A static voltage stability analysis method and device for a new energy power grid

Abstract

This invention discloses a method and apparatus for static voltage stability analysis of a power grid containing new energy sources. The method includes calculating the equivalent line after the new energy source is connected to the grid based on a pre-constructed static voltage stability index calculation method using UPFC (Upstream Power Generation Controller) to obtain a corrected Jacobian matrix. Singular value decomposition is then performed on the corrected Jacobian matrix to obtain the magnitude of the singular values ​​of the Jacobian matrix of the equivalent line, which represents the margin of the static voltage stability limit point of the node after the new energy source is connected to the grid. This determines the sensitivity relationship between the optimal installation location and capacity of the UPFC and the minimum singular value of the Jacobian matrix. This invention can rationally utilize dispatchable resources such as power generation equipment and FACTS (Fuel Accelerator and Reactor) equipment in the power grid, promoting the absorption of new energy sources while ensuring the safe and stable operation of the new energy power grid. It solves the static voltage safety and stability problem caused by the large-scale integration of new energy sources into the power grid, and is beneficial to improving the safety and stability of the new energy power grid.

Description

Technical Field

[0001] This invention relates to a method and apparatus for static voltage stability analysis of a power grid containing new energy sources, belonging to the field of power system technology. Background Technology

[0002] The rapid growth in the scale of renewable energy power grids and load demand has impacted the security of grid operation. The intermittent and volatile nature of renewable energy sources poses significant challenges to the stable operation of the power system. Domestic and international scholars have conducted extensive and in-depth research on the static voltage stability problem after renewable energy is integrated into the grid, proposing corresponding static voltage stability indices. Traditional static voltage stability analysis is generally based on power flow calculations to find the critical point of static voltage stability and then calculate the voltage stability margin of the current system nodes. Commonly used methods include continuous power flow methods, direct methods, and nonlinear programming methods. While these studies have all played a positive role in the safe and stable operation of the power grid, most existing static voltage stability indices are designed based on predetermined models, neglecting factors such as load fluctuations and the uncertainty of renewable energy generation. This makes it difficult to fully reflect the overall operating state of the power system after disturbances, limiting the universality of static voltage stability indices. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and apparatus for analyzing the static voltage stability of a power grid containing new energy sources, to solve the problem of static voltage safety and stability caused by the large-scale integration of new energy sources into the power grid, and to provide a method for analyzing the static voltage stability of a power grid containing new energy sources, thereby improving the safety and stability of the new energy power grid.

[0004] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0005] In a first aspect, the present invention provides a method for static voltage stability analysis of a power grid containing new energy sources, comprising:

[0006] Based on a pre-built static voltage stability index calculation method based on UPFC, the equivalent line after new energy grid connection is calculated, and the corrected Jacobian matrix is ​​obtained.

[0007] Singular value decomposition is performed on the modified Jacobian matrix to obtain the magnitude of the singular values ​​of the equivalent line Jacobian matrix. This value is used to represent the margin of the static voltage stability limit point of the node after the new energy is connected to the grid, and then the sensitivity relationship between the optimal installation location and capacity of UPFC and the minimum singular value of the Jacobian matrix is ​​determined.

[0008] Furthermore, the construction of the UPFC-based static voltage stability index calculation method includes:

[0009] Based on the compensation characteristics of UPFC and the equivalent model on the line, the mathematical model of UPFC is constructed using the equivalent power injection method.

[0010] An equivalent power injection model of UPFC and power flow equations of the power system are constructed. The UPFC is configured on the i-side of node i of line ij. The power flow equations at both ends of the line where the UPFC is configured are modified, while the power flow equations of other nodes remain unchanged. Under the constraint of line PQ, a method for calculating static voltage stability index based on UPFC is constructed.

[0011] Furthermore, the UPFC is composed of two back-to-back voltage source converters sharing a DC-side capacitor, with one converter being equivalent to a series voltage source U. T One converter is connected in series with a transformer to inject voltage with adjustable amplitude and phase angle into the system, thereby regulating the power flow of the line. Another converter is connected to the system via the leakage reactance of a parallel transformer. This converter absorbs or injects reactive power into the system through the parallel transformer, and can be equivalent to a series current source I within the device. sh .

[0012] Furthermore, under the constraint of line PQ, a method for calculating static voltage stability index based on UPFC is constructed, including:

[0013] In a power system, the voltage at the beginning of node i of branch is U. i The voltage at the end node is U j R+jX is the branch impedance; B c This is the admittance to ground; P and Q are the active and reactive power at the end of the branch, respectively, thus yielding the corresponding voltage equation:

[0014]

[0015] Simplified to It means that it will Then a1=(1-XB) c / 2), b1=R, a2=RB c / 2, b2=X, and Therefore there is After simplification, it becomes:

[0016]

[0017] In the formula: c2=2(a1b1+a2b2); c3=2(a1b2-a2b1); make Get ax 2 +bx+c=0, where a=c1, c = c4(P) 2 +Q2 ),therefore:

[0018]

[0019] Therefore, the condition for the voltage at node j to be stable is U j There are real solutions; when the system is operating normally and stably, U j There are two positive real roots, of which the larger root U j One is a stable solution, and the other is a smaller root U. j The solution is unstable; when the system is critically stable, the two roots reach the same value, which is the critical voltage. At this time, Δ = (b 2 -4ac)=0; therefore, we conclude that:

[0020]

[0021] Then the point on the curve is Q. cr and P cr Let x = Q, y = P, then we have:

[0022] Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0

[0023] The horizontal and vertical axes of this curve represent the reactive power and active power on the system's transmission lines, respectively. (x1, y1) represents the system's operating state. Therefore, the voltage stability safety margin is expressed as:

[0024]

[0025] Let the initial system (Q0, P0) be (x0, y0), and the critical stable operating power of the system (Q) be... cr ,P cr Let (x1, y1) be the equation; substituting it into the equation and differentiating with respect to x, we get: 2Ax + By + Bxy' + 2Cyy' + D + Ey' = 0. Since (x1, y1) is the shortest distance to (x0, y0), the simplified result is: Using Matlab to solve for (Q) from (x1, y1) eq ,P eq ).

[0026] Furthermore, the UPFC device improves the static voltage stability of the system by adjusting the line power flow; the formula for the voltage stability value of the load node j at the end of the line is as follows:

[0027] L VSIj =min(d vc1 ,d vc2 ...d vcN )

[0028] In the formula: N is the total number of branches in the system with node j as the end.

[0029] Furthermore, the overall voltage stability of the power grid is directly proportional to the voltage stability margin of the nodes, with branches ending at nodes having a stability margin of 0.

[0030] Furthermore, the minimum node voltage stability margin under different operating conditions is defined as the weakest node in the system. The magnitude of this node's safety margin reflects the overall static voltage stability of the system, as shown in the following formula:

[0031] a VSI =min(L VSI1 ,L VSI2 ...L VSIk )

[0032] In the formula, k is the number of load nodes in the system; when the system faces the phenomenon of node voltage collapse due to the increase of load, the weak node has the highest probability of reaching the critical operating point.

[0033] Furthermore, singular value decomposition is performed on the modified Jacobian matrix to obtain the magnitude of the singular values ​​of the equivalent line Jacobian matrix. This magnitude is used to represent the margin of the static voltage stability limit point at the node after the new energy source is connected to the grid. This, in turn, determines the sensitivity relationship between the optimal installation location and capacity of the UPFC and the minimum singular value of the Jacobian matrix, including:

[0034] The corrected Jacobian matrix is ​​obtained based on the equivalent circuit after new energy sources are connected to the grid.

[0035] Perform singular value decomposition on the modified Jacobian matrix to determine the relational equation between the minimum singular value of the matrix and its corresponding left singular vector. Differentiate both sides of the relational equation, then transpose both sides of the differentiated relational equation and multiply them by the left singular vector on the right.

[0036] At the critical voltage stability point, the Jacobian matrix singularity corresponds to a minimum singular value. The minimum singular value of the Jacobian matrix of the equivalent circuit is used to represent the static voltage stability margin after the new energy is connected to the grid.

[0037] The relationship between the UPFC's improved static voltage stability margin and singular value sensitivity was calculated.

[0038] Secondly, the present invention provides a static voltage stability analysis device for a renewable energy power grid that takes into account UPFC, comprising:

[0039] The calculation unit is used to calculate the equivalent line after new energy is connected to the grid based on a pre-built static voltage stability index calculation method based on UPFC, and obtain the corrected Jacobian matrix.

[0040] The acquisition unit is used to perform singular value decomposition on the modified Jacobian matrix to obtain the magnitude of the singular values ​​of the equivalent line Jacobian matrix. This value is used to represent the margin of the static voltage stability limit point of the node after the new energy is connected to the grid, and then to determine the sensitivity relationship between the optimal installation location and capacity of the UPFC and the minimum singular value of the Jacobian matrix.

[0041] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the methods described above.

[0042] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0043] This invention provides a method and apparatus for static voltage stability analysis of a power grid containing new energy sources. The method of this invention has the advantages of being easy to implement and flexible in application. It can make reasonable use of dispatchable resources such as power generation equipment and FACTS equipment in the power grid, promote the consumption of new energy sources while ensuring the safe and stable operation of the new energy power grid, solve the static voltage safety and stability problem caused by the large-scale integration of new energy sources into the power grid, and help improve the safety and stability of the new energy power grid. Attached Figure Description

[0044] Figure 1 The flowchart shows the static voltage stability analysis method for power grids containing new energy sources.

[0045] Figure 2 The equivalent circuit diagram of UPFC;

[0046] Figure 3 This is the static voltage safety and stability operation curve. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0048] Example 1

[0049] This embodiment introduces a static voltage stability analysis method and apparatus for a power grid containing new energy sources, including:

[0050] Based on a pre-built static voltage stability index calculation method based on UPFC, the equivalent line after new energy grid connection is calculated, and the corrected Jacobian matrix is ​​obtained.

[0051] Singular value decomposition is performed on the modified Jacobian matrix to obtain the magnitude of the singular values ​​of the equivalent line Jacobian matrix. This value is used to represent the margin of the static voltage stability limit point of the node after the new energy is connected to the grid, and then the sensitivity relationship between the optimal installation location and capacity of UPFC and the minimum singular value of the Jacobian matrix is ​​determined.

[0052] The static voltage stability analysis method and apparatus for a power grid containing new energy sources provided in this embodiment involve the following steps in their application:

[0053] Step 1: Analyze the structure and working principle of UPFC, and conduct research based on the compensation characteristics of UPFC and the equivalent model on the line. Construct a mathematical model of UPFC using the equivalent power injection method.

[0054] Step Two: Following Step One, an equivalent power injection model of UPFC and power flow equations for the power system are constructed. The UPFC is configured on the node i side of line ij, and the power flow equations at both ends of the line where the UPFC is configured are modified, while the power flow equations at other nodes remain unchanged. Under the PQ constraint conditions of the line, a new method for calculating the static voltage stability index based on UPFC is proposed.

[0055] Step 3: Based on the static voltage stability index of UPFC, power flow calculation is performed. The equivalent line after renewable energy grid integration is used to obtain the corrected Jacobian matrix. Singular value decomposition is then performed on the corrected Jacobian matrix. The magnitude of the singular values ​​of the equivalent line Jacobian matrix represents the margin of the static voltage stability limit point of the nodes after renewable energy grid integration. This invention has advantages such as ease of implementation and flexible application. It can rationally utilize dispatchable resources such as power generation equipment and FACTS equipment in the power grid, promoting the consumption of renewable energy while ensuring the safe and stable operation of the renewable energy grid.

[0056] In further step 1), the UPFC is composed of two back-to-back voltage source converters sharing a DC-side capacitor, one of which is equivalent to a series voltage source U. T One converter is connected in series with a transformer to inject voltage with adjustable amplitude and phase angle into the system, thereby regulating the line power flow. Another converter is connected to the system via the leakage reactance of a parallel transformer. This converter can absorb or inject reactive power into the system through the parallel transformer, and can be equivalent to a series current source I within the device. sh .

[0057] In further step 2), the voltage stability index proposed by UPFC is derived under the PQ constraint of the line, and a new static voltage stability calculation formula based on UPFC is obtained to obtain the corresponding static voltage stability index.

[0058] For any power system, its branch model can be simplified as follows: Figure 1 As shown. The voltage at the beginning of node i of branch is U. i The voltage at the end node is U j R+jX is the branch impedance; B cThis is the admittance to ground; P and Q are the active and reactive power at the end of the branch, respectively. Therefore, the corresponding voltage equation can be obtained:

[0059]

[0060] It can be simplified to It means that it will Then a1=(1-XB) c / 2), b1=R, a2=RB c / 2, b2=X, and Therefore there is After simplification, we get:

[0061]

[0062] In the formula: c2=2(a1b1+a2b2); c3=2(a1 b2-a2b1); make We can get ax 2 +bx+c=0, where a=c1, c = c4(P) 2 +Q 2 ),therefore:

[0063]

[0064] Therefore, the condition for the voltage at node j to be stable is U j There are real solutions. Under normal and stable operating conditions, U j There are two positive real roots, of which the larger root U j One is a stable solution, and the other is a smaller root U. j The solution is unstable; when the system is critically stable, the two roots reach the same value, which is the critical voltage. At this time, Δ = (b 2 -4ac)=0. Therefore, we can obtain:

[0065]

[0066] Then the point on the curve is Q. cr and P cr Let x = Q, y = P, then we have:

[0067] Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0

[0068] like Figure 3As shown, the horizontal and vertical axes of this curve represent the reactive power and active power on the system's transmission lines, respectively, and (x1, y1) represents the system's operating state. Therefore, the voltage stability safety margin in this paper can be expressed as:

[0069]

[0070] Let the initial system (Q0, P0) be (x0, y0), and the critical stable operating power of the system (Q) be... cr ,P cr Let (x1, y1) be the shortest distance to (x0, y0). Substituting this into the equation and differentiating with respect to x, we get: 2Ax + By + Bxy' + 2Cyy' + D + Ey' = 0. Since (x1, y1) is the shortest distance to (x0, y0), after simplification, we get: Using Matlab, we can obtain (Q) from (x1, y1). eq ,P eq ).

[0071] UPFC devices improve system static voltage stability by regulating line power flow. The voltage stability value at load node j at the end of the line can be expressed as:

[0072] L VSIj =min(d vc1 ,d vc2 ...d vcN )

[0073] In the formula: N is the total number of branches in the system with node j as the terminal. The overall voltage stability of the power grid is directly proportional to the voltage stability margin of the nodes. When a branch with node j as the terminal has a stability margin of 0, that is, the branch voltage stability is in a critical state. Exceeding the critical operating state will result in voltage collapse at this node, and the original balancing node of the transmission line will be lost. The minimum node voltage stability margin under different operating states is defined as the weakest node in the system. The size of the safety margin of this node reflects the overall static voltage stability of the system, that is:

[0074] a VSI =min(L VSI1 ,L VSI2 ...L VSIk )

[0075] In the formula, k is the number of load nodes in the system. When the system faces node voltage collapse due to load growth, the weakest node has the highest probability of reaching the critical operating point.

[0076] Further, in step 3), based on the proposed static voltage stability index, the sensitivity relationship between the optimal installation location and capacity of the UPFC and the minimum singular value of the Jacobian matrix corresponding to the node is determined, including the following steps:

[0077] (1) Obtain the corrected Jacobian matrix based on the equivalent circuit after new energy grid connection;

[0078] (2) Perform singular value decomposition on the modified Jacobi matrix to determine the relational equation between the minimum singular value of the matrix and its corresponding left singular vector. Differentiate both sides of the relational equation, then transpose both sides of the differentiated relational equation and multiply them by the left singular vector on the right.

[0079] (3) At the critical voltage stability point, the Jacobian matrix singularity corresponds to a minimum singular value. The minimum singular value of the Jacobian matrix of the equivalent circuit is used to represent the static voltage stability margin after the new energy is connected to the grid.

[0080] (4) The relationship between the static voltage stability margin of UPFC and the singular value sensitivity was calculated.

[0081] Example 2

[0082] This embodiment provides a static voltage stability analysis device for a power grid with new energy sources that takes into account UPFC, including:

[0083] The calculation unit is used to calculate the equivalent line after new energy is connected to the grid based on a pre-built static voltage stability index calculation method based on UPFC, and obtain the corrected Jacobian matrix.

[0084] The acquisition unit is used to perform singular value decomposition on the modified Jacobian matrix to obtain the magnitude of the singular values ​​of the equivalent line Jacobian matrix. This value is used to represent the margin of the static voltage stability limit point of the node after the new energy is connected to the grid, and then to determine the sensitivity relationship between the optimal installation location and capacity of the UPFC and the minimum singular value of the Jacobian matrix.

[0085] Example 3

[0086] This embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the methods described in Embodiment 1.

[0087] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for static voltage stability analysis of a power grid with new energy sources, characterized in that, Comprise: Based on the pre-built UPFC-based static voltage stability index calculation method, the equivalent line after the new energy access is calculated, and the corrected Jacobian matrix is obtained; The singular value decomposition is carried out on the corrected Jacobian matrix, and the size of the singular value of the equivalent line Jacobian matrix is obtained, which is used to represent the margin of the node static voltage stability limit point after the new energy access, and then the sensitivity relationship between the UPFC optimal installation position, capacity and the minimum singular value of the Jacobian matrix is determined; The construction of the UPFC-based static voltage stability index calculation method comprises: Based on the compensation characteristics of UPFC and the equivalent model on the line, the mathematical model of UPFC is constructed using the equivalent power injection method; The UPFC equivalent power injection model and the power system flow equation are constructed, the UPFC is configured on the node i side of the line i-j, the flow equation of the line ends configured with UPFC is modified, and the flow equation of other nodes remains unchanged, and under the constraint condition of line P-Q, the UPFC-based static voltage stability index calculation method is constructed; The UPFC is composed of two back-to-back voltage source converters sharing a DC capacitor, one of which is equivalent to a series voltage source U T , which is connected to the system through a transformer and injects a voltage with adjustable amplitude and phase angle into the system to regulate the line power flow; the other converter is connected to the system through the leakage reactance of a parallel transformer, which absorbs or injects reactive power into the system through the parallel transformer, and is equivalent to a series current source I sh in the device; Under the constraint condition of line P-Q, the UPFC-based static voltage stability index calculation method is constructed, which comprises: In power system, the voltage at the first end of branch i is U i , and the voltage at the end node is U j ; R+jX is the branch impedance; B c is the admittance to the ground; P and Q are the active and reactive power at the end of the branch, respectively, so that the corresponding voltage equation is obtained: Simplify to Denote, by then a1 = (1 - XB c / 2), b1 = R, a2 = RB c / 2, b2 = X, and So we have Simplify to: wherein: c2= 2(a1b1+ a2b2); c3= 2(a1b2- a2b1); Let ax 2 + bx + c = 0, where a = c1, c = c4(P 2 + Q 2 ), so that: The condition for voltage stability at the jth node is U j There is a real solution; the system is in normal stable operation, U j There are two positive real roots, the larger root U j is a stable solution, and the other, the smaller root U j is an unstable solution, and the two roots reach the same value, the critical voltage, when the system is in critical stability At this point, Δ = (b 2 - 4ac) = 0; thus we have: Then the point on the curve is Q cr and P cr Let x = Q and y = P then we have: Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0 The horizontal and vertical coordinates of this curve are the reactive power and active power on the system transmission line respectively, (x1, y1) is the operating state of the system, and therefore the voltage stability safety margin is represented as: Let the initial system (Q0, P0) be (x0, y0), and the critical stable operation power (Q cr ,P cr ) be (x1, y1); the derivative of the equation with respect to x is 2Ax + By + Bxy' + 2Cyy' + D + Ey' = 0, and since (x1, y1) is the shortest distance from (x0, y0), it is simplified to: (Q eq ,P eq ) is obtained from (x1, y1) by using Matlab.

2. The method for static voltage stability analysis of new energy power grid according to claim 1, characterized in that: The UPFC device improves the static voltage stability of the system by adjusting the line flow; the voltage stability value formula of the load node j at the end of the line is as follows: L VSIj = min(d vc1 , d vc2 ,..., d vcN ) In the formula, N is the total number of branches with j as the node end in the system.

3. The method for static voltage stability analysis of a new energy power grid according to claim 2, characterized in that: The strength of the overall voltage stability of the power grid is proportional to the node voltage stability margin, and the branch at the end of the node is in a stable margin of 0.

4. The method for static voltage stability analysis of new energy power grid according to claim 3, characterized in that: The minimum node voltage stability margin of the system under different operating states is defined as the weakest node of the system, and the size of the safety margin of the node can reflect the static voltage stability of the overall system, and the formula is as follows: a VSI = min(L VSI1 , L VSI2 … L VSIk ) In the formula, k is the number of load nodes in the system; when the system faces the phenomenon of node voltage collapse due to load growth, the probability of the weakest node reaching the critical operating point is the largest.

5. The method for static voltage stability analysis of new energy power grid according to claim 4, characterized in that: The singular value decomposition is carried out on the corrected Jacobian matrix, and the size of the singular value of the equivalent line Jacobian matrix is obtained, which is used to represent the margin of the node static voltage stability limit point after the new energy access, and then the sensitivity relationship between the UPFC optimal installation position, capacity and the minimum singular value of the Jacobian matrix is determined, comprising: Based on the new energy access equivalent circuit to obtain the corrected Jacobian matrix; The singular value decomposition is carried out on the corrected Jacobian matrix, the relationship equation of the minimum singular value of the matrix and the corresponding left singular vector is determined, the relationship equation is derived on both sides, and then the transposition of the derived relationship equation is multiplied by the left singular vector; The singular value of the Jacobian matrix corresponds to a minimum singular value at the critical stability of the voltage, and the minimum singular value of the equivalent circuit Jacobian matrix is used to represent the static voltage stability margin after the new energy access; The relationship between the UPFC static voltage stability margin and the singular value sensitivity is calculated.

6. A device for static voltage stability analysis of a power grid containing new energy sources considering UPFC, for realizing the static voltage stability analysis method of the power grid containing new energy sources according to claim 1, characterized in that, Comprise: The computing unit is configured to calculate the equivalent line after the new energy is connected to the grid based on a pre-constructed UPFC-based static voltage stability index calculation method, and obtain a corrected Jacobian matrix. The obtaining unit is configured to perform singular value decomposition on the corrected Jacobian matrix, and obtain the size of the singular value of the equivalent line Jacobian matrix, which is used to represent the margin of the static voltage stability limit point of the node after the new energy is connected to the grid, and further determine the sensitivity relationship between the optimal installation position and capacity of the UPFC and the minimum singular value of the Jacobian matrix.

7. A computer readable storage medium having stored thereon a computer program, characterized in that: The program is executed by the processor to implement the steps of the method in any one of claims 1-5.

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