CN108683191B - A kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor - Google Patents

Abstract

The invention discloses a kind of Three-phase Power Flow analysis methods of sagging control type isolated island micro-capacitance sensor, belong to Power System Analysis technical field, initially set up each sagging control type DG in isolated island micro-capacitance sensor, the node admittance matrix Y of the triphase flow of load and circuit element and computing system, column write the node power equilibrium equation of vertical control type isolated island micro-capacitance sensor, obtain Three-phase Power Flow equation group, then the calculation formula of update equation formula and Jacobian matrix J of the Three-phase Power Flow equation group when using Newton Algorithm is derived, finally calculate sagging node power and branch power, export calculation of tidal current, the present invention solves the problems, such as Trust Region Load flow calculation amount conventional Newton method difficulty convergence greatly in the Three-phase Power Flow method of sagging control type isolated island micro-capacitance sensor existing in the prior art.

Description

A kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor

Technical field

The invention belongs to Power System Analysis technical fields, and in particular to a kind of three-phase of sagging control type isolated island micro-capacitance sensor Tidal current analysis method.

Background technique

Load flow calculation is to determine electricity according to the service condition of the elements such as given electric network composition, parameter and generator, load The calculating of Force system each section steady-state operating condition parameter is a key areas of electric power network technique research, is that progress power grid is steady The basis of qualitative analysis, planning and operation study.

Micro-capacitance sensor has grid-connected and two kinds of forms of isolated operation as a kind of flexible and efficient form using distributed energy. Isolated island micro-capacitance sensor has master & slave control and equity two kinds of structures of control.There is main power source to provide voltage in the micro-capacitance sensor of master & slave control structure Frequency support, operation mechanism is similar with traditional power grid, in Load flow calculation, by main power source as balance nodes, other DG mono- As be all made of power limitation control, can be treated to be PQ or PV node.And in reciprocity control structure, by multiple controllable type distributed generation resources (Distributed Generation, DG) participates in voltage, frequency regulation and control jointly, these DG generally use sagging control Method, the operation mechanism and traditional power grid of system have significant difference.Therefore, traditional tidal current computing method is no longer applicable in it, The characteristics of it is necessary to combine sagging control, studies the Load flow calculation problem of such isolated island micro-capacitance sensor.

Currently, the research to micro-capacitance sensor Load flow calculation, does not consider reciprocity control strategy or the sagging control strategy of dispersion mostly Under isolated island micro-capacitance sensor Load flow calculation.When considering to disperse sagging control strategy, there are two class calculation methods in document at present: letter Rely domain method and Newton method.Using letter domain method solve the trend of isolated island micro-capacitance sensor of sagging control when, iterative process must be repeatedly Hessian matrix and its inverse matrix are recalculated, causes the calculation amount in extensive trend excessive, calculating speed is slower than newton pressgang Inferior method；And Newton method is used in the tide for calculating the sagging control type isolated island micro-capacitance sensor trend especially isolated island micro-capacitance sensor of asymmetrical three-phase When stream calculation, convergence is poor, the case where difficult convergence often occurs.

Summary of the invention

The object of the present invention is to provide a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor, solve existing There is Trust Region Load flow calculation amount in the Three-phase Power Flow method of sagging control type isolated island micro-capacitance sensor present in technology big and conventional The problem of Newton method difficulty restrains.

The technical scheme adopted by the invention is that a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor, It is specifically implemented according to the following steps:

Step 1, establish each sagging control type DG in isolated island micro-capacitance sensor, load and circuit element triphase flow and calculate and be The node admittance matrix Y of system；

Step 2, column write the node power equilibrium equation of vertical control type isolated island micro-capacitance sensor, obtain Three-phase Power Flow equation group f (x)=0；

Step 3 derives update equation formula and Jacobi of the Three-phase Power Flow equation group of step 2 when using Newton Algorithm The calculation formula of matrix J；

Step 4, setting the number of iterations k=0, set the initial value of PV node voltage magnitude as its given value, other each nodes The initial value of voltage magnitude is per unit value 1, and node voltage phase angle initial value is 0, and system frequency initial value is per unit value 1, and is corresponded to The correspondence initial value x of unknown quantity to be asked⁽⁰⁾；

Step 5, by x^(k)The expression formula for substituting into f (x), is calculated f (x^(k)), and judge whether it meets convergence criterion max|f(x^(k)) | < ε, ε are desired computational accuracy；If meeting convergence criterion, 10 are gone to step；Otherwise step 6 is carried out；

Step 6 calculates Jacobian matrix J^(k), computed correction Δ x^(k)；

Step 7 determines Optimal Multiplier using the higher-order expansion information of the Taylor series of power flow equation

Step 8, in every step iteration withIt is modified as correction amount；

Step 9, the number of iterations k=k+1；Go to step 5；

Step 10 calculates sagging node power and branch power, exports calculation of tidal current.

The features of the present invention also characterized in that

Step 1 is specifically implemented according to the following steps:

Step 1.1, the triphase flow for initially setting up sagging control type micro battery:

If the collection that all nodes are constituted in micro-capacitance sensor is combined into B, and B_PQ、B_PVAnd B_DroopRespectively indicate PQ node in micro-capacitance sensor, The set of PV node and the sagging node of Droop, when Droop node is run by active/idle limitation, by the calculating of PQ node, three-phase In asymmetric isolated island micro-capacitance sensor, have to the node containing sagging control type DG:

Wherein:The total active power of three-phase and reactive power of respectively sagging control type DG output；Respectively its single-phase active power and reactive power value, wherein m={ a, b, c }；m_Pi、n_QiFor sagging section The active and idle equivalent adjustment factor of point；ω is system angular frequency；And ω₀For the voltage and angular frequency of sagging control DG Setting value；For the positive sequence voltage amplitude of sagging node i, ifAnd θ_i ^mThe respectively m phase voltage amplitude and phase angle of node i, Wherein, m={ a, b, c }, then have:

Meanwhile the three-phase voltage amplitude of sagging node is equal, waveform symmetry, it may be assumed that

Step 1.2, the State characteristics for establishing three-phase load are as follows:

In formula,The respectively active power of m phase load, reactive power；Respectively m phase is born Active power rated value, the reactive power rated value of lotus；U_Li0For the rated value of the voltage of node i；ω is the angular frequency of system, ω_L0For the rated value of angular frequency；WithIt is m phase load active power static voltage characteristic coefficient respectively,WithIt is m phase load reactive power static voltage characteristic coefficient respectively,WithIt is that m phase load is active respectively The static frequency characteristic coefficient of power and reactive power；

Step 1.3, the equivalent circuit for establishing three-phase line:

In asymmetrical three-phase isolated island micro-capacitance sensor, the route of branch is indicated with three-phase impedance matrix between node i and j:

Wherein,The three-phase impedance matrix of branch between node i and j,The three-phase of branch between node i and j Between impedance, wherein m={ a, b, c }, n={ a, b, c }；

Step 1.4 establishes node admittance matrix Y.

Step 2 is specifically implemented according to the following steps:

Column write the node power equilibrium equation of vertical control type isolated island micro-capacitance sensor, to arbitrary node i, if the p of injection node i Phase active power and reactive power are denoted as P respectively_i ^pWithWherein, p={ a, b, c }, then its power balance equation indicates are as follows:

Wherein: Δ P_i ^p、The p phase of respectively node i is active and reactive power amount of unbalance；P_i ^p、Respectively save The active and idle injecting power of the p phase of point i；WithThe respectively m of the p phase of node admittance matrix interior joint i and node k The real and imaginary parts of the admittance array element element of phase, m={ a, b, c }；For the phase of the voltage of the m phase of the p phase and node k of node i Angular difference.

For each PQ node, unbalanced power amount expression formula is corresponding with 6 equations:

Wherein,WithRespectively such as wind power generating set or the photovoltaic in addition to sagging control type DG of node i access The p phase active power and reactive power of the DG such as unit, p={ a, b, c }, if without Wind turbines or photovoltaic cells, value zero；

For each PV node, since node voltage is constant, and reactive power amount of unbalance equation is not considered, power is flat Weighing apparatus equation group is 3 equations:

The power balance equation group of each sagging node will include 12 equality constraints:

There are 12 unknown quantitys for each sagging node, usesIt indicates each phase voltage amplitude of sagging node, usesIt indicates a phase phase angle, and b and c phase phase angle is used respectivelyWithIt substitutes into, simultaneously willWithIt is indicated and is eliminated with droop characteristic relational expressionWithThe then unknown quantization of sagging node Letter is 6Its node power equilibrium equation are as follows:

Assuming that taking the phase angle theta of node 1₁ ^aFor Reference Phase Angle, i.e. θ₁ ^a=0, for convenience of stating, ifIt indicates to remove sagging section The three phases active power amount of unbalance column vector of the outer other nodes of point,Indicate that the three phases active power of PQ node is uneven Column vector is measured,WithRespectively indicate that sagging node three-phase is active and reactive power amount of unbalance column vector, and Note IfIt indicates to remove reference mode and sagging node The three-phase voltage phase angle column vector of outer other nodes,Indicate the voltage magnitude column vector of PQ node,WithPoint The a phase voltage phase angle and amplitude column vector of each sagging control node are not indicated,AndRespectively indicate sagging node A phase and b phase be active and reactive power column vector, and remembers Then formula (6)~(10) Three-phase Power Flow equation group is write as following shape Formula:

Formula (11) isolated island micro-capacitance sensor power flow equation is further collectively expressed as following form:

F (x)=0 (12)

In formula,

Step 3 is specifically implemented according to the following steps:

Using the above-mentioned Three-phase Power Flow equation group of Newton Algorithm, its update equation formula is derived, as follows:

Wherein, Δ x₁Δx₂Δx₃For variable x₁、x₂And x₃Correction amount；Each sub-block calculation formula of Jacobian matrix J It is as follows:

Each Jacobian matrix sub-block J in formula (14)~formula (18)₁₁、J₁₂、J₂₁And J₂₂In H, N, M, L piecemeal each element Definition is identical as the essence definition of piecemeal element is corresponded in conventional three-phase Load flow calculation, and only each sub-block is corresponding separate and saves Point set is different, specifically, H, M piecemeal and conventional three-phase Load flow calculation Jacobian matrix J_origElement expression does not have area Not, and N, L piecemeal need to be in J_origOn the basis of element expression, it need to modify adjustment to its main diagonal element, ifWithRespectively J_origAny diagonal element of middle N and L piecemeal, i ∈ B, m={ a, b, c }, j ∈ B_PQ∪B_Droop, m=a, b, C },WithThe correspondence diagonal element of N and L piecemeal in respectively isolated island micro-capacitance sensor Jacobian matrix J is usedWith It respectively indicates it and modifies superposition amount, i.e.,Have:

J₁₁In E₁₁And F₁₁Piecemeal and J₂₁In E₂₁And F₂₁Piecemeal is column vector, any elementt∈B,m ={ a, b, c } ands∈B_PQ∪B_Droop, m={ a, b, c } distinguishes as follows:

J according to definition, in Jacobian matrix₁₃Middle whole element is zero；And J₂₃In in addition to following element remaining member Element is zero:

Step 6 is specifically implemented according to the following steps:

Calculate Jacobian matrix J^(k), correction amount x^(k)It is acquired according to formula (13) by following formula:

Δx^(k)=-(J^(k))^-1·f(x^(k)) (24)。

Step 7 determines Optimal Multiplier using the higher-order expansion information of the Taylor series of power flow equationSpecifically according to Lower step is implemented:

By each equation number consecutively in power flow equation group f (x)=0 of formula (12), if the general equation of power flow equation group Number is n_f, i.e.,It constructs objective function F (x), the solution of non-linear power flow equation group It is of equal value when f (x)=0 and objective function F (x) are zero:

When kth time iteration, x^(k)It is acquired by Newton-Laphson method, above formula deformation are as follows:

Wherein, H_i(Δx^(k)) power flow equation f when being kth time iteration_i(x) non-linear total item of Taylor expansion, by f_i(x) Taylor expansion calculate this non-linear total item, Δ x^(k)It is obtained by formula (24), then:

H_i(Δx^(k))=f_i(x^(k)+Δx^(k)) (27)

It enables:

a_i ^(k)=f_i(x^(k)) (28)

c_i ^(k)=f_i(x^(k)+Δx^(k)) (29)

Formula (24)~(26) are substituted into formula (23), and omits subscript k and is write as general type:

Optimal Multiplier F (obtained at x+ μ Δ x) minimum value:

For the simple cubic equation of (32), with Newton Algorithm, if equation has solution, at least one reality of equation Root, other two root or real root, or a pair of of Conjugate complex roots, when equation is there are two compound radical, when only one real root, real root is For the Optimal Multiplier of current iterationIt is centainly corresponding with the minimum value of objective function F；If there are three real root μ₁、μ₂And μ₃ When, three roots have the minimum of a corresponding objective function, when there are three real root, choose μ₁、μ₂And μ₃In make objective function F obtains the Optimal Multiplier that minimum value person is current iteration

Step 8 is specifically implemented according to the following steps:

Based on step-length optimisation technique, in every step iteration withIt is modified as correction amount, i.e.,

The invention has the advantages that the Newton method based on the optimisation technique containing step-length, by micro- in sagging control type isolated island Amendment step-length is optimized multiplied by Optimal Multiplier in the iterative process of the three-phase power flow of power grid, there is algorithm good Convergence；And need to only make to work on a small quantity on the basis of conventional Newton-Raphson approach tidal current computing method and can be realized, it does not need Complicated mathematical computations, calculation amount are small, it is easy to accomplish and promote and apply.

Detailed description of the invention

Fig. 1 is a kind of Three-phase Power Flow analysis method flow chart of sagging control type isolated island micro-capacitance sensor of the present invention；

Fig. 2 is the micro-capacitance sensor used in a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor of the present invention Line chart；

Fig. 3 is that 25 nodes obtained in a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor of the present invention are lonely Island micro-capacitance sensor node voltage result.

Specific embodiment

The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.

A kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor of the present invention, flow chart is as shown in Figure 1, specific It follows the steps below to implement:

Step 1, establish each sagging control type DG in isolated island micro-capacitance sensor, load and circuit element triphase flow and calculate and be The node admittance matrix Y of system, is specifically implemented according to the following steps:

Step 1.1, the triphase flow for initially setting up sagging control type micro battery:

If the collection that all nodes are constituted in micro-capacitance sensor is combined into B, and B_PQ、B_PVAnd B_DroopRespectively indicate PQ node in micro-capacitance sensor, The three-phase voltage amplitude of the set of PV node and the sagging node of Droop, sagging node is equal, waveform symmetry, sagging node according to System frequency, positive sequence voltage amplitude adjust the total active power of three-phase and total reactive power of DG unit respectively, and consider inverter The switching mode of power supply, when Droop node is run by active/idle limitation, by the calculating of PQ node, the micro- electricity of asymmetrical three-phase isolated island In net, have to the node containing sagging control type DG:

Wherein:The total active power of three-phase and reactive power of respectively sagging control type DG output；Respectively its single-phase active power and reactive power value, wherein m={ a, b, c }；m_Pi、n_QiFor sagging section The active and idle equivalent adjustment factor of point；ω is system angular frequency；And ω₀For the voltage and angular frequency of sagging control DG Setting value；For the positive sequence voltage amplitude of sagging node i, ifAnd θ_i ^mThe respectively m phase voltage amplitude and phase angle of node i, Wherein, m={ a, b, c }, then have:

Meanwhile the three-phase voltage amplitude of sagging node is equal, waveform symmetry, it may be assumed that

Load is used constant-impedance, three kinds of constant current, invariable power moulds by step 1.2, the influence for considering node voltage and frequency Type combines to be described, and the State characteristics for establishing three-phase load are as follows:

In formula,The respectively active power of m phase load, reactive power；Respectively m phase is born Active power rated value, the reactive power rated value of lotus；U_Li0For nodeiVoltage rated value；ω is the angular frequency of system, ω_L0For the rated value of angular frequency；WithIt is m phase load active power static voltage characteristic coefficient respectively,WithIt is m phase load reactive power static voltage characteristic coefficient respectively,WithIt is that m phase load has respectively The static frequency characteristic coefficient of function power and reactive power；

Step 1.3, the equivalent circuit for establishing three-phase line:

In asymmetrical three-phase isolated island micro-capacitance sensor, consider inductive coupling between phase and ground between conducting wire three-phase, node i and The route of branch is indicated with three-phase impedance matrix between j:

Wherein,The three-phase impedance matrix of branch between node i and j,The three of branch between node i and j Impedance between phase, wherein m={ a, b, c }, n={ a, b, c }；

Step 1.4 establishes node admittance matrix Y；

Step 2, column write the node power equilibrium equation of vertical control type isolated island micro-capacitance sensor, obtain Three-phase Power Flow equation group f (x)=0 it, is specifically implemented according to the following steps:

Column write the node power equilibrium equation of vertical control type isolated island micro-capacitance sensor, to arbitrary node i, if the p of injection node i Phase active power and reactive power are denoted as P respectively_i ^pWithWherein, p={ a, b, c }, then its power balance equation indicates are as follows:

Wherein: Δ P_i ^p、The p phase of respectively node i is active and reactive power amount of unbalance；P_i ^p、Respectively save The active and idle injecting power of the p phase of point i；WithThe respectively m of the p phase of node admittance matrix interior joint i and node k The real and imaginary parts of the admittance array element element of phase, m={ a, b, c }；For the phase of the voltage of the m phase of the p phase and node k of node i Angular difference.

For each PQ node, unbalanced power amount expression formula is corresponding with 6 equations:

Wherein,WithRespectively such as wind power generating set or the photovoltaic in addition to sagging control type DG of node i access The p phase active power and reactive power of the DG such as unit, p={ a, b, c }, if without Wind turbines or photovoltaic cells, value zero；

For each PV node, since node voltage is constant, and reactive power amount of unbalance equation is not considered, power is flat Weighing apparatus equation group is 3 equations:

The power balance equation group of each sagging node will include 12 equality constraints:

There are 12 unknown quantitys for each sagging node, usesIt indicates each phase voltage amplitude of sagging node, usesIt indicates a phase phase angle, and b and c phase phase angle is used respectivelyWithIt substitutes into, simultaneously willWithIt is indicated and is eliminated with droop characteristic relational expressionWithThe then unknown quantity abbreviation of sagging node It is 6Its node power equilibrium equation are as follows:

Assuming that taking the phase angle theta of node 1₁ ^aFor Reference Phase Angle, i.e. θ₁ ^a=0, for convenience of stating, ifIt indicates to remove sagging section The three phases active power amount of unbalance column vector of the outer other nodes of point,Indicate that the three phases active power of PQ node is uneven Column vector is measured,WithRespectively indicate that sagging node three-phase is active and reactive power amount of unbalance column vector, and Note IfIt indicates to remove reference mode and sagging node The three-phase voltage phase angle column vector of outer other nodes,Indicate the voltage magnitude column vector of PQ node,WithPoint The a phase voltage phase angle and amplitude column vector of each sagging control node are not indicated,AndRespectively indicate sagging node A phase and b phase be active and reactive power column vector, and remembers Then formula (6)~(10) Three-phase Power Flow equation group is write as following shape Formula:

Formula (11) isolated island micro-capacitance sensor power flow equation is further collectively expressed as following form:

F (x)=0 (12)

In formula,

Step 3 derives update equation formula and Jacobi of the Three-phase Power Flow equation group of step 2 when using Newton Algorithm The calculation formula of matrix J, is specifically implemented according to the following steps:

Using the above-mentioned Three-phase Power Flow equation group of Newton Algorithm, its update equation formula is derived, as follows:

Wherein, Δ x₁Δx₂Δx₃For variable x₁、x₂And x₃Correction amount；Each sub-block calculation formula of Jacobian matrix J It is as follows:

Each Jacobian matrix sub-block J in formula (14)~formula (18)₁₁、J₁₂、J₂₁And J₂₂In H, N, M, L piecemeal each element Definition is identical as the essence definition of piecemeal element is corresponded in conventional three-phase Load flow calculation, and only each sub-block is corresponding separate and saves Point set is different, specifically, H, M piecemeal and conventional three-phase Load flow calculation Jacobian matrix J_origElement expression does not have area Not, and N, L piecemeal need to be in J_origOn the basis of element expression, it need to modify adjustment to its main diagonal element, ifWithRespectively J_origAny diagonal element of middle N and L piecemeal, i ∈ B, m={ a, b, c }, j ∈ B_PQ∪B_Droop, m=a, b, C },WithThe correspondence diagonal element of N and L piecemeal in respectively isolated island micro-capacitance sensor Jacobian matrix J is usedWith It respectively indicates it and modifies superposition amount, i.e.,Have:

J₁₁In E₁₁And F₁₁Piecemeal and J₂₁In E₂₁And F₂₁Piecemeal is column vector, any elementT ∈ B, m ={ a, b, c } ands∈B_PQ∪B_Droop, m={ a, b, c } distinguishes as follows:

J according to definition, in Jacobian matrix₁₃Middle whole element is zero；And J₂₃In in addition to following element remaining member Element is zero:

Step 4, setting the number of iterations k=0, set the initial value of PV node voltage magnitude as its given value, other each nodes The initial value of voltage magnitude isPer unit value1, node voltage phase angle initial value is 0, and system frequency initial value isPer unit value1, and corresponded to The correspondence initial value x of unknown quantity to be asked⁽⁰⁾；

Step 5, by x^(k)The expression formula for substituting into f (x), is calculated f (x^(k)), and judge whether it meets convergence criterion max|f(x^(k)) | < ε, ε are desired computational accuracy；If meeting convergence criterion, 10 are gone to step；Otherwise step 6 is carried out；

Step 6 calculates Jacobian matrix J^(k), computed correction Δ x^(k), it is specifically implemented according to the following steps:

Correction amount x^(k)It is acquired according to formula (13) by following formula:

Δx^(k)=-(J^(k))^-1·f(x^(k)) (24)；

Step 7 determines Optimal Multiplier using the higher-order expansion information of the Taylor series of power flow equationSpecifically according to Lower step is implemented:

By each equation number consecutively in power flow equation group f (x)=0 of formula (12), if the general equation of power flow equation group Number is n_f, i.e.,It constructs objective function F (x), the solution of non-linear power flow equation group It is of equal value when f (x)=0 and objective function F (x) are zero:

When kth time iteration, x^(k)It is acquired by Newton-Laphson method, above formula deformation are as follows:

Wherein, H_i(Δx^(k)) power flow equation f when being kth time iteration_i(x) safeStrangle expansionNon-linear total item, in polar coordinates Under, non-linear total item contain it is infinite multinomial, can not by after calculating item by item add up method obtain.Herein by f_i(x) Thailand It strangles expansion and calculates this non-linear total item, Δ x^(k)It is obtained by formula (24), then:

H_i(Δx^(k))=f_i(x^(k)+Δx^(k)) (27)

It enables:

a_i ^(k)=f_i(x^(k)) (28)

c_i ^(k)=f_i(x^(k)+Δx^(k)) (29)

Formula (24)~(26) are substituted into formula (23), and omits subscript k and is write as general type:

Optimal Multiplier F (obtained at x+ μ Δ x) minimum value:

For the simple cubic equation of (32), with Newton Algorithm, if equation has solution, at least one reality of equation Root, other two root or real root, or a pair of of Conjugate complex roots, when equation is there are two compound radical, when only one real root, real root is For the Optimal Multiplier of current iterationIt is centainly corresponding with the minimum value of objective function F；If there are three real root μ₁、μ₂And μ₃ When, three roots have the minimum of a corresponding objective function, when there are three real root, choose μ₁、μ₂And μ₃In make objective function F obtains the Optimal Multiplier that minimum value person is current iteration

Step 8, in every step iteration withIt is modified as correction amount, it is specifically real according to the following steps It applies:

Based on step-length optimisation technique, in every step iteration withIt is modified as correction amount, i.e.,

Step 9, the number of iterations k=k+1；Go to step 5；

Step 10 calculates sagging node power and branch power, exports calculation of tidal current.

Referring to Fig. 2, tested using IEEE25 node system, branch impedance data and three-phase load power can be by texts Offer [Raju G K V, Bijwe P R.Efficient reconfiguration of balanced and unbalanced distribution systems for loss minimisation[J].Iet Generation Transmission& Distribution, 2008,2 (1): 7-12.] it obtains, it is not restrained when carrying out Load flow calculation using traditional ox daraf(reciprocal of farad), more than Algorithm is calculated:

In assumed load model Static Load frequency characteristic coefficient,Micro- source access system of four sagging control is constituted into microgrid, It is disconnected with major network and is used as isolated operation, table 1 is the distributed generation resource of 25 node isolated island micro-capacitance sensor node, 13,19,25 node access Parameter:

Table 1, the controllable on-position Wei Yuan and parameter

DG#	Node	Rated capacity	U0	ω0	mPi	nQi
							1	13	0.7	1.05	1.0	0.004	0.080
2	19	0.5	1.05	1.0	0.005	0.100
							3	25	0.7	1.05	1.0	0.004	0.080

When carrying out Load flow calculation to this isolated island micro-capacitance sensor using traditional Newton method, does not restrain, be iterated using the present invention After step-length optimization, the node voltage being calculated is as shown in Table 2 and Fig. 3, and the amount of mismatch and step-length in iterative process optimize multiplier It is as shown in table 3:

The node voltage of table 2,25 node isolated island micro-capacitance sensors

Amount of mismatch and optimization step-length multiplier in 3 25 node isolated island micro-capacitance sensor iterative process of table

The number of iterations	Optimal Multiplier	Amount of mismatch	The number of iterations	Optimal Multiplier	Amount of mismatch
						1	0.4771	3.663E-1	12	0.5593	4.187E-4
2	0.6277	2.497E-1	13	0.5581	1.918E-4
						3	0.5043	1.485E-1	14	0.5574	1.046E-4
4	0.6188	8.508E-2	15	0.5549	4.616E-5
						5	0.5528	4.414E-2	16	0.5560	2.565E-5
6	0.5853	2.310E-2	17	0.5520	1.098E-5
						7	0.5652	1.213E-2	18	0.5546	6.198E-6
8	0.5693	6.224E-3	19	0.5496	2.618E-6
						9	0.5648	3.139E-3	20	0.5533	1.481E-6
10	0.5625	1.637E-3	21	0.5474	6.211E-7
						11	0.5616	7.845E-4	22	0.5520	3.506E-7

Algorithm validity analysis:

Traditional Newton method calculates the trend of sagging control isolated island micro-capacitance sensor, it is easy to the phenomenon that appearance does not restrain；And pass through Using the amendment direction in step-length optimisation technique adjustment iterative process, keep iterated revision more acurrate, avoids makeover process decline To outside load flow feasible region, thus make Load flow calculation convergence be improved significantly.

Claims (7)

1. a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor, which is characterized in that specifically according to the following steps Implement:

Step 1, the triphase flow and computing system for establishing each sagging control type DG, load and circuit element in isolated island micro-capacitance sensor Node admittance matrix Y；

Step 2, column write the node power equilibrium equation of vertical control type isolated island micro-capacitance sensor, obtain Three-phase Power Flow equation group f (x)= 0；

Step 3 derives update equation formula and Jacobian matrix of the Three-phase Power Flow equation group of step 2 when using Newton Algorithm The calculation formula of J；

Step 4, setting the number of iterations k=0, set the initial value of PV node voltage magnitude as its given value, other each node voltages The initial value of amplitude is per unit value 1, and node voltage phase angle initial value is 0, and system frequency initial value is per unit value 1, and is obtained corresponding wait ask The correspondence initial value x of unknown quantity⁽⁰⁾；

Step 5, by x^(k)The expression formula for substituting into f (x), is calculated f (x^(k)), and judge whether it meets convergence criterion max | f (x^(k)) | < ε, ε are desired computational accuracy；If meeting convergence criterion, 10 are gone to step；Otherwise step 6 is carried out；

Step 6 calculates Jacobian matrix J^(k), computed correction Δ x^(k)；

Step 7 determines Optimal Multiplier using the higher-order expansion information of the Taylor series of power flow equation

Step 8, in every step iteration withIt is modified as correction amount；

Step 9, the number of iterations k=k+1；Go to step 5；

Step 10 calculates sagging node power and branch power, exports calculation of tidal current.

2. a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor according to claim 1, feature exist In the step 1 is specifically implemented according to the following steps:

Step 1.1, the triphase flow for initially setting up sagging control type micro battery:

If the collection that all nodes are constituted in micro-capacitance sensor is combined into B, and B_PQ、B_PVAnd B_DroopRespectively indicate PQ node in micro-capacitance sensor, PV section The set of point and the sagging node of Droop, when Droop node is run by active/idle limitation, by the calculating of PQ node, three-phase is not right Claim in isolated island micro-capacitance sensor, have to the node containing sagging control type DG:

Wherein:The total active power of three-phase and reactive power of respectively sagging control type DG output；Respectively its single-phase active power and reactive power value, wherein m={ a, b, c }；m_Pi、n_QiFor sagging section The active and idle equivalent adjustment factor of point；ω is system angular frequency；And ω₀For the voltage and angular frequency of sagging control DG Setting value；For the positive sequence voltage amplitude of sagging node i, ifWithThe respectively m phase voltage amplitude and phase angle of node i, Wherein, m={ a, b, c }, then have:

Meanwhile the three-phase voltage amplitude of sagging node is equal, waveform symmetry, it may be assumed that

Step 1.2, the State characteristics for establishing three-phase load are as follows:

In formula,The respectively active power of m phase load, reactive power；Respectively m phase load Active power rated value, reactive power rated value；U_Li0For the rated value of the voltage of node i；ω is the angular frequency of system, ω_L0For The rated value of angular frequency；WithIt is m phase load active power static voltage characteristic coefficient respectively, WithIt is m phase load reactive power static voltage characteristic coefficient respectively,WithIt is m phase load active power and nothing respectively The static frequency characteristic coefficient of function power；

Step 1.3, the equivalent circuit for establishing three-phase line:

In asymmetrical three-phase isolated island micro-capacitance sensor, the route of branch is indicated with three-phase impedance matrix between node i and j:

Wherein,The three-phase impedance matrix of branch between node i and j,Between node i and j between the three-phase of branch Impedance, wherein m={ a, b, c }, n={ a, b, c }.

3. a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor according to claim 2, feature exist In the step 2 is specifically implemented according to the following steps:

Column write the node power equilibrium equation of vertical control type isolated island micro-capacitance sensor, to arbitrary node i, if the p phase of injection node i has Function power and reactive power are denoted as P respectively_i ^pWithWherein, p={ a, b, c }, then its power balance equation indicates are as follows:

Wherein: Δ P_i ^p、The p phase of respectively node i is active and reactive power amount of unbalance；P_i ^p、Respectively node i The active and idle injecting power of p phase；WithRespectively the p phase of node admittance matrix interior joint i and the m phase of node k The real and imaginary parts of admittance array element element, m={ a, b, c }；For the phase angle difference of the voltage of the m phase of the p phase and node k of node i.

For each PQ node, unbalanced power amount expression formula is corresponding with 6 equations:

Wherein,WithRespectively such as wind power generating set or the photovoltaic cells in addition to sagging control type DG of node i access The p phase active power and reactive power of equal DG, p={ a, b, c }, if without Wind turbines or photovoltaic cells, value zero；

For each PV node, since node voltage is constant, and reactive power amount of unbalance equation, power-balance side are not considered 3 equations of Cheng Zuwei:

The power balance equation group of each sagging node will include 12 equality constraints:

There are 12 unknown quantitys for each sagging node, usesIt indicates each phase voltage amplitude of sagging node, uses It indicates a phase phase angle, and b and c phase phase angle is used respectivelyWithIt substitutes into, simultaneously willWithIt is indicated and is eliminated with droop characteristic relational expressionWithThen the unknown quantity abbreviation of sagging node is 6Its node power equilibrium equation are as follows:

Assuming that taking the phase angle of node 1For Reference Phase Angle, i.e.,For convenience of statement, ifIt indicates to remove sagging node The three phases active power amount of unbalance column vector of outer other nodes,Indicate the three phases active power amount of unbalance of PQ node Column vector,WithIt respectively indicates that sagging node three-phase is active and reactive power amount of unbalance column vector, and remembers IfIt indicates to remove reference mode and sagging node The three-phase voltage phase angle column vector of outer other nodes,Indicate the voltage magnitude column vector of PQ node,With The a phase voltage phase angle and amplitude column vector of each sagging control node are respectively indicated,AndRespectively indicate sagging node A phase and b phase be active and reactive power column vector, and remember Then formula (6)~(10) Three-phase Power Flow equation group is write as following shape Formula:

Formula (11) isolated island micro-capacitance sensor power flow equation is further collectively expressed as following form:

F (x)=0 (12)

In formula,

4. a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor according to claim 3, feature exist In the step 3 is specifically implemented according to the following steps:

Using the above-mentioned Three-phase Power Flow equation group of Newton Algorithm, its update equation formula is derived, as follows:

Wherein, Δ x₁Δx₂Δx₃For variable x₁、x₂And x₃Correction amount；Each sub-block calculation formula of Jacobian matrix J is as follows:

Each Jacobian matrix sub-block J in formula (14)~formula (18)₁₁、J₁₂、J₂₁And J₂₂In H, N, M, L piecemeal each element definition It is identical as the essence definition of piecemeal element is corresponded in conventional three-phase Load flow calculation, the only corresponding separate and node collection of each sub-block Close difference, specifically, H, M piecemeal and conventional three-phase Load flow calculation Jacobian matrix J_origElement expression is not different, and N, L piecemeal need to be in J_origOn the basis of element expression, it need to modify adjustment to its main diagonal element, ifWithPoint It Wei not J_origAny diagonal element of middle N and L piecemeal, i ∈ B, m={ a, b, c }, j ∈ B_PQ∪B_Droop, m={ a, b, c }, WithThe correspondence diagonal element of N and L piecemeal in respectively isolated island micro-capacitance sensor Jacobian matrix J is usedWithTable respectively Show that it modifies superposition amount, i.e.,Have:

J₁₁In E₁₁And F₁₁Piecemeal and J₂₁In E₂₁And F₂₁Piecemeal is column vector, any elementT ∈ B, m= { a, b, c } ands∈B_PQ∪B_Droop, m={ a, b, c } distinguishes as follows:

J according to definition, in Jacobian matrix₁₃Middle whole element is zero；And J₂₃In in addition to following element remaining element it is equal It is zero:

5. a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor according to claim 4, feature exist In the step 6 is specifically implemented according to the following steps:

Calculate Jacobian matrix J^(k), correction amount x^(k)It is acquired according to formula (13) by following formula:

Δx^(k)=-(J^(k))^-1·f(x^(k)) (24)。

6. a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor according to claim 5, feature exist In the step 7 determines Optimal Multiplier using the higher-order expansion information of the Taylor series of power flow equationSpecifically according to following Step is implemented:

By each equation number consecutively in power flow equation group f (x)=0 of formula (12), if the general equation number of power flow equation group is n_f, i.e.,It constructs objective function F (x), the solution f (x) of non-linear power flow equation group It is of equal value when=0 and objective function F (x) are zero:

When kth time iteration, x^(k)It is acquired by Newton-Laphson method, above formula deformation are as follows:

Wherein, H_i(Δx^(k)) power flow equation f when being kth time iteration_i(x) non-linear total item of Taylor expansion, by f_i(x) Thailand It strangles expansion and calculates this non-linear total item, Δ x^(k)It is obtained by formula (24), then:

H_i(Δx^(k))=f_i(x^(k)+Δx^(k)) (27)

It enables:

a_i ^(k)=f_i(x^(k)) (28)

c_i ^(k)=f_i(x^(k)+Δx^(k)) (29)

Formula (24)~(26) are substituted into formula (23), and omits subscript k and is write as general type:

Optimal Multiplier F (obtained at x+ μ Δ x) minimum value:

For the simple cubic equation of (32), with Newton Algorithm, if equation has a solution, at least one real root of equation, separately Outer two roots or real root, or a pair of of Conjugate complex roots, when equation is there are two compound radical, when only one real root, real root is to work as The Optimal Multiplier of preceding iterationIt is centainly corresponding with the minimum value of objective function F；If there are three real root μ₁、μ₂And μ₃When, Three roots have the minimum of a corresponding objective function, when there are three real root, choose μ₁、μ₂And μ₃In objective function F is taken Obtain the Optimal Multiplier that minimum value person is current iteration

7. a kind of Three-phase Power Flow analysis method of sagging control type isolated island micro-capacitance sensor according to claim 6, feature exist In the step 8 is specifically implemented according to the following steps:

Based on step-length optimisation technique, in every step iteration withIt is modified as correction amount, i.e.,