Method and device for calculating actual inertia constant value of power grid

Abstract

The application discloses a kind of actual inertia constant numerical value of power grid and its calculation method and device, the method includes: obtaining admittance matrix of two-machine system, and first electromagnetic power equation is calculated according to admittance matrix;According to the first electromagnetic power equation, the equivalent inertia time constant calculation formula of two-machine system is calculated;According to the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes of multi-machine system, the expression of second electromagnetic power is calculated;Wherein, the expression of second electromagnetic power includes the electromagnetic power influence between multiple generator nodes;According to the expression of second electromagnetic power and the equivalent inertia time constant calculation formula of two-machine system, the equivalent inertia time constant of multi-machine system is calculated.The application embodiment improves the calculation precision of power grid inertia constant numerical value, reflects the real-time inertia level of power grid, and guarantees the stability of power grid.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and apparatus for calculating the actual inertia constant of a power grid. Background Technology

[0002] The inertial time constant based on the generator's rated capacity is usually called the rated inertial time constant. When the generator is unloaded, if the prime mover delivers a value equal to the rated torque M... N constant torque (M) T* =1) is added to the rotor, then the rotor will move from a stationary state (Ω) * =0) Start-up until the speed reaches the rated value (Ω) * The time required to achieve 1) is the rated inertial time constant of the generator set.

[0003] The inertia constant reflects the frequency response at the network inertia center. Although the network topology is also included when calculating the equivalent system inertia center, this method of calculating the equivalent inertia constant of the whole network means that the equivalent inertia is a constant as long as the parameters of the synchronous machine in the system do not change, regardless of the power grid structure or system operating state. Only the position of the inertia center changes, which cannot intuitively reflect the influence of the network and operating state on the system inertia level.

[0004] As can be seen from the above, the existing methods for calculating the power grid inertia constant do not yield accurate numerical values ​​and cannot reflect the real-time inertia level of the power grid. This makes it impossible for power grid operators and dispatchers to accurately grasp the current system inertia level and take targeted measures such as virtual inertia compensation or other frequency regulation measures, ultimately leading to low power grid stability. Summary of the Invention

[0005] This invention provides a method and apparatus for calculating the actual inertia constant of a power grid, which improves the calculation accuracy of the inertia constant, reflects the real-time inertia level of the power grid, and ensures the stability of the power grid.

[0006] The first aspect of this application provides a method for calculating the actual inertia constant of a power grid, including:

[0007] Obtain the admittance matrix of the two-engine system, and calculate the first electromagnetic power equation based on the admittance matrix;

[0008] Based on the first electromagnetic power equation, the formula for calculating the equivalent inertial time constant of the two-machine system is obtained;

[0009] Based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system, the expression for the second electromagnetic power is calculated; wherein, the expression for the second electromagnetic power includes the electromagnetic power influence between multiple generator nodes.

[0010] Based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of a two-machine system, the equivalent inertial time constant of a multi-machine system is calculated.

[0011] In one possible implementation of the first aspect, the first electromagnetic power equation is calculated based on the admittance matrix, specifically as follows:

[0012] The admittance matrix is ​​shown below:

[0013]

[0014]

[0015] The two-machine system includes a first generator and a second generator; Y 11 Y is the self-admittance of the first generator node. 22 Y is the self-admittance of the second generator node. 12 X is the mutual admittance between the first generator node and the second generator node; d1 X is the equivalent reactance of the first generator. T1 X is the equivalent reactance of the transformer connected to the first generator in the system. L1 X is the equivalent reactance of the line connecting the first generator to the system. d2 X is the equivalent reactance of the second generator. T2 X is the equivalent reactance of the transformer connected to the second generator in the system. L2 R is the equivalent reactance of the line connecting the second generator to the system. L This is the equivalent resistance to ground of the line;

[0016] The first electromagnetic power equation includes: the electromagnetic power P of the first generator. e1 The expression for the electromagnetic power P of the second generator e2 The expression for the electromagnetic power P of the first generator; e1 The expression for the electromagnetic power P of the second generator e2 The expression is as follows:

[0017]

[0018]

[0019] Where, δ 12=δ1-δ2, E1 is the potential amplitude of the first generator; E2 is the potential amplitude of the second generator; δ1 is the potential angle difference of the first generator; δ2 is the potential angle difference of the second generator; B 12 G represents the susceptance value of the corresponding element in the power network admittance matrix; 12 This represents the conductance value of the corresponding element in the power network admittance matrix.

[0020] In one possible implementation of the first aspect, the formula for calculating the equivalent inertial time constant of the two-machine system is obtained based on the first electromagnetic power equation, specifically as follows:

[0021] Based on the electromagnetic power P of the first generator e1 The expression yields the change in electromagnetic power ΔP of the first generator. e1 The expression is as follows:

[0022] ΔP e1 =E1E2Δδ 12 (B 12 cosδ 120 -G 12 sinδ 120 );

[0023] Where, δ 120 Δδ represents the potential angle difference between the first and second generators before the inertial response. 12 This represents the potential angle difference between the first and second generators after the inertial response.

[0024] According to the electromagnetic power P of the second generator e2 The expression yields the change in electromagnetic power ΔP of the second generator. e2 The expression is as follows:

[0025] ΔP e2 =E1E2Δδ 21 (B 12 cosδ 210 -G 12 sinδ 210 );

[0026] Where, δ 210 Δδ represents the potential angle difference between the second and first generators before the inertial response. 21 This represents the potential angle difference between the second generator and the first generator after the inertial response.

[0027] The change in electromagnetic power ΔP of the first generator e1 The change in electromagnetic power ΔP of the second generator e2Substituting these values ​​into the formula for calculating the total inertial support energy of the two-engine system, the formula for calculating the equivalent inertial time constant of the two-engine system is obtained, as shown below:

[0028]

[0029] Among them, H i Let be the rated inertia constant of the i-th generator;

[0030]

[0031] Wherein, H1 is the rated inertia constant of the first generator, and H2 is the rated inertia constant of the second generator;

[0032] Due to Δδ 12 =-Δδ 21 The formula for calculating the equivalent inertial time constant of the two-machine system is further simplified to the following formula:

[0033]

[0034] Among them, △PH av,sys The total inertial support energy for the two-engine system; H av,sys1 Let be the equivalent inertial time constant of the two-machine system.

[0035] In one possible implementation of the first aspect, the expression for the second electromagnetic power is calculated based on the first electromagnetic power equation and the potential amplitude and potential angle difference of the multiple generator nodes in the multi-machine system, as shown below:

[0036]

[0037] Among them, P ei E represents the electromagnetic power of generator i in a multi-machine system (i.e., the second electromagnetic power); i Let Ei be the potential amplitude at generator node i; Ej be the potential amplitude at generator node j; δ i δ represents the potential angle difference at generator node i; j B represents the potential angle difference at generator node j; ij G represents the susceptance value of the corresponding element in the power network admittance matrix; ij This represents the conductance value of the corresponding element in the power network admittance matrix.

[0038] In one possible implementation of the first aspect, the equivalent inertial time constant of the multi-machine system is calculated based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system, specifically as follows:

[0039] According to the second electromagnetic power P eiThe expression yields the change in electromagnetic power ΔP of the i-th generator in a multi-machine system. ei The expression is as follows:

[0040]

[0041] Among them, P ei P' represents the electromagnetic power of generator i in the multi-machine system, which is also the output electromagnetic power of generator i in the multi-machine system before the inertial response; ei δ represents the output electromagnetic power of generator i in the multi-machine system after inertial response. ij0 δ represents the potential angle difference between nodes i and j before the inertial response. ij This represents the potential angle difference between nodes i and j after the inertial response.

[0042] The change in electromagnetic power ΔP of the i-th generator in the multi-machine system ei Substituting these values ​​into the formula for calculating the total inertial support energy of a two-machine system, the equivalent inertial time constant H of the multi-machine system is obtained. av,sys2 As shown below:

[0043]

[0044] A second aspect of this application provides a device for calculating the actual inertia constant of a power grid, comprising: a first calculation module, a second calculation module, a third calculation module, and a fourth calculation module;

[0045] The first calculation module is used to obtain the admittance matrix of the two-machine system and calculate the first electromagnetic power equation based on the admittance matrix.

[0046] The second calculation module is used to calculate the equivalent inertial time constant calculation formula of the two-machine system based on the first electromagnetic power equation;

[0047] The third calculation module is used to calculate the expression for the second electromagnetic power based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system; wherein, the expression for the second electromagnetic power includes the electromagnetic power influence between multiple generator nodes.

[0048] The fourth calculation module is used to calculate the equivalent inertial time constant of the multi-machine system based on the expression of the second electromagnetic power and the calculation formula of the equivalent inertial time constant of the two-machine system.

[0049] In one possible implementation of the second aspect, the first electromagnetic power equation is calculated based on the admittance matrix, specifically as follows:

[0050] The admittance matrix is ​​shown below:

[0051]

[0052]

[0053] The two-machine system includes a first generator and a second generator; Y 11 Y is the self-admittance of the first generator node. 22 Y is the self-admittance of the second generator node. 12 X is the mutual admittance between the first generator node and the second generator node; d1 X is the equivalent reactance of the first generator. T1 X is the equivalent reactance of the transformer connected to the first generator in the system. L1 X is the equivalent reactance of the line connecting the first generator to the system. d2 X is the equivalent reactance of the second generator. T2 X is the equivalent reactance of the transformer connected to the second generator in the system. L2 R is the equivalent reactance of the line connecting the second generator to the system. L This is the equivalent resistance to ground of the line;

[0054] The first electromagnetic power equation includes: the electromagnetic power P of the first generator. e1 The expression for the electromagnetic power P of the second generator e2 The expression for the electromagnetic power P of the first generator; e1 The expression for the electromagnetic power P of the second generator e2 The expression is as follows:

[0055]

[0056]

[0057] Where, δ 12 =δ1-δ2, E1 is the potential amplitude of the first generator; E2 is the potential amplitude of the second generator; δ1 is the potential angle difference of the first generator; δ2 is the potential angle difference of the second generator; B 12 G represents the susceptance value of the corresponding element in the power network admittance matrix; 12 This represents the conductance value of the corresponding element in the power network admittance matrix.

[0058] In one possible implementation of the second aspect, the formula for calculating the equivalent inertial time constant of the two-machine system is obtained based on the first electromagnetic power equation, specifically as follows:

[0059] Based on the electromagnetic power P of the first generator e1 The expression yields the change in electromagnetic power ΔP of the first generator. e1 The expression is as follows:

[0060] ΔP e1 =E1E2Δδ 12 (B 12 cosδ 120 -G 12 sinδ 120 );

[0061] Where, δ 120 Δδ represents the potential angle difference between the first and second generators before the inertial response. 12 This represents the potential angle difference between the first and second generators after the inertial response.

[0062] According to the electromagnetic power P of the second generator e2 The expression yields the change in electromagnetic power ΔP of the second generator. e2 The expression is as follows:

[0063] ΔP e2 =E1E2Δδ 21 (B 12 cosδ 210 -G 12 sinδ 210 );

[0064] Where, δ 210 Δδ represents the potential angle difference between the second and first generators before the inertial response. 21 This represents the potential angle difference between the second generator and the first generator after the inertial response.

[0065] The change in electromagnetic power ΔP of the first generator e1 The change in electromagnetic power ΔP of the second generator e2 Substituting these values ​​into the formula for calculating the total inertial support energy of the two-engine system, the formula for calculating the equivalent inertial time constant of the two-engine system is obtained, as shown below:

[0066]

[0067] Among them, H i Let be the rated inertia constant of the i-th generator;

[0068]

[0069] Wherein, H1 is the rated inertia constant of the first generator, and H2 is the rated inertia constant of the second generator;

[0070] Due to Δδ 12 =-Δδ 21 The formula for calculating the equivalent inertial time constant of the two-machine system is further simplified to the following formula:

[0071]

[0072] Among them, △PH av,sys The total inertial support energy for the two-engine system; H av,sys1 Let be the equivalent inertial time constant of the two-machine system.

[0073] In one possible implementation of the second aspect, the expression for the second electromagnetic power is calculated based on the first electromagnetic power equation and the potential amplitude and potential angle difference of the multiple generator nodes in the multi-machine system, as shown below:

[0074]

[0075] Among them, P ei E represents the electromagnetic power of generator i in a multi-machine system (i.e., the second electromagnetic power); i Let Ei be the potential amplitude at generator node i; Ej be the potential amplitude at generator node j; δ i δ represents the potential angle difference at generator node i; j B represents the potential angle difference at generator node j; ij G represents the susceptance value of the corresponding element in the power network admittance matrix; ij This represents the conductance value of the corresponding element in the power network admittance matrix.

[0076] In one possible implementation of the second aspect, the equivalent inertial time constant of the multi-machine system is calculated based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system, specifically as follows:

[0077] According to the second electromagnetic power P ei The expression yields the change in electromagnetic power ΔP of the i-th generator in a multi-machine system. ei The expression is as follows:

[0078]

[0079] Among them, P ei P' represents the electromagnetic power of generator i in the multi-machine system, which is also the output electromagnetic power of generator i in the multi-machine system before the inertial response; ei δ represents the output electromagnetic power of generator i in the multi-machine system after inertial response. ij0 δ represents the potential angle difference between nodes i and j before the inertial response. ij This represents the potential angle difference between nodes i and j after the inertial response.

[0080] The change in electromagnetic power ΔP of the i-th generator in the multi-machine system ei Substituting these values ​​into the formula for calculating the total inertial support energy of a two-machine system, the equivalent inertial time constant H of the multi-machine system is obtained.av,sys2 As shown below:

[0081]

[0082] Compared to existing technologies, this invention provides a method and apparatus for calculating the actual inertial constant of a power grid. The method includes: obtaining the admittance matrix of a two-machine system; calculating a first electromagnetic power equation based on the admittance matrix; calculating an equivalent inertial time constant calculation formula for the two-machine system based on the first electromagnetic power equation; calculating an expression for a second electromagnetic power based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in a multi-machine system; wherein the expression for the second electromagnetic power includes the electromagnetic power influence between multiple generator nodes; and calculating the equivalent inertial time constant of the multi-machine system based on the expression for the second electromagnetic power and the equivalent inertial time constant calculation formula for the two-machine system.

[0083] Its beneficial effects are as follows: In calculating the actual inertia constant of the power grid, the influence of electromagnetic power between generators is considered, ensuring that the actual inertia constant reflects the real-time inertia level of the power grid. Therefore, the actual inertia constant calculated in this embodiment of the invention has higher accuracy. A more accurate actual inertia constant helps power grid operators better understand the current system inertia level in the context of continuously decreasing inertia in new power systems. This allows for targeted inertia compensation measures, such as virtual inertia, or supplementary frequency regulation measures, ensuring the power grid can effectively cope with faults, facilitating stable frequency control, and guaranteeing the safe and stable operation of the power grid. Attached Figure Description

[0084] Figure 1 This is a flowchart illustrating a method for calculating the actual inertia constant of a power grid according to an embodiment of the present invention.

[0085] Figure 2 This is a schematic diagram of the structure of a two-machine system provided in an embodiment of the present invention;

[0086] Figure 3 This is an equivalent impedance diagram of a two-machine system provided in an embodiment of the present invention;

[0087] Figure 4 This is a schematic diagram of the structure of a device for calculating the actual inertia constant of a power grid according to an embodiment of the present invention. Detailed Implementation

[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0089] Reference Figure 1 , Figure 1 This is a flowchart illustrating a method for calculating the actual inertia constant of a power grid according to an embodiment of the present invention, including steps S101-S104:

[0090] S101: Obtain the admittance matrix of the two-machine system, and calculate the first electromagnetic power equation based on the admittance matrix.

[0091] In this embodiment, the calculation of the first electromagnetic power equation based on the admittance matrix specifically involves:

[0092] The admittance matrix is ​​shown below:

[0093]

[0094]

[0095] The two-machine system includes a first generator and a second generator; Y 11 Y is the self-admittance of the first generator node. 22 Y is the self-admittance of the second generator node. 12 X is the mutual admittance between the first generator node and the second generator node; d1 X is the equivalent reactance of the first generator. T1 X is the equivalent reactance of the transformer connected to the first generator in the system. L1 X is the equivalent reactance of the line connecting the first generator to the system. d2 X is the equivalent reactance of the second generator. T2 X is the equivalent reactance of the transformer connected to the second generator in the system. L2 R is the equivalent reactance of the line connecting the second generator to the system. L This is the equivalent resistance to ground of the line;

[0096] The first electromagnetic power equation includes: the electromagnetic power P of the first generator. e1 The expression for the electromagnetic power P of the second generator e2 The expression for the electromagnetic power P of the first generator; e1 The expression for the second generator and the electromagnetic power P e2 The expression is as follows:

[0097]

[0098]

[0099] Where, δ 12 =δ1-δ2, E1 is the potential amplitude of the first generator; E2 is the potential amplitude of the second generator; δ1 is the potential angle difference of the first generator; δ2 is the potential angle difference of the second generator; B 12 G represents the susceptance value of the corresponding element in the power network admittance matrix; 12 This represents the conductance value of the corresponding element in the power network admittance matrix.

[0100] S102: Based on the first electromagnetic power equation, the formula for calculating the equivalent inertial time constant of the two-machine system is obtained.

[0101] In this embodiment, the formula for calculating the equivalent inertial time constant of the two-machine system based on the first electromagnetic power equation is as follows:

[0102] According to the electromagnetic power P of the first generator e1 The expression yields the change in electromagnetic power ΔP of the first generator. e1 The expression is as follows:

[0103] ΔP e1 =E1E2Δδ 12 (B 12 cosδ 120 -G 12 sinδ 120 );

[0104] Where, δ 120 The potential angle difference between the first and second generators before the inertial response; Δδ 12 This represents the potential angle difference between the first and second generators after the inertial response.

[0105] According to the electromagnetic power P of the second generator e2 The expression yields the change in electromagnetic power ΔP of the second generator. e2 The expression is as follows:

[0106] ΔP e2 =E1E2Δδ 21 (B 12 cosδ 210 -G 12 sinδ 210 );

[0107] Where, δ 210Δδ represents the potential angle difference between the second and first generators before the inertial response. 21 This represents the potential angle difference between the second generator and the first generator after the inertial response.

[0108] The change in electromagnetic power ΔP of the first generator e1 and the change in electromagnetic power ΔP of the second generator e2 Substituting these values ​​into the formula for calculating the total inertial support energy of the two-engine system, the formula for calculating the equivalent inertial time constant of the two-engine system is obtained, as shown below:

[0109]

[0110] Among them, H i Let be the rated inertia constant of the i-th generator;

[0111]

[0112] Wherein, H1 is the rated inertia constant of the first generator, and H2 is the rated inertia constant of the second generator;

[0113] Due to Δδ 12 =-Δδ 21 The formula for calculating the equivalent inertial time constant of the two-machine system is further simplified to the following formula:

[0114]

[0115] Among them, ΔPH av，sys H represents the total inertial support energy of the two-machine system. av，sys1 Let be the equivalent inertial time constant of the two-machine system.

[0116] S103: Based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system, the expression for the second electromagnetic power is calculated.

[0117] The expression for the second electromagnetic power includes the electromagnetic power influence between multiple generator nodes.

[0118] In this embodiment, the expression for the second electromagnetic power is calculated based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system, as shown below:

[0119]

[0120] Among them, P ei E represents the electromagnetic power of generator i in a multi-machine system (i.e., the second electromagnetic power); iLet Ei be the potential amplitude at generator node i; Ej be the potential amplitude at generator node j; δ i δ represents the potential angle difference at generator node i; j B represents the potential angle difference at generator node j; ij G represents the susceptance value of the corresponding element in the power network admittance matrix; ij This represents the conductance value of the corresponding element in the power network admittance matrix.

[0121] S104: The equivalent inertial time constant of the multi-machine system is calculated based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system.

[0122] In this embodiment, the calculation of the equivalent inertial time constant of the multi-machine system based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system is specifically as follows:

[0123] According to the second electromagnetic power P ei The expression yields the change in electromagnetic power ΔP of the i-th generator in a multi-machine system. ei The expression is as follows:

[0124]

[0125] Among them, P ei P' represents the electromagnetic power of generator i in the multi-machine system, which is also the output electromagnetic power of generator i in the multi-machine system before the inertial response; ei δ represents the output electromagnetic power of generator i in the multi-machine system after inertial response. ij0 δ represents the potential angle difference between nodes i and j before the inertial response. ij This represents the potential angle difference between nodes i and j after the inertial response.

[0126] The change in electromagnetic power ΔP of the i-th generator in the multi-machine system ei Substituting these values ​​into the formula for calculating the total inertial support energy of a two-machine system, the equivalent inertial time constant H of the multi-machine system is obtained. av,sys2 As shown below:

[0127]

[0128] In a preferred embodiment, the method for calculating the actual inertial constant specifically includes the following steps:

[0129] 1) Determine the output electromagnetic power of the generator before and after the inertial response of the two-machine system:

[0130] For a two-machine system, the schematic diagram of the two-machine system is as follows: Figure 2 As shown, Figure 2This is a schematic diagram of a two-machine system provided in an embodiment of the present invention; the equivalent impedance diagram of the two-machine system is as follows. Figure 3 As shown, Figure 3 This is an equivalent impedance diagram of a two-machine system provided in an embodiment of the present invention. According to... Figure 2 and Figure 3 The rated inertia constants of the synchronous generators are H1 and H2, respectively. Therefore, the admittance matrix of the two-generator system is:

[0131]

[0132] in:

[0133]

[0134] The electromagnetic power expressions for the two generators (including: the electromagnetic power P of the first generator) e1 The expression for the electromagnetic power P of the second generator e2 The expression is:

[0135]

[0136]

[0137] in:

[0138] δ 12 =δ1-δ2; (4)

[0139] Before and after the disturbance, taking the first generator as an example, the change in electromagnetic power ΔP of the first generator. e1 for:

[0140] ΔP e1 =E1E2[B 12 (sinδ 12 -sinδ 120 )+G 12 (cosδ 12 -cosδ 120 (5)

[0141] Where: δ 120 δ represents the difference in voltage angle between the two generators before the disturbance occurs. 12 This represents the difference in voltage angle between the two generators after the inertial support takes effect. Since the inertial support lasts for a short time and the generator rotor speed does not change abruptly, the change in the phase angle difference between the two generators before and after the disturbance is not significant, i.e., Δδ. 12 =δ 12 -δ 120 ≈0, therefore, applying Taylor expansion we have:

[0142] sinδ 12=sin(δ) 120 +Δδ 12 )=sinδ 120 +cosδ 120 Δδ 12 +0(Δδ 12 (6)

[0143] cosδ 12 =cos(δ 120 +Δδ 12 )=cosδ 120 -sinδ 120 Δδ 12 +0(Δδ 12 (7)

[0144] Therefore, equation (5) simplifies to:

[0145] ΔP e1 =E1E2Δδ 12 (B 12 cosδ 120 -G 12 sinδ 120 (8)

[0146] Similarly, the change in electromagnetic power ΔP of the second generator e2 for:

[0147] ΔP e2 =E1E2Δδ 21 (B 12 cosδ 210 -G 12 sinδ 210 (9)

[0148] 2) Considering the inertial time constant of the two-machine system based on the power grid structure:

[0149] According to the law of conservation of system energy, the total actual inertial support energy of the entire system is:

[0150]

[0151] Where ΔP is the total unbalanced power of the system power disturbance event, and H av，sys1 Let ΔP be the equivalent actual inertial time constant of the two-machine system. ei Let be the change in electromagnetic power of generator i in the two-machine system.

[0152] Based on the change in generator electromagnetic power obtained in step 1), substituting it into equation (10) yields the equivalent inertial time constant of the two-machine system as follows:

[0153]

[0154] Due to Δδ 12 =-Δδ 21 ,have:

[0155]

[0156] When the power grid topology changes, it will affect the admittance matrix parameters, leading to B 12 G 12 The change; when the system operating state changes, the potential angle difference δ between the first two nodes in the inertial response. 120 δ 210 The actual inertial time constant will change, thus leading to a change in the actual inertial time constant. Therefore, it can be seen from equation (12) that the actual available inertial time constant of the system is related to the generator's inertial constant H, the network topology, and the current operating state of the system.

[0157] 3) Determine the output electromagnetic power of the generator before and after the inertia response of the multi-machine system:

[0158] By analogy with the derivation methods of the two-machine system in steps 1) and 2), taking an n-node system as an example, we derive the expression for the electromagnetic power of the synchronous generator in a multi-machine system with m generator nodes.

[0159] Analogous to equation (3), instead of considering nodes 1 and 2, the consideration is changed to node i in the multi-machine system and all nodes j except node i. In this case, each node will affect the electromagnetic power expression of synchronous generator i. Therefore, the second part of equation (3) needs to consider the influence of each other node on synchronous generator i, which is different from P in equation (3). ei The second part of the expression should be the sum of the electromagnetic power effects generated by all nodes j except node i, which can be expressed as:

[0160]

[0161] Among them, P ei E represents the electromagnetic power of generator i in a multi-machine system (i.e., the second electromagnetic power); i Let Ei be the potential amplitude at generator node i; Ej be the potential amplitude at generator node j; δ i δ represents the potential angle difference at generator node i; j B represents the potential angle difference at generator node j; ij G represents the susceptance value of the corresponding element in the power network admittance matrix; ij This represents the conductance value of the corresponding element in the power network admittance matrix.

[0162] Assuming the node voltage remains constant at its rated voltage, then:

[0163]

[0164] Among them, P ei P' represents the electromagnetic power of generator i in the multi-machine system, which is also the output electromagnetic power of generator i in the multi-machine system before the inertial response; ei δ represents the output electromagnetic power of generator i in the multi-machine system after inertial response. ij0 δ represents the potential angle difference between nodes i and j before the inertial response. ij This represents the potential angle difference between nodes i and j after the inertial response.

[0165] 4) Considering the inertial time constant of a multi-machine system with a power grid structure:

[0166] Based on the electromagnetic power equation of the multi-machine system generator obtained in step 3), by analogy with equation (11) and using the formula for calculating the inertial time constant, the equivalent inertial constant of the system can be obtained as:

[0167]

[0168] It should be noted that multi-machine systems differ from two-machine systems. In multi-machine systems, there are almost no direct connections between generators. That is, when both i and j represent generator nodes, B ij and G ij Since the Δδ is 0, a set of opposite Δδ values ​​will not appear simultaneously in equation (15). ij and △δ ji Therefore, all Δδ in the formula ij This represents the change in the voltage angle difference between the generator node and its connected nodes before and after the inertia response. Since the inertia response time is very short and the rotor speed does not change abruptly, it is approximately Δδ. ij =△δ, then we have:

[0169]

[0170] According to equation (16), the inertia level of the multi-machine system that actually provides inertia support for the power impedance frequency change can be calculated, which is the actual inertia constant and also the final value of the inertia assessment. The actual inertia constant can reflect the influence of the power grid topology, parameters, and operating status on the actual inertia level of the system.

[0171] In step 2), the inertial time constant calculation method of the two-machine system is optimized by considering the influence of factors such as power grid structure and system operating status. In step 4), the inertial time constant calculation method considering the influence of network structure is extended to multi-machine power networks to obtain the equivalent inertial time constant of the power grid.

[0172] This invention, in calculating the actual inertia constant, considers factors such as the power grid structure and the mutual influence between generators, optimizing the calculation method for the power grid inertia time constant. Therefore, it can obtain a more accurate actual inertia constant. A more accurate actual inertia constant helps power grid operators better understand the current system inertia level, especially given the continuously decreasing inertia of new power systems. This allows for targeted inertia compensation measures, such as virtual inertia, or supplementary frequency regulation measures, ensuring the power grid can effectively cope with faults, facilitating stable frequency control, and guaranteeing the safe and stable operation of the power grid.

[0173] To further explain the calculation device for the actual inertial constant of the power grid, please refer to... Figure 4 , Figure 4 This is a schematic diagram of the structure of a calculation device for the actual inertia constant value of a power grid according to an embodiment of the present invention, including: a first calculation module 401, a second calculation module 402, a third calculation module 403 and a fourth calculation module 404.

[0174] The first calculation module is used to obtain the admittance matrix of the two-machine system and calculate the first electromagnetic power equation based on the admittance matrix.

[0175] The second calculation module is used to calculate the equivalent inertial time constant calculation formula of the two-machine system based on the first electromagnetic power equation;

[0176] The third calculation module is used to calculate the expression for the second electromagnetic power based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system; wherein, the expression for the second electromagnetic power includes the electromagnetic power influence between the multiple generator nodes.

[0177] The fourth calculation module is used to calculate the equivalent inertial time constant of the multi-machine system based on the expression of the second electromagnetic power and the calculation formula of the equivalent inertial time constant of the two-machine system.

[0178] In this embodiment, the calculation of the first electromagnetic power equation based on the admittance matrix specifically involves:

[0179] The admittance matrix is ​​shown below:

[0180]

[0181]

[0182] The two-machine system includes a first generator and a second generator; Y 11 Y is the self-admittance of the first generator node. 22 Y is the self-admittance of the second generator node. 12X is the mutual admittance between the first generator node and the second generator node; d1 X is the equivalent reactance of the first generator. T1 X is the equivalent reactance of the transformer connected to the first generator in the system. L1 X is the equivalent reactance of the line connecting the first generator to the system. d2 X is the equivalent reactance of the second generator. T2 X is the equivalent reactance of the transformer connected to the second generator in the system. L2 R is the equivalent reactance of the line connecting the second generator to the system. L This is the equivalent resistance to ground of the line;

[0183] The first electromagnetic power equation includes: the electromagnetic power P of the first generator. e1 The expression for the electromagnetic power P of the second generator e2 The expression for the electromagnetic power P of the first generator; e1 The expression for the second generator and the electromagnetic power P e2 The expression is as follows:

[0184]

[0185]

[0186] Where, δ 12 =δ1-δ2, E1 is the potential amplitude of the first generator; E2 is the potential amplitude of the second generator; δ1 is the potential angle difference of the first generator; δ2 is the potential angle difference of the second generator; B 12 G represents the susceptance value of the corresponding element in the power network admittance matrix; 12 This represents the conductance value of the corresponding element in the power network admittance matrix.

[0187] In this embodiment, the formula for calculating the equivalent inertial time constant of the two-machine system based on the first electromagnetic power equation is as follows:

[0188] According to the electromagnetic power P of the first generator e1 The expression yields the change in electromagnetic power ΔP of the first generator. e1 The expression is as follows:

[0189] ΔP e1 =E1E2Δδ 12 (B 12 cosδ 120 -G 12 sinδ 120 );

[0190] Where, δ 120Δδ represents the potential angle difference between the first and second generators before the inertial response. 12 This represents the potential angle difference between the first and second generators after the inertial response.

[0191] According to the electromagnetic power P of the second generator e2 The expression yields the change in electromagnetic power ΔP of the second generator. e2 The expression is as follows:

[0192] ΔP e2 =E1E2Δδ 21 (B 12 cosδ 210 -G 12 sinδ 210 );

[0193] Where, δ 210 Δδ represents the potential angle difference between the second and first generators before the inertial response. 21 This represents the potential angle difference between the second generator and the first generator after the inertial response.

[0194] The change in electromagnetic power ΔP of the first generator e1 and the change in electromagnetic power ΔP of the second generator e2 Substituting these values ​​into the formula for calculating the total inertial support energy of the two-engine system, the formula for calculating the equivalent inertial time constant of the two-engine system is obtained, as shown below:

[0195]

[0196] Among them, H i Let be the rated inertia constant of the i-th generator;

[0197]

[0198] Wherein, H1 is the rated inertia constant of the first generator, and H2 is the rated inertia constant of the second generator;

[0199] Due to Δδ 12 =-Δδ 21 The formula for calculating the equivalent inertial time constant of the two-machine system is further simplified to the following formula:

[0200]

[0201] Among them, ΔPH av，sys H represents the total inertial support energy of the two-machine system. av，sys1 Let be the equivalent inertial time constant of the two-machine system.

[0202] In one specific embodiment, the expression for calculating the second electromagnetic power based on the first electromagnetic power equation and the potential amplitude and potential angle difference of the multiple generator nodes in the multi-machine system is as follows:

[0203]

[0204] Among them, P ei E represents the electromagnetic power of generator i in a multi-machine system (i.e., the second electromagnetic power); i Let Ei be the potential amplitude at generator node i; Ej be the potential amplitude at generator node j; δ i δ represents the potential angle difference at generator node i; j B represents the potential angle difference at generator node j; ij G represents the susceptance value of the corresponding element in the power network admittance matrix; ij This represents the conductance value of the corresponding element in the power network admittance matrix.

[0205] In one specific embodiment, the step of calculating the equivalent inertial time constant of the multi-machine system based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system is as follows:

[0206] According to the second electromagnetic power P ei The expression yields the change in electromagnetic power ΔP of the i-th generator in a multi-machine system. ei The expression is as follows:

[0207]

[0208] Among them, P ei P' represents the electromagnetic power of generator i in the multi-machine system, which is also the output electromagnetic power of generator i in the multi-machine system before the inertial response; ei δ represents the output electromagnetic power of generator i in the multi-machine system after inertial response. ij0 δ represents the potential angle difference between nodes i and j before the inertial response. ij This represents the potential angle difference between nodes i and j after the inertial response.

[0209] The change in electromagnetic power ΔP of the i-th generator in the multi-machine system ei Substituting these values ​​into the formula for calculating the total inertial support energy of a two-machine system, the equivalent inertial time constant H of the multi-machine system is obtained. av,sys2 As shown below:

[0210]

[0211] In this embodiment of the invention, the admittance matrix of the two-machine system is obtained by the first calculation module 401, and the first electromagnetic power equation is calculated based on the admittance matrix; the equivalent inertial time constant calculation formula of the two-machine system is calculated by the second calculation module 402 based on the first electromagnetic power equation; the expression of the second electromagnetic power is calculated by the third calculation module 403 based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes of the multi-machine system; wherein the expression of the second electromagnetic power includes the electromagnetic power influence between multiple generator nodes; and the equivalent inertial time constant of the multi-machine system is calculated by the fourth calculation module 404 based on the expression of the second electromagnetic power and the equivalent inertial time constant calculation formula of the two-machine system.

[0212] In calculating the actual inertia constant of the power grid, this invention considers the electromagnetic power influence between generators to ensure that the actual inertia constant reflects the real-time inertia level of the power grid. Therefore, the actual inertia constant calculated by this invention has higher accuracy. A more accurate actual inertia constant helps power grid operators better understand the current system inertia level, especially given the continuously decreasing inertia of new power systems. This allows for targeted inertia compensation measures, such as virtual inertia, or supplementary frequency regulation measures, ensuring the power grid can effectively cope with faults, facilitating stable frequency control, and guaranteeing the safe and stable operation of the power grid.

[0213] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for calculating the actual inertia constant of a power grid, characterized in that, include: Obtain the admittance matrix of the two-engine system, and calculate the first electromagnetic power equation based on the admittance matrix; wherein the admittance matrix is ​​shown below: ； ； The two-machine system includes a first generator and a second generator; Y 11 Y is the self-admittance of the first generator node. 22 Y is the self-admittance of the second generator node. 12 The mutual admittance between the first generator node and the second generator node; X d1 The equivalent reactance of the first generator, X T1 The equivalent reactance of the transformer connected to the first generator in the system. X L1 The equivalent reactance of the line connecting the first generator to the system; X d2 The equivalent reactance of the second generator. X T2 The equivalent reactance of the transformer connected to the second generator system. X L2 The equivalent reactance of the line connecting the second generator to the system. R L This is the equivalent resistance to ground of the line; The first electromagnetic power equation includes: the electromagnetic power P of the first generator. e1 The expression for the electromagnetic power P of the second generator e2 The expression for the electromagnetic power P of the first generator; e1 The expression for the second generator and the electromagnetic power P e2 The expression is as follows: ； ； in, E1 is the potential amplitude of the first generator; E2 is the potential amplitude of the second generator; δ1 is the potential angle difference of the first generator; δ2 is the potential angle difference of the second generator; B 12 G represents the susceptance value of the corresponding element in the power network admittance matrix; 12 This represents the conductance value of the corresponding element in the power network admittance matrix; According to the electromagnetic power P of the first generator e1 The expression yields the change in electromagnetic power ΔP of the first generator. e1 The expression is as follows: ； Where, δ 120 The potential angle difference between the first and second generators before the inertial response; Δδ 12 This represents the change in the potential angle difference between the first and second generators after the inertial response. According to the electromagnetic power P of the second generator e2 The expression yields the change in electromagnetic power ΔP of the second generator. e2 The expression is as follows: ； Where, δ 210 The potential angle difference between the second generator and the first generator before the inertial response; Δδ 21 This represents the change in the potential angle difference between the second generator and the first generator after the inertial response. The change in electromagnetic power of the first generator, ΔP e1 and the change in electromagnetic power ΔP of the second generator e2 Substituting these values ​​into the formula for calculating the total inertial support energy of the two-engine system, the formula for calculating the equivalent inertial time constant of the two-engine system is obtained, as shown below: ； Among them, H i Let be the rated inertia constant of the i-th generator; ； Wherein, H1 is the rated inertia constant of the first generator, and H2 is the rated inertia constant of the second generator; because The formula for calculating the equivalent inertial time constant of the two-machine system is further simplified to the following formula: ； Among them, △PH av,sys1 H represents the total inertial support energy of the two-machine system. av,sys1 Let be the equivalent inertial time constant of the two-machine system; Based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system, the expression for the second electromagnetic power is calculated; wherein, the expression for the second electromagnetic power includes the electromagnetic power influence between the multiple generator nodes. The equivalent inertial time constant of the multi-machine system is calculated based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system.

2. The method for calculating the actual inertia constant of a power grid according to claim 1, characterized in that, The expression for the second electromagnetic power is calculated based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system, as shown below: ； Among them, P ei Generator in a multi-machine system electromagnetic power; E i E represents the potential amplitude at generator node i; j δ represents the potential amplitude at generator node j; i δ represents the potential angle difference at generator node i; j B represents the potential angle difference at generator node j; ij G represents the susceptance value of the corresponding element in the power network admittance matrix; ij This represents the conductance value of the corresponding element in the power network admittance matrix.

3. The method for calculating the actual inertia constant of a power grid according to claim 2, characterized in that, The equivalent inertial time constant of the multi-machine system is calculated based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system, specifically as follows: According to the second electromagnetic power P ei The expression yields the change in electromagnetic power ΔP of the i-th generator in a multi-machine system. ei The expression is as follows: ； Among them, P ei P' represents the electromagnetic power of generator i in the multi-machine system, which is also the output electromagnetic power of generator i in the multi-machine system before the inertial response; ei δ represents the output electromagnetic power of generator i in the multi-machine system after inertial response. ij0 δ represents the potential angle difference between nodes i and j before the inertial response. ij This represents the potential angle difference between nodes i and j after the inertial response. The change in the potential angle difference between nodes i and j before and after the inertial response; the change in the electromagnetic power ΔP of the i-th generator in the multi-machine system. ei Substituting these values ​​into the formula for calculating the total inertial support energy of a two-machine system, the equivalent inertial time constant H of the multi-machine system is obtained. av,sys2 As shown below: 。 4. A device for calculating the actual inertia constant of a power grid, characterized in that, include: The first calculation module, the second calculation module, the third calculation module, and the fourth calculation module; The first calculation module is used to obtain the admittance matrix of the two-machine system and calculate the first electromagnetic power equation based on the admittance matrix; wherein the admittance matrix is ​​as follows: ； ； The two-machine system includes a first generator and a second generator; Y 11 Y is the self-admittance of the first generator node. 22 Y is the self-admittance of the second generator node. 12 The mutual admittance between the first generator node and the second generator node; X d1 The equivalent reactance of the first generator, X T1 The equivalent reactance of the transformer connected to the first generator in the system. X L1 The equivalent reactance of the line connecting the first generator to the system; X d2 The equivalent reactance of the second generator. X T2 The equivalent reactance of the transformer connected to the second generator system. X L2 The equivalent reactance of the line connecting the second generator to the system. R L This is the equivalent resistance to ground of the line; The first electromagnetic power equation includes: the electromagnetic power P of the first generator. e1 The expression for the electromagnetic power P of the second generator e2 The expression for the electromagnetic power P of the first generator; e1 The expression for the second generator and the electromagnetic power P e2 The expression is as follows: ； ； in, E1 is the potential amplitude of the first generator; E2 is the potential amplitude of the second generator; δ1 is the potential angle difference of the first generator; δ2 is the potential angle difference of the second generator; B 12 G represents the susceptance value of the corresponding element in the power network admittance matrix; 12 This represents the conductance value of the corresponding element in the power network admittance matrix; The second calculation module is used to calculate the electromagnetic power P of the first generator. e1 The expression yields the change in electromagnetic power ΔP of the first generator. e1 The expression is as follows: ； Where, δ 120 The potential angle difference between the first and second generators before the inertial response; Δδ 12 This represents the change in the potential angle difference between the first and second generators after the inertial response. According to the electromagnetic power P of the second generator e2 The expression yields the change in electromagnetic power ΔP of the second generator. e2 The expression is as follows: ； Where, δ 210 The potential angle difference between the second generator and the first generator before the inertial response; Δδ 21 This represents the change in the potential angle difference between the second generator and the first generator after the inertial response. The change in electromagnetic power of the first generator, ΔP e1 and the change in electromagnetic power ΔP of the second generator e2 Substituting these values ​​into the formula for calculating the total inertial support energy of the two-engine system, the formula for calculating the equivalent inertial time constant of the two-engine system is obtained, as shown below: ； Among them, H i Let be the rated inertia constant of the i-th generator; ； Wherein, H1 is the rated inertia constant of the first generator, and H2 is the rated inertia constant of the second generator; because The formula for calculating the equivalent inertial time constant of the two-machine system is further simplified to the following formula: ； Among them, △PH av,sys1 H represents the total inertial support energy of the two-machine system. av,sys1 Let be the equivalent inertial time constant of the two-machine system; The third calculation module is used to calculate the expression for the second electromagnetic power based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system; wherein, the expression for the second electromagnetic power includes the electromagnetic power influence between the multiple generator nodes. The fourth calculation module is used to calculate the equivalent inertial time constant of the multi-machine system based on the expression of the second electromagnetic power and the calculation formula of the equivalent inertial time constant of the two-machine system.

5. The device for calculating the actual inertia constant of a power grid according to claim 4, characterized in that, The expression for the second electromagnetic power is calculated based on the first electromagnetic power equation and the potential amplitude and potential angle difference of multiple generator nodes in the multi-machine system, as shown below: ； Among them, P ei Generator in a multi-machine system electromagnetic power; E i Let Ei be the potential amplitude at generator node i; Ej be the potential amplitude at generator node j; δ i δ represents the potential angle difference at generator node i; j B represents the potential angle difference at generator node j; ij G represents the susceptance value of the corresponding element in the power network admittance matrix; ij This represents the conductance value of the corresponding element in the power network admittance matrix.

6. The device for calculating the actual inertia constant of a power grid according to claim 5, characterized in that, The equivalent inertial time constant of the multi-machine system is calculated based on the expression for the second electromagnetic power and the formula for calculating the equivalent inertial time constant of the two-machine system, specifically as follows: According to the second electromagnetic power P ei The expression yields the change in electromagnetic power ΔP of the i-th generator in a multi-machine system. ei The expression is as follows: ； Among them, P ei P' represents the electromagnetic power of generator i in the multi-machine system, which is also the output electromagnetic power of generator i in the multi-machine system before the inertial response; ei δ represents the output electromagnetic power of generator i in the multi-machine system after inertial response. ij0 δ represents the potential angle difference between nodes i and j before the inertial response. ij This represents the potential angle difference between nodes i and j after the inertial response. This represents the change in the potential angle difference between nodes i and j before and after the inertial response; The change in electromagnetic power ΔP of the i-th generator in the multi-machine system ei Substituting these values ​​into the formula for calculating the total inertial support energy of a two-machine system, the equivalent inertial time constant H of the multi-machine system is obtained. av,sys2 As shown below: 。

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