CN103246804A - Method and device for calculating power system node voltage - Google Patents

Abstract

The invention discloses a method and a device for calculating power system node voltage and belongs to the field of power transmission. The method includes: acquiring network structures and element parameters of nodes of a power system; generating a general iteration equation of a PV node, a general iteration equation of a PQ node, and an iteration equation of a slow-convergence PQ node according to the network structures and the element parameters; and calculating voltage of the PV node and the PQ node according to the general iteration equation of the PV node, the general iteration equation of the PQ node and the iteration equation of the slow-convergence PQ node. Due to the fact that the general iteration equation of the PV node, the general iteration equation of the PQ node and the iteration equation of the slow-convergence PQ node are generated according to the network structures and the element parameters of the power system, and the voltage of the PV node and the PQ node are calculated according to the general iteration equation of the PV node, the general iteration equation of the PQ node and the iteration equation of the slow-convergence PQ node, convergence is calculated by increasing node voltage.

Description

Electric Power System Node Voltage computing method and device

Technical field

The present invention relates to the electric power transportation art, particularly a kind of Electric Power System Node Voltage computing method and device.

Background technology

It is under given power system network topology, component parameters and generating, load parameter conditions, to the calculating of active power, reactive power and the voltage distribution in power network that trend is calculated.Wherein, be most crucial part during trend is calculated to the voltage magnitude of each node and the calculating of voltage phase angle.

Node in the electric system can comprise at least one PV node, at least one PQ node and a balance node.Wherein, the active power P of PV node and voltage magnitude V are known, and the active power P of PQ node and reactive power Q are known, and the voltage magnitude V of balance node and voltage phase angle θ are known.When each node is carried out trend calculating, only need to calculate the voltage magnitude of PQ node and the voltage phase angle of voltage phase angle and PV node.The method of the voltage magnitude of existing calculating PQ node and the voltage phase angle of voltage phase angle and PV node mainly comprises the steps:

The first, network structure and the component parameters according to electric system generates the iterative equation of PV node and the iterative equation of PQ node; The second, the voltage initial value according to each node that sets in advance calculates PV node injection reactive power, inject reactive power according to the PV node again and calculate the injection electric current of PV node and the iterative equation of substitution PV node, according to the voltage magnitude of given PV node the result of calculation of the iterative equation of PV node is revised at last, obtained the voltage (node voltage comprises voltage magnitude and voltage phase angle) of PV node; Three, calculate the voltage of PQ node according to the iterative equation of the voltage of the PV node that obtains and PQ node.

In realizing process of the present invention, the inventor finds that there is following problem at least in prior art:

The voltage method of existing calculating PQ node and PV node, when handling the PV node, need calculate the reactive power of PV node, PV number of nodes in electric system more for a long time, the reactive power of PV node is calculated the relatively poor not even convergence of convergence, thereby further influences the convergence that the node iterative equation calculates.

Summary of the invention

In order to solve the problem of node voltage calculating poor astringency in the prior art, the embodiment of the invention provides a kind of Electric Power System Node Voltage computing method and device.Described technical scheme is as follows:

On the one hand, provide a kind of Electric Power System Node Voltage computing method, described method comprises:

Obtain network structure and the component parameters of each node of electric system, described node comprises at least: at least one PV node and at least one PQ node, self active power and the voltage magnitude of described PV node are known, self active power and the reactive power of described PQ node are known, include at least one slow convergence PQ node in the described PQ node;

Generate the iteration general equation of described PV node and the iteration general equation of described PQ node according to described network structure and component parameters, and generate the iterative equation of described slow convergence PQ node according to described network structure and component parameters;

Calculate the electric current injection rate IR of each node according to the voltage initial value of each node that sets in advance;

Calculate the actual active power of described PV node according to the electric current injection rate IR of described each node, and calculate the voltage of described PV node according to the iteration general equation of the actual active power of described PV node and described PV node;

Calculate the voltage of described PQ node according to the iterative equation of the iteration general equation of the voltage of described PV node, described PQ node and described slow convergence PQ node.

Describedly generate before the iterative equation of described slow convergence PQ node according to described network structure and component parameters, described method also comprises:

Calculate the converging factor of described PQ node;

According to described converging factor order from big to small described PQ node is sorted, and the forward n node that will sort is defined as described slow convergence PQ node, the sum of the described PQ node of described n=predetermined ratio *.

The converging factor of the described PQ node of described calculating comprises:

Calculate the converging factor of described PQ node according to the converging factor computing formula, described converging factor computing formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{(\∞)}\right|}^2};$

Wherein, α is converging factor, and Z is the direct impedance of PQ node, and S is self active power and reactive power sum of PQ node, U ^(∞)For the voltage of PQ node is finally separated.

Describedly generate the iterative equation of described slow convergence PQ node according to described network structure and component parameters, comprising:

Generate the impedance matrix of described PQ node according to described network structure and component parameters;

Generate the iterative equation of described slow convergence PQ node according to the impedance matrix of described PQ node;

Wherein, the iterative equation of described slow convergence PQ node is:

$U_B^{(k+1)}=Z_{\mathrm{BA}}{I}_A^{(k+1)}+Z_{\mathrm{BB}}{I}_B^{\left(k\right)};$

Wherein,

Be the voltage of the described slow convergence PQ node of the k+1 time iterative computation gained, described Z _BAFor restraining the PQ node fast to the impedance matrix of described slow convergence PQ node, described Z _BBBe the impedance matrix of described slow convergence PQ node self,

Be the electric current injection rate IR of the described quick convergence PQ node of the k+1 time iterative computation gained,

Be the electric current injection rate IR of the described slow convergence PQ node of the k time iterative computation gained, wherein, described quick convergence PQ node is the PQ node except described slow convergence PQ node.

The iteration general equation of described voltage according to described PV node, described PQ node and the iterative equation of described slow convergence PQ node calculate the voltage of described PQ node, comprising:

Voltage to described PQ node carries out iterative computation q time, and wherein, q is the integer greater than 1;

When carrying out the 1st iterative computation, find the solution the iteration general equation of described PQ node according to the voltage of described PV node, obtain to calculate for the 1st time the voltage before the correction of the voltage of described quick convergence PQ node of gained and the described slow convergence PQ node that calculates gained the 1st time; Revise according to the iterative equation of the described slow convergence PQ node voltage before to the correction of the described slow convergence PQ node that calculates gained for the 1st time, obtain to calculate for the 1st time the revised voltage of the described slow convergence PQ node of gained; The 1st time of obtaining calculated the voltage that the voltage of described quick convergence PQ node of gained and the revised voltage that calculates the described slow convergence PQ node of gained the 1st time are defined as calculating for the 1st time gained;

When carrying out the q time iterative computation, recomputate the electric current injection rate IR of each node according to the voltage of the voltage of the q-1 time iterative computation gained and described PV node, recomputate the actual active power of described PV node according to the electric current injection rate IR of described each node that recomputates, and recomputate the voltage of described PV node according to the iteration general equation of the actual active power of the described PV node that recomputates and described PV node, find the solution the iteration general equation of described PQ node according to the voltage of the described PV node that recomputates, obtain to calculate for the q time the voltage of described quick convergence PQ node of gained and the preceding voltage of correction of the described slow convergence PQ node that calculates gained the q time; Revise according to the iterative equation of the described slow convergence PQ node voltage before to the correction of the described slow convergence PQ node that calculates gained for the q time, obtain the revised voltage of the described slow convergence PQ node of the q time calculating gained; The revised voltage that the q time of obtaining is calculated the described slow convergence PQ node of the voltage of described quick convergence PQ node of gained and the q time calculating gained is defined as the voltage of the q time calculating gained;

Whether the change in voltage mould value of judging the q time calculating changes threshold values less than default PQ node voltage, wherein, the mould value of the difference of the voltage of the described change in voltage mould value of calculating for the q time voltage that is described the q time calculating gained and described the q-1 time iterative computation gained;

If the change in voltage mould value of described the q time calculating changes threshold values less than default PQ node voltage, then the voltage of described the q time calculating gained is defined as the voltage of described PQ node;

Change threshold values if the change in voltage mould value of described the q time calculating is not less than default PQ node voltage, then proceed iterative computation the q+1 time.

The voltage of described iterative equation according to described slow convergence PQ node before to the correction of the described slow convergence PQ node that calculates gained for the q time is revised, and obtains the revised voltage of the described slow convergence PQ node of the q time calculating gained, comprising:

Keep the voltage of the described described quick convergence PQ node that calculates gained for the q time constant, to calculate voltage before the correction of described slow convergence PQ node of gained for the q time as initial value, according to the iterative equation of described slow convergence PQ node the voltage of described slow convergence PQ node is carried out iterative computation m time, and with the voltage of the described slow convergence PQ node of the m time iterative computation gained revised voltage as described slow convergence PQ node, wherein, m is the integer more than or equal to 1.

On the other hand, provide a kind of Electric Power System Node Voltage calculation element, it is characterized in that described device comprises:

Acquisition module, be used for obtaining network structure and the component parameters of each node of electric system, described node comprises at least: at least one PV node and at least one PQ node, self active power and the voltage magnitude of described PV node are known, self active power and the reactive power of described PQ node are known, include at least one slow convergence PQ node in the described PQ node;

The first equation generation module is used for iteration general equation that the network structure that gets access to according to described acquisition module and component parameters generate described PV node and the iteration general equation of described PQ node;

The second equation generation module is used for the iterative equation that the network structure that gets access to according to described acquisition module and component parameters generate described slow convergence PQ node;

The electric current computing module is used for calculating according to the voltage initial value of each node that sets in advance the electric current injection rate IR of each node;

Active power is calculated module, calculates the actual active power of described PV node for the electric current injection rate IR of each node that calculates according to described electric current computing module;

The first voltage computing module, the iteration general equation that is used for the PV node that actual active power and the described first equation generation module according to described PV node generate calculates the voltage of described PV node;

The second voltage computing module, the iterative equation that is used for the iteration general equation of the voltage of the PV node that calculates according to the described first voltage computing module, PQ node that the described first equation generation module generates and the slow convergence PQ node that the described second equation generation module generates calculates the voltage of described PQ node.

Described device also comprises:

The converging factor computing module is used for calculating the converging factor of described PQ node before network structure that the described second equation generation module gets access to according to described acquisition module and component parameters generate the iterative equation of described slow convergence PQ node;

The node determination module, the converging factor order from big to small that is used for calculating according to described converging factor computing module sorts to described PQ node, and the forward n node that will sort is defined as described slow convergence PQ node, the sum of the described PQ node of described n=predetermined ratio *.

Described converging factor computing module, for the converging factor of calculating described PQ node according to the converging factor computing formula, described converging factor computing formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{(\∞)}\right|}^2};$

Wherein, α is converging factor, and Z is the direct impedance of PQ node, and S is self active power and reactive power sum of PQ node, U ^(∞)For the voltage of PQ node is finally separated.

The described second equation generation module comprises:

The impedance matrix generation unit is used for generating according to described network structure and component parameters the impedance matrix of described PQ node;

The iterative equation generation unit, the impedance matrix that is used for the PQ node that generates according to described impedance matrix generation unit generates the iterative equation of described slow convergence PQ node;

Wherein, the iterative equation of described slow convergence PQ node is:

$U_B^{(k+1)}=Z_{\mathrm{BA}}{I}_A^{(k+1)}+Z_{\mathrm{BB}}{I}_B^{\left(k\right)};$

Wherein,

Be the voltage of the described slow convergence PQ node of the k+1 time iterative computation gained, described Z _BAFor restraining the PQ node fast to the impedance matrix of described slow convergence PQ node, described Z _BBBe the impedance matrix of described slow convergence PQ node self,

Be the electric current injection rate IR of the described quick convergence PQ node of the k+1 time iterative computation gained,

Be the electric current injection rate IR of the described slow convergence PQ node of the k time iterative computation gained, wherein, described quick convergence PQ node is the PQ node except described slow convergence PQ node.

The described second voltage computing module comprises:

The voltage computing unit is used for the voltage of described PQ node is carried out iterative computation q time, and wherein, q is the integer greater than 1;

Described voltage computing unit comprises:

The voltage computation subunit, be used for when carrying out the 1st iterative computation, the voltage of the PV node that calculates according to the described first voltage computing module is found the solution the iteration general equation of described PQ node, obtains to calculate for the 1st time the voltage before the correction of the voltage of described quick convergence PQ node of gained and the described slow convergence PQ node that calculates gained the 1st time;

Voltage correction subelement, voltage before the correction of the described slow convergence PQ node that calculates gained for the 1st time that is used for according to the iterative equation of described slow convergence PQ node described voltage computation subunit being obtained is revised, and obtains to calculate for the 1st time the revised voltage of the described slow convergence PQ node of gained;

Voltage is determined subelement, and the revised voltage that be used for described voltage computation subunit is obtained the 1st time calculate that the voltage of described quick convergence PQ node of gained and described voltage correction subelement obtain the 1st time calculates the described slow convergence PQ node of gained is defined as calculating for the 1st time the voltage of gained;

When carrying out the q time iterative computation, described electric current computing module also is used for determining that according to described voltage the voltage of the voltage of the q-1 time iterative computation gained that subelement is determined and the PV node that the described first voltage computing module calculates recomputates the electric current injection rate IR of each node;

Described active power is calculated module, also recomputates the actual active power of described PV node for the electric current injection rate IR of described each node that recomputates according to described electric current computing module;

The described first voltage computing module also is used for recomputating according to the iteration general equation that described active power is calculated the actual active power of the described PV node that module recomputates and described PV node the voltage of described PV node;

Described voltage computation subunit, be used for when carrying out the q time iterative computation, the voltage of the described PV node that recomputates according to the described first voltage computing module is found the solution the iteration general equation of described PQ node, obtains to calculate for the q time the voltage of described quick convergence PQ node of gained and the preceding voltage of correction of the described slow convergence PQ node that calculates gained the q time;

Described voltage correction subelement, voltage before the correction of the described slow convergence PQ node that calculates gained for the q time that is used for according to the iterative equation of described slow convergence PQ node described voltage computation subunit being obtained is revised, and obtains the revised voltage of the described slow convergence PQ node of the q time calculating gained;

Described voltage is determined subelement, and the revised voltage that be used for described voltage computation subunit is obtained the q time calculates the described slow convergence PQ node of the voltage of described quick convergence PQ node of gained and the q time calculating gained that described voltage correction subelement obtains is defined as the voltage of the q time calculating gained;

The described second voltage computing module also comprises:

Judging unit, be used for judging whether the change in voltage mould value of the q time calculating changes threshold values less than default PQ node voltage, wherein, the change in voltage mould value of described the q time calculating is the mould value that described voltage is determined the difference of the voltage of the q time calculating gained that subelement is determined and the voltage that described voltage is determined the q-1 time iterative computation gained that subelement is determined;

The voltage determining unit changes threshold values if go out the change in voltage mould value of described the q time calculating for described judgment unit judges less than default PQ node voltage, then the voltage of described the q time calculating gained is defined as the voltage of described PQ node;

Described voltage computing unit is not less than default PQ node voltage variation threshold values if go out the change in voltage mould value of calculating for the q time for described judgment unit judges, then proceeds iterative computation the q+1 time.

Described voltage correction subelement, be used for to keep the voltage of described quick convergence PQ node of the q time calculating gained that described voltage computation subunit calculates constant, voltage before the correction of the described slow convergence PQ node that calculates gained for the q time that described voltage computation subunit is calculated is as initial value, according to the iterative equation of described slow convergence PQ node the voltage of described slow convergence PQ node is carried out iterative computation m time, and with the voltage of the described slow convergence PQ node of the m time iterative computation gained revised voltage as described slow convergence PQ node, wherein, m is the integer more than or equal to 1.

The beneficial effect that the technical scheme that the embodiment of the invention provides is brought is:

The iteration general equation, the iteration general equation of PQ node and the iterative equation of slow convergence PQ node that generate the PV node by network structure and component parameters according to the electric system that receives, and calculate the voltage of PV node according to the iteration general equation of the actual active power of PV node and PV node, further calculate the voltage of PQ node according to the iterative equation of the iteration general equation of the voltage of PV node, PQ node and slow convergence PQ node, reach and improve node voltage and calculate constringent purpose.

Description of drawings

In order to be illustrated more clearly in the technical scheme in the embodiment of the invention, the accompanying drawing of required use is done to introduce simply in will describing embodiment below, apparently, accompanying drawing in describing below only is some embodiments of the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to these accompanying drawings.

Fig. 1 is the method flow diagram of the Electric Power System Node Voltage computing method that provide of the embodiment of the invention one;

Fig. 2 is the method flow diagram of the Electric Power System Node Voltage computing method that provide of the embodiment of the invention two;

Fig. 3 is the structure drawing of device of the Electric Power System Node Voltage calculation element that provides of the embodiment of the invention three;

Fig. 4 is the structure drawing of device of the Electric Power System Node Voltage calculation element that provides of the embodiment of the invention four.

Embodiment

For making the purpose, technical solutions and advantages of the present invention clearer, embodiment of the present invention is described further in detail below in conjunction with accompanying drawing.

Embodiment one

Please refer to Fig. 1, it shows the method flow diagram of the Electric Power System Node Voltage computing method that the embodiment of the invention one provides.This method can be applied to calculate the voltage of each node in the electric system, and wherein, the node in the electric system can comprise: at least one PQ node, at least one PV node and a balance node.These Electric Power System Node Voltage computing method can comprise:

Step 101, obtain network structure and the component parameters of each node of electric system, this node comprises at least: at least one PV node and at least one PQ node, self active power and the voltage magnitude of this PV node are known, self active power and the reactive power of this PQ node are known, include at least one slow convergence PQ node in this PQ node;

Step 102 generates the iteration general equation of this PV node and the iteration general equation of this PQ node according to this network structure and component parameters;

Step 103 generates the iterative equation of this slow convergence PQ node according to network structure and component parameters;

Step 104 is calculated the electric current injection rate IR of each node according to the voltage initial value of each node that sets in advance;

Step 105 is calculated the actual active power of this PV node according to the electric current injection rate IR of each node, and calculates the voltage of this PV node according to the iteration general equation of the actual active power of this PV node and this PV node;

Step 106 is calculated the voltage of this PQ node according to the iterative equation of the iteration general equation of the voltage of this PV node, this PQ node and this slow convergence PQ node.

In sum, the Electric Power System Node Voltage computing method that the embodiment of the invention one provides, the iteration general equation that generates the PV node by network structure and component parameters according to the electric system that receives, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node, and calculate the voltage of PV node according to the iteration general equation of the actual active power of PV node and PV node, further according to the voltage of PV node, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node calculates the voltage of PQ node, reaches the raising node voltage and calculates constringent purpose.

Embodiment two

For the Electric Power System Node Voltage computing method that the embodiment of the invention one is provided are further described, please refer to Fig. 2, it shows the method flow diagram of the Electric Power System Node Voltage computing method that the embodiment of the invention two provides.This method can be used for calculating the voltage of each node of electric system, and this electric system comprises: at least one PQ node, at least one PV node and a balance node; Wherein, because balance node voltage magnitude and voltage phase angle are known quantity, therefore, only need to calculate the voltage magnitude of PQ node and the voltage phase angle of voltage phase angle and PV node.These Electric Power System Node Voltage computing method can comprise:

Step 201, the voltage calculation element receives electric system each meshed network structure and component parameters;

Step 202 is write the electric power system tide equation according to each meshed network structure and component parameters row, and is generated the iteration general equation of PQ node and the iteration general equation of PV node according to this electric power system tide equation;

According to the difference of node injection condition, network node can be divided into 3 classes usually: PQ node, PV node and balance node.

Wherein, the PQ node is generally load bus or network connection node, and its active power P and reactive power Q are known, and voltage magnitude U and voltage phase angle θ ask for waiting; The PV node is generally the generator outlet node, and himself active power P and voltage magnitude U are known, and voltage phase angle θ asks for waiting; Balance node is generally the generator outlet node, and its voltage magnitude U and voltage phase angle θ are known, and, there is and has only a balance node in the electric system.

Known conditions, the unknown variable of PQ node, PV node and balance node are different, therefore, when making up nodal voltage equation, handle respectively at different joint forms.

The processing of 202a, PQ node:

To n node power system, at first suppose not contain in the network PV node, 1 of balance node, establishing the balance node sequence number is n.Structure node admittance matrix Y, and further the structure node voltage equation is:

$\left[\begin{array}{cc}{Y}_{\mathrm{PQPQ}}& Y_{\mathrm{PQVV}}\\ 0& Y_{\mathrm{VVVV}}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{PQ}}\\ U_{\mathrm{VV}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{PQ}}\\ U_{\mathrm{VV}}\end{array}\right]---(2-1)$

U wherein _PQ=[U ₁U _N-1] ^T, U _i=[U _IAU _IBU _IC] ^TI=1,2 ..., n-1.U _IA, U _IB, U _ICA, B, the C three-phase voltage of difference corresponding node i.U _VV=[U _VVA U _VVB U _VVC] ^T。I _PQ=[I ₁I _N-1] ^TFor node injects electric current, I _i=[I _IAI _IBI _IC] ^TI=1,2 ..., n-1,

ψ=A, B, C, P, Q are the node injecting power.

The processing of 202b, PV node:

Because the known conditions number of PV node is less than unknown condition, therefore, need insert the generator built-in potential node of equivalent power supply at PV node place, and the PV node is converted into the PQ node.

Because the generator internal resistance is net resistance, common given zero sequence, positive sequence, negative sequence neactance value are respectively: xGi0, xGi1, xGi2, not coupling between three orders.By conversion, can try to achieve transformer three-phase admittance matrix YGi.

$Y_{\mathrm{Gi}}=T\left[\begin{array}{ccc}\frac{1}{j{x}_{\mathrm{Gi}1}}& & \\ & \frac{1}{j{x}_{\mathrm{Gi}2}}& \\ & & \frac{1}{j{x}_{\mathrm{Gi}0}}\end{array}\right]T^{-1}---(2-2)$

Wherein: $T=\left[\begin{array}{ccc}1& 1& 1\\ {\mathrm{\α}}^2& \mathrm{\α}& 1\\ \mathrm{\α}& {\mathrm{\α}}^2& 1\end{array}\right],$ α=e ^{J120 °}, T ^-1Inverse matrix for matrix T.

To PV node, generator built-in potential node row nodal voltage equation be:

$\left[\begin{array}{cc}{Y}_{\mathrm{Gi}}& {-Y}_{\mathrm{Gi}}\\ -Y_{\mathrm{Gi}}& Y_{\mathrm{Gi}}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{PVi}}\\ U_{\mathrm{Gi}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{PVLi}}\\ I_{\mathrm{Gi}}\end{array}\right]---(2-3)$

$U_{\mathrm{PVi}}=\left[\begin{array}{c}{U}_{\mathrm{PViA}}\\ U_{\mathrm{PViB}}\\ U_{\mathrm{PViC}}\end{array}\right],U_{\mathrm{Gi}}=\left[\begin{array}{c}{U}_{\mathrm{GiA}}\\ U_{\mathrm{GiB}}\\ U_{\mathrm{GiC}}\end{array}\right],I_{\mathrm{PVLi}}=\left[\begin{array}{c}{S^{*}}_{\mathrm{PVLiA}}/U_{\mathrm{PViA}}^{*}\\ {S^{*}}_{\mathrm{PVLiB}}/{U^{*}}_{\mathrm{PViB}}\\ {S^{*}}_{\mathrm{PVLiC}}/{U^{*}}_{\mathrm{PViC}}\end{array}\right],I_{\mathrm{Gi}}=\left[\begin{array}{c}{S^{*}}_{\mathrm{GiA}}/{U^{*}}_{\mathrm{GiA}}\\ {S^{*}}_{\mathrm{GiB}}/{U^{*}}_{\mathrm{GiB}}\\ {S^{*}}_{\mathrm{GiC}}/{U^{*}}_{\mathrm{GiC}}\end{array}\right].$

U wherein _GiA, U _GiB, U _GiCBe respectively the PV node i and connect A, B, the C three-phase voltage phasor of generator built-in potential node, U _PViA, U _PViB, U _PViCBe respectively A, B, the C three-phase voltage phasor of PV node i.Because YGi is the net resistance element, does not consume active power, therefore have:

$\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{P}_{\mathrm{Gi\β}}=\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{P}_{\mathrm{PVGi\β}}---(2-4)$

Definition

Then have

Therefore have:

Wherein $U_{\mathrm{PVi}}=\left[\begin{array}{c}{U}_{\mathrm{PViA}}\\ U_{\mathrm{PViB}}\\ U_{\mathrm{PViC}}\end{array}\right],I_{\mathrm{PVLi}}={\left[\begin{array}{c}-S_{\mathrm{PVLiA}}/U_{\mathrm{PViA}}\\ -S_{\mathrm{PVLiB}}/U_{\mathrm{PViB}}\\ -S_{\mathrm{PVLiC}}/U_{\mathrm{PViC}}\end{array}\right]}^{*},I_{\mathrm{GiA}}=\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{S^{*}}_{\mathrm{Gi\β}}/{U^{*}}_{\mathrm{GiA}}.$

All PV nodes are increased the generator node according to formula (2-9), can obtain formula (2-1) correction

$\left[\begin{array}{cccc}{Y}_{\mathrm{PQPQ}}& Y_{\mathrm{PQPV}}& Y_{\mathrm{PQVV}}& \\ Y_{\mathrm{PVPQ}}& Y_{\mathrm{PVPV}}+Y_{\mathrm{PVPV}}^{\′}& Y_{\mathrm{PVVV}}& Y_{\mathrm{PVGA}}\\ Y_{\mathrm{VVPQ}}& Y_{\mathrm{VVPV}}& Y_{\mathrm{VVVV}}& \\ & Y_{\mathrm{GAPV}}& & Y_{\mathrm{GAGA}}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{PQ}}\\ U_{\mathrm{PV}}\\ U_{\mathrm{VV}}\\ U_{\mathrm{GA}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{PQ}}\\ I_{\mathrm{PVL}}\\ I_{\mathrm{VV}}\\ I_{\mathrm{GA}}\end{array}\right]---(2-10)$

The processing of 202c, balance node:

Balance node voltage magnitude, phase angle are set-point, and directly are not connected with load usually.Application formula (2-9) establishes an equation and can obtain balance node

Wherein $U_{\mathrm{VV}}=\left[\begin{array}{c}{U}_{\mathrm{VVA}}\\ U_{\mathrm{VVB}}\\ U_{\mathrm{VVC}}\end{array}\right],I_{\mathrm{VV}}=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right],I_{\mathrm{GVVA}}=\underset{\mathrm{\β}=A,B,C}{\mathrm{\Σ}}{S^{*}}_{\mathrm{GVV\β}}/{U^{*}}_{\mathrm{GVVA}}.$

With formula (2-11) amendment type (2-10), obtain:

$\left[\begin{array}{ccccc}{Y}_{\mathrm{PQPQ}}& Y_{\mathrm{PQPV}}& Y_{\mathrm{PQVV}}& & \\ Y_{\mathrm{PVPQ}}& Y_{\mathrm{PVPV}}+Y_{\mathrm{PVPV}}^{\′}& Y_{\mathrm{PVVV}}& Y_{\mathrm{PVGA}}& \\ Y_{\mathrm{VVPQ}}& Y_{\mathrm{VVPV}}& Y_{\mathrm{VVVV}}+Y_{\mathrm{VVVV}}^{\′}& & Y_{\mathrm{VVGVVA}}\\ & Y_{\mathrm{GAPV}}& & Y_{\mathrm{GAGA}}& \\ & & Y_{\mathrm{GVVAVV}}& & Y_{\mathrm{GVVAGVVA}}^{\′}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{PQ}}\\ U_{\mathrm{PV}}\\ U_{\mathrm{VV}}\\ U_{\mathrm{GA}}\\ U_{\mathrm{GVVA}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{PQ}}\\ I_{\mathrm{PVL}}\\ I_{\mathrm{VV}}\\ I_{\mathrm{GA}}\\ I_{\mathrm{GVVA}}\end{array}\right]---(2-12)$

Y ＇ wherein _VVVV, Y _VVGVVA, Y _GVVAVV, Y ＇ _GVVAGVVABe the correction matrix of balance node to bus admittance matrix.

The foundation of 202d, electric power system tide equation:

According to above-mentioned derivation of equation result, establish network node and add up to n, wherein, the PV node adds up to m, and balance node adds up to 1.(2-12) sets up equation according to formula, and equation left side matrix is carried out elementary transformation, and it is abbreviated as following formula:

$\left[\begin{array}{ccccc}{Y}_{\mathrm{PQPQ}}^{\′}& Y_{\mathrm{PQPV}}^{\′}& Y_{\mathrm{PQVV}}^{\′}& Y_{\mathrm{PQPVA}}^{\′}& Y_{\mathrm{PQVVA}}^{\′}\\ Y_{\mathrm{PVPQ}}^{\′}& Y_{\mathrm{PVPV}}^{\′}& Y_{\mathrm{PVVV}}^{\′}& Y_{\mathrm{PVPVA}}^{\′}& Y_{\mathrm{PVVVA}}^{\′}\\ Y_{\mathrm{VVPQ}}^{\′}& Y_{\mathrm{VVPV}}^{\′}& Y_{\mathrm{VVVV}}^{\′}& Y_{\mathrm{VVPVA}}^{\′}& Y_{\mathrm{VVVVA}}^{\′}\\ Y_{\mathrm{PVAPQ}}^{\′}& Y_{\mathrm{PVAPV}}^{\′}& Y_{\mathrm{PVAVV}}^{\′}& Y_{\mathrm{PVAPVA}}^{\′}& Y_{\mathrm{PVAVVA}}^{\′}\\ P_{\mathrm{VVAPQ}}^{\′}& Y_{\mathrm{VVAPV}}^{\′}& Y_{\mathrm{VVAVV}}^{\′}& Y_{\mathrm{VVAPVA}}^{\′}& Y_{\mathrm{VVAVVA}}^{\′}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{PQ}}\\ U_{\mathrm{PV}}^{\′}\\ U_{\mathrm{VV}}^{\′}\\ U_{\mathrm{PVA}}\\ U_{\mathrm{VVA}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{PQ}}\\ I_{\mathrm{PVL}}\\ I_{\mathrm{VV}}\\ I_{\mathrm{GA}}\\ I_{\mathrm{GVVA}}\end{array}\right]---(2-13)$

Wherein

$U_{\mathrm{PQ}}=\left[\begin{array}{c}\left[\begin{array}{c}{U}_{\mathrm{PQ}1A}\\ U_{\mathrm{PQ}1B}\\ U_{\mathrm{PQ}1C}\end{array}\right]\\ ...\\ \left[\begin{array}{c}{U}_{\mathrm{PQ}(n-m-1)A}\\ U_{\mathrm{PQ}(n-m-1)B}\\ U_{\mathrm{PQ}(n-m-1)C}\end{array}\right]\end{array}\right],$ $U_{\mathrm{PV}}^{\′}=\left[\begin{array}{c}\left[\begin{array}{c}{U}_{G1A}\\ U_{\mathrm{PV}1B}\\ U_{\mathrm{PV}1C}\end{array}\right]\\ ...\\ \left[\begin{array}{c}{U}_{\mathrm{GmA}}\\ U_{\mathrm{PVmB}}\\ U_{\mathrm{PVmC}}\end{array}\right]\end{array}\right],$ $U_{\mathrm{VV}}^{\′}=\left[\begin{array}{c}{U}_{\mathrm{GVVA}}\\ U_{\mathrm{VVB}}\\ U_{\mathrm{VVC}}\end{array}\right],$ $U_{\mathrm{PVA}}=\left[\begin{array}{c}{U}_{\mathrm{PV}1A}\\ ...\\ U_{\mathrm{PVmA}}\end{array}\right]$

In the formula, equation left side U _PQ, U ＇ _PV, U ' _VVIn each variable amplitude, phase angle be and wait to ask U _PVAIn each variable amplitude known, phase angle the unknown, U _VVAKnown.I _PQ, I _PVL, I _VVActive power in the equation is known, and reactive power is known; I _GAActive power in the equation is known, reactive power the unknown.Merge the item that has identical known conditions, waits to ask condition, (2-13) is reduced to formula:

$\left[\begin{array}{ccc}{Y}_{\mathrm{\ω\ω}}& Y_{\mathrm{\ω\ϵ}}& Y_{\mathrm{\ω\ξ}}\\ Y_{\mathrm{\ϵ\ω}}& Y_{\mathrm{\ϵ\ϵ}}& Y_{\mathrm{\ϵ\ξ}}\\ Y_{\mathrm{\ξ\ω}}& Y_{\mathrm{\ξ\ϵ}}& Y_{\mathrm{\ξ\ξ}}\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{\ω}}\\ U_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{\ω}}\\ I_{\mathrm{\ϵ}}\\ I_{\mathrm{\ξ}}\end{array}\right]---(2-14)$

Wherein, U _ω=[U _PQU ＇ _PVU ' _VV], U _ε=[U _PVA],

Wherein, U _ξBe known conditions, rewriting formula (2-14) is:

$\left[\begin{array}{ccc}{Y}_{\mathrm{\ω\ω}}& Y_{\mathrm{\ω\ϵ}}& Y_{\mathrm{\ω\ξ}}\\ Y_{\mathrm{\ϵ\ω}}& Y_{\mathrm{\ϵ\ϵ}}& Y_{\mathrm{\ϵ\ξ}}\\ & & 1\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{\ω}}\\ U_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{\ω}}\\ I_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]---(2-15)$

(2-15) carries out gaussian elimination to formula, obtains:

$\left[\begin{array}{ccc}{Y}_{\mathrm{\ω\ω}}& Y_{\mathrm{\ω\ϵ}}& Y_{\mathrm{\ω\ξ}}\\ & Y_{\mathrm{\ϵ\ϵ}}^{\′}& Y_{\mathrm{\ϵ\ξ}}^{\′}\\ & & 1\end{array}\right]\left[\begin{array}{c}{U}_{\mathrm{\ω}}\\ U_{\mathrm{\ϵ}}\\ U_{\mathrm{\ξ}}\end{array}\right]=\left[\begin{array}{c}{I}_{\mathrm{\ω}}\\ I_{\mathrm{\ϵ}}^{\′}\\ U_{\mathrm{\ξ}}\end{array}\right]---(2-16)$

Wherein, formula (2-16) is electric system Gauss power flow equation.

Expansion (2-16) is:

$\left\{\begin{array}{c}{Y}_{\mathrm{\ω\ω}}{U}_{\mathrm{\ω}}+Y_{\mathrm{\ω\ϵ}}{U}_{\mathrm{\ϵ}}+Y_{\mathrm{\ω\ξ}}{U}_{\mathrm{\ξ}}=I_{\mathrm{\ω}}\\ Y_{\mathrm{\ϵ\ϵ}}^{\′}{U}_{\mathrm{\ϵ}}+Y_{\mathrm{\ϵ\ξ}}^{\′}{U}_{\mathrm{\ξ}}=I_{\mathrm{\ϵ}}^{\′}\end{array}\right.---(2-17)$

The iteration general equation of structure PQ node and the iteration general equation of PV node are:

$\left\{\begin{array}{c}{Y}_{\mathrm{\ω\ω}}{U}_{\mathrm{\ω}}^{(k+1)}+Y_{\mathrm{\ω\ϵ}}{U}_{\mathrm{\ϵ}}^{(k+1)}+{Y_{\mathrm{\ω\ξ}}U}_{\mathrm{\ξ}}=I_{\mathrm{\ω}}^{\left(k\right)}\\ Y_{\mathrm{\ϵ\ϵ}}^{\′}{U}_{\mathrm{\ϵ}}^{(k+1)}+Y_{\mathrm{\ϵ\ξ}}^{\′}{U}_{\mathrm{\ξ}}=I_{\mathrm{\ϵ}}^{\′\left(k\right)}\end{array}\right.---(2-18)$

The first half is the iteration general equation of PQ node in the formula (2-18), and the latter half is the iteration general equation of PV node, the corresponding the k time iterative computation of k.

Can calculate according to node active power, reactive power and the k time iteration magnitude of voltage;

It is known that middle node injects active power, reactive power the unknown.

Step 203, voltage calculation element generate the iterative equation of slow convergence PQ node according to network structure and component parameters;

The voltage calculation element needed at first to determine which node is slow convergence PQ node in the PQ node before the iterative equation according to network structure and component parameters generation slow convergence PQ node.

Concrete, the voltage calculation element at first calculates the converging factor of each PQ node; And according to converging factor order from big to small each PQ node is sorted, and the forward n node that will sort is defined as slow convergence PQ node, wherein, the sum of n=predetermined ratio * PQ node, be about to the node of the predetermined ratio of converging factor maximum in the PQ node as slow convergence PQ node, such as, as slow convergence PQ node, other PQ nodes except slow convergence PQ node then can be called quick convergence PQ node with 20% node of converging factor maximum in all PQ nodes.

Concrete, write the modal equation of n node system as matrix form, wherein subscript E represents all nodes except node i

$\left[\begin{array}{cc}{Y}_{\mathrm{EE}}& Y_{\mathrm{Ei}}\\ Y_{\mathrm{iE}}& Y_{\mathrm{ii}}\end{array}\right]\left[\begin{array}{c}{U}_E\\ U_i\end{array}\right]=\left[\begin{array}{c}{I}_E\\ I_i\end{array}\right]---(2-19)$

To the admittance matrix substitution formula (2-19) of inverting, obtain

$\left[\begin{array}{c}{U}_E\\ U_i\end{array}\right]=\left[\begin{array}{cc}{Z}_{\mathrm{EE}}& Z_{\mathrm{Ei}}\\ Z_{\mathrm{iE}}& Z_{\mathrm{ii}}\end{array}\right]\left[\begin{array}{c}{I}_E\\ I_i\end{array}\right]---(2-20)$

The iterative formula of node i in the process of solving an equation

$U_i^{(k+1)}=Z_{\mathrm{ii}}\frac{P_i-j{Q}_i}{{\left[U_i^{\left(k\right)}\right]}^{*}}+Z_{\mathrm{iE}}{I}_E^{\left(k\right)}---(2-21)$

Investigate node i, the final solution of establishing this trend is

, it satisfies

$U_i^{(\∞)}=Z_{\mathrm{ii}}\frac{P_i-j{Q}_i}{{\left[U_i^{(\∞)}\right]}^{*}}+Z_{\mathrm{iE}}{I}_E^{(\∞)}---(2-22)$

Then the voltage when iteration the k time and k+1 time can be expressed as end value and departure and form, even

$U_i^{(k+1)}=U_i^{(\∞)}+{\mathrm{\ΔU}}_i^{(k+1)}---(2-23)$

$U_i^{\left(k\right)}=U_i^{(\∞)}+{\mathrm{\ΔU}}_i^{\left(k\right)}---(2-24)$

Formula (2-24) can be converted into the form of representing with the final solution of voltage and departure

$U_i^{(\∞)}+{\mathrm{\ΔU}}_i^{(k+1)}=Z_{\mathrm{ii}}\frac{P_i-j{Q}_i}{{[U_i^{(\∞)}+{\mathrm{\ΔU}}_i^{\left(k\right)}]}^{*}}+Z_{\mathrm{iE}}[I_E^{(\∞)}+{\mathrm{\ΔI}}_E^{\left(k\right)}]---(2-25)$

Obtain

${\mathrm{\ΔU}}_i^{(k+1)}=Z_{\mathrm{ii}}\frac{P_i-j{Q}_i}{{[U_i^{(\∞)}+{\mathrm{\ΔU}}_i^{\left(k\right)}]}^{*}{\left[U_i^{(\∞)}\right]}^{*}}{\left[{\mathrm{\ΔU}}_i^{(\∞)}\right]}^{*}+Z_{\mathrm{iE}}{\mathrm{\ΔI}}_E^{\left(k\right)}---(2-26)$

In the case, if satisfy the voltage difference that the voltage difference of other node in the network is significantly less than node i, namely can ignore for back one, simultaneously definition

$p=\frac{\left|U_i^{\left(k\right)}\right|}{\left|U_i^{(\∞)}\right|}---(2-27)$

Then under assumed conditions, can obtain

$\left|{\mathrm{\ΔU}}_i^{(k+1)}\right|=\left|Z_{\mathrm{ii}}\right|\frac{\left|S_i\right|}{{\left|U_i^{(\∞)}\right|}^{2}p}\left|{\mathrm{\ΔU}}_i^{\left(k\right)}\right|---(2-28)$

When The time, when namely the iteration result is near final the solution, p → 1.When trend approached convergence, if ignore the influence of other node errors, the voltage magnitude of node i can be according to slope α _iLinear convergence, wherein,

${\mathrm{\α}}_i=\left|Z_{\mathrm{ii}}\right|\frac{\left|S_i\right|}{{\left|U_i^{(\∞)}\right|}^2}---(2-29)$

Definition α is converging factor, and converging factor is more little, and it is more fast that trend is calculated speed of convergence.

Therefore, when calculating the converging factor of PQ node, can calculate the converging factor of PQ node according to the converging factor computing formula, this converging factor computing formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{(\∞)}\right|}^2};$

Wherein, α is converging factor, and Z is the direct impedance of PQ node, and S is self active power and reactive power sum of PQ node, U ^(∞)For the voltage of PQ node is finally separated.

In addition, the voltage calculation element can generate the impedance matrix of PQ node according to network structure and component parameters, and generates the iterative equation of slow convergence PQ node according to the impedance matrix of PQ node.Its computing method are as follows:

$\left[\begin{array}{c}{U}_A^{(k+1)}\\ U_B^{(k+1)}\end{array}\right]=\left[\begin{array}{cc}{Z}_{\mathrm{AA}}& Z_{\mathrm{AB}}\\ Z_{\mathrm{BA}}& Z_{\mathrm{BB}}\end{array}\right]\left[\begin{array}{c}{I}_A^{\left(k\right)}\\ I_B^{\left(k\right)}\end{array}\right]---(2-30)$

In the formula, the corresponding convergence fast of subscript A PQ node, the corresponding slow convergence PQ of subscript B node.The iterative equation of structure slow convergence PQ node is:

$U_B^{(k+1)}=Z_{\mathrm{BA}}{I}_A^{(k+1)}+Z_{\mathrm{BB}}{I}_B^{\left(k\right)}---(2-31)$

Wherein,

Be the voltage of the slow convergence PQ node of the k+1 time iterative computation gained, Z _BAFor restraining the PQ node fast to the impedance matrix of slow convergence PQ node, Z _BBBe the impedance matrix of slow convergence PQ node self, Be the electric current injection rate IR of the quick convergence PQ node of the k+1 time iterative computation gained,

It is the electric current injection rate IR of the slow convergence PQ node of the k time iterative computation gained.

Step 204 is to the voltage initialize of each node;

Owing to have unknown quantity in the voltage magnitude of each node and the voltage phase angle, therefore, the voltage magnitude initial value with the unknown is made as 1 usually, and the voltage phase angle initial value of the unknown is made as 0.

Step 205 is calculated the electric current injection rate IR of each node according to the voltage of each node;

Concrete, the voltage calculation element can calculate each node current injection rate IR according to following formula,

YU=I （2-32）

Wherein, U is the node voltage column vector; Y is bus admittance matrix; I is that node injects the electric current column vector.

Step 206, the equivalence that calculates the PV node according to the electric current injection rate IR of each node injects electric current;

Concrete, can be with the result of calculation substitution formula (2-16) of step 205, and obtain the equivalent electric current that injects of PV node by each node current injection rate IR of former generation progressively.

Step 207, the actual active power of calculating PV node;

The actual active power of PV node comprises that the PV node injects active power and PV node self active power; Wherein, the PV node injects active power and can inject electric current calculating acquisition by PV node equivalence; PV node self active power is known quantity, and it is included in the component parameters and depends on the PV node voltage.

Concrete, the voltage calculation element can calculate the PV node and injects active power according to the equivalent electric current that injects of PV node, and calculates the actual active power of PV node according to self active power that the PV node injects PV node that active power and component parameters carry.

Step 208 is found the solution the iteration general equation of PV node according to the actual active power of PV node, obtains the voltage of PV node;

Concrete, to arbitrary node i, row are write node active power equation and are:

$U_i\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}})=P_i---(2-33)$

Expansion (2-33), and cosine in the formula partly moved to the equation right side, obtain:

$\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}=\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}---(2-34)$

To formula (2-34) distortion, obtain:

$\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{\mathrm{ij}}(\sin {\mathrm{\δ}}_i\cos {\mathrm{\δ}}_j-\cos {\mathrm{\δ}}_i\sin {\mathrm{\δ}}_j)=\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}---(2-35)$

To formula (2-35) distortion, obtain:

$-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{\mathrm{ij}}\sin {\mathrm{\δ}}_j=\frac{1}{\cos {\mathrm{\δ}}_i}(\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{\mathrm{ij}}\sin {\mathrm{\δ}}_i\cos {\mathrm{\δ}}_j)---(2-36)$

According to formula (2-36) structure phase angle unknown node iterative equation be:

B′(δ)U′(δ)=I′(δ) （2-37）

Wherein, $B^{\′}\left(\mathrm{\δ}\right)=\left[\begin{array}{ccccc}{B}_{1j}& ...& -B_{1i}& ...& -B_{1m}\\ ...& ...& ...& ...& ...\\ -B_{i1}& ...& B_{\mathrm{ij}}& ...& {-B}_{\mathrm{im}}\\ ...& ...& ...& ...& ...\\ -B_{m1}& ...& -B_{\mathrm{mi}}& ...& B_{\mathrm{mj}}\end{array}\right],$ $U^{\′}\left(\mathrm{\δ}\right)=\left[\begin{array}{c}{U}_1\sin {\mathrm{\δ}}_1\\ ...\\ U_i\sin {\mathrm{\δ}}_i\\ ...\\ U_m\sin {\mathrm{\δ}}_m\end{array}\right],$

$I^{\′}\left(\mathrm{\δ}\right)=\left[\begin{array}{c}\frac{1}{\cos {\mathrm{\δ}}_1}(\frac{P_1}{U_1}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{1j}\cos {\mathrm{\δ}}_{1j}-\sin {\mathrm{\δ}}_1\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{1j}\cos {\mathrm{\δ}}_j)\\ ...\\ \frac{1}{\cos {\mathrm{\δ}}_i}(\frac{P_i}{U_i}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}-\sin {\mathrm{\δ}}_i\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{\mathrm{ij}}\cos {\mathrm{\δ}}_j)\\ ...\\ \frac{1}{\cos {\mathrm{\δ}}_m}(\frac{P_m}{U_m}-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{G}_{\mathrm{mj}}\cos {\mathrm{\δ}}_{\mathrm{mj}}-\sin {\mathrm{\δ}}_m\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{U}_j{B}_{\mathrm{mj}}\cos {\mathrm{\δ}}_j)\end{array}\right].$

Can calculate PV node voltage phase angle according to formula (2-36), and obtain the PV node voltage according to PV node voltage phase angle and known PV node voltage amplitude.

Step 209 judges whether PV node voltage changing pattern value changes threshold values less than default PV node voltage, if, enter step 210, otherwise, step 207 returned;

Concrete, the voltage calculation element need carry out iterative computation p time to the voltage of PV node, and wherein, p is the integer greater than 1; When carrying out the 1st iterative computation, find the solution the iteration general equation of PV node according to the actual active power of PV node, obtain to calculate for the 1st time the voltage phase angle of gained, and calculate the voltage of the 1st iterative computation gained according to the voltage magnitude of the voltage phase angle that calculates gained for the 1st time and PV node; When carrying out the p time iterative computation, return step 207, the actual active power of voltage correction PV node according to the p-1 time iterative computation gained, and find the solution the iteration general equation of PV node according to the actual active power of revised PV node, obtain to calculate for the p time the voltage phase angle of gained, and calculate the voltage of the p time iterative computation gained according to the voltage magnitude of the voltage phase angle of the p time calculating gained and PV node; Wherein, during according to the actual active power of the described PV node of voltage correction of the p-1 time iterative computation gained, recomputate earlier self active power of PV node according to the voltage of the p-1 time iterative computation gained, and according to the actual active power of self active power correction PV node of the PV node that recomputates.

Wherein, the change in voltage mould value of calculating for the p time is to calculate the mould value of difference of the voltage of the voltage of gained and the p-1 time calculating gained for the p time;

If the change in voltage mould value of calculating for the p time changes threshold values less than default PV node voltage, then calculate the voltage of gained as the voltage of PV node with the p time;

Change threshold values if the change in voltage mould value of calculating for the p time is not less than default PV node voltage, then return step 207, proceed the p+1 time and calculate.

Step 210 is calculated the PQ node voltage according to the voltage of PV node, the iteration general equation of PQ node and the iterative equation of slow convergence PQ node;

Concrete, in the iteration general equation of voltage calculation element with the voltage substitution PQ node of the PV node of step 209 gained, obtain the voltage of PQ node.

Step 211 judges whether PQ node voltage changing pattern value changes threshold values less than default PQ node voltage, if, enter step 212, otherwise, step 205 returned;

Like PV node voltage compute classes, the voltage calculation element need carry out iterative computation q time to the voltage of PQ node, and wherein, q is the integer greater than 1; When carrying out the 1st iterative computation, find the solution the iteration general equation of PQ node according to the voltage of PV node, obtain to calculate for the 1st time the voltage before the correction of the voltage of quick convergence PQ node of gained and the slow convergence PQ node that calculates gained the 1st time; Revise according to the iterative equation of the slow convergence PQ node voltage before to the correction of the slow convergence PQ node that calculates gained for the 1st time, obtain to calculate for the 1st time the revised voltage of the slow convergence PQ node of gained; The 1st time of obtaining calculated the voltage that the voltage of quick convergence PQ node of gained and the revised voltage that calculates the slow convergence PQ node of gained the 1st time are defined as calculating for the 1st time gained.

When carrying out the q time iterative computation, return step 205, recomputate each node current injection rate IR according to the voltage of the q-1 time iterative computation gained and the voltage of PV node, recomputate the actual active power of PV node according to each the node current injection rate IR that recomputates, and recomputate the voltage of PV node according to the iteration general equation of the actual active power of the PV node that recomputates and PV node, find the solution the iteration general equation of PQ node according to the voltage of the PV node that recomputates, obtain to calculate for the q time the voltage of quick convergence PQ node of gained and the preceding voltage of correction of the slow convergence PQ node that calculates gained the q time; Revise according to the iterative equation of the slow convergence PQ node voltage before to the correction of the slow convergence PQ node that calculates gained for the q time, obtain the revised voltage of the slow convergence PQ node of the q time calculating gained; The revised voltage that the q time of obtaining is calculated the slow convergence PQ node of the voltage of quick convergence PQ node of gained and the q time calculating gained is defined as the voltage of the q time calculating gained.

The voltage calculation element judges whether the change in voltage mould value of the q time calculating changes threshold values less than default PQ node voltage, wherein, the change in voltage mould value of calculating for the q time is the mould value of difference of the voltage of the voltage of the q time calculating gained and the q-1 time iterative computation gained; If the change in voltage mould value of calculating for the q time changes threshold values less than default PQ node voltage, then calculate the voltage of gained as the voltage of PQ node with the q time; Change threshold values if the change in voltage mould value of calculating for the q time is not less than default PQ node voltage, then proceed the q+1 time and calculate.

Wherein, the voltage calculation element is revised according to the iterative equation of the slow convergence PQ node voltage before to the correction of the slow convergence PQ node that calculates gained for the q time, when obtaining to calculate for the q time the revised voltage of slow convergence PQ node of gained, the voltage of quick convergence PQ node that keeps calculating for the q time gained is constant, to calculate voltage before the correction of slow convergence PQ node of gained for the q time as initial value, according to the iterative equation of slow convergence PQ node the voltage of slow convergence PQ node is carried out iterative computation m time, and with the voltage of the slow convergence PQ node of the m time iterative computation gained revised voltage as slow convergence PQ node, wherein, m is the integer more than or equal to 1.

See also formula (2-31), wherein, Z _BAAnd Z _BBFor known, when the voltage of the quick convergence PQ node that keeps the q time calculating gained is constant, have

, at this moment, only need to calculate

Namely can through type (2-31) voltage of slow convergence PQ node be carried out independent iterative computation.Concrete, can be to the independent iteration of voltage of slow convergence PQ node m time, m is predetermined value, and m is the integer more than or equal to 1.

When the 1st voltage to slow convergence PQ node carries out iterative computation, can calculate the electric current injection rate IR that restrains the PQ node fast according to the voltage before the correction of the voltage of the quick convergence PQ node that the q time of the voltage of PQ node is calculated gained and the slow convergence PQ node that calculates gained the q time

Electric current injection rate IR with slow convergence PQ node

, because

, basis then

Can calculate the voltage that the 1st voltage to slow convergence PQ node carries out this slow convergence PQ node of independent iterative computation gained with the iterative equation of slow convergence PQ node.When the m time voltage to slow convergence PQ node carries out iterative computation, can calculate the electric current injection rate IR of slow convergence PQ node according to the voltage that the m-1 time voltage to slow convergence PQ node carries out the slow convergence PQ node of independent iterative computation gained

, and according to

Can calculate the voltage that the m time voltage to slow convergence PQ node carries out this slow convergence PQ node of iterative computation gained with the iterative equation of slow convergence PQ node, the voltage that the m time voltage to slow convergence PQ node is carried out this slow convergence PQ node of iterative computation gained is defined as the revised voltage that the slow convergence PQ node of gained is calculated in to the voltage of PQ node the q time at last.

Because the PV node voltage amplitude in the electric system is known, restrain easily with respect to the PQ node, therefore, the convergence of algorithm performance is mainly determined by the PQ node, and in the PQ node, the node that converging factor is more big, its speed of convergence is more slow, therefore, the core thinking of the embodiment of the invention two steps 210 is: when the PQ node voltage is carried out iterative computation, after each iteration general equation according to the PQ node calculates the voltage of each PQ node, keep the voltage of quick convergence PQ node constant, according to the iterative equation of slow convergence PQ node the voltage of slow convergence PQ node is carried out the iterative computation of pre-determined number separately, the voltage of the slow convergence PQ node of each iterative computation is revised, improve the speed of convergence that whole node voltage calculates with this.

Step 212 is defined as result of calculation with the voltage of PV node and the voltage of PQ node.

PV node voltage and PQ node voltage that the voltage calculation element will finally obtain are exported as result of calculation.

Can run into a large amount of matrixes and calculating thereof in the computing method that present embodiment provides.According to electric network composition as can be known, having only the small part element in these matrixes is non-null matrix.Therefore, during calculating, only calculate nonzero element, do not calculate neutral element, can improve the computing velocity of algorithm greatly.Simultaneously, in data storage procedure, only store nonzero element, also save memory greatly.

In the practical application, adopt the storage format storage data of triangle retrieval usually, such as certain matrix A, according to the last triangular portions nonzero element of row storage A, according to the following triangular portions nonzero element of row storage A.If A is n * n rank square formation, its storage mode is as follows:

U---deposit the value of non-zero entry of the last triangular portions of A, by row storage successively;

JU---deposit the row number of non-zero entry of the last triangular portions of A;

IU---deposit and go up the position of first non-zero entry of the every row of triangular portions in U among the A;

L---by the value of triangle nonzero element under being listed as among the storage A;

IL---by the row of triangle nonzero element number down among the row storages A;

JL---deposit the following position of first non-zero entry of the every row of triangular portions in L among the A;

D---the value of the diagonal element of storage A, its retrieval subscript does not need storage.

In sum, the Electric Power System Node Voltage computing method that the embodiment of the invention two provides, the iteration general equation that generates the PV node by network structure and component parameters according to the electric system that receives, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node, and calculate the voltage of PV node according to the iteration general equation of the actual active power of PV node and PV node, further according to the voltage of PV node, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node calculates the voltage of PQ node, reaches the raising node voltage and calculates constringent purpose; In addition, the Electric Power System Node Voltage computing method that the embodiment of the invention two provides, by at every turn after the iteration general equation according to the PQ node calculates the voltage of each PQ node, according to the iterative equation of slow convergence PQ node the voltage of slow convergence PQ node is carried out the iterative computation of pre-determined number separately, reach the purpose that improves the speed of convergence that whole node voltage calculates.

Embodiment three

Please refer to Fig. 3, it shows the structure drawing of device of the Electric Power System Node Voltage calculation element that the embodiment of the invention three provides.This Electric Power System Node Voltage calculation element can be used for the voltage of each node of calculating electric system.This Electric Power System Node Voltage calculation element can comprise:

Acquisition module 301, be used for obtaining network structure and the component parameters of each node of electric system, node comprises at least: at least one PV node and at least one PQ node, self active power and the voltage magnitude of PV node are known, self active power and the reactive power of PQ node are known, include at least one slow convergence PQ node in the PQ node;

The first equation generation module 302 is used for iteration general equation that the network structure that gets access to according to acquisition module 301 and component parameters generate this PV node and the iteration general equation of this PQ node;

The second equation generation module 303 is for the iterative equation of the network structure that gets access to according to acquisition module 301 and component parameters generation slow convergence PQ node;

Electric current computing module 304 is used for calculating according to the voltage initial value of each node that sets in advance the electric current injection rate IR of each node;

Active power is calculated module 305, calculates the actual active power of this PV node for the electric current injection rate IR of each node that calculates according to electric current computing module 304;

The first voltage computing module 306, the iteration general equation that is used for the PV node that actual active power and the first equation generation module 302 according to this PV node generate calculates the voltage of this PV node;

The second voltage computing module 307, the iterative equation that is used for the iteration general equation of the voltage of the PV node that calculates according to the first voltage computing module 306, PQ node that the first equation generation module 302 generates and the slow convergence PQ node that the second equation generation module 303 generates calculates the voltage of this PQ node.

In sum, the Electric Power System Node Voltage calculation element that the embodiment of the invention three provides, the iteration general equation that generates the PV node by network structure and component parameters according to the electric system that receives, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node, and calculate the voltage of PV node according to the iteration general equation of the actual active power of PV node and PV node, further according to the voltage of PV node, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node calculates the voltage of PQ node, reaches the raising node voltage and calculates constringent purpose.

Embodiment four

For the Electric Power System Node Voltage calculation element that the embodiment of the invention three is provided is described further, please refer to Fig. 4, it shows the structure drawing of device of the Electric Power System Node Voltage calculation element that the embodiment of the invention four provides.This Electric Power System Node Voltage calculation element can comprise:

Acquisition module 301, be used for obtaining network structure and the component parameters of each node of electric system, node comprises at least: at least one PV node and at least one PQ node, self active power and the voltage magnitude of PV node are known, self active power and the reactive power of PQ node are known, include at least one slow convergence PQ node in the PQ node;

The first equation generation module 302, the network structure and the component parameters that are used for getting access to according to acquisition module 301 generate the iteration general equation of PV node and the iteration general equation of PQ node;

The second equation generation module 303 is for the iterative equation of the network structure that gets access to according to acquisition module 301 and component parameters generation slow convergence PQ node;

Electric current computing module 304 is used for calculating according to the voltage initial value of each node that sets in advance the electric current injection rate IR of each node;

Active power is calculated module 305, calculates the actual active power of PV node for the electric current injection rate IR of each node that calculates according to electric current computing module 304;

The first voltage computing module 306, the iteration general equation that is used for the PV node that actual active power and the first equation generation module 302 according to the PV node generate calculates the voltage of PV node;

The second voltage computing module 307, the iterative equation that is used for the iteration general equation of the voltage of the PV node that calculates according to the first voltage computing module 306, PQ node that the first equation generation module 302 generates and the slow convergence PQ node that the second equation generation module 303 generates calculates the voltage of PQ node.

This device also comprises:

Converging factor computing module 308 is used for calculating the converging factor of this PQ node before network structure that the second equation generation module 303 gets access to according to acquisition module 301 and component parameters generate the iterative equation of slow convergence PQ node;

Node determination module 309, the converging factor order from big to small that is used for calculating according to converging factor computing module 308 sorts to the PQ node, and the forward n node that will sort is defined as slow convergence PQ node, the sum of n=predetermined ratio * PQ node.

Converging factor computing module 308 is used for the converging factor according to converging factor computing formula calculating PQ node, and this converging factor computing formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{(\∞)}\right|}^2};$

Wherein, α is converging factor, and Z is the direct impedance of PQ node, and S is self active power and reactive power sum of PQ node, U ^(∞)For the voltage of PQ node is finally separated.

The second equation generation module 303 comprises:

Impedance matrix generation unit 3031 is used for the impedance matrix that the network structure obtained according to acquisition module 301 and component parameters generate this PQ node;

Iterative equation generation unit 3032, the impedance matrix that is used for the PQ node that generates according to impedance matrix generation unit 3031 generates the iterative equation of slow convergence PQ node;

Wherein, the iterative equation of this slow convergence PQ node is:

$U_B^{(k+1)}=Z_{\mathrm{BA}}{I}_A^{(k+1)}+Z_{\mathrm{BB}}{I}_B^{\left(k\right)};$

Wherein,

Be the voltage of the slow convergence PQ node of the k+1 time iterative computation gained, Z _BAFor restraining the PQ node fast to the impedance matrix of slow convergence PQ node, Z _BBBe the impedance matrix of slow convergence PQ node self,

Be the electric current injection rate IR of the quick convergence PQ node of the k+1 time iterative computation gained,

Be the electric current injection rate IR of the slow convergence PQ node of the k time iterative computation gained, wherein, restrain the PQ node fast and be the PQ node except slow convergence PQ node.

The second voltage computing module 307 comprises:

Voltage computing unit 3071 is used for the voltage of PQ node is carried out iterative computation q time, and wherein, q is the integer greater than 1;

Voltage computing unit 3071 comprises:

Voltage computation subunit 3071a, be used for when carrying out the 1st iterative computation, the voltage of the PV node that calculates according to the first voltage computing module 306 is found the solution the iteration general equation of PQ node, obtains to calculate for the 1st time the voltage before the correction of the voltage of quick convergence PQ node of gained and the slow convergence PQ node that calculates gained the 1st time;

Voltage correction subelement 3071b, voltage before the correction of the slow convergence PQ node that calculates gained for the 1st time that is used for according to the iterative equation of slow convergence PQ node voltage computation subunit 3071a being obtained is revised, and obtains to calculate for the 1st time the revised voltage of the slow convergence PQ node of gained;

Voltage is determined subelement 3071c, and the revised voltage that be used for voltage computation subunit 3071a is obtained the 1st time calculate that the voltage of quick convergence PQ node of gained and voltage correction subelement 3071b obtain the 1st time calculates the slow convergence PQ node of gained is defined as calculating for the 1st time the voltage of gained;

When carrying out the q time iterative computation, electric current computing module 304 also is used for determining that according to voltage the voltage of the voltage of the q-1 time iterative computation gained that subelement 3071c determines and the PV node that the first voltage computing module 306 calculates recomputates the electric current injection rate IR of each node;

Active power is calculated module 305, also recomputates the actual active power of PV node for the electric current injection rate IR of each node that recomputates according to electric current computing module 304;

The first voltage computing module 306 also is used for recomputating according to the iteration general equation that active power is calculated the actual active power of the PV node that module 305 recomputates and PV node the voltage of PV node;

Voltage computation subunit 3071a, be used for when carrying out the q time iterative computation, the voltage of the PV node that recomputates according to the first voltage computing module 306 is found the solution the iteration general equation of PQ node, obtains to calculate for the q time the voltage of quick convergence PQ node of gained and the preceding voltage of correction of the slow convergence PQ node that calculates gained the q time;

Voltage correction subelement 3071b, voltage before the correction of the slow convergence PQ node that calculates gained for the q time that is used for according to the iterative equation of slow convergence PQ node voltage computation subunit 3071a being obtained is revised, and obtains the revised voltage of the slow convergence PQ node of the q time calculating gained;

Voltage is determined subelement 3071c, and the revised voltage that be used for voltage computation subunit 3071a is obtained the q time calculates the slow convergence PQ node of the voltage of quick convergence PQ node of gained and the q time calculating gained that voltage correction subelement 3071b obtains is defined as the voltage of the q time calculating gained;

The second voltage computing module 307 also comprises:

Judging unit 3072, be used for judging whether the change in voltage mould value of the q time calculating changes threshold values less than default PQ node voltage, wherein, the change in voltage mould value of calculating for the q time is the mould value that voltage is determined the difference of the voltage of the q time calculating gained that subelement 3071c determines and the voltage that voltage is determined the q-1 time iterative computation gained that subelement 3071c determines;

Voltage determining unit 3073 changes threshold values if judge the change in voltage mould value of the q time calculating for judging unit 3072 less than default PQ node voltage, then the voltage of this q time calculating gained is defined as the voltage of PQ node;

Voltage computing unit 3071 is judged the change in voltage mould value of calculating for the q time and is not less than default PQ node voltage variation threshold values if be used for judging unit 3073, then proceeds iterative computation the q+1 time.

Voltage correction subelement 3071b, be used for to keep the voltage of quick convergence PQ node of the q time calculating gained that voltage computation subunit 3071a calculates constant, voltage before the correction of the slow convergence PQ node that calculates gained for the q time that voltage computation subunit 3071a is calculated is as initial value, according to the iterative equation of slow convergence PQ node the voltage of slow convergence PQ node is carried out iterative computation m time, and with the voltage of the slow convergence PQ node of the m time iterative computation gained revised voltage as slow convergence PQ node, wherein, m is the integer more than or equal to 1.

Concrete, see also formula (2-31), wherein, Z _BAAnd Z _BBFor known, when the voltage of the quick convergence PQ node that keeps the q time calculating gained is constant, have

, at this moment, only need to calculate Namely can through type (2-31) voltage of slow convergence PQ node be carried out independent iterative computation.Concrete, can be to the independent iteration of voltage of slow convergence PQ node m time, m is predetermined value, and m is the integer more than or equal to 1.

When the 1st voltage to slow convergence PQ node carried out iterative computation, voltage correction subelement 3071b can calculate the electric current injection rate IR that restrains the PQ node fast according to the voltage before the correction of the voltage of the quick convergence PQ node that the q time of the voltage of PQ node is calculated gained and the slow convergence PQ node that calculates gained the q time

Electric current injection rate IR with slow convergence PQ node

, because

, voltage correction subelement 3071b basis then

Can calculate the voltage that the 1st voltage to slow convergence PQ node carries out this slow convergence PQ node of independent iterative computation gained with the iterative equation of slow convergence PQ node.When the m time voltage to slow convergence PQ node carried out iterative computation, voltage correction subelement 3071b can calculate the electric current injection rate IR of slow convergence PQ node according to the voltage that the m-1 time voltage to slow convergence PQ node carries out the slow convergence PQ node of independent iterative computation gained

, and according to

Can calculate the voltage that the m time voltage to slow convergence PQ node carries out this slow convergence PQ node of iterative computation gained with the iterative equation of slow convergence PQ node, the voltage that last voltage correction subelement 3071b carries out this slow convergence PQ node of iterative computation gained with the m time voltage to slow convergence PQ node is defined as the revised voltage to the slow convergence PQ node of the q time calculating gained of the voltage of PQ node.

In sum, the Electric Power System Node Voltage calculation element that the embodiment of the invention four provides, the iteration general equation that generates the PV node by network structure and component parameters according to the electric system that receives, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node, and calculate the voltage of PV node according to the iteration general equation of the actual active power of PV node and PV node, further according to the voltage of PV node, the iterative equation of the iteration general equation of PQ node and slow convergence PQ node calculates the voltage of PQ node, reaches the raising node voltage and calculates constringent purpose; In addition, the Electric Power System Node Voltage calculation element that the embodiment of the invention four provides, by at every turn after the iteration general equation according to the PQ node calculates the voltage of each PQ node, according to the iterative equation of slow convergence PQ node the voltage of slow convergence PQ node is carried out the iterative computation of pre-determined number separately, reach the purpose that improves the speed of convergence that whole node voltage calculates.

Need to prove: the device that the Electric Power System Node Voltage that above-described embodiment provides is calculated is when calculating the voltage of each node of electric system, only the division with above-mentioned each functional module is illustrated, in the practical application, can as required the above-mentioned functions distribution be finished by different functional modules, the inner structure that is about to device is divided into different functional modules, to finish all or part of function described above.In addition, the Electric Power System Node Voltage calculation element that above-described embodiment provides and Electric Power System Node Voltage computing method embodiment belong to same design, and its specific implementation process sees method embodiment for details, repeats no more here.

The invention described above embodiment sequence number does not represent the quality of embodiment just to description.

The all or part of step that one of ordinary skill in the art will appreciate that realization above-described embodiment can be finished by hardware, also can instruct relevant hardware to finish by program, described program can be stored in a kind of computer-readable recording medium, the above-mentioned storage medium of mentioning can be ROM (read-only memory), disk or CD etc.

The above only is preferred embodiment of the present invention, and is in order to limit the present invention, within the spirit and principles in the present invention not all, any modification of doing, is equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (12)

1. Electric Power System Node Voltage computing method is characterized in that, described method comprises:

Obtain network structure and the component parameters of each node of electric system, described node comprises at least: at least one PV node and at least one PQ node, self active power and the voltage magnitude of described PV node are known, self active power and the reactive power of described PQ node are known, include at least one slow convergence PQ node in the described PQ node;

Generate the iteration general equation of described PV node and the iteration general equation of described PQ node according to described network structure and component parameters, and generate the iterative equation of described slow convergence PQ node according to described network structure and component parameters;

Calculate the electric current injection rate IR of each node according to the voltage initial value of each node that sets in advance;

Calculate the actual active power of described PV node according to the electric current injection rate IR of described each node, and calculate the voltage of described PV node according to the iteration general equation of the actual active power of described PV node and described PV node;

Calculate the voltage of described PQ node according to the iterative equation of the iteration general equation of the voltage of described PV node, described PQ node and described slow convergence PQ node.

2. method according to claim 1 is characterized in that, describedly generates before the iterative equation of described slow convergence PQ node according to described network structure and component parameters, and described method also comprises:

Calculate the converging factor of described PQ node;

According to described converging factor order from big to small described PQ node is sorted, and the forward n node that will sort is defined as described slow convergence PQ node, the sum of the described PQ node of described n=predetermined ratio *.

3. method according to claim 2 is characterized in that, the converging factor of the described PQ node of described calculating comprises:

Calculate the converging factor of described PQ node according to the converging factor computing formula, described converging factor computing formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{(\∞)}\right|}^2};$

Wherein, α is converging factor, and Z is the direct impedance of PQ node, and S is self active power and reactive power sum of PQ node, U ^(∞)For the voltage of PQ node is finally separated.

4. according to the arbitrary described method of claim 1 to 3, it is characterized in that, describedly generate the iterative equation of described slow convergence PQ node according to described network structure and component parameters, comprising:

Generate the impedance matrix of described PQ node according to described network structure and component parameters;

Generate the iterative equation of described slow convergence PQ node according to the impedance matrix of described PQ node;

Wherein, the iterative equation of described slow convergence PQ node is:

$U_B^{(k+1)}=Z_{\mathrm{BA}}{I}_A^{(k+1)}+Z_{\mathrm{BB}}{I}_B^{\left(k\right)};$

Wherein,

Be the voltage of the described slow convergence PQ node of the k+1 time iterative computation gained, described Z _BAFor restraining the PQ node fast to the impedance matrix of described slow convergence PQ node, described Z _BBBe the impedance matrix of described slow convergence PQ node self,

Be the electric current injection rate IR of the described quick convergence PQ node of the k+1 time iterative computation gained,

Be the electric current injection rate IR of the described slow convergence PQ node of the k time iterative computation gained, wherein, described quick convergence PQ node is the PQ node except described slow convergence PQ node.

5. method according to claim 4 is characterized in that, the iteration general equation of described voltage according to described PV node, described PQ node and the iterative equation of described slow convergence PQ node calculate the voltage of described PQ node, comprising:

Voltage to described PQ node carries out iterative computation q time, and wherein, q is the integer greater than 1;

When carrying out the 1st iterative computation, find the solution the iteration general equation of described PQ node according to the voltage of described PV node, obtain to calculate for the 1st time the voltage before the correction of the voltage of described quick convergence PQ node of gained and the described slow convergence PQ node that calculates gained the 1st time; Revise according to the iterative equation of the described slow convergence PQ node voltage before to the correction of the described slow convergence PQ node that calculates gained for the 1st time, obtain to calculate for the 1st time the revised voltage of the described slow convergence PQ node of gained; The 1st time of obtaining calculated the voltage that the voltage of described quick convergence PQ node of gained and the revised voltage that calculates the described slow convergence PQ node of gained the 1st time are defined as calculating for the 1st time gained;

When carrying out the q time iterative computation, recomputate the electric current injection rate IR of each node according to the voltage of the voltage of the q-1 time iterative computation gained and described PV node, recomputate the actual active power of described PV node according to the electric current injection rate IR of described each node that recomputates, and recomputate the voltage of described PV node according to the iteration general equation of the actual active power of the described PV node that recomputates and described PV node, find the solution the iteration general equation of described PQ node according to the voltage of the described PV node that recomputates, obtain to calculate for the q time the voltage of described quick convergence PQ node of gained and the preceding voltage of correction of the described slow convergence PQ node that calculates gained the q time; Revise according to the iterative equation of the described slow convergence PQ node voltage before to the correction of the described slow convergence PQ node that calculates gained for the q time, obtain the revised voltage of the described slow convergence PQ node of the q time calculating gained; The revised voltage that the q time of obtaining is calculated the described slow convergence PQ node of the voltage of described quick convergence PQ node of gained and the q time calculating gained is defined as the voltage of the q time calculating gained;

Whether the change in voltage mould value of judging the q time calculating changes threshold values less than default PQ node voltage, wherein, the mould value of the difference of the voltage of the described change in voltage mould value of calculating for the q time voltage that is described the q time calculating gained and described the q-1 time iterative computation gained;

If the change in voltage mould value of described the q time calculating changes threshold values less than default PQ node voltage, then the voltage of described the q time calculating gained is defined as the voltage of described PQ node;

Change threshold values if the change in voltage mould value of described the q time calculating is not less than default PQ node voltage, then proceed iterative computation the q+1 time.

6. method according to claim 5, it is characterized in that, the voltage of described iterative equation according to described slow convergence PQ node before to the correction of the described slow convergence PQ node that calculates gained for the q time is revised, obtain the revised voltage of the described slow convergence PQ node of the q time calculating gained, comprising:

Keep the voltage of the described described quick convergence PQ node that calculates gained for the q time constant, to calculate voltage before the correction of described slow convergence PQ node of gained for the q time as initial value, according to the iterative equation of described slow convergence PQ node the voltage of described slow convergence PQ node is carried out iterative computation m time, and with the voltage of the described slow convergence PQ node of the m time iterative computation gained revised voltage as described slow convergence PQ node, wherein, m is the integer more than or equal to 1.

7. an Electric Power System Node Voltage calculation element is characterized in that, described device comprises:

Acquisition module, be used for obtaining network structure and the component parameters of each node of electric system, described node comprises at least: at least one PV node and at least one PQ node, self active power and the voltage magnitude of described PV node are known, self active power and the reactive power of described PQ node are known, include at least one slow convergence PQ node in the described PQ node;

The first equation generation module is used for iteration general equation that the network structure that gets access to according to described acquisition module and component parameters generate described PV node and the iteration general equation of described PQ node;

The second equation generation module is used for the iterative equation that the network structure that gets access to according to described acquisition module and component parameters generate described slow convergence PQ node;

The electric current computing module is used for calculating according to the voltage initial value of each node that sets in advance the electric current injection rate IR of each node;

Active power is calculated module, calculates the actual active power of described PV node for the electric current injection rate IR of each node that calculates according to described electric current computing module;

The first voltage computing module, the iteration general equation that is used for the PV node that actual active power and the described first equation generation module according to described PV node generate calculates the voltage of described PV node;

The second voltage computing module, the iterative equation that is used for the iteration general equation of the voltage of the PV node that calculates according to the described first voltage computing module, PQ node that the described first equation generation module generates and the slow convergence PQ node that the described second equation generation module generates calculates the voltage of described PQ node.

8. device according to claim 7 is characterized in that, described device also comprises:

The converging factor computing module is used for calculating the converging factor of described PQ node before network structure that the described second equation generation module gets access to according to described acquisition module and component parameters generate the iterative equation of described slow convergence PQ node;

The node determination module, the converging factor order from big to small that is used for calculating according to described converging factor computing module sorts to described PQ node, and the forward n node that will sort is defined as described slow convergence PQ node, the sum of the described PQ node of described n=predetermined ratio *.

9. device according to claim 8 is characterized in that, described converging factor computing module, and for the converging factor of calculating described PQ node according to the converging factor computing formula, described converging factor computing formula is:

$\mathrm{\α}=\left|Z\right|\frac{\left|S\right|}{{\left|U^{(\∞)}\right|}^2};$

Wherein, α is converging factor, and Z is the direct impedance of PQ node, and S is self active power and reactive power sum of PQ node, U ^(∞)For the voltage of PQ node is finally separated.

10. according to the arbitrary described device of claim 7 to 9, it is characterized in that the described second equation generation module comprises:

The impedance matrix generation unit is used for generating according to described network structure and component parameters the impedance matrix of described PQ node;

The iterative equation generation unit, the impedance matrix that is used for the PQ node that generates according to described impedance matrix generation unit generates the iterative equation of described slow convergence PQ node;

Wherein, the iterative equation of described slow convergence PQ node is:

$U_B^{(k+1)}=Z_{\mathrm{BA}}{I}_A^{(k+1)}+Z_{\mathrm{BB}}{I}_B^{\left(k\right)};$

Wherein,

Be the voltage of the described slow convergence PQ node of the k+1 time iterative computation gained, described Z _BAFor restraining the PQ node fast to the impedance matrix of described slow convergence PQ node, described Z _BBBe the impedance matrix of described slow convergence PQ node self,

Be the electric current injection rate IR of the described quick convergence PQ node of the k+1 time iterative computation gained,

Be the electric current injection rate IR of the described slow convergence PQ node of the k time iterative computation gained, wherein, described quick convergence PQ node is the PQ node except described slow convergence PQ node.

11. device according to claim 10 is characterized in that, the described second voltage computing module comprises:

The voltage computing unit is used for the voltage of described PQ node is carried out iterative computation q time, and wherein, q is the integer greater than 1;

Described voltage computing unit comprises:

The voltage computation subunit, be used for when carrying out the 1st iterative computation, the voltage of the PV node that calculates according to the described first voltage computing module is found the solution the iteration general equation of described PQ node, obtains to calculate for the 1st time the voltage before the correction of the voltage of described quick convergence PQ node of gained and the described slow convergence PQ node that calculates gained the 1st time;

Voltage correction subelement, voltage before the correction of the described slow convergence PQ node that calculates gained for the 1st time that is used for according to the iterative equation of described slow convergence PQ node described voltage computation subunit being obtained is revised, and obtains to calculate for the 1st time the revised voltage of the described slow convergence PQ node of gained;

Voltage is determined subelement, and the revised voltage that be used for described voltage computation subunit is obtained the 1st time calculate that the voltage of described quick convergence PQ node of gained and described voltage correction subelement obtain the 1st time calculates the described slow convergence PQ node of gained is defined as calculating for the 1st time the voltage of gained;

When carrying out the q time iterative computation, described electric current computing module also is used for determining that according to described voltage the voltage of the voltage of the q-1 time iterative computation gained that subelement is determined and the PV node that the described first voltage computing module calculates recomputates the electric current injection rate IR of each node;

Described active power is calculated module, also recomputates the actual active power of described PV node for the electric current injection rate IR of described each node that recomputates according to described electric current computing module;

The described first voltage computing module also is used for recomputating according to the iteration general equation that described active power is calculated the actual active power of the described PV node that module recomputates and described PV node the voltage of described PV node;

Described voltage computation subunit, be used for when carrying out the q time iterative computation, the voltage of the described PV node that recomputates according to the described first voltage computing module is found the solution the iteration general equation of described PQ node, obtains to calculate for the q time the voltage of described quick convergence PQ node of gained and the preceding voltage of correction of the described slow convergence PQ node that calculates gained the q time;

Described voltage correction subelement, voltage before the correction of the described slow convergence PQ node that calculates gained for the q time that is used for according to the iterative equation of described slow convergence PQ node described voltage computation subunit being obtained is revised, and obtains the revised voltage of the described slow convergence PQ node of the q time calculating gained;

Described voltage is determined subelement, and the revised voltage that be used for described voltage computation subunit is obtained the q time calculates the described slow convergence PQ node of the voltage of described quick convergence PQ node of gained and the q time calculating gained that described voltage correction subelement obtains is defined as the voltage of the q time calculating gained;

The described second voltage computing module also comprises:

Judging unit, be used for judging whether the change in voltage mould value of the q time calculating changes threshold values less than default PQ node voltage, wherein, the change in voltage mould value of described the q time calculating is the mould value that described voltage is determined the difference of the voltage of the q time calculating gained that subelement is determined and the voltage that described voltage is determined the q-1 time iterative computation gained that subelement is determined;

The voltage determining unit changes threshold values if go out the change in voltage mould value of described the q time calculating for described judgment unit judges less than default PQ node voltage, then the voltage of described the q time calculating gained is defined as the voltage of described PQ node;

Described voltage computing unit is not less than default PQ node voltage variation threshold values if go out the change in voltage mould value of calculating for the q time for described judgment unit judges, then proceeds iterative computation the q+1 time.

12. device according to claim 11, it is characterized in that, described voltage correction subelement, be used for to keep the voltage of described quick convergence PQ node of the q time calculating gained that described voltage computation subunit calculates constant, voltage before the correction of the described slow convergence PQ node that calculates gained for the q time that described voltage computation subunit is calculated is as initial value, according to the iterative equation of described slow convergence PQ node the voltage of described slow convergence PQ node is carried out iterative computation m time, and with the voltage of the described slow convergence PQ node of the m time iterative computation gained revised voltage as described slow convergence PQ node, wherein, m is the integer more than or equal to 1.

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