of (s) is:

[0118]

[0119] The trigger angle transfer function under fixed turn-off angle control is:

[0120]

[0121] Among them, K pG 、T iG are the proportional coefficient and integral constant of the PI link of the fixed turn-off angle control; G γ is a proportional coefficient of the control error of the fixed shut-off angle, G γ =1 / 147.75; under current deviation control, the trigger angle transfer function is:

[0122]

[0123] Among them, K m_dIdcK is the proportional coefficient of the current deviation control piecewise function, m_dIdc =0.25;

[0124]

[0125] DC line modeling, DC line adopts Π-type equivalent line; the lumped parameter model of Π-type equivalent line is as follows Figure 8 As shown. The impedance and admittance of the π-type equivalent circuit are:

[0126]

[0127] Where sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, L is the line length, γ is the propagation coefficient, and Z c is the wave impedance.

[0128] The present invention also provides a conventional DC transmission system stability analysis method. Based on the above-mentioned modeling method, the method uses an impedance analysis method to perform stability analysis, including: first, obtaining the DC impedance of the rectifier side and the inverter side. The derivation of the DC impedance requires combining the converter model, the phase-locked loop model, the controller model, and the AC side dq axis impedance;

[0129] The dq-axis impedance matrix of resistor R is:

[0130]

[0131] The dq-axis impedance matrix of the inductor L is:

[0132]

[0133] The dq-axis admittance matrix of capacitor C is:

[0134]

[0135] The admittance matrix and the impedance matrix are inversely related; the expression of the dq-axis admittance on the AC side is as follows

[0136]

[0137] Among them, Y dd is the admittance corresponding to the d-axis voltage and d-axis current, Y dq is the admittance corresponding to the q-axis voltage and d-axis current, Y qd is the admittance corresponding to the d-axis voltage and q-axis current, Y qq is the admittance corresponding to the q-axis voltage and q-axis current; the dq-axis impedance or admittance is obtained according to the AC system impedance of the specific model;

[0138] If the small perturbation formula of the firing angle is only about ΔU d , ΔUq , ΔI dc If the perturbation is , the fourth column of the K matrix is ​​directly eliminated. The K matrix after eliminating the fourth column is:

[0139]

[0140] If the trigger angle perturbation formula contains a perturbation about Δγ, then the trigger angle perturbation formula is combined with the fifth row of the K matrix Δγ=K 51 ΔU d +K 52 ΔU q +K 53 ΔI dc +K 54 Δα, we get:

[0141]

[0142] If the trigger angle small perturbation formula contains the information about ΔU dc The small perturbation formula of trigger angle is combined with the third row of K matrix ΔU dc =K 31 ΔU d +K 32 ΔU q +K 33 ΔI dc +K 34 Δα, we get:

[0143]

[0144] Then eliminate the fourth column of the K matrix and get the result of formula (47); the third row of the K matrix ΔU dc =K 31 ΔU d +K 32 ΔU q +K 33 ΔI dc The expression of DC side impedance is derived from the dq axis impedance formula:

[0145]

[0146] The DC side impedance also needs to consider the impedance of the damping loop. The damping loop impedance is connected in parallel with the DC side impedance, such as Figure 9 As shown; the DC side impedance expression after considering the damping loop impedance is:

[0147]

[0148] Among them, Z eq is the equivalent impedance of the DC side of the damping circuit, and its expression is formula (19).

[0149] The stability analysis uses the impedance analysis method to divide the system into two subsystems, and the system stability is judged by the impedance ratio; the DC system is divided into two subsystems Z at the DC side outlet of the inverter side converter rec and Z inv , where the DC side impedance of the rectifier side and the DC line impedance are combined as Z rec , the DC side impedance of the inverter side is Z inv ,like Figure 10 shown; according to Figure 10 We can get:

[0150]

[0151] Where T(s) is the closed-loop transfer function of the system. The stability of the system is determined based on the characteristic roots of T(s). A necessary and sufficient condition for system stability is that all the real parts of T(s)'s characteristic roots lie in the left half plane of s. Conversely, if one or more of the characteristic roots have a positive real part, the system is unstable. By analyzing and determining that the dominant poles under different AC voltages and control parameters all lie in the left half plane of s, the stability of the DC system under different AC voltages and control parameters can be determined. This allows the stability region of the DC system to be mapped under different AC voltages and control parameters.

[0152] Example

[0153] Take the CIGRE HVDC standard test model and the Guiguang II project model as examples. The CIGRE model is a single-pole system with a rated DC voltage of 500kV and a rated DC power of 1000MW. The circuit structure is as follows: Figure 11 The specific parameters are shown in Table 1 below.

[0154]

[0155] Table 1

[0156] The Guiguang II model is a bipolar system with a rated DC voltage of ±500kV and a rated DC power of 3000MW. The circuit structure and specific parameters of the Guiguang II model are as follows: Figure 12 shown.

[0157] The Guiguang II project model will invest a certain number of AC filters based on the reactive power exchanged between the converter station and the AC system. Figure 12As shown in the figure, the Guiguang II project model includes three types of AC filters: double-tuned and triple-tuned AC filters, and capacitor banks. The rectifier-side AC busbar is equipped with four double-tuned AC filters (DT11 / 13), three triple-tuned AC filters (TT3 / 24 / 36), and three capacitor banks (SC). The inverter-side AC busbar is equipped with six double-tuned AC filters (DT12 / 24) and six capacitor banks (SC). Each pole in the Guiguang II project model is equipped with a DC filter to filter out DC harmonics. The specific parameters of the AC and DC filters in the Guiguang II project model are shown in Table 2.

[0158]

[0159] Table 2

[0160] The basic parameters of the Guiguang II model are shown in Table 3 below.

[0161]

[0162] Table 3

[0163] The DC side impedance under different AC voltages and different control modes is verified by frequency sweeping. Table 4 below shows the control mode when the AC voltage on the rectifier side of the CIGRE model changes.

[0164]

[0165] Table 4

[0166] At 0~500Hz, different U acr The frequency sweep verification is carried out under the working conditions, and the results are as follows Figure 13 The calculated DC side impedance of the CIGRE model is basically consistent with the PSCAD / EMTDC frequency sweep results. The average error between the frequency sweep results and the calculated values ​​is 4.08%, proving the correctness of the modeling.

[0167] In the Guiguang II model, different numbers of AC filters will be put into operation under different AC voltage conditions. Different AC filters correspond to different AC measurement dq axis impedances, so the DC impedance will also be different. As shown in Table 5 below, the number of AC filter groups and control modes under different AC voltages of the Guiguang II model are given.

[0168]

[0169] Table 5

[0170] The DC side impedance under different working conditions in Table 5 is calculated and verified by frequency sweep. The calculation results and frequency sweep results are shown in the figure below. Figure 14As shown. The impedance calculation of the Guiguang II model is basically consistent with the frequency sweep results. The average error between the frequency sweep results and the calculated values ​​is 3.88%, which proves the correctness of the impedance calculation. After proving the correctness of the DC side impedance calculation, the closed-loop transfer function of the DC system can be obtained according to the impedance analysis method, and then the small signal stability of the DC system can be judged according to the characteristic roots of the closed-loop transfer function. Figure 15a and Figure 15b As shown, it is the DC current control proportional coefficient K of the rectifier side of the CIGRE model pIdc The characteristic root distribution (i.e., zero-pole diagram) and simulation waveform verification diagram during changes.

[0171] Figure 15a X is the pole, O is the zero point, and the box is the dominant pole. Figure 15b It is with K pIdc The DC current waveform was simulated, with the control parameters varied every 2 seconds between 2 and 14 seconds. FFT analysis of the DC current was performed to obtain the DC current oscillation amplitude and frequency. The control parameters, dominant pole coordinates, simulation time, and oscillation frequency (amplitude) are summarized in Table 6 below.

[0172]

[0173] Table 6

[0174] The real part of the dominant pole is related to the amplitude of the oscillation component. The smaller the real part, the smaller the amplitude of the oscillation component. The imaginary part of the dominant pole corresponds to the oscillation frequency. As K pIdc As K increases, the dominant pole moves to the right half plane, and the resonant component of the DC current simulation waveform also increases. pIdc When it increases to 2.1, the dominant pole coordinates cross the right half plane of s, and the system oscillation intensifies. Simulation data shows that the calculated imaginary part of the dominant coordinates can accurately reflect the oscillation frequency. The simulation results in Table 6 confirm that the small-signal stability of the DC system based on the characteristic roots (poles) of the closed-loop transfer function is accurate. Next, we calculate the stability region.

[0175] First, the control modes corresponding to the CIGRE model under different AC voltages are shown in Table 7 below. acr The control mode corresponding to the CIGRE model when changing.

[0176]

[0177] Table 7

[0178] like Figure 16 As shown, it is the CIGRE model U acr Stability domain under different parameters during changes; Figure 16The stability region under different parameters when the AC voltage on the inverter side changes is shown. The square grid represents the unstable region, and the horizontal stripes represent the stable region. acr When the voltage is greater than 0.86 pu, the inverter side is in fixed turn-off angle control, and when it is less than 0.86 pu, the inverter side is in constant current control. Therefore, the stability domain analysis range of the fixed turn-off angle control parameter is U acr =1pu~0.85pu, the stability domain analysis range of the constant current control parameter is 0.85pu~0.3pu. Figure 16 It can be seen from (a), (b), and (c) that when the rectifier side enters the minimum trigger angle control and current deviation control is started, the system stability is weakened and the unstable area increases. When the inverter side enters the constant current control, the system stability is enhanced and the unstable area decreases.

[0179] As shown in Table 8 below, aci The control mode corresponding to the CIGRE model when changing.

[0180]

[0181] Table 8

[0182] like Figure 17 As shown, U aci After it drops to 0.92pu, VDCOL starts, and the unstable area of ​​the DC system increases. aci When it drops below 0.41 pu, VDCOL control is exited and minimum current control is activated. At this time, the unstable area of ​​the DC system is generally reduced. Therefore, in the CIGRE model, the stability of VDCOL control is weaker than that of normal constant current control and minimum current control.

[0183] Changes in control parameters can also cause the system to move from a stable region to an unstable region. For example, a time constant that is too small or a proportional coefficient that is too large can cause system instability. Therefore, the control parameters need to be set within a reasonable range so that the DC system can maintain stable operation.

[0184] As shown in Table 9 below, acr The control mode corresponding to the Guiguang II model when changes occur.

[0185]

[0186] Table 9

[0187] like Figure 18 As shown, it is the Guiguang II model U acrThe stability domains of different control parameters when changing, including the comparison of the stability domains of strong and weak systems; the figure compares the stability domains of weak system (SCR = 4) and strong system (SCR = 19). The stability domain of DC control parameters is not completely linearly positively correlated with the strength of AC system. In some working conditions, especially low AC voltage conditions, the stability of strong system is worse than that of weak system. For example, when U acr When it is less than 0.5pu, in a strong system, K pIdc If it is greater than 2, it will enter the unstable region. In weak system, K pIdc The system remains stable when it is greater than 2. In strong systems, the grid impedance combines with the converter impedance and the AC filter impedance to produce resonance points. When the system enters these operating conditions, there is a risk of oscillation and instability. If necessary, special consideration and design for these operating conditions are required to improve the stable operation of the HVDC system under all operating conditions.

[0188] As shown in Table 10 below, aci The control mode corresponding to the Guiguang II model when changes occur.

[0189]

[0190] Table 10

[0191] like Figure 19 As shown, it is the Guiguang II model U aci The stability domains of different control parameters when changing, and the stability domains of strong and weak systems are compared. Figure 19 Available, when U aci When it is less than 0.41pu, the system enters VDCOL control and becomes unstable. iIdc , K pG 、T iG In the stable region, the short-circuit ratio decreases and the stable region also decreases.

[0192] It should also be noted that, in this specification, terms such as "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or apparatus comprising the element.

[0193] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-operating impedance modeling method for a conventional DC transmission system, characterized in that: Including converter modeling, AC system modeling, phase-locked loop modeling, control system modeling and DC line modeling; Converter modeling: Using the AC voltage, DC current, and actual trigger angle in the dq synchronous rotating coordinate system as input, and the AC current, DC voltage, commutation angle, and actual turn-off angle in the dq synchronous rotating coordinate system as output, a 12-pulse converter small signal model is established. Phase-locked loop modeling: Based on the structure of the normalized SRF phase-locked loop, obtain the transfer function of the SRF phase-locked loop; obtain the transfer function of the MAF phase-locked loop; Control system modeling, including CIGRE model control system modeling and Guiguang II model control system modeling under different control modes of AC voltage drop conditions; DC line modeling,The DC line adopts a π-type equivalent line, and a lumped parameter model of the π-type equivalent line is established.

2. A conventional DC transmission system multi-operating condition impedance modeling method according to claim 1, characterized in that: The converter modeling is as follows: AC voltage U in dq synchronous rotating coordinate system d and U q , DC current I dc , the actual trigger angle α is input, and the AC current I in the dq synchronous rotating coordinate system d and I q , DC voltage U dc , commutation angle μ, and actual turn-off angle γ are output, and a small signal model of a 6-pulse converter is established: The commutation angle and turn-off angle of the 6-pulse converter are sampled and held every 60° electrical angle. Therefore, the fourth and fifth rows of the K matrix need to be multiplied by the zero-order holder. The transfer function of the zero-order holder is: Wherein, T is the sampling period, s represents the complex frequency, s=σ+jω, σ is the real part, ω is the imaginary part, ω represents the angular frequency, ω=2πf, and f is the frequency.

3. A conventional DC transmission system multi-operating condition impedance modeling method according to claim 2, characterized in that: The DC project uses a 12-pulse converter composed of two 6-pulse converters connected in series. Its DC voltage and AC current are twice that of the 6-pulse converter. The DC voltages on the inverter-side converter and the rectifier-side converter are in opposite directions, so the third row of the K matrix of the inverter-side converter model needs to be multiplied by -1. The expressions for the 12-pulse converter models on the rectifier and inverter sides are as follows: Where ΔU and ΔY represent the converter input and output, respectively. The subscript rec represents the rectifier side, the subscript inv represents the inverter side, x represents the xth column of the K matrix, and H represents the transfer function of the zero-order holder. To achieve dynamic voltage balancing of series-connected thyristors and suppress commutation overshoot, a damping circuit exists in the actual converter. Therefore, this circuit must be considered during modeling. Because the conduction conditions of the converter valves differ between commutation and non-commutation periods, an averaging approach is used to calculate the equivalent impedance of the damping circuit. For a 12-pulse converter, the equivalent impedance on the DC side of the damping circuit is expressed as follows: Among them, Z eq is the equivalent impedance of the damping circuit, μ0 is the commutation angle, Z RC4 Indicates the damping circuit impedance in the non-commutation stage, Z RC5 Represents the damping circuit impedance during the commutation phase, Z RC4 and Z RC5 The expression is: Among them, R is the damping loop resistance, and C is the damping loop capacitance.

4. A conventional DC transmission system multi-operating condition impedance modeling method according to claim 2, characterized in that: The phase-locked loop modeling is specifically as follows: Due to the existence of the phase-locked loop, there are two dq coordinate systems in the system. One is the dq coordinate system on the system side. Let the dq axis voltage on the system side be and θ S Synchronous, the other is the dq coordinate system on the controller side, assuming the dq axis voltage on the controller side is and θ PLL Synchronous; set is the normalized q-axis voltage on the controller side, ω0 is the fundamental angular frequency, K pPLL 、T iPLL are the proportional coefficient and integral constant of the phase-locked loop PI link respectively; According to the structure of the per-unit SRF phase-locked loop, the open-loop transfer function of the SRF phase-locked loop is: The small disturbance transfer function G between the phase of the phase-locked loop output and the q-axis voltage on the system side SRF-PLL for: The phase-locked loop of the Guiguang II project model is a MAF phase-locked loop, which adds a sliding average filter to the SRF-PLL. The transfer function of the MAF phase-locked loop is: Among them, T d is the sliding window length of MAF, and the transfer function of the MAF phase-locked loop is obtained as follows:

5. The multi-operating-condition impedance modeling method for a conventional direct current transmission system according to claim 2, characterized in that: The CIGRE model control system modeling is specifically as follows: The control structure of the CIGRE model includes constant current, constant voltage, constant turn-off angle control, VDCOL control, and current deviation control. The trigger angle transfer function of the constant current control is: Among them, K Idc 、T Idc is the proportional coefficient and integral constant of the first-order inertia link of constant current control; K pIdc 、T iIdc are the proportional coefficient and integral constant of the PI link of constant current control respectively; the trigger angle transfer function of constant voltage control is: Among them, K Udc 、T Udc is the proportional coefficient and integral constant of the first-order inertia link of constant voltage control, K pUdc 、T iUdc is the proportional coefficient and integral constant of the constant voltage control PI link; the trigger angle transfer function of the fixed turn-off angle control is: Among them, T G K is the time constant of the first-order inertia link of fixed turn-off angle control, pG 、T iG are the proportional coefficient and integral constant of the PI link of the fixed turn-off angle control; when the current deviation takes effect, the trigger angle transfer function of the fixed turn-off angle control is: Among them, K CEC is the slope of the current deviation control curve.

6. A conventional DC transmission system multi-operating condition impedance modeling method according to claim 5, characterized in that: In the CIGRE model, when the rectifier side is in constant current control and VDCOL control is started, the DC voltage disturbance on the inverter side will be transmitted to the DC current command value on the rectifier side through VDCOL. Therefore, it is necessary to obtain the relationship between the DC voltage on the rectifier side and the DC voltage on the inverter side. If there is a voltage disturbance ΔU on the rectifier side, dcr , the voltage disturbance response on the inverter side is ΔU dci , according to the idea of ​​voltage division, ΔU dcr With ΔU dci The relationship is: Among them, K ur_ui is the transfer function between the DC voltage on the rectifier side and the DC voltage on the inverter side, Z dci is the DC impedance of the inverter side, R dc , L dc 、C dc are the resistance, inductance, and capacitance on the DC line. When the rectifier side has a constant current and VDCOL control is started, the transfer function of the trigger angle is: Among them, K VDCOL is the slope of the VDCOL curve; when the inverter side is in constant current control and VDCOL control is enabled, the transfer function of its trigger angle is: When the inverter side is in fixed turn-off angle control and VDCOL control is enabled, the transfer function of its trigger angle is: Among them, K pIdc 、T iIdc They are the proportional coefficient and integral constant of the constant current control PI link respectively.

7. A conventional DC transmission system multi-operating condition impedance modeling method according to claim 6, characterized in that: The specific modeling of Guiguang II model control system is as follows: The control structure of the Guiguang II model has a VDCOL control link on both the rectifier and inverter sides. The trigger angle transfer function under constant current control is: Among them, α ord0 is the trigger angle of steady-state working condition; K m_Idc is the proportional coefficient of the constant current control piecewise function, K m_Idc =0.75; G α_Idc is the constant DC current controller ΔI dc to Δα ord The transfer function of Constant current controlled anti-aliasing filter G AAFI The transfer function of (s) is: Digital filter G IIR The transfer function of (s) is: Among them, T c is the execution step length of Guiguang II engineering control system, T c =0.625ms; the input of constant voltage control in the Guiguang II circuit project model is the voltage U after smoothing reactor filtering. dcL , U dcL The DC voltage U at the converter output dc The small perturbation relationship is: ΔU dcL =ΔU dc +sLΔI dc (21) The firing angle transfer function under DC voltage control is obtained as follows: Among them, K pUdc 、T iUdc They are the proportional coefficient and integral constant of the constant voltage control PI link; the constant voltage control anti-aliasing filter G AAFU The transfer function of (s) is: The trigger angle transfer function under fixed turn-off angle control is: Among them, K pG 、T iG are the proportional coefficient and integral constant of the PI link of the fixed turn-off angle control; G γ is a proportional coefficient of the control error of the fixed shut-off angle, G γ =1 / 147.75; under current deviation control, the trigger angle transfer function is: Among them, K m_dIdc K is the proportional coefficient of the current deviation control piecewise function, m_dIdc =0.25; 8. The method for multi-operating-condition impedance modeling of a conventional direct current transmission system according to claim 1, characterized in that: DC line modeling uses a π-type equivalent circuit. The impedance and admittance of the π-type equivalent circuit of the transmission line are: Where sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, L is the line length, γ is the propagation coefficient, and Z c is the wave impedance.

9. A conventional DC transmission system stability analysis method, characterized in that: Based on the modeling method according to any one of claims 1 to 8, the method adopts impedance analysis to perform stability analysis, comprising: First, the DC impedance of the rectifier and inverter sides needs to be obtained. The derivation of DC impedance requires combining the converter model, phase-locked loop model, controller model, and AC side dq axis impedance. The dq-axis impedance matrix of resistor R is: The dq-axis impedance matrix of the inductor L is: The dq-axis admittance matrix of capacitor C is: The admittance matrix and the impedance matrix are inversely related; the expression of the dq-axis admittance on the AC side is as follows Among them, Y dd is the admittance corresponding to the d-axis voltage and d-axis current, Y dq is the admittance corresponding to the q-axis voltage and d-axis current, Y qd is the admittance corresponding to the d-axis voltage and q-axis current, Y qq is the admittance corresponding to the q-axis voltage and q-axis current; The dq-axis impedance or admittance is obtained based on the AC system impedance of the specific model; If the small perturbation formula of the firing angle is only about ΔU d , ΔU q , ΔI dc If the perturbation is , the fourth column of the K matrix is ​​directly eliminated. The K matrix after eliminating the fourth column is: If the trigger angle perturbation formula contains a perturbation about Δγ, then the trigger angle perturbation formula is combined with the fifth row of the K matrix Δγ=K 51 ΔU d +K 52 ΔU q +K 53 ΔI dc +K 54 Δα, we get: If the trigger angle small perturbation formula contains the information about ΔU dc The trigger angle small perturbation formula is combined with the third row of K matrix ΔU dc =K 31 ΔU d +K 32 ΔU q +K 33 ΔI dc +K 34 Δα, we get: Then eliminate the fourth column of the K matrix and obtain the result of formula (32); The third row of the simultaneous K matrix ΔU dc =K 31 ΔU d +K 32 ΔU q +K 33 ΔI dc The expression of DC side impedance is derived from the dq axis impedance formula: The DC side impedance also needs to consider the impedance of the damping loop. The damping loop impedance is connected in parallel with the DC side impedance. The DC side impedance expression after considering the damping loop impedance is: Among them, Z eq is the equivalent impedance of the DC side of the damping circuit, and its expression is formula (4).

10. A conventional DC transmission system stability analysis method according to claim 9, characterized in that: Stability analysis uses impedance analysis to divide the system into two subsystems and judge the system stability by the impedance ratio; At the DC side outlet of the inverter side converter, the DC system is divided into two subsystems Z rec and Z inv , where the DC side impedance of the rectifier side and the DC line impedance are combined as Z rec , the DC side impedance of the inverter side is Z inv ; Where T(s) is the closed-loop transfer function of the system. The stability of the system is determined by the characteristic roots of T(s). It is a necessary and sufficient condition for the stability of the system that all the real parts of the characteristic roots of T(s) lie in the left half plane of s. Conversely, when one or more roots among the characteristic roots have positive real parts, the system is unstable.

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