CN104218577A - Method for calculating three-phase load flow of active power distribution network based on node voltage - Google Patents

Abstract

The invention provides a method for calculating the three-phase load flow of an active power distribution network based on a node voltage. The method comprises the steps of taking the real part and the imaginary part of the phase voltage of a node as state variables, selecting the real part and the imaginary part of each phase of injection current of the node as known variables, establishing a relation between the known variables and unknown variables by use of a node voltage equation, and directly calculating a factor table through a formula. The method for calculating the three-phase load flow of the active power distribution network based on the node voltage is capable of processing multiple PV nodes and links and is not limited by the number of the links; the factor table of a jacobian matrix is directly calculated through the formula, and factorization is avoided during calculation so that the calculation amount can be greatly reduced; the jacobian matrix is highly sparse and thus convenient for storage and calculation; in each iteration, the three phases are completely decoupled; the calculation result is capable of guaranteeing that zero injection constraint is strictly satisfied.

Description

A kind of three-phase load flow of active distribution network computational methods based on node voltage

Technical field

The invention belongs to Distribution Automation Technology field, be specifically related to a kind of three-phase load flow of active distribution network computational methods based on node voltage.

Background technology

Distribution power system load flow calculation is calculation of distribution network and the basic tool in analysis, and it according to network topology, root node voltage, each node voltage amplitude of feeder load computing network and phase angle, and provides the whole network via net loss.Conventional Power Flow Calculation Methods For Distribution Network is forward-backward sweep method, Newton method etc.Because power distribution network closed loop design, open loop operation make the Load flow calculation of power distribution network have radial feature, forward-backward sweep method has distinct, the simple and easy feature such as realization, better astringency of physical concept, is suitable for solving radial distribution networks trend.Newton method is better than forward-backward sweep method convergence, but all needs again to form Jacobian matrix due to each iteration, and amount of calculation is large, have impact on computational speed.The feature of the many loops of active distribution network, multi-voltage grade, many PV node, brings difficulty to the three-phase power flow of power distribution network.Forward-backward sweep method process is comparatively difficult when processing loop and PV node, will greatly affect computational speed and precision.Although Newton method can process many loops, many PV node, amount of calculation is larger.Therefore, the rapidly and efficiently Three-phase Power Flow Calculation Method for Distribution System towards features such as multi-voltage grade, many PV node, many loops is very necessary with control for the real time execution of active distribution network.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of three-phase load flow of active distribution network computational methods based on node voltage, can directly process many PV node and loop, and not by the restriction of loop number.

In order to realize foregoing invention object, the present invention takes following technical scheme:

The invention provides a kind of three-phase load flow of active distribution network computational methods based on node voltage, said method comprising the steps of:

Step 1: the three-phase voltage of each node in initialization system;

Step 2: according to the three-phase voltage of node each in system, determines that non-zero injects real part and the imaginary part of each phase Injection Current of node;

Step 3: determine that non-zero injects each calculated value injecting active power, reactive power and voltage magnitude mutually of node;

Step 4: determine that non-zero injects each amount of unbalance injecting active power, reactive power and voltage magnitude mutually of node;

Step 5: determine that non-zero injects the correction of a, b, c phase voltage of node;

Step 6: magnitude of voltage non-zero being injected to node a, b, c phase is revised, obtains the magnitude of voltage that revised non-zero injects node a, b, c phase;

Step 7: the magnitude of voltage determining zero injection node a, b, c phase;

Step 8: judge Δ W ^a, Δ W ^b, Δ W ^cin the absolute value of each element whether be all less than the threshold value of setting, then return step 2 if not, if then terminate;

Wherein, Δ W ^a, Δ W ^b, Δ W ^cbe respectively the amount of unbalance that non-zero injects node a, b, c phase.

In described step 2, set up system node voltage equation, have:

Y ^abcU ^abc＝I ^abc (1)

Wherein, Y ^abcfor the three-phase node admittance matrix under system rectangular coordinate, U ^abcfor the node three-phase complex voltage column vector under rectangular coordinate, I ^abcfor the node three-phase telegram in reply stream column vector under rectangular coordinate;

Obtain non-zero according to following formula and inject the three-phase telegram in reply stream column vector I of node under rectangular coordinate _n:

Y _NZU _Z+Y _NNU _N＝I _N (2)

Wherein, Y _nZfor Y ^abcin correspond to non-zero and inject node and zero and inject the part of transadmittance between node, Y _nNfor Y ^abcin correspond to non-zero and inject the part of node, U _zbe the three-phase complex voltage column vector of zero injection node, U _nfor non-zero injects the three-phase complex voltage column vector of node.

Formula (2) is obtained by following formula:

$\left[\begin{array}{cc}{Y}_{\mathrm{ZZ}}& Y_{\mathrm{ZN}}\\ Y_{\mathrm{NZ}}& Y_{\mathrm{NN}}\end{array}\right]\left[\begin{array}{c}{U}_Z\\ U_N\end{array}\right]=\left[\begin{array}{c}0\\ I_N\end{array}\right]---\left(3\right)$

Also can be obtained by formula (3):

Y _ZZU _Z+Y _ZNU _N＝0 (4)

Wherein, Y _zZfor Y ^abcin correspond to zero and inject the part of node, Y _zNfor Y ^abcin correspond to zero and inject the part that node and non-zero inject transadmittance between node.

In described step 3, each calculated value injecting active power, reactive power and voltage magnitude mutually that non-zero injects node is used respectively with represent, and have:

$P_i^k=U_{i,r}^k{I}_{i,r}^k-U_{i,x}^k{I}_{i,x}^k---\left(5\right)$

$Q_i^k=U_{i,r}^k{I}_{i,x}^k+U_{i,x}^k{I}_{i,r}^k---\left(6\right)$

$U_i^k=\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}---\left(7\right)$

Wherein, the real part of the k phase voltage of node i is injected for non-zero, the real part of the k phase voltage of node i is injected for non-zero, the real part of the k phase Injection Current of node i is injected for non-zero, the imaginary part of the k phase Injection Current of node i is injected for non-zero, and k=a, b, c, i=1,2 ..., n-1, wherein n is that in system, non-zero injects node total number.

In described step 4, each amount of unbalance injecting active power, reactive power and voltage magnitude mutually that non-zero injects node is used respectively with represent, specifically have:

$\mathrm{\Δ}{P}_i^k=P_i^k-P_{i,s}^k---\left(8\right)$

$\mathrm{\Δ}{Q}_i^k=Q_i^k-Q_{i,s}^k---\left(9\right)$

$\mathrm{\Δ}{U}_i^k=U_i^k-U_{i,s}^k---\left(10\right)$

Wherein, with the k phase being respectively non-zero injection node i injects the set-point of active power, k phase for non-zero injection node i injects the set-point of reactive power, for non-zero injects the k phase voltage amplitude set-point of node i.

In described step 5, the update equation that non-zero injects node k phase amount of unbalance is defined as:

ΔW ^k＝-H ^kΔV ^k (11)

Wherein, $\mathrm{\Δ}{W}^k={\left[\begin{array}{ccccccc}\mathrm{\Δ}{P}_1^k& \mathrm{\Δ}{Q}_1^k& \mathrm{\Δ}{P}_2^k& \mathrm{\Δ}{U}_2^k& ...& \mathrm{\Δ}{P}_{n-1}^k& \mathrm{\Δ}{Q}_{n-1}^k\end{array}\right]}^T,$ Δ W ^kfor non-zero injects the k phase amount of unbalance of node; Δ V ^kthe correction of the k phase voltage of node is injected for non-zero; H _kfor non-zero injects the k phase Jacobian matrix of node;

Can obtain according to formula (5) and (6):

$\left\{\begin{array}{c}\frac{\∂P_i^k}{\∂U_{i,r}^k}=I_{i,r}^k\\ \frac{\∂P_i^k}{\∂U_{i,x}^k}=-I_{i,x}^k\end{array}\right.---\left(12\right)$

$\left\{\begin{array}{c}\frac{\∂Q_i^k}{\∂U_{i,r}^k}=I_{i,x}^k\\ \frac{\∂Q_i^k}{\∂U_{i,x}^k}=-I_{i,r}^k\end{array}\right.---\left(13\right)$

Can obtain according to formula (7):

$\left\{\begin{array}{c}\frac{\∂U_i^k}{\∂U_{i,r}^k}=\frac{U_{i,r}^k}{\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}}\\ \frac{\∂U_i^k}{\∂U_{i,x}^x}=\frac{U_{i,x}^k}{\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}}\end{array}\right.---\left(14\right)$

Can obtain according to formula (12), (13) and (14):

$H^k=\left[\begin{array}{ccccccc}{I}_{1,r}^k& {-I}_{1,x}^k& 0& 0& ...& 0& 0\\ I_{1,x}^k& I_{1,r}^k& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& -I_{2,x}^k& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{\∂U_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& I_{n-1,r}^k& {-I}_{n-1,x}^k\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k\end{array}\right]---\left(15\right)$

To H _kcarry out LU decomposition, normalization and cancellation computing obtain matrix by row

$H_1^k=\left[\begin{array}{ccccccc}{I}_{1,r}^k& \frac{{-I}_{1,x}^k}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ I_{i,x}^k& I_{i,r}^k+\frac{{\left(I_{1,x}^k\right)}^2}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& \frac{-I_{2,x}^k}{I_{2,x}^k}& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{\∂U_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}+\frac{\∂U_{2,x}^k}{\∂U_{2,r}^k}\frac{I_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& I_{n-1,r}^k& \frac{-I_{n-1,x}^k}{I_{n-1,r}^k}\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k+\frac{{\left(I_{n-1,x}^k\right)}^2}{I_{n-1,r}^k}\end{array}\right.2---\left(16\right)$

From in obtain inferior triangular flap L _kwith unit upper triangular matrix U _k, wherein L _kby element composition below middle diagonal and diagonal, U _kdiagonal element be 1 entirely, on it triangle element by element composition more than middle diagonal, is expressed as:

$L^k\left[\begin{array}{ccccccc}{I}_{1,r}^k& 0& 0& 0& ...& 0& 0\\ I_{i,x}^k& I_{i,r}^k+\frac{{\left(I_{1,x}^k\right)}^2}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& 0& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{{\∂U}_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}+\frac{\∂U_2^k}{\∂U_{2,r}^k}\frac{I_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ 0& 0& 0& 0& ...& ...& ...\\ ...& ...& 0& 0& ...& I_{n-1,r}^k& 0\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k+\frac{{\left(I_{n-1,x}^k\right)}^2}{I_{n-1,r}^k}\end{array}\right]---\left(17\right)$

$U^k=\left[\begin{array}{ccccccc}1& \frac{-I_{1,x}^k}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 1& 0& 0& ...& 0& 0\\ 0& 0& 1& \frac{{-I}_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ 0& 0& 0& 1& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& 1& \frac{{-I}_{n-1,x}^k}{I_{n-1,r}^k}\\ 0& 0& 0& 0& ...& 0& 1\end{array}\right]---\left(18\right)$

Decompose according to LU, H _kbe expressed as:

H ^k＝L ^kU ^k (19)

So formula (11) is expressed as:

L ^kU ^kΔV ^k＝-ΔW ^k (20)

Through type (20), utilizes the method for solving of the former generation back substitution of system of linear equations, obtains

$\mathrm{\Δ}{V}^k={\left[\begin{array}{ccccccc}\mathrm{\Δ}{U}_{1,r}^k& \mathrm{\Δ}{U}_{1,x}^k& \mathrm{\Δ}{U}_{2,r}^k& \mathrm{\Δ}{U}_{2,x}^k& ...& \mathrm{\Δ}{U}_{n-1,r}^k& \mathrm{\Δ}{U}_{n-1,x}^k\end{array}\right]}^T,k=a,b,c.$

In described step 6, revised by the magnitude of voltage of following formula to non-zero power node k phase, obtain the magnitude of voltage V of revised non-zero power node k phase ^k:

$V^k=V_{\mathrm{old}}^k+\mathrm{\Δ}{V}^k---\left(21\right)$

Wherein, the magnitude of voltage of node k phase is injected, k=a, b, c for revising front non-zero.

In described step 7, if U _n=U _n,R+ jU _n,X, U _z=U _z,R+ jU _z,X, Y _zZ=G _zZ+ jB _zZ, Y _zN=G _zN+ jB _zN; Wherein U _z,Rand U _z,Xfor U _zreal part and imaginary part; (4) are converted to the real number equation under following rectangular coordinate:

$\left[\begin{array}{cc}{B}_{\mathrm{ZZ}}& G_{\mathrm{ZZ}}\\ G_{\mathrm{ZZ}}& -B_{\mathrm{ZZ}}\end{array}\right]\left[\begin{array}{c}{U}_{Z,R}\\ U_{Z,X}\end{array}\right]+\left[\begin{array}{cc}{B}_{\mathrm{ZN}}& G_{\mathrm{ZN}}\\ G_{\mathrm{ZN}}& {-B}_{\mathrm{ZN}}\end{array}\right]\left[\begin{array}{c}{U}_{N,R}\\ U_{N,X}\end{array}\right]=0---\left(22\right)$

Then zero injects node voltage value V _zbe expressed as:

$V_Z=\left[\begin{array}{c}{U}_{Z,R}\\ U_{Z,X}\end{array}\right]=-{\left[\begin{array}{cc}{B}_{\mathrm{ZZ}}& G_{\mathrm{ZZ}}\\ G_{\mathrm{ZZ}}& -B_{\mathrm{ZZ}}\end{array}\right]}^{-1}\left[\begin{array}{cc}{B}_{\mathrm{ZN}}& G_{\mathrm{ZN}}\\ G_{\mathrm{ZN}}& {-B}_{\mathrm{ZN}}\end{array}\right]\left[\begin{array}{c}{U}_{N,R}\\ U_{N,X}\end{array}\right]---\left(23\right)$

Compared with prior art, beneficial effect of the present invention is:

The present invention for quantity of state, and selects the real part of the every phase Injection Current of node and imaginary part to be known quantity with the real part of node phase voltage and imaginary part, is set up the relation of known quantity and unknown quantity, by the direct calculated factor table of formula by nodal voltage equation.Its advantage is:

1), many PV node can directly be processed;

2), directly loop can be processed, not by the restriction of loop number;

3), directly calculated the factor table of Jacobian matrix by formula, avoid Factorization, reduce amount of calculation, improve computational speed;

4), Jacobian matrix height is sparse, gives to store to bring conveniently with calculating;

5), in the iteration often walked, three-phase is full decoupled;

6), result of calculation can ensure that zero injection-constraint can strictly meet.

Accompanying drawing explanation

Fig. 1 is the three-phase load flow of active distribution network computational methods flow chart based on node voltage.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

As Fig. 1, sky of the present invention provides a kind of three-phase load flow of active distribution network computational methods based on node voltage, said method comprising the steps of:

Step 1: the three-phase voltage of each node in initialization system;

Step 2: according to the three-phase voltage of node each in system, determines that non-zero injects real part and the imaginary part of each phase Injection Current of node;

Step 3: determine that non-zero injects each calculated value injecting active power, reactive power and voltage magnitude mutually of node;

Step 4: determine that non-zero injects each amount of unbalance injecting active power, reactive power and voltage magnitude mutually of node;

Step 5: determine that non-zero injects the correction of a, b, c phase voltage of node;

Step 6: magnitude of voltage non-zero being injected to node a, b, c phase is revised, obtains the magnitude of voltage that revised non-zero injects node a, b, c phase;

Step 7: the magnitude of voltage determining zero injection node a, b, c phase;

Step 8: judge Δ W ^a, Δ W ^b, Δ W ^cin the absolute value of each element whether be all less than the threshold value of setting, then return step 2 if not, if then terminate;

Wherein, Δ W ^a, Δ W ^b, Δ W ^cbe respectively the amount of unbalance that non-zero injects node a, b, c phase.

In described step 2, set up system node voltage equation, have:

Y ^abcU ^abc＝I ^abc (1)

Wherein, Y ^abcfor the three-phase node admittance matrix under system rectangular coordinate, U ^abcfor the node three-phase complex voltage column vector under rectangular coordinate, I ^abcfor the node three-phase telegram in reply stream column vector under rectangular coordinate;

Obtain non-zero according to following formula and inject the three-phase telegram in reply stream column vector I of node under rectangular coordinate _n:

Y _NZU _Z+Y _NNU _N＝I _N (2)

Wherein, Y _nZfor Y ^abcin correspond to non-zero and inject node and zero and inject the part of transadmittance between node, Y _nNfor Y ^abcin correspond to non-zero and inject the part of node, U _zbe the three-phase complex voltage column vector of zero injection node, U _nfor non-zero injects the three-phase complex voltage column vector of node.

Formula (2) is obtained by following formula:

$\left[\begin{array}{cc}{Y}_{\mathrm{ZZ}}& Y_{\mathrm{ZN}}\\ Y_{\mathrm{NZ}}& Y_{\mathrm{NN}}\end{array}\right]\left[\begin{array}{c}{U}_Z\\ U_N\end{array}\right]=\left[\begin{array}{c}0\\ I_N\end{array}\right]---\left(3\right)$

Also can be obtained by formula (3):

Y _ZZU _Z+Y _ZNU _N＝0 (4)

Wherein, Y _zZfor Y ^abcin correspond to zero and inject the part of node, Y _zNfor Y ^abcin correspond to zero and inject the part that node and non-zero inject transadmittance between node.

In described step 3, each calculated value injecting active power, reactive power and voltage magnitude mutually that non-zero injects node is used respectively with represent, and have:

$P_i^k=U_{i,r}^k{I}_{i,r}^k-U_{i,x}^k{I}_{i,x}^k---\left(5\right)$

$Q_i^k=U_{i,r}^k{I}_{i,x}^k+U_{i,x}^k{I}_{i,r}^k---\left(6\right)$

$U_i^k=\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}---\left(7\right)$

Wherein, the real part of the k phase voltage of node i is injected for non-zero, the real part of the k phase voltage of node i is injected for non-zero, the real part of the k phase Injection Current of node i is injected for non-zero, the imaginary part of the k phase Injection Current of node i is injected for non-zero, and k=a, b, c, i=1,2 ..., n-1, wherein n is that in system, non-zero injects node total number.

In described step 4, each amount of unbalance injecting active power, reactive power and voltage magnitude mutually that non-zero injects node is used respectively with represent, specifically have:

$\mathrm{\Δ}{P}_i^k=P_i^k-P_{i,s}^k---\left(8\right)$

$\mathrm{\Δ}{Q}_i^k=Q_i^k-Q_{i,s}^k---\left(9\right)$

$\mathrm{\Δ}{U}_i^k=U_i^k-U_{i,s}^k---\left(10\right)$

Wherein, with the k phase being respectively non-zero injection node i injects the set-point of active power, k phase for non-zero injection node i injects the set-point of reactive power, for non-zero injects the k phase voltage amplitude set-point of node i.

In described step 5, the update equation that non-zero injects node k phase amount of unbalance is defined as:

ΔW ^k＝-H ^kΔV ^k (11)

Wherein, $\mathrm{\Δ}{W}^k={\left[\begin{array}{ccccccc}\mathrm{\Δ}{P}_1^k& \mathrm{\Δ}{Q}_1^k& \mathrm{\Δ}{P}_2^k& \mathrm{\Δ}{U}_2^k& ...& \mathrm{\Δ}{P}_{n-1}^k& \mathrm{\Δ}{Q}_{n-1}^k\end{array}\right]}^T,$ Δ W ^kfor non-zero injects the k phase amount of unbalance of node; Δ V ^kthe correction of the k phase voltage of node is injected for non-zero; H _kfor non-zero injects the k phase Jacobian matrix of node;

Can obtain according to formula (5) and (6):

$\left\{\begin{array}{c}\frac{\∂P_i^k}{\∂U_{i,r}^k}=I_{i,r}^k\\ \frac{\∂P_i^k}{\∂U_{i,x}^k}=-I_{i,x}^k\end{array}\right.---\left(12\right)$

$\left\{\begin{array}{c}\frac{\∂Q_i^k}{\∂U_{i,r}^k}=I_{i,x}^k\\ \frac{\∂Q_i^k}{\∂U_{i,x}^k}=-I_{i,r}^k\end{array}\right.---\left(13\right)$

Can obtain according to formula (7):

$\left\{\begin{array}{c}\frac{\∂U_i^k}{\∂U_{i,r}^k}=\frac{U_{i,r}^k}{\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}}\\ \frac{\∂U_i^k}{\∂U_{i,x}^x}=\frac{U_{i,x}^k}{\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}}\end{array}\right.---\left(14\right)$

Can obtain according to formula (12), (13) and (14):

$H^k=\left[\begin{array}{ccccccc}{I}_{1,r}^k& {-I}_{1,x}^k& 0& 0& ...& 0& 0\\ I_{1,x}^k& I_{1,r}^k& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& -I_{2,x}^k& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{\∂U_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& I_{n-1,r}^k& {-I}_{n-1,x}^k\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k\end{array}\right]---\left(15\right)$

To H _kcarry out LU decomposition, normalization and cancellation computing obtain matrix by row

$H_1^k=\left[\begin{array}{ccccccc}{I}_{1,r}^k& \frac{{-I}_{1,x}^k}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ I_{i,x}^k& I_{i,r}^k+\frac{{\left(I_{1,x}^k\right)}^2}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& \frac{-I_{2,x}^k}{I_{2,x}^k}& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{\∂U_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}+\frac{\∂U_{2,x}^k}{\∂U_{2,r}^k}\frac{I_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& I_{n-1,r}^k& \frac{-I_{n-1,x}^k}{I_{n-1,r}^k}\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k+\frac{{\left(I_{n-1,x}^k\right)}^2}{I_{n-1,r}^k}\end{array}\right.2---\left(16\right)$

From in obtain inferior triangular flap L _kwith unit upper triangular matrix U _k, wherein L _kby element composition below middle diagonal and diagonal, U _kdiagonal element be 1 entirely, on it triangle element by element composition more than middle diagonal, is expressed as:

$L^k\left[\begin{array}{ccccccc}{I}_{1,r}^k& 0& 0& 0& ...& 0& 0\\ I_{i,x}^k& I_{i,r}^k+\frac{{\left(I_{1,x}^k\right)}^2}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& 0& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{{\∂U}_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}+\frac{\∂U_2^k}{\∂U_{2,r}^k}\frac{I_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ 0& 0& 0& 0& ...& ...& ...\\ ...& ...& 0& 0& ...& I_{n-1,r}^k& 0\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k+\frac{{\left(I_{n-1,x}^k\right)}^2}{I_{n-1,r}^k}\end{array}\right]---\left(17\right)$

$U^k=\left[\begin{array}{ccccccc}1& \frac{-I_{1,x}^k}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 1& 0& 0& ...& 0& 0\\ 0& 0& 1& \frac{{-I}_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ 0& 0& 0& 1& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& 1& \frac{{-I}_{n-1,x}^k}{I_{n-1,r}^k}\\ 0& 0& 0& 0& ...& 0& 1\end{array}\right]---\left(18\right)$

Decompose according to LU, H _kbe expressed as:

H ^k＝L ^kU ^k (19)

So formula (11) is expressed as:

L ^kU ^kΔV ^k＝-ΔW ^k (20)

Through type (20), utilizes the method for solving of the former generation back substitution of system of linear equations, obtains

$\mathrm{\Δ}{V}^k={\left[\begin{array}{ccccccc}\mathrm{\Δ}{U}_{1,r}^k& \mathrm{\Δ}{U}_{1,x}^k& \mathrm{\Δ}{U}_{2,r}^k& \mathrm{\Δ}{U}_{2,x}^k& ...& \mathrm{\Δ}{U}_{n-1,r}^k& \mathrm{\Δ}{U}_{n-1,x}^k\end{array}\right]}^T,k=a,b,c.$

In described step 6, revised by the magnitude of voltage of following formula to non-zero power node k phase, obtain the magnitude of voltage V of revised non-zero power node k phase ^k:

$V^k=V_{\mathrm{old}}^k+\mathrm{\Δ}{V}^k---\left(21\right)$

Wherein, the magnitude of voltage of node k phase is injected, k=a, b, c for revising front non-zero.

In described step 7, if U _n=U _n,R+ jU _n,X, U _z=U _z,R+ jU _z,X, Y _zZ=G _zZ+ jB _zZ, Y _zN=G _zN+ jB _zN; Wherein U _z,Rand U _z,Xfor U _zreal part and imaginary part; (4) are converted to the real number equation under following rectangular coordinate:

$\left[\begin{array}{cc}{B}_{\mathrm{ZZ}}& G_{\mathrm{ZZ}}\\ G_{\mathrm{ZZ}}& -B_{\mathrm{ZZ}}\end{array}\right]\left[\begin{array}{c}{U}_{Z,R}\\ U_{Z,X}\end{array}\right]+\left[\begin{array}{cc}{B}_{\mathrm{ZN}}& G_{\mathrm{ZN}}\\ G_{\mathrm{ZN}}& {-B}_{\mathrm{ZN}}\end{array}\right]\left[\begin{array}{c}{U}_{N,R}\\ U_{N,X}\end{array}\right]=0---\left(22\right)$

Then zero injects node voltage value V _zbe expressed as:

$V_Z=\left[\begin{array}{c}{U}_{Z,R}\\ U_{Z,X}\end{array}\right]=-{\left[\begin{array}{cc}{B}_{\mathrm{ZZ}}& G_{\mathrm{ZZ}}\\ G_{\mathrm{ZZ}}& -B_{\mathrm{ZZ}}\end{array}\right]}^{-1}\left[\begin{array}{cc}{B}_{\mathrm{ZN}}& G_{\mathrm{ZN}}\\ G_{\mathrm{ZN}}& {-B}_{\mathrm{ZN}}\end{array}\right]\left[\begin{array}{c}{U}_{N,R}\\ U_{N,X}\end{array}\right]---\left(23\right).$

Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit; those of ordinary skill in the field still can modify to the specific embodiment of the present invention with reference to above-described embodiment or equivalent replacement; these do not depart from any amendment of spirit and scope of the invention or equivalent replacement, are all applying within the claims of the present invention awaited the reply.

Claims (8)

1., based on three-phase load flow of active distribution network computational methods for node voltage, it is characterized in that: said method comprising the steps of:

Step 1: the three-phase voltage of each node in initialization system;

Step 2: according to the three-phase voltage of node each in system, determines that non-zero injects real part and the imaginary part of each phase Injection Current of node;

Step 3: determine that non-zero injects each calculated value injecting active power, reactive power and voltage magnitude mutually of node;

Step 4: determine that non-zero injects each amount of unbalance injecting active power, reactive power and voltage magnitude mutually of node;

Step 5: determine that non-zero injects the correction of a, b, c phase voltage of node;

Step 6: magnitude of voltage non-zero being injected to node a, b, c phase is revised, obtains the magnitude of voltage that revised non-zero injects node a, b, c phase;

Step 7: the magnitude of voltage determining zero injection node a, b, c phase;

Step 8: judge Δ W ^a, Δ W ^b, Δ W ^cin the absolute value of each element whether be all less than the threshold value of setting, then return step 2 if not, if then terminate;

Wherein, Δ W ^a, Δ W ^b, Δ W ^cbe respectively the amount of unbalance that non-zero injects node a, b, c phase.

2. the three-phase load flow of active distribution network computational methods based on node voltage according to claim 1, is characterized in that: in described step 2, set up system node voltage equation, have:

Y ^abcU ^abc＝I ^abc (1)

Wherein, Y ^abcfor the three-phase node admittance matrix under system rectangular coordinate, U ^abcfor the node three-phase complex voltage column vector under rectangular coordinate, I ^abcfor the node three-phase telegram in reply stream column vector under rectangular coordinate;

Obtain non-zero according to following formula and inject the three-phase telegram in reply stream column vector I of node under rectangular coordinate _n:

Y _NZU _Z+Y _NNU _N＝I _N (2)

Wherein, Y _nZfor Y ^abcin correspond to non-zero and inject node and zero and inject the part of transadmittance between node, Y _nNfor Y ^abcin correspond to non-zero and inject the part of node, U _zbe the three-phase complex voltage column vector of zero injection node, U _nfor non-zero injects the three-phase complex voltage column vector of node.

3. the three-phase load flow of active distribution network computational methods based on node voltage according to claim 2, is characterized in that: formula (2) is obtained by following formula:

$\left[\begin{array}{cc}{Y}_{\mathrm{ZZ}}& Y_{\mathrm{ZN}}\\ Y_{\mathrm{NZ}}& Y_{\mathrm{NN}}\end{array}\right]\left[\begin{array}{c}{U}_Z\\ U_N\end{array}\right]=\left[\begin{array}{c}0\\ I_N\end{array}\right]---\left(3\right)$

Also can be obtained by formula (3):

Y _ZZU _Z+Y _ZNU _N＝0 (4)

Wherein, Y _zZfor Y ^abcin correspond to zero and inject the part of node, Y _zNfor Y ^abcin correspond to zero and inject the part that node and non-zero inject transadmittance between node.

4. the three-phase load flow of active distribution network computational methods based on node voltage according to claim 1, is characterized in that: in described step 3, and each calculated value injecting active power, reactive power and voltage magnitude mutually that non-zero injects node is used respectively with represent, and have:

$P_i^k=U_{i,r}^k{I}_{i,r}^k-U_{i,x}^k{I}_{i,x}^k---\left(5\right)$

$Q_i^k=U_{i,r}^k{I}_{i,x}^k+U_{i,x}^k{I}_{i,r}^k---\left(6\right)$

$U_i^k=\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}---\left(7\right)$

Wherein, the real part of the k phase voltage of node i is injected for non-zero, the real part of the k phase voltage of node i is injected for non-zero, the real part of the k phase Injection Current of node i is injected for non-zero, the imaginary part of the k phase Injection Current of node i is injected for non-zero, and k=a, b, c, i=1,2 ..., n-1, wherein n is that in system, non-zero injects node total number.

5. the three-phase load flow of active distribution network computational methods based on node voltage according to claim 4, is characterized in that: in described step 4, and each amount of unbalance injecting active power, reactive power and voltage magnitude mutually that non-zero injects node is used respectively with represent, specifically have:

$\mathrm{\Δ}{P}_i^k=P_i^k-P_{i,s}^k---\left(8\right)$

$\mathrm{\Δ}{Q}_i^k=Q_i^k-Q_{i,s}^k---\left(9\right)$

$\mathrm{\Δ}{U}_i^k=U_i^k-U_{i,s}^k---\left(10\right)$

Wherein, with the k phase being respectively non-zero injection node i injects the set-point of active power, k phase for non-zero injection node i injects the set-point of reactive power, for non-zero injects the k phase voltage amplitude set-point of node i.

6. the three-phase load flow of active distribution network computational methods based on node voltage according to claim 5, is characterized in that: in described step 5, and the update equation that non-zero injects node k phase amount of unbalance is defined as:

ΔW ^k＝-H ^kΔV ^k (11)

Wherein, $\mathrm{\Δ}{W}^k={\left[\begin{array}{ccccccc}\mathrm{\Δ}{P}_1^k& \mathrm{\Δ}{Q}_1^k& \mathrm{\Δ}{P}_2^k& \mathrm{\Δ}{U}_2^k& ...& \mathrm{\Δ}{P}_{n-1}^k& \mathrm{\Δ}{Q}_{n-1}^k\end{array}\right]}^T,$ Δ W ^kfor non-zero injects the k phase amount of unbalance of node; Δ V ^kthe correction of the k phase voltage of node is injected for non-zero; H _kfor non-zero injects the k phase Jacobian matrix of node;

Can obtain according to formula (5) and (6):

$\left\{\begin{array}{c}\frac{\∂P_i^k}{\∂U_{i,r}^k}=I_{i,r}^k\\ \frac{\∂P_i^k}{\∂U_{i,x}^k}=-I_{i,x}^k\end{array}\right.---\left(12\right)$

$\left\{\begin{array}{c}\frac{\∂Q_i^k}{\∂U_{i,r}^k}=I_{i,x}^k\\ \frac{\∂Q_i^k}{\∂U_{i,x}^k}=-I_{i,r}^k\end{array}\right.---\left(13\right)$

Can obtain according to formula (7):

$\left\{\begin{array}{c}\frac{\∂U_i^k}{\∂U_{i,r}^k}=\frac{U_{i,r}^k}{\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}}\\ \frac{\∂U_i^k}{\∂U_{i,x}^x}=\frac{U_{i,x}^k}{\sqrt{{\left(U_{i,r}^k\right)}^2+{\left(U_{i,x}^k\right)}^2}}\end{array}\right.---\left(14\right)$

Can obtain according to formula (12), (13) and (14):

$H^k=\left[\begin{array}{ccccccc}{I}_{1,r}^k& {-I}_{1,x}^k& 0& 0& ...& 0& 0\\ I_{1,x}^k& I_{1,r}^k& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& -I_{2,x}^k& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{\∂U_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& I_{n-1,r}^k& {-I}_{n-1,x}^k\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k\end{array}\right]---\left(15\right)$

To H _kcarry out LU decomposition, normalization and cancellation computing obtain matrix by row

$H_1^k=\left[\begin{array}{ccccccc}{I}_{1,r}^k& \frac{{-I}_{1,x}^k}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ I_{i,x}^k& I_{i,r}^k+\frac{{\left(I_{1,x}^k\right)}^2}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& \frac{-I_{2,x}^k}{I_{2,x}^k}& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{\∂U_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}+\frac{\∂U_{2,x}^k}{\∂U_{2,r}^k}\frac{I_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& I_{n-1,r}^k& \frac{-I_{n-1,x}^k}{I_{n-1,r}^k}\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k+\frac{{\left(I_{n-1,x}^k\right)}^2}{I_{n-1,r}^k}\end{array}\right.2---\left(16\right)$

From in obtain inferior triangular flap L _kwith unit upper triangular matrix U _k, wherein L _kby element composition below middle diagonal and diagonal, U _kdiagonal element be 1 entirely, on it triangle element by element composition more than middle diagonal, is expressed as:

$L^k\left[\begin{array}{ccccccc}{I}_{1,r}^k& 0& 0& 0& ...& 0& 0\\ I_{i,x}^k& I_{i,r}^k+\frac{{\left(I_{1,x}^k\right)}^2}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 0& I_{2,r}^k& 0& ...& 0& 0\\ 0& 0& \frac{\∂U_2^k}{{\∂U}_{2,r}^k}& \frac{\∂U_2^k}{\∂U_{2,x}^k}+\frac{\∂U_2^k}{\∂U_{2,r}^k}\frac{I_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ 0& 0& 0& 0& ...& ...& ...\\ ...& ...& 0& 0& ...& I_{n-1,r}^k& 0\\ 0& 0& 0& 0& ...& I_{n-1,x}^k& I_{n-1,r}^k+\frac{{\left(I_{n-1,x}^k\right)}^2}{I_{n-1,r}^k}\end{array}\right]---\left(17\right)$

$U^k=\left[\begin{array}{ccccccc}1& \frac{-I_{1,x}^k}{I_{1,r}^k}& 0& 0& ...& 0& 0\\ 0& 1& 0& 0& ...& 0& 0\\ 0& 0& 1& \frac{{-I}_{2,x}^k}{I_{2,r}^k}& ...& 0& 0\\ 0& 0& 0& 1& ...& 0& 0\\ ...& ...& ...& ...& ...& ...& ...\\ 0& 0& 0& 0& ...& 1& \frac{{-I}_{n-1,x}^k}{I_{n-1,r}^k}\\ 0& 0& 0& 0& ...& 0& 1\end{array}\right]---\left(18\right)$

Decompose according to LU, H _kbe expressed as:

H ^k＝L ^kU ^k (19)

So formula (11) is expressed as:

L ^kU ^kΔV ^k＝-ΔW ^k (20)

Through type (20), utilizes the method for solving of the former generation back substitution of system of linear equations, obtains

$\mathrm{\Δ}{V}^k={\left[\begin{array}{ccccccc}\mathrm{\Δ}{U}_{1,r}^k& \mathrm{\Δ}{U}_{1,x}^k& \mathrm{\Δ}{U}_{2,r}^k& \mathrm{\Δ}{U}_{2,x}^k& ...& \mathrm{\Δ}{U}_{n-1,r}^k& \mathrm{\Δ}{U}_{n-1,x}^k\end{array}\right]}^T,k=a,b,c.$

7. the three-phase load flow of active distribution network computational methods based on node voltage according to claim 6, it is characterized in that: in described step 6, revised by the magnitude of voltage of following formula to non-zero power node k phase, obtain the magnitude of voltage V of revised non-zero power node k phase ^k:

$V^k=V_{\mathrm{old}}^k+\mathrm{\Δ}{V}^k---\left(21\right)$

Wherein, the magnitude of voltage of node k phase is injected, k=a, b, c for revising front non-zero.

8. the three-phase load flow of active distribution network computational methods based on node voltage according to claim 7, is characterized in that: in described step 7, if U _n=U _n,R+ jU _n,X, U _z=U _z,R+ jU _z,X, Y _zZ=G _zZ+ jB _zZ, Y _zN=G _zN+ jB _zN; Wherein U _z,Rand U _z,Xfor U _zreal part and imaginary part; (4) are converted to the real number equation under following rectangular coordinate:

$\left[\begin{array}{cc}{B}_{\mathrm{ZZ}}& G_{\mathrm{ZZ}}\\ G_{\mathrm{ZZ}}& -B_{\mathrm{ZZ}}\end{array}\right]\left[\begin{array}{c}{U}_{Z,R}\\ U_{Z,X}\end{array}\right]+\left[\begin{array}{cc}{B}_{\mathrm{ZN}}& G_{\mathrm{ZN}}\\ G_{\mathrm{ZN}}& {-B}_{\mathrm{ZN}}\end{array}\right]\left[\begin{array}{c}{U}_{N,R}\\ U_{N,X}\end{array}\right]=0---\left(22\right)$

The then magnitude of voltage V of zero injection node _zbe expressed as:

$V_Z=\left[\begin{array}{c}{U}_{Z,R}\\ U_{Z,X}\end{array}\right]=-{\left[\begin{array}{cc}{B}_{\mathrm{ZZ}}& G_{\mathrm{ZZ}}\\ G_{\mathrm{ZZ}}& -B_{\mathrm{ZZ}}\end{array}\right]}^{-1}\left[\begin{array}{cc}{B}_{\mathrm{ZN}}& G_{\mathrm{ZN}}\\ G_{\mathrm{ZN}}& {-B}_{\mathrm{ZN}}\end{array}\right]\left[\begin{array}{c}{U}_{N,R}\\ U_{N,X}\end{array}\right]---\left(23\right).$