Consideration of symmetric current control distributed power low-voltage distribution network resistance state estimation method

Abstract

This invention discloses a robust state estimation method for low-voltage distribution networks considering symmetrically current-controlled distributed generation, comprising the following steps: 1) acquiring basic data of the power grid; 2) establishing a node admittance matrix for the low-voltage distribution network based on the basic data of the power grid; 3) establishing measurement equations for power generation nodes, load nodes, symmetrically current-controlled distributed generation, and tie nodes in the distribution network; 4) establishing Jacobian matrices for each type of node based on the measurement equations; 5) establishing a modified equation based on exponential weight functions, zero-injection constraints, and symmetrical current constraints, and updating the state variable x. (time) 6) Determine if the iteration termination condition is met. If yes, output the state variable; otherwise, set time = time + 1 and return to step 5). This invention first solves the admittance matrix, Jacobian matrix, and correction equation of the low-voltage distribution network system, and then uses an exponential weight function to iteratively solve the state estimation of the low-voltage distribution network.

Description

Technical Field

[0001] This invention relates to the field of power system dispatch automation, specifically to a method for estimating the robust state of low-voltage distribution networks considering symmetrical current control of distributed generation. Background Technology

[0002] With the rapid development of the power industry and the increasing prominence of energy shortages, more and more distributed power sources are being connected to low-voltage distribution networks, posing significant challenges to power supply structure, power supply methods, and power supply reliability. Three-phase state estimation of low-voltage distribution networks is a fundamental function of advanced application software in distribution management systems. Utilizing redundant measurement data to improve the accuracy and completeness of real-time information is a prerequisite for low-voltage power flow calculation and plays a crucial role in distribution network planning and operation.

[0003] Existing studies on the robustness estimation of low-voltage distribution networks containing distributed generation mostly assume that the distributed generation is connected to the low-voltage distribution network through a "three-phase four-arm converter", that is, a three-phase four-wire connection method, and that phase-to-phase power and voltage control methods are used to reduce the three-phase imbalance of the distribution network.

[0004] However, in actual distribution networks, in order to take into account factors such as implementation difficulty, local consumption and reduced investment, most distributed power sources are currently connected to the distribution network through "three-phase three-bridge-arm converters" and adopt a three-phase symmetrical current control method. Summary of the Invention

[0005] The purpose of this invention is to provide a method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed generation, comprising the following steps:

[0006] 1) Obtain basic data about the power grid;

[0007] Furthermore, the basic data of the power grid includes the network structure, power grid parameters, and measurements from smart meters;

[0008] The network structure includes the power grid topology connections;

[0009] The power grid parameters include line resistance, reactance, and rated voltage in the power grid.

[0010] The smart meter measures the active power, reactive power, and voltage amplitude of the three phases at the load endpoint relative to the neutral point; the active power, reactive power, voltage amplitude, and current amplitude of the three phases at the low-voltage side endpoint of the distribution transformer relative to the neutral point; and the active power, reactive power, and voltage of the two lines at the endpoint of the symmetrical current-controlled distributed power source.

[0011] 2) Establish the admittance matrix of low-voltage distribution network nodes based on the basic data of the power grid;

[0012] Furthermore, the steps for establishing the node admittance matrix of the low-voltage distribution network based on the basic data of the power grid include:

[0013] 2.1) Calculate the injected current I at the midpoint j of the power grid branch ij. j ,Right now:

[0014]

[0015] In the formula, I j Let j be the injected current at endpoint j; Let be the self-admittance matrix of endpoint j; Let i be the mutual admittance matrix between endpoint j and endpoint i; Let J be the admittance matrix between endpoints j and p. Let j be the set of endpoints directly connected to j, and Y ji Y is the admittance matrix of the branch; jj V is the admittance matrix of the parallel branches at the endpoints; i V j V p I represents the voltage at terminals i, j, and p. ji I is the current flowing through branch ji; jj Let N be the vector of currents flowing out of each node within the endpoint; j = 1, 2, ..., N; N is the total number of endpoints;

[0016] Wherein, the self-admittance matrix of endpoint j The mutual admittance matrix between endpoint j and endpoint i As shown below:

[0017]

[0018] 2.2) Correcting the self-admittance matrix of endpoint j, we obtain:

[0019]

[0020] In the formula, Let j be the set of other endpoints directly connected to endpoint j, and

[0021] 2.3) Establish the endpoint admittance matrix of the low-voltage distribution network. Right now:

[0022]

[0023] In the formula, N is the total number of endpoints.

[0024] 3) Establish measurement equations for power source nodes, load nodes, symmetrical current-controlled distributed power sources, and tie nodes in the distribution network;

[0025] Furthermore, the measurement equations for power source nodes and load nodes in the distribution network include equivalent injected current measurement equations, virtual injected current measurement equations, current amplitude measurement equations, and voltage amplitude measurement equations:

[0026] The equivalent injection current measurement equations for power supply nodes and load nodes are shown below:

[0027]

[0028] In the formula, P i dn and This represents the active and reactive power of phase d relative to the neutral point n; and f i d Indicates voltage The real and imaginary parts; f is the real part of the voltage at neutral point n; i n This represents the imaginary part of the voltage at the neutral point n. and Indicate admittance The real and imaginary parts; This represents the set of endpoints connected to endpoint i, and includes endpoint i. and Indicates voltage Real and imaginary parts; set B1 = {a, b, c, n};

[0029] The equations for virtual injection current measurement at power nodes and load nodes are shown below:

[0030]

[0031] In the formula, and Indicate admittance The real and imaginary parts;

[0032] The equations for measuring the current amplitude at power supply nodes and load nodes are shown below:

[0033]

[0034] In the formula, This refers to the amplitude of the three-phase current.

[0035] The equations for measuring the voltage amplitude at power supply nodes and load nodes are shown below:

[0036]

[0037] In the formula, Let n be the voltage magnitude of the three phases at node n relative to the neutral point n.

[0038] Furthermore, the measurement equations for the distributed power source include line power measurement equations, line voltage amplitude measurement equations, and symmetrical current measurement equations.

[0039] The equation for line power measurement is as follows:

[0040]

[0041] In the formula, The two phase lines are active. The two-phase line is reactive; and Indicates voltage The real and imaginary parts; and Indicates voltage The real and imaginary parts; and Indicates voltage The real and imaginary parts; and Indicate admittance The real and imaginary parts; set B p = {a, b, c}; α ∈ {a, b};

[0042] The equation for measuring line voltage amplitude is as follows:

[0043]

[0044] In the formula, This represents the amplitude of the two-phase line voltage αc.

[0045] The symmetrical current serves as both a virtual measurement and an equality constraint, and its measurement equation is as follows:

[0046]

[0047] In the formula, and Indicates voltage Real part and imaginary part; and Indicate admittance The real and imaginary parts; and Indicate admittance The real and imaginary parts; and Indicate admittance The real and imaginary parts.

[0048] Furthermore, the measurement equations for the connection nodes are as follows:

[0049]

[0050] In the formula, and Indicate admittance The real and imaginary parts; and Indicates voltage Real and imaginary parts; set B = {a, b, c, n}.

[0051] 4) Establish the Jacobian matrix for each type of node based on the measurement equation;

[0052] Furthermore, the Jacobian matrices of each type of node include the Jacobian matrix of power nodes, the Jacobian matrix of load nodes, the Jacobian matrix of distributed power sources, and the Jacobian matrix of interconnection nodes.

[0053] The power node Jacobian matrix includes its own Jacobian matrix H. ss (1:14, 1:8), the Jacobian matrix H of all nodes except itself. sj (1:14, 1:8);

[0054] Among them, the Jacobian matrix H ss (1:14, 1:8) includes the Jacobian matrix H corresponding to the current amplitude of the power supply. ss (1:3, 1:8), the Jacobian matrix H corresponding to the voltage amplitude of the power supply. ss (4:6, 1:8), equivalent current corresponding Jacobian matrix H ss (7:14, 1:8);

[0055] The current amplitude of the power supply corresponds to the Jacobian matrix H. ss (1:3, 1:8) is shown below:

[0056]

[0057] In the formula, Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts; Indicates voltage Real and imaginary parts; set B p = {a, b, c}; t ∈ B p ;

[0058] H ss (4:6, 1:8) is the Jacobian matrix corresponding to the voltage amplitude of the power supply, specifically:

[0059]

[0060] In the formula, Indicates voltage Real part and imaginary part; Indicates voltage Real part and imaginary part; Indicates voltage Real part and imaginary part; Indicates voltage Real part and imaginary part;

[0061] H ss (7:14, 1:8) is the Jacobian matrix corresponding to the equivalent current, specifically:

[0062]

[0063] In the formula, Indicate admittance The real and imaginary parts; δ1,δ2∈{a,b,c,n}.

[0064] Wherein, matrix ΔH ss (1:8, 1:8) is shown below:

[0065]

[0066] parameter As shown below:

[0067]

[0068] parameter As shown below:

[0069]

[0070] Jacobian matrix H sj (1:14, 1:8) includes matrix H sj (1:3, 1:8), matrix H sj (4:6, 1:8), matrix H sj (7:14, 1:8), that is:

[0071]

[0072] H sj (4:6, 1:8) = [0] 3×8 (20)

[0073]

[0074] In the formula, Indicate admittance The real and imaginary parts; Indicates voltage Real part and imaginary part; Indicate admittance The real and imaginary parts;

[0075] The load node Jacobian matrix includes its own Jacobian matrix H. jj (1:11, 1:8), the Jacobian matrix H of all nodes except itself. jq (1:11, 1:8);

[0076] Jacobian matrix H jj (1:11, 1:8) includes the Jacobian matrix H corresponding to the equivalent current of the load. jj (1:8,1:8)=H ss (7:14, 1:8), Jacobian matrix H corresponding to voltage amplitude jj (9:11, 1:8) = H ss (4:6, 1:8);

[0077] Jacobian matrix H jq (1:11, 1:8) includes the Jacobian matrix H jq (1:8,1:8)=H sj (7:14, 1:8), Jacobian matrix H jq (9:11, 1:8) = H sj (4:6, 1:8);

[0078] The distributed power supply Jacobian matrix includes its own Jacobian matrix H. vv (1:10, 1:6), the Jacobian matrix H of all nodes except itself. vj (1:10, 1:6);

[0079] Jacobian matrix H vv (1:10, 1:6) includes the Jacobian matrix H corresponding to the symmetric current. vv (1:4, 1:6), Jacobian matrix H corresponding to linear active power. vv (5:6, 1:6), Jacobian matrix H corresponding to linear reactive power vv (7:8, 1:6), Jacobian matrix H corresponding to voltage amplitude vv (9:10, 1:6);

[0080] The Jacobian matrix H corresponding to symmetrical current vv (1:4, 1:6) includes matrix H vv (1:2,1:6), matrix H vv (3:4,1:6), that is:

[0081]

[0082] In the formula, Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts;

[0083] Linear active power corresponds to the Jacobian matrix H vv (5:6, 1:6) is shown below:

[0084]

[0085] Among them, parameters parameter parameter parameter parameter parameter As shown below:

[0086]

[0087]

[0088] In the formula, α, α1, α2 ∈ {a, b, c}; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts;

[0089] Linear reactive power corresponding Jacobian matrix H vv (7:8, 1:6) is shown below:

[0090]

[0091] Among them, parameters parameter parameter parameter parameter parameter As shown below:

[0092]

[0093]

[0094] Voltage amplitude corresponds to Jacobian matrix H vv (9:10, 1:6) is shown below.

[0095]

[0096] Jacobian matrix H vj (1:10, 1:6) includes matrix Hvj (1:4,1:6)=H vv (1:4, 1:6), matrix H vj (5:6, 1:6), matrix H vj (7:8,1:6)H vj (5:6, 1:6), matrix H vj (9:10, 1:6), that is:

[0097]

[0098]

[0099] H vj (9:10, 1:6) = [0] 2×6 (32)

[0100] The Jacobian matrix of the connecting node includes its own Jacobian matrix H. hh (1:8, 1:8), the Jacobian matrix H of all nodes except itself. hj (1:8, 1:8);

[0101] Among them, the Jacobian matrix H hh (1:8, 1:8) and H hj (1:8, 1:8) represents the Jacobian matrix corresponding to the virtual current measurement at the connection endpoint, and is respectively related to H ss (7:14, 1:8) and H sj (7:14, 1:8) are the same.

[0102] 5) Based on the exponential weight function, zero injection constraint, and symmetrical current constraint, establish a modified equation and update the state variable x. (time) ;

[0103] Furthermore, a modified equation is established based on the exponential weight function, zero injection constraint, and symmetric current constraint to update the state variable x. (time) The content is as follows:

[0104] 5.1) Using residual exponential weighting, establish an exponentially weighted least squares estimation model, namely:

[0105]

[0106] In the formula, z represents the measurement; h(x) represents the measurement function; W represents the weight matrix; J(x) represents the objective function value; min represents taking the minimum value; and x represents the state variable.

[0107] The diagonal elements w in the weight matrix W i * The calculation formula is as follows:

[0108]

[0109] In the formula: Represents fixed weights; σ represents the Parzen window width; r Ni Represents the standardized residual;

[0110] 5.2) Establish iterative equations considering zero-injection power constraints and symmetrical current constraints of distributed sources, and use Newton's method to solve iterative equation (35) and update state variables;

[0111]

[0112] In the formula, H, C, and D represent the Jacobian matrices of measurement functions h(x), c(x), and d(x); k represents the iteration number; λ1 k , λ2 k Represents the eigenvalue; Δx k This represents the adjustment amount for the state variable.

[0113] 6) Determine if the iteration termination condition is met. If yes, output the state variable; otherwise, set time = time + 1 and return to step 5.

[0114] Furthermore, the iteration termination condition includes the correction amount Δx of the state variable. (time) Satisfy max(|Δx) (time) |)<ε, or max(|Δx) (time) |)≥ε and the number of iterations time≥Tmax; Tmax is the maximum number of iterations; ε is the correction threshold.

[0115] The technical effectiveness of this invention is undeniable. This invention proposes a robust state estimation method for low-voltage distribution networks considering symmetrically current-controlled distributed power sources. This method connects a symmetrically current-controlled, three-phase three-wire distributed power source to a three-phase four-wire low-voltage distribution network, establishing a measurement model for the symmetrically current-controlled distributed power source. Two sets of inter-line active power, inter-line reactive power, and line voltage are used as measurement data, and the symmetrical current is used as a virtual measurement and equality constraint. This invention first solves for the admittance matrix, Jacobian matrix, and correction equations of the low-voltage distribution network system, and then uses an iterative solution based on an exponential weighting function to estimate the state of the low-voltage distribution network. Attached Figure Description

[0116] Figure 1 A schematic diagram of a method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources;

[0117] Figure 2 This is a connection diagram for a three-phase, three-wire distributed power source connected to a low-voltage distribution network.

[0118] Figure 3 Wiring diagram for the IEEE-13 node power distribution system. Detailed Implementation

[0119] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0120] Example 1:

[0121] See Figures 1 to 3 A robust state estimation method for low-voltage distribution networks considering symmetrical current-controlled distributed generation includes the following steps:

[0122] 1) Obtain basic data about the power grid;

[0123] The basic data of the power grid includes the network structure, power grid parameters, and smart meter measurements.

[0124] The network structure includes the power grid topology connections;

[0125] The power grid parameters include line resistance, reactance, and rated voltage in the power grid.

[0126] The smart meter measures the active power, reactive power, and voltage amplitude of the three phases at the load endpoint relative to the neutral point; the active power, reactive power, voltage amplitude, and current amplitude of the three phases at the low-voltage side endpoint of the distribution transformer relative to the neutral point; and the active power, reactive power, and voltage of the two lines at the endpoint of the symmetrical current-controlled distributed power source.

[0127] 2) Establish the admittance matrix of low-voltage distribution network nodes based on the basic data of the power grid;

[0128] The steps for establishing the node admittance matrix of a low-voltage distribution network based on the basic data of the power grid include:

[0129] 2.1) Calculate the injected current I at the midpoint j of the power grid branch ij. j ,Right now:

[0130]

[0131] In the formula, I j Let j be the injected current at endpoint j; Let be the self-admittance matrix of endpoint j; Let i be the mutual admittance matrix between endpoint j and endpoint i; Let J be the admittance matrix between endpoints j and p. Let j be the set of endpoints directly connected to j, and Y ji Y is the admittance matrix of the branch; jj V is the admittance matrix of the parallel branches at the endpoints; i V j V p I represents the voltage at terminals i, j, and p. ji I is the current flowing through branch ji; jj Let N be the vector of currents flowing out of each node within the endpoint; j = 1, 2, ..., N; N is the total number of endpoints;

[0132] Wherein, the self-admittance matrix of endpoint j The mutual admittance matrix between endpoint j and endpoint i As shown below:

[0133]

[0134] 2.2) Correcting the self-admittance matrix of endpoint j, we obtain:

[0135]

[0136] In the formula, Let j be the set of other endpoints directly connected to endpoint j, and

[0137] 2.3) Establish the endpoint admittance matrix of the low-voltage distribution network. Right now:

[0138]

[0139] In the formula, N is the total number of endpoints.

[0140] 3) Establish measurement equations for power source nodes, load nodes, symmetrical current-controlled distributed power sources, and tie nodes in the distribution network;

[0141] The measurement equations for power source nodes and load nodes in the distribution network include equivalent injected current measurement equations, virtual injected current measurement equations, current amplitude measurement equations, and voltage amplitude measurement equations.

[0142] The equivalent injection current measurement equations for power supply nodes and load nodes are shown below:

[0143]

[0144] In the formula, P i dn and This represents the active and reactive power of phase d relative to the neutral point n; and f i d Indicates voltage The real and imaginary parts; f is the real part of the voltage at neutral point n; i n This represents the imaginary part of the voltage at the neutral point n. and Indicate admittance The real and imaginary parts; This represents the set of endpoints connected to endpoint i, and includes endpoint i. and Indicates voltage Real and imaginary parts; set B1 = {a, b, c, n};

[0145] The equations for virtual injection current measurement at power nodes and load nodes are shown below:

[0146]

[0147] In the formula, and Indicate admittance The real and imaginary parts;

[0148] The equations for measuring the current amplitude at power supply nodes and load nodes are shown below:

[0149]

[0150] In the formula, This refers to the amplitude of the three-phase current.

[0151] The equations for measuring the voltage amplitude at power supply nodes and load nodes are shown below:

[0152]

[0153] In the formula, Let n be the voltage magnitude of the three phases at node n relative to the neutral point n.

[0154] The measurement equations for the distributed power source include the line power measurement equation, the line voltage amplitude measurement equation, and the symmetrical current measurement equation.

[0155] The equation for line power measurement is as follows:

[0156]

[0157] In the formula, The two phase lines are active. The two-phase line is reactive; and Indicates voltage The real and imaginary parts; and Indicates voltage The real and imaginary parts; and Indicates voltage The real and imaginary parts; and Indicate admittance The real and imaginary parts; set B p = {a, b, c}; α ∈ {a, b};

[0158] The equation for measuring line voltage amplitude is as follows:

[0159]

[0160] In the formula, This represents the amplitude of the two-phase line voltage αc.

[0161] The symmetrical current serves as both a virtual measurement and an equality constraint, and its measurement equation is as follows:

[0162]

[0163] In the formula, and Indicates voltage Real part and imaginary part; and Indicate admittance The real and imaginary parts; and Indicate admittance The real and imaginary parts; and Indicate admittance The real and imaginary parts.

[0164] The measurement equations for the connection node are shown below:

[0165]

[0166] In the formula, and Indicate admittance The real and imaginary parts; and Indicates voltage Real and imaginary parts; set B = {a, b, c, n}.

[0167] 4) Establish the Jacobian matrix for each type of node based on the measurement equation;

[0168] The Jacobian matrices of each type of node include the Jacobian matrix of power nodes, the Jacobian matrix of load nodes, the Jacobian matrix of distributed power sources, and the Jacobian matrix of interconnection nodes.

[0169] The power node Jacobian matrix includes its own Jacobian matrix H. ss(1:14, 1:8), the Jacobian matrix H of all nodes except itself. sj (1:14, 1:8);

[0170] Among them, the Jacobian matrix H ss (1:14, 1:8) includes the Jacobian matrix H corresponding to the current amplitude of the power supply. ss (1:3, 1:8), the Jacobian matrix H corresponding to the voltage amplitude of the power supply. ss (4:6, 1:8), equivalent current corresponding Jacobian matrix H ss (7:14, 1:8);

[0171] The current amplitude of the power supply corresponds to the Jacobian matrix H. ss (1:3, 1:8) is shown below:

[0172]

[0173] In the formula, Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts; Indicates voltage Real and imaginary parts; set B p = {a, b, c}; t ∈ B p ;

[0174] H ss (4:6, 1:8) is the Jacobian matrix corresponding to the voltage amplitude of the power supply, specifically:

[0175]

[0176] In the formula, Indicates voltage Real part and imaginary part; Indicates voltage Real part and imaginary part; Indicates voltage Real part and imaginary part; Indicates voltage Real part and imaginary part;

[0177] H ss (7:14, 1:8) is the Jacobian matrix corresponding to the equivalent current, specifically:

[0178]

[0179] In the formula, Indicate admittance The real and imaginary parts; δ1,δ2∈{a,b,c,n}.

[0180] Wherein, matrix ΔH ss (1:8, 1:8) is shown below:

[0181]

[0182] In the formula, set B l ={a,b,c};

[0183] parameter As shown below:

[0184]

[0185] parameter As shown below:

[0186]

[0187] Jacobian matrix H sj (1:14, 1:8) includes matrix H sj (1:3, 1:8), matrix H sj (4:6, 1:8), matrix H sj (7:14, 1:8), that is:

[0188]

[0189] H sj (4:6, 1:8) = [0] 3×8 (20)

[0190]

[0191] In the formula, Indicate admittance The real and imaginary parts; Indicates voltage Real part and imaginary part; Indicate admittance The real and imaginary parts;

[0192] The load node Jacobian matrix includes its own Jacobian matrix H. jj (1:11, 1:8), the Jacobian matrix H of all nodes except itself. jq (1:11, 1:8);

[0193] Jacobian matrix H jj (1:11, 1:8) includes the Jacobian matrix H corresponding to the equivalent current of the load. jj (1:8,1:8)=H ss (7:14, 1:8), Jacobian matrix H corresponding to voltage amplitude jj(9:11, 1:8) = H ss (4:6, 1:8);

[0194] Jacobian matrix H jq (1:11, 1:8) includes the Jacobian matrix H jq (1:8,1:8)=H sj (7:14, 1:8), Jacobian matrix H jq (9:11, 1:8) = H sj (4:6, 1:8);

[0195] The distributed power supply Jacobian matrix includes its own Jacobian matrix H. vv (1:10, 1:6), the Jacobian matrix H of all nodes except itself. vj (1:10, 1:6);

[0196] Jacobian matrix H vv (1:10, 1:6) includes the Jacobian matrix H corresponding to the symmetric current. vv (1:4, 1:6), Jacobian matrix H corresponding to linear active power. vv (5:6, 1:6), Jacobian matrix H corresponding to linear reactive power vv (7:8, 1:6), Jacobian matrix H corresponding to voltage amplitude vv (9:10, 1:6);

[0197] The Jacobian matrix H corresponding to symmetrical current vv (1:4, 1:6) includes matrix H vv (1:2,1:6), matrix H vv (3:4,1:6), that is:

[0198]

[0199] In the formula, Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts;

[0200] Linear active power corresponds to the Jacobian matrix H vv (5:6, 1:6) is shown below:

[0201]

[0202] Among them, parameters parameter parameter parameter parameter parameter As shown below:

[0203]

[0204]

[0205] In the formula, α, α1, α2 ∈ {a, b, c}; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts;

[0206] Linear reactive power corresponding Jacobian matrix H vv (7:8, 1:6) is shown below:

[0207]

[0208] Among them, parameters parameter parameter parameter parameter parameter As shown below:

[0209]

[0210]

[0211] Voltage amplitude corresponds to Jacobian matrix H vv (9:10, 1:6) is shown below.

[0212]

[0213] Jacobian matrix H vj (1:10, 1:6) includes matrix H vj (1:4,1:6)=H vv (1:4, 1:6), matrix H vj (5:6, 1:6), matrix H vj (7:8,1:6)H vj (5:6, 1:6), matrix H vj (9:10, 1:6), that is:

[0214]

[0215]

[0216] H vj (9:10, 1:6) = [0] 2×6 (32)

[0217] The Jacobian matrix of the connecting node includes its own Jacobian matrix H. hh (1:8, 1:8), the Jacobian matrix H of all nodes except itself. hj (1:8, 1:8);

[0218] Among them, the Jacobian matrix H hh (1:8, 1:8) and H hj (1:8, 1:8) represents the Jacobian matrix corresponding to the virtual current measurement at the connection endpoint, and is respectively related to H ss (7:14, 1:8) and H sj (7:14, 1:8) are the same, that is, H hh (1:8,1:8)=H ss (7:14, 1:8), H hj (1:8,1:8)=H sj (7:14, 1:8).

[0219] 5) Based on the exponential weight function, zero injection constraint, and symmetrical current constraint, establish a modified equation and update the state variable x. (time) ;

[0220] A modified equation is established based on the exponential weight function, zero injection constraint, and symmetric current constraint to update the state variable x. (time) The content is as follows:

[0221] 5.1) Using residual exponential weighting, establish an exponentially weighted least squares estimation model, namely:

[0222]

[0223] In the formula, z represents the measurement; h(x) represents the measurement function; W represents the weight matrix; J(x) represents the objective function value; min represents taking the minimum value; and x represents the state variable.

[0224] The diagonal elements w in the weight matrix W i * The calculation formula is as follows:

[0225]

[0226] In the formula: Represents fixed weights; σ represents the Parzen window width; r Ni Represents the standardized residual;

[0227] 5.2) Establish iterative equations considering zero-injection power constraints and symmetrical current constraints of distributed sources, and use Newton's method to solve iterative equation (35) and update state variables;

[0228]

[0229] In the formula, H, C, and D represent the Jacobian matrices of the measurement functions h(x), c(x), and d(x) at each node, respectively; k represents the iteration number; λ1 k , λ2 k Represents the eigenvalue; Δx k This represents the adjustment amount for the state variable.

[0230] 6) Determine if the iteration termination condition is met. If yes, output the state variable; otherwise, set time = time + 1 and return to step 5.

[0231] The iteration termination condition includes the correction amount Δx of the state variable. (time) Satisfy max(|Δx) (time) |)<ε, or max(|Δx) (time) |)≥ε and the number of iterations time≥Tmax; Tmax is the maximum number of iterations; ε is the correction threshold.

[0232] Example 2:

[0233] A method for estimating the robust state of low-voltage distribution networks considering symmetrically current-controlled distributed generation includes the following steps:

[0234] 1. Obtain basic data about the power grid;

[0235] The basic data of the power grid includes the grid structure, grid parameters, and smart meter measurements.

[0236] The network structure includes the power grid topology connections.

[0237] The power grid parameters include line resistance, reactance, and rated voltage in the power grid.

[0238] The smart meter measures the active power, reactive power, and voltage amplitude of the three phases at the load endpoint relative to the neutral point; the active power, reactive power, voltage amplitude, and current amplitude of the three phases at the low-voltage side endpoint of the distribution transformer relative to the neutral point; and the active power, reactive power, and voltage of the two sets of lines at the endpoint of the symmetrical current-controlled distributed power source.

[0239] 2. Establish the admittance matrix of low-voltage distribution network nodes based on the basic data of the power grid;

[0240] The steps for establishing the node admittance matrix of a low-voltage distribution network based on the basic data of the power grid include:

[0241] 1) Calculate the injected current I at the midpoint j of the power grid branch ij. j ,Right now:

[0242]

[0243] In the formula, I j Let j be the injected current at endpoint j; Let be the self-admittance matrix of endpoint j; Let i be the mutual admittance matrix between endpoint j and endpoint i; Let J be the admittance matrix between endpoints j and p. Let j be the set of endpoints directly connected to j, and Y ji Y is the admittance matrix of the branch; jj V is the admittance matrix of the parallel branches at the endpoints; i V j V p I represents the voltage at terminals i, j, and p. ji I is the current flowing through branch ji; jj It is a vector composed of the currents flowing out of each node within the endpoint;

[0244] Wherein, the self-admittance matrix of endpoint j The mutual admittance matrix between endpoint j and endpoint i As shown below:

[0245]

[0246] 2) Correcting the self-admittance matrix of endpoint j, we get:

[0247]

[0248] In the formula, Let j be the set of other endpoints directly connected to endpoint j, and

[0249] 3) Establish the endpoint admittance matrix of the low-voltage distribution network. Right now:

[0250]

[0251] In the formula, N is the total number of endpoints.

[0252] 3. Establish measurement equations for power supply nodes, load nodes, symmetrical current-controlled distributed power sources, and tie nodes in the distribution network;

[0253] 1) Measurement equations for power nodes

[0254] The equivalent injection current measurement equation is as follows:

[0255]

[0256] In the formula: P i dn and This represents the active and reactive power of phase d relative to the neutral point n; and f i d express The real and imaginary parts; and express The real and imaginary parts; Let B1 represent the set of endpoints connected to endpoint i, including endpoint i; B1 = {a, b, c, n}; B p ={a,b,c}.

[0257] The equation for virtual injection current measurement is as follows:

[0258]

[0259] The equation for measuring current amplitude is as follows:

[0260]

[0261] In the formula, This represents the amplitude of the three-phase current.

[0262] The equation for voltage amplitude measurement is as follows:

[0263]

[0264] In the formula, Let n be the voltage magnitude of the three phases at node n relative to the neutral point n.

[0265] 2) Measurement equations for load nodes

[0266] The equation for measuring the equivalent injected current at the load node is the same as equation (5); the equation for measuring the virtual injected current is the same as equation (6); and the equation for measuring the voltage amplitude is the same as equation (8).

[0267] 3) Measurement equations for distributed power sources

[0268] The equation for line power measurement is as follows:

[0269]

[0270] In the formula, according to For the two-phase line active power, The two-phase line is reactive.

[0271] The equation for measuring line voltage amplitude is as follows:

[0272]

[0273] In the formula: This represents the amplitude of the two-phase line voltage αc.

[0274] The symmetrical current serves as both a virtual measurement and an equality constraint, and its measurement equation is as follows:

[0275]

[0276] 4) Measurement equations for connection nodes

[0277] For zero-injection power at the connection endpoint, both virtual measurement and equality constraints are applied, and the measurement equation is as follows:

[0278]

[0279] 4. Establish the Jacobian matrix for each type of node based on the measurement equation;

[0280] The power node Jacobian matrix includes its own Jacobian matrix H. ss (1:14, 1:8), the Jacobian matrix H for other nodes sj (1:14, 1:8); The load node Jacobian matrix includes its own Jacobian matrix H. jj (1:11, 1:8), the Jacobian matrix H for other nodes jq (1:11, 1:8); the distributed power source Jacobian matrix relative to its own Jacobian matrix H vv (1:10, 1:6), the Jacobian matrix H for other nodes vj (1:10, 1:6); The Jacobian matrix of the connecting node includes its own Jacobian matrix H. hh (1:8, 1:8), the Jacobian matrix H for other nodes hj (1:8,1:8); For the Jacobian matrix of the power node, load node and tie node for the three-phase three-wire connected distributed power node, only columns 4 and 8 of the corresponding Jacobian matrix need to be deleted.

[0281] Among them, the Jacobian matrix H ss (1:14, 1:8) is shown below:

[0282] H ss (1:3, 1:8) represents the Jacobian matrix corresponding to the current amplitude of the power supply, specifically:

[0283]

[0284] H ss(4:6, 1:8) is the Jacobian matrix corresponding to the voltage amplitude of the power supply, specifically:

[0285]

[0286] H ss (7:14, 1:8) is the Jacobian matrix corresponding to the equivalent current, specifically:

[0287]

[0288] In the formula, matrix ΔH ss (1:8, 1:8) is shown below:

[0289]

[0290] parameter As shown below:

[0291]

[0292] parameter As shown below:

[0293]

[0294] Among them, the Jacobian matrix H sj (1:14, 1:8) is shown below:

[0295]

[0296] H sj (4:6, 1:8) = [0] 3×8 (20)

[0297]

[0298] Among them, the Jacobian matrix H jj (1:11, 1:8) is shown below:

[0299] H jj (1:8, 1:8) is the Jacobian matrix corresponding to the equivalent current of the load, and H ss (7:14, 1:8) Same. H jj (9:11, 1:8) is the Jacobian matrix corresponding to the voltage amplitude, and H ss (4:6, 1:8) are the same.

[0300] Among them, the Jacobian matrix H jq (1:11, 1:8) is shown below:

[0301] H jq (1:8,1:8) and H sj(7:14, 1:8) are the same, H jq (9:11, 1:8) and H sj (4:6, 1:8) are the same.

[0302] Among them, the Jacobian matrix H vv (1:10, 1:6) is shown below:

[0303] H vv (1:4, 1:6) is the Jacobian matrix corresponding to the symmetric current, specifically:

[0304]

[0305] H vv (5:6, 1:6) is the Jacobian matrix corresponding to the linear active power, specifically:

[0306]

[0307] In the formula:

[0308]

[0309]

[0310] In the formula, α, α1, α2 ∈ {a, b, c}; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts; Indicate admittance The real and imaginary parts;

[0311] H vv (7:8, 1:6) is the Jacobian matrix corresponding to linear reactive power, specifically:

[0312]

[0313] In the formula:

[0314]

[0315]

[0316] H vv (9:10, 1:6) is the Jacobian matrix corresponding to the voltage amplitude, specifically:

[0317]

[0318] Among them, the Jacobian matrix H vj (1:10, 1:6) is shown below:

[0319] H vj (1:4,1:6) and H vv (1:4, 1:6) are the same.

[0320]

[0321]

[0322] H vj (9:10, 1:6) = [0] 2×6 (32)

[0323] Among them, the Jacobian matrix H hh (1:8, 1:8) and H hj (1:8, 1:8) represents the Jacobian matrix corresponding to the virtual current measurement at the connection endpoint, and is respectively related to H ss (7:14, 1:8) and H sj (7:14, 1:8) are the same.

[0324] 5. Based on the exponential weight function, zero injection constraint, and symmetrical current constraint, establish a modified equation and update the state variable x. (time) ;

[0325] 1) Establish an exponentially weighted least squares estimation model

[0326] Using residual exponent weighting, the following least squares estimation model EFWLS is established:

[0327]

[0328] In the formula: z represents measurement; h(x) represents measurement function; W represents weight matrix; J(x) represents objective function value; min represents minimum value; x represents state variable.

[0329] In the weight matrix W, the diagonal element w i * The calculation formula is as follows:

[0330]

[0331] In the formula: Represents fixed weights; σ represents the Parzen window width; r Ni This represents the standardized residual.

[0332] 2) Establish constrained iterative equations

[0333] Using Newton's method, considering the zero-injection power constraint and the symmetrical current constraint of the distributed source, the corrected equations for the state variables are obtained as follows:

[0334]

[0335] H, C, and D represent the Jacobi matrices of h(x), c(x), and d(x); k represents the number of iterations.

[0336] 6. Determine if the iteration termination condition is met. If yes, output the state variable; otherwise, set time = time + 1 and return to step 5.

[0337] The iteration termination condition includes the correction amount Δx of the state variable. (time) Satisfy max(|Δx) (time) |)<ε, or max(|Δx) (time) |)≥ε and the number of iterations time≥Tmax; Tmax is the maximum number of iterations; ε is the correction threshold.

[0338] Example 3:

[0339] See Figure 3 The simulation experiment for robust state estimation of low-voltage distribution networks considering symmetrical current-controlled distributed power sources mainly includes the following steps:

[0340] An asymmetric correction system is constructed based on the IEEE-13 node standard system. The construction process of the IEEE-13 node correction system is as follows:

[0341] ① Select endpoint 1 as the balance endpoint, with its neutral point connected to the ground as the zero potential reference point; endpoints 2, 3, 4, 6, 8, 9, 11, and 12 are load endpoints; endpoints 5 and 7 are zero injection endpoints; and endpoint 13 is the distributed power source endpoint.

[0342] ② The parallel capacitors, voltage regulators and distribution transformers in the system were ignored.

[0343] ③ Set the model of each branch to 501, resulting in a total of 12 branches.

[0344] ④ All loads are constant power Y-connected;

[0345] ⑤ The distributed power supply is a three-phase three-wire connection.

[0346] A simulation experiment on robust state estimation of a low-voltage distribution network was conducted on the constructed corrected system. To verify the accuracy of the state estimation results, the system estimation error S1 and the maximum estimation error S2 were used as evaluation indicators. S1(V) and S1(θ) are the system estimation errors of voltage amplitude and phase angle, respectively, and S2(V) and S2(θ) are the maximum estimation errors of voltage amplitude and phase angle, respectively.

[0347]

[0348]

[0349] In the formula: This represents the estimated value of the d-phase state quantity at the i-th endpoint; This represents the true value of the state variable of phase d at the i-th endpoint; n represents the number of endpoints; max represents taking the maximum value.

[0350] Design the following two simulation conditions:

[0351] Simulation condition 1: The system has no bad data; all normal measurements are superimposed with normally distributed random measurement errors. Assume the standard deviations of the measurement errors for voltage amplitude and node injected power are 0.01 and 0.02, respectively.

[0352] Simulation condition two: The system contains bad data; the method for constructing normal measurement data is the same as in simulation condition one. Table 1 shows the simulation results of the system error and maximum error of network endpoint state estimation.

[0353] Table 1 Simulation results of systematic error and maximum error

[0354]

[0355] Table 1 shows that when random errors are superimposed on the measurements, the systematic errors of voltage amplitude and phase angle are at level E-2, while the maximum errors are at levels E-4 and E-3, respectively. When bad data exists in the measurements, the systematic errors of voltage amplitude and phase angle are at levels E-2 and E-1, respectively, while the maximum errors are at levels E-3 and E-2, respectively. The systematic errors and maximum errors increase, but are still within a reasonable range. The simulation results show that when a low-voltage distribution network containing distributed power sources contains a small amount of bad data, the robust state estimation of the low-voltage distribution network with symmetrical current control of distributed power sources can automatically reduce the weight of bad data through the weight function and assign higher weights to normal measurement data, achieving the effect of eliminating bad data and improving estimation accuracy.

[0356] Example 4:

[0357] See Figure 3 In the simulation experiment of robust state estimation of low-voltage distribution network considering symmetrical current control of distributed power source, Example 3 uses the symmetrical current of distributed power source as both equality constraint and virtual measurement, which improves the accuracy of state estimation.

[0358] To verify the importance of symmetrical current as an equality constraint and virtual measurement, the following simulation was set up: the measurement data of the distributed power source were changed to: two sets of line active power, two sets of line reactive power, and two sets of line voltage, without considering the symmetrical current constraint. State estimation was performed under the condition of bad measurement data, and S1 and S2 were compared. Table 2 shows the comparison of the state estimation results of voltage measurement superimposed random error under the conditions of considering symmetrical characteristics and not considering symmetrical characteristics.

[0359] Table 2 Comparison of robustness estimation results for low-voltage distribution networks with and without symmetric constraints.

[0360]

[0361] As shown in Table 2, under the same measurement conditions, without symmetrical current constraints, the systematic errors of voltage amplitude and phase angle are in the E-1 level, while the maximum errors are in the E-2 and E-3 levels, respectively. When all measurements are considered, but symmetrical current virtual measurements and constraints are taken into account, the systematic errors of voltage amplitude and phase angle are in the E-2 level, while the maximum errors are in the E-4 and E-3 levels, respectively, significantly improving the accuracy of state estimation. Furthermore, when all measurements are superimposed with random errors or bad data exists, if symmetrical current constraints are not considered, the state estimation may even fail to converge.

[0362] The simulations above demonstrate that the low-voltage distribution state estimation method for distributed power sources considering symmetrical current control proposed in this invention is feasible. By adding virtual measurements of the symmetrical current and equality constraints, the data accuracy and convergence can be significantly improved.

[0363] This invention proposes a method for estimating the robust state of low-voltage distribution networks considering symmetrical current-controlled distributed generation, and performs simulation analysis based on a real system. The method of this invention has the following characteristics:

[0364] (1) The model takes into account the characteristics of the distributed power source using a three-phase three-bridge-arm converter when connected to the grid. The distributed power source with symmetrical current control and three-phase three-wire connection is connected to the three-phase four-wire low-voltage distribution network, and the Newton method is used to calculate the robust state estimation of the low-voltage distribution network.

[0365] (2) The three-phase current of distributed power source in the differential state estimation of low voltage distribution network is symmetrical. This invention uses the symmetrical current as both a virtual measurement and an equality constraint, and compares it with the state estimation without considering the symmetrical current constraint. The former can improve the accuracy and convergence of the state estimation data.

Claims

1. A method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed generation, characterized in that, Includes the following steps: Step 1) Obtain basic power grid data; Step 2) Establish the admittance matrix of low-voltage distribution network nodes based on the basic data of the power grid; Step 3) Establish the measurement equations for power source nodes, load nodes, symmetrical current-controlled distributed power sources, and tie nodes in the distribution network; Step 4) Establish the Jacobian matrix for each type of node according to the measurement equation; Step 5) Establish modified equations based on exponential weight functions, zero injection constraints, and symmetrical current constraints, and update state variables. ; Step 6) Determine if the iteration termination condition is met. If yes, output the state variable; otherwise, set the iteration count time = time + 1 and return to step 5). A modified equation is established based on the exponential weight function, zero injection constraint, and symmetric current constraint to update the state variables. The content is as follows: Step 1) Using the residual exponential weighting, establish an exponentially weighted least squares estimation model, i.e.: （33） In the formula, Indicative measurement; Represents the measurement function; Represents the weight matrix; Represents the objective function value; This indicates taking the minimum value; x represents the state variable; weight matrix diagonal element w in i * The calculation formula is as follows: （34） In the formula: Indicates fixed weight; Indicates the width of the Parzen window; Represents the standardized residual; Step 2) Establish iterative equations considering zero-injection power constraints and symmetrical current constraints of distributed sources, and solve iterative equations (35) using the Newton method to update the state variables; （35） In the formula, H, C, and D represent the Jacobian matrices of measurement functions h(x), c(x), and d(x); k represents the iteration number; , Represents eigenvalues; This represents the adjustment amount for the state variable.

2. The method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources according to claim 1, characterized in that, The basic data of the power grid includes the network structure, power grid parameters, and smart meter measurements. The network structure includes the power grid topology connections; The power grid parameters include line resistance, reactance, and rated voltage in the power grid. The smart meter measures the active power, reactive power, and voltage amplitude of the three phases at the load endpoint relative to the neutral point; the active power, reactive power, voltage amplitude, and current amplitude of the three phases at the low-voltage side endpoint of the distribution transformer relative to the neutral point; and the active power, reactive power, and voltage of the two lines at the endpoint of the symmetrical current-controlled distributed power source.

3. The method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources according to claim 1, characterized in that, The steps for establishing the node admittance matrix of a low-voltage distribution network based on the basic data of the power grid include: Step 1) Calculate the injected current at endpoint j of the power grid branch ij. ,Right now: （1） In the formula, Let j be the injected current at endpoint j; Let be the self-admittance matrix of endpoint j; Let i be the mutual admittance matrix between endpoint j and endpoint i; Let J be the admittance matrix between endpoints j and p. Let j be the set of endpoints directly connected to j, and ; The admittance matrix of the branch; The admittance matrix of the parallel branches at the endpoints; , , Let be the voltage at terminals i, j, and p; The current flowing through branch ji; Let N be the vector of currents flowing out of each node within the endpoint; j = 1, 2, ..., N; N is the total number of endpoints. Wherein, the self-admittance matrix of endpoint j The mutual admittance matrix between endpoint j and endpoint i As shown below: （2） Step 2) Correct the self-admittance matrix of endpoint j to obtain: （3） In the formula, Let j be the set of other endpoints directly connected to endpoint j, and ; Step 3) Establish the low-voltage distribution network endpoint admittance matrix ,Right now: （4） In the formula, N is the total number of endpoints.

4. The method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources according to claim 1, characterized in that, The measurement equations for power supply nodes and load nodes in the distribution network include equivalent injection current measurement equations, virtual injection current measurement equations, current amplitude measurement equations, and voltage amplitude measurement equations. The equivalent injection current measurement equations for power supply nodes and load nodes are shown below: （5） In the formula, and This represents the active and reactive power of phase d relative to the neutral point n; and Indicates voltage The real and imaginary parts; Let n be the real part of the voltage at the neutral point n; This represents the imaginary part of the voltage at the neutral point n. and Indicate admittance The real and imaginary parts; This represents the set of endpoints connected to endpoint i, and includes endpoint i. and Indicates voltage Real and imaginary parts; sets ; The equations for virtual injection current measurement at power nodes and load nodes are shown below: （6） In the formula, ; and Indicate admittance The real and imaginary parts; and This represents the active and reactive power of phase d relative to the neutral point n; The equations for measuring the current amplitude at power supply nodes and load nodes are shown below: （7） In the formula, This refers to the amplitude of the three-phase current. The equations for measuring the voltage amplitude at power supply nodes and load nodes are shown below: （8） In the formula, Let n be the voltage magnitude of the three phases at node n relative to the neutral point n.

5. The method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources according to claim 1, characterized in that, The measurement equations for the distributed power source include the line power measurement equation, the line voltage amplitude measurement equation, and the symmetrical current measurement equation. The equation for line power measurement is as follows: （9） In the formula, The two phase lines are active. The two-phase line is reactive; and Indicates voltage The real and imaginary parts; and Indicates voltage The real and imaginary parts; and Indicates voltage The real and imaginary parts; and Indicate admittance Real and imaginary parts; set ; ; The equation for measuring line voltage amplitude is as follows: （10） In the formula, express Two-phase line voltage amplitude; The symmetrical current serves as both a virtual measurement and an equality constraint, and its measurement equation is as follows: （11） In the formula, and Indicates voltage Real part and imaginary part; and Indicate admittance The real and imaginary parts; and Indicate admittance The real and imaginary parts; and Indicate admittance The real and imaginary parts.

6. The method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources according to claim 1, characterized in that, The measurement equations for the connection node are shown below: （12） In the formula, and Indicate admittance The real and imaginary parts; and Indicates voltage Real and imaginary parts; sets .

7. The method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources according to claim 1, characterized in that, The Jacobian matrices of each type of node include the Jacobian matrix of power nodes, the Jacobian matrix of load nodes, the Jacobian matrix of distributed power sources, and the Jacobian matrix of interconnection nodes. The power node Jacobian matrix includes its own Jacobian matrix. For the Jacobian matrix of nodes other than itself ; Among them, the Jacobian matrix Including the Jacobian matrix corresponding to the current amplitude of the power supply. The Jacobian matrix corresponding to the voltage amplitude of the power supply Equivalent current corresponding Jacobian matrix ; The Jacobian matrix corresponding to the current amplitude of the power supply As shown below: （13） In the formula, , Indicate admittance The real and imaginary parts; , Indicate admittance The real and imaginary parts; , Indicates voltage Real and imaginary parts; sets ; ; The Jacobian matrix corresponding to the voltage amplitude of the power supply is as follows: （14） In the formula, , Indicates voltage Real part and imaginary part; , Indicates voltage Real part and imaginary part; , Indicates voltage Real part and imaginary part; , Indicates voltage Real part and imaginary part; The Jacobian matrix corresponding to the equivalent current is as follows: （15） In the formula, , Indicate admittance The real and imaginary parts; ; Among them, matrix As shown below: （16） parameter As shown below: （17） parameter As shown below: （18） Jacobi matrix Including matrices ,matrix ,matrix ,Right now: （19） （20） （21） In the formula, , Indicate admittance The real and imaginary parts; , Indicates voltage Real part and imaginary part; , Indicate admittance The real and imaginary parts; The load node Jacobian matrix includes its own Jacobian matrix. For the Jacobian matrix of nodes other than itself ; Jacobi matrix Includes the Jacobian matrix corresponding to the equivalent current of the load. = Jacobian matrix corresponding to voltage amplitude = ; Jacobi matrix Including the Jacobian matrix = Jacobian matrix = ; The distributed power supply Jacobian matrix includes its own Jacobian matrix. For the Jacobian matrix of nodes other than itself ; Jacobi matrix Including the Jacobian matrix corresponding to symmetrical currents The active power of the line corresponds to the Jacobian matrix. Jacobian matrix corresponding to linear reactive power The Jacobian matrix corresponding to voltage amplitude ; The Jacobian matrix corresponding to symmetrical current Including matrices ,matrix ,Right now: （22） In the formula, , Indicate admittance The real and imaginary parts; , Indicate admittance The real and imaginary parts; , Indicate admittance The real and imaginary parts; Linear active power corresponds to Jacobian matrix As shown below: （23） Among them, parameters ,parameter ,parameter ,parameter ,parameter ,parameter As shown below: （24） （25） In the formula, ; , Indicate admittance The real and imaginary parts; , Indicate admittance The real and imaginary parts; , Indicate admittance The real and imaginary parts; Jacobian matrix corresponding to linear reactive power As shown below: （26） Among them, parameters ,parameter ,parameter ,parameter ,parameter ,parameter As shown below: （27） （28） Voltage amplitude corresponding to Jacobian matrix As shown below （29） Jacobi matrix Including matrices = ,matrix ,matrix ,matrix ,Right now: （30） （31） （32） The Jacobian matrix of the connecting node includes its own Jacobian matrix. For the Jacobian matrix of nodes other than itself ; Among them, the Jacobian matrix and The Jacobian matrix corresponding to the virtual current measurement at the connection endpoint is respectively compared with... and same.

8. The method for estimating the robust state of a low-voltage distribution network considering symmetrical current-controlled distributed power sources according to claim 1, characterized in that, The iteration termination condition includes the correction amount of the state variables. satisfy ,or And the number of iterations ; This represents the maximum number of iterations. This is the threshold for correction.

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