Calculation method, model and equipment for distribution network sensitivity under random charging load

Abstract

The present invention discloses a method, model and device for calculating the sensitivity of a distribution network under random charging load. The method comprises: assuming that the column vector of active power injected by each node is P, the column vector of reactive power injected by each node is Q, P and Q are combined into an input data column vector X, X=[P T ,Q T ] T , the node voltage amplitude column vector is taken as the output variable Y, and S is the sensitivity matrix of node injection power to node voltage amplitude; S ab is the element in the ath row and bth column of the S matrix, #imgabs0#S ab represents the power injected by node b X b The voltage amplitude U at node a a The sensitivity of the data is obtained by calculating the objective function based on the least squares regression method, and a linear constraint condition is constructed to make the elements of different rows of the S matrix have a constraint relationship; the values ​​of ΔX and ΔY are obtained through measurement data, and the linear sensitivity parameters are calculated by the least squares regression method. The present invention can greatly improve the accuracy of data-driven sensitivity regression while being able to solve the problem conveniently.

Description

Technical Field

[0001] The present invention relates to the field of distribution network control, and in particular to a distribution network sensitivity calculation method, model and device under random charging load. Background Art

[0002] At present, sensitivity analysis is widely used as a basic operation analysis tool in centralized and distributed optimal voltage control, minimizing network losses, and optimal reactive power compensation. However, the operation and maintenance level of medium and low voltage distribution networks is relatively low, line impedance data is difficult to obtain, and traditional precise physical models are difficult to apply.

[0003] Existing data-driven sensitivity modeling is generally based on the premise that high-precision phase measurement data is available. However, there are many nodes in medium and low voltage distribution networks, and it is difficult to economically access high-precision measurement units on a large scale. Therefore, it is difficult to fully obtain μPMU measurement data in practice, and operating data can only be obtained through measurement terminals such as smart meters. Therefore, errors are inevitably introduced into the measurement data.

[0004] Reference 1: "Distribution Line Parameter Estimation Considering Measurement Tolerance", author: AM Prostejovsky, O. Gehrke, AM Kosek, T. Strasser and HW Bindner, published in IEEE Transactions on Industrial Informatics, Vol. 12, No. 2, pp. 726-735, published in April 2016; the document records that the error is caused by the following reasons: including measurement device tolerance, noise disturbance and asynchronous measurement error, which together constitute a combined error, so the actual measurement error is large. With the gradual increase in the number of electric vehicles, the charging load with strong power randomness and uncertainty will cause the asynchronous measurement error to be further amplified, and the combined error may even be greater than the actual voltage fluctuation amplitude under different operating conditions. Since the voltage is stable and the fluctuation is small under normal operation of the distribution network, compared with the power flow model, the impact of such errors is more significant when calculating the sensitivity of the node injection power to the voltage amplitude. Multiple test examples in Reference 1 show that a 1% error introduced by a measurement error will cause a regression coefficient error of more than 40%, so the measurement error in actual scenarios has a more serious impact.

[0005] In response to the above problems, existing research has established physical constraints to improve the accuracy of sensitivity modeling in the context of large errors in measurement data. According to the mathematical structure, it can be divided into three types:

[0006] 1) Introducing the sparse characteristics of the Jacobi matrix. Among them, document 2: "Estimation of PMU voltage and power sensitivity of distribution network considering the sparsity of the Jacobi matrix", published in IEEE Access, Volume 6, Pages 31307-31316, published in 2018; this document incorporates the sparse characteristics of the Jacobi matrix of the power flow model into the sensitivity parameter regression, and the sparse empty positions of the sparse matrix are zeroed, which improves the overall regression accuracy of the Jacobi matrix to a certain extent. However, this method is based on the Jacobi matrix of the inverse of the sensitivity matrix, and requires the measurement of the voltage phase, which greatly limits the application of this type of method in medium and low voltage distribution networks.

[0007] 2) Introduce the correlation characteristics of active and reactive power to voltage sensitivity. Reference 3: "Data-driven estimation of voltage and power sensitivity considering the mutual dependence of voltage and power in medium-voltage distribution networks", published in "IEEE Transactions on Power Systems", Vol. 37, No. 4, pp. 3173-3176, published in July 2022; This document records that there is a certain correlation between active power-voltage sensitivity and reactive power-voltage sensitivity. Based on this, a linear regression model is established to obtain a sensitivity mapping relationship that considers the correlation between active and reactive sensitivities, which can achieve higher accuracy under the premise of determining the distribution network impedance ratio. However, the complex line structure of the actual medium and low voltage network makes it difficult to meet its assumptions, which limits the practical application of this method.

[0008] In summary, the existing power flow constraints have the following defects and shortcomings:

[0009] (1) In actual projects, due to the limitations of cost and site conditions, high-precision phase measurement equipment for medium and low voltage distribution networks is very limited, and phase angle data is actually difficult to obtain, which limits the application of existing methods such as those based on the Jacobi matrix.

[0010] (2) In actual distribution networks, due to the large number of branch lines, the selection of line diameters of different branch lines is determined according to the load size of the branch, making it difficult to achieve consistency in impedance ratios of all lines. Therefore, the impedance ratio constraint method for distribution networks derived through physical model analysis lacks the conditions that meet its basic assumptions in actual applications and is difficult to apply in practice. Summary of the invention

[0011] The present invention provides a method, model and device for calculating the sensitivity of a distribution network under random charging load in order to solve the technical problems existing in the known technology.

[0012] The technical solution adopted by the present invention to solve the technical problems existing in the known technology is:

[0013] A method for calculating the sensitivity of a distribution network under random charging loads, the method comprising: assuming that the column vector of active power injected by each node is P, the column vector of reactive power injected by each node is Q, P and Q are combined into an input data column vector X, X=[P T ,Q T ] T , the node voltage amplitude column vector is taken as the output variable Y, and S is the sensitivity matrix of node injection power to node voltage amplitude; S ab is the element in the ath row and bth column of the S matrix, S ab represents the power injected by node b X b The voltage amplitude U at node a a Sensitivity;

[0014] The following objective function is established based on the least squares regression method:

[0015]

[0016]

[0017] Construct linear constraints that constrain elements in different rows of the S matrix;

[0018] The values ​​of ΔX and ΔY are obtained from the measured data, and the linear sensitivity parameters are calculated by the least squares regression method.

[0019] Furthermore, the linear constraint condition includes one or a combination of the following constraint conditions: size relationship constraint condition, symmetry constraint condition, active and reactive power equivalence constraint condition, active and reactive power mutual constraint condition and active non-negativity constraint condition; wherein:

[0020] The size relationship constraint condition means that there is a numerical size relationship between the sensitivities of the nodes;

[0021] The symmetry constraint condition means that the sensitivity of the active power injected into the node to the voltage amplitude is symmetrical to the sensitivity of the voltage amplitude to the active power injected into the node;

[0022] The active-reactive equivalence constraint condition refers to the sensitivity of the active power injected by the node to the voltage amplitude, which is consistent with the trend of the sensitivity of the reactive power injected by the node to the voltage amplitude;

[0023] The mutual constraint condition of active and reactive power refers to the sensitivity of the active power injected by the node to the voltage amplitude, which is consistent with the trend of the sensitivity of the reactive power injected by the node to the voltage amplitude, and is used to remove some spikes;

[0024] The active non-negativity constraint condition means that the sensitivity of the active power injected by the node to the voltage amplitude is greater than or equal to 0.

[0025] Furthermore, for the radial distribution network, the balancing node is defined as the root node, and the root node is defined as the head end of the network; the low-voltage busbar of the upper substation of the medium-voltage network is set as the root node, and between the nodes with a connection relationship, a reference node i is set in the topological relationship, and the node closer to the root node relative to node i is the upstream node of node i, otherwise it is the downstream node of node i; set N U,i Represents the upstream node set of node i, let N D,i Represents the downstream node combination of node i, and determines N by a tree search method starting from the root node U,i and N D,i ; By N U,i and N D,i The logical judgment is used to obtain the topological position relationship between different nodes, which is used to establish the sensitivity size relationship constraint conditions between nodes at different positions in the radial distribution network.

[0026] Furthermore, the method for establishing the sensitivity size relationship constraint conditions between nodes at different locations in the radial distribution network includes:

[0027] Assume that in the radial distribution network, a branch extending from the root node is R p , p is the corresponding branch number; suppose branch R p Set i u 、i、i d , k, j, l nodes, where i u 、i d is the adjacent point of i; suppose there is a branch R p The branch path starting from node i on the iq , q is the branch road number starting from node i; let branch road R iq Set nodes m and n in sequence, then node i u is the upstream node of node i, node i d , k, j, l, m, n are all downstream nodes of node i, and nodes k, j, l are downstream nodes of node i d , nodes j and l are the downstream nodes of node k, node l is the downstream node of node j; node n is the downstream node of node m.

[0028] According to the topological positions between different nodes and the sensitivity relationship characteristics between adjacent points, the following constraints on the sensitivity relationship between nodes are established:

[0029] 1) In the same network branch R p The closer the node i is to the downstream node, the greater its sensitivity:

[0030] S ki ≤Sji if{(j,k∈N D,i )∩(j,∈N D,k )}

[0031] 2) In the same network branch R p In the above, the sensitivity of node j to node j is greater than the sensitivity of node j to its upstream node, and the sensitivity of node j to the upstream node is smaller:

[0032]

[0033] 3) In the same network branch R p In the figure, the sensitivity difference between nodes i and k to the common downstream node is approximately equal:

[0034] S ji -S jk ≈S li -S lk ;

[0035] st{l,j∈(N D,i ∩N D,k );

[0036] 4) Branch S p A node on the branch road R iq Multiple nodes on the branch have a common upstream node, and these nodes corresponding to the upstream node are all downstream nodes. p The downstream node on the branch road R iq The sensitivities of multiple downstream nodes on are approximately equal:

[0037]

[0038] 5) The sensitivity difference between node i and its downstream nodes j and k is small:

[0039]

[0040] 6) Branch S p The downstream node j of node i on the branch path R iq The sensitivity of node i to its downstream nodes is between the sensitivity of node j to its upstream and downstream neighbors:

[0041] S idj ≥S mj ≥S iuj ;

[0042]

[0043] Where:

[0044] N D,kis the set of downstream nodes of node k;

[0045] N U,j is the set of upstream nodes of node j;

[0046] N U,k is the set of upstream nodes of node k;

[0047] N U,n is the set of upstream nodes of node n;

[0048] N D,m is the set of downstream nodes of node m;

[0049] N D,j is the set of downstream nodes of node j;

[0050] S ki is the sensitivity of the injected power at node i to the voltage amplitude at node k; S ji is the sensitivity of the injected power at node i to the voltage amplitude at node j;

[0051] S jj is the sensitivity of the injected power at node j to the voltage amplitude at node j;

[0052] S kj is the sensitivity of the injected power at node j to the voltage amplitude at node k;

[0053] S ij is the sensitivity of the injected power at node j to the voltage amplitude at node i;

[0054] S jk is the sensitivity of the injected power at node k to the voltage amplitude at node j;

[0055] S li is the sensitivity of the injected power at node i to the voltage amplitude at node l;

[0056] S lk is the sensitivity of the injected power at node k to the voltage amplitude at node l;

[0057] S mj is the sensitivity of the injected power at node j to the voltage amplitude at node m;

[0058] S nj is the sensitivity of the injected power at node j to the voltage amplitude at node n;

[0059] Inject power to node j to adjacent downstream node i d Sensitivity of voltage amplitude;

[0060] Inject power to node j to the adjacent upstream node iu Sensitivity of voltage amplitude;

[0061] ε def is the boundary threshold;

[0062] is the i-th topological adjacency matrix d row, the element of the i-th column;

[0063] is the i-th topological adjacency matrix u The element at row, column i.

[0064] Furthermore, let the difference in sensitivity between nodes i and k to their common downstream node j be within the range of ±10% of the average value of the difference between nodes i and k to all downstream nodes of node k:

[0065]

[0066] Where:

[0067] v is the downstream node of node k;

[0068] S vk is the sensitivity of the injected power at node k to the voltage amplitude at node v;

[0069] S vi is the sensitivity of the injected power at node i to the voltage amplitude at node v;

[0070] n D,k is the number of downstream nodes of node k.

[0071] Furthermore, the constraint condition of sensitivity symmetry between nodes is as follows:

[0072] (S ab -S ef )(S ba -S fe )≥0;

[0073] Where:

[0074] S ab The sensitivity of the injected power at node b to the voltage amplitude at node a;

[0075] S ba The sensitivity of the injected power at node a to the voltage amplitude at node b;

[0076] S ef The sensitivity of the injected power at node f to the voltage amplitude at node e;

[0077] S fe The sensitivity of the injected power at node e to the voltage amplitude at node f.

[0078] Furthermore, the constraint condition of equivalence between active power and reactive power is as follows:

[0079]

[0080] Where:

[0081] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0082] The sensitivity of the reactive power injected into node b to the voltage amplitude of node a;

[0083] The sensitivity of the active power injected into node f to the voltage amplitude of node e;

[0084] The sensitivity of the reactive power injected into node f to the voltage amplitude of node e.

[0085] Furthermore, the mutual constraints between active power and reactive power are as follows:

[0086]

[0087] Where:

[0088] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0089] The sensitivity of the reactive power injected into node b to the voltage amplitude at node a.

[0090] The present invention also provides a distribution network sensitivity calculation model under random charging load, which is composed of the objective function and linear constraints in the above-mentioned distribution network sensitivity calculation method under random charging load.

[0091] The present invention also provides a device for calculating the sensitivity of a distribution network under random charging loads, comprising a memory and a processor, wherein the memory is used to store a computer program; the processor is used to execute the computer program and implement the steps of the method for calculating the sensitivity of a distribution network under random charging loads as described above when executing the computer program.

[0092] The advantages and positive effects of the present invention are: based on the operating characteristics of radial network operation data, resolvable constraints are mined and established, aiming to improve the accuracy of data-driven sensitivity modeling based on content measurement error data. Multiple types of constraints are established, including constraints describing the size relationship of the sensitivity of upstream and downstream nodes, symmetry constraints, active and reactive power equivalence constraints, and non-negative constraints on active and reactive power mutual constraints. These constraints are added to the optimization problem of traditional least squares parameter regression to form a constrained least squares regression method. The established constraints are all linear constraints, which can greatly improve the accuracy of data-driven sensitivity regression while being easy to solve.

[0093] Compared with the prior art, the present invention has the following characteristics:

[0094] 1) The method of the present invention does not rely on voltage phase measurement data and has higher application value under the condition of measurable data of the actual distribution network.

[0095] 2) Based on the radial structure of the medium-voltage power grid, analytical constraints are established to improve the accuracy of sensitivity parameter regression and have strong anti-error characteristics.

[0096] 3) The radial network constraints established are all linear constraints, which are easy to solve. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 It is a schematic diagram of constraints of type 1.1 in the method proposed in the present invention.

[0098] Figure 2 It is a schematic diagram of constraints of type 1.2 in the method proposed in the present invention.

[0099] Figure 3 It is a schematic diagram of type 2 constraints in the method proposed in the present invention.

[0100] Figure 4 It is a schematic diagram of type 3 constraints in the method proposed in the present invention.

[0101] Figure 5 It is a schematic diagram of type 4 constraints in the method proposed in the present invention.

[0102] Figure 6 It is a comparison chart of sensitivity calculation results of the method proposed in the present invention, the precise reference value method and the unconstrained least squares method.

[0103] Figure 7 This is an analysis diagram of the impact of the constraint conditions of the method proposed in the present invention on the parameter regression accuracy.

[0104] Figure 8 This is the modified IEEE 33-node system topology used in the test of Example 2.

[0105] Fig. 9 It is a comparison diagram of node voltage distribution between the method proposed by the present invention and the control method.

[0106] Fig.10 It is a flow chart of a method for calculating the sensitivity of a distribution network under random charging loads of the present invention.

[0107] Figures 1 to 5 middle:

[0108] i u 、i、i d , k, j, l, N, m, n are radial distribution network nodes; 0 represents the root node.

[0109] S ki is the sensitivity of the injected power at node i to the voltage amplitude at node k; S ji is the sensitivity of the injected power at node i to the voltage amplitude at node j;

[0110] S kj is the sensitivity of the injected power at node j to the voltage amplitude at node k;

[0111] S ij is the sensitivity of the injected power at node j to the voltage amplitude at node i;

[0112] S jk is the sensitivity of the injected power at node k to the voltage amplitude at node j;

[0113] S li is the sensitivity of the injected power at node i to the voltage amplitude at node l;

[0114] S lk is the sensitivity of the injected power at node k to the voltage amplitude at node l;

[0115] S mj is the sensitivity of the injected power at node j to the voltage amplitude at node m;

[0116] S nj is the sensitivity of the injected power at node j to the voltage amplitude at node n;

[0117] S idj Inject power to node j to adjacent downstream node i d Sensitivity of voltage amplitude;

[0118] S iuj Inject power to node j to the adjacent upstream node i u Sensitivity of voltage amplitude.

[0119] Figure 7 In Chinese: Constraint 1) to constraint 8) represent constraint type 1 to constraint type 8.

[0120] Figure 8 In the figure: CS1~CS6 represent the first to sixth electric vehicle charging stations (Charging station, CS) respectively; SVC1~SVC4 represent the first to fourth static var compensators (Static var compensator, SVC) respectively; 1~33 represent the distribution network node numbers respectively. DETAILED DESCRIPTION

[0121] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0122] In the description of the present invention, the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and do not require that the present invention must be constructed and operated in a specific orientation. Therefore, they should not be understood as limitations on the present invention. The terms "connected" and "connected" used in the present invention should be understood in a broad sense. For example, it can be a fixed connection or a detachable connection; it can be a direct connection or an indirect connection through an intermediate component. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0123] See also Figures 1 to 10 A method for calculating the sensitivity of a distribution network under random charging loads, the method comprising: assuming that the column vector of active power injected by each node is P, the column vector of reactive power injected by each node is Q, P and Q are combined into an input data column vector X, X = [P T ,Q T ] T , the node voltage amplitude column vector is taken as the output variable Y, and S is the sensitivity matrix of node injection power to node voltage amplitude; S ab is the element in the ath row and bth column of the S matrix, S ab represents the power injected by node b X b The voltage amplitude U at node a a sensitivity.

[0124] The following objective function is established based on the least squares regression method:

[0125]

[0126]

[0127] Construct linear constraints that constrain elements in different rows of the S matrix;

[0128] The values ​​of ΔX and ΔY are obtained from the measured data, and the linear sensitivity parameters are calculated by the least squares regression method.

[0129] Preferably, the linear constraint condition may include one or a combination of the following constraint conditions: size relationship constraint condition, symmetry constraint condition, active and reactive power equivalence constraint condition, active and reactive power mutual constraint condition and active non-negativity constraint condition; wherein:

[0130] The size relationship constraint condition means that there is a numerical size relationship between the sensitivities of the nodes;

[0131] The symmetry constraint condition means that the sensitivity of the active power injected into the node to the voltage amplitude is symmetrical to the sensitivity of the voltage amplitude to the active power injected into the node;

[0132] The active-reactive equivalence constraint condition refers to the sensitivity of the active power injected by the node to the voltage amplitude, which is consistent with the trend of the sensitivity of the reactive power injected by the node to the voltage amplitude;

[0133] The mutual constraint condition of active and reactive power refers to the sensitivity of the active power injected by the node to the voltage amplitude, which is consistent with the trend of the sensitivity of the reactive power injected by the node to the voltage amplitude, and is used to remove some spikes;

[0134] The active non-negativity constraint condition means that the sensitivity of the active power injected by the node to the voltage amplitude is greater than or equal to 0.

[0135] Preferably, for the radial distribution network, the balancing node can be defined as the root node, and the root node can be defined as the network head end; the low-voltage busbar of the upper-level substation of the medium-voltage network can be set as the root node, and between the nodes with a connection relationship, a reference node i is set in the topological relationship, and the node closer to the root node relative to node i is the upstream node of node i, otherwise it is the downstream node of node i; set N U,i Represents the upstream node set of node i, let N D,i Represents the downstream node combination of node i, and determines N by a tree search method starting from the root node U,i and N D,i ; By N U,i and N D,i The logical judgment is used to obtain the topological position relationship between different nodes, which is used to establish the sensitivity size relationship constraint conditions between nodes at different positions in the radial distribution network.

[0136] Preferably, the method for establishing the sensitivity size relationship constraint condition between nodes at different locations in the radial distribution network may include:

[0137] In the radial distribution network, a branch extending from the root node can be assumed to be R p, p is the corresponding branch number; branch R can be set p Set i u 、i、i d , k, j, l nodes, where i u 、i d is the adjacent point of i; we can set a branch R p The branch path starting from node i on the iq , q is the branch road number starting from node i; the branch road R iq Set nodes m and n in sequence, then node i u is the upstream node of node i, node i d , k, j, l, m, n are all downstream nodes of node i, and nodes k, j, l are downstream nodes of node i d , nodes j and l are the downstream nodes of node k, node l is the downstream node of node j; node n is the downstream node of node m.

[0138] According to the topological positions between different nodes and the sensitivity relationship characteristics between adjacent points, the following constraints on the sensitivity relationship between nodes can be established:

[0139] 1) In the same network branch R p The closer the node i is to the downstream node, the greater its sensitivity:

[0140] S ki ≤S ji if{(j,k∈N D,i )∩(j,∈N D,k )}

[0141] 2) In the same network branch R p In the above, the sensitivity of node j to node j is greater than the sensitivity of node j to its upstream node, and the sensitivity of node j to the upstream node is smaller:

[0142]

[0143] 3) In the same network branch R p In the figure, the sensitivity difference between nodes i and k to the common downstream node is approximately equal:

[0144] S ji -S jk ≈S li -S lk ;

[0145] st{l,j∈(N D,i ∩N D,k );

[0146] 4) Branch S pA node on the branch road R iq Multiple nodes on the branch have a common upstream node, and these nodes corresponding to the upstream node are all downstream nodes. p The downstream node on the branch road R iq The sensitivities of multiple downstream nodes on are approximately equal:

[0147]

[0148] 5) The sensitivity difference between node i and its downstream nodes j and k is small:

[0149]

[0150] 6) Branch S p The downstream node j of node i on the branch path R iq The sensitivity of node i to its downstream nodes is between the sensitivity of node j to its upstream and downstream neighbors:

[0151] S idj ≥S mj ≥S iuj ;

[0152]

[0153] Where:

[0154] N D,k is the set of downstream nodes of node k;

[0155] N U,j is the set of upstream nodes of node j;

[0156] N U,k is the set of upstream nodes of node k;

[0157] N U,n is the set of upstream nodes of node n;

[0158] N D,m is the set of downstream nodes of node m;

[0159] N D,j is the set of downstream nodes of node j;

[0160] S ki is the sensitivity of the injected power at node i to the voltage amplitude at node k; S ji is the sensitivity of the injected power at node i to the voltage amplitude at node j;

[0161] S jj is the sensitivity of the injected power at node j to the voltage amplitude at node j;

[0162] S kjis the sensitivity of the injected power at node j to the voltage amplitude at node k;

[0163] S ij is the sensitivity of the injected power at node j to the voltage amplitude at node i;

[0164] S jk is the sensitivity of the injected power at node k to the voltage amplitude at node j;

[0165] S li is the sensitivity of the injected power at node i to the voltage amplitude at node l;

[0166] S lk is the sensitivity of the injected power at node k to the voltage amplitude at node l;

[0167] S mj is the sensitivity of the injected power at node j to the voltage amplitude at node m;

[0168] S nj is the sensitivity of the injected power at node j to the voltage amplitude at node n;

[0169] Inject power to node j to adjacent downstream node i d Sensitivity of voltage amplitude;

[0170] Inject power to node j to the adjacent upstream node i u Sensitivity of voltage amplitude;

[0171] ε def is the boundary threshold;

[0172] is the i-th topological adjacency matrix d row, the element of the i-th column;

[0173] is the i-th topological adjacency matrix u The element at row, column i.

[0174] Preferably, the difference in sensitivity between nodes i and k to the common downstream node j of the two nodes can be set to be within the range of ±10% of the average value of the difference between nodes i and k to all downstream nodes of node k:

[0175]

[0176] Where:

[0177] v is the downstream node of node k;

[0178] S vk is the sensitivity of the injected power at node k to the voltage amplitude at node v;

[0179] S vi is the sensitivity of the injected power at node i to the voltage amplitude at node v;

[0180] n D,k is the number of downstream nodes of node k.

[0181] Preferably, the sensitivity symmetry constraint condition between nodes can be expressed as follows:

[0182] (S ab -S ef )(S ba -S fe )≥0;

[0183] Where:

[0184] S ab The sensitivity of the injected power at node b to the voltage amplitude at node a;

[0185] S ba The sensitivity of the injected power at node a to the voltage amplitude at node b;

[0186] S ef The sensitivity of the injected power at node f to the voltage amplitude at node e;

[0187] S fe The sensitivity of the injected power at node e to the voltage amplitude at node f.

[0188] Preferably, the active power and reactive power equivalence constraint condition can be expressed as follows:

[0189]

[0190] Where:

[0191] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0192] The sensitivity of the reactive power injected into node b to the voltage amplitude of node a;

[0193] The sensitivity of the active power injected into node f to the voltage amplitude of node e;

[0194] The sensitivity of the reactive power injected into node f to the voltage amplitude of node e.

[0195] Preferably, the mutual constraint condition between active power and reactive power can be expressed as follows:

[0196]

[0197] Where:

[0198] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0199] The sensitivity of the reactive power injected into node b to the voltage amplitude at node a.

[0200] Preferably, the non-negativity constraint condition of the sensitivity of the node injected active power to the node voltage amplitude can be expressed as follows:

[0201]

[0202] Where:

[0203] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0204] N B Represents the set of all nodes.

[0205] The present invention also provides a distribution network sensitivity calculation model under random charging load, which is composed of the objective function and linear constraints in the above-mentioned distribution network sensitivity calculation method under random charging load.

[0206] The present invention also provides a device for calculating the sensitivity of a distribution network under random charging loads, comprising a memory and a processor, wherein the memory is used to store a computer program; the processor is used to execute the computer program and implement the steps of the method for calculating the sensitivity of a distribution network under random charging loads as described above when executing the computer program.

[0207] The following is a preferred embodiment of the present invention to further illustrate the working process and working principle of the present invention:

[0208] 1.1 Parametric regression model

[0209] The basic least squares regression method is used for parameter regression, and additional sensitivity property constraints are added on this basis. In calculating the sensitivity of the node injected power-voltage amplitude, all PQ node injected active power P column vectors and reactive power Q column vectors are selected as the input data column vector X = [P T ,Q T ] T , the node voltage amplitude V is used as the output variable Y.

[0210] The distribution transformer time scale and distribution transformer number of the same medium voltage distribution line under the same topology are obtained in the distribution automation system; the corresponding distribution transformer operation data is obtained from the marketing metering automation system.

[0211] The marketing metering automation system is established on the basis of computer information transmission technology and communication technology. It is also usually called the electric energy metering automation system. It is mainly composed of four parts: 1. Distribution point detection and metering system; 2. Plant and station electric energy metering and telemetry system; 3. Large customer load management system; 4. Low-voltage centralized meter reading system.

[0212] Finally, the least squares regression of linear sensitivity parameters is performed using the measurement data of the marketing measurement automation system.

[0213]

[0214] The matrix S represents the sensitivity matrix of node injection power-voltage amplitude. Let S ab is the element in the ath row and bth column of the S matrix, S ab represents the power injected by node b X b The voltage amplitude U at node a a sensitivity.

[0215] 1.2 Constraints on sensitivity characteristics of radial distribution networks

[0216] For radial distribution networks, operation data has unique characteristics. For radial distribution networks, the balance node (root node) is defined as the head end of the network, and in the topological relationship, the node close to the root node is the upstream node.

[0217] The radial distribution network has the following characteristics:

[0218] (1) The root node is a balancing node, and only one balancing node provides voltage support;

[0219] (2) A node has only one directly connected upstream node, but may have multiple directly connected downstream nodes.

[0220] The traditional adjacency matrix A represents the connection relationship between nodes. If two nodes i and j are directly connected, the adjacency matrix A ij =1, otherwise it is equal to 0. To simplify the definition, the low-voltage busbar of the upper substation of the medium-voltage network is considered to be the root node. Among the nodes with a connection relationship, the one closer to the root node in the topological relationship is the upstream node, otherwise it is the downstream node. U,i , N D,i They represent the upstream node set and the downstream node of node i respectively, and are determined by the tree search method starting from the root node. U,i , N D,iThe topological position relationship between different nodes can be obtained by logical judgment, which is used to establish the characteristic relationship between different positions. The connection relationship of the nodes is statistically summarized and summarized, and the corresponding constraint indicators are extracted and analyzed as follows.

[0221] Type 1, adjacency size constraint:

[0222] Type 1.1, constraints on downstream nodes:

[0223] like Figure 1 As shown, among the common downstream nodes j and k of node i, when node j is the downstream node of node k, the closer to the downstream node, the greater the sensitivity.

[0224] S ki ≤S ji if{(j,k∈N D,i )∩(j,∈N D,k )} (2);

[0225] Type 1.2, upstream node constraints:

[0226] like Figure 2 As shown in Figure 1, the sensitivity of node j to node j is greater than the sensitivity of node j to its upstream node. And the sensitivity to the upstream node is smaller.

[0227]

[0228] Type 2, constraints on the difference of common downstream nodes of nodes:

[0229] like Figure 3 As shown, the sensitivity difference between nodes i and k to the common downstream node.

[0230]

[0231] In order to avoid artificially introducing too many extreme thresholds, formula (4) is modified to be within the range of ±10% of the average value of the difference between the common downstream paths of ij, while still maintaining the linear characteristics of the constraint.

[0232]

[0233] The sensitivity difference of node i to its downstream node jk is small.

[0234]

[0235] ε def is the boundary threshold, n D,k is the number of downstream nodes of node k.

[0236] Type 3, such as Figure 4As shown in the figure, the downstream nodes of node j have approximately the same sensitivity to different downstream nodes of upstream node i:

[0237]

[0238] Type 4, such as Figure 5 As shown in the figure, the sensitivity of the branch downstream node i of node j and other downstream nodes of i, and the constraints within the upstream and downstream node interval of node i:

[0239] For node j, the other downstream branches (m, n) of the upper node i are between the root nodes of the branch.

[0240] S idj ≥S mj ≥S iuj (8);

[0241]

[0242] In the above formulas:

[0243] N D,k is the set of downstream nodes of node k;

[0244] N U,j is the set of upstream nodes of node j;

[0245] N U,k is the set of upstream nodes of node k;

[0246] N U,n is the set of upstream nodes of node n;

[0247] N D,m is the set of downstream nodes of node m;

[0248] N D,j is the set of downstream nodes of node j;

[0249] S ki is the sensitivity of the injected power at node i to the voltage amplitude at node k; S ji is the sensitivity of the injected power at node i to the voltage amplitude at node j;

[0250] S jj is the sensitivity of the injected power at node j to the voltage amplitude at node j;

[0251] S kj is the sensitivity of the injected power at node j to the voltage amplitude at node k;

[0252] S ij is the sensitivity of the injected power at node j to the voltage amplitude at node i;

[0253] Sjk is the sensitivity of the injected power at node k to the voltage amplitude at node j;

[0254] S li is the sensitivity of the injected power at node i to the voltage amplitude at node l;

[0255] S lk is the sensitivity of the injected power at node k to the voltage amplitude at node l;

[0256] S mj is the sensitivity of the injected power at node j to the voltage amplitude at node m;

[0257] S nj is the sensitivity of the injected power at node j to the voltage amplitude at node n;

[0258] Inject power to node j to adjacent downstream node i d Sensitivity of voltage amplitude;

[0259] Inject power to node j to the adjacent upstream node i u Sensitivity of voltage amplitude;

[0260] ε def is the boundary threshold;

[0261] is the i-th topological adjacency matrix d row, the element of the i-th column;

[0262] is the i-th topological adjacency matrix u The element at row, column i.

[0263] Type 5, symmetry constraints:

[0264] The above relationship from active power to voltage and from voltage to active power is symmetrical.

[0265] (S ab -S ef )(S ba -S fe )≥0 (9); where:

[0266] S ab The sensitivity of the injected power at node b to the voltage amplitude at node a;

[0267] S ba The sensitivity of the injected power at node a to the voltage amplitude at node b;

[0268] S ef The sensitivity of the injected power at node f to the voltage amplitude at node e;

[0269] S fe The sensitivity of the injected power at node e to the voltage amplitude at node f.

[0270] Type 6, active and reactive power equivalence constraints:

[0271] The trends of active power to voltage and reactive power to voltage are consistent

[0272]

[0273] Where:

[0274] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0275] The sensitivity of the reactive power injected into node b to the voltage amplitude of node a;

[0276] The sensitivity of the active power injected into node f to the voltage amplitude of node e;

[0277] The sensitivity of the reactive power injected into node f to the voltage amplitude of node e.

[0278] Type 7, active and reactive power mutual constraints:

[0279] The trends of active power to voltage and reactive power to voltage remain consistent; some spikes are removed.

[0280]

[0281] Where:

[0282] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0283] The sensitivity of the reactive power injected into node b to the voltage amplitude at node a.

[0284] Type 8, active non-negativity constraint:

[0285] The above relationship from active power to voltage and from voltage to active power is symmetrical.

[0286]

[0287] Where:

[0288] The sensitivity of the active power injected into node b to the voltage amplitude of node a;

[0289] N B Represents the set of all nodes.

[0290] Through the above physical characteristics of tidal flow sensitivity, the sensitivity is directly constrained in the parameter regression process, thereby improving the accuracy.

[0291] 1.3 Constraint Characteristics

[0292] Formula (2) is the objective function, and Formula (2) to Formula (12) constitute the constraint conditions, which together constitute the constrained least squares method model. However, it should also be noted that unlike the unconstrained least squares method, which can solve the sensitivity matrix row by row without affecting the accuracy, the constraints of the present invention have a constraint relationship between the elements of different rows of the sensitivity matrix. Therefore, in the parameter regression, it is necessary to perform parameter regression on all elements of the sensitivity difficulty matrix at the same time. However, all the constraints of the present invention are linear constraints, so the difficulty of solving is relatively low, and the solution can be quickly completed using a commercial solver.

[0293] 1.4 A method for calculating the sensitivity of distribution network under random charging load:

[0294] Step 1: Extract the distribution network topology information and preprocess the operation measurement data of the active power, reactive power and voltage amplitude of the distribution transformers in the distribution network. Remove the data of the missing time section and only retain the data with complete measurement information.

[0295] Step 2: Based on the known radial topology information, establish the operating characteristic constraints using formulas (2)-(12).

[0296] Step 3: Substitute the constraint conditions established in step 2 into formula (2) to form a calculation method for data-driven sensitivity with constrained least squares.

[0297] 2. Example Analysis

[0298] 2000 training data sets and 1000 test data sets were randomly generated by Monte Carlo simulation (MCS), in which the load power was superimposed with two different ranges of variation, namely ±20% and ±50%. The power and voltage amplitude errors used in the embodiment were set to 1%.

[0299] 2.1 Example 1

[0300] The IEEE 33 node system is used to verify the calculation accuracy of the sensitivity, and the unconstrained least squares estimation method is used to evaluate the effectiveness of the constraint conditions established by this method. Figure 6 shown. Figure 6 (c) Overall trend and benchmark value Figure 6(a) is basically consistent and has good accuracy. However, the sensitivity surface of the unconstrained least squares estimation method has a large number of burrs and spikes, and some nodes have negative values, which seriously deviates from the reference value and has a large error. It can be seen that the method of the present invention has a significant accuracy advantage.

[0301] The regression errors of the IEEE33, 69, 141 node system under different operating ranges of the data set are shown in Table 1. It can be seen that the method of the present invention is significantly better than the unconstrained least squares method in terms of both the mean absolute error and the maximum absolute error under different examples. The mean absolute error and the maximum absolute error are both reduced by more than 10 times compared with the unconstrained least squares method, indicating that the method of the present invention has a significant accuracy advantage over the control method.

[0302] In order to evaluate the impact of adding constraints on the accuracy of parameter regression, the IEEE69 node system with the best error reduction effect is taken as an example to evaluate the impact of different constraint superposition on accuracy by continuously adding constraints. Since constraint types 5 and 6 are symmetry and active and reactive equivalence constraints, they are compatible with all other constraints, so they are used as the starting point with constraints. Figure 7 It can be seen that after adding constraint types 1, 5, and 6, the calculation accuracy can be significantly improved, and the average error is reduced by 20 times. Finally, after adding other constraints, the error is further reduced by 3 times. The parameter regression through all constraints can finally reach 1.9% of the unconstrained least squares method in the IEEE69 node calculation example. It shows that the constraints established by the method proposed in the present invention have a significant effect on improving the regression accuracy of sensitivity parameters.

[0303] Table 1

[0304]

[0305] 2.2 Example 2

[0306] In order to evaluate the adaptability of the method of the present invention in the optimization problem, the reactive power optimization of the distribution network is carried out by embedding the optimization model: the reactive power regulation is minimized as the optimization goal, and the reactive power regulation is carried out by the arranged static var compensator (SVC). The modified IEEE33 wiring system is used for example analysis, in which a charging station (CS) and a static var compensator (SVC) are added, as shown in the following figure. Figure 8 shown.

[0307] In the voltage regulation example of Example 2, two comparison methods are used: 1) unconstrained least squares method; 2) Newton-Raphson method: the sensitivity matrix is ​​obtained by inverting the Newton-Raphson Jacobian matrix based on accurate impedance parameters and accurate operating state information.

[0308] The sensitivity matrix calculated by the method of the present invention and the control method is brought into the above optimization model. The voltage distribution after voltage regulation and the optimized adjustment amount in the optimization result are respectively as follows: Fig. 9 As shown. It can be seen that the low voltage problem before voltage regulation has been effectively solved in different calculation methods. The method of the present invention is basically consistent with the Newton-Raphson method of precise parameters, while the unconstrained least square method has a large number of burrs and large errors. In terms of the adjustment amount, the calculation results of the method of the present invention and the Newton-Raphson method have the same trend, but the adjustment amount is too large, which is mainly caused by the sensitivity error, corresponding to Fig. 9 The voltage after adjustment is higher than that of Newton-Raphson method. The calculation results are significantly better than those of the unconstrained method, indicating that the sensitivity of the method of the present invention is feasible when applied as a constraint condition to the optimization problem.

[0309] The embodiments described above are only used to illustrate the technical ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The patent scope of the present invention cannot be limited only by this embodiment, that is, any equivalent changes or modifications made to the spirit disclosed by the present invention still fall within the patent scope of the present invention.

Claims

1. A method for calculating the sensitivity of a distribution network under random charging loads, characterized in that: The method includes: assuming that the column vector of active power injected by each node is P, the column vector of reactive power injected by each node is Q, and P and Q form an input data column vector X, X=[P T ,Q T ] T , take the node voltage amplitude column vector as the output variable Y, let S be the sensitivity matrix of node injection power to node voltage amplitude; let S ab is the element in row a and column b of the S matrix, S ab represents the injection power X of node b b Voltage amplitude U at node a a sensitivity; The following objective function is established based on the least squares regression method: Construct linear constraints that constrain elements in different rows of the S matrix; The values ​​of ΔX and ΔY are obtained from the measured data, and the linear sensitivity parameters are calculated by the least squares regression method; Linear constraints include one or a combination of the following constraints: magnitude constraint, symmetry constraint, active and reactive power equivalence constraint, active and reactive power mutual constraint, and active power non-negativity constraint; among them: The size relationship constraint condition means that there is a numerical size relationship between the sensitivities of the nodes; The symmetry constraint condition means that the sensitivity of the active power injected into the node to the voltage amplitude is symmetrical to the sensitivity of the voltage amplitude to the active power injected into the node; The active / reactive power equivalence constraint refers to the sensitivity of the active power injected by the node to the voltage amplitude, which should be consistent with the sensitivity of the reactive power injected by the node to the voltage amplitude. The mutual constraint between active and reactive power refers to the sensitivity of the active power injected by the node to the voltage amplitude, which is consistent with the sensitivity of the reactive power injected by the node to the voltage amplitude, and is used to remove some spikes. The active power non-negativity constraint condition means that the sensitivity of the active power injected by the node to the voltage amplitude is greater than or equal to 0; For radial distribution network, the balance node is defined as the root node, and the root node is defined as the network head end; the low voltage bus of the upper substation of the medium voltage network is set as the root node. Among the nodes with connection relationship, a reference node i is set in the topological relationship. The node closer to the root node relative to node i is the upstream node of node i, otherwise it is the downstream node of node i; set N U,i Represents the upstream node set of node i, let N D,i Represents the downstream node combination of node i, and determines N by the tree search method starting from the root node U,i and N D,i ; By N U,i and N D,i The logical judgment is used to obtain the topological position relationship between different nodes, which is used to establish the sensitivity size relationship constraint conditions between nodes at different positions in the radial distribution network; Methods for establishing sensitivity constraint conditions between nodes at different locations in a radial distribution network include: Assume that in the radial distribution network, a branch extending from the root node is R p , p is the corresponding branch number; suppose branch R p Set i u 、i、i d , k, j, l nodes, where i u 、i d is the adjacent point of i; suppose there is a branch R p The branch road that starts to branch out from the node i on the iq , q is the branch road number starting from node i; let branch road R iq Set nodes m and n in sequence, then node i u is the upstream node of node i, node i d , k, j, l, m, n are all downstream nodes of node i, and nodes k, j, l are downstream nodes of node i d , nodes j and l are the downstream nodes of node k, node l is the downstream node of node j; node n is the downstream node of node m; According to the topological positions between different nodes and the sensitivity relationship characteristics between adjacent points, the following constraints on the sensitivity relationship between nodes are established: 1) In the same network branch R p On the other hand, the closer the node i is to the downstream node, the greater its sensitivity: S ki ≤S ji if{(j,k∈N D,i )∩(j,∈N D,k )}2) In the same network branch R p In the figure, the sensitivity of node j to node j is greater than the sensitivity of node j to its upstream node, and the sensitivity of node j to the upstream node is smaller: 3) In the same network branch R p In the figure above, the sensitivity difference between nodes i and k to the common downstream node is approximately equal: S ji -S jk ≈S li -S lk ; s.t.{l,j∈(N D,i ∩N D,k ); 4) Branch S p A node on the branch road R iq Multiple nodes on the same node have a common upstream node, and these nodes are all downstream nodes corresponding to the upstream node. p The downstream node on the branch road R iq The sensitivities of multiple downstream nodes on are approximately equal: 5) The sensitivity difference between node i and its downstream nodes j and k is small: 6) Branch S p The downstream node j of node i on the branch road R iq The sensitivity of node i to its downstream nodes is between the sensitivity of node j to its upstream and downstream neighbors: S idj ≥S mj ≥S iuj ; Where: N D,k is the set of downstream nodes of node k; N U,j is the set of upstream nodes of node j; N U,k is the set of upstream nodes of node k; N U,n is the set of upstream nodes of node n; N D,m is the set of downstream nodes of node m; N D,j is the set of downstream nodes of node j; S ki is the sensitivity of the injected power at node i to the voltage amplitude at node k; S ji is the sensitivity of the injected power at node i to the voltage amplitude at node j; S jj is the sensitivity of the injected power at node j to the voltage amplitude at node j; S kj is the sensitivity of the injected power at node j to the voltage amplitude at node k; S ij is the sensitivity of the injected power at node j to the voltage amplitude at node i; S jk is the sensitivity of the injected power at node k to the voltage amplitude at node j; S li is the sensitivity of the injected power at node i to the voltage amplitude at node l; S lk is the sensitivity of the injected power at node k to the voltage amplitude at node l; S mj is the sensitivity of the injected power at node j to the voltage amplitude at node m; S nj is the sensitivity of the injected power at node j to the voltage amplitude at node n; S idj Inject power from node j to node i adjacent to downstream node i d Sensitivity to voltage amplitude; Inject power for node j to node i adjacent to upstream node i u Sensitivity to voltage amplitude; ε def is the boundary threshold; is the i-th topological adjacency matrix d The element of row, column i; is the i-th topological adjacency matrix u The element at row, column i.

2. The method for calculating the sensitivity of the distribution network under random charging load according to claim 1, characterized in that: Assume that the difference in sensitivity between nodes i and k to their common downstream node j is within ±10% of the average of the difference in sensitivity between nodes i and k to all downstream nodes of node k: Where: v is the downstream node of node k; S vk is the sensitivity of the injected power at node k to the voltage amplitude at node v; S vi is the sensitivity of the injected power at node i to the voltage amplitude at node v; n D,k is the number of downstream nodes of node k.

3. The method for calculating the sensitivity of the distribution network under random charging load according to claim 1, characterized in that: The sensitivity symmetry constraint between nodes is as follows: (S ab -S ef )(S ba -S fe )≥0; Where: S ab The sensitivity of the injected power at node b to the voltage amplitude at node a is: S ba The sensitivity of the injected power at node a to the voltage amplitude at node b is: S ef is the sensitivity of the injected power at node f to the voltage amplitude at node e; S fe is the sensitivity of the injected power at node e to the voltage amplitude at node f.

4. The method for calculating the sensitivity of a distribution network under random charging load according to claim 1, wherein: The equivalence constraint of active power and reactive power is as follows: Where: The sensitivity of the active power injected into node b to the voltage amplitude of node a; The sensitivity of the reactive power injected into node b to the voltage amplitude of node a; is the sensitivity of the active power injected into node f to the voltage amplitude of node e; is the sensitivity of the reactive power injected into node f to the voltage amplitude at node e.

5. The method for calculating the sensitivity of the distribution network under random charging load according to claim 1, characterized in that: The mutual constraints between active power and reactive power are shown in the following formula: Where: The sensitivity of the active power injected into node b to the voltage amplitude of node a; The sensitivity of the reactive power injected into node b to the voltage amplitude at node a.

6. A distribution network sensitivity calculation model under random charging load, characterized by: The model is composed of the objective function and linear constraints in the method for calculating the sensitivity of the distribution network under random charging loads described in any one of claims 1 to 5.

7. A device for calculating the sensitivity of a distribution network under random charging load, comprising a memory and a processor, characterized in that: The memory is used to store a computer program; the processor is used to execute the computer program and implement the steps of the method for calculating the sensitivity of the distribution network under random charging loads as described in any one of claims 1 to 5 when executing the computer program.

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