CN101964525B - Method for estimating state of distribution network for supporting large-scale current measurement - Google Patents

Abstract

The invention relates to a method for estimating state of a distribution network for supporting large-scale current measurement, and belongs to the automatic dispatching field of power systems. The method comprises the following steps of: squaring a branch head end power and a branch current amplitude to obtain an evaluated variable, and establishing a new state estimation model of an exponential target function according to a power grid model of an actual power grid and real-time measurement data; and estimating the branch head end power and the branch current amplitude by adopting a Lagrangian multiplier method so as to calculate active power and passive power of equipment such as a circuit, a transformer, a generator, a load and the like. The method can directly establish measurement equations for branch current amplitude measurement, branch power measurement, node voltage measurement and injection power measurement, does not need measurement conversion, does not introduce measurement conversion errors, is convenient to implement, and has high calculation efficiency.

Description

A kind of State Estimation for Distribution Network of supporting extensive current measurement

Technical field

The present invention relates to a kind of State Estimation for Distribution Network of supporting extensive current measurement, belong to dispatching automation of electric power systems and grid simulation technical field.

Background technology

Power distribution network is different from power transmission network, and it is not enough that it measures redundancy, only at the feeder line root voltage magnitude and power measurement is arranged, and generally only gathers Current magnitude measurement on feeder switch.For the measure configuration characteristics of power distribution network, existing many documents are studied the distribution state estimation, and according to the difference that quantity of state is chosen, the distribution method for estimating state can be divided into:

(1) method take node voltage as quantity of state

Lu, C.N., Teng J.H, Liu, W.-H E.Distribution System State Estimation.IEEE Trans on Power System, 1995,10 (1): 229-240 and Whei-Min Lin, Jen-Hao Teng.State Estimation for Distribution Systems with Zero-Injection Constraints.IEEE Trans on Power System, 1996,11 (1): 518-524 proposes the method.This class methods utilization is surveyed conversion, and the multiple current measurement of node injection, the multiple current measurement of branch road and the node complex voltage that power, current amplitude and voltage magnitude are transformed into equivalence measure, thereby realize measurement Jacobian matrix constant.But it not is actual measurements that the equivalence that obtains behind the Transformed Measurement measures, and there is the problem of non-equivalence in the weight that the weight of simultaneously voltage and current amplitude measurement is converted to complex voltage and multiple current measurement, thereby affects estimated accuracy.

(2) method take branch road telegram in reply stream as quantity of state

MesutE.Baran, ArtherW.Kelly.A Branch-Current Based state Estimation Method for Distribution Systems.IEEE Transaction on Power Systems, 1995,10 (1): 483-491 proposes the method.These class methods have been ignored the voltage measurement, virtual load power are measured and the power measurement of branch road one end is converted to the multiple current measurement of corresponding load and branch road is answered current measurement, need node complex voltage given in advance in the conversion.And it is non-constant term that the branch current amplitude measures corresponding measurement Jacobian matrix element.For the situation that exists voltage to measure and a large amount of branch current amplitude measures, the method estimation effect is bad.

(3) method for estimating state of branch power

Sun Hongbin, Zhang Baiming, Xiang Niande. based on the power status method of estimation of branch power. Automation of Electric Systems, 1998,22 (8): 12-16 proposes the method.The method is applicable to the situation that system only exists a small amount of realtime power to measure, and the state estimation problem is converted to the trend matching problem dexterously, but does not provide the processing method of considering that voltage and current measures.

Summary of the invention

The objective of the invention is to propose a kind of State Estimation for Distribution Network of supporting extensive current measurement, utilize the current measurements of a large amount of existence in the distribution to improve the pseudo-precision that measures of load.Directly utilize voltage magnitude measurement, power measurement and current measurement, need not to carry out measurement conversion, and can process the situations such as radiation electrical network, weak looped network and cable charging capacitor.

The State Estimation for Distribution Network of the extensive current measurement of support that the present invention proposes may further comprise the steps:

(1) set up one based on the state of electric distribution network estimation model of exponential type target function:

$\max J\left(X\right)=\underset{i}{\mathrm{\Σ}}\exp (-\frac{1}{R_{\mathrm{ii}}}{(z_i-h_i\left(X\right))}^2)$

s.t c(X)＝0

In the following formula, Z _iBe the real-time measurement values of power distribution network electric parameters, comprise that the active power of the active power of voltage magnitude, generator of the active power of circuit in the power distribution network or transformer and reactive power, bus and reactive power, load and reactive power and branch current measure R _IiThe variance of each real-time measurement values, h _i(X) be the measurement expression formula of each real-time measurement values, X wherein is the state variable of power distribution network, comprise the active power of all power distribution network branch road head ends and the current amplitude on reactive power and the power distribution network branch road square, definition branch current amplitude square | I _Ij| ²=A _Ij, c (X) is the equality constraint equation;

The definition, above-mentioned busbar voltage amplitude square | V _i| ²=B _i, power distribution network branch road resistance and reactance are respectively R _Ij, X _Ij, definition (.) ^mBe the measuring value of respective electrical tolerance, P _i, Q _iBe respectively the power distribution network node and inject meritorious and reactive power, P _Ij, Q _IjBe respectively head end active power and the reactive power of power distribution network branch road, i is headend node, and j is endpoint node, according to above-mentioned definition, obtains above-mentioned real-time measurement equation h _i(X) be respectively:

Branch current amplitude measurement equation: (A _Ij) ^m=A _Ij,

Branch road head end power measurement equation: (P _Ij) ^m=P _Ij, (Q _Ij) ^m=Q _Ij,

The terminal power measurement equation of branch road: (P _Ij) ^m=P _Ij+ A _IjR _Ij, (Q _Ji) ^m=Q _Ij+ A _IjX _Ij,

Node injecting power measurement equation: ${\left(P_j\right)}^m=\underset{i\∈j}{\mathrm{\Σ}}{P}_{\mathrm{ij}}-\underset{i\∈j}{\mathrm{\Σ}}{A}_{\mathrm{ij}}{R}_{\mathrm{ij}}-\underset{k\∈j}{\mathrm{\Σ}}{P}_{\mathrm{jk}},$

${\left(Q_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{X}_{\mathrm{ij}}-\underset{l\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{jl}}-\frac{{\mathrm{<figure-callout\; id="2"\; label="P\; jl"\; filenames="22686DEST\_PATH\_HSB00000363712200012.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{jl}}^{}+Q_{\mathrm{jl}}^2}{A_{\mathrm{jl}}{X}_{\mathrm{cj}}},$

Wherein, i ∈ j, l ∈ j represent the node that links to each other with node j, X _CjBe the capacitor of node j and the reactance value of charging capacitor,

The measurement equation of node voltage square: ${\left(B_j\right)}^m=\frac{{(P_{\mathrm{Lij}}-A_{\mathrm{ij}}{R}_{\mathrm{ij}})}^2+{(Q_{\mathrm{Lij}}-A_{\mathrm{ij}}{X}_{\mathrm{ij}})}^2}{A_{\mathrm{ij}}}$

According to above-mentioned definition, obtain above-mentioned equality constraint equation c (X) and be respectively:

Node j voltage constraint equation: $0=\frac{{(P_{\mathrm{Lij}}-A_{\mathrm{ij}}{R}_{\mathrm{ij}})}^2+{(Q_{\mathrm{Lij}}-A_{\mathrm{ij}}{X}_{\mathrm{ij}})}^2}{A_{\mathrm{ij}}}-\frac{{\left(P_{\mathrm{Ljl}}\right)}^2+{\left(Q_{\mathrm{Ljl}}\right)}^2}{A_{\mathrm{jl}}}$

Wherein l represents the node that links to each other with node j, all contains this voltage constraint equation for all with downstream leg that node j directly links to each other;

(2) adopt method of Lagrange multipliers, above-mentioned state estimation model found the solution, may further comprise the steps:

(2-1) initial value of the state variable X in the state estimation model is set, this initial value measures according to the puppet of power distribution network load and calculates by trend;

(2-2) iterations counter k, k=0 are set;

(2-3) to iteration variable X ^K+1Revise according to following formula:

$\left[\begin{array}{cc}{H}^{T}W(I-\mathrm{diag}\{\frac{{(z-h\left(x\right))}^2}{{\mathrm{\&sigma;}}^2}\left\}\right)H& {\mathrm{<figure-callout\; id="0"\; label="C\; T\; C"\; filenames="627477DEST\_PATH\_HSB00000363712200011.png,837058DEST\_PATH\_HSB00000363712200013.png"\; state="\{\{state\}\}">C</figure-callout>}}^T& \\ C& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;x}\\ -\mathrm{\&lambda;}\end{array}\right]$

$=\left[\begin{array}{c}{H}^{T}W(Z-h\left(x^k\right))\\ -c\left(x^{\left(k\right)}\right)\end{array}\right]$

Wherein, H is the measurement jacobian matrix of m * n, and m is the number of the real-time measurement values of power distribution network electric parameters, and n is the number of state of electric distribution network variable X, Δ x=x ^K+1-x ^k,

W (X) is the diagonal matrix of m * m, and wherein diagonal element is $W_{\mathrm{ii}}\left(X\right)=2\frac{{\mathrm{\&omega;}}_i\left(X\right)}{R_{\mathrm{ii}}},$ ${\mathrm{\&omega;}}_i\left(X\right)=\exp (-\frac{1}{R_{\mathrm{ii}}}{(z_i-h_i\left(X\right))}^2);$

$C=\frac{\&PartialD;c\left(X\right)}{\&PartialD;X}$ Be the measurement jacobian matrix of p * n dimension, p is the number of equality constraint equation c (X);

(2-4) judge respectively inequality || Δ X ^(k)|| ₂≤ ξ ₁And c (X ^K+1)≤ξ ₂Whether set up simultaneously, if be false, then make k=k+1, and forward step (2-3) to, if establishment, then output state variable, wherein ξ ₁And ξ ₂Span be 10 ^-5-10 ^-6

In the above-mentioned method for estimating state, when power distribution network is ring network, above-mentioned steps (1) set up the state of electric distribution network estimation model time, selecting a branch road in the power distribution network loop is chord, with this any end that connects the branch branch road as split vertexes, wherein, s is split vertexes number, r is the upstream node that is attached thereto number, and t is the downstream node that is attached thereto number, then also has:

The voltage measurement equation of split vertexes is: ${\left(B_s\right)}^m=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}$

Split vertexes voltage constraint equation is: $0=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}-\frac{{(P_{\mathrm{ts}}-A_{\mathrm{ts}}{R}_{\mathrm{ts}})}^2+{(Q_{\mathrm{ts}}-A_{\mathrm{ts}}{X}_{\mathrm{ts}})}^2}{A_{\mathrm{ts}}}$

Split vertexes power measurement equation is: (P _s) ^m=P _Rs-A _RsR _Rs+ P _Ts-A _TsR _Ts

${\left(Q_s\right)}^m=Q_{\mathrm{ts}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}}+Q_{\mathrm{ts}}-A_{\mathrm{ts}}{X}_{\mathrm{ts}}-\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}+X_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}{X}_{\mathrm{cs}}},$

X _CsBe the capacitor of node s and the reactance value of charging capacitor.

A kind of State Estimation for Distribution Network of supporting extensive current measurement that the present invention proposes is a measurement equation that measures based on the power distribution network branch current, can directly process current measurement, has the following advantages:

1, is applicable to measure as main state of electric distribution network estimation take the branch current amplitude, compares with branch current method for estimating state in the past, do not have the problem of measurement conversion, make state estimation more correct.

2, method for estimating state of the present invention can effectively be processed the state estimation problem of the power distribution network that comprises loop, also can process for the charging capacitor branch road, therefore applicable various types of power distribution networks, and the scope of application is wider.

3, method for estimating state of the present invention adopts the exponential type target function to carry out state estimation, measures redundant enough situations for the part, has robustness, do not need built-in extra bad data identification program, so estimation procedure is more terse.

Fig. 1 is an embodiment who utilizes the inventive method, comprises the schematic diagram of 69 radial network system examples of node.

Fig. 2 is the radial grid nodes load of 69 nodes result of calculation.

Fig. 3 is the radial grid nodes load of 69 nodes residual result.

Fig. 4 is the radial grid branch Current calculation of 69 nodes result.

Fig. 5 is the weak power network with circle structure node load result of calculations of 69 nodes.

Fig. 6 is the weak power network with circle structure node load residual result of 69 nodes.

Fig. 7 is the weak power network with circle structure branch current residual result of 69 nodes.

Embodiment

The State Estimation for Distribution Network of the extensive current measurement of support that the present invention proposes may further comprise the steps:

(1) set up one based on the state of electric distribution network estimation model of exponential type target function:

$\max J\left(X\right)=\underset{i}{\mathrm{\&Sigma;}}\exp (-\frac{1}{R_{\mathrm{ii}}}{(z_i-h_i\left(X\right))}^2)$

s.t c(X)＝0

In the following formula, Z _iBe the real-time measurement values of power distribution network electric parameters, comprise that the active power of the active power of voltage magnitude, generator of the active power of circuit in the power distribution network or transformer and reactive power, bus and reactive power, load and reactive power and branch current measure R _IiThe variance of each real-time measurement values, h _i(X) be the measurement expression formula of each real-time measurement values, X wherein is the state variable of power distribution network, comprise the active power of all power distribution network branch road head ends and the current amplitude on reactive power and the power distribution network branch road square, definition branch current amplitude square | I _Ij| ²=A _Ij, c (X) is the equality constraint equation;

The definition, above-mentioned busbar voltage amplitude square | V _i| ²=B _i, power distribution network branch road resistance and reactance are respectively R _Ij, X _Ij, definition () ^mBe the measuring value of respective electrical tolerance, P _i, Q _iBe respectively the power distribution network node and inject meritorious and reactive power, P _Ij, Q _IjBe respectively head end active power and the reactive power of power distribution network branch road, i is headend node, and j is endpoint node, according to above-mentioned definition, obtains above-mentioned real-time measurement equation h _i(X) be respectively:

Branch current amplitude measurement equation: (A _Ij) ^m=A _Ij,

Branch road head end power measurement equation: (P _Ij) ^m=P _Ij, (Q _Ij) ^m=Q _Ij,

The terminal power measurement equation of branch road: (P _Ji) ^m=P _Ij+ A _IjR _Ij, (Q _Ji) ^m=Q _Ij+ A _IjX _Ij,

Node injecting power measurement equation: ${\left(P_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{R}_{\mathrm{ij}}-\underset{k\&Element;j}{\mathrm{\&Sigma;}}{P}_{\mathrm{jk}},$

${\left(Q_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{X}_{\mathrm{ij}}-\underset{l\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{jl}}-\frac{{\mathrm{<figure-callout\; id="2"\; label="P\; jl"\; filenames="22686DEST\_PATH\_HSB00000363712200012.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{jl}}^{}+Q_{\mathrm{jl}}^2}{A_{\mathrm{jl}}{X}_{\mathrm{cj}}},$

Wherein, i ∈ j, l ∈ j represent the node that links to each other with node j, X _CjBe the capacitor of node j and the reactance value of charging capacitor,

The measurement equation of node voltage square: ${\left(B_j\right)}^m=\frac{{(P_{\mathrm{Lij}}-A_{\mathrm{ij}}{R}_{\mathrm{ij}})}^2+{(Q_{\mathrm{Lij}}-A_{\mathrm{ij}}{X}_{\mathrm{ij}})}^2}{A_{\mathrm{ij}}}$

According to above-mentioned definition, obtain above-mentioned equality constraint equation c (X) and be respectively:

Node j voltage constraint equation: $0=\frac{{(P_{\mathrm{Lij}}-A_{\mathrm{ij}}{R}_{\mathrm{ij}})}^2+{(Q_{\mathrm{Lij}}-A_{\mathrm{ij}}{X}_{\mathrm{ij}})}^2}{A_{\mathrm{ij}}}-\frac{{\left(P_{\mathrm{Ljl}}\right)}^2+{\left(Q_{\mathrm{Ljl}}\right)}^2}{A_{\mathrm{jl}}}$

Wherein l represents the node that links to each other with node j, all contains this voltage constraint equation for all with downstream leg that node j directly links to each other;

(2) adopt method of Lagrange multipliers, above-mentioned state estimation model found the solution, may further comprise the steps:

(2-1) initial value of the state variable X in the state estimation model is set, this initial value measures according to the puppet of power distribution network load and calculates by trend;

(2-2) iterations counter k, k=0 are set;

(2-3) to iteration variable X ^K+1Revise according to following formula:

$\left[\begin{array}{cc}{H}^{T}W(I-\mathrm{diag}\{\frac{{(z-h\left(x\right))}^2}{{\mathrm{\&sigma;}}^2}\left\}\right)H& {\mathrm{<figure-callout\; id="0"\; label="C\; T\; C"\; filenames="627477DEST\_PATH\_HSB00000363712200011.png,837058DEST\_PATH\_HSB00000363712200013.png"\; state="\{\{state\}\}">C</figure-callout>}}^T& \\ C& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;x}\\ -\mathrm{\&lambda;}\end{array}\right]$

$=\left[\begin{array}{c}{H}^{T}W(Z-h\left(x^k\right))\\ -c\left(x^{\left(k\right)}\right)\end{array}\right]$

Wherein, H is the measurement jacobian matrix of m * n, and m is the number of the real-time measurement values of power distribution network electric parameters, and n is the number of state of electric distribution network variable X, Δ x=x ^K+1-x ^k,

W (X) is the diagonal matrix of m * m, and wherein diagonal element is $W_{\mathrm{ii}}\left(X\right)=2\frac{{\mathrm{\&omega;}}_i\left(X\right)}{R_{\mathrm{ii}}},$

${\mathrm{\&omega;}}_i\left(X\right)=\exp (-\frac{1}{R_{\mathrm{ii}}}{(z_i-h_i\left(X\right))}^2);$

$C=\frac{\&PartialD;c\left(X\right)}{\&PartialD;X}$ Be the measurement jacobian matrix of p * n dimension, p is the number of equality constraint equation c (X);

(2-4) judge respectively inequality || Δ X ^(k)|| ₂≤ ξ ₁And c (X ^K+1)≤ξ ₂Whether set up simultaneously, if be false, then make k=k+1, and forward step (2-3) to, if establishment, then output state variable, wherein ξ ₁And ξ ₂Span be 10 ^-5-10 ^-6

Above-mentioned method for estimating state, when power distribution network is ring network, above-mentioned steps (1) set up the state of electric distribution network estimation model time, selecting a branch road in the power distribution network loop is chord, as split vertexes, wherein, s is split vertexes number with this any end that connects the branch branch road, r is the upstream node that is attached thereto number, and t is the downstream node that is attached thereto number.Then also have:

The voltage measurement equation of split vertexes is: ${\left(B_s\right)}^m=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}$

Split vertexes voltage constraint equation is: $0=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}-\frac{{(P_{\mathrm{ts}}-A_{\mathrm{ts}}{R}_{\mathrm{ts}})}^2+{(Q_{\mathrm{ts}}-A_{\mathrm{ts}}{X}_{\mathrm{ts}})}^2}{A_{\mathrm{ts}}}$

Split vertexes power measurement equation is: (P _s) ^m=P _Rs-A _RsR _Rs+ P _Ts-A _TsR _Ts

${\left(Q_s\right)}^m=Q_{\mathrm{ts}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}}+Q_{\mathrm{ts}}-A_{\mathrm{ts}}{X}_{\mathrm{ts}}-\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}+X_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}{X}_{\mathrm{cs}}}.$

X _CsBe the capacitor of node s and the reactance value of charging capacitor.

Introduce an embodiment of the inventive method below in conjunction with accompanying drawing:

Carry the electricity article of minute periodical the 2nd phase of April in 1989 " considering the power distribution network network reconstruct of load balancing and network loss " (Mesut E.Baran and Felix F.Wu.Network Reconfiguration in Distribution Systems for Loss Reduction and Load Balancing.IEEE Trans.on Power Delivery according to international electrical engineering magazine, April 1989,4 (2)): 69 node systems as shown in Figure 1 that the 1401-1407 page or leaf proposes, design two examples the validity of the inventive method described.

In order to study current measurement to state estimation result's impact, definition characterizes the index that branch current measures coverage in the inventive embodiments:

$s=\frac{n_{m-\mathrm{branch}}}{n_{\mathrm{branch}}}\&times;100\%$

Wherein, n _M-branchFor branch current measures quantity, n _BranchBe a way.

The measuring value that adopts in the embodiment of the invention is to add that in the trend solution white noise of normal distribution produces.In order to characterize the precision of estimated result, the average estimated bias that the definition load power measures is:

$r=\frac{\mathrm{\&Sigma;}|S_{\mathrm{loadi}}-S_{\mathrm{loadi}}^{\mathrm{se}}|}{2n_{\mathrm{Load}}}$

Wherein, n _LoadBe load number, S _LoadiBe the power P of load i, the actual value of Q,

Be the power P of load i, the state estimation result of Q.

The average estimated bias that definition branch current rate measures is:

$r=\frac{\mathrm{\&Sigma;}|S_{\mathrm{flow}}-S_{\mathrm{se}}|}{n_{\mathrm{Line}}}$

Wherein, n _LineBe branch road number, S _FlowBe branch current trend solution A, i.e. actual value, S _SeBe the state estimation result.

Branch current measures the principle that increases in the embodiment of the invention, and when topological analysis, defined good branch number is for branch number＜s ^*Prop up the branch road of way, increase branch current and measure.If this branch road definition is chord, then is furnished with branch current and measures.All load buses are furnished with pseudo-the measurement.Only measure and the node voltage measurement at root node configuration node injecting power.

In following examples, the pseudo-measurement of load bus weight is 10, and all the other measure weights is 0.1.

Embodiment 1: the state estimation of radial distribution networks

The fiducial value of the used example power of present embodiment is S _B=100MVA, line voltage reference value are V _B=10kV.Main wiring diagram as shown in Figure 6.On former network foundation, at node 18,47,52,58,89 places the charging capacitor branch road is arranged, reactance value is 1000 ohm.

In order to consider the state estimation result under the different error in measurement conditions, present embodiment is considered the error in measurement of the normal distribution of adding varying level, forms following example:

Situation 1: node voltage and branch current error in measurement average are 0, and variance is 0.000001; Root node injecting power error in measurement average is 0, and variance is 0.000001; Load power error in measurement average is 0, and variance is 0.01.

Situation 2 load power error in measurement variances are increased to 0.05, and all the other measure configurations are constant.

Situation 3: load power error in measurement variance is for being increased to 0.13, and all the other measure configurations are constant.

Situation 4: load power measures variance and is increased to 0.14, and all the other measure configurations are constant.

The state estimation convergence conditions is:

||Δx|| ₂＜10 ^-5。σ ²＝0.1。

Fig. 2 is the load power precision of state estimation design sketch of embodiment 1, and abscissa is the index s that branch current measures coverage among Fig. 2, and ordinate is the average estimated bias r that load power measures.As can be seen from Figure 2, along with branch current measures increasing of quantity, the state estimation result of load is tending towards true value gradually.For the large measurement of load error in measurement, state estimation is more obvious to the correction effect that load measures.

Fig. 3 is radial grid nodes load residual result, and as can be seen from Figure 3, along with branch current measures increasing of quantity, the pseudo-residual error that measures of load increases gradually.Above presentation of results branch current measures the estimated accuracy that can improve well load.

Increase bad data in situation 4, the head end on the branch road bs2-bs3 is gained merit and idle measurement is bad data (P ^m=0.01P.U., P=1.24948P.U., Q ^m=0.01p.u, Q=0.860884P.U.).As can be seen from Figure 2, measuring in the redundant situation, have or not bad data that the state estimation result is affected not quite.Illustrate that this method has preferably automatically robustness, does not need built-in extra bad data recognition module.

Fig. 4 is branch current result of calculation, and as can be seen from Figure 4, along with branch current measures increasing of quantity, state estimation result is tending towards true value gradually, and the larger effect of load bus error in measurement is more obvious.Explanation improves along with branch current measures redundancy, not only can improve the pseudo-estimated accuracy that measures of load, can improve the estimated accuracy of self simultaneously.

Embodiment 2: weak meshed distribution network

The 70-10 that closes on power distribution network basis shown in Figure 1, three branch roads of 90-14 and 54-26 form weak ring power distribution network.

In order to consider the state estimation result under the different error in measurement conditions, the embodiment of the invention considers that the error in measurement of the normal distribution of adding varying level forms following example:

Situation 1: node voltage and branch current error in measurement average are 0, and variance is 0.000001; Root node injecting power measurement noise average is 0, and variance is 0.000001; Load power measurement noise average is 0, and variance is 0.01.

Situation 2: load power error in measurement variance increases to 0.05, and all the other measure configurations are constant.

Situation 3: load power error in measurement variance increases to 0.09, and all the other measure configurations are constant.

Situation 4: load power error in measurement variance increases to 0.1, and all the other measure configurations are constant.

The state estimation convergence conditions is:

||Δx|| ₂＜10 ^-5。σ ²＝0.1。

Fig. 5 is weak power network with circle structure node load result of calculation, and abscissa is the index s that branch current measures coverage among Fig. 5, and ordinate is that load power measures relative average estimated bias r.

As can be seen from Figure 5, exist in the situation of looped network, along with branch current measures increasing of quantity, the state estimation result of load is tending towards true value gradually.For the large measurement of load error in measurement, state estimation is more obvious to the correction effect that load measures.

Fig. 6 is weak power network with circle structure node load residual result, and as can be seen from Figure 6, along with branch current measures increasing of quantity, the pseudo-residual error that measures of load increases gradually.Above presentation of results branch current measures the estimated accuracy that can improve well load.

Increase bad data in situation 4, the head end on the branch road bs2-bs3 is gained merit and idle measurement is bad data (P ^m=0.01P.U., P=0.954696.U., Q ^m=0.01p.u, Q=0.548273.U.).As can be seen from Figure 5, measuring in the redundant situation, have or not bad data that the state estimation result is affected not quite.Illustrate that this method has preferably automatically robustness equally for looped network, does not need built-in extra bad data recognition module.

Fig. 7 is the branch current result of calculation that embodiment 2 obtains, and can find out, along with branch current measures increasing of quantity, the current estimation result is tending towards true value gradually.Explanation improves along with branch current measures redundancy, not only can improve the pseudo-estimated accuracy that measures of load, can improve the estimated accuracy of self simultaneously.

Claims (2)

1. State Estimation for Distribution Network of supporting extensive current measurement is characterized in that the method may further comprise the steps:

(1) set up one based on the state of electric distribution network estimation model of exponential type target function:

$\max J\left(X\right)=\underset{i}{\mathrm{\&Sigma;}}\exp (-\frac{1}{R_{\mathrm{ii}}}{(z_i-h_i\left(X\right))}^2)$

s.t c(X)＝0

In the following formula, Z _iBe the real-time measurement values of power distribution network electric parameters, comprise that the active power of the active power of voltage magnitude, generator of the active power of circuit in the power distribution network or transformer and reactive power, bus and reactive power, load and reactive power and branch current measure R _IiThe variance of each real-time measurement values, h _i(X) be the measurement expression formula of each real-time measurement values, X wherein is the state variable of power distribution network, comprise the active power of all power distribution network branch road head ends and the current amplitude on reactive power and the power distribution network branch road square, definition branch current amplitude square | I _Ij| ²=A _Ij, c (X) is the equality constraint equation;

The definition, the voltage magnitude of above-mentioned bus square | V _i| ²=B _i, power distribution network branch road resistance and reactance are respectively R _Ij, X _Ij, definition (.) ^mBe the measuring value of respective electrical tolerance, P _i, Q _iBe respectively the power distribution network node and inject meritorious and reactive power, P _Ij, Q _IjBe respectively head end active power and the reactive power of power distribution network branch road, i is headend node, and j is endpoint node, according to above-mentioned definition, obtains above-mentioned real-time measurement equation h _i(X) be respectively:

Branch current amplitude measurement equation: (A _Ij) ^m=A _Ij,

Branch road head end power measurement equation: (P _Ij) ^m=P _Ij, (Q _Ij) ^m=Q _Ij,

The terminal power measurement equation of branch road: (P _Ji) ^m=P _Ij+ A _IjR _Ij, (Q _Ji) ^m=Q _Ij+ A _IjX _Ij,

Node injecting power measurement equation: ${\left(P_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{R}_{\mathrm{ij}}-\underset{k\&Element;j}{\mathrm{\&Sigma;}}{P}_{\mathrm{jk}},$

${\left(Q_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{X}_{\mathrm{ij}}-\underset{l\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{jl}}-\frac{P_{\mathrm{jl}}^2+Q_{\mathrm{jl}}^2}{A_{\mathrm{jl}}{X}_{\mathrm{cj}}},$

Wherein, i ∈ j, l ∈ j represent the node that links to each other with node j, X _CjBe the capacitor of node j and the reactance value of charging capacitor,

The measurement equation of node voltage square: ${\left(B_j\right)}^m=\frac{{(P_{\mathrm{ij}}-A_{\mathrm{ij}}{R}_{\mathrm{ij}})}^2+{(Q_{\mathrm{ij}}-A_{\mathrm{ij}}{X}_{\mathrm{ij}})}^2}{A_{\mathrm{ij}}}$

According to above-mentioned definition, obtain above-mentioned equality constraint equation c (X) and be respectively:

Node j voltage constraint equation: $0=\frac{{(P_{\mathrm{ij}}-A_{\mathrm{ij}}{R}_{\mathrm{ij}})}^2+{(Q_{\mathrm{ij}}-A_{\mathrm{ij}}{X}_{\mathrm{ij}})}^2}{A_{\mathrm{ij}}}-\frac{{\left(P_{\mathrm{jl}}\right)}^2+{\left(Q_{\mathrm{jl}}\right)}^2}{A_{\mathrm{jl}}}$

Wherein l represents the node that links to each other with node j, all contains this voltage constraint equation for all with downstream leg that node j directly links to each other;

(2) adopt method of Lagrange multipliers, above-mentioned state estimation model found the solution, may further comprise the steps:

(2-1) initial value of the state variable X in the state estimation model is set, this initial value measures according to the puppet of power distribution network load and calculates by trend;

(2-2) iterations counter k, k=0 are set;

(2-3) to iteration variable X ^K+1Revise according to following formula:

$\left[\begin{array}{cc}{H}^{T}W(I-\mathrm{diag}\{\frac{{(z-h\left(x\right))}^2}{{\mathrm{\&sigma;}}^2}\left\}\right)H& C^T\\ C& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;x}\\ -\mathrm{\&lambda;}\end{array}\right]$

$=\left[\begin{array}{c}{H}^{T}W(Z-h\left(x^k\right))\\ -c\left(x^{\left(k\right)}\right)\end{array}\right]$

Wherein, H is the measurement jacobian matrix of m * n, and m is the number of the real-time measurement values of power distribution network electric parameters, and n is the number of state of electric distribution network variable X, Δ x=x ^K+1-x ^k,

W (X) is the diagonal matrix of m * m, and wherein diagonal element is ${\mathrm{\&omega;}}_i\left(X\right)=\exp (-\frac{1}{R_{\mathrm{ii}}}{(z_i-h_i\left(X\right))}^2);$

Be the measurement jacobian matrix of p * n dimension, p is the number of equality constraint equation c (X), and σ is the variance of measurement amount, and λ is the Lagrange multiplier of Solve problems;

(2-4) judge respectively inequality || Δ X ^(k)|| ₂≤ ξ ₁And c (X ^K+1)≤ξ ₂Whether set up simultaneously, if be false, then make k=k+1, and forward step (2-3) to, if establishment, then output state variable, wherein ξ ₁And ξ ₂Span be 10 ^-5-10 ^-6, Δ X ^(k)It is the solving result of the quantity of state of k step iteration;

2. method for estimating state as claimed in claim 1, it is characterized in that when power distribution network is ring network, step (1) set up the state of electric distribution network estimation model time, selecting a branch road in the power distribution network loop is chord, with any end of this chord branch road as split vertexes, wherein, s is split vertexes number, r is the upstream node that is attached thereto number, and t is the downstream node that is attached thereto number, then also has:

The voltage measurement equation of split vertexes is: ${\left(B_s\right)}^m=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}$

Split vertexes voltage constraint equation is: $0=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}-\frac{{(P_{\mathrm{ts}}-A_{\mathrm{ts}}{R}_{\mathrm{ts}})}^2+{(Q_{\mathrm{ts}}-A_{\mathrm{ts}}{X}_{\mathrm{ts}})}^2}{A_{\mathrm{ts}}}$

Split vertexes power measurement equation is: (P _s) ^m=P _Rs-A _RsR _Rs+ P _Ts-A _TsR _Ts

${\left(Q_s\right)}^m=Q_{\mathrm{ts}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}}+Q_{\mathrm{ts}}-A_{\mathrm{ts}}{X}_{\mathrm{ts}}-\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}{X}_{\mathrm{cs}}},$

X _CsBe the capacitor of node s and the reactance value of charging capacitor.

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