Short-circuit calculation method for 100% converter type power supply distribution network based on double-layer iteration

Abstract

The application discloses a 100% converter type power supply distribution network short-circuit calculation method based on double-layer iteration, and belongs to the technical field of relay protection, and comprises the following steps: S1, constructing a 100% converter type power supply distribution network short-circuit calculation mathematical model; S2, defining a double-layer iteration short-circuit calculation method based on outer-layer voltage approximation inner-layer spectral gradient iteration; S3, performing specific implementation of the spectral gradient inner-layer iteration algorithm according to the defined double-layer iteration short-circuit calculation method; and S4, proving global convergence of the spectral gradient inner-layer iteration algorithm. The 100% converter type power supply distribution network short-circuit calculation method based on double-layer iteration can solve the problem that the convergence of the traditional iteration algorithm is easily affected by the capacity of the converter type power supply and the fault working condition, can meet the needs of the 100% converter type power supply distribution network fault steady-state short-circuit calculation, and can accurately depict the short-circuit current level and distribution characteristics of the whole network.

Description

Technical Field

[0001] This invention relates to the field of relay protection technology, and in particular to a short-circuit calculation method for 100% converter-type power distribution networks based on two-layer iteration. Background Technology

[0002] In the existing technology, with the continuous development of power electronic equipment and the widespread access of distributed power sources, off-grid microgrids built entirely by converter-type power sources such as photovoltaics and energy storage, and AC / DC hybrid active distribution networks built on multi-port energy routers and with multi-point distributed access to converter-type distributed power sources have become important development methods for building flexible and low-carbon new distribution networks.

[0003] Typically, converter-type power sources are controlled current or voltage sources, and their fault response characteristics are determined by their fault ride-through control strategies, which differ significantly from the fault characteristics of traditional synchronous generators. The fact that all power sources in a 100% converter-type power distribution network are controlled makes its short-circuit calculations more complex than those of conventional active distribution networks. Furthermore, protection adaptability analysis and research into new protection principles rely heavily on short-circuit calculation analysis that can accurately characterize fault features.

[0004] Establishing and solving the mathematical model for short-circuit calculation is the key and challenging aspect of short-circuit calculation for 100% converter-type power grids. The controlled nonlinearity of the equivalent fault model for converter-type power grids dictates that the mathematical model for short-circuit calculation in 100% converter-type power grids is generally a set of nonlinear equations. Existing techniques typically combine the equivalent fault model, the node voltage equations of the fault equivalent circuit, and fault boundary conditions to establish a set of nonlinear equations for short-circuit calculation, which is then solved using a fixed-point iteration method. However, the fixed-point iteration method usually has a slow convergence speed, and the convergence of the iteration sequence for short-circuit calculation is affected by the capacity of the converter-type power supply and the fault conditions. Some studies have proposed a short-circuit calculation method that calculates the node voltages based on the assumption that the output current of each converter-type power supply remains constant before and after the fault, and then updates the fault current calculation results according to the equivalent fault model. This is essentially the first iteration in the fixed-point iteration calculation, which is fast, simple, and practical, but suffers from significant errors in the calculated phase of the short-circuit current. Some studies have also adopted short-circuit calculation methods based on the inverse Broyden rank-1 quasi-Newton method, which has the advantages of not requiring differentiation or inversion and being able to achieve superlinear convergence, but can only guarantee local convergence and does not have global convergence. Summary of the Invention

[0005] The purpose of this invention is to provide a short-circuit calculation method for 100% converter-type power distribution networks based on two-layer iteration. This method can be applied to 100% converter-type power distribution networks where the system voltage is established by converter-type power sources based on V / f (constant voltage and constant frequency) control and multiple points are distributedly connected to converter-type distributed power sources with grid-type control. This method solves the problem that the convergence of traditional iterative algorithms is easily affected by the capacity and fault conditions of the converter-type power sources. It can meet the needs of steady-state short-circuit calculation for 100% converter-type power distribution networks and accurately characterize the short-circuit current level and distribution characteristics of the entire network.

[0006] To achieve the above objectives, this invention provides a short-circuit calculation method for 100% converter-type power distribution networks based on two-layer iteration, comprising the following steps:

[0007] S1. Construct a mathematical model for short-circuit calculation of a 100% converter-type power distribution network;

[0008] S2. Define a two-layer iterative short-circuit calculation method based on the outer layer voltage approximation of the inner layer spectrum gradient.

[0009] S3. Implement the inner layer iterative algorithm of spectral gradient according to the defined two-layer iterative short-circuit calculation method;

[0010] S4. Prove the global convergence of the inner-layer iterative algorithm for the spectral gradient.

[0011] Preferably, step S1 further includes the following step:

[0012] S11. Establish a fault equivalent model for a V / f controlled converter power supply;

[0013] Actively adjusting the voltage based on the output current value to achieve fault current limiting and retain voltage source characteristics is a typical fault ride-through control strategy for V / f-controlled converter power supplies. Under this fault ride-through control strategy, the V / f-controlled converter power supply is equivalent to a voltage source controlled by its own output current. The fault steady-state equivalent model of the V / f-controlled converter power supply is as follows:

[0014] U Vf =max{0,U Vf.N (1-max{0,λ Ilim (I Vf / I Vf.N -I set )})};

[0015] In the formula, U Vf and I Vf These are the AC side voltage and output current of the V / f controlled converter, U Vf.N and I Vf.N These represent the AC side rated voltage and rated output current of the V / f controlled converter, respectively.set This is the current reference value for fault current limiting control, typically taken as 1.05, λ. Ilim This is the active blood pressure reduction factor, which is usually taken as 1;

[0016] S12. Establish a fault equivalent model for grid-connected converter-type distributed power sources;

[0017] The grid-connected converter-type distributed generation adopts a low-voltage ride-through control strategy that injects reactive current according to the voltage drop and limits the output current. Under this control strategy, the grid-connected converter-type distributed generation is equivalent to a current source controlled by the grid connection point voltage. The fault steady-state equivalent model of the grid-connected converter-type distributed generation is as follows:

[0018]

[0019] In the formula, I DG.q and I DG .d represents the grid connection point voltage phase, reactive component of output current, and active component of output current of a converter-type distributed power source with grid-connected control, respectively, and j is the imaginary unit;

[0020] I DG.q and I DG.d The specific expression is

[0021]

[0022] In the formula, U DG I DG.N and P DG.ref These are the grid connection point voltage, rated output current, and active power command value before the fault for a converter-type distributed power source with grid-connected control. It's U DG With rated voltage U DG.N The per-unit value as the baseline; the scaling factor α DG Take values ​​between 1.5 and 2.5, and the coefficient β DG Take 1.05, current limiting coefficient γ DG Take 1.2 to 1.5;

[0023] S13. Construct a set of nonlinear equations for short-circuit calculation;

[0024] The equivalent circuit node voltage equation for a short-circuit fault in a 100% converter-type power distribution network is as follows:

[0025]

[0026] In the formula, U=[U re T U im T ]T and I=[I re TI im T ] T These are the node voltage vector and the node injected current vector, respectively, with the subscript " re "and" im "" represents the real and imaginary parts respectively; R and X are the real and imaginary parts of the node impedance matrix respectively; only the injected current at the power supply node is non-zero in I; I in the formula is composed of U and U Vf To determine the appropriate approach, a set of nonlinear equations for short-circuit calculations is constructed by combining the fault equivalent circuit node voltage equations and the fault equivalent model of the converter-type power supply. The expressions are as follows:

[0027]

[0028] In the formula, f re and f im They represent I respectively re and I im with U re U im and U Vf The functional mapping relationship between them.

[0029] Preferably, S2 includes an outer iterative algorithm based on voltage approximation and an inner iterative algorithm based on spectral gradient method;

[0030] The outer iterative algorithm based on voltage approximation includes the following steps:

[0031] S21. Given initial values and its upper limit and lower limit of values and the maximum number of iterations t of the outer layer max The convergence accuracy of the outer iteration is ε1; let the number of outer iterations t be 0;

[0032] S22, U Vf Treat it as a constant, enter the inner iteration, and substitute it. Solve the nonlinear equation system until the inner iteration converges;

[0033] S23, Utilization and Z Vf Calculation of bus voltage obtained from inner layer iteration Among them, Z Vf The equivalent impedance of the lines and transformers between the output of the V / f controlled converter and the distribution network bus will be... Substituting into the fault steady-state equivalent model of the V / f controlled converter power supply, we get:

[0034]

[0035] S24. Determine whether the following expression is true.

[0036]

[0037] If true, the outer iteration converges; otherwise, proceed to the next step.

[0038] S25. Determine whether the following expression is true.

[0039]

[0040] If true, then update U using the following formula. Vf The range of values ​​and their values:

[0041]

[0042] If this is not true, then update U using the following formula. Vf The range of values ​​and their values:

[0043]

[0044] Let t = t + 1, if t <t max If the outer iteration does not converge, then return to step S22; otherwise, the outer iteration will not converge.

[0045] The preferred inner-layer iterative algorithm based on the spectral gradient method is as follows:

[0046] The nonlinear equations for short-circuit calculations are written in general nonlinear equation form:

[0047] F(U) = G(U) - U = 0;

[0048] In the formula, the operator G involves two operations. The first step is to use U... Vf (t) and U (k) Calculate I (k) The second step is to use I (k) Calculate U (k+1) Where k represents the number of inner iterations;

[0049] The iterative formula based on the spectral gradient method is shown in the following equation:

[0050] U (k+1) =U (k) +μ (k) d (k) ;

[0051] Given the iterative format and initial value U (0) Generate iterative sequence {U (k)}, when {U (k)} is well-defined and converges to U. * At that time, U* It is the solution to the nonlinear equation system for short-circuit calculation; where μ is the step size, d is the spectral gradient direction, and d (k) The specific formula is as follows:

[0052] d (k) (μ)=-b (k) q (k) (μ);

[0053] In the formula, b (k) and q (k) (μ) are respectively:

[0054]

[0055]

[0056] In the formula, s (k-1) and z (k-1) They are respectively:

[0057] s (k-1) =U (k) -U (k-1) ;

[0058]

[0059] In the formula, C>0 and η>0 are given constants, and γ (k-1) Specifically:

[0060] γ (k-1) =F(U (k-1) +F(U (k) )-F(U (k-1) ))-F(U (k-1) );

[0061] Define θ(U) and its gradient as shown in the following equation;

[0062]

[0063] In the formula, For Hamiltonian operators, J F (k) For F(U) (k) ) for U (k) Find the derivative of the Jacobian matrix.

[0064] Preferably, step S3 specifically includes the following steps:

[0065] S31, Given U (0) positive number b (0) C>0, η>0, non-negative integer M, σ1>0, σ2>0, ρ ∈ (0, 1), maximum number of iterations k maxThe inner iteration convergence accuracy is ε2, and the number of inner iterations is set to k = 0.

[0066] S32. Determine whether the convergence condition is met:

[0067] θ(U (k) )≤ε2;

[0068] If the conditions are met, the iteration converges, and the process returns to the outer iteration to continue the short-circuit calculation; otherwise, proceed to the next step.

[0069] S33. The spectral gradient direction d is calculated using the following method. (k) and iteration step size μ (k) , let U (k+1) =U (k) +μ (k) d (k) ;

[0070] Let μ = ρ i Let i be a natural number, and select the smallest integer i that satisfies the following formula.

[0071]

[0072] Let d (k) =d (k) (ρ i ), q (k) =q (k) (ρ i If i = 0, let μ (k) =1; otherwise, take τ. ∈ The largest integer τ in {0,1,2,…,i-1} that satisfies the following expression, and let μ (k) =ρ i-τ ;

[0073]

[0074] S34, according to the above b (k) Calculate b (k) Let k = k + 1; if k <k max If the condition is met, return to step S32; otherwise, the inner iteration ends.

[0075] Preferably, in S4, specifically: by s (k) The calculation formula yields (z) (k) ) T s (k) for:

[0076]

[0077] Obviously, (z (k) ) T s (k) and (s)(k) ) T s (k) Neither is negative, due to b (k) The calculation formula yields b (k) ≥0;

[0078] If F is Lipschitz continuous, that is:

[0079] ||F(U (k+1) )-F(U (k) )||≤L||U (k+1) -U (k) ||;

[0080] In the formula, L is the Lipschitz constant of F, and L>0;

[0081] Then (z) (k) ) T s (k) The range of values ​​for is as follows:

[0082] [C||F(U (k) )|| η ||s (k) || 2 ,(L 2 +C||F(U (k) )|| η )||s (k) || 2 ];

[0083] If there exist constants C1>0 and C2>0 such that C1≤||F(U) (k) If ||≤C2, then there exist constants M1 and M2>0 such that:

[0084] M1≤b (k) ≤M2;

[0085] By q (k) From the definition of θ(U), when μ (k) When the time is sufficient, we have:

[0086]

[0087] When U (k) When the system is not a general system of nonlinear equations, sufficiently small μ such that:

[0088]

[0089] Spectral gradient direction d in step S33 (k) and iteration step size μ (k) Under the calculation method, d (k) and μ (k) satisfy:

[0090]

[0091] Let μ (k) ′=μ (k) / ρ, if μ (k) If μ ≠ 1, then μ (k) 'satisfy:

[0092] θ(U (k) +μ (k) 'd (k) )≥θ(U (k) )-σ1||μ (k) 'd (k) || 2 -σ2||μ (k) 'F(U (k) )|| 2 ;

[0093] Let d (k) and μ (k) For the calculation formula to satisfy k→∞, we have:

[0094]

[0095] Therefore, d (k) and μ (k) satisfy:

[0096]

[0097] Suppose F is in a bounded level set {U|θ(U)≤θ(U)} (0) If the Lipschitz continuity condition is satisfied on}, then the gradient of θ(U) contains (J) F (k) ) T The corresponding ||(J) F (k) ) T ||Bounded;

[0098] If lim k→∞ supμ (k) >0, therefore:

[0099]

[0100] In the formula, sup represents the supremum, inf represents the infremum, and means that the iterative sequence {U} is equal to the summum of all possible values. (k) It can converge globally to the stability point of a general nonlinear system of equations;

[0101] If lim k→∞ μ (k) =0, assume there exists a constant ξ>0 such that:

[0102]

[0103] From the above equation and the gradient of θ(U), we get ||F(U) (k) Since F is in the bounded level set {U|θ(U)≤θ(U)}, the condition is true. (0) If the Lipschitz continuity condition is satisfied on the )}, then M1≤b (k) ≤M2 holds; therefore, the iterative search direction sequence {d} is known. (k)} is bounded, therefore, there exist infinite subsequences {U}. (k)},{d (k) There is a limit U * d * ,and:

[0104]

[0105] In the inequality θ(U) (k) +μ (k) 'd (k) )≥θ(U (k) )-σ1||μ (k) 'd (k) || 2 -σ2||μ (k) 'F(U (k) )|| 2 In the middle, let k→∞, lim k→∞ μ (k) =0, therefore:

[0106]

[0107] Furthermore:

[0108]

[0109] There exists a constant C3 > 0 such that:

[0110]

[0111] Furthermore:

[0112]

[0113] This is the same as the formula Contradiction, therefore The assumption is invalid, in lim k→∞ μ (k) When = 0, the following must hold:

[0114]

[0115] Therefore, it can be concluded that in the bounded level set {U|θ(U)≤θ(U)}, ...(0) Given that the Lipschitz continuity condition is satisfied on )}, the iterative sequence {U} (k) As k→∞, it will always converge globally to the stability point U of the general nonlinear system of equations. * Or make θ(U) (k) It was reduced to the minimum level and remained unchanged.

[0116] Therefore, the beneficial effects of the above-mentioned short-circuit calculation method for 100% converter-type power distribution networks based on two-layer iteration in this invention are as follows:

[0117] (1) The method of the present invention can be applied to a 100% converter-type power distribution network that establishes system voltage based on converter-type power supply with multiple distributed accesses to the grid-type distributed power supply.

[0118] (2) Compared with the prior art, the method proposed in this invention can be immune to the influence of converter power supply capacity and fault conditions when performing short-circuit calculation. It can meet the needs of steady-state short-circuit calculation of 100% converter power supply distribution network faults and accurately characterize the short-circuit current level and distribution characteristics of the whole network.

[0119] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0120] Figure 1 This is a typical schematic diagram of a 100% converter-type power distribution network.

[0121] Figure 2 It is a 100% converter-type power distribution network three-phase short-circuit fault equivalent circuit;

[0122] Figure 3 This is a flowchart of the short-circuit calculation method for 100% converter-type power distribution networks based on two-layer iteration, as described in this invention. Detailed Implementation

[0123] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0124] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0125] Example 1

[0126] This invention provides a short-circuit calculation method for 100% converter-type power distribution networks based on two-layer iteration, including the following steps:

[0127] S1. Construct a mathematical model for short-circuit calculation of a 100% converter-type power distribution network.

[0128] For a 100% converter-type power distribution network that establishes AC system voltage for converter-type power sources based on V / f (constant voltage and constant frequency) control and is distributed and connected to grid-type power sources at multiple points, a set of nonlinear equations for short-circuit calculation is constructed by combining the fault equivalent model and fault equivalent circuit node voltage equations of converter-type power sources.

[0129] A typical 100% converter-type power distribution network, such as Figure 1 As shown, distributed power sources are connected to the distribution network in a decentralized manner through grid-controlled converters and step-up transformers. The AC side of the V / f-controlled converter is connected to the distribution network via a transformer, while the DC side is connected to the DC bus of an energy storage system or a high-capacity multi-port energy router. This embodiment focuses on the steady-state short-circuit calculation of a typical 100% converter-type power distribution network when a short-circuit fault occurs.

[0130] S11. Establish a fault equivalent model for a V / f controlled converter-type power supply.

[0131] Actively adjusting the voltage based on the output current value to achieve fault current limiting and retain voltage source characteristics is a typical fault ride-through control strategy for V / f controlled converter power supplies. Under this fault ride-through control strategy, the V / f controlled converter power supply is equivalent to a voltage source controlled by its own output current. The fault steady-state equivalent model of the V / f controlled converter power supply is shown in equation (1):

[0132] UVf =max{0,U Vf.N (1-max{0,λ Ilim (I Vf / I Vf.N -I set (1)

[0133] In equation (1), U Vf and I Vf These are the AC side voltage and output current of the V / f controlled converter, U Vf.N and I Vf.N These are the AC side rated voltage and rated output current of the V / f controlled converter, respectively. set This is the current reference value for fault current limiting control, which is typically taken as 1.05. Ilim It is the active pressure reduction factor, which is usually taken as 1.

[0134] S12. Establish a fault equivalent model for grid-type converter-type distributed power sources.

[0135] Grid-connected converter-type distributed generation typically employs a low-voltage ride-through control strategy that injects reactive current based on the voltage drop and limits the output current. Under this control strategy, grid-connected converter-type distributed generation can be considered equivalent to a current source controlled by the grid connection point voltage. Therefore, the barrier steady-state equivalent model of grid-connected converter-type distributed generation is shown in equation (2):

[0136]

[0137] In equation (2), I DG.q and I DG.d These are the grid connection point voltage phase, reactive component of output current, and active component of output current for a converter-type distributed power source with grid-connected control.

[0138] I DG.q and I DG.d Specifically, as shown in equation (3):

[0139]

[0140] In equation (3), U DG I DG.N and P DG.ref These are the grid connection point voltage, rated output current, and active power command value before the fault for a converter-type distributed power source with grid-connected control. It's U DG With rated voltage U DG.N The per-unit value is used as the baseline. The scaling factor α. DG Take values ​​between 1.5 and 2.5, and the coefficient β DGTake 1.05, current limiting coefficient γ DG Take 1.2 to 1.5.

[0141] S13. Construct a set of nonlinear equations for short-circuit calculation.

[0142] When a three-phase short-circuit fault occurs in a power distribution line, the equivalent short-circuit fault circuit converted to a 100% converter-type power distribution network of the same voltage level is as follows: Figure 2 As shown. Figure 2 In the diagram, the round dots represent bus nodes, and the square dots represent distributed power supply access nodes. It is the output current of the w-th grid-connected distributed generation, and m is the number of distributed generation sources. This is the output voltage of the V / f controlled converter. Z Vf This refers to the equivalent impedance of the lines and transformers between the output of the V / f controlled converter and the distribution network bus.

[0143] The equivalent circuit node voltage equation for a 100% converter-type power distribution network under short-circuit fault is shown in equation (4):

[0144]

[0145] In formula (4), U=[U re T U im T ] T and I=[I re T I im T ] T These are the node voltage vector and the node injected current vector, respectively, with the subscript " re "and" im "" represents the real part and the imaginary part respectively; R and X are the real part and the imaginary part of the node impedance matrix respectively; I is only non-zero for the injected current of the power supply node.

[0146] by With the phase as a reference, the voltages of the bus node and the w-th distributed power access node are U... re.Bus +jU im.Bus and U re.DG.w +jU im.DG.w The node injection currents are I re.Bus +jI im.Bus and I re.DG.w +jI im.DG.w j is the imaginary unit. re.Bus I im.Bus and I re.DG.w ,

[0147] I im.DG.wSpecifically, see equations (5) to (8).

[0148]

[0149] In equations (5) to (6), R Vf and X Vf Z Vf The real and imaginary parts. In equations (7) to (8), U DG.w It is the voltage amplitude of the w-th grid-controlled converter-type distributed power source access node, I DG.w.d and I DG.w.q According to equation (3), U DG.w Decide.

[0150] It can be seen that I in equation (4) is composed of U and U Vf The decision is made by combining the fault equivalent circuit node voltage equations and the fault equivalent model of the converter power supply. A set of nonlinear equations for short-circuit calculation can be constructed as shown in equation (9).

[0151]

[0152] In equation (9), f re and f im They represent I respectively re and I im with U re U im and U Vf The functional mapping relationship between them.

[0153] For asymmetrical faults such as single-phase grounding, two-phase short circuit, and two-phase grounding, a set of nonlinear equations similar to equation (9) can be written based on the equivalent circuits of positive-sequence, negative-sequence, and zero-sequence faults, the equivalent model of converter-type power supply faults, and the boundary conditions of the fault points. Furthermore, each element of the node injection current vector in the set of equations is determined by the handling of the negative-sequence and zero-sequence components of the converter-type power supply fault and the grounding method of the transformer neutral point.

[0154] Currently, converter-type power supplies have several equivalent methods for negative-sequence and zero-sequence networks, including equivalent impedance, controlled current source, and open circuit. Therefore, the nonlinear equations for short-circuit calculation under different fault types are not fundamentally different from those in this embodiment, and the method in this embodiment is still applicable.

[0155] S2. Define a two-layer iterative short-circuit calculation method based on the outer layer voltage approximation of the inner layer spectrum gradient.

[0156] This embodiment proposes a two-layer iterative short-circuit calculation method based on outer-layer voltage approximation and inner-layer spectral gradient iteration to solve the nonlinear equations for short-circuit calculation. The outer-layer iterative algorithm based on voltage approximation continuously approximates U using the convergence result of the inner-layer iteration during the outer-layer iteration.Vf The inner-layer iterative algorithm based on the spectral gradient method involves applying U during the inner-layer iteration. Vf Treating it as a constant, the nonlinear equations of the expression are solved using the spectral gradient iterative method until both iterations converge. Finally, the U value of the iterative convergence result is used. Vf U calculates the short-circuit current of the entire network based on Kirchhoff's laws.

[0157] The outer iterative algorithm based on voltage approximation includes the following steps:

[0158] S21. Given initial values and its upper limit and lower limit of values and the maximum number of iterations t of the outer layer max The convergence accuracy of the outer iteration is ε1. Let the number of outer iterations t be 0.

[0159] S22, U Vf Treat it as a constant, enter the inner iteration, and substitute it. Solve the nonlinear equation system of equation (9) until the inner iteration converges.

[0160] S23, Utilization and Z Vf Calculation of bus voltage obtained from inner layer iteration Will Substituting into equation (1), we get:

[0161]

[0162] S24. Determine whether the following expression is true:

[0163]

[0164] If true, the outer iteration converges; otherwise, proceed to the next step.

[0165] S25. Determine whether the following expression is true.

[0166]

[0167] If true, then update U using the following formula. Vf The range of values ​​and their values:

[0168]

[0169] If this is not true, then update U using the following formula. Vf The range of values ​​and their values:

[0170]

[0171] Let t = t + 1, if t <t maxIf the outer iteration does not converge, then return to step S22; otherwise, the outer iteration will not converge.

[0172] Since equation (1) is a continuous function, as long as the inner iteration is globally converged, the outer voltage approximation iteration must also be globally converged.

[0173] The inner-layer iterative algorithm based on the spectral gradient method is as follows:

[0174] Equation (9) can be written in the form of a general system of nonlinear equations:

[0175] F(U)=G(U)-U=0 (15)

[0176] In equation (15), the operator G involves two steps. The first step is to use U according to equations (5) to (8) and equation (3). Vf (t) and U (k) Calculate I (k) The second step is to use I according to equation (4). (k) Calculate U (k+1) , where k represents the number of inner iterations, k = 0, 1, 2, ...

[0177] The iterative scheme based on the spectral gradient method is shown in equation (16), which consists of the iterative scheme and the initial value U. (0) Generate iterative sequence {U (k)}, when {U (k)} is well-defined and converges to U. * At that time, U * It is the solution to equation (9).

[0178] U (k+1) =U (k) +μ (k) d (k) (16)

[0179] In equation (16), μ is the step size, d is the spectral gradient direction, and d (k) Specifically, as shown in equation (17):

[0180] d (k) (μ)=-b (k) q (k) (μ) (17)

[0181] In equation (17), b (k) and q (k) (μ) are respectively:

[0182]

[0183] In equation (18), s (k-1) and z (k-1) They are respectively:

[0184] s (k-1) =U (k) -U (k-1) (20)

[0185]

[0186] In equation (21), C>0 and η>0 are given constants, and γ (k-1) Specifically, as shown in equation (22):

[0187] γ (k-1) =F(U (k-1) +F(U (k) )-F(U (k-1) ))-F(U (k-1) ) (twenty two)

[0188] Define θ(U) as shown in equation (23), and its gradient is shown in the following equation;

[0189]

[0190]

[0191] In the formula, For Hamiltonian operators, J F (k) For F(U) (k) ) for U (k) Find the derivative of the Jacobian matrix.

[0192] S3. Implement the inner-layer iterative algorithm of the spectral gradient according to the defined two-layer iterative short-circuit calculation method, which includes the following steps:

[0193] S31, Given U (0) positive number b (0) C>0, η>0, non-negative integer M, σ1>0, σ2>0, ρ ∈ (0, 1), maximum number of iterations k max Let the inner iteration convergence accuracy be ε2, and let the number of inner iterations be k = 0.

[0194] S32. Determine whether the convergence condition is met:

[0195] θ(U (k) )≤ε2 (25)

[0196] If the conditions are met, the iteration converges, and the process returns to the outer iteration to continue short-circuit calculation; otherwise, proceed to the next step.

[0197] S33. The spectral gradient direction d is calculated using the following method. (k) and iteration step size μ (k) , let U (k+1) =U(k) +μ (k) d (k) Let μ = ρ i Let i be a natural number, and select the smallest integer i that satisfies the following formula.

[0198]

[0199] Let d (k) =d (k) (ρ i ), q (k) =q (k) (ρ i If i = 0, let μ (k) =1. Otherwise, take τ. ∈ The largest integer τ in {0,1,2,…,i-1} that satisfies the following expression, and let μ (k) =ρ i-τ .

[0200]

[0201] S34. Calculate b according to formula (18). (k) Let k = k + 1. If k <k max If the condition is met, return to step S32; otherwise, the inner iteration ends.

[0202] S4. Prove the global convergence of the inner-layer iterative algorithm for the spectral gradient.

[0203] From equation (21), we can obtain (z) (k) ) T s (k) for:

[0204]

[0205] Obviously, (z (k) ) T s (k) and (s) (k) ) T s (k) Since both are non-negative, we can obtain b from equation (18). (k) ≥0.

[0206] If F is Lipschitz continuous, that is:

[0207] ||F(U (k+1) )-F(U (k) )||≤L||U (k+1) -U (k) || (29)

[0208] In equation (29), L is the Lipschitz constant of F, and L>0.

[0209] From equations (21), (28), and (29), we can obtain (z) (k) ) T s (k) The range of values ​​for is as follows:

[0210] [C||F(U (k) )|| η ||s (k) || 2 ,(L 2 +C||F(U (k) )|| η )||s (k) || 2 (30)

[0211] If there exist constants C1>0 and C2>0 such that C1≤||F(U) (k) If ||≤C2, then from equations (18) and (30), we know that there exist constants M1 and M2>0 such that:

[0212] M1≤b (k) ≤M2 (31)

[0213] By q (k) From the definition of θ(U), when μ (k) When the time is sufficient, we have:

[0214]

[0215] From equation (17), equation (32) and b (k) Since U is non-negative, when U (k) When it is not a stable point of equation (15), a sufficiently small μ makes:

[0216]

[0217] In the spectral gradient direction d of equation (26) (k) The iteration step size μ of equation (27) (k) Under the calculation method, d (k) and μ (k) satisfy:

[0218]

[0219] Let μ (k) '=μ (k) / ρ, if μ (k) If μ ≠ 1, then μ (k) 'satisfy:

[0220]

[0221] In equation (34), let k→∞, we have:

[0222]

[0223] Therefore, d (k) and μ (k) satisfy:

[0224]

[0225] Suppose F is in a bounded level set {U|θ(U)≤θ(U)} (0) If the Lipschitz continuity condition is satisfied on}, that is, equation (29) holds, then the gradient of θ(U) is given by (J) F (k) ) T The corresponding ||(J) F (k) ) T ||Bounded.

[0226] If lim k→∞ supμ (k) If the result is greater than 0, then from equation (38) we can obtain:

[0227]

[0228] In the formula, sup represents the supremum, inf represents the infremum, and means that the iterative sequence {U} is equal to the summum of all possible values. (k) It can converge globally to the stable point of equation (15).

[0229] If lim k→∞ μ (k) =0, equations (32) and (35) hold. In this case, assume there exists a constant ξ>0 such that:

[0230]

[0231] From equations (24) and (40), we can see that ||F(U (k) Since F is in the bounded level set {U|θ(U)≤θ(U)}, the condition is true. (0) Equation (31) holds if the Lipschitz continuity condition is satisfied on )}. Combining equations (17), (31), (24), and (32), the iterative search direction sequence {d} is known. (k)} is bounded. Therefore, there exist infinite subsequences {U}. (k)},{d (k) There is a limit U * d * ,and:

[0232]

[0233] In inequality (35), let k→∞, limk→∞ μ (k) =0, therefore:

[0234]

[0235] Furthermore:

[0236]

[0237] From equations (17), (31), and (41), it can be seen that there exists a constant C3 > 0 such that:

[0238]

[0239] Furthermore:

[0240]

[0241] This contradicts equation (43), therefore the assumption of equation (40) is invalid, and in lim k→∞ μ (k) When = 0, the following must hold:

[0242]

[0243] Therefore, it can be concluded that in the bounded level set {U|θ(U)≤θ(U)}, ... (0) Given that the Lipschitz continuity condition is satisfied on )}, the iterative sequence {U} (k) As k→∞, it will globally converge to the stable point U of equation (15). * Or make θ(U) (k) It was reduced to the minimum level and remained unchanged.

[0244] Because the output current of a converter-type power supply is limited, under any converter-type power supply capacity and any fault condition, I (k) Both have supremum, and R and X are constant matrices. Therefore, G(U (k) Any element in ) will fall within a certain range. Therefore, there exists a closed set D within the domain of U such that for any U (t) ∈ D, all have G(U) (k) ) ∈ D. Therefore, θ(U) corresponding to F(U) is a bounded level set. Furthermore, the Jacobian matrix J of the derivative of F(U) with respect to U is... F J is equal to the Jacobian matrix J obtained by differentiating G(U) with respect to U. G Subtract one identity matrix.

[0245] Therefore, in the short-circuit calculation of the 100% converter-type power distribution network, F(U) is relatively easy to satisfy Lipschitz and can be immune to the effects of converter-type power capacity and fault conditions. Therefore, the short-circuit calculation method for the 100% converter-type power distribution network based on two-layer iteration in this embodiment has global convergence.

[0246] Therefore, the present invention adopts the above-mentioned method for calculating short circuits in 100% converter-type power distribution networks based on two-layer iteration. This method can be applied to 100% converter-type power distribution networks where the system voltage is established by converter-type power sources based on V / f (constant voltage and constant frequency) control and multiple points are distributedly connected to converter-type distributed power sources with grid-type control. This solves the problem that the convergence of traditional iterative algorithms is easily affected by the capacity and fault conditions of converter-type power sources. It can meet the needs of steady-state short-circuit calculation for faults in 100% converter-type power distribution networks and accurately characterize the short-circuit current level and distribution characteristics of the entire network.

[0247] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A 100% converter-type power supply network short-circuit calculation method based on double-layer iteration, characterized in that, Comprising the following steps: S1, constructing a 100% converter type power supply distribution network short circuit calculation mathematical model; S1 further comprises the following steps: S11, establishing a fault equivalent model of the V / f control converter type power supply; According to the output current value, the voltage is actively adjusted to realize fault current limiting and reserve voltage source characteristics, which is a typical fault ride-through control strategy of the V / f control converter type power supply, and under the fault ride-through control strategy, the V / f control converter type power supply is equivalent to a voltage source controlled by its own output current; S12, establishing a fault equivalent model of the grid-connected converter type distributed power supply; The grid-connected converter type distributed power supply adopts a low voltage ride-through control strategy of injecting reactive current according to voltage drop degree and limiting the output current, and under the control strategy, the grid-connected converter type distributed power supply is equivalent to a current source controlled by the grid-connected point voltage; S13, constructing a nonlinear equation set for short circuit calculation; S2, defining a double-layer iteration short circuit calculation method based on outer voltage approximation and inner spectral gradient iteration; comprising an outer iteration algorithm based on voltage approximation and an inner iteration algorithm based on spectral gradient method; The outer iteration algorithm based on voltage approximation comprises the following steps: S21, given initial value and upper value limit and lower value limit and maximum number of outer iterations t max and outer iteration convergence accuracy ε 1; let the number of outer iterations t be 0; S22, will U Vf Treat it as a constant, enter the inner iteration, and substitute it. Solve the nonlinear equation system until the inner iteration converges; S23, utilize and Z Vf and inner layer iteration resulting bus voltage calculation wherein, Z Vf is the equivalent impedance of the line and transformer between the outlet of the V / f controlled converter and the busbar of the distribution network, and is substituted into the fault steady-state equivalent model of the V / f controlled converter type power supply, The inner iteration algorithm based on spectral gradient method is specifically: The nonlinear equation set for short circuit calculation is written in the form of a general nonlinear equation set: ； where the operator G The operation contains two steps, the first step is to calculate U Vf (t) and U (k) I (k) The second step is to calculate I (k) U (k+1) where k denotes the number of inner iterations.​​ The iteration format based on spectral gradient method is as follows: ； from the iteration format and iteration initial value U (0) generating an iteration sequence U (k)} when U (k)} is well-conditioned and converges to , is the solution of the nonlinear system of equations of short-circuit calculation; where μ is the step size, d is the spectral gradient direction; S3, specific implementation of the spectral gradient inner iteration algorithm according to the defined double-layer iteration short circuit calculation method; S3 specifically comprises the following steps: S31, given U (0) , positive number b (0) , C > 0, η > 0, non-negative integer M , σ 1 > 0, σ 2 > 0, ρ (0, 1), maximum iteration number k max , inner iteration convergence precision ε 2, let the inner iteration number k = 0; S32, judging whether the convergence condition is met: ； If met, the iteration converges, and the outer iteration is returned to continue short circuit calculation, otherwise, the next step is entered; S33, calculate the spectral gradient direction by the following method d (k) and iteration step size μ (k) , let U (k+1) = U (k) + μ (k) d (k) ; Let μ = ρ i , i be a natural number, take the smallest integer i that can satisfy the following formula ； Let , q (k) = q (k) ( ρ i ), wherein b (k) and q (k) ( μ ) are respectively: ； ； If i = 0, let μ (k) = 1; otherwise, take τ {0, 1, 2,..., i − 1} that satisfies τ , and let μ (k) = ρ i−τ ; ； S34, as described above b (k) Calculation formula b (k) ,make k = k +1; if k < k max If the condition is met, return to step S32; otherwise, the inner iteration ends. S4, global convergence proof of the spectral gradient inner iteration algorithm.

2. The double-layer iteration-based 100% converter-type power supply distribution network short-circuit calculation method according to claim 1, characterized in that: The fault steady-state equivalent model of the V / f control converter type power supply is: ； wherein, U Vf and I Vf V and I are the AC side voltage and output current of the V / f controlled converter, respectively, U Vf.N and I Vf.N V and I are the AC side rated voltage and rated output current of the V / f controlled converter, respectively, I set is the current reference value of the fault current limiting control, taken as 1.05, λ Ilim is the active voltage reduction coefficient, taken as 1; The fault steady-state equivalent model of the grid-connected converter type distributed power supply is: ； wherein, , I DG.q and I DG.d are the phase of the grid-connected point voltage, the reactive component of the output current and the active component of the output current of the grid-connected converter-type distributed power source, respectively, and j is the imaginary unit. I DG.q and I DG.d The specific expression is ； ； In the formula, U DG , I DG.N and P DG.ref are the grid-connected point voltage, rated output current and active instruction value of the grid-connected converter type distributed power supply respectively, is U DG the rated voltage U DG.N as the benchmark; the proportional coefficient α DG takes 1.5-2.5, the coefficient β DG takes 1.05, the current limiting coefficient γ DG takes 1.2-1.5; The short circuit fault equivalent circuit node voltage equation of the 100% converter type power supply distribution network is: ； wherein, U [ U re T U im T ] T and I [ I re T I im T ] T are the node voltage vector and the node injected current vector, respectively, and the subscripts re ” and im ” represent the real and imaginary parts, respectively; R and X are the real and imaginary parts of the node impedance matrix, respectively; I only the injected currents of the source access nodes are not zero; and I are determined by U and U Vf , in combination with the fault equivalent circuit node voltage equation and the fault equivalent model of the converter type power source, a nonlinear equation set for short circuit calculation is constructed, and the expression is as follows: ； In the formula, f re and f im respectively represent I re and I im and U re , U im and U Vf the functional mapping relationship between 3. The short circuit calculation method for power distribution network of 100% converter type power supply based on double-layer iteration according to claim 2, characterized in that: In S2, based on the voltage approximation outer iteration algorithm in S23, we have Substituting the fault steady-state equivalent model of the V / f control converter-type power source, we have ； Further comprising the following steps: S24, judging whether the following formula is established, ； If established, the outer iteration converges, otherwise, the next step is entered; S25, judging whether the following formula is established, ； If true, update with U Vf Value range and value: ； If not, update with the following formula U Vf Value range and value: ； Let t = 0 t + 1, if t t max then go to step S22, otherwise the outer iteration does not converge.​ 4. The double-layer iteration based 100% converter type power supply distribution network short circuit calculation method according to claim 3, characterized in that: s (k-1) and z (k-1) respectively. ； ； In the formula, C > 0, η > 0 is a given constant, γ (k-1) Specifically: ； Definitions θ U and its gradient is given by the following equation;​ ； ； wherein is a Hamiltonian operator, J F (k) is F ( U (k) ) the Jacobian matrix of the derivative U (k) .

5. The short-circuit calculation method for power distribution network of 100% converter type power supply based on double-layer iteration according to claim 4, characterized in that: In S4, specifically: calculated by s (k) ) z (k) ) T s (k) is: ； Clearly, ( z (k) ) T s (k) and ( s (k) ) T s (k) are non-negative, by b (k) the calculation formula b (k) ≥ 0; If F is Lipschitz continuous, i.e.: ； wherein L is F a Lipschitz constant of L, L > 0; Then z (k) ) T s (k) The value range of is as follows: ； if there exist constants C 1>0 and C 2>0 such that C 1≤|| F ( U (k) )||≤ C 2, then there exist constants M1, M2>0 such that: ； By q (k) and θ ( U ) the definition of μ (k) sufficiently small, there is: ； When U (k) is not a stable point of the general nonlinear system of equations, sufficiently small μ such that: ； The spectral gradient direction in step S33 d (k) And the iteration step size μ (k) Under the calculation method, d (k) And μ (k) Satisfies: ； Let μ (k) = μ (k) / ρ , if μ (k) ≠ 1, then μ (k) satisfies: ； Let d (k) and μ (k) in the calculation formula k →∞, there is: ； ； Thus, d (k) and μ (k) satisfies: ； Assume F On a bounded level set U | θ ( U )≤ θ ( U (0) )} satisfies the Lipschitz continuity condition, then θ ( U ) gradient formula in ( J F (k) ) T Corresponding to the ||( J F (k) ) T || is bounded; If , we have: ； where sup denotes the supremum, inf denotes the infimum, and means the iteration sequence U (k)} can globally converge to the stationary point of a general nonlinear system of equations; If , assume that there exists a constant ξ > 0, such that: ； By the above and θ ( U ) of the gradient F ( U (k) )||>0, and by F on the bounded level set U | θ ( U )≤ θ ( U (0) )} satisfying the Lipschitz continuity condition holds; knowing that the iterative search direction sequence d (k)} is bounded, there exists an infinite subsequence U (k)}, { d (k)} has a limit , and: ； In the inequality k →∞, there is:​ ； Further, ； The existence constant C 3>0 makes it so that: ； Further, ； This is in contradiction with the formula and thus the assumption that the formula is not valid, in which case necessarily ​ ； Therefore, it is concluded that in F On bounded level sets U | θ ( U )≤ θ ( U (0) ) under the condition of satisfying Lipschitz continuity on U (k) , the iterative sequence k →∞ must globally converge to the stable point of the general nonlinear equation system or make θ ( U (k) ) reduce to the lowest level and remain unchanged.

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