CN102879668A - Asymmetric fault analysis method for power distribution network including inverted distribution type power supply - Google Patents

Abstract

The invention discloses an asymmetric fault analysis method for a power distribution network including an inverted distribution type power supply. The asymmetric fault analysis method comprises the steps as follows: firstly, calculating a voltage amplitude value UPCC of a point of common coupling PCC when the power distribution network runs normally in combination with a fault through control strategy and an output characteristic of the distribution type power supply; and secondly, building an equation set of a positive sequence voltage amplitude value of the PCC when the power distribution network has a fault to calculate a positive sequence voltage of the PCC when the power distribution network has the fault so as to finish fault analysis of the power distribution network including the inverted distribution type power supply. Compared with the prior art, the accuracy of fault analysis is improved.

Description

The asymmetric fault analytical approach of distribution network comprising inverse distributed power

Technical field

The present invention relates to the power system fault analysis method, particularly the asymmetric fault analytical approach of distribution network comprising inverse distributed power.

Background technology

Symmetrical component method is that asymmetric fault is analyzed topmost method, for traditional synchronous motor, can adopt voltage source equivalent in positive sequence network, and can adopt impedance equivalent in negative sequence network.Yet inverse distributed power is fully different from traditional synchronous motor type of power, and its output characteristics is determined by its control strategy fully under the asymmetric fault condition, all can not adopt traditional synchronous motor Equivalent Model in positive and negative sequence network.Therefore, existing failure analysis methods will inevitably produce larger error.For realizing the asymmetric fault Accurate Analysis of distribution network comprising inverse distributed power, must be improved from Equivalent Model and the distribution network failure analytical model of inverse type power supply.

Summary of the invention

For the above-mentioned shortcoming and deficiency that overcomes prior art, the present invention is directed to the inverse distributed power of positive-sequence component control, propose to take into account the power distribution network asymmetric fault analytical approach of fault traversing control strategy and output characteristics, realized the Accurate Analysis of the asymmetric fault of distribution network comprising inverse distributed power.

Purpose of the present invention is achieved through the following technical solutions: the asymmetric fault analytical approach of distribution network comprising inverse distributed power may further comprise the steps (each variable in the following step all represents perunit value):

The voltage magnitude U of the common connecting point (PCC) when S1 calculating power distribution network normally moves _PCC

Compound sequence network when S2 sets up distribution network failure, distributed power source only are included in the positive sequence network, the positive sequence voltage amplitude of the PCC when setting up distribution network failure

The solving equation group, specifically may further comprise the steps:

Nodal voltage equation when the compound sequence network of S21 during according to distribution network failure obtains fault:

$\left[Y^{\′}\right]{\stackrel{\·}{U}}_f={\stackrel{\·}{I}}_f---\left(1\right)$

Wherein, $\left[Y^{\′}\right]=\left[\begin{array}{cccc}{Y^{\′}}_{11}& {Y^{\′}}_{12}& \·\·\·& {Y^{\′}}_{1m}\\ {Y^{\′}}_{21}& {Y^{\′}}_{22}& \·\·\·& {Y^{\′}}_{2m}\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ {Y^{\′}}_{m1}& {Y^{\′}}_{m2}& \·\·\·& {Y^{\′}}_{\mathrm{mm}}\end{array}\right]$ Bus admittance matrix during the expression fault; Diagonal element Y _IiSelf-admittance during for the node i fault, its value are connected to all branch road admittance sums of node i when equaling fault; Off-diagonal element Y ' _IjFor the transadmittance during fault between node i, j, when having branch road between node i, j, Y ' _IjEqual directly to be connected in the negative value of the branch road admittance between node i, j; When not having branch road between node i, j, Y ' _Ij=0;

${\stackrel{\·}{U}}_f=\left[\begin{array}{c}{\stackrel{\·}{U}}_{1\·f}\\ {\stackrel{\·}{U}}_{2\·f}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{\mathrm{PCC}\·f}^{+}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{\mathrm{PCC}\·f}^{-}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{m\·f}\end{array}\right]$ Node voltage during the expression fault, wherein

The positive and negative sequence voltage of PCC when being respectively fault;

${\stackrel{\·}{I}}_f=\left[\begin{array}{c}{\stackrel{\·}{I}}_{1\·f}\\ {\stackrel{\·}{I}}_{2\·f}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_{\mathrm{DG}\·f}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_{m\·f}\end{array}\right]$ The Injection Current of node during the expression fault, wherein

Distributed power source during for fault (DG) injects the electric current of PCC;

Be expressed as: ${\stackrel{\·}{I}}_{\mathrm{DG}\·f}=I_{d\·f}-{\mathrm{jI}}_{q\·f}---\left(2\right)$

Wherein, $\left\{\begin{array}{c}{I}_{d\·f}=P_{\left(0\right)}/U_{\mathrm{PCC}\·f}^{+}\\ I_{q\·f}=I_{q\left(0\right)}+k_q(U_{\mathrm{PCC}}-U_{\mathrm{PCC}\·f}^{+})\end{array}\right.$

In the formula, I _Df, I _QfDistributed power source output active current and reactive current when representing fault respectively; P ₍₀₎, I _{Q (0)}The active power and the reactive current that represent respectively normal motion time cloth formula power supply output,

Q ₍₀₎The reactive power that represents normal motion time cloth formula power supply output, k _qThe expression coefficient;

S22 carries out linear transformation to formula (1), obtains

The solving equation group;

S3 finds the solution

S4 finds the solution I _Df, I _Qf

S5 defines I _Ad=I _Df+ I _Qf, and judge I _AdWhether surpass inverter rated current I _VSCnIf, do not surpass and then carry out step S6, otherwise, I made _Df=I _VSCn-I _Qf, with I _Df, I _QfExpression formula substitution formula (1), and recomputate

After carry out step S6;

S6 utilizes formula (1) to calculate

In remove

Outer node voltage;

S7 is according to the branch current between following formula computing node j and the node k:

${\stackrel{\·}{I}}_{\mathrm{jk}\·f}=\frac{{\stackrel{\·}{U}}_{i\·f}-{\stackrel{\·}{U}}_{k\·f}}{Z_{\mathrm{jk}}}$

Wherein,

Z _JkRepresent respectively branch current and branch impedance between node j and the k,

The voltage of node j, k when representing distribution network failure respectively.

The voltage magnitude U of PCC when the described calculating power distribution network of step S1 normally moves _PCC, specifically may further comprise the steps:

Nodal voltage equation when the power distribution network equal-value map is normally moved during the normal operation of S11 basis:

$\left[Y\right]\stackrel{\·}{U}=\stackrel{\·}{I}$

Wherein, $\left[Y\right]=\left[\begin{array}{cccc}{Y}_{11}& Y_{12}& \·\·\·& Y_{1n}\\ Y_{21}& Y_{22}& \·\·\·& Y_{2n}\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ Y_{n1}& Y_{n2}& \·\·\·& Y_{\mathrm{nn}}\end{array}\right]$ Bus admittance matrix during the normal operation of expression; Diagonal element Y _IjSelf-admittance when normally moving for node i, its value equal to be connected to when normally moving all branch road admittance sums of node i; Off-diagonal element Y _IjFor the transadmittance during normal operation between node i, j, when having branch road between node i, j, Y _IjEqual directly to be connected in the negative value of the branch road admittance between node i, j; When not having branch road between node i, j, Y _Ij=0;

$\stackrel{\·}{U}=\left[\begin{array}{c}{\stackrel{\·}{U}}_1\\ {\stackrel{\·}{U}}_2\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{\mathrm{PCC}}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_n\end{array}\right]$ Node voltage during the normal operation of expression,

The voltage of PCC during for normal operation;

$\stackrel{\·}{I}=\left[\begin{array}{c}{\stackrel{\·}{I}}_1\\ {\stackrel{\·}{I}}_2\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_{\mathrm{DG}}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_n\end{array}\right]$ The Injection Current of node during the normal operation of expression,

DG injects the electric current of PCC node during for normal operation;

S12 tries to achieve according to nodal voltage equation

Then take absolute value and obtain U _PCC

Compared with prior art, the present invention has the following advantages and beneficial effect: the present invention is by taking into account inverse distributed power control strategy and output characteristics, set up new distributed power source transient state Equivalent Model, can reflect more truly the fault current characteristics of distributed power source; Set up on this basis new distribution network failure analytical model, improved the accuracy of fault analysis.This method has very strong practicality for the lectotype selection of distribution network comprising inverse distributed power and the protection aspect such as adjust provides the foundation of science in engineering practice.

Description of drawings

Fig. 1 is the power distribution network line chart of embodiments of the invention.

Fig. 2 is the process flow diagram of asymmetric fault analytical approach of the distribution network comprising inverse distributed power of embodiments of the invention.

Compound sequence network figure when Fig. 3 is distribution network failure shown in Figure 1 in the embodiments of the invention.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment

The present embodiment adopts the asymmetric fault analytical approach of distribution network comprising inverse distributed power of the present invention to carry out fault analysis take power distribution network shown in Figure 1 as example, as shown in Figure 2, may further comprise the steps:

The voltage magnitude U of PCC when S1 calculating power distribution network normally moves _PCC, specifically may further comprise the steps:

Nodal voltage equation when the power distribution network equal-value map is normally moved during the normal operation of S11 basis:

$\left[Y\right]\stackrel{\·}{U}=\stackrel{\·}{I}$

Nodal voltage equation when normally moving in the present embodiment is:

$\left[\begin{array}{cc}\frac{1}{Z_s}+\frac{1}{Z_{L1}}& -\frac{1}{L_1}\\ -\frac{1}{Z_{L1}}& \frac{1}{Z_{L1}}+\frac{1}{Z_{L2}}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_M\\ {\stackrel{\·}{U}}_{\mathrm{PCC}}\end{array}\right]=\left[\begin{array}{c}\frac{{\stackrel{\·}{E}}_s}{Z_s}\\ {\stackrel{\·}{I}}_{\mathrm{DG}}\end{array}\right]$

Wherein

The self-admittance of node M, PCC when being respectively normal operation,

Be the transadmittance between node M, the PCC; Z _s, Z _L1, Z _L2Represent respectively equivalent impedance, the L1 impedance of PCC lines upstream and the circuit L2 impedance of PCC downstream of system;

Expression system equivalent electromotive force,

Value is the distributed power source rated current;

The voltage of node M during for normal operation; The voltage of PCC during for normal operation;

The electric current of ordering for injecting M.

S12 tries to achieve according to nodal voltage equation

Then take absolute value and obtain U _PCC

Compound sequence network when S2 sets up distribution network failure (as shown in Figure 3), distributed power source only are included in the positive sequence network, the positive sequence voltage of the PCC when setting up electric network fault The solving equation group, concrete steps are as follows:

Nodal voltage equation when the compound sequence network of S21 during according to distribution network failure obtains fault:

$\left[Y^{\′}\right]{\stackrel{\·}{U}}_f={\stackrel{\·}{I}}_f---\left(1\right)$

Wherein, $\left[Y^{\′}\right]=\left[\begin{array}{cccc}{Y^{\′}}_{11}& {Y^{\′}}_{12}& \·\·\·& {Y^{\′}}_{1m}\\ {Y^{\′}}_{21}& {Y^{\′}}_{22}& \·\·\·& {Y^{\′}}_{2m}\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ {Y^{\′}}_{m1}& {Y^{\′}}_{m2}& \·\·\·& {Y^{\′}}_{\mathrm{mm}}\end{array}\right]$ The admittance matrix of node during the expression fault; Diagonal element Y _IiSelf-admittance during for the node i fault, its value are connected to all branch road admittance sums of node i when equaling fault; Off-diagonal element Y ' _IjFor the transadmittance during fault between node i, j, when having branch road between node i, j, Y ' _IjEqual directly to be connected in the negative value of the branch road admittance between node i, j, when not having branch road between node i, j, Y ' _Ij=0;

Namely $\left[\begin{array}{ccc}\frac{1}{Z_s}+\frac{1}{Z_{L1}}& -\frac{1}{Z_{L1}}& 0\\ -\frac{1}{Z_{L1}}& \frac{1}{Z_{L1}}+\frac{1}{2\mathrm{\β}{Z}_{L2}}& -\frac{1}{2\mathrm{\β}{Z}_{L2}}\\ 0& -\frac{1}{2\mathrm{\β}{Z}_{L2}}& \frac{1}{2\mathrm{\β}{Z}_{L2}}+\frac{1}{Z_s}+\frac{1}{Z_{L1}}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{M\·f}\\ {\stackrel{\·}{U}}_{\mathrm{PCC}\·f}^{+}\\ {\stackrel{\·}{U}}_{\mathrm{PCC}\·f}^{-}\end{array}\right]=\left[\begin{array}{c}\frac{{\stackrel{\·}{E}}_s}{Z_s}\\ {\stackrel{\·}{I}}_{\mathrm{DG}\·f}\\ 0\end{array}\right]$

Wherein The self-admittance of node M, PCC positive sequence voltage node, PCC negative sequence voltage node when being respectively fault;

Transadmittance during for fault between node M, the PCC positive sequence voltage node; ,

Transadmittance between expression PCC positive sequence voltage node and the PCC negative sequence voltage node, β is the abort situation that is illustrated among the circuit L2, value is 0 ~ 100%;

The positive and negative sequence voltage of PCC when being respectively fault;

DG injects the electric current of PCC during for fault; According to the distributed power source control strategy,

Be expressed as:

${\stackrel{\·}{I}}_{\mathrm{DG}\·f}=I_{d\·f}-{\mathrm{jI}}_{q\·f}---\left(2\right)$

Wherein, $\left\{\begin{array}{c}{I}_{d\·f}=P_{\left(0\right)}/U_{\mathrm{PCC}\·f}^{+}\\ I_{q\·f}=I_{q\left(0\right)}+k_q(U_{\mathrm{PCC}}-U_{\mathrm{PCC}\·f}^{+})\end{array}\right.$

In the formula, I _Df, I _QfFault current, active current and the reactive current of distributed power source output when representing fault respectively; P ₍₀₎, I _{Q (0)}The active power and the reactive current that represent respectively normal motion time cloth formula power supply output,

Q ₍₀₎The reactive power that represents normal motion time cloth formula power supply output, k _qThe expression coefficient;

S22 carries out linear transformation to formula (1), obtains

The solving equation group, be specially:

With

Voltage-phase is benchmark, then

${\stackrel{\·}{E}}_s=E_s(\cos \mathrm{\α}+j\sin \mathrm{\α}),$ Obtain The solving equation group:

$\left\{\begin{array}{c}a{\left(U_{\mathrm{PCC}\·f}^{+}\right)}^2+e{U}_{\mathrm{PCC}\·f}^{+}-c=E_s{U}_{\mathrm{PCC}\·f}^{+}\cos \mathrm{\α}\\ b{\left(U_{\mathrm{PCC}\·f}^{+}\right)}^2+f{U}_{\mathrm{PCC}\·f}^{+}-d=E_s{U}_{\mathrm{PCC}\·f}^{+}\sin \mathrm{\α}\end{array}\right.$

In the formula, a+jb=[1/ (2 β Z _L2+ Z _s+ Z _L1)+1/ (Z _s+ _L1)-jk _q/ U _n] (Z _s+ Z _L1), c+jd=U _PCCI _{D (0)}(Z _s+ Z _L1), e+jf=j (I _{Q (0)}+ k _qU _PCC/ U _n) (Z _s+ Z _L1);

S3 finds the solution

S4 finds the solution I _Df, I _Qf

S5 defines I _Ad=I _Df+ I _Qf, and judge I _AdWhether surpass inverter rated current I _VACnIf, do not surpass and then carry out step S6, otherwise, I made _Df=I _VSCn-I _Qf, with I _Df, I _QfExpression formula substitution formula (1) and formula (2), and recomputate After carry out step S6;

Wherein, recomputate

Process as follows:

With I _Df, I _QfExpression formula substitution formula (1) and formula (2) obtain

The solving equation group:

$\left\{\begin{array}{c}{U}_{\mathrm{PCC}\·f}^{+}(a-K_q/U_n)c{E}_s\cos \mathrm{\α}+d{E}_s\sin \mathrm{\α}=I_{\max }-(I_{q\left(0\right)}+K_q{U}_{\mathrm{PCC}\·f}^{+}/U_n)\\ U_{\mathrm{PCC}\·f}^{+}(b-K_q/U_n)-d{E}_s\cos \mathrm{\α}-c{E}_s\sin \mathrm{\α}=-(I_{q\left(0\right)}{K}_q{U}_{\mathrm{PCC}}/U_n)\end{array}\right.$

In the formula, a+jb=1/ (2 β Z _L2+ Z _s+ Z _L1)+1/ (Z _s+ Z _L1), c+jd=1/ (Z _s+ Z _L1); S6 utilizes formula (1) to calculate

In remove Outer node voltage;

S7 is according to the branch current between following formula computing node j and the k:

${\stackrel{\·}{I}}_{\mathrm{jk}\·f}=\frac{{\stackrel{\·}{U}}_{i\·f}-{\stackrel{\·}{U}}_{k\·f}}{Z_{\mathrm{jk}}}$

Wherein,

Z _JkRepresent respectively branch current and branch impedance between node j and the k,

The voltage of node j, k when representing distribution network failure respectively.

Among Fig. 1 of the present embodiment, the equivalent impedance Z of distribution network system _sBe 1.3j (Ω) the equivalent impedance Z of circuit L1 _L1, L2 equivalent impedance Z _L2Be respectively 1.18+3.56j (Ω), 0.59+1.78j (Ω), distributed power source rated capacity and inverter interface rated capacity are respectively 4MW, 8MVA, k _qBe 2.Can obtain I by above-mentioned condition _VSCn=0.46kA.The meritorious ratings that is output as of distributed power source before the fault idlely is output as zero.

The below enumerates two kinds of different short circuit condition and is explained:

Situation 1:

Two-phase short-circuit fault occurs in the L2 line end, and namely β=100% carries out step S1 ~ S4, calculates

Value be 7.26kV, U _PCCBe 10.1kV.By U _PCC, Can get I _Df, I _Qf, I _DGfBe respectively 0.32kA, 0.13kA, 0.35kA.Because I _Df+ I _Qf＜I _VSCn, with I _Df, I _QfNodal voltage equation can be tried to achieve during the substitution distribution network failure

Be 4.10kV,

Be respectively 0.365kA, 0.48kA,

All be 0.48kA.

Situation 2:

Two-phase short-circuit fault occurs in L2 circuit 70% place, and namely β=70% carries out step S1 ~ S4, and obtains

The solving equation group is calculated

Value be 6.92kV, U _PCCBe 10.1kV.By U _PCC,

Can get I _Df, I _QfBe respectively 0.33kA, 0.14kA.Because I _Df+ I _QfI _VSCn, recomputate I _Df, I _DGfBe 0.32kA, 0.35kA.Try to achieve at last

Be 4.10kV,

Be respectively 0.39kA, 0.52kA,

All be 0.52Ka.

Above-described embodiment is the better embodiment of the present invention; but embodiments of the present invention are not limited by the examples; other any do not deviate from change, the modification done under Spirit Essence of the present invention and the principle, substitutes, combination, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (2)

1. the asymmetric fault analytical approach of distribution network comprising inverse distributed power is characterized in that, may further comprise the steps:

The voltage magnitude U of common connecting point PCC when S1 calculating power distribution network normally moves _PCC

Compound sequence network when S2 sets up distribution network failure, distributed power source only are included in the positive sequence network, the positive sequence voltage amplitude of the common connecting point PCC when setting up distribution network failure

The solving equation group, specifically may further comprise the steps:

Nodal voltage equation when the compound sequence network of S21 during according to distribution network failure obtains fault:

$\left[Y^{\′}\right]{\stackrel{\·}{U}}_f={\stackrel{\·}{I}}_f---\left(1\right)$

Wherein, $\left[Y^{\′}\right]=\left[\begin{array}{cccc}{Y^{\′}}_{11}& {Y^{\′}}_{12}& \·\·\·& {Y^{\′}}_{1m}\\ {Y^{\′}}_{21}& {Y^{\′}}_{22}& \·\·\·& {Y^{\′}}_{2m}\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ {Y^{\′}}_{m1}& {Y^{\′}}_{m2}& \·\·\·& {Y^{\′}}_{\mathrm{mm}}\end{array}\right]$ Bus admittance matrix during the expression fault; Diagonal element Y _IiSelf-admittance during for the node i fault, its value are connected to all branch road admittance sums of node i when equaling fault; Off-diagonal element Y ' _IjFor the transadmittance during fault between node i, j, when having branch road between node i, j, Y ' _IjEqual directly to be connected in the negative value of the branch road admittance between node i, j, when not having branch road between node i, j, Y ' _Ij=0;

${\stackrel{\·}{U}}_f=\left[\begin{array}{c}{\stackrel{\·}{U}}_{1\·f}\\ {\stackrel{\·}{U}}_{2\·f}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{\mathrm{PCC}\·f}^{+}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{\mathrm{PCC}\·f}^{-}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{m\·f}\end{array}\right]$ Node voltage during the expression fault, wherein

The positive and negative sequence voltage of common connecting point PCC when being respectively fault;

${\stackrel{\·}{I}}_f=\left[\begin{array}{c}{\stackrel{\·}{I}}_{1\·f}\\ {\stackrel{\·}{I}}_{2\·f}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_{\mathrm{DG}\·f}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_{m\·f}\end{array}\right]$ The Injection Current of node during the expression fault, wherein

Distributed power source injects the electric current of common connecting point PCC during for fault;

Be expressed as: ${\stackrel{\·}{I}}_{\mathrm{DG}\·f}=I_{d\·f}-{\mathrm{jI}}_{q\·f}---\left(2\right)$

Wherein, $\left\{\begin{array}{c}{I}_{d\·f}=P_{\left(0\right)}/U_{\mathrm{PCC}\·f}^{+}\\ I_{q\·f}=I_{q\left(0\right)}+k_q(U_{\mathrm{PCC}}-U_{\mathrm{PCC}\·f}^{+})\end{array}\right.$

In the formula, I _Df, I _QfActive current and the reactive current of distributed power source output when representing fault respectively; P ₍₀₎, I _{Q (0)}The active power and the reactive current that represent respectively normal motion time cloth formula power supply output,

Q ₍₀₎The reactive power that represents normal motion time cloth formula power supply output, k _qThe expression coefficient;

S22 carries out linear transformation to formula (1), obtains

The solving equation group;

S3 finds the solution

S4 finds the solution I _Df, I _Qf

S5 defines I _Ad=T _Df+ I _Qf, and judge I _AdWhether surpass inverter rated current I _VSCnIf, do not surpass and then carry out step S6, otherwise, I made _Df=I _VSCn-I _Qf, with I _Df, I _QfExpression formula substitution formula (1) and formula (2), and recomputate

After carry out step S6;

S6 utilizes formula (1) to calculate In remove

Outer node voltage;

S7 is according to the branch current between following formula computing node j and the node k:

${\stackrel{\·}{I}}_{\mathrm{jk}\·f}=\frac{{\stackrel{\·}{U}}_{i\·f}-{\stackrel{\·}{U}}_{k\·f}}{Z_{\mathrm{jk}}}$

Wherein,

Z _JkRepresent respectively branch current and branch impedance between node j and the k,

The voltage of node j, k when representing distribution network failure respectively.

2. according to the asymmetric fault analytical approach of distribution network comprising inverse distributed power, it is characterized in that the voltage magnitude U of the common connecting point PCC when the described calculating power distribution network of step S1 normally moves _PCC, specifically may further comprise the steps:

Nodal voltage equation when the power distribution network equal-value map is normally moved during the normal operation of S11 basis:

$\left[Y\right]\stackrel{\·}{U}=\stackrel{\·}{I}$

Wherein, $\left[Y\right]=\left[\begin{array}{cccc}{Y}_{11}& Y_{12}& \·\·\·& Y_{1n}\\ Y_{21}& Y_{22}& \·\·\·& Y_{2n}\\ \·& \·& & \·\\ \·& \·& & \·\\ \·& \·& & \·\\ Y_{n1}& Y_{n2}& \·\·\·& Y_{\mathrm{nn}}\end{array}\right],$ Bus admittance matrix during the normal operation of expression; Diagonal element Y _IiSelf-admittance when normally moving for node i, its value equal to be connected to when normally moving all branch road admittance sums of node i; Off-diagonal element Y _IjFor the transadmittance during normal operation between node i, j, when having branch road between node i, j, Y _IjEqual directly to be connected in the negative value of the branch road admittance between node i, j; When not having branch road between node i, j, Y _Ij=0;

$\stackrel{\·}{U}=\left[\begin{array}{c}{\stackrel{\·}{U}}_1\\ {\stackrel{\·}{U}}_2\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_{\mathrm{PCC}}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{U}}_n\end{array}\right]$ Node voltage during the normal operation of expression,

The voltage of common connecting point PCC during for normal operation;

$\stackrel{\·}{I}=\left[\begin{array}{c}{\stackrel{\·}{I}}_1\\ {\stackrel{\·}{I}}_2\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_{\mathrm{DG}}\\ \·\\ \·\\ \·\\ {\stackrel{\·}{I}}_n\end{array}\right]$ The Injection Current of node during the normal operation of expression,

Inject the electric current of common connecting point PCC node for normal motion time cloth formula power supply;

S12 tries to achieve according to nodal voltage equation

Then take absolute value and obtain U _PCC

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