CN102842908A - Three-phase decoupling power flow calculation method for power distribution network containing multiple transformer branches - Google Patents

Abstract

The invention discloses a three-phase decoupling power flow calculation method for a power distribution network containing multiple transformer branches. According to the characteristics of basically symmetrical three-phase line parameters, unbalanced three-phase load and the tree structure of the power distribution network, the method comprises the following steps: performing sequence component decoupling on the three-phase unbalanced network of the power distribution network by a symmetrical component method; in a power distribution three-sequence network model, transforming the transformer branches into the common branches by a phase transformation technology; and calculating the sequence network power flow of the power distribution system by a path matrix-based loop analysis method and transforming sequence component power flow into phase component power flow by an inverse transformation principle so as to realize three-phase decoupling power flow calculation of the three-phase unbalanced system of the power distribution network containing multiple transformer branches and reduce calculated quantity. The method is clear in calculation process, simple in programming and high in calculation speed. The correctness and high convergence property of the method are verified through 34 bus test calculation examples. The method has high generality and practicability.

Description

The power distribution network three-phase decoupling zero tidal current computing method that contains the multiple transformers branch road

Technical field

The present invention relates to a kind of power distribution network three-phase decoupling zero tidal current computing method that contains the multiple transformers branch road, belong to power system analysis and computing field.

Background technology

Distribution power system load flow calculation is the focus of academic research for many years always, and distribution power system load flow calculation is the basis that distribution network is analyzed.Because the characteristic of power distribution network is different with power transmission network, generally has the tree network design feature of higher R/X ratio, three-phase imbalance and closed loop design open loop operation, so traditional power transmission network power flow algorithm can not directly apply to power distribution network.Chinese scholars has proposed various distribution power flow algorithms according to the characteristics of power distribution network, as preceding pushing back for method, implicit expression Zbus Gaussian processes, impedance loop method, modified Newton method and quick decoupling method etc.Wherein before push back Dai Fa owing to made full use of the design feature of power distribution network, and it has that physical concept is distinct, programming is simple, do not have that large matrix calculates, computational speed is fast, better astringency, be very suitable for finding the solution advantage such as radial distribution networks trend and be widely used.Line parameter circuit value in the power distribution network all is the space symmetry basically, generally is the characteristics that on load, have three-phase imbalance property.

Summary of the invention

Goal of the invention: to the problem and shortage that exists in the prior art, the present invention provides a kind of power distribution network three-phase decoupling zero tidal current computing method that contains the multiple transformers branch road.

Technical scheme: a kind of power distribution network three-phase decoupling zero tidal current computing method that contains the multiple transformers branch road may further comprise the steps:

1) establishing first node is power supply and node as a reference; Power supply node three-phase voltage phase moment matrix is

(3 * 1 rank); Each node three-phase voltage phase moment matrix is

(3n * 1 rank); In the distribution system sequence network; The three sequence voltage matrixes that can draw power supply node are

(3 * 1 rank), and each node three sequence voltage matrix is

(3n * 1 rank).Wherein, make a=e ^{J2 π/3}, $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ N is the number of isolated node, and then separate branches bar number is b=n.Promptly to having three-phase radial (tree-like) power distribution network of N node, suppose that first node is power supply and node as a reference, then the isolated node number is n=N-1, the separate branches bar is counted b=n.

2) according to the number K of transformer in the power distribution network, be divided into K piece zone to power distribution network accordingly, according to reference node, the mode of connection of each transformer calculates the phse conversion matrix Θ in each piece zone successively _k, and calculate the regional decoupling zero conversion matrix A of each piece _k=Θ _kA (3 * 3 rank).Wherein, k representes k piece zone in the power distribution network, k ∈ 1,2 ..., K}; Θ is the phse conversion matrix, is one 3 * 3 diagonal matrix, and θ ₀, θ ₁And θ ₂Be respectively zero sequence, positive sequence and negative phase-sequence phase-shift phase in the three sequence network systems, subscript " 0 ", " 1 " and " 2 " are represented zero sequence, positive sequence and negative phase-sequence in the three preface nets respectively; Also can obtain $A_k^{-1}=A^{-1}{\mathrm{\Θ}}_k^{-1}.$

3) calculate the diagonal matrix (n * n rank) that each sequence network parameter

forms for the preface impedance

based on branch road i; Wherein, Subscript s=0; 1; 2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively.Three phase of impedance of branch road i do

Suppose that it belongs to k piece zone, then has

Wherein, ${\mathrm{<figure-callout\; id="0"\; label="Z\; Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="Z\; Bi"\; filenames="HDA00002125554000011.png,HDA00002125554000021.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="Z\; Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">Z</figure-callout>\; </figure-callout>\; </figure-callout>}}_{\mathrm{Bi}}^{}=\left[\begin{array}{ccc}{Z}_{\mathrm{<figure-callout\; id="0"\; label="Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">Bi</figure-callout>}}^0& 0& 0\\ 0& {\mathrm{<figure-callout\; id="1"\; label="Z\; Bi"\; filenames="HDA00002125554000011.png,HDA00002125554000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\mathrm{Bi}}^{}& 0\\ 0& 0& {\mathrm{<figure-callout\; id="2"\; label="Z\; Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\mathrm{Bi}}^{}\end{array}\right],$ $Z_{\mathrm{Bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{Iaa}}& Z_{\mathrm{Iab}}& Z_{\mathrm{Iac}}\\ Z_{\mathrm{Iba}}& Z_{\mathrm{Ibb}}& Z_{\mathrm{Ibc}}\\ Z_{\mathrm{Ica}}& Z_{\mathrm{Icb}}& Z_{\mathrm{Icc}}\end{array}\right];$ A wherein _kDecoupling zero transformation matrix for branch road i region.

4) in each preface pessimistic concurrency control circuit of decoupling zero, calculate the path matrix T of each sequence network _sBe zero node for injecting the preface electric current in addition, at the path matrix T of each preface net _sIn leave out the back to this node institute corresponding row to form new matrix be T _SgWherein, subscript s=0,1,2, represent zero sequence, positive sequence and negative sequence network in the sequence network model respectively.

5) calculate each preface net middle impedance sensitivity matrix

6) compose initial value for each node three-phase voltage of power distribution network

E wherein _n=[E, E ..., E] ^T, being total to n E, E is 3 * 3 unit matrixs.

Each phase current that node i is injected when 7) calculating d iteration

Wherein

Be each phase injecting power of node i, Y _i ^pBe the node i admittance sum that respectively is in parallel, p=a, b, c, i=1,2 ..., m.M is that node injects the non-vanishing node number of preface electric current, and d is the iterations variable.

Each preface electric current i=1 that node i is injected when 8) calculating d iteration; 2;, m.Wherein, A _kDecoupling zero transformation matrix for the node i region.

when 9) calculating d iteration wherein;

removes that to inject the preface electric current be the new injection preface current matrix (m * 1 rank) that forms behind the zero node when d iteration; M is that node injects the non-vanishing node number of preface electric current; Subscript s=0; 1; 2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively.

When 10) calculating d iteration

Wherein, 1 _n=[1,1 ..., 1] ^T, n individual 1 altogether; S=0,1,2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively.

Node i three-phase voltage phasor

i=1 when 11) calculating d iteration based on inverse transformation; 2;, n.Wherein, A _kDecoupling zero transformation matrix for the node i region.

Whether the difference of 12) judging

and

amplitude satisfies the convergence precision requirement, satisfies finishing iteration; Not satisfying changes step 7).

Beneficial effect: compared with prior art; A kind of power distribution network three-phase decoupling zero tidal current computing method that contains the multiple transformers branch road that the present invention proposes is in conjunction with based on the loop analysis and the preface component Decoupling Analysis method of path matrix, in decoupling zero preface net; Utilize the phse conversion technology; Simplify and fall transformer, thereby realized that being used as common branch road to the transformer branch road handles, realized containing the power distribution network three-phase trend calculating of multiple transformers branch road.On the one hand; The utilization symmetrical component method carries out three-phase decoupling zero trend and calculates the good calculating advantage that has; Can one group asymmetric " a ", " b ", " c " three phase components be decomposed into three group of three symmetrical preface component; So, the three-phase trend is calculated just to have become and is calculated three group of three phase in the symmetrical preface component.Therefore, the amount of calculation that power distribution network three-phase imbalance trend is calculated can reduce 2/3, calculates for power distribution network three-phase trend and bring computational speed faster under the convergence situation keeping preferably.On the other hand, in distribution preface net, realize that the transformer branch road is transformed into common branch road and can be more prone to, no matter and transformer with which kind of mode of connection, can be transformed into common branch road to the transformer branch road after through the phse conversion technical finesse and calculate.Therefore, amount of calculation of the present invention is few, and computational efficiency is high, has good versatility and practicality.The computational process of whole invention is clear, and programming is simple, and computational speed is fast.At last, correctness of the present invention and good convergence have been verified through 34 buses test example.

Description of drawings

Fig. 1 is a method flow diagram of the present invention;

Fig. 2 is the three-phase imbalance distribution system that 34 buses contain the multiple transformers branch road;

Fig. 3 is each node three-phase voltage distribution map of trend convergence back under the Case1 situation;

Fig. 4 is each node three-phase voltage distribution map of trend convergence back under the Case5 situation.

Embodiment

Below in conjunction with specific embodiment; Further illustrate the present invention; Should understand these embodiment only be used to the present invention is described and be not used in the restriction scope of the present invention; After having read the present invention, those skilled in the art all fall within the application's accompanying claims institute restricted portion to the modification of the various equivalent form of values of the present invention.

Fig. 1 is an overview flow chart of the present invention, specifically comprises the steps:

1) establishing first node is power supply and node as a reference; Power supply node three-phase voltage phase moment matrix is (3 * 1 rank); Each node three-phase voltage phase moment matrix is

(3n * 1 rank); In the distribution system sequence network; The three sequence voltage matrixes that can draw power supply node are

(3 * 1 rank), and each node three sequence voltage matrix is (3n * 1 rank).Wherein, make a=e ^{J2 π/3}, $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ N is the number of isolated node, and then separate branches bar number is b=n.Promptly to having three-phase radial (tree-like) power distribution network of N node, suppose that first node is power supply and node as a reference, then the isolated node number is n=N-1, the separate branches bar is counted b=n.

2) according to the number K of transformer in the power distribution network, be divided into K piece zone to power distribution network accordingly, according to reference node, the mode of connection of each transformer calculates the phse conversion matrix Θ in each piece zone successively _k, and calculate the regional decoupling zero conversion matrix A of each piece _k=Θ _kA (3 * 3 rank).Wherein, k representes k piece zone in the power distribution network, k ∈ 1,2 ..., K}; Θ is the phse conversion matrix, is one 3 * 3 diagonal matrix, and

θ ₀, θ ₁And θ ₂Be respectively zero sequence, positive sequence and negative phase-sequence phase-shift phase in the three sequence network systems, subscript " 0 ", " 1 " and " 2 " are represented zero sequence, positive sequence and negative phase-sequence in the three preface nets respectively; Also can obtain $A_k^{-1}=A^{-1}{\mathrm{\&Theta;}}_k^{-1}.$

3) calculate the diagonal matrix (n * n rank) that each sequence network parameter

forms for the preface impedance

based on branch road i; Wherein, Subscript s=0; 1; 2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively.Three phase of impedance of branch road i do

Suppose that it belongs to k piece zone, then has

Wherein, ${\mathrm{<figure-callout\; id="0"\; label="Z\; Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">\; <figure-callout\; id="1"\; label="Z\; Bi"\; filenames="HDA00002125554000011.png,HDA00002125554000021.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="Z\; Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">Z</figure-callout>\; </figure-callout>\; </figure-callout>}}_{\mathrm{Bi}}^{}=\left[\begin{array}{ccc}{Z}_{\mathrm{<figure-callout\; id="0"\; label="Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">Bi</figure-callout>}}^0& 0& 0\\ 0& {\mathrm{<figure-callout\; id="1"\; label="Z\; Bi"\; filenames="HDA00002125554000011.png,HDA00002125554000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\mathrm{Bi}}^{}& 0\\ 0& 0& {\mathrm{<figure-callout\; id="2"\; label="Z\; Bi"\; filenames="HDA00002125554000021.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{\mathrm{Bi}}^{}\end{array}\right],$ $Z_{\mathrm{Bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{Iaa}}& Z_{\mathrm{Iab}}& Z_{\mathrm{Iac}}\\ Z_{\mathrm{Iba}}& Z_{\mathrm{Ibb}}& Z_{\mathrm{Ibc}}\\ Z_{\mathrm{Ica}}& Z_{\mathrm{Icb}}& Z_{\mathrm{Icc}}\end{array}\right];$ A wherein _kDecoupling zero transformation matrix for branch road i region.

4) in each preface pessimistic concurrency control circuit of decoupling zero, calculate the path matrix T of each sequence network _sBe zero node for injecting the preface electric current in addition, at the path matrix T of each preface net _sIn leave out the back to this node institute corresponding row to form new matrix be T _SgWherein, subscript s=0,1,2, represent zero sequence, positive sequence and negative sequence network in the sequence network model respectively.

5) calculate each preface net middle impedance sensitivity matrix

6) compose initial value for each node three-phase voltage of power distribution network

E wherein _n=[E, E ..., E] ^T, being total to n E, E is 3 * 3 unit matrixs.

Each phase current that node i is injected when 7) calculating d iteration Wherein

Be each phase injecting power of node i, Y _i ^pBe the node i admittance sum that respectively is in parallel, p=a, b, c, i=1,2 ..., m.M is that node injects the non-vanishing node number of preface electric current, and d is the iterations variable.

Each preface electric current

i=1 that node i is injected when 8) calculating d iteration; 2;, m.Wherein, A _kDecoupling zero transformation matrix for the node i region.

when 9) calculating d iteration wherein;

removes that to inject the preface electric current be the new injection preface current matrix (m * 1 rank) that forms behind the zero node when d iteration; M is that node injects the non-vanishing node number of preface electric current; Subscript s=0; 1; 2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively.

The derivation of equation in the step 9) is following:

Three-phase to having N node radial (tree-like) power distribution network supposes that first node is power supply and node as a reference, and then the isolated node number is n=N-1, and the separate branches bar is counted b=n.The road of a node be meant node along set root the set of fingers on the path of process; What the road of node was stressed is the branch road on the path, and for a given tree, the road of node is unique; The road of node only is made up of tree Zhi Zhilu, and T describes road with path matrix.Wherein path matrix T is a n * n rank square formation, and the positive direction of supposing road all is to point to each node from power supply point, and each branch road positive direction is identical with the road positive direction, if branch road j on road i, then T (i, j)=1, otherwise T (i, j)=0.Path matrix T is a sparse triangle battle array down, utilizes sparse technology can reduce memory requirements.

In the distribution sequence network, establish For node injects preface current vector matrix (n * 1 rank), establish

Be branch order current vector matrix (n * 1 rank) that in each preface pessimistic concurrency control circuit of decoupling zero, the path matrix that can obtain each sequence network is respectively T ₀, T ₁And T ₂, and according to the KCL current law, the branch order electric current Inject the preface electric current with node

Satisfy following equality:

${\stackrel{\&CenterDot;}{I}}_b^s=T_s^T{\stackrel{\&CenterDot;}{I}}_n^s---\left(1\right)$

Wherein, s=0,1,2, represent zero sequence, positive sequence and negative sequence network in the sequence network model respectively.

Formula (1) has provided

Between association, still, be not that each node all has and injects the preface electric current in real system, be zero node for injecting the preface electric current, at the path matrix T of each preface net _sIn leave out the back to this node institute corresponding row to form new matrix be T _Sg, this up-to-date style (1) becomes

${\stackrel{\&CenterDot;}{I}}_b^s=T_{\mathrm{sg}}^T{\stackrel{\&CenterDot;}{I}}_g^s---\left(2\right)$

is the new injection preface current matrix (m * 1 rank) that forms behind zero the node for remove injecting the preface electric current in the formula (2), and m is that node injects the non-vanishing node number of preface electric current.

In arbitrary radial distribution system preface component circuit model, have based on Ohm's law

${\stackrel{\&CenterDot;}{U}}_b^s=Z_b^s{\stackrel{\&CenterDot;}{I}}_b^s---\left(3\right)$

Wherein,

is power distribution network branch order voltage matrix (n * 1 rank);

is the diagonal matrix (n * n rank) that the preface impedance

based on branch road i forms; S=0; 1; 2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively.

If power supply node three-phase voltage phase moment matrix does (3 * 1 rank), each node three-phase voltage phase moment matrix does (3n * 1 rank), in the distribution sequence network, the three sequence voltage matrixes that can draw power supply node do

(3 * 1 rank), each node three sequence voltage matrix does

(3n * 1 rank), so, in each sequence network model, the sequence voltage difference that can know arbitrary node and power supply node equal node from then on begin along the road of this node arrive power supply node through the branch order voltage sum of branch road, promptly (establish 1 _n=[1,1 ..., 1] ^T, n individual 1 altogether; S=0,1,2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively):

$\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{U}}_n^s=1_n{\stackrel{\&CenterDot;}{U}}_0^s-{\stackrel{\&CenterDot;}{U}}_n^s=T_s{\stackrel{\&CenterDot;}{U}}_b^s=T_s{Z}_b^s{\stackrel{\&CenterDot;}{I}}_b^s=T_s{Z}_b^s{T}_{\mathrm{sg}}^T{\stackrel{\&CenterDot;}{I}}_g^s=\mathrm{\&Delta;}{Z}_t^s{\stackrel{\&CenterDot;}{I}}_g^s---\left(4\right)$

Wherein,

is defined as each preface net middle impedance sensitivity matrix:

$\mathrm{\&Delta;}{Z}_t^s=T_s{Z}_b^s{T}_{\mathrm{sg}}^T---\left(5\right)$

${\stackrel{\&CenterDot;}{U}}_n^s=1_n{\stackrel{\&CenterDot;}{U}}_0^s-\mathrm{\&Delta;}{\stackrel{\&CenterDot;}{U}}_n^s---\left(6\right)$

When 10) calculating d iteration

Wherein, 1 _n=[1,1 ..., 1] ^T, n individual 1 altogether; S=0,1,2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively.

Node i three-phase voltage phasor

i=1 when 11) calculating d iteration based on inverse transformation; 2;, n.Wherein, A _kDecoupling zero transformation matrix for the node i region.

12) judgment

and whether the difference between the amplitude accuracy to meet the convergence requirements.Satisfy finishing iteration; Not satisfying changes step 7).

Sample calculation analysis

Like Fig. 2 is the three-phase imbalance power distribution network that 34 buses contain the multiple transformers branch road, and system has been carried out some adjustment, removes three-phase regulator; And put aside the loop situation; Supposing the system is the open loop operation, the line parameter circuit value symmetry, and promptly circuit phase component impedance matrix is symmetrical fully; And three-phase load is uneven, so relatively near domestic distribution network system.

T1 is positioned at step-down substation among Fig. 2, and in order to react and be fit to the characteristics of domestic three-phase imbalance power distribution network, T1 adopts the common △-Y of domestic present main step-down substation _gConfiguration is reduced to 24.9kV to 69kV voltage, and capacity is 2500kVA.Three transformer nominal transformation ratios of T2 ~ T4 are identical, reduce to 4.16kV to 24.9kV.System's total load is 1379kW, 878kvar, and it is uneven to distribute.For the emulation comparative analysis, transformer T1 is fixed as △-Y _gConfiguration, and transformer T2 ~ T4 is respectively at Y _g-Y _g, △-Y _gGet a kind of configuration with optional in three kinds of configurations of Y-△, have 27 groups of combining forms, as shown in table 1, table 1 has provided the center and has divided the combination form, and it is as shown in table 2 that its trend based on algorithm of the present invention is calculated the convergence situation.

The configuration combination of table 1 transformer T1 ~ T4

Table 2 34 bus-bar system trends convergence back iterations

Can find out that from table 2 the convergence difference is little under the different configuring conditions, visible this paper algorithm has better convergence performance.

Fig. 3 and Fig. 4 be respectively under Case1 and the Case5 situation trend calculate each node A of convergence back mutually, B mutually and C phase voltage distribution map; Distribute than balance from the three-phase voltage of Fig. 3 and the relatively more visible Case5 of Fig. 4; And the three-phase voltage difference of Case1 is bigger; Center partial node voltage C phase voltage (less than 0.9) obviously excessively on the low side this shows, can improve the excessive problem on the low side of three-phase imbalance distribution system node voltage single-phase voltage through transformer being carried out the various combination configuration.

Claims (1)

1. a power distribution network three-phase decoupling zero tidal current computing method that contains the multiple transformers branch road is characterized in that, may further comprise the steps:

1) establishing first node is power supply and node as a reference, and power supply node three-phase voltage phase moment matrix does

Each node three-phase voltage phase moment matrix does In the distribution system sequence network, the three sequence voltage matrixes that draw power supply node do

Each node three sequence voltage matrix does

Wherein, make a=e ^{J2 π/3}, $A=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right],$ $A^{-1}=\left[\begin{array}{ccc}1& 1& 1\\ 1& a^2& a\\ 1& a& a^2\end{array}\right];$ N is the number of isolated node, and then separate branches bar number is b=n; Promptly to having three-phase radial (tree-like) power distribution network of N node, suppose that first node is power supply and node as a reference, then the isolated node number is n=N-1, the separate branches bar is counted b=n;

2) according to the number K of transformer in the power distribution network, be divided into K piece zone to power distribution network accordingly, according to reference node, the mode of connection of each transformer calculates the phse conversion matrix Θ in each piece zone successively _k, and calculate the regional decoupling zero conversion matrix A of each piece _k=Θ _kA; Wherein, k representes k piece zone in the power distribution network, k ∈ 1,2 ..., K}; Θ is the phse conversion matrix, is one 3 * 3 diagonal matrix, and θ ₀, θ ₁And θ ₂Be respectively zero sequence, positive sequence and negative phase-sequence phase-shift phase in the three sequence network systems, subscript " 0 ", " 1 " and " 2 " are represented zero sequence, positive sequence and negative phase-sequence in the three preface nets respectively; Obtain simultaneously $A_k^{-1}=A^{-1}{\mathrm{\&Theta;}}_k^{-1}.$

3) calculate each sequence network parameter

Be preface impedance based on branch road i

The diagonal matrix that forms, wherein, subscript s=0,1,2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively; Three phase of impedance of branch road i do

Suppose that it belongs to k piece zone, then has

Wherein, $Z_{\mathrm{Bi}}^{\mathrm{0,1,2}}=\left[\begin{array}{ccc}{Z}_{\mathrm{Bi}}^0& 0& 0\\ 0& Z_{\mathrm{Bi}}^1& 0\\ 0& 0& Z_{\mathrm{Bi}}^2\end{array}\right],$ $Z_{\mathrm{Bi}}^{a,b,c}=\left[\begin{array}{ccc}{Z}_{\mathrm{Iaa}}& Z_{\mathrm{Iab}}& Z_{\mathrm{Iac}}\\ Z_{\mathrm{Iba}}& Z_{\mathrm{Ibb}}& Z_{\mathrm{Ibc}}\\ Z_{\mathrm{Ica}}& Z_{\mathrm{Icb}}& Z_{\mathrm{Icc}}\end{array}\right];$ A wherein _kDecoupling zero transformation matrix for branch road i region;

4) in each preface pessimistic concurrency control circuit of decoupling zero, calculate the path matrix T of each sequence network _sBe zero node for injecting the preface electric current in addition, at the path matrix T of each preface net _sIn leave out the back to this node institute corresponding row to form new matrix be T _SgWherein, subscript s=0,1,2, represent zero sequence, positive sequence and negative sequence network in the sequence network model respectively;

5) calculate each preface net middle impedance sensitivity matrix

6) compose initial value for each node three-phase voltage of power distribution network

E wherein _n=[E, E ..., E] ^T, being total to n E, E is 3 * 3 unit matrixs;

Each phase current that node i is injected when 7) calculating d iteration

Wherein

Be each phase injecting power of node i, Y _i ^pBe the node i admittance sum that respectively is in parallel, p=a, b, c, i=1,2 ..., m; M is that node injects the non-vanishing node number of preface electric current, and d is the iterations variable;

Each preface electric current that node i is injected when 8) calculating d iteration

I=1,2 ..., m; Wherein, A _kDecoupling zero transformation matrix for the node i region;

when 9) calculating d iteration wherein;

removes that to inject the preface electric current be the new injection preface current matrix that forms behind the zero node when d iteration; M is that node injects the non-vanishing node number of preface electric current; Subscript s=0; 1; 2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively;

When 10) calculating d iteration

Wherein, 1 _n=[1,1 ..., 1] ^T, n individual 1 altogether; S=0,1,2, represent zero sequence, positive sequence and negative sequence network model in the sequence network model respectively;

Node i three-phase voltage phasor when 11) calculating d iteration based on inverse transformation

I=1,2 ..., n; Wherein, A _kDecoupling zero transformation matrix for the node i region;

12) judgment

and

whether the difference between the amplitude accuracy to meet the convergence requirements; meet end iterator; satisfied go to step 7).

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