CN104283211B - A kind of single-thee phase admixture method of estimation - Google Patents

Abstract

A kind of single-thee phase admixture method of estimation.It comprises the following step performed in order: step 1) set up three-phase state estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value; Step 2) calculate the positive sequence of every bar branch road, zero sequence and negative-sequence current, according to threshold marker single-thee phase network; Step 3) set up single-thee phase admixture estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value.Single-thee phase admixture method of estimation provided by the invention compared with prior art beneficial effect is: pass through setting threshold, and divide single three-phase network according to the size of zero-sequence current, can need to regulate threshold size according to the precision of Practical Calculation and speed, flexibility is good, different engineer applied requirements can be met, there is good future in engineering applications.

Description

A kind of single-thee phase admixture method of estimation

Technical field

The invention belongs to Power system state estimation technical field, particularly relate to and a kind ofly consider three-phase symmetrical system and the interconnected single-thee phase admixture method of estimation of three-phase unsymmetrical winding.

Background technology

Distribution state estimation is the most basic software of DEMS in intelligent network distribution, and its computational accuracy and computational speed directly affect the runnability of other advanced applied software, thus directly affects fail safe, the economy of system cloud gray model.Asymmetric due to load, and the reason of the aspect such as network parameter is asymmetric, distribution is actually a dissymmetric network, and system scale its scale for power transmission network is much bigger, therefore how realizing rapidity that distribution estimates and accuracy, is one of important subject anxious to be resolved.

In standing state method of estimation, great majority are that simple single phase is estimated, all the other are that simple three-phase state is estimated, and for the power transmission and distribution integrated system of reality, electric pressure is higher often, its symmetry is better, electric pressure is lower, its symmetry is poorer, even simple power distribution network, due to a large amount of existence of single-phase load, add the grid-connected of the grid-connected and microgrid of distributed power generation in recent years, these equipment and systems are all much single-phase, and electric pressure is all lower, and be grid-connectedly degrading distribution low-voltage subnetwork symmetry further, but along with the rising of electric pressure, its symmetry is also become better and better.Therefore, no matter power transmission and distribution integrated system, or distribution system, adopt single phase method of estimation if unified, the serious node estimated accuracy of system asymmetrical three-phase is not high; According to full three-phase state method of estimation, dimension is too high, and its amount of calculation will increase by 3 times, and adds unnecessary amount of calculation for the network that symmetry is good, and overall computational efficiency is not high.And current unique consideration electrical power trans mission/distribution system unifies the dual stage process of state estimation, then because the symmetry between electric pressure network different in distribution does not exist obvious boundary, therefore cannot be applied in engineering.

Summary of the invention

In order to solve the problem, the object of the present invention is to provide a kind of single-thee phase admixture method of estimation.

In order to achieve the above object, single-thee phase admixture method of estimation provided by the invention comprises the following step performed in order:

Step 1) set up three-phase state estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value;

Step 2) calculate the positive sequence of every bar branch road, zero sequence and negative-sequence current, according to threshold marker single-thee phase network;

Step 3) set up single-thee phase admixture estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value.

In step 2) in, described threshold value specifically comprises: zero-sequence current is less than quality coefficient λ times forward-order current, wherein quality coefficient λ <<1.

In step 3) in, the described method setting up single-thee phase admixture estimation model comprises the following steps:

Step 31) set up weighted least-squares method state estimation model:

z＝h(x)+υ

In formula, z is that n dimension measures vector, is made up of the injecting power of the every phase of node, line power, voltage magnitude; H (x) is n dimension measurement function vectors; X is that m ties up state vector (m<n), x=(x ⁺, x ^p), x ⁺=(V ⁺, θ ⁺), x ^p=(V ^p, θ ^p), p=a, b, c; υ is that n ties up measure error vector;

The target of weighted least-squares method finds a m to tie up state vector exactly make following formula minimum:

J(x)＝[z-h(x)] ^TR ^-1[z-h(x)]

Step 32) accounting equation that measures of structure boundary branch power:

$\begin{array}{c}{P}_{\mathrm{\&pi;i}}^{+}=V_i^{+}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_k^{+}(G_{\mathrm{ik}}^{++}\cos {\mathrm{\&theta;}}_{\mathrm{ik}}^{++}+B_{\mathrm{ik}}^{++}\sin {\mathrm{\&theta;}}_{\mathrm{ik}}^{++})\\ +V_i^{+}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p(G_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}+B_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p})\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;i}}^{+}=V_i^{+}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_k^{+}(G_{\mathrm{ik}}^{++}\sin {\mathrm{\&theta;}}_{\mathrm{ik}}^{++}-B_{\mathrm{ik}}^{++}\cos {\mathrm{\&theta;}}_{\mathrm{ik}}^{++})\\ +V_i^{+}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p(G_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}-B_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p})\end{array}$

In formula, for active power and reactive power are injected in the equivalence of the single-phase side gusset i of boundary branch road; for the positive sequence voltage amplitude of node i; for node i and the positive sequence voltage adjoining single-phase node k thereof, be respectively the single-phase transconductance of respective branch in admittance matrix, mutually susceptance, as k=i be node i single-phase self-conductance and from susceptance; for node i, the positive sequence phase angle difference of k; for the p phase voltage amplitude of the adjacent three-phase node j of node i, be respectively boundary branch road single-phase side gusset i to the p equivalent transconductance of three-phase side node j and mutual susceptance, namely real part and imaginary part; for the positive sequence phase angle of node i and the p phase phase angle difference of node j;

$\begin{array}{c}{P}_{\mathrm{\&pi;i}}^p=V_i^p\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_j^{+}(G_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}+B_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+})\\ +V_i^p\underset{l=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_l^t(G_{\mathrm{il}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}}+B_{\mathrm{il}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}})\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;i}}^p=V_i^p\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_j^{+}(G_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}-B_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+})\\ +V_i^p\underset{l=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_l^t(G_{\mathrm{il}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}}-B_{\mathrm{il}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}})\end{array}$

In formula, for the p equivalent of boundary branch road three-phase side node i injects active power and reactive power; for the p phase voltage amplitude of node i; for the positive sequence voltage amplitude of the adjacent single-phase node j of node i; be respectively the equivalent transconductance of the relatively single-phase side gusset j of p of boundary branch road three-phase side node i and mutual susceptance, namely real part and imaginary part; for the t phase voltage amplitude of the adjacent single-phase node l of node i; with be respectively the t phase transconductance of p phase with node l of node i, mutually susceptance and phase angle difference;

$P_{\mathrm{\&pi;ij}}^{+}=g_{\mathrm{ij}}^{+}{V}_i^{{+}^2}-V_i^{+}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p[g_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}+b_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}]$

$Q_{\mathrm{\&pi;ij}}^{+}=-(b_{\mathrm{ij}}^{+}+y_0^{+})V_i^{{+}^2}-V_i^{+}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p[g_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}-b_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}]$

In formula, for branch road ij side, boundary line equivalent active power and reactive power; for the positive sequence voltage amplitude of node i; for the p phase voltage amplitude of node j; g ₁, b ₁be respectively positive sequence conductance and the susceptance of boundary branch road; be respectively the single-phase side gusset i of boundary branch road to the p equivalent conductance of three-phase side node j and susceptance, namely real part and imaginary part; for the positive sequence phase angle of node i and the p phase phase angle difference of node j;

$\begin{array}{c}{P}_{\mathrm{\&pi;ij}}^p=\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}\left[V_i^p{V}_i^t(g_{\mathrm{ij}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}}+b_{\mathrm{ij}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}})\right]\\ -V_i^p{V}_j^{+}[g_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}+b_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}]\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;ij}}^p=\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}\left[V_i^p{V}_i^t(g_{\mathrm{ij}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}}-b_{\mathrm{ij}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}})\right]\\ -V_i^p{V}_j^{+}[g_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}-b_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}]\end{array}$

In formula, be respectively boundary branch road ij side line road p equivalent active power and reactive power; with be respectively the p phase of node i, t phase voltage amplitude and phase angle difference; be respectively the t phase transconductance of p phase with node j of node i, mutually susceptance; for the positive sequence voltage amplitude of node j; be respectively equivalent conductance and the susceptance of the relatively single-phase side gusset j of t of boundary branch road three-phase side node i, namely real part and imaginary part; for the p phase phase angle of node i and the positive sequence phase angle difference of node j;

In various above:

$g_1+{\mathrm{jb}}_1=\left[T_2\right][Y_{\mathrm{sht}}^{\mathrm{abc}}+Y_{\mathrm{ser}}^{\mathrm{abc}}]\left[T_1\right]$

$G_{31}+{\mathrm{jB}}_{31}=Y_{31}^{\mathrm{abc}}=[-Y_{\mathrm{ser}}^{\mathrm{abc}}]\left[T_1\right]$

$G_{31}+{\mathrm{jB}}_{31}=Y_{31}^{\mathrm{abc}}=\left[T_2\right][-Y_{\mathrm{ser}}^{\mathrm{abc}}]$

T ₁＝[1α ²α] ^T

$T_2=\frac{1}{3}\left[\begin{array}{ccc}1& \mathrm{\&alpha;}& {\mathrm{\&alpha;}}^2\end{array}\right]$

$Y_{\mathrm{sht}}^{\mathrm{abc}}={\left[\begin{array}{ccc}{Y}_0^{\mathrm{aa}}& Y_0^{\mathrm{ab}}& Y_0^{\mathrm{ac}}\\ Y_0^{\mathrm{ba}}& Y_0^{\mathrm{bb}}& Y_0^{\mathrm{bc}}\\ Y_0^{\mathrm{ca}}& Y_0^{\mathrm{cb}}& Y_0^{\mathrm{cc}}\end{array}\right]}_{3\&times;3}$

$Y_{\mathrm{ser}}^{\mathrm{abc}}={\left[\begin{array}{ccc}{Y}^{\mathrm{aa}}& Y^{\mathrm{ab}}& Y^{\mathrm{ac}}\\ Y^{\mathrm{ba}}& Y^{\mathrm{bb}}& Y^{\mathrm{bc}}\\ Y^{\mathrm{ca}}& Y^{\mathrm{cb}}& Y^{\mathrm{cc}}\end{array}\right]}_{3\&times;3}$

Step 33) structure measurement jacobian matrix:

In formula, with be respectively the measurement jacobian matrix of boundary branch road Correlated Case with ARMA Measurement, boundary branch road Correlated Case with ARMA Measurement is that branch power measures, the voltage magnitude of branch road two end node measures and injecting power measures; with be respectively except the branch road Correlated Case with ARMA Measurement of boundary, the measurement jacobian matrix of single phase networks and three-phase network; with be respectively step 32) in the accounting equation of boundary branch road Correlated Case with ARMA Measurement; h ⁺(x) and h ^px () is respectively the accounting equation of non-boundary branch road Correlated Case with ARMA Measurement;

Step 34) correction of solving state variable

Obtained by following Newton iteration method

$W\left({\hat{x}}^k\right)=H{\left({\hat{x}}^k\right)}^T{R}^{-1}\mathrm{\&Delta;z}$

${\hat{x}}^{k+1}={\hat{x}}^k+\mathrm{\&Delta;}{\hat{x}}^k$

In formula, R is for measuring covariance matrix; for information matrix; for the correction value of kth time iterative state variable; for the difference of kth time iteration measuring value and calculated value; for the measurement jacobian matrix of kth time iteration;

If then state estimation terminates; Otherwise by step 2) mark single-thee phase network, then repeat step 33) and step 34).

Single-thee phase admixture method of estimation provided by the invention compared with prior art beneficial effect is: pass through setting threshold, and divide single three-phase network according to the size of zero-sequence current, can need to regulate threshold size according to the precision of Practical Calculation and speed, flexibility is good, different engineer applied requirements can be met, there is good future in engineering applications.

Accompanying drawing explanation

Fig. 1 is single-thee phase admixture method of estimation implementing procedure figure provided by the invention.

Fig. 2 is the example system diagram of 136 nodes.

Embodiment

Below in conjunction with the drawings and specific embodiments, single-thee phase admixture method of estimation provided by the invention is described in detail.

Single-thee phase admixture method of estimation provided by the invention comprises the following step performed in order:

Step 1) set up three-phase state estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value;

Step 2) calculate the positive sequence of every bar branch road, zero sequence and negative-sequence current, according to threshold marker single-thee phase network;

Step 3) set up single-thee phase admixture estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value.

In step 2) in, described threshold value specifically comprises:

Zero-sequence current is less than quality coefficient λ (λ <<1) times forward-order current, and λ is arranged the requirement of precision of state estimation according in engineering, and λ less expression precision of state estimation is higher.

In step 3) in, the described method setting up single-thee phase admixture estimation model comprises the following steps:

Step 31) set up weighted least-squares method state (WLS) estimation model:

z＝h(x)+υ

In formula, z is that n dimension measures vector, is made up of the injecting power of the every phase of node, line power, voltage magnitude; H (x) is n dimension measurement function vectors; X is that m ties up state vector (m<n), x=(x ⁺, x ^p), x ⁺=(V ⁺, θ ⁺), x ^p=(V ^p, θ ^p), p=a, b, c; υ is that n ties up measure error vector;

The target of WLS finds a m to tie up state vector exactly make following formula minimum:

J(x)＝[z-h(x)] ^TR ^-1[z-h(x)]

Step 32) accounting equation that measures of structure boundary branch power:

$\begin{array}{c}{P}_{\mathrm{\&pi;i}}^{+}=V_i^{+}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_k^{+}(G_{\mathrm{ik}}^{++}\cos {\mathrm{\&theta;}}_{\mathrm{ik}}^{++}+B_{\mathrm{ik}}^{++}\sin {\mathrm{\&theta;}}_{\mathrm{ik}}^{++})\\ +V_i^{+}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p(G_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}+B_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p})\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;i}}^{+}=V_i^{+}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_k^{+}(G_{\mathrm{ik}}^{++}\sin {\mathrm{\&theta;}}_{\mathrm{ik}}^{++}-B_{\mathrm{ik}}^{++}\cos {\mathrm{\&theta;}}_{\mathrm{ik}}^{++})\\ +V_i^{+}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p(G_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}-B_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p})\end{array}$

In formula, for active power and reactive power are injected in the equivalence of the single-phase side gusset i of boundary branch road; for the positive sequence voltage amplitude of node i; for node i and the positive sequence voltage adjoining single-phase node k thereof, be respectively the single-phase transconductance of respective branch in admittance matrix, mutually susceptance, as k=i be node i single-phase self-conductance and from susceptance; for node i, the positive sequence phase angle difference of k; for the p phase voltage amplitude of the adjacent three-phase node j of node i, be respectively boundary branch road single-phase side gusset i to the p equivalent transconductance of three-phase side node j and mutual susceptance, namely real part and imaginary part; for the positive sequence phase angle of node i and the p phase phase angle difference of node j;

$\begin{array}{c}{P}_{\mathrm{\&pi;i}}^p=V_i^p\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_j^{+}(G_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}+B_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+})\\ +V_i^p\underset{l=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_l^t(G_{\mathrm{il}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}}+B_{\mathrm{il}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}})\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;i}}^p=V_i^p\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_j^{+}(G_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}-B_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+})\\ +V_i^p\underset{l=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_l^t(G_{\mathrm{il}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}}-B_{\mathrm{il}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{il}}^{\mathrm{pt}})\end{array}$

In formula, for the p equivalent of boundary branch road three-phase side node i injects active power and reactive power; for the p phase voltage amplitude of node i; for the positive sequence voltage amplitude of the adjacent single-phase node j of node i; be respectively the equivalent transconductance of the relatively single-phase side gusset j of p of boundary branch road three-phase side node i and mutual susceptance, namely real part and imaginary part; for the t phase voltage amplitude of the adjacent single-phase node l of node i; with be respectively the t phase transconductance of p phase with node l of node i, mutually susceptance and phase angle difference;

$P_{\mathrm{\&pi;ij}}^{+}=g_{\mathrm{ij}}^{+}{V}_i^{{+}^2}-V_i^{+}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p[g_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}+b_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}]$

$Q_{\mathrm{\&pi;ij}}^{+}=-(b_{\mathrm{ij}}^{+}+y_0^{+})V_i^{{+}^2}-V_i^{+}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p[g_{{13}_{\mathrm{ij}}}^{+p}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}-b_{{13}_{\mathrm{ij}}}^{+p}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{+p}]$

In formula, for branch road ij side, boundary line equivalent active power and reactive power; for the positive sequence voltage amplitude of node i; for the p phase voltage amplitude of node j; g ₁, b ₁be respectively positive sequence conductance and the susceptance of boundary branch road; be respectively the single-phase side gusset i of boundary branch road to the p equivalent conductance of three-phase side node j and susceptance, namely real part and imaginary part; for the positive sequence phase angle of node i and the p phase phase angle difference of node j;

$\begin{array}{c}{P}_{\mathrm{\&pi;ij}}^p=\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}\left[V_i^p{V}_i^t(g_{\mathrm{ij}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}}+b_{\mathrm{ij}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}})\right]\\ -V_i^p{V}_j^{+}[g_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}+b_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}]\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;ij}}^p=\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}\left[V_i^p{V}_i^t(g_{\mathrm{ij}}^{\mathrm{pt}}\sin {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}}-b_{\mathrm{ij}}^{\mathrm{pt}}\cos {\mathrm{\&theta;}}_{\mathrm{ii}}^{\mathrm{pt}})\right]\\ -V_i^p{V}_j^{+}[g_{{31}_{\mathrm{ij}}}^{p+}\sin {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}-b_{{31}_{\mathrm{ij}}}^{p+}\cos {\mathrm{\&theta;}}_{\mathrm{ij}}^{p+}]\end{array}$

In formula, be respectively boundary branch road ij side line road p equivalent active power and reactive power; with be respectively the p phase of node i, t phase voltage amplitude and phase angle difference; be respectively the t phase transconductance of p phase with node j of node i, mutually susceptance; for the positive sequence voltage amplitude of node j; be respectively equivalent conductance and the susceptance of the relatively single-phase side gusset j of t of boundary branch road three-phase side node i, namely real part and imaginary part; for the p phase phase angle of node i and the positive sequence phase angle difference of node j;

In various above:

$g_1+{\mathrm{jb}}_1=\left[T_2\right][Y_{\mathrm{sht}}^{\mathrm{abc}}+Y_{\mathrm{ser}}^{\mathrm{abc}}]\left[T_1\right]$

$G_{31}+{\mathrm{jB}}_{31}=Y_{31}^{\mathrm{abc}}=[-Y_{\mathrm{ser}}^{\mathrm{abc}}]\left[T_1\right]$

$G_{31}+{\mathrm{jB}}_{31}=Y_{31}^{\mathrm{abc}}=\left[T_2\right][-Y_{\mathrm{ser}}^{\mathrm{abc}}]$

T ₁＝[1α ²α] ^T

$T_2=\frac{1}{3}\left[\begin{array}{ccc}1& \mathrm{\&alpha;}& {\mathrm{\&alpha;}}^2\end{array}\right]$

$Y_{\mathrm{sht}}^{\mathrm{abc}}={\left[\begin{array}{ccc}{Y}_0^{\mathrm{aa}}& Y_0^{\mathrm{ab}}& Y_0^{\mathrm{ac}}\\ Y_0^{\mathrm{ba}}& Y_0^{\mathrm{bb}}& Y_0^{\mathrm{bc}}\\ Y_0^{\mathrm{ca}}& Y_0^{\mathrm{cb}}& Y_0^{\mathrm{cc}}\end{array}\right]}_{3\&times;3}$

$Y_{\mathrm{ser}}^{\mathrm{abc}}={\left[\begin{array}{ccc}{Y}^{\mathrm{aa}}& Y^{\mathrm{ab}}& Y^{\mathrm{ac}}\\ Y^{\mathrm{ba}}& Y^{\mathrm{bb}}& Y^{\mathrm{bc}}\\ Y^{\mathrm{ca}}& Y^{\mathrm{cb}}& Y^{\mathrm{cc}}\end{array}\right]}_{3\&times;3}$

Step 33) structure measurement jacobian matrix:

In formula, with be respectively the measurement jacobian matrix of boundary branch road Correlated Case with ARMA Measurement (branch power measures, the voltage magnitude of branch road two end node measures and injecting power measures); with be respectively except the branch road Correlated Case with ARMA Measurement of boundary, the measurement jacobian matrix of single phase networks and three-phase network; with be respectively step 32) in the accounting equation of boundary branch road Correlated Case with ARMA Measurement; h ⁺(x) and h ^px () is respectively the accounting equation of non-boundary branch road Correlated Case with ARMA Measurement;

Step 34) correction of solving state variable

Obtained by following Newton iteration method

$W\left({\hat{x}}^k\right)=H{\left({\hat{x}}^k\right)}^T{R}^{-1}\mathrm{\&Delta;z}$

${\hat{x}}^{k+1}={\hat{x}}^k+\mathrm{\&Delta;}{\hat{x}}^k$

In formula, R is for measuring covariance matrix; for information matrix; for the correction value of kth time iterative state variable; for the difference of kth time iteration measuring value and calculated value; for the measurement jacobian matrix of kth time iteration;

If then state estimation terminates; Otherwise by step 2) mark single-thee phase network, then repeat step 33) and step 34).

Overall consideration three-phase symmetrical system and the interconnected single-thee phase admixture method of estimation implementing procedure provided by the invention of three-phase unsymmetrical winding are as shown in Figure 1.

Embodiment:

Carry out 2 IEEE69 node systems to splice the example system obtaining 136 nodes shown in Fig. 2, its metric data is that the three-phase injecting power of each node measures and three-phase voltage amplitude measures, and the standard deviation sigma of error in measurement all gets 0.01; Metric data is simulated as follows: Gaussian noise calculation of tidal current being added its value 2%, obtains the raw data tested, and by node 35,41,54,56, the B phase of 58,69 is injected the rise of meritorious power measurement m%, C phase and is injected meritorious power measurement downward m%; By node 102, the B phase of 106,108,121,123,125,136 is injected the downward of meritorious power measurement m%, C phase and is injected meritorious power measurement rise m%; Convergence threshold ζ=0.00001 of Newton iteration method.

When adopting two benches mixed method, choose trunk node 1-27,36-39,70-94 are three-phase symmetrical node, adopt single-phase estimation, and all the other nodes then adopt three-phase to estimate; The threshold value of automatic mixed method is set as λ=0.001.

(1) computational accuracy of different conditions method of estimation and velocity contrast

When m gets different value respectively, computational accuracy and velocity contrast's result of respective three-phase, single-phase, Twostep Estimation and single-thee phase admixture method of estimation provided by the invention (be called for short and automatically mix) are as shown in table 1:

Each method computational accuracy and velocity contrast under the different degree of balance of table 1

As can be seen from Table 1, the iterations of 4 kinds of method for estimating state is identical, and the computing time of single-phase estimation, Twostep Estimation and automatic hybrid estimation 3 kinds of methods is all short than three-phase method of estimation, but there is certain error; When degree of unbalance is lower, the estimated result error of 4 kinds of methods is more or less the same; When degree of unbalance increases gradually, the error of single-phase estimation and Twostep Estimation shows especially gradually; Automatic mixed method can select suitable equivalent interface position automatically according to the size of zero-sequence current and forward-order current, adopt the nodes of three-phase method of estimation can have certain increase along with the increase of degree of unbalance, therefore its evaluated error compared with single-phase estimation and Twostep Estimation methodical error little; And what adopt when first time iteration due to automatic mixed method is that full three-phase is estimated to calculate zero sequence, forward-order current to determine initial equivalent interface position, therefore its computing time relative to single-phase estimation and two benches mixed method long.

(2) the automatic mixed method estimated result under different accuracy restriction

This automatic mixed method can provide different estimation computational accuracies, and table 2 is depicted as m=10, changes the automatic mixed method efficiency that quality coefficient λ obtains; λ is less, and computational accuracy is higher, but consuming time also corresponding increase; Be not difficult to find out, the raising of computational accuracy must exchange for sacrifice computing time.

The efficiency of automatic mixed method under the different λ of table 2

Claims (1)

1. a single-thee phase admixture method of estimation, described single-thee phase admixture method of estimation comprises the following step performed in order:

Step 1) set up three-phase state estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value;

Step 2) calculate the positive sequence of every bar branch road, zero sequence and negative-sequence current, according to threshold marker single-thee phase network;

Step 3) set up single-thee phase admixture estimation model, adopt Newton iteration method to solve the correction obtaining state variable, upgrade state variable value;

It is characterized in that: in step 3) in, the described method setting up single-thee phase admixture estimation model comprises the following steps:

Step 31) set up weighted least-squares method state estimation model:

z＝h(x)+υ

In formula, z is that n dimension measures vector, is made up of the injecting power of the every phase of node, line power, voltage magnitude; H (x) is n dimension measurement function vectors; X is that m ties up state vector (m<n), x=(x ⁺, x ^p), x ⁺=(V ⁺, θ ⁺), x ^p=(V ^p, θ ^p), p=a, b, c; υ is that n ties up measure error vector;

The target of weighted least-squares method finds a m to tie up state vector exactly make following formula minimum:

J(x)＝[z-h(x)] ^TR ^-1[z-h(x)]

Step 32) accounting equation that measures of structure boundary branch power:

$\begin{array}{c}{P}_{\mathrm{\&pi;}i}^{+}=V_i^{+}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_k^{+}(G_{ik}^{++}{\mathrm{cos\&theta;}}_{ik}^{++}+B_{ik}^{++}{\mathrm{sin\&theta;}}_{ik}^{++})\\ +V_i^{+}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p(G_{{13}_{ij}}^{+p}{\mathrm{cos\&theta;}}_{ij}^{+p}+B_{{13}_{ij}}^{+p}{\mathrm{sin\&theta;}}_{ij}^{+p})\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;}i}^{+}=V_i^{+}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_k^{+}(G_{ik}^{++}{\mathrm{sin\&theta;}}_{ik}^{++}-B_{ik}^{++}{\mathrm{cos\&theta;}}_{ik}^{++})\\ +V_i^{+}\underset{j=1}{\overset{k}{\mathrm{\&Sigma;}}}\underset{p=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_j^p(G_{{13}_{ij}}^{+p}{\mathrm{sin\&theta;}}_{ij}^{+p}-B_{{13}_{ij}}^{+p}{\mathrm{cos\&theta;}}_{ij}^{+p})\end{array}$

In formula, for active power and reactive power are injected in the equivalence of the single-phase side gusset i of boundary branch road; V _i ⁺for the positive sequence voltage amplitude of node i; for node i and the positive sequence voltage adjoining single-phase node k thereof, be respectively the single-phase transconductance of respective branch in admittance matrix, mutually susceptance, as k=i be node i single-phase self-conductance and from susceptance; for node i, the positive sequence phase angle difference of k; for the p phase voltage amplitude of the adjacent three-phase node j of node i, be respectively boundary branch road single-phase side gusset i to the p equivalent transconductance of three-phase side node j and mutual susceptance, namely real part and imaginary part; for the positive sequence phase angle of node i and the p phase phase angle difference of node j;

$\begin{array}{c}{P}_{\mathrm{\&pi;}i}^p=V_i^p\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_j^{+}(G_{{31}_{ij}}^{p+}{\mathrm{cos\&theta;}}_{ij}^{p+}+B_{{31}_{ij}}^{p+}{\mathrm{sin\&theta;}}_{ij}^{p+})\\ +V_i^p\underset{l=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_l^t(G_{il}^{pt}{\mathrm{cos\&theta;}}_{il}^{pt}+B_{il}^{pt}{\mathrm{sin\&theta;}}_{il}^{pt})\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;}i}^p=V_i^p\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{V}_j^{+}(G_{{13}_{ij}}^{p+}{\mathrm{sin\&theta;}}_{ij}^{p+}-B_{{31}_{ij}}^{p+}{\mathrm{cos\&theta;}}_{ij}^{p+})\\ +V_i^p\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}{V}_l^t(G_{il}^{pt}{\mathrm{sin\&theta;}}_{il}^{pt}-B_{il}^{pt}{\mathrm{cos\&theta;}}_{il}^{pt})\end{array}$

In formula, for the p equivalent of boundary branch road three-phase side node i injects active power and reactive power; V _i ^pfor the p phase voltage amplitude of node i; for the positive sequence voltage amplitude of the adjacent single-phase node j of node i; be respectively the equivalent transconductance of the relatively single-phase side gusset j of p of boundary branch road three-phase side node i and mutual susceptance, namely real part and imaginary part; for the t phase voltage amplitude of the adjacent single-phase node l of node i; with be respectively the t phase transconductance of p phase with node l of node i, mutually susceptance and phase angle difference;

$P_{\mathrm{\&pi;}ij}^{+}=g_{ij}^{+}{V}_i^{{+}^2}-V_i^{+}\underset{p=a}{\overset{c}{\&Sigma;}}{V}_j^p\&lsqb;g_{{13}_{ij}}^{+p}{\mathrm{cos\&theta;}}_{ij}^{+p}+b_{{13}_{ij}}^{+p}{\mathrm{sin\&theta;}}_{ij}^{+p}\&rsqb;$

$Q_{\mathrm{\&pi;}ij}^{+}=-(b_{ij}^{+}+y_0^{+})V_i^{{+}^2}-V_i^{+}\underset{p=a}{\overset{c}{\&Sigma;}}{V}_j^p\&lsqb;g_{{13}_{ij}}^{+p}{\mathrm{sin\&theta;}}_{ij}^{+p}-b_{{13}_{ij}}^{+p}{\mathrm{cos\&theta;}}_{ij}^{+p}\&rsqb;$

In formula, for branch road ij side, boundary line equivalent active power and reactive power; V _i ⁺for the positive sequence voltage amplitude of node i; for the p phase voltage amplitude of node j; g ₁, b ₁be respectively positive sequence conductance and the susceptance of boundary branch road; be respectively the single-phase side gusset i of boundary branch road to the p equivalent conductance of three-phase side node j and susceptance, namely real part and imaginary part; for the positive sequence phase angle of node i and the p phase phase angle difference of node j;

$\begin{array}{c}{P}_{\mathrm{\&pi;}ij}^p=\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}\&lsqb;V_i^p{V}_i^t(g_{ij}^{pt}{\mathrm{cos\&theta;}}_{ii}^{pt}+b_{ij}^{pt}{\mathrm{sin\&theta;}}_{ii}^{pt})\\ -V_i^p{V}_j^{+}(g_{{13}_{ij}}^{p+}{\mathrm{cos\&theta;}}_{ij}^{p+}+b_{{13}_{ij}}^{p+}{\mathrm{sin\&theta;}}_{ij}^{p+})\&rsqb;\end{array}$

$\begin{array}{c}{Q}_{\mathrm{\&pi;}ij}^p=\underset{t=a}{\overset{c}{\mathrm{\&Sigma;}}}\&lsqb;V_i^p{V}_i^t(g_{ij}^{pt}{\mathrm{sin\&theta;}}_{ii}^{pt}-b_{ij}^{pt}{\mathrm{cos\&theta;}}_{ii}^{pt})\&rsqb;\\ -V_i^p{V}_j^{+}(g_{{13}_{ij}}^{p+}{\mathrm{sin\&theta;}}_{ij}^{p+}-b_{{13}_{ij}}^{p+}{\mathrm{cos\&theta;}}_{ij}^{p+})\&rsqb;\end{array}$

In formula, be respectively boundary branch road ij side line road p equivalent active power and reactive power; V _i ^p, V _i ^twith be respectively the p phase of node i, t phase voltage amplitude and phase angle difference; be respectively the t phase transconductance of p phase with node j of node i, mutually susceptance; for the positive sequence voltage amplitude of node j; be respectively equivalent conductance and the susceptance of the relatively single-phase side gusset j of t of boundary branch road three-phase side node i, namely real part and imaginary part; for the p phase phase angle of node i and the positive sequence phase angle difference of node j;

In various above:

$g_1+{\mathrm{jb}}_1=\&lsqb;T_2\&rsqb;\&lsqb;Y_{sht}^{abc}+Y_{ser}^{abc}\&rsqb;\&lsqb;T_1\&rsqb;$

$G_{31}+{\mathrm{jB}}_{31}=Y_{31}^{abc}=\&lsqb;-Y_{ser}^{abc}\&rsqb;\&lsqb;T_1\&rsqb;$

$G_{31}+{\mathrm{jB}}_{31}=Y_{13}^{abc}=\&lsqb;T_2\&rsqb;\&lsqb;-Y_{ser}^{abc}\&rsqb;$

T ₁＝[1α ²α] ^T

$T_2=\frac{1}{3}\left[\begin{array}{ccc}1& \mathrm{\&alpha;}& {\mathrm{\&alpha;}}^2\end{array}\right]$

$Y_{sht}^{abc}={\left[\begin{array}{ccc}{Y}_0^{aa}& Y_0^{ab}& Y_0^{ac}\\ Y_0^{ba}& Y_0^{bb}& Y_0^{bc}\\ Y_0^{ca}& Y_0^{cb}& Y_0^{cc}\end{array}\right]}_{3\&times;3}$

$Y_{ser}^{abc}={\left[\begin{array}{ccc}{Y}^{aa}& Y^{ab}& Y^{ac}\\ Y^{ba}& Y^{bb}& Y^{bc}\\ Y^{ca}& Y^{cb}& Y^{cc}\end{array}\right]}_{3\&times;3}$

Step 33) structure measurement jacobian matrix:

In formula, with be respectively the measurement jacobian matrix of boundary branch road Correlated Case with ARMA Measurement, boundary branch road Correlated Case with ARMA Measurement is that branch power measures, the voltage magnitude of branch road two end node measures and injecting power measures; with be respectively except the branch road Correlated Case with ARMA Measurement of boundary, the measurement jacobian matrix of single phase networks and three-phase network; with be respectively step 32) in the accounting equation of boundary branch road Correlated Case with ARMA Measurement; h ⁺(x) and h ^px () is respectively the accounting equation of non-boundary branch road Correlated Case with ARMA Measurement;

Step 34) correction of solving state variable

Obtained by following Newton iteration method

$W\left({\hat{x}}^k\right)=H{\left({\hat{x}}^k\right)}^T{R}^{-1}\mathrm{\&Delta;}z$

${\hat{x}}^{k+1}={\hat{x}}^k+\mathrm{\&Delta;}{\hat{x}}^k$

In formula, R is for measuring covariance matrix; for information matrix; for the correction value of kth time iterative state variable; for the difference of kth time iteration measuring value and calculated value; for the measurement jacobian matrix of kth time iteration;

If then state estimation terminates; Otherwise by step 2) mark single-thee phase network, then repeat step 33) and step 34).