Method for calculating short circuit of 100% converter type power supply distribution network based on double-layer iteration

Abstract

The invention discloses a 100% converter type power distribution network short circuit calculation method based on double-layer iteration, and belongs to the technical field of relay protection, and the method comprises the following steps: S1, constructing a 100% converter type power 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 spectrum gradient iteration; s3, performing specific implementation of a spectral gradient inner layer iteration algorithm according to the defined double-layer iteration short circuit calculation method; and S4, carrying out global convergence proving on the spectral gradient inner layer iterative algorithm. By the adoption of the 100% converter type power distribution network short circuit calculation method based on double-layer iteration, the problem that the convergence of a traditional iterative algorithm is prone to being affected by the converter type power capacity and the fault working condition can be solved, and the requirement for 100% converter type power distribution network fault steady-state short circuit calculation can be met; and the short-circuit current level and distribution characteristics of the whole network are accurately described.

Description

Technical Field

[0001] The present invention relates to the technical field of relay protection, in particular to a double-layer iteration-based 100% converter type power distribution network short-circuit calculation method. Background Art

[0002] In existing technologies, with the continuous development of power electronics equipment and the widespread access to distributed power sources, off-grid microgrids constructed 100% by converter-type power sources such as photovoltaics and energy storage, and AC / DC hybrid active distribution networks constructed based 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, significantly different from those of traditional synchronous generators. The fact that all power sources in a 100% converter-type power distribution network are controlled makes short-circuit calculations more complex than those in conventional active distribution networks. Protection adaptability analysis and research into new protection principles require short-circuit calculations that accurately characterize fault characteristics.

[0004] Establishing and solving the mathematical model for short-circuit calculation is a key and challenging aspect of short-circuit calculation for power grids with 100% converter power sources. The controlled nonlinearity of the converter power supply fault equivalent model dictates that the mathematical model for short-circuit calculation for power grids with 100% converter power sources is generally a nonlinear system of equations. Existing techniques typically combine the power supply fault equivalent model with the node voltage equations in the fault equivalent circuit and the fault boundary conditions to formulate the nonlinear system for short-circuit calculation and employ fixed-point iteration to solve it. However, fixed-point iteration often suffers from slow convergence, and the convergence of the short-circuit calculation iteration sequence is affected by the converter power supply capacity and fault conditions. Some studies have also proposed short-circuit calculation methods that calculate node voltages based on the assumption that the output currents of each converter power supply remain unchanged before and after the fault, and then update the fault current calculation results based on the power supply fault equivalent model. This method, which is essentially the first iteration of the fixed-point iteration, offers fast computational speed, simplicity, and practicality, but suffers from large errors in the short-circuit current phase calculation results. Some studies have also adopted a short-circuit calculation method based on the inverse Broyden rank 1 quasi-Newton method, which has the advantages of not requiring differentiation or inversion and being able to converge superlinearly, but can only guarantee local convergence and does not have global convergence. Summary of the Invention

[0005] The purpose of the present invention is to provide a 100% converter type power distribution network short-circuit calculation method based on double-layer iteration, which can be applied to a 100% converter type power distribution network in which a converter type power source based on V / f (constant voltage and constant frequency) control establishes a system voltage and a multi-point distributed access converter type distributed power source with grid-type control solves the problem that the convergence of traditional iterative algorithms is easily affected by the capacity and fault conditions of the converter type power source. It can meet the needs of steady-state short-circuit calculation of faults in a 100% converter type power distribution network and accurately characterize the short-circuit current level and distribution characteristics of the entire network.

[0006] To achieve the above object, the present invention provides a double-layer iteration-based 100% converter type power distribution network short circuit calculation method, comprising the following steps:

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

[0008] S2. Define a double-layer iterative short-circuit calculation method based on the outer layer voltage approximating the inner layer spectrum gradient iteration;

[0009] S3, implementing the spectral gradient inner layer iteration algorithm according to the defined double-layer iterative short-circuit calculation method;

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

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

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

[0013] Actively adjusting the voltage according to the output current value to achieve fault current limiting and maintain voltage source characteristics is a typical fault ride-through control strategy for V / f controlled converter-type power supplies. Under this fault ride-through control strategy, the V / f controlled converter-type 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-type power supply is:

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

[0015] Where U Vf and I Vf They are the AC side voltage and output current of the V / f controlled converter, U Vf.N and I Vf.N are the AC side rated voltage and rated output current of the V / f controlled converter, Iset is the current reference value for fault current limiting control, usually 1.05, λ Ilim is the active pressure reduction coefficient, usually set to 1;

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

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

[0018]

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

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

[0021]

[0022] Where U DG , I DG.N and P DG.ref They are the grid connection point voltage, rated output current and active power instruction value before the fault of the converter type distributed power supply controlled by the grid. It's U DG With rated voltage U DG.N The per-unit value is the benchmark; the proportional coefficient α DG Take 1.5~2.5, coefficient β DG Take 1.05, current limiting coefficient γ DG Take 1.2~1.5;

[0023] S13, constructing a nonlinear equation system for short-circuit calculation;

[0024] The short-circuit fault equivalent circuit node voltage equation of the 100% converter power distribution network is:

[0025]

[0026] In the formula, U=[U re T U im T ]T and I=[I re TI im T ] T They are the node voltage vector and the node injection current vector, respectively. re "and" im " represents the real part and the imaginary part respectively; R and X represent the real part and the imaginary part of the node impedance matrix respectively; in I, only the injection current of the power access node is non-zero; I in the formula is composed of U and U Vf To determine, combined with the fault equivalent circuit node voltage equation and the fault equivalent model of the converter type power supply, a nonlinear equation group for short-circuit calculation is constructed, which is expressed as follows:

[0027]

[0028] Where, f re and f im Respectively represent I re and I im with U re 、U im and U Vf The function 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 value and its upper limit and the lower limit of the value And the maximum number of iterations t of the outer layer max and the outer iteration convergence accuracy ε1; let the outer iteration number t be 0;

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

[0033] S23. Utilization and Z Vf and the bus voltage calculated by inner iteration Among them, Z Vf is the equivalent impedance of the line and transformer between the output of the V / f controlled converter and the distribution network busbar, 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 formula is true,

[0036]

[0037] If it holds, the outer iteration converges, otherwise it proceeds to the next step;

[0038] S25, determine whether the following formula is true,

[0039]

[0040] If it holds, update U using the following formula Vf Value range and its value:

[0041]

[0042] If not, update U using the following formula: Vf Value range and its value:

[0043]

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

[0045] Preferably, the inner layer iterative algorithm based on the spectral gradient method is specifically:

[0046] The nonlinear equations for short-circuit calculations can be written as a general nonlinear equations system:

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

[0048] In the formula, the operation of operator G contains two steps. The first step is to use U Vf (t) and U (k) Computation I (k) The second step is to use I (k) Calculate U (k+1) , where k represents the number of inner layer iterations;

[0049] The iterative format based on the spectral gradient method is shown below:

[0050] U (k+1) =U (k) +μ (k) d (k) ;

[0051] By the iteration format and the iteration initial value U (0) Generate iterative sequence {U (k)}, when {U (k)} is well-posed and converges to U * When U* is the solution of the nonlinear equations 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] Where b (k) and q (k) (μ) are:

[0054]

[0055]

[0056] Where s (k-1) and z (k-1) They are:

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

[0058]

[0059] Where, C>0, η>0 is a given constant, 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 below;

[0062]

[0063] Where, is the Hamiltonian operator, J F (k) F(U (k) ) (k) The Jacobian matrix to be derived.

[0064] Preferably, 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 max, the inner iteration convergence accuracy ε2, let the inner iteration number k = 0;

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

[0067] θ(U (k) )≤ε2;

[0068] If satisfied, the iteration converges and returns to the outer iteration to continue the short-circuit calculation, otherwise proceed to the next step;

[0069] S33, calculate the spectral gradient direction d by the following method (k) and the iteration step μ (k) , let U (k+1) =U (k) +μ (k) d (k) ;

[0070] Let μ = ρ i , i is a natural number, take 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 formula, and let μ (k) =ρ i-τ ;

[0073]

[0074] S34, according to the above b (k) Calculation formula b (k) , let k=k+1; if k <k max , then return to step S32, otherwise the inner layer iteration ends.

[0075] Preferably, in S4, specifically: (k) The calculation formula is calculated to get (z (k) ) T s (k) for:

[0076]

[0077] Obviously, (z (k) ) T s (k) and (s(k) ) T s (k) are non-negative, by b (k) The calculation formula is 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] Where L is the Lipschitz constant of F, L>0;

[0081] Then (z (k) ) T s (k) The value range of 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) )||≤C2, then there exist constants M1,M2>0 such that:

[0084] M1≤b (k) ≤M2;

[0085] By q (k) and θ(U) are defined as follows: (k) Full hours include:

[0086]

[0087] When U (k) When it is not a stable point of a general nonlinear system, μ is sufficiently small so that:

[0088]

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

[0090]

[0091] Let μ (k) ′=μ (k) / ρ, if μ (k) ≠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) In the calculation formula that satisfies the condition k→∞, we have:

[0094]

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

[0096]

[0097] Assume that F is in a bounded level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition, then the gradient of θ(U) is (J F (k) ) T Corresponding ||(J F (k) ) T ||Bounded;

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

[0099]

[0100] In the formula, sup represents the upper bound, inf represents the lower bound, which means that the iterative sequence {U (k)}It can globally converge to the stable point of a general nonlinear system of equations;

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

[0102]

[0103] From the above formula and the gradient of θ(U), we can get ||F(U (k) )||>0, and F is bounded in the level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition and M1≤b (k) ≤M2 holds; knowing the iterative search direction sequence {d (k)} is bounded, so there exists an infinite subsequence {U (k)}, {d (k)} has 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 example, let k→∞, lim k→∞ μ (k) =0, we have:

[0106]

[0107] Then we have:

[0108]

[0109] It is known that there exists a constant C3>0 such that:

[0110]

[0111] Then we have:

[0112]

[0113] This is similar to the formula Contradiction, therefore The assumption is not valid, in lim k→∞ μ (k) =0, then:

[0114]

[0115] Therefore, it is concluded that in the bounded level set {U|θ(U)≤θ(U(0) )} satisfies the Lipschitz continuity condition, the iterative sequence {U (k)}When k→∞, it must converge globally to the stable point U of the general nonlinear system of equations * Or let θ(U (k) ) is reduced to a minimum level and remains constant.

[0116] Therefore, the beneficial effects of the present invention's use of the above-mentioned double-layer iteration-based 100% converter-type power distribution network short-circuit calculation method are as follows:

[0117] (1) The method of the present invention can be applied to a 100% converter type power distribution network that establishes a system voltage based on a converter type power supply with V / f (constant voltage and constant frequency) control and has multiple points of decentralized access to a converter type distributed power supply with grid-type control.

[0118] (2) Compared with the existing technology, the convergence of the iterative algorithm of the method proposed in the present invention is immune to the influence of the converter type power supply capacity and fault conditions when performing short-circuit calculations. It can meet the needs of 100% converter type power supply distribution network fault steady-state short-circuit calculations and accurately characterize the short-circuit current level and distribution characteristics of the entire network.

[0119] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Figure 1 This is a typical 100% converter type power distribution network diagram;

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

[0122] Figure 3 It is a flow chart of the double-layer iteration-based 100% converter type power distribution network short circuit calculation method of the present invention. DETAILED DESCRIPTION

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

[0124] Unless otherwise defined, the technical or scientific terms used in the present invention shall have the usual meanings understood by persons of ordinary skill in the field to which the present invention belongs. The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprise" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0125] Example 1

[0126] The present invention provides a double-layer iteration-based 100% converter type power distribution network short circuit calculation method, comprising 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 with converter-type distributed power sources controlled by V / f (constant voltage and frequency) and multiple points of distributed access to grid-following control, a set of nonlinear equations for short-circuit calculation is constructed by combining the fault equivalent model of the converter-type power source and the fault equivalent circuit node voltage equation.

[0129] A typical 100% converter type power distribution network is as follows Figure 1 As shown, distributed power sources are connected to the distribution network via grid-following controlled converters and step-up transformers. The AC side of a V / f controlled converter is connected to the distribution network via a transformer, and the DC side is connected to the DC bus of an energy storage system or a large-capacity multi-port energy router. This example focuses on the steady-state short-circuit calculation for a typical 100% converter-based power distribution network with a short circuit.

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

[0131] Actively adjusting the voltage according to the output current value to achieve fault current limiting and retain the voltage source characteristics is a typical fault ride-through control strategy for V / f controlled converter-type power supplies. Under this fault ride-through control strategy, the V / f controlled converter-type 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-type 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 formula (1), U Vf and I Vf They are the AC side voltage and output current of the V / f controlled converter, U Vf.N and I Vf.N I are the rated voltage and rated output current of the AC side of the V / f controlled converter. set Is the current reference value for fault current limiting control, usually taken as 1.05. Ilim is the active pressure reduction coefficient, which can usually be taken as 1.

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

[0135] Grid-following controlled converter-type distributed power sources typically adopt 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-following controlled converter-type distributed power source can be equivalent to a current source controlled by the grid connection point voltage. Therefore, the barrier steady-state equivalent model of the grid-following converter-type distributed power source is shown in Equation (2):

[0136]

[0137] In formula (2), I DG.q and I DG.d They are the grid connection point voltage phase, the reactive component of the output current and the active component of the output current of the converter-type distributed power supply with grid-following control.

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

[0139]

[0140] In formula (3), U DG , I DG.N and P DG.ref They are the grid connection point voltage, rated output current and active power instruction value before the fault of the converter type distributed power supply controlled by the grid. It's U DG With rated voltage U DG.N The proportional coefficient α is the standard value of the benchmark. DG Take 1.5~2.5, coefficient β DGTake 1.05, current limiting coefficient γ DG Take 1.2~1.5.

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

[0142] When a three-phase short circuit fault occurs in the distribution line, the short circuit fault equivalent circuit of the 100% converter type power distribution network converted to the same voltage level is as follows: Figure 2 shown. Figure 2 In the figure, the circles are busbar nodes and the squares are distributed generation access nodes. is the output current of the wth grid-connected distributed power source, and m is the number of distributed power sources. is the output voltage of the V / f controlled converter. Vf It is the equivalent impedance of the line and transformer between the outlet of the V / f controlled converter and the distribution network bus.

[0143] The short-circuit fault equivalent circuit node voltage equation of the 100% converter power distribution network is shown in formula (4):

[0144]

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

[0146] by The phase of is taken as reference, and the voltages of the bus node and the wth distributed generation access node are U re.Bus +jU im.Bus and U re.DG.w +jU im.DG.w , the node injection current is I re.Bus +jI im.Bus and I re.DG.w +jI im.DG.w . j is the imaginary unit. I re.Bus , I im.Bus and I re.DG.w 、

[0147] I im.DG.wThe details are shown in formulas (5) to (8).

[0148]

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

[0150] It can be seen that I in formula (4) is composed of U and U Vf Combining the fault equivalent circuit node voltage equation and the fault equivalent model of the converter type power supply, a nonlinear equation group for short circuit calculation can be constructed as shown in Equation (9).

[0151]

[0152] In formula (9), f re and f im Respectively represent I re and I im with U re 、U im and U Vf The function mapping relationship between them.

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

[0154] Currently, there are roughly several equivalent methods for converter-type power supplies in negative-sequence and zero-sequence networks, such as impedance, controlled current source, and open circuit. Therefore, there is no essential difference between the nonlinear equations and formulas for short-circuit calculation under different fault types, and the method of this embodiment is still applicable.

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

[0156] This embodiment proposes a double-layer iterative short-circuit calculation method with outer layer voltage approximation and inner layer spectrum gradient iteration to solve the short-circuit calculation nonlinear equations. The outer layer iteration algorithm based on voltage approximation is to continuously bisection approximate U according to the convergence result of the inner layer iteration in the outer layer iteration.Vf The inner layer iteration algorithm based on the spectral gradient method is to use U Vf Consider it as a constant, and solve the nonlinear equations of the formula based on the spectral gradient iteration method until both layers of iteration converge. Finally, use the U of the iterative convergence result Vf The short-circuit current of the entire network is calculated based on Kirchhoff's law.

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

[0158] S21, given initial value and its upper limit and the lower limit of the value And the maximum number of iterations t of the outer layer max And the outer iteration convergence accuracy ε1. Let the outer iteration number t be 0.

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

[0160] S23. Utilization and Z Vf and the bus voltage calculated by inner iteration Will Substituting into formula (1) we get:

[0161]

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

[0163]

[0164] If it holds, the outer iteration converges, otherwise proceed to the next step.

[0165] S25, determine whether the following formula is true,

[0166]

[0167] If it holds, update U using the following formula Vf Value range and its value:

[0168]

[0169] If not, update U using the following formula: Vf Value range and its value:

[0170]

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

[0172] Since Equation (1) is a continuous function, as long as the inner iteration converges globally, the outer iteration of voltage approximation must also converge globally.

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

[0174] Write equation (9) in the form of a general nonlinear system of equations:

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

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

[0177] The iterative format based on the spectral gradient method is shown in formula (16), which is composed of the iterative format and the initial value U (0) Generate iterative sequence {U (k)}, when {U (k)} is well-posed and converges to U * When U * is the solution of formula (9).

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

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

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

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

[0182]

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

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

[0185]

[0186] In formula (21), C>0, η>0 is a given constant, γ (k-1) Specifically as shown in formula (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 formula (23), and its gradient is as follows;

[0189]

[0190]

[0191] Where, is the Hamiltonian operator, J F (k) F(U (k) ) (k) The Jacobian matrix to be derived.

[0192] S3. Implementing the spectral gradient inner layer iteration algorithm according to the defined double-layer iterative short-circuit calculation method, specifically including 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 , the inner iteration convergence accuracy is ε2, and the number of inner iterations k=0.

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

[0195] θ(U (k) )≤ε2 (25)

[0196] If satisfied, the iteration converges and returns to the outer iteration to continue the short-circuit calculation, otherwise proceed to the next step.

[0197] S33, calculate the spectral gradient direction d by the following method (k) and the iteration step μ (k) , let U (k+1) =U(k) +μ (k) d (k) , let μ = ρ i , i is a natural number, take 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 formula, 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 , then return to step S32, otherwise the inner layer iteration ends.

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

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

[0204]

[0205] Obviously, (z (k) ) T s (k) and (s (k) ) T s (k) are all non-negative, and from formula (18) we can get b (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 formula (29), L is the Lipschitz constant of F, L>0.

[0209] From formula (21), formula (28) and formula (29), we can get (z (k) ) T s (k) The value range of 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) )||≤C2, then from equations (18) and (30), we can see that there exist constants M1, M2>0 such that:

[0212] M1≤b (k) ≤M2 (31)

[0213] By q (k) and θ(U) are defined as follows: (k) Full hours include:

[0214]

[0215] From formula (17), formula (32) and b (k) It is known that when U (k) When it is not a stable point of formula (15), μ is sufficiently small so that:

[0216]

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

[0218]

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

[0220]

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

[0222]

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

[0224]

[0225] Assume that F is in a bounded level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition, that is, Equation (29) holds, then the gradient of θ(U) is (J F (k) ) T Corresponding ||(J F (k) ) T ||Bounded.

[0226] If lim k→∞ supμ (k) >0, then from formula (38) we can get:

[0227]

[0228] In the formula, sup represents the upper bound, inf represents the lower bound, which means that the iterative sequence {U (k)} can globally converge to the stable point of formula (15).

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

[0230]

[0231] From formula (24) and formula (40), we can know that ||F(U (k) )||>0, and F is bounded in the level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition, and Equation (31) holds. Combining Equations (17), (31), (24), and (32), we can know that the iterative search direction sequence {d (k)} is bounded. Therefore, there exists an infinite subsequence {U (k)}, {d (k)} has a limit U * , d * ,and:

[0232]

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

[0234]

[0235] Then we have:

[0236]

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

[0238]

[0239] Then we have:

[0240]

[0241] This contradicts Equation (43), so the assumption of Equation (40) is invalid. k→∞ μ (k) =0, then:

[0242]

[0243] Therefore, it is concluded that in the bounded level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition, the iterative sequence {U (k)}When k→∞, it must converge globally to the stable point U of equation (15) * Or let θ(U (k) ) is reduced to a minimum level and remains constant.

[0244] Since the output current of the converter type power supply is limited, under any converter type power supply capacity and any fault condition, I (k) Both have upper bounds, and R and X are constant matrices. Therefore, G(U (k) ) will be within a certain range. Therefore, there exists a closed set D in the domain of U such that for any U (t) ∈ D, both have G(U (k) ) ∈ D. Therefore, θ(U) corresponding to F(U) is a bounded level set. And the Jacobian matrix J of the derivative of F(U) with respect to U is F Equal to the Jacobian matrix J of the derivative of G(U) with respect to U G Subtract the identity matrix.

[0245] Therefore, in the short-circuit calculation of a 100% converter-based power distribution network, F(U) easily satisfies the Lipschitz criterion and is immune to the effects of converter-based power capacity and fault conditions. Therefore, the double-layer iteration-based short-circuit calculation method for a 100% converter-based power distribution network in this embodiment exhibits global convergence.

[0246] Therefore, the present invention adopts the above-mentioned 100% converter type power distribution network short-circuit calculation method based on double-layer iteration, which can be applied to a 100% converter type power distribution network based on a converter type power supply with V / f (constant voltage and constant frequency) control to establish a system voltage and a multi-point distributed access to a converter type distributed power supply with grid-type control. It solves the problem that the convergence of the traditional iterative algorithm is easily affected by the capacity and fault conditions of the converter type power supply, can meet the needs of steady-state short-circuit calculation of faults in a 100% converter type power distribution network, 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 rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A double-layer iterative 100% converter type power distribution network short circuit calculation method, characterized in that: The following steps are involved: S1. Construct a mathematical model for short-circuit calculation of 100% converter-type power distribution network; S2. Define a double-layer iterative short-circuit calculation method based on the outer layer voltage approximating the inner layer spectrum gradient iteration; S3, implementing the spectral gradient inner layer iteration algorithm according to the defined double-layer iterative short-circuit calculation method; S4. Prove the global convergence of the spectral gradient inner layer iterative algorithm.

2. The double-layer iteration-based 100% converter power distribution network short-circuit calculation method according to claim 1 is characterized in that: S1 also includes the following steps: S11. Establish a fault equivalent model of a V / f controlled converter type power supply; Actively adjusting the voltage according to the output current value to achieve fault current limiting and maintain voltage source characteristics is a typical fault ride-through control strategy for V / f controlled converter-type power supplies. Under this fault ride-through control strategy, the V / f controlled converter-type 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-type power supply is: U Vf =max{0,U Vf.N (1-max{0,λ Ilim (I Vf / I Vf.N -I set )})}; Where U Vf and I Vf They are the AC side voltage and output current of the V / f controlled converter, U Vf.N and I Vf.N are the AC side rated voltage and rated output current of the V / f controlled converter, I set is the current reference value for fault current limiting control, usually 1.05, λ Ilim is the active pressure reduction coefficient, usually set to 1; S12. Establish a fault equivalent model for grid-connected converter-type distributed power sources; The grid-following controlled converter-type distributed power source adopts a low voltage ride-through control strategy that injects reactive current according to the voltage drop level and limits the output current. Under this control strategy, the grid-following controlled converter-type distributed power source is equivalent to a current source controlled by the grid connection point voltage. The fault steady-state equivalent model of the grid-following converter-type distributed power source is: Where, I DG.q and I DG.d They are the grid connection point voltage phase, the reactive component of the output current and the active component of the output current of the converter type distributed power source with grid-following control, respectively. j is an imaginary unit. I DG.q and I DG.d The specific expression is Where U DG , I DG.N and P DG.ref They are the grid connection point voltage, rated output current and active power instruction value before the fault of the converter type distributed power supply controlled by the grid. It's U DG With rated voltage U DG.N The per-unit value is the benchmark; the proportional coefficient α DG Take 1.5~2.5, coefficient β DG Take 1.05, current limiting coefficient γ DG Take 1.2~1.5; S13, constructing a nonlinear equation system for short-circuit calculation; The short-circuit fault equivalent circuit node voltage equation of the 100% converter power distribution network is: In the formula, 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 injection current vector, respectively. re "and" im " represents the real part and the imaginary part respectively; R and X represent the real part and the imaginary part of the node impedance matrix respectively; in I, only the injection current of the power access node is non-zero; I in the formula is composed of U and U Vf To determine, combined with the fault equivalent circuit node voltage equation and the fault equivalent model of the converter type power supply, a nonlinear equation group for short-circuit calculation is constructed, which is expressed as follows: Where, f re and f im Respectively represent I re and I im with U re 、U im and U Vf The function mapping relationship between them.

3. The double-layer iteration-based 100% converter power distribution network short-circuit calculation method according to claim 2 is characterized in that: In S2, it includes an outer iterative algorithm based on voltage approximation and an inner iterative algorithm based on spectral gradient method; The outer iterative algorithm based on voltage approximation includes the following steps: S21, given initial value and its upper limit and the lower limit of the value And the maximum number of iterations t of the outer layer max and the outer iteration convergence accuracy ε1; let the outer iteration number t be 0; S22, U Vf Treat it as a constant, enter the inner iteration, and substitute Solve the nonlinear system of equations until the inner iteration converges; S23. Utilization and Z Vf and the bus voltage calculated by inner iteration Among them, Z Vf is the equivalent impedance of the line and transformer between the output of the V / f controlled converter and the distribution network busbar, Substituting into the fault steady-state equivalent model of the V / f controlled converter power supply, we get: S24, determine whether the following formula is true, If it holds, the outer iteration converges, otherwise it proceeds to the next step; S25, determine whether the following formula is true, If it holds, update U using the following formula Vf Value range and its value: If not, update U using the following formula: Vf Value range and its value: Let t = t + 1, if t <t max , then return to step S22, otherwise the outer iteration does not converge.

4. The double-layer iteration-based 100% converter power distribution network short-circuit calculation method according to claim 3 is characterized in that: The inner layer iterative algorithm based on the spectral gradient method is specifically as follows: The nonlinear equations for short-circuit calculations can be written as a general nonlinear equations system: F(U)=G(U)-U=0; In the formula, the operation of operator G contains two steps. The first step is to use U Vf (t) and U (k) Computation I (k) The second step is to use I (k) Calculate U (k+1) , where k represents the number of inner layer iterations; The iterative format based on the spectral gradient method is shown below: The (k+1) =U (k) +μ (k) d (k) ; By the iteration format and the iteration initial value U (0) Generate iterative sequence {U (k) }, when {U (k) } is well-posed and converges to U * When U * is the solution of the nonlinear equations 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: d (k) (μ)=-b (k) q (k) (m); Where b (k) and q (k) (μ) are: Where s (k-1) and z (k-1) They are: with (k-1) =U (k) -IN (k-1) ; Where, C>0, η>0 is a given constant, γ (k-1) Specifically: γ (k-1) =F(U (k-1) +F(U (k) )-F(U (k-1) ))-F(U (k-1) ); Define θ(U) and its gradient as shown below; Where, is the Hamiltonian operator, J F (k) F(U (k) ) (k) The Jacobian matrix to be derived.

5. The double-layer iteration-based 100% converter power distribution network short-circuit calculation method according to claim 4 is characterized in that: In S3, the following steps are specifically included: 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 , the inner iteration convergence accuracy ε2, let the inner iteration number k = 0; S32. Determine whether the convergence condition is met: θ(U (k) )≤ε2; If satisfied, the iteration converges and returns to the outer iteration to continue the short-circuit calculation, otherwise proceed to the next step; S33, calculate the spectral gradient direction d by the following method (k) and the iteration step μ (k) , let U (k+1) =U (k) +μ (k) d (k) ; Let μ = ρ i , i is a natural number, take the smallest integer i that satisfies the following formula, 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 formula, and let μ (k) =ρ i-τ ; S34, according to the above b (k) Calculation formula b (k) , let k=k+1; if k <k max , then return to step S32, otherwise the inner layer iteration ends.

6. The double-layer iteration-based 100% converter power distribution network short-circuit calculation method according to claim 5, characterized in that: In S4, specifically: by s (k) The calculation formula is calculated to get (z (k) ) T s (k) for: Obviously, (z (k) ) T s (k) and (s (k) ) T s (k) are non-negative, by b (k) The calculation formula is b (k) ≥0; If F is Lipschitz continuous, that is: ||F(U (k+1) )-F(U (k) )||≤L||U (k+1) -IN (k) ||; Where L is the Lipschitz constant of F, L>0; Then (z (k) ) T s (k) The value range of is as follows: [C||F(U (k) )|| η ||s (k) || 2 ,(L 2 +C||F(U (k) )|| η )||s (k) || 2 ]; If there exist constants C1>0 and C2>0, such that C1≤||F(U (k) )||≤C2, then there exist constants M1,M2>0 such that: M1≤b (k) ≤M2; By q (k) and θ(U) are defined as follows: (k) Full hours include: When U (k) When it is not a stable point of a general nonlinear system, μ is sufficiently small so that: The spectral gradient direction d in step S33 (k) and the iteration step μ (k) Under the calculation method, d (k) and μ (k) satisfy: Let μ (k) '=μ (k) / ρ, if μ (k) ≠1, then μ (k) 'satisfy: θ(U (k) +m (k) 'd (k) )≥θ(U (k) )-σ1||μ (k) 'd (k) || 2 -σ2||μ (k) 'F(U (k) )|| 2 ; Let d (k) and μ (k) In the calculation formula that satisfies the condition k→∞, we have: Therefore, d (k) and μ (k) satisfy: Assume that F is in a bounded level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition, then the gradient of θ(U) is (J F (k) ) T Corresponding ||(J F (k) ) T ||Bounded; If lim k→∞ supμ (k) >0, we get: In the formula, sup represents the upper bound, inf represents the lower bound, which means that the iterative sequence {U (k) }It can globally converge to the stable point of a general nonlinear system of equations; If lim k→∞ μ (k) =0, assuming that there exists a constant ξ>0 such that: From the above formula and the gradient of θ(U), we can get ||F(U (k) )||>0, and F is bounded in the level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition and M1≤b (k) ≤M2 holds; knowing the iterative search direction sequence {d (k) } is bounded, so there exists an infinite subsequence {U (k) }, {d (k) } has a limit U * , d * ,and: 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 example, let k→∞, lim k→∞ μ (k) =0, we have: Then we have: It is known that there exists a constant C3>0 such that: Then we have: This is similar to the formula Contradiction, therefore The assumption is not valid, in lim k →∞μ (k) =0, then: Therefore, it is concluded that in the bounded level set {U|θ(U)≤θ(U (0) )} satisfies the Lipschitz continuity condition, the iterative sequence {U (k) }When k→∞, it must converge globally to the stable point U of the general nonlinear system of equations * Or let θ(U (k) ) is reduced to a minimum level and remains constant.

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