Online calculation method and analysis system for coupling impedance between multi-feed direct current systems

Abstract

The invention discloses an online calculation method and analysis system for coupling impedance between multi-feed direct current systems, and belongs to the technical field of high-voltage direct current transmission control. The online calculation method of the coupling impedance is provided for solving the problems that the coupling impedance of a multi-feed direct current system under large-scale new energy access is complex and changeable, and off-line calculation is difficult, and the method further comprises the steps that an equivalent model of the multi-feed high-voltage direct current power transmission system is constructed; on the basis of the equivalent model, the coupling impedance can be calculated in real time to use the electrical quantity in a steady state. The method not only can be used for researching the interactive coupling characteristic in a large power grid, but also can be used for analyzing the risk of an anticipated accident so as to cope with a complex and changeable operation mode of new energy.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-voltage direct current transmission control and analysis, and in particular relates to an online calculation method and analysis system for coupling impedance between multi-fed direct current systems. Background Art

[0002] High-voltage direct current (LCC-HVDC) transmission is widely used due to its advantages of long transmission distances and large transmission capacity. With the development of high-voltage transmission and multi-regional power grids, multiple LCC-HVDC systems are densely connected to the same grid, forming multi-infeed HVDC systems. Currently, research on multi-infeed HVDC systems focuses primarily on multi-infeed systems. To evaluate the interactions between multi-infeed systems, the multi-infeed interaction factor (MIIF) has been proposed, and MIIF calculation methods based on the power flow Jacobian matrix have been widely studied. Prior art also proposes a method to derive the MIIF based on a simplified power flow Jacobian matrix for comprehensive analysis of voltage interactions. A calculation method for the multi-infeed voltage interaction factor (MIIF) based on a hybrid multi-infeed system model is proposed, which can effectively evaluate the voltage interactions between LCC-HVDC and flexible direct current (VSC-HVDC). Furthermore, prior art uses the obtained MIIF to equate a multi-infeed system to a virtual single-infeed system. The MIIF can also be used to study commutation failures in multi-infeed HVDC systems.

[0003] Currently, most research on multi-infeed systems is based on MIIF, but the calculation of coupling impedances between multi-infeed systems has not been studied. This makes rapid equivalent modeling of multi-infeed systems difficult. To address this issue, this paper proposes a method for calculating coupling impedances between multi-infeed DC systems. This method not only enables rapid equivalent modeling of multi-infeed systems but can also be used to study the interactive coupling characteristics within large power grids and analyze the risks of anticipated accidents. Summary of the Invention

[0004] Purpose of the Invention: This invention provides an online calculation method for the coupling impedance between multi-fed DC systems. This method calculates the coupling impedance using the equivalent parameters and steady-state electrical quantities of each system. This method can be used to analyze the cross-coupling characteristics between multi-fed DC systems and also enables rapid equivalent modeling of the systems. The invention also provides a multi-fed DC analysis system that performs analysis and simulation based on the constructed equivalent model and the method.

[0005] Technical solution: An online calculation method for the coupling impedance between multi-fed DC systems. This method represents the coupling relationship between multi-fed DC systems by equivalent power sources and equivalent impedances, and only one coupling impedance is used to characterize the coupling degree between any two DC lines.

[0006] Based on the calculation of the equivalent model, considering that the reactive power exchange between the multi-fed DC systems is balanced under normal operation, the reactive power calculation relationship for any node k in the equivalent model exists:

[0007]

[0008] Where Q drk Indicates the reactive power consumed by the rectifier corresponding to node k, Q ck is the reactive power generated by the reactive power compensation device corresponding to node k, Q ack is the reactive interaction between the AC and DC on the rectifier side corresponding to node k, Q ki Represents the reactive power transmitted from node k to other nodes i on the rectifier-side coupling impedance;

[0009] In a multi-feed DC system, the voltage at any point is expressed as:

[0010]

[0011] Where, k∈(1,n), U Lrk represents the commutation bus voltage on the rectifier side corresponding to node k, Z k(k+1) represents the equivalent impedance of the AC system from node k to node k+1, Q k(k+1) Represents the reactive power transmitted from node k to node k+1 on the rectifier-side coupling impedance;

[0012] Based on the relationship between reactive power and impedance, the object is calculated at node k, and then any node m is selected to construct the reactive power Q between the two. km Relationship:

[0013]

[0014] By measuring the equivalent power supply of the sending-end AC system, the commutation bus voltage on the rectifier side, the equivalent impedance of the sending-end AC system, the reactive interaction between AC and DC on the rectifier side, and the reactive power transmitted on the coupling impedance on the rectifier side, the simultaneous equations (1) to (3) can realize the online calculation of the coupling impedance between multi-feed DC systems, and the electrical quantities in steady state are calculated in real time based on the coupling impedance.

[0015] The above method is used for double-fed and triple-fed DC systems. The specific calculation is as follows:

[0016] Formula (1) and formula (2) are expressed as:

[0017] Q 12 =Q c1 +Q ac1 -Q dr1 (4)

[0018]

[0019] Substituting equation (4) into equation (5), we can get the coupling impedance Z of the double-fed system: 12 can be calculated as:

[0020]

[0021] For a three-feed DC system, equations (1) and (2) are expressed as:

[0022]

[0023] According to formula (7), Z 12 and Z 13 The relationship is expressed as follows:

[0024]

[0025] a, b, c are represented as:

[0026]

[0027] Combining equations (5) and (3), Z 13 is calculated as:

[0028]

[0029] The meanings of a and c in formula (10) are the same as those in formula (9). Substituting formula (10) into formula (8), Z 12 can be calculated as:

[0030]

[0031] Substituting equation (11) into equation (8), Z 13 is calculated as:

[0032]

[0033] Similarly, Z 23 Arranged as:

[0034]

[0035] Among them, d and e are expressed as:

[0036]

[0037] Through the above calculation, this method can realize the online calculation of the coupling impedance of the double-fed and triple-fed DC systems.

[0038] Furthermore, the method includes constructing an equivalent model of a multi-feed HVDC transmission system, representing the interactive coupling relationship between any two DC lines by connecting them through coupling impedances, and expressing the degree of coupling by impedance. Based on this, the method can analyze the coupling characteristics of the multi-feed DC system.

[0039] The present invention provides a multi-fed DC online analysis system for analyzing the interactive coupling characteristic relationship between multi-fed DC systems. The system constructs an equivalent model of a multi-fed HVDC transmission system according to the described method, and performs online calculation of the coupling impedance between multi-fed DC systems based on the described method.

[0040] Beneficial Effects: To address the existing problem of inability to calculate coupling impedance between multi-fed DC systems, the present invention proposes a method for calculating coupling impedance between multi-fed DC systems. By using the equivalent model constructed using the method described herein to calculate coupling impedance, it is also possible to calculate equivalent parameters and steady-state electrical quantities passing through each system. This method can be used to analyze the cross-coupling characteristics between multi-fed DC systems and also enables rapid equivalent modeling of the systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is the distribution of some HVDC transmission lines in a certain area;

[0042] Figure 2 is the coupling relationship between multi-feed DC systems;

[0043] Figure 3 It is an equivalent model of a multi-feed HVDC transmission system. DETAILED DESCRIPTION

[0044] This paper addresses the complex and variable coupling impedances of multi-fed DC systems under large-scale renewable energy integration, making offline calculation difficult. This paper proposes an online calculation method for coupling impedances between multi-fed DC systems. This method enables online calculation of coupling impedances and enables real-time calculation and analysis of steady-state electrical quantities. This method can be used not only to study the interactive coupling characteristics within large power grids but also to analyze the risks of anticipated accidents, addressing the complex and variable operation of renewable energy sources.

[0045] Combine Figure 1In the scenario shown, based on factors such as geographic location, the grid layout can be roughly divided into six major grids: Northwest China, North China, Northeast China, Southwest China, Central China, and East China. This creates a multi-feed DC system with the Northwest and Southwest grids serving as energy transmission bases, and a multi-feed DC system with the Central China and East China grids serving as load centers. Multi-circuit DC systems create closer electrical connections between DC groups at the sending or receiving end.

[0046] For a multi-fed DC system, if a DC line experiences voltage fluctuations, other DC lines in the area will also be affected accordingly. The extent of the impact can be expressed by the magnitude of the coupling impedance. If the impact is large, it means that the disturbed DC line is close to the other DC lines, and the coupling impedance is small; if the impact is small, it means that the disturbed DC line is far away from the other DC lines, and the coupling impedance is large. Moreover, there is an interactive coupling relationship between any two DC lines in this area. Figure 1 For example, the coupling relationship between multi-feed DC systems can be Figure 2 express.

[0047] Figure 2 The left frame in the figure represents the equivalent power source and equivalent impedance of the multi-feed DC system, the middle frame represents the coupling impedance relationship between the multi-feed DC systems, and the right frame represents the transformer and converter station of the multi-feed DC system. Figure 2 It can be seen that any two DC lines are connected by a coupling impedance, and the degree of coupling can be reflected by the impedance. Therefore, in order to facilitate the analysis of the coupling characteristics of the multi-feed DC system, any two DC lines can be characterized by only one coupling impedance. Figure 2 The coupling relationship between the multi-feed DC systems in Figure 3 express.

[0048] exist Figure 3 In the example, there are n high-voltage direct current transmission lines. The subscripts m and k represent any two nodes in the AC / DC system, m, k∈[1,n], E1, E m , E k and E n Both represent the equivalent power of the AC system at the sending end of each node (or power transmission path); U Lrm 、U Lrk and U Lrn Corresponding to the commutation bus voltage on the rectifier side; Z m , Z k and Z n The equivalent impedance of the sending-end AC system on the path corresponding to each node; Z mk , Z kn and Z mn is the coupling impedance between different AC systems; Q acm , Q ack and Q acnis the reactive interaction between AC and DC on the rectifier side; Q drm ,Q drk ,Q drn is the reactive power consumed by the rectifier; Q cm , Q ck and Q cn is the reactive power generated by the reactive compensation device; Q mk , Q kn and Q mn It is the reactive power transmitted on the coupling impedance on the rectifier side.

[0049] Combining the above technical solutions and mathematical relationships, in formula (1), the reactive power Q transmitted from node k to other node i on the rectifier side coupling impedance is ki is the object to be solved, and other variables are obtained through measurement. Then, the solution is performed based on the relationship between formula (2) and formula (3) as the constraint relationship for solution. For formula (3), the present invention provides a combination of Figure 3 The equivalent model of gives the relationship between reactive power and impedance, which is the necessary connection between equation (2) and equation (1).

[0050] Based on the above technical solution, the following experimental analysis is provided below.

[0051] Based on the CIGRE Benchmark model, models of two- and three-fed DC systems were built on the PSCAD test platform. The actual and calculated coupling impedances for the two- and three-fed DC systems are shown in Tables 1 and 2.

[0052] Table 1 Coupling impedance in two-fed DC system

[0053] Case A B C D <![CDATA[Z 12 Actual value / Ω]]> 31.4 94.2 157.0 219.8 <![CDATA[Z 12 Calculated value / Ω]]> 32.3 94.7 157.1 219.2 error / % 2.87％ 0.53％ 0.06％ 0.27％

[0054] Coupling impedance Z 12 The size of Z can indicate the distance between two DC systems. 12 The larger the value, the farther the distance between the two DC systems is, and the smaller the interaction is. In Table 1, four cases are verified.

[0055] In Case A: U Lr1 =1.064pu,U Lr2 =1.041pu,Q c1 =961.9Mvar, Q ac1 =-169.3Mvar, Q dr1 =704.4Mvar.

[0056] In Case B: U Lr1 =1.076pu,U Lr2 =1.032pu,Q c1 =982.5Mvar, Q ac1=-199.3Mvar;, Q dr1 =726.1Mvar.

[0057] In Case C: U Lr1 =1.082pu,U Lr2 =1.027pu,Q c1 =992.5Mvar, Q ac1 =-212.1Mvar; Q dr1 =737.6Mvar.

[0058] In Case D: U Lr1 =1.083pu,U Lr2 =1.024pu,Q c1 =994.8Mvarr, Q ac1 =-219.5Mvar; Q dr1 =742.5Mvar.

[0059] As can be seen from Table 1, the maximum error between the calculated and actual coupling impedance values ​​in the four cases is within 3%, and the minimum is 0.06%. The cases in Table 1 verify the correctness of the proposed method in a two-fed DC system.

[0060] Table 2 Coupling impedance in three-fed DC system

[0061] Coupling impedance <![CDATA[Z 12 ]]> <![CDATA[Z 13 ]]> <![CDATA[Z 23 ]]> Actual value / Ω 94.2 / 219.8 125.6 / 270.5 75.4 / 188.4 Calculated value / Ω 96.1 / 214.7 125.2 / 282.2 72.8 / 195.9 error / % 2.02％ / 2.32％ 0.19％ / 4.32％ 1.27％ / 3.98％

[0062] As can be seen from Table 2, the two cases are set in a three-infeed DC system.

[0063] Case A:Z 12 It is 94.2 euros; Z 13 It is 125.6 ohms; Z 23 It is 75.4 euros.

[0064] Case 2: Z 12 It is 219.8 euros; Z 13 It is 270.5 euros; Z 23 It is 188.4 euros.

[0065] In steady state, the electrical quantities in Case 1 are: U Lr1 =1.074pu; U Lr2 =1.055pu; U Lr3 =1.036pu;Q c1 =977.9Mvar, Q dr1 =717.3Mvar, Q ac1 =-194.6Mvar, Q c3 =673.1Mvar, Q dr3 =642.7Mvar, Qac3 =-97.2Mvar.

[0066] In steady state, the electrical quantities in Case B are U Lr1 =1.082pu; U Lr2 =1.052pu; U Lr3 =1.029pu;Q c1 =899.9Mvar; Q dr1 =734.9Mvar; Q ac1 =-214.5Mvar, Q c3 =663.5Mvar, Q dr3 =622.6Mvar, Q ac3 =-78.3Mvar.

[0067] As can be seen from Table 2, the maximum error between the calculated value and the actual value of the coupling impedance in both cases is within 5%, and the minimum can reach 0.2%. The main reason for the error is that the influence of active power is ignored in Equation (2). The simulation results in Tables 1 and 2 verify the correctness of the proposed method in multi-feed DC systems. By measuring U Lr1 、U Lr2 and UL r3, Z 12 can be calculated.

[0068] To further verify the applicability of the proposed method, two-infeed and three-infeed DC system models were established in the PSCAD platform. The actual and calculated values ​​of the coupling impedance for the two-infeed and three-infeed DC systems are shown in Tables 3 and 4.

[0069] Table 3 Coupling impedance in two-feed DC system

[0070] Case A B C D <![CDATA[Z 12 Actual value / Ω]]> 62.8 125.6 188.4 251.2 Calculated value / Ω 62.1 125.4 187.2 250.8 error / % 1.11％ 0.16％ 0.64％ 0.16％

[0071] In Case A, U Li1 =1.081pu,U Li2 =1.024pu,Q c1 =921.2Mvar, Q ac1 =-305.7Mvar; Q di1 =565.8Mvar.

[0072] In Case B, U Li1 =1.087pu,U Li2 =1.014pu,Q c1 =938.8Mvar, Q ac1 =-334.6Mvar; Q di1 =573Mvar.

[0073] In Case C: ULi1 =1.094pu,U Li2 =1.008pu,Q c1 =947.2Mvar, Q ac1 =-348Mvar; Q di1 =574.8Mvar.

[0074] In Case D: U Li1 =1.097pu,U Li2 =1.005pu,Q c1 =955.5Mvar, Q ac1 =-360.8Mvar; Q di1 =574.4Mvar.

[0075] Table 4 Coupling impedance in three-feed DC system

[0076] Coupling impedance <![CDATA[Z 12 ]]> <![CDATA[Z 13 ]]> <![CDATA[Z 23 ]]> Actual value / Ω 125.6 / 188.4 157.0 / 235.6 94.2 / 251.2 Calculated value / Ω 123.9 / 182.4 160.0 / 245.2 93.1 / 256.3 error / % 1.35％ / 3.18％ 1.91％ / 4.07％ 1.17％ / 2.03％

[0077] As can be seen from Table 4, the two cases are set in a three-infeed DC system.

[0078] Case A:Z 12 It is 125.6 ohms; Z 13 It is 157.0 euros; Z 23 It is 94.2 euros.

[0079] Case 2: Z 12 It is 188.4 euros; Z 13 It is 219.8 euros; Z 23 It is 251.2 euros.

[0080] In steady state, the electrical quantities in Case 1 are U Li1 =1.09pu,U Li2 =1.051pu; U Li3 =1.023pu;Q c1 =934Mvar, Q ac1 =570.3Mvar; Q ac1 =-323.4Mvar, Q c3 =651.1Mvar, Q dr3 =543.8Mvar, Q ac3 =-144.8Mvar.

[0081] In steady state, the electrical quantities in Case B are U Li1 =1.096pu,U Li2 =1.054pu,U Li3 =1.015pu,Q c1 =943.4Mvar, Q dr1=570.6Mvar, Q ac1 =-342.7Mvar, Q c3 =640.8Mvar, Q dr3 =543.1Mvar, Q ac3 =-123.6Mvar.

[0082] The simulation results in Tables 3 and 4 show that for a two-infeed DC system, the maximum error of the proposed calculation method is within 1.2%; for a three-infeed DC system, the maximum error is within 5%. Tables 3 and 4 verify the effectiveness of the proposed calculation method for multi-infeed DC systems.

[0083] In summary, this invention provides an online calculation method for the coupling impedance between multi-fed DC systems in large-scale renewable energy integration. The coupling impedance can be calculated in real time using steady-state electrical quantities. Simulation results demonstrate that the proposed online calculation method is effective in calculating the coupling impedance. Future research will focus on equivalent modeling of multi-fed DC systems with high renewable energy penetration.

Claims

1. An online calculation method for coupling impedance between multi-fed DC systems, characterized in that: This method represents the coupling relationship between multi-feed DC systems by equivalent power sources and equivalent impedances, and only one coupling impedance is used to characterize the coupling degree between any two DC lines. Based on the calculation of the equivalent model, considering that the reactive power exchange between the multi-fed DC systems is balanced under normal operation, the reactive power calculation relationship for any node k in the equivalent model exists: Where Q drk Indicates the reactive power consumed by the rectifier corresponding to node k, Q ck is the reactive power generated by the reactive power compensation device corresponding to node k, Q ack is the reactive interaction between the AC and DC on the rectifier side corresponding to node k, Q ki Represents the reactive power transmitted from node k to other nodes i on the rectifier-side coupling impedance; In a multi-feed DC system, the voltage at any node is expressed as: Where, k∈[1,n], U Lrk represents the commutation bus voltage on the rectifier side corresponding to node k, Z k(k+1) represents the equivalent impedance of the AC system from node k to node k+1, Q k(k+1) Represents the reactive power transmitted from node k to node k+1 on the rectifier-side coupling impedance; Based on the relationship between reactive power and impedance, the object is calculated at node k, and then any node m is selected to construct the reactive power Q between the two. km Relationship: By measuring the equivalent power supply of the sending-end AC system, the commutation bus voltage on the rectifier side, the equivalent impedance of the sending-end AC system, the reactive interaction between AC and DC on the rectifier side, and the reactive power transmitted on the coupling impedance on the rectifier side, the simultaneous equations (1) to (3) can realize the online calculation of the coupling impedance between multi-feed DC systems, and the electrical quantities in the steady state can be obtained based on the real-time calculation of the coupling impedance.

2. The online calculation method for coupling impedance between multi-fed DC systems according to claim 1, characterized in that: For doubly-fed and triple-fed DC systems, the specific calculation of this method is as follows: Formula (1) and formula (2) are expressed as: Q 12 =Q c1 +Q ac1 -Q dr1 (4) Substituting equation (4) into equation (5), we can get the coupling impedance Z of the double-fed system: 12 can be calculated as: For a three-feed DC system, equations (1) and (2) are expressed as: According to formula (7), Z 12 and Z 13 The relationship is expressed as follows: a, b, c are represented as: Combining equations (5) and (3), Z 13 is calculated as: The meanings of a and c in formula (10) are the same as those in formula (9). Substituting formula (10) into formula (8), Z 12 can be calculated as: Substituting equation (11) into equation (8), Z 13 is calculated as: Similarly, Z 23 Arranged as: Among them, d and e are expressed as: Through the above calculation, this method can realize the online calculation of the coupling impedance of the double-fed and triple-fed DC systems.

3. The online calculation method for coupling impedance between multi-fed DC systems according to claim 1 or 2, characterized in that: The method includes constructing an equivalent model of a multi-feed high-voltage direct current transmission system, connecting any two direct currents through coupling impedance to represent the mutual coupling relationship, and expressing the degree of coupling by impedance. Based on this method, the coupling characteristics of the multi-feed direct current system can be analyzed.

4. The online calculation method for coupling impedance between multi-fed DC systems according to claim 1, characterized in that: The equivalent model of this method for a multi-feed HVDC system is shown in Figure 3.

5. A multi-fed DC online analysis system for analyzing the interaction coupling characteristics between multi-fed DC systems, characterized in that: The system constructs an equivalent model of a multi-feed high-voltage direct current transmission system according to the method described in any one of claims 1 to 3, and performs online calculation of coupling impedances between multi-feed direct current systems based on the method.

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