A method for evaluating equivalent short circuit ratio of hybrid direct current feeding system
By reducing the Jacobian matrix order and using the Schul transform, the corrected power and admittance of the equivalent conventional high-voltage direct current system are calculated. Combined with the static voltage stability critical condition, a characteristic equation with the short-circuit ratio (SCR) as an explicit function is established, solving the static voltage stability analysis problem of the hybrid DC-fed system and realizing an accurate assessment of the grid strength of the system.
Patent Information
- Application Number
- CN202210617711.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-01
- Publication Date
- 2025-12-23
- Estimated Expiration
- 2042-06-01
AI Technical Summary
Existing technologies struggle to accurately quantify the static voltage stability of hybrid DC-DC feed systems like LCC-HVDC and VSC-HVDC, and lack an analysis of the mechanism of action of indices based on the singularity of the Jacobian matrix, making it difficult to establish a physical understanding of the static voltage stability analysis results.
By reducing the Jacobian matrix order and using the Schul transform, the corrected power, admittance, and reactive voltage sensitivity of the equivalent conventional HVDC system are calculated. Combined with the static voltage stability critical condition, a characteristic equation with the short-circuit ratio (SCR) as an explicit function is established to evaluate the static voltage stability of the hybrid DC-fed system.
It provides a clear physical mechanism, can accurately assess the grid strength of the system, improves the traditional short-circuit ratio calculation method, and enhances the accuracy and reliability of static voltage stability analysis of hybrid DC-fed systems.
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of static voltage stability analysis of AC / DC hybrid system, and particularly relates to an equivalent short-circuit ratio evaluation method for LCC-HVDC and VSC-HVDC hybrid infeed system. BACKGROUND
[0002] A typical hybrid-infeed high voltage direct current system has been formed, which is specifically manifested as that multiple line commutated converter based high voltage direct current (LCC-HVDC) and voltage source converter based high voltage direct current (VSC-HVDC) with short electrical distance feed into the same receiving end power grid, and the formed hybrid-infeed high voltage direct current system has become one of the representatives of the typical mode of the new power system in China, and the safe and stable operation thereof is a key to realizing the strategic goal of "carbon peak and carbon neutral".
[0003] Strong interaction between DC systems and between AC / DC systems is a key to affecting the stable operation of the multi-infeed system, and therefore, accurate quantification of the transmission limit and the grid strength of the system is very important for system planning and operation.
[0004] In the existing research, the VSC-HVDC is usually impedance equivalent or power equivalent, and on this basis, the short-circuit ratio index of the traditional LCC-HVDC single-infeed system is corrected, and the index mechanism analysis starting from the singularity of the Jacobian matrix is lacking, which leads to difficulty in establishing the physical understanding of the static voltage stability analysis results of the LCC-HVDC and VSC-HVDC hybrid-infeed high voltage direct current system. SUMMARY
[0005] The present application aims to overcome the shortcomings of the prior art and provides an equivalent short-circuit ratio evaluation method for a hybrid-infeed high voltage direct current system, which can directly analyze the static voltage stability of the LCC-HVDC and VSC-HVDC hybrid-infeed high voltage direct current system through the equivalent short-circuit ratio index, and the physical mechanism is clear, so as to evaluate the grid strength of the system, and the method is specifically implemented by the following technical solutions:
[0006] The equivalent short-circuit ratio evaluation method for the hybrid-infeed high voltage direct current system, the hybrid-infeed high voltage direct current system is a same receiving end power grid in which line commutated converter based high voltage direct current and voltage source converter based high voltage direct current are fed in, and the method specifically comprises the following steps:
[0007] Step 1) according to the AC-DC system flow equation, write the Jacobian matrix of the mixed DC feed-in system;
[0008] Step 2) by matrix elementary transformation and Schur transformation, the Jacobian matrix is reduced, and the modified power ΔP1, the modified admittance ΔB 11 , the modified reactive voltage sensitivity ΔT, the equivalent conventional HVDC single feed-in system containing equivalent power, equivalent admittance, equivalent reactive voltage sensitivity is calculated;
[0009] Step 3) based on the static voltage stability critical condition, the characteristic equation of the short circuit ratio SCR is obtained, and the short circuit ratio SCR and the corresponding critical value CSCR of the mixed DC feed-in system in the sense of static voltage stability are calculated;
[0010] Step 4) according to the comparison result of the short circuit ratio SCR and the critical value CSCR of the mixed DC feed-in system, the static voltage stability of the short circuit ratio of the mixed DC feed-in system is judged.
[0011] The further design of the equivalent short circuit ratio evaluation method of the mixed DC feed-in system is that in the step 1), the Jacobian matrix is as formula (1),
[0012]
[0013] Wherein, B represents the admittance matrix corresponding to the mixed DC feed-in system, B ij The element corresponding to i row and j column in the corresponding admittance matrix, i and j will be 1 or 2 respectively, U1 and U2 correspond to the converter bus voltage of conventional HVDC and flexible DC transmission respectively, P1 and P2 are the active power injected into the AC side of conventional HVDC and flexible DC transmission respectively, Q2 is the reactive power injected into the AC side of flexible DC transmission, and T represents the reactive voltage sensitivity of conventional HVDC.
[0014] The further design of the equivalent short circuit ratio evaluation method of the mixed DC feed-in system is that in the step 2), the matrix elementary transformation and Schur transformation are carried out according to formula (2),
[0015]
[0016] The further design of the equivalent short circuit ratio evaluation method of the mixed DC feed-in system is that in the step 2), the equivalent conventional HVDC single feed-in system containing equivalent power, equivalent admittance, equivalent reactive voltage sensitivity is calculated according to formula (3),
[0017] Equivalent power: P1' = P1 + ΔP1
[0018] Equivalent admittance: B 11 ' = B11 + ΔB 11
[0019] Equivalent reactive voltage sensitivity: T' = T + ΔT (3)
[0020] The further design of the equivalent short-circuit ratio evaluation method of the hybrid DC feeder system is that, in the step 3), the critical condition of static voltage stability of the singular corresponding system is determined based on the Jacobian matrix J sys The characteristic equation of the critical condition of static voltage stability of the singular corresponding system is:
[0021] Based on the above characteristic equation, the explicit function of the short-circuit ratio SCR is as formula (4),
[0022] ρT' + ρwSCR- 1- SCR = 0
[0023] SCR = -P'1×B 11 ′ (4)
[0024] Solving formula (4), the critical value CSCR of the short-circuit ratio is represented as:
[0025] The further design of the equivalent short-circuit ratio evaluation method of the hybrid DC feeder system is that, in the step 4), the static voltage stability of the short-circuit ratio of the hybrid DC feeder system is determined according to the comparison result of the short-circuit ratio SCR and the critical value CSCR of the hybrid DC feeder system.
[0026] When the actual short-circuit ratio SCR of the hybrid DC feeder system is greater than the critical short-circuit ratio CSCR, the static voltage of the hybrid DC feeder system is stable, and the conventional high-voltage DC can be stably operated at the rated operating point.
[0027] When the actual short-circuit ratio SCR of the hybrid DC feeder system is less than the critical short-circuit ratio CSCR, the static voltage of the hybrid DC feeder system is unstable, and it is determined that the output power of the conventional high-voltage DC cannot reach the rated power.
[0028] When the actual short-circuit ratio SCR of the hybrid DC feeder system is equal to the critical short-circuit ratio CSCR, the static voltage of the hybrid DC feeder system is critical, and it is determined that the maximum output power of the conventional high-voltage DC is the rated power.
[0029] Advantages of the present application:
[0030] The equivalent short-circuit ratio evaluation method of the hybrid DC feeding system of the application improves the short-circuit ratio calculation method of the traditional LCC-HVDC system to make it applicable to analyze the static voltage stability after the VSC-HVDC is accessed, and mathematically, the SCR proposed has a clear explicit function relationship with the critical stability boundary in the hybrid DC feeding system; physically, the SCR represents the result of converting the external parameters of the VSC-HVDC to the LCC-HVDC side, and based on this application, the grid strength of the system can be effectively evaluated. BRIEF DESCRIPTION OF DRAWINGS
[0031] Figure 1 It is a flowchart of the equivalent short-circuit ratio evaluation method of the hybrid DC feeding system of the application.
[0032] Figure 2 It is the topology structure of the LCC-HVDC and VSC-HVDC hybrid double feeding system of the application.
[0033] Figure 3 It is the LCC-HVDC DC standard model structure used in the application.
[0034] Figure 4 It is the transmission limit comparison of the hybrid double feeding system and the equivalent single feeding system in the simulation verification of the embodiment of the application.
[0035] Figure 5 It is the comparison of the critical short-circuit ratio obtained by the application and the critical short-circuit ratio obtained by the electromagnetic transient simulation calculation. DETAILED DESCRIPTION
[0036] The technical solutions of the application are further described in combination with the drawings.
[0037] The equivalent short-circuit ratio evaluation method of the hybrid DC feeding system of the embodiment, the hybrid DC feeding system is the same receiving end grid fed by the conventional high-voltage direct current and the flexible direct current transmission, which is shown in Figure 2 . For example Figure 1 , the method specifically includes the following steps:
[0038] Step 1) According to the AC / DC system flow equation, the Jacobian matrix of the hybrid DC feeding system is written. In step 1), the Jacobian matrix is as formula (1),
[0039]
[0040] Wherein, B represents the admittance matrix corresponding to the hybrid DC feeding system, B ijThe element corresponding to the i-th row and j-th column in the admittance matrix, i and j will be 1 or 2 respectively, U1 and U2 respectively correspond to the converter bus voltage of the conventional high voltage direct current and the flexible direct current, P1 and P2 respectively are the active power injected into the alternating current side of the conventional high voltage direct current and the flexible direct current, Q2 is the reactive power injected into the alternating current side of the flexible direct current, and T represents the reactive voltage sensitivity of the conventional high voltage direct current.
[0041] Step 2) The Jacobian matrix is reduced by matrix elementary transformation and Schur transformation, and the modified power ΔP1, the modified admittance ΔB and the modified reactive voltage sensitivity ΔT are calculated. 11 , the equivalent physical quantities including the equivalent power, the equivalent admittance and the equivalent reactive voltage sensitivity of the equivalent conventional high voltage direct current single-infeed system are calculated. In step 2) of the embodiment, the matrix elementary transformation and Schur transformation are performed according to formula (2),
[0042]
[0043] Further, in step 2), the equivalent physical quantities including the equivalent power, the equivalent admittance and the equivalent reactive voltage sensitivity of the equivalent conventional high voltage direct current single-infeed system are calculated according to formula (3),
[0044] Equivalent power: P1' = P1 + ΔP1
[0045] Equivalent admittance: B 11 ' = B 11 + ΔB 11
[0046] Equivalent reactive voltage sensitivity: T' = T + ΔT (3)
[0047] Step 3) Based on the critical condition of static voltage stability, the characteristic equation of the short-circuit ratio SCR as an explicit function is obtained, and the short-circuit ratio SCR and the corresponding critical value CSCR of the hybrid direct current infeed system in the sense of static voltage stability are calculated.
[0048] In step 3), the Jacobian matrix J sys ' of the singular corresponding system is based on the critical condition of static voltage stability, and the characteristic equation is: Based on the above characteristic equation, the explicit function about the short-circuit ratio SCR is as formula (4),
[0049] ρT' + ρ 2 SCR -1 - SCR = 0
[0050] SCR = -P'1×B 11 ' (4)
[0051] Solving formula (4), the short-circuit ratio critical value CSCR is represented as:
[0052] Step 4) judging the static voltage stability of the short-circuit ratio of the hybrid DC feeding system according to the comparison result of the short-circuit ratio SCR of the hybrid DC feeding system and the critical value CSCR.
[0053] Further, judging the static voltage stability of the short-circuit ratio of the hybrid DC feeding system according to the comparison result of the short-circuit ratio SCR of the hybrid DC feeding system and the critical value CSCR specifically comprises:
[0054] When the actual short-circuit ratio SCR of the hybrid DC feeding system is greater than the critical short-circuit ratio CSCR, the static voltage of the hybrid DC feeding system is stable, and the conventional HVDC can be stably operated at the rated operating point;
[0055] When the actual short-circuit ratio SCR of the hybrid DC feeding system is less than the critical short-circuit ratio CSCR, the static voltage of the hybrid DC feeding system is unstable, and it is determined that the output power of the conventional HVDC cannot reach the rated power;
[0056] When the actual short-circuit ratio SCR of the hybrid DC feeding system is equal to the critical short-circuit ratio CSCR, the static voltage of the hybrid DC feeding system is critical stable, and it is determined that the maximum output power of the conventional HVDC is the rated power.
[0057] The method is used for processing, wherein the LCC-HVDC adopts a CIGRE standard system model, and the VSC-HVDC adopts a constant power control mode, and the control parameters are shown in Table 1. Figure 3 The equivalent short-circuit ratio and the critical value thereof can be calculated according to the given system admittance values. According to the results of the equivalent LCC-HVDC single feeding system, the active power transmission limits of the LCC-HVDC in the equivalent single feeding system and the hybrid DC double feeding system are compared, and the error result analysis is performed on the critical short-circuit ratio obtained by simulation and the critical short-circuit ratio obtained by the analysis method of the embodiment.
[0058] Table 1 VSC-HVDC control link parameters
[0059]
[0060] Table 2 system network parameters
[0061]
[0062] Table 3 system per unit value
[0063] Table A1 MIDC system per unit value
[0064]
[0065] AsFigure 4 The solid black line represents the curves showing the changes in the transmission limit of LCC-HVDC and the transmission power of VSC-HVDC in an equivalent single-infeed system, while the dashed black line represents the corresponding curves showing the changes in the transmission limit of LCC-HVDC and the transmission power of VSC-HVDC in a hybrid DC dual-infeed system. The figure shows that the power transmission limit of the LCC-HVDC system in the hybrid DC infeed system is very close to that in the equivalent single-infeed system, with a maximum relative error of 6.04%.
[0066] like Figure 5 The curves in the figure show the change of the critical short-circuit ratio with P1 in the hybrid dual-feed system in the PSCAD electromagnetic transient calculation example. The black dashed line represents the curve of the critical short-circuit ratio with P1 obtained by the short-circuit ratio calculation method used in this invention. The two curves are very close, with a maximum error of 2.12%. This proves the effectiveness of the equivalent method proposed in this invention.
[0067] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method of evaluating equivalent short circuit ratio of a hybrid DC feed-in system, characterized by The mixed DC feeding system is a same receiving end power grid fed by a conventional HVDC and a flexible DC power transmission, and the method specifically comprises the following steps: Step 1) according to an AC / DC system power flow equation, a Jacobian matrix of the mixed DC feeding system is written; Step 2) The Jacobian matrix is reduced by matrix elementary transformation and Schur transformation, and the modified power ΔP1, the modified admittance ΔB, the modified reactive voltage sensitivity ΔT are calculated 11 , and the equivalent physical quantities of the conventional high-voltage direct-current single-infeed system including the equivalent power, the equivalent admittance and the equivalent reactive voltage sensitivity are calculated. Step 3) based on a static voltage stability critical condition, a characteristic equation of which a short circuit ratio SCR is an explicit function is obtained, and the short circuit ratio SCR of the mixed DC feeding system under the static voltage stability and a corresponding critical value CSCR are calculated; Step 4) according to a comparison result of the short circuit ratio SCR of the mixed DC feeding system and the critical value CSCR, static voltage stability of the short circuit ratio of the mixed DC feeding system is judged; In the step 1), the Jacobian matrix is as formula (1), wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to the hybrid DC feed-in system, B ij wherein B represents the admittance matrix corresponding to In the step 2), according to formula (2), matrix elementary transformation and Schur transformation are performed, In the step 2), according to formula (3), physical quantities including equivalent power, equivalent admittance and equivalent reactive voltage sensitivity of the equivalent conventional HVDC single feeding system are calculated, Equivalent power: P1' = P1 + ΔP1 Equivalent admittance: B 11 ′ = B 11 + ΔB 11 Equivalent reactive voltage sensitivity: T' = T + ΔT (3) In the step 4), according to the comparison result of the short circuit ratio SCR of the mixed DC feeding system and the critical value CSCR, static voltage stability of the short circuit ratio of the mixed DC feeding system is specifically as follows: When the actual short circuit ratio SCR of the mixed DC feeding system is greater than the critical short circuit ratio CSCR, the mixed DC feeding system is static voltage stable, and the conventional HVDC can be stably operated at a rated operating point; When the actual short circuit ratio SCR of the mixed DC feeding system is less than the critical short circuit ratio CSCR, the mixed DC feeding system is static voltage unstable, and it is determined that the output power of the conventional HVDC cannot reach the rated power; when the actual short circuit ratio SCR of the mixed DC feeding system is equal to the critical short circuit ratio CSCR, the mixed DC feeding system is critical static voltage stable, and it is determined that the maximum output power of the conventional HVDC is the rated power.
2. The method of evaluating equivalent short circuit ratio of a hybrid DC feed-in system according to claim 1, characterized in that The step 3) in the Jacobian matrix J sys The characteristic equation of the critical condition of static voltage stability of the singular corresponding system is: det(J sys ) = B 11 ′U1 2 × B 11 ′U1 2 + P1U1 2 ρT′- P1′ 2 × (B 11 ′U1 2 ) -1 = 0; Based on the above characteristic equation, an explicit function about the short circuit ratio SCR is as formula (4), pT' + p 2 SCR -1 - SCR = 0 SCR = -P1'B 11 (4) Solving formula (4), the short circuit ratio critical value CSCR is represented as: