CN102005758A - Internal network actual information based method for external network static equivalents of two ports - Google Patents

Abstract

The invention provides an internal network actual information based method for external network static equivalents of two ports, which comprises the following steps of: (1) establishing a simplified Ward equivalent circuit (SWM for short) of an external network; (2) establishing a multiperiod least-squares estimation model of an SWM equivalent parameter according to boundary nodes and state information of an internal network in multiple periods, and solving the SWM equivalent parameter by using Gauss-Newton method; (3) establishing a Ward equivalent circuit of an expanded voltage source branch (EWM for short) of the same external network; (4) establishing a multiperiod least-squares estimation model of an EWM equivalent parameter according to the constrain relation between the SWM parameter and the EWM parameter, the boundary nodes and the state information of the internal network in multiple periods, and solving the EWM equivalent parameter by using a Gauss-Newton method, wherein the obtained EWM is the final equivalent circuit of the external network. The method has the advantages of no need of any information of the external network, high engineering adaptability and very high equivalent accuracy no matter the tidal current of the internal network changes greatly or slightly.

Description

A kind of two-port outer net Static Equivalent method based on the Intranet real measured data

Technical field

The invention belongs to electric power system Static Equivalent technical field, particularly a kind of two-port outer net Static Equivalent method based on the Intranet real measured data.

Background technology

To lose interest in or unobservable part in the common requirement of line computation of extensive multizone interconnected network, promptly outer mesh portions is carried out equivalence.Wherein, the equivalence method that is adopted during stable state behavior such as research electric power system tide and static security is called the Static Equivalent method.

Traditional Static Equivalent method has Ward equivalence method, REI equivalence method and various improving one's methods, and cushions the expansion Ward equivalent method of netting as keeping, etc.The something in common of these methods is to require complete model of known outer net and state information.Yet, under a lot of situations, can not realize complete exchanges data between each subsystem.Particularly under Power Market, interconnection subsystem generally can be protected the electric network data of oneself, and for the internal electric network of certain specific subsystem or primary study, external system or outer net are "black box"es.In this case, above-mentioned Static Equivalent method all can not be suitable for.

Therefore, having only under the situation of intranet data, how to realize effective equivalence of "black box" outer net, becoming the key issue that the assurance Intranet is independently calculated accuracy.

The existing Static Equivalent method of only utilizing intranet data, the type according to being suitable for outer net can be divided into following two classes:

(1) is applicable to the equivalence method of single port outer net.These class methods are come equivalent external electrical network with the Dai Weinan circuit usually, and the multi-period injecting power and the voltage real measured data of application boundary node are set up measurement equation, and then realize the estimation of equivalent parameters.The shortcoming of these class methods is the equivalences that are only applicable to the single port outer net.

(2) be applicable to the equivalence method of multiport outer net.Debs AS is at Estimation of external network equivalents from internal system data[J] .IEEE Trans on PAS, 1975, PAS-94 (2): proposed a kind of external network equivalent method among the 273-279 based on intranet data.This method is come equivalent outer net with conventional Ward model, and equivalent parameters comprises the injecting power of boundary node and admittance over the ground, and the admittance of equivalent branch road between the boundary node; The injecting power of supposing Intranet branch breaking front and back boundary node is constant, sets up the virtual measurement equation by the measurement information that the Intranet branch road repeatedly cut-offs, and determines the equivalent parameters of outer net based on least-squares estimation.The shortcoming of this method be must depend on the Intranet branch road repeatedly cut-off operation, applicable elements is very harsh, the engineering practical value is limited.

Summary of the invention

The objective of the invention is in order to overcome above-mentioned the deficiencies in the prior art, propose a kind of two-port outer net Static Equivalent method based on the Intranet real measured data.

The two-port outer net Static Equivalent method that the present invention proposes based on the Intranet real measured data, its step is as follows:

Step 1: set up the simplification Ward equivalent circuit of two-port outer net, abbreviate SWM as.The equivalent parameters of SWM is the equivalent injecting power P of boundary node l _l+ jQ _l, the equivalent injecting power P of boundary node k _k+ jQ _k, and the electricity that connects the equivalent branch road of two boundary nodes is led g _LkWith susceptance b _Lk

Step 2: the equivalent parameters of finding the solution SWM.According to the real measured data of a plurality of period boundary nodes and Intranet, set up the multi-period least-squares estimation model of SWM equivalent parameters, and use gauss-newton method and find the solution the estimated value of SWM equivalent parameters, specify as follows:

According to t period (t=1,2 ..., N, down with) boundary node and the voltage magnitude of Intranet node and the measurement amount of phase angle, set up the injecting power equation of two boundary nodes:

$0=P_l-V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t+B_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(1\right)$

$0=Q_l-V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t-B_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(2\right)$

$0=P_k-V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t+B_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(3\right)$

$0=Q_k-V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t-B_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(4\right)$

In the formula, P _lAnd Q _lThe equivalence that is respectively boundary node l injects active power and reactive power; P _kAnd Q _kThe equivalence that is respectively boundary node k injects active power and reactive power;

Be the measurement amount of the voltage magnitude of node j, subscript t represents t period, down with;

With

Be respectively the measurement amount of the voltage phase angle of node i and node j; G _Lj, G _KjReal part for the node admittance matrix corresponding element; B _Lj, B _KjImaginary part for the node admittance matrix corresponding element; Φ _lAnd Φ _kRepresent the node set that directly links to each other with boundary node l and boundary node k respectively.

Following general type can be write as in formula (1)～(4):

$0=f_m^t\left(x_S\right),m=\mathrm{1,2,3,4}---\left(5\right)$

In the formula, x _S=[P _l, Q _l, P _k, Q _k, g _Lk, b _Lk] be the equivalent parameters vector of SWM,

The general expression formula of segmentation (1)～(4) when being t, then the multi-period least-squares estimation model of SWM equivalent parameters is:

$J=\min \underset{t=1}{\overset{N}{\mathrm{\Σ}}}\underset{m=1}{\overset{4}{\mathrm{\Σ}}}{\left[f_m^t\left(x_S\right)\right]}^2---\left(6\right)$

In the formula, hop count when N is, N 〉=3.

Use gauss-newton method and find the solution formula (6), solve the estimated value x of SWM equivalent parameters _S

Step 3: to the described same two-port outer net of step 1, set up expansion voltage source branch road Ward equivalent circuit, abbreviate EWM as.EWM substitutes the equivalent injecting power of boundary node among the SWM with the branch road of voltage source series impedance.The equivalent parameters of EWM is the voltage magnitude E of voltage source in two expansion branch roads _l, E _kAnd phase angle theta ^t _l, θ ^t _k, the electricity of two expansion branch roads is led g _l, g _kWith susceptance b _l, b _k, and the electricity that connects the equivalent branch road of two boundary nodes is led g ' _LkWith susceptance b ' _Lk

Step 4: the equivalent parameters of finding the solution EWM.SWM and EWM are two kinds of equivalent circuits of same two-port outer net, the equivalent parameters of SWM and EWM satisfies certain restriction relation, according to these restriction relations and with step 2 in the boundary node of identical period and the real measured data of Intranet, set up the multi-period least-squares estimation model of EWM equivalent parameters, and using the equivalent parameters that gauss-newton method is found the solution EWM, gained EWM is the final Equivalent Model of two-port outer net.Specify as follows:

According to the restriction relation of SWM and EWM equivalent parameters, set up following equation:

$0\≈g_{\mathrm{lk}}-g_{\mathrm{lk}}^{\′}---\left(7\right)$

$0\≈b_{\mathrm{lk}}-b_{\mathrm{lk}}^{\′}---\left(8\right)$

$0\≈P_l+{\left(V_l^t\right)}^2{g}_l-V_l^t{E}_l[g_l\cos ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)+b_l\sin ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)]---\left(9\right)$

$0\≈Q_l-{\left(V_l^t\right)}^2{b}_l+V_l^t{E}_l[b_l\cos ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)-g_l\sin ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)]---\left(10\right)$

$0\≈P_k+{\left(V_k^t\right)}^2{g}_k-V_k^t{E}_k[g_k\cos ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)+b_k\sin ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)]---\left(11\right)$

$0\≈Q_k-{\left(V_k^t\right)}^2{b}_k+V_k^t{E}_k[b_k\cos ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)-g_k\sin ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)]---\left(12\right)$

In addition, according to t period (t=1,2 ..., N, down with) boundary node and the voltage magnitude of Intranet node and the measurement amount of phase angle, set up the injecting power equation of two boundary nodes:

$0=V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t+B_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(13\right)$

$0=V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t-B_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(14\right)$

$0=V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t+B_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(15\right)$

$0=V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t-B_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(16\right)$

It should be noted that with formula (1)～formula (4) and compare that formula (13)～formula (16) has 2 differences: 1. formula (13)～formula (16) comprises the supply voltage of two expansion branch roads and the admittance of series arm; 2. formula (13)～formula (16) contains the equivalent parameters g ' of EWM _LkAnd b ' _Lk, and do not contain the equivalent parameters g of SWM _LkAnd b _Lk

Formula (7)～(8) and formula (9)～(16) can be write as following general type respectively:

0＝h _m(x _E)m＝1，2 (17)

$0=h_n^t\left(x_E\right),n=\mathrm{1,2},\·\·\·,8---\left(18\right)$

In the formula, x _E=[E _l, E _k, g _l, b _l, g _k, b _k, g ' _Lk, b ' _Lk, θ ¹ _l, θ ² _l..., θ ^N _l, θ ¹ _k, θ ² _k..., θ ^N _k] be the equivalent parameters vector of EWM, h _m() is the general expression formula of formula (7) and formula (8);

The general expression formula of segmentation (9)～(16) when being t; Then the multi-period least-squares estimation model of EWM equivalent parameters is:

$J=\min \underset{m=1}{\overset{2}{\mathrm{\Σ}}}{\left[h_m\left(x_E\right)\right]}^2+\underset{t=1}{\overset{N}{\mathrm{\Σ}}}\underset{n=1}{\overset{8}{\mathrm{\Σ}}}{\left[h_n^t\left(x_E\right)\right]}^2---\left(19\right)$

Use gauss-newton method and find the solution formula (19), solve the estimated value x of EWM equivalent parameters _EIn the iterative process, with the equivalent parameters g of the SWM that solves in the step 2 _LkAnd b _LkRespectively as EWM equivalent parameters g ' _LkAnd b ' _LkInitial value.

Compared with the prior art, the inventive method has following advantage:

(1) the inventive method is set up the Equivalent Model of outer net based on Intranet information, need not any information of outer net, can be used for solving the Static Equivalent problem of two-port " black box outer net ".

Only need the Intranet flow data of three periods when (2) application the inventive method is carried out external network equivalent, need not Intranet is carried out any operation of cut-offfing, engineering practicability is strong; The inventive method gained external network equivalent parameter is strong to the adaptive capacity that the Intranet trend changes, and is equivalent effective.

Description of drawings

Fig. 1 is for being applied to the 39 node system winding diagrams of the inventive method, numeral node serial number among the figure among the embodiment.Break branch road 9-39 at standard IEEE 39 node systems, promptly obtain system shown in Figure 1.In this system, node 1,2,25～30,37～39 is the outer net node, and node 3 and 17 is a boundary node, and all the other nodes are the Intranet node, and promptly empty frame partly is to need equivalent outer net among the figure.

Fig. 2 is the system wiring figure behind the equivalent outer net of usefulness SWM among the embodiment, is SWM in the empty frame, and its equivalent parameters is the equivalent injecting power P of boundary node 3 and 17 ₃+ jQ ₃And P ₁₇+ jQ ₁₇, and the electricity that connects the equivalent branch road of two boundary nodes is led g _3-17With susceptance b _3-17

Fig. 3 is the system wiring figure behind the equivalent outer net of usefulness EWM among the embodiment, is EWM in the empty frame, and its equivalent parameters is the voltage magnitude E of voltage source in two expansion branch roads ₃, E ₁₇And phase angle theta ^t ₃, θ ^t ₁₇, the electricity of two expansion branch roads is led g ₃, g ₁₇With susceptance b ₃, b ₁₇, and the electricity that connects the equivalent branch road of two boundary nodes is led g ' _3-17With susceptance b ' _3-17

Embodiment

Below in conjunction with drawings and Examples, method of the present invention is described further.

In 39 node systems shown in Figure 1, node 1,2,25～30,37～39 is the outer net node, and node 3 and 17 is a boundary node, and all the other nodes are the Intranet node, and empty frame is partly for needing equivalent outer net.Use the inventive method the outer net among Fig. 1 is carried out equivalence, its step is as follows:

Step 1:, obtain inserting the equivalent electrical network of SWM, as shown in Figure 2 with the outer mesh portions of equivalent 39 node systems shown in Figure 1 of SWM.The equivalent parameters of SWM to be asked is the equivalent injecting power P of boundary node 3 and 17 ₃+ jQ ₃And P ₁₇+ jQ ₁₇, and the electricity that connects the equivalent branch road of two boundary nodes is led g _3-17With susceptance b _3-17, equivalent parameters promptly to be asked is x _S=[P ₃, Q ₃, P ₁₇, Q ₁₇, g _3-17, b _3-17].

Step 2: the equivalent parameters of finding the solution SWM.According to the actual measurement status data of N period boundary node and Intranet, set up the multi-period least-squares estimation model of SWM equivalent parameters, and use gauss-newton method and find the solution, be described as follows:

Get the Intranet of 3 periods and the state information of boundary node, comprise the voltage of boundary node 3 and node 17

With

Load power P _L3+ jQ _L3And P _L17+ jQ _L17, and node 4,16 that directly links to each other with boundary node and 18 voltage

With

In the practical engineering application, these state informations can obtain by the Intranet state estimation.

In the simulation analysis, original flow state based on 39 node systems, meritorious the exerting oneself of considering outer net load power and generator increases progressively by 0.02% step-length, and the Intranet load power increases progressively by 0.3% step-length, can obtain the flow state of several periods thus.Table 1 is the state information of 3 continuous times wherein.Each voltage and power are per unit value in the table 1, and power reference is 100MVA; Voltage phasor is represented with real part and imaginary part.

Table 1

According to the state information in the table 1, set up the least-squares estimation model of SWM equivalent parameters as the formula (6), get and wait to ask equivalent parameters x _SInitial value be x _S0Gauss-newton method iterative formula (6) is used in=[1,1,1,1,1 ,-1].Table 2 is the estimated value of the SWM equivalent parameters that solves, and each power and admittance are per unit value in the table 2, power reference 100MVA.

Table 2

P 3

Q 3

P 17

Q 17

g 3-17

b 3-17

6.0497

0.2472

1.4069

0.7314

12.739

-10.578

Step 3:, obtain inserting the equivalent electrical network of EWM, as shown in Figure 3 with the outer mesh portions of equivalent 39 node systems shown in Figure 1 of EWM.The equivalent parameters of EWM to be asked is the voltage magnitude E of voltage source in two expansion branch roads ₃, E ₁₇And phase angle theta ^t ₃, θ ^t ₁₇, the electricity of two expansion branch roads is led g ₃, g ₇With susceptance b ₃, b ₇, and the electricity that connects the equivalent branch road of two boundary nodes is led g ' _3-17With susceptance b ' _3-17

Step 4: the equivalent parameters of finding the solution EWM.According to the Intranet of 3 periods shown in the table 1 and the state information of boundary node, and the restriction relation between EWM and the SWM equivalent parameters, set up the least-squares estimation model of EWM equivalent parameters, and use gauss-newton method and find the solution, be described as follows:

Equivalent parameters to be asked among the EWM is

Its least-squares estimation model is suc as formula (19).If

With

Initial value be respectively the equivalent parameters g of SWM in the table 2 _3-17And b _3-17, promptly 12.739 and-10.578, the initial value of voltage source voltage magnitude and phase angle is respectively 1 and 0, and chooses the initial value of all the other equivalent parameters arbitrarily, for example, gets x _EInitial value be x _E0=[1,1,1,1,1,1,12.739 ,-10.578,0,0,0,0,0,0].Use gauss-newton method iterative formula (19).Table 3 is the estimated value of the EWM equivalent parameters that solves, and the phase angular unit is degree in the table 3, and all the other parameters are per unit value.

Table 3

So far, application the inventive method has been finished the Static Equivalent to two-port outer net among Fig. 1, and its equivalent circuit is EWM shown in Figure 3, and equivalent parameters is as shown in table 3.Need to prove, the value of arbitrary period in the desirable table 3 of the phase place of voltage source among the EWM, as get the θ of the 1st period ¹ ₃And θ ¹ ₁₇Respectively as the phase angle of two voltage sources.

For the validity of checking the inventive method, be example with 39 node systems shown in Figure 1, the equivalent precision of checking the inventive method.The method relatively of participating in has two: 1. conventional Ward equivalence method; 2. the method that proposes of the present invention.

Of particular note: 1. conventional Ward equivalence method is basic operational mode with the original flow state of 39 node systems shown in Figure 1, and its equivalent process need comprises the model and the status data of the whole network of outer net; When 2. using the inventive method, get the Intranet of three periods shown in the table 1 and the state information of boundary node, carry out SWM and EWM equivalence by preceding method, its equivalent parameters is respectively shown in table 2 and table 3.EWM is final external network equivalent model, gets the θ of the 1st period in the table 3 ¹ ₃, θ ¹ ₁₇Respectively as the phase angle of two voltage source voltages among the EWM.

For the precision of two kinds of equivalence methods quantitatively is described, define two evaluation indexes: relative error index and error on the safe side index.The numerical value of these two kinds of indexs is more little, illustrates that equivalent precision is high more.

The relative error index is defined as follows:

$\mathrm{\ΔP}=\max \{\frac{|P_l-{\hat{P}}_l|}{P_l}\×100\%,l\∈{\mathrm{\Φ}}_{\mathrm{line}}\}---\left(20\right)$

$\mathrm{\ΔQ}=\max \{\frac{|Q_l-{\hat{Q}}_l|}{Q_l}\×100\%,l\∈{\mathrm{\Φ}}_{\mathrm{line}}\}---\left(21\right)$

More than in two formulas, Δ P and Δ Q are respectively the relative error of Intranet branch road active power and reactive power; P _lAnd Q _lBe respectively the active power of Intranet branch road l and the true value of reactive power (before equivalent the whole network being carried out the trend result calculated);

With

Be respectively the active power of branch road l and the estimated value of reactive power (outer net is carried out result of calculation behind the equivalence); Φ _LineBe the Intranet set of fingers.

The error on the safe side index is defined as follows:

${\mathrm{SI}}_P=\max \{\frac{|P_l-{\hat{P}}_l|}{S_{\mathrm{base}}}\×100\%,l\∈{\mathrm{\Φ}}_{\mathrm{line}}\}---\left(22\right)$

${\mathrm{SI}}_Q=\max \{\frac{|Q_l-{\hat{Q}}_l|}{S_{\mathrm{base}}}\×100\%,l\∈{\mathrm{\Φ}}_{\mathrm{line}}\}---\left(23\right)$

More than in two formulas, SI _PAnd SI _QBe respectively the error on the safe side of Intranet branch road active power and reactive power; S _BaseBe the measuring basis value of branch power, for example, the 500kV circuit got S _Base=1082MVA gets S to the 220kV circuit _Base=305MVA, or the like; The implication cotype (20) of all the other parameters and formula (21).

Consider that following two kinds of variations appear in the Intranet operational mode:

(1) the Intranet load power slightly changes, and promptly all Intranet load powers increase by 2% and 5% on the basis of original flow state, and table 4 is the error criterion of two kinds of equivalence methods.

Table 4

Can observe following phenomenon by table 4: 1. under three kinds of load levels, the systematic error of the inventive method is all less, and worst error is 18.4%; 2. under the basic flow state, be that load level increases by 0%, two meritorious error criterions of conventional Ward equivalence method are slightly less than the inventive method, but, when load level increases by 2% and 5%, the error of conventional Ward equivalence method enlarges markedly, and all error criterions all are far longer than the inventive method.

(2) Intranet branch road 13-14 cut-offs, and small size variation appears in Intranet load power simultaneously, and promptly all Intranet load powers increase by 2% and 5% on the basis of original flow state, and table 5 is the error criterion of two kinds of equivalence methods.

Table 5

Can be observed and table 4 similar phenomenon by table 5: 1. under three kinds of load levels, the systematic error of the inventive method is all less, and worst error is 15.4%; 2. under first kind of load level, promptly load level increases by 0%, and two meritorious error criterions of conventional Ward equivalence method are more less than the index of the inventive method, and under all the other situations, the error of conventional Ward equivalence method is all much larger than the inventive method.

The simulation result shows of table 4 and table 5: although conventional Ward equivalence method needs the information of the whole network, and the inventive method only needs the Intranet trend information of three periods, but the inventive method can adapt to the trend that load slightly changes and branch breaking causes well to be changed, and its equivalent precision has a clear superiority in respect to conventional Ward equivalence method.

Claims (2)

1. two-port outer net Static Equivalent method based on the Intranet real measured data is characterized in that step is as follows:

Step 1: set up the simplification Ward equivalent circuit of two-port outer net, abbreviate SWM as, the equivalent parameters of SWM is the equivalent injecting power P of boundary node l _l+ jQ _l, the equivalent injecting power P of boundary node k _k+ jQ _k, and the electricity that connects the equivalent branch road of two boundary nodes is led g _LkWith susceptance b _Lk

Step 2: find the solution the equivalent parameters of SWM,, set up the multi-period least-squares estimation model of SWM equivalent parameters, and use gauss-newton method and find the solution the estimated value of SWM equivalent parameters, specify as follows according to the real measured data of a plurality of period boundary nodes and Intranet:

According to t period (t=1,2 ..., N, down with) boundary node and the voltage magnitude of Intranet node and the measurement amount of phase angle, set up the injecting power equation of two boundary nodes:

$0=P_l-V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t+B_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(1\right)$

$0=Q_l-V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t-B_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(2\right)$

$0=P_k-V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t+B_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(3\right)$

$0=Q_k-V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t-B_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(4\right)$

In the formula, P _lAnd Q _lThe equivalence that is respectively boundary node l injects active power and reactive power; P _kAnd Q _kThe equivalence that is respectively boundary node k injects active power and reactive power; Be the measurement amount of the voltage magnitude of node j, subscript t represents t period, down with;

With Be respectively the measurement amount of the voltage phase angle of node i and node j; G _Lj, G _KjReal part for the node admittance matrix corresponding element; B _Lj, B _KjImaginary part for the node admittance matrix corresponding element; Φ _lAnd Φ _kRepresent the node set that directly links to each other with boundary node l and boundary node k respectively;

Following general type can be write as in formula (1)～(4):

$0=f_m^t\left(x_S\right),m=\mathrm{1,2,3,4}---\left(5\right)$

In the formula, x _S=[P _l, Q _l, P _k, Q _k, g _Lk, b _Lk] be the equivalent parameters vector of SWM,

The general expression formula of segmentation (1)～(4) when being t, then the multi-period least-squares estimation model of SWM equivalent parameters is:

$J=\min \underset{t=1}{\overset{N}{\mathrm{\Σ}}}\underset{m=1}{\overset{4}{\mathrm{\Σ}}}{\left[f_m^t\left(x_S\right)\right]}^2---\left(6\right)$

In the formula, hop count when N is;

Use gauss-newton method and find the solution formula (6), solve the estimated value x of SWM equivalent parameters _S

Step 3: to the described same two-port outer net of step 1, set up expansion voltage source branch road Ward equivalent circuit, abbreviate EWM as, the equivalent parameters of EWM is the voltage magnitude E of voltage source in two expansion branch roads _l, E _kAnd phase angle theta ^t _l, θ ^t _k, the electricity of two expansion branch roads is led g _l, g _kWith susceptance b _l, b _k, and the electricity that connects the equivalent branch road of two boundary nodes is led g ' _LkWith susceptance b ' _Lk

Step 4: the equivalent parameters of finding the solution EWM, according to the restriction relation of SWM and EWM equivalent parameters and with step 2 in the boundary node of identical period and the real measured data of Intranet, set up the multi-period least-squares estimation model of EWM equivalent parameters, and the application gauss-newton method is found the solution the equivalent parameters of EWM, gained EWM is the final Equivalent Model of two-port outer net, specifies as follows:

According to the restriction relation of SWM and EWM equivalent parameters, set up following equation:

$0\≈g_{\mathrm{lk}}-g_{\mathrm{lk}}^{\′}---\left(7\right)$

$0\≈b_{\mathrm{lk}}-b_{\mathrm{lk}}^{\′}---\left(8\right)$

$0\≈P_l+{\left(V_l^t\right)}^2{g}_l-V_l^t{E}_l[g_l\cos ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)+b_l\sin ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)]---\left(9\right)$

$0\≈Q_l-{\left(V_l^t\right)}^2{b}_l+V_l^t{E}_l[b_l\cos ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)-g_l\sin ({\mathrm{\δ}}_l^t-{\mathrm{\θ}}_l^t)]---\left(10\right)$

$0\≈P_k+{\left(V_k^t\right)}^2{g}_k-V_k^t{E}_k[g_k\cos ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)+b_k\sin ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)]---\left(11\right)$

$0\≈Q_k-{\left(V_k^t\right)}^2{b}_k+V_k^t{E}_k[b_k\cos ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)-g_k\sin ({\mathrm{\δ}}_k^t-{\mathrm{\θ}}_k^t)]---\left(12\right)$

In addition, according to t period (t=1,2 ..., N, down with) boundary node and the voltage magnitude of Intranet node and the measurement amount of phase angle, set up the injecting power equation of two boundary nodes:

$0=V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t+B_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(13\right)$

$0=V_l^t\underset{j\∈{\mathrm{\Φ}}_l}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{lj}}\sin {\mathrm{\δ}}_{\mathrm{lj}}^t-B_{\mathrm{lj}}\cos {\mathrm{\δ}}_{\mathrm{lj}}^t)---\left(14\right)$

$0=V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t+B_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(15\right)$

$0=V_k^t\underset{j\∈{\mathrm{\Φ}}_k}{\mathrm{\Σ}}{V}_j^t(G_{\mathrm{kj}}\sin {\mathrm{\δ}}_{\mathrm{kj}}^t-B_{\mathrm{kj}}\cos {\mathrm{\δ}}_{\mathrm{kj}}^t)---\left(16\right)$

Formula (7)～(8) and formula (9)～(16) can be write as following general type respectively:

0＝h _m(x _E)m＝1，2 (17)

$0=h_n^t\left(x_E\right),n=\mathrm{1,2},\·\·\·,8---\left(18\right)$

In the formula, x _E=[E _l, E _k, g _l, b _l, g _k, b _k, g ' _Lk, b ' _Lk, θ ¹ _l, θ ² _l..., θ ^N _l, θ ¹ _k, θ ² _k..., θ ^N _k] be the equivalent parameters vector of EWM, h _m() is the general expression formula of formula (7) and formula (8),

The general expression formula of segmentation (9)～(16) when being t, then the multi-period least-squares estimation model of EWM equivalent parameters is:

$J=\min \underset{m=1}{\overset{2}{\mathrm{\Σ}}}{\left[h_m\left(x_E\right)\right]}^2+\underset{t=1}{\overset{N}{\mathrm{\Σ}}}\underset{n=1}{\overset{8}{\mathrm{\Σ}}}{\left[h_n^t\left(x_E\right)\right]}^2---\left(19\right)$

Use gauss-newton method and find the solution formula (19), solve the estimated value x of EWM equivalent parameters _E

2. the two-port outer net Static Equivalent method based on the Intranet real measured data according to claim 1, it is characterized in that, set up in step 2 when setting up the least-squares estimation model of EWM equivalent parameters in the least-squares estimation model of SWM equivalent parameters and the step 4, the time hop count N of required Intranet real measured data must satisfy N 〉=3.

Images