CN101964525A - Method for estimating state of distribution network for supporting large-scale current measurement - Google Patents

Abstract

The invention relates to a distribution network tolerance state estimation method supporting large-scale current measurement, which belongs to the field of power system scheduling automation. The method includes: taking the head-end power of the branch and the square of the amplitude of the branch current as variables to be obtained, and establishing a new state estimation model of an exponential objective function according to the power grid model of the actual power grid and real-time measurement data. The Lagrangian multiplier method is used to estimate the head-end power of the branch and the amplitude of the branch current, so as to calculate the active and reactive power of the line, transformer, generator, load and other equipment. The present invention can directly establish measurement equations for branch current amplitude measurement, branch power measurement, node voltage measurement and injection power measurement, without the need for measurement conversion, without introducing measurement conversion errors, and easy to implement , with high computational efficiency.

Description

A kind of state of electric distribution network method of estimation of supporting extensive current measurement

Technical field

The present invention relates to a kind of state of electric distribution network method of estimation 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 measures the redundancy deficiency, only at the feeder line root voltage magnitude and power measurement is arranged, and generally only gathers current amplitude and measure on feeder switch.At the measurement 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) with the node voltage is the method for 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 survey of node injection telegram in reply flow, the branch road telegram in reply flow that power, current amplitude and voltage magnitude are transformed into equivalence are surveyed and the measurement of node complex voltage, thereby realize measurement Jacobian matrix constantization.But it not is actual measurements that the equivalence that obtains after the measurement conversion measures, and there is the problem of non-equivalence in the weight that the weight of voltage and current amplitude measurement simultaneously is converted to complex voltage and the flow of sending a telegram in reply is surveyed, thereby influences estimated accuracy.

(2) be the method for quantity of state with branch road telegram in reply stream

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 flow survey that is converted to that corresponding load telegram in reply flow is surveyed and branch road is sent a telegram in reply of the power measurement of branch road one end, 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, this 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.This 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 of electric distribution network method of estimation 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 measure conversion, and can handle situations such as radiation electrical network, weak looped network and cable charging capacitor.

The state of electric distribution network method of estimation of the extensive current measurement of support that the present invention proposes may further comprise the steps:

(1) set up a state of electric distribution network estimation model based on the 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 _IiBe the 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 the head end active power and the reactive power of power distribution network branch road, i is a headend node, and j is an 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: ${\left(P_j\right)}^m=\underset{i\∈j}{\mathrm{\Σ}}{P}_{\mathrm{ij}}-\underset{i\∈j}{\mathrm{\Σ}}{A}_{\mathrm{ij}}{R}_{\mathrm{ij}}-\underset{k\∈j}{\mathrm{\Σ}}{P}_{\mathrm{jk}},$

${\left(Q_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{X}_{\mathrm{ij}}-\underset{l\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{jl}}-\frac{{\mathrm{<figure-callout\; id="2"\; label="P\; jl"\; filenames="HSA00000168275400011.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{jl}}^{}+Q_{\mathrm{jl}}^2}{A_{\mathrm{jl}}{X}_{\mathrm{cj}}},$

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:

$\left[\begin{array}{cc}{H}^{T}W(I-\mathrm{diag}\{\frac{{(z-h\left(x\right))}^2}{{\mathrm{\&sigma;}}^2}\left\}\right)H& {\mathrm{<figure-callout\; id="0"\; label="C\; T\; C"\; filenames="DEST\_PATH\_HSB00000294166400012.png,DEST\_PATH\_HSB00000294166400014.png"\; state="\{\{state\}\}">C</figure-callout>}}^T& \\ C& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;x}\\ -\mathrm{\&lambda;}\end{array}\right]$

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

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 inequality respectively || Δ X ^(k)|| ₂≤ ξ ₁And c (X ^K+1)≤ξ ₂Whether set up simultaneously,, then make k=k+1, and forward step (2-3) to, if establishment, then output state variable, wherein ξ if be false 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 the division node, wherein, s is the division node 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 division node is: ${\left(B_s\right)}^m=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}$

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

Division node 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 of electric distribution network method of estimation 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 handle current measurement, has the following advantages:

1, is applicable to the state of electric distribution network estimation that measures based on the branch current amplitude, compares, measure the problem of conversion, make state estimation more correct with branch current method for estimating state in the past.

2, method for estimating state of the present invention can effectively be handled the state estimation problem of the power distribution network that comprises loop, also can handle for the charging capacitor branch road, therefore is suitable for 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 anti-difference ability, do not need built-in extra bad data identification program, so estimation procedure is more terse.

Description of drawings

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 a nodes result of calculation.

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

Fig. 4 is the radial grid branch electric current of 69 a nodes result of calculation.

Fig. 5 is the weak ring-type grid nodes load of 69 a nodes result of calculation.

Fig. 6 is the weak ring-type grid nodes load of 69 a nodes residual result.

Fig. 7 is the weak ring-type grid branch electric current residual result of 69 nodes.

Embodiment

The state of electric distribution network method of estimation of the extensive current measurement of support that the present invention proposes may further comprise the steps:

(1) set up a state of electric distribution network estimation model based on the 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 _IiBe the 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 the head end active power and the reactive power of power distribution network branch road, i is a headend node, and j is an 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: ${\left(P_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{R}_{\mathrm{ij}}-\underset{k\&Element;j}{\mathrm{\&Sigma;}}{P}_{\mathrm{jk}},$

${\left(Q_j\right)}^m=\underset{i\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}-\underset{i\&Element;j}{\mathrm{\&Sigma;}}{A}_{\mathrm{ij}}{X}_{\mathrm{ij}}-\underset{l\&Element;j}{\mathrm{\&Sigma;}}{Q}_{\mathrm{jl}}-\frac{{\mathrm{<figure-callout\; id="2"\; label="P\; jl"\; filenames="HSA00000168275400011.png"\; state="\{\{state\}\}">P</figure-callout>}}_{\mathrm{jl}}^{}+Q_{\mathrm{jl}}^2}{A_{\mathrm{jl}}{X}_{\mathrm{cj}}},$

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:

$\left[\begin{array}{cc}{H}^{T}W(I-\mathrm{diag}\{\frac{{(z-h\left(x\right))}^2}{{\mathrm{\&sigma;}}^2}\left\}\right)H& {\mathrm{<figure-callout\; id="0"\; label="C\; T\; C"\; filenames="DEST\_PATH\_HSB00000294166400012.png,DEST\_PATH\_HSB00000294166400014.png"\; state="\{\{state\}\}">C</figure-callout>}}^T& \\ C& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;x}\\ -\mathrm{\&lambda;}\end{array}\right]$

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

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 inequality respectively || Δ X ^(k)|| ₂≤ ξ ₁And c (X ^K+1)≤ξ ₂Whether set up simultaneously,, then make k=k+1, and forward step (2-3) to, if establishment, then output state variable, wherein ξ if be false 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 the division node, wherein, s is the division node 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 division node is: ${\left(B_s\right)}^m=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}$

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

Division node 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 electricity to divide article " considering the power distribution network network reconstruct of load balancing and network loss " (the Mesut E.Baran and Felix F.Wu.Network Reconfiguration in Distribution Systems for Loss Reduction and Load Balancing.IEEE Trans.on Power Delivery of periodical the 2nd phase of April in 1989 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 the influence of current measurement to the state estimation result, 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 separate the white noise that adds normal distribution in trend to produce.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 _FlowFor the branch current trend is separated A, i.e. actual value, S _SeBe the state estimation result.

Branch current measures the principle that increases in the embodiment of the invention, when topological analysis, has defined branch number, for branch number＜s ^*Prop up the branch road of way, increase branch current and measure.If this branch road definition is a 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, there is the charging capacitor branch road at 18,47,52,58,89 places at node, and 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 it is constant that all the other measure configuration.

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

Situation 4: load power measures variance and is increased to 0.14, and it is constant that all the other measure configuration.

The state estimation convergence conditions is:

||Δx|| ₂＜10 ^-5。σ ²＝0.1。

Fig. 2 is the load power state estimation precision 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 big measurement of load error in measurement, state estimation is obvious more 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 load well.

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 under the redundant situation, have or not bad data that the state estimation result is influenced not quite.Illustrate that this method has anti-automatically preferably difference ability, does not need built-in extra bad data recognition module.

Fig. 4 is a 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 big more effect of load bus error in measurement is obvious more.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 cyclic ligand electrical 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 it is constant that all the other measure configuration.

Situation 3: load power error in measurement variance increases to 0.09, and it is constant that all the other measure configuration.

Situation 4: load power error in measurement variance increases to 0.1, and it is constant that all the other measure configuration.

The state estimation convergence conditions is:

||Δx|| ₂＜10 ^-5。σ ²＝0.1。

Fig. 5 is weak ring-type grid nodes 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 under 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 big measurement of load error in measurement, state estimation is obvious more to the correction effect that load measures.

Fig. 6 is weak ring-type grid nodes 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 load well.

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 under the redundant situation, have or not bad data that the state estimation result is influenced not quite.Illustrate that this method has anti-automatically preferably difference ability 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 as can be seen, along with branch current measures increasing of quantity, the electric current estimated 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 of electric distribution network method of estimation of supporting extensive current measurement is characterized in that this method may further comprise the steps:

(1) set up a state of electric distribution network estimation model based on the 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 _IiBe the 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 the head end active power and the reactive power of power distribution network branch road, i is a headend node, and j is an 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: ${\left(B_j\right)}^m=\frac{{(P_{\mathrm{Lij}}-A_{\mathrm{ij}}{R}_{\mathrm{ij}})}^2+{(Q_{\mathrm{Lij}}-A_{\mathrm{ij}}{X}_{\mathrm{ij}})}^2}{A_{\mathrm{ij}}}$

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:

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

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

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

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

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

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 this any end that connects the branch branch road as the division node, wherein, s is the division node 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 division node is: ${\left(B_s\right)}^m=\frac{{(P_{\mathrm{rs}}-A_{\mathrm{rs}}{R}_{\mathrm{rs}})}^2+{(Q_{\mathrm{rs}}-A_{\mathrm{rs}}{X}_{\mathrm{rs}})}^2}{A_{\mathrm{rs}}}$

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

Division node 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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