CN102012967B - Method for rapidly calculating transmission capacity of time and space-labeled high-voltage grid - Google Patents

Abstract

The invention relates to a method for rapidly calculating transmission capacity of a time and space-labeled high-voltage grid, which comprises the following steps: setting up a time and space-labeled transmission capacity algorithm based on a procedure-oriented theory; establishing a time procedure-oriented transmission capacity/energy model and a power model; extracting feature data based on pattern recognition; and searching the maximum value and the minimum value representing the cross-section transmission capacity to finish rapid calculation. In the method, the problem that in the traditional calculation method, historical data is only used but mass data can not be on-line processed and calculated in real-time is solved; and the method has the characteristics of strong adaptability and high calculation speed, is simple in operation, and can be used for the rapid on-line calculation of the procedure-oriented high-voltage grid transmission capacity.

Description

There is the high-voltage fence ability to transmit electricity quick calculation method of Spatio-Temporal Label

Technical field

The invention belongs to field of power, be specifically related to a kind of high-voltage fence ability to transmit electricity quick calculation method with Spatio-Temporal Label of procedure-oriented theory.

Background technology

Nationwide integrated power grid is interconnected makes transregional transmission of electricity become possibility, and we consider a problem starting point from partial electric grid to nationwide integrated power grid.Because nationwide power supply, load distribution are uneven, cause electric energy from superfluous area to scarce areas flowing, in order to obtain maximum economic benefit, each bulk power grid falls over each other to send electric power or buy cheap electric power.Due to China's land resource shortage, therefore the construction of the power transmission network of expropriation of land increase is on a large scale very difficult, under generating set and transmission system often operate in the level close to stability limit, improves ability to transmit electricity, improves security and becomes focus.

After external large-scale blackout several times, various countries have recognized the importance utilizing WAMS (WAMS) to carry out dynamic realtime monitoring.China has started application.The data that WAMS provides not only have free token, and have time mark function.Electric power enterprise urgently wishes to obtain real-time ability to transmit electricity information in time, and adjustment generation schedule, obtains profit as much as possible under the prerequisite ensureing safe operation.Therefore build the ability to transmit electricity algorithm based on time effects, quick and precisely find the characteristic affecting power grid security, construct the mathematical model of the real-time ability to transmit electricity based on multiple security constraint, very important.

Summary of the invention

The object of the present invention is to provide a kind of high-voltage fence ability to transmit electricity quick calculation method with Spatio-Temporal Label based on procedure-oriented theory.The ability to transmit electricity quick calculation method with Spatio-Temporal Label is built according to procedure-oriented theory, set up the ability to transmit electricity electric flux model towards time course and power module, characteristic based on pattern-recognition is extracted, and finds the maximal value and minimum value that characterize section ability to transmit electricity, calculates fast.Adopt computing method of the present invention to overcome existing computing method and can only adopt historical data, can not real-time online process mass data and computational problem, there is strong adaptability, use simple, the feature that computing velocity is fast, can be applied to the quick calculating of processor-oriented online high-voltage fence ability to transmit electricity.

For achieving the above object, the invention provides a kind of high-voltage fence ability to transmit electricity quick calculation method with Spatio-Temporal Label set up based on procedure-oriented theory, described method adopts mode identification method to carry out compression process to mass data, introduce Lagrange factor, be optimized algorithm, these computing method comprise the steps:

Steps A: set up electrical network to be asked has Spatio-Temporal Label ability to transmit electricity electric flux model and power module towards time course, realize transmitting capacity of the electric wire netting and calculate in real time online, calculating data acquisition WAMS device is distant copies remote measurement real time data;

Step B: build the ability to transmit electricity concept based on time effects, the concept of definition time transmission cross-section, time course, described ability to transmit electricity is section ability to transmit electricity and process ability to transmit electricity, pass between described time course and time transmission cross-section is that the set of time transmission cross-section forms time course, realizes the infinitesimal analysis that section ability to transmit electricity and process ability to transmit electricity calculate and changes;

Step C: the characteristic set up based on pattern-recognition extracts fast algorithm, first adopts Karhunen-Loeve transformation method that the magnanimity real time data characterizing section ability to transmit electricity is carried out dimensionality reduction compression; Adopt power method and inverse power method maximizing and minimum value in the set characterizing section ability to transmit electricity again, make other section ability to transmit electricity numerical value between these two numerical value, improve computing velocity;

Step D: introduce Lagrange multiplier and set up the optimized algorithm based on section ability to transmit electricity and process ability to transmit electricity with Spatio-Temporal Label, for improve computing velocity and calculating accuracy rate.

Wherein, in described step B, following formula is adopted to carry out definition time transmission cross-section:

A _i(t)＝{N _i(t)，P _i(t)，Ctr _i(t)，G _i(t)} (1)

In formula: use A _it () represents time transmission cross-section, N _it () represents time dependent network parameter, P _it () represents time varying system status information amount, Ctr _it () represents time dependent control information amount, G _it () represents time dependent relation/logic.

Wherein, in described step C, first adopt Karhunen-Loeve transformation method that the magnanimity real time data characterizing section ability to transmit electricity is carried out dimensionality reduction compression, then adopt the concrete methods of realizing of power method and inverse power method maximizing and minimum value in the set of sign section ability to transmit electricity as follows:

P＝(p ₁，p ₂，......p _n) ^T

Wherein: X is power to be asked, P is realtime power proper vector, n × n square formation, it is n dimensional vector; Matrix by the column vector of n Line independent composition, if so only use m feature, then error delta X (m) is

Wherein, X is power to be asked, m () is the estimator of X

By the criterion of mean square deviation as the validity of tolerance m proper vector subset, have

Will m () is set to b _iwith function; In order to by the realtime power characterization time section ability to transmit electricity being mapped to the lower feature space of dimension, and not influence time section ability to transmit electricity size or reduce gap as far as possible, then ask for making the b of the best of (m) minimalization _iwith value,

$\frac{\∂}{{\∂b}_i}E\left[{(p_i-b_i)}^2\right]=-2[E\left(p_i\right)-b_i]=0---\left(5\right)$

Try to achieve

In other words for the component p of those P do not retained _i, replace just obtaining best b with mean value _ivalue, best b _iafter trying to achieve, try to achieve m () is as follows

∑ _X＝E[(X-E(X))(X-E(X)) ^T] (8)

Formula (8) is the covariance matrix of X, introduces Lagrange multiplier λ in this formula _i, obtain formula (9)

m () minimum necessary condition is:

Calculating is tried to achieve:

Make become the covariance matrix ∑ of X _xlatent vector, and λ _ibecome i-th eigenvalue of covariance matrix, so the best after trying to achieve, tried to achieve by following formula (12) (m):

Wherein, the concrete grammar setting up optimized algorithm in described step D is as follows:

Objective function:

$\max f\left(t\right)=\underset{t_b}{\overset{t_e}{\∫}}P\left(t\right)\mathrm{dt}=\mathrm{\Σ}\underset{t_i}{\overset{t_{i+1}}{\∫}}{P}_{\mathrm{avgi}}\left(t\right)\mathrm{dt}=\mathrm{\Σ}{P}_{\mathrm{avg}}\left(\mathrm{\ξ}\right)(t_{i+1}-t_i)---\left(13\right)$

Equality constraint:

H _i(t)＝0 (14)

Inequality constrain condition:

N _min≤N _i(t)≤N _max(15)

Ctr _min≤Ctr _i(t)≤Ctr _max

G _min≤G _i(t)≤G _max

Wherein: f (t) represents electric flux procedure function, P (t) represents not the effective value of power samples in the same time, P _avgrepresent average power in one-period, N _it () represents time dependent network parameter, Ctr _it () represents time dependent control information amount, G _it () represents time dependent relation/logic; Slack variable n is introduced in three inequality constrains of formula (15) _1i(t), n _2i(t), c _1i(t), c _2i(t), g _1i(t), g _2it (), all slack variables are all greater than 0, then inequality constrain is separately converted to equality constraint

N _i(t)+n _1i(t)＝N _max(16)

N _i(t)-n _2i(t)＝N _min

Ctr _i(t)+c _1i(t)＝Ctr _max

Ctr _i(t)-c _2i(t)＝Ctr _min

G _i(t)+g _1i(t)＝G _max

G _i(t)-g _2i(t)＝G _min

Introduce barrier parameter u, v, w, and barrier parameter is all greater than zero, transform objective function as barrier function, this barrier function is similar to former objective function f (t feasible zone planted agent simultaneously _i), and become very large when border, therefore obtain objective function:

maxf _i(t)-u(∑linn _1i(t)+∑linn _2i(t))-v(∑linc _1i(t)+∑linc _2i(t))-

w(∑ling _1i(t)+∑ling _2i(t)) (17)

Make U _i(t)=u ∑ linn _1i(t)+u ∑ linn _2i(t) (18)

V _i(t)＝v∑linc _1i(t)+v∑linc _2i(t)

W _i(t)＝w∑ling _1i(t)+w∑ling _2i(t)

Then objective function is reduced to maxf _i(t)-U _i(t)-V _i(t)-W _i(t) (19)

Equality constraint

H _i(t)＝0 (20)

N _i(t)+n _1i(t)＝N _max

N _i(t)-n _2i(t)＝N _min

Ctr _i(t)+c _1i(t)＝Ctr _max

Ctr _i(t)-c _2i(t)＝Ctr _min

G _i(t)+g _1i(t)＝G _max

G _i(t)-g _2i(t)＝G _min

Solving of this function can be converted into optimization extreme-value problem, introduces Lagrange multiplier λ ₁, λ ₂, λ ₃, λ ₄, λ ₅, λ ₆, order

X _i(t)＝λ ₁(N(t _i)+n ₁(t _i)-N _max)+λ ₂(N(t _i)-n ₂(t _i)-N _min) (21)

Y _i(t)＝λ ₃(Ctr(t _i)+c ₁(t _i)-Ctr _max)+λ ₄(Ctr(t _i)-c ₂(t _i)+Ctr _min)

Z _i(t)＝λ ₅(G(t _i)+g ₁(t _i)-G _max)+λ ₆(G(t _i)+g ₂(t _i)+G _min)

Obtain Lagrangian function maxf _i(t)-U _i(t)-V _i(t)-W _i(t)-X _i(t)-Y _i(t)-Z _i(t) (22)

F _i(t)＝maxf _i(t)-U _i(t)-V _i(t)-W _i(t)-X _i(t)-Y _i(t)-Z _i(t) (23)

This problem maximum value existent condition is the partial derivative of Lagrangian function to all variablees and Lagrange multiplier is zero, asks local derviation, make derivative be zero, solve above-mentioned formula.

Beneficial effect of the present invention: a kind of high-voltage fence ability to transmit electricity quick calculation method with Spatio-Temporal Label set up based on procedure-oriented theory of the present invention overcomes existing computing method and can only adopt historical data, can not real-time online process mass data and computational problem, there is strong adaptability, use simple, the feature that computing velocity is fast, can be applied to the quick calculating of processor-oriented online high-voltage fence ability to transmit electricity.

Accompanying drawing explanation

Fig. 1 is the improvement INTEGRAL THEOREM OF MEAN that the inventive method adopts;

Fig. 2 is the IEEE30 node electrical transmission network systems figure that the inventive method adopts;

Fig. 3 is the process flow diagram of quick calculation method of the present invention.

Embodiment

As shown in Figure 3, a kind of step with the high-voltage fence ability to transmit electricity quick calculation method of Spatio-Temporal Label based on the foundation of procedure-oriented theory of the present invention is as follows:

Steps A: set up electrical network to be asked has Spatio-Temporal Label ability to transmit electricity electric flux model and power module towards time course, realize transmitting capacity of the electric wire netting and calculate in real time online, calculating data acquisition WAMS device is distant copies remote measurement real time data;

Step B: build the ability to transmit electricity concept based on time effects, the concept of definition time transmission cross-section, time course, described ability to transmit electricity is section ability to transmit electricity and process ability to transmit electricity, pass between described time course and time transmission cross-section is that the set of time transmission cross-section forms time course, realizes the infinitesimal analysis that section ability to transmit electricity and process ability to transmit electricity calculate and changes;

Step C: the characteristic set up based on pattern-recognition extracts fast algorithm, first adopts Karhunen-Loeve transformation method that the magnanimity real time data characterizing section ability to transmit electricity is carried out dimensionality reduction compression; Adopt power method and inverse power method maximizing and minimum value in the set characterizing section ability to transmit electricity again, make other section ability to transmit electricity numerical value between these two numerical value, improve computing velocity;

Step D: introduce Lagrange multiplier and set up the optimized algorithm based on section ability to transmit electricity and process ability to transmit electricity with Spatio-Temporal Label, for improve computing velocity and calculating accuracy rate.

What procedure-oriented of the present invention theory was set up have in the step B of the high-voltage fence ability to transmit electricity quick calculation method of Spatio-Temporal Label proposes formula and derivation is as follows:

As shown in Figure 1, transmission cross-section divides according to Different factor the one group of interconnection summation formed.For reflecting the real shape in transmission cross-section region, adopt projective representation's method of section, cutting plane perpendicular to by the axis of cutting object or outline line, only should represent the shape in cross sectional area, and must mark section symbols in cross sectional area during projection.The curve of ability to transmit electricity can matching, and its calculating is made up of a series of parameter that is mutually related, quantity of state, controlled quentity controlled variable etc., and therefore any one transmission cross-section is all made up of a series of parameter that is mutually related, quantity of state, controlled quentity controlled variable etc.

A _i(t)＝{N _i(t)，P _i(t)，Ctr _i(t)，G _i(t)} (1)

In formula: use A _it () represents time transmission cross-section, N _it () represents time dependent network parameter, P _it () represents time varying system status information amount, Ctr _it () represents time dependent control information amount, G _it () represents time dependent relation/logic.

From geometric meaning, by procedure function f (t) (t _b≤ t≤t _e) the trapezoidal area in the bent limit that forms, equal certain section amount f (t _ξ) area of each piecemeal rectangle corresponding to horizontal linear section, as shown in Figure 1, wherein horizontal ordinate t represents the time, and ordinate f (t) represents procedure function, P _avg(ξ) average power in one-period is represented.

Therefore ask for ability to transmit electricity key be to locate P (t) characterization functional integration and an important section.

Then based on the section ability to transmit electricity objective function of time course:

$\max f\left(t\right)=\underset{t_b}{\overset{t_e}{\∫}}P\left(t\right)\mathrm{dt}=\mathrm{\Σ}\underset{t_i}{\overset{t_{i+1}}{\∫}}{P}_{\mathrm{avgi}}\left(t\right)\mathrm{dt}=\mathrm{\Σ}{P}_{\mathrm{avg}}\left(\mathrm{\ξ}\right)(t_{i+1}-t_i)---\left(13\right)$

Equality constraint:

H _i(t)＝0 (14)

Inequality constrain condition:

N _min≤N _i(t)≤N _max(15)

Ctr _min≤Ctr _i(t)≤Ctr _max

G _min≤G _i(t)≤G _max

Wherein: f (t) represents electric flux procedure function, P (t) represents not the effective value of power samples in the same time, P _avgrepresent average power in one-period.N _it () represents time dependent network parameter, Ctr _it () represents time dependent control information amount, G _it () represents time dependent relation/logic.Slack variable n is introduced in above three inequality constrains _1i(t), n _2i(t), c _1i(t), c _2i(t), g _1i(t), g _2it (), all slack variables are all greater than 0, then inequality constrain is separately converted to equality constraint

N _i(t)+n _1i(t)＝N _max(16)

N _i(t)-n _2i(t)＝N _min

Ctr _i(t)+c _1i(t)＝Ctr _max

Ctr _i(t)-c _2i(t)＝Ctr _min

G _i(t)+g _1i(t)＝C _max

G _i(t)-g _2i(t)＝G _min

Introduce barrier parameter u, v, w, and barrier parameter is all greater than zero simultaneously.Transform objective function as barrier function.This function is similar to former objective function f (t feasible zone planted agent _i), and become very large when border.Therefore objective function can be obtained:

maxf _i(t)-u(∑linn _1i(t)+∑linn _2i(t))-v(∑linc _1i(t)+∑linc _2i(t))-

w(∑ling _1i(t)+∑ling _2i(t)) (17)

Make U _i(t)=u ∑ linn _1i(t)+u ∑ linn _2i(t) (18)

V _i(t)＝v∑linc _1i(t)+v∑linc _2i(t)

W _i(t)＝w∑ling _1i(t)+w∑ling _2i(t)

Then objective function is reduced to maxf _i(t)-U _i(t)-V _i(t)-W _i(t) (19)

Equality constraint

H _i(t)＝0 (20)

N _i(t)+n _1i(t)＝N _max

N _i(t)-n _2i(t)＝N _min

Ctr _i(t)+c _1i(t)＝Ctr _max

Ctr _i(t)-c _2i(t)＝Ctr _min

G _i(t)+g _1i(t)＝G _max

G _i(t)-g _2i(t)＝G _min

Solving of this function can be converted into optimization extreme-value problem, introduces Lagrange multiplier λ ₁, λ ₂, λ ₃, λ ₄, λ ₅, λ ₆, order

X _i(t)＝λ _i(N(t _i)+n ₁(t _i)-N _max)+λ ₂(N(t _i)-n ₂(t _i)-N _min) (21)

Y _i(t)＝λ ₃(Ctr(t _i)+c ₁(t _i)-Ctr _max)+λ ₄(Ctr(t _i)-c ₂(t _i)+Ctr _min)

Z _i(t)＝λ ₅(G(t _i)+g ₁(t _i)-G _max)+λ ₆(G(t _i)+g ₂(t _i)+G _min)

Obtain Lagrangian function maxf _i(t)-U _i(t)-V _i(t)-W _i(t)-X _i(t)-Y _i(t)-Z _i(t) (22)

F _i(t)＝maxf _i(t)-U _i(t)-V _i(t)-W _i(t)-X _i(t)-Y _i(t)-Z _i(t) (23)

This problem maximum value existent condition is the partial derivative of Lagrangian function to all variablees and multiplier is zero.Local derviation is asked to above-mentioned formula, makes derivative be zero, solve.

So far, the ability to transmit electricity electric flux algorithm model based on time course has been built successfully.Because the object of building the ability to transmit electricity electric flux algorithm of time course being in order to ensureing that the ability to transmit electricity under power grid security prerequisite is maximum, therefore mass data being compressed, extreme value is asked to above-mentioned model.

Its basic thought be exactly high dimension vector is mapped to the lower feature space of dimension and not Effect Mode classification.Namely from original n-dimensional space N to a mapping of the lower m dimensional feature space M of dimension, m < n.Here discontinuity surface pattern when random vector X represents is tieed up with n.If g:N → M, X/ → P=g (x) here P is exactly a realtime power proper vector chosen.G is the mapping from N to M.Object is by the not Effect Mode classification to the lower feature space of dimension of higher-dimension instantaneous power maps feature vectors.

P＝(p ₁，p ₂，......p _n) ^T

Wherein: P is realtime power proper vector, n × n square formation, it is n dimensional vector.Matrix by the column vector of n Line independent composition, if so we are only by m feature, then error is

By the criterion of mean square deviation as the validity of tolerance m proper vector subset, have

By son m () is set to b _iwith function, in order to by the realtime power characterization time section ability to transmit electricity being mapped to the lower feature space of dimension, and not influence time section ability to transmit electricity size or reduce gap as far as possible, then ask for making the b of the best of (m) minimalization _iwith value.

$\frac{\&PartialD;}{\&PartialD;b_i}E\left[{(p_i-b_i)}^2\right]=-2[E\left(p_i\right)-b_i]=0---\left(5\right)$

Try to achieve

In other words for the component p of those P do not retained _i, replace just obtaining best b with mean value _ivalue.Best b _iafter trying to achieve, try to achieve m () is as follows

∑ _X＝E[(X-E(X))(X-E(X)) ^T] (8)

Formula (8) is the covariance matrix of X, introduces Lagrange multiplier λ in this formula _i, obtain formula (9)

m () minimum necessary condition is:

Calculating is tried to achieve:

Make become the covariance matrix ∑ of X _xlatent vector, and λ _ibecome i-th eigenvalue of covariance matrix, so the best after trying to achieve, tried to achieve by following formula (12) (m):

In pattern-recognition, p ₁, p ₂..., p _nregard the feature chosen from original measurement X as, these features have following feature:

(1) each feature p _irepresenting the validity in X by the eigenvalue λ corresponding with it _idetermined.If a feature p _ibe omitted, then square error increases λ _i.Feature large for those eigenvalues should be remained as much as possible.If eigenvalue descending order is numbered, make

λ ₁≥λ ₂≥......λ _n＞0 (24)

Then it can be used as the foundation of feature selecting.

(2) each feature is uncorrelated mutually, and that is the covariance matrix of P is diagonal angle, this is because:

When X be normal distribution in particular cases, each feature pi is separate.

(3) ∑ _xlatent vector make m () is minimum in all selections of orthonormal base vector.

Below that the present invention calculates on the basis of data at IEEE30 node power transmission network, adopt the high-voltage fence ability to transmit electricity quick calculation method with Spatio-Temporal Label to calculate, adopt Karhunen-Loeve transformation method that the magnanimity real time data characterizing section ability to transmit electricity is carried out the example of dimensionality reduction compression.

Fig. 2 is that the present invention adopts Karhunen-Loeve transformation method the magnanimity real time data characterizing section ability to transmit electricity to be carried out the IEEE30 node electrical transmission network systems figure of dimensionality reduction compression employing.

If branch power P _ithe instantaneous power proper vector of a sign section ability to transmit electricity chosen, can find out P exactly _ibe 41 × 41 rank matrixes, namely can obtain P by original table _{41 × 41}be a sparse matrix, can replace with X.Can be reduced to

X/→P _41×41(26)

By 41 × 41 rank matrix compressions of P, replace P with lower-order approximate matrix _{41 × 41}.If for unit matrix, so

In this example, the IEEE30 node transmission system parameter of IEEE30 node power transmission network alternator data and data processing is as shown in Table 1 and Table 2:

Table 1IEEE30 node power transmission network alternator data

The IFFE30 node transmission system parameter of table 2 data processing

Ergodic algorithm is adopted to find maximum power value P _maxwith minimal power values P _min, ask for with this number percent for reference value, setting one is greater than the number percent of this reference value as the cut off value judging to affect ability to transmit electricity size, selecting in this example 20% is cut off value: respectively by the active power of each branch road divided by maximum power value, by the absolute value of acquired results respectively compared with 20%, be less than or equal to 20%, namely this branch road is little on ability to transmit electricity impact; Be greater than 20%, namely this branch road is larger on ability to transmit electricity impact.

Error analysis: replace with previously selected constant those component subset not retaining P, form following estimator

The variance of X: E (X)=1.46 as calculated

get unit matrix:

Can obtain: b _i=1.46

The above-mentioned active power data by each branch road are divided into little on ability to transmit electricity impact and larger on ability to transmit electricity impact two parts, select to form new matrix to the larger part data of ability to transmit electricity impact and replace former P in this example _{41 × 41}matrix, then error is

Then former P _{41 × 41}matrix only replaces just to calculate ability to transmit electricity fast with the new matrix that dimension ability to transmit electricity being affected to larger part data composition is lower.

Procedure schema feature extraction: construct this part example raw data.Suppose that certain system divides is 4 regions, wherein region 1 is the interregional interconnection section be connected with its exterior, and region 2, region 3, region 4 are internal system section.For simplifying, consider that structure time course is one hour, gathered section active power data every 15 minutes, fraction part is omitted, and only retains integral part.Its section active power data see the following form 3:

Table 3 section active power data (MW)

Its vector table is: $p=\left[\begin{array}{cccc}2036& 247& 315& 139\\ 567& 1178& 1098& 856\\ 978& 769& 696& 1254\\ 498& 1456& 1578& 189\end{array}\right]$

If there is a number λ and non-vanishing vector, then meet: px=λ x (29)

Utilize power method iterative equation formula and iterative program, calculating is tried to achieve proper vector and is referred to table 4:

The characteristic value data that table 4 is tried to achieve by dark method

Utilize inverse power method iterative equation formula and iterative program, calculating is tried to achieve proper vector and is referred to table 5:

The characteristic value data that table 5 is tried to achieve by anti-dark method

Therefore power method is utilized to obtain eigenvalue of maximum λ ₁=2976.426, the value 2036 in corresponding matrix P is exactly maximum vector, i.e. maximum transmission cross-section.Inverse power method is utilized to obtain eigenvalue of maximum λ ₁=78.8769, the value 189 in corresponding matrix P is exactly minimum vector, i.e. minimum transmission cross-section.

Convergence:

Because of the proper vector x of P ₁..., x _nbetween be linear independence, power method is adopted to carry out first time iteration can obtain when kth walks due to as k → ∞, vectorial y ^(k)will with proper vector x ₁direction reach unanimity, and due to the impact of round-off error, to make along x ₁direction has nonzero element to there is (initial vector x ₀except) therefore the method be convergence.

It is more than the detailed description of the present invention being carried out for the ease of understanding the present invention; but it may occur to persons skilled in the art that; not departing from the scope that claim of the present invention contains and can also make other changes and modifications, these changes and amendment are all in protection scope of the present invention.

Claims (1)

1. there is a high-voltage fence ability to transmit electricity quick calculation method for Spatio-Temporal Label, it is characterized in that: these computing method comprise the steps:

Steps A: set up electrical network to be asked has Spatio-Temporal Label ability to transmit electricity electric flux model and power module towards time course, realize transmitting capacity of the electric wire netting and calculate in real time online, calculating data acquisition WAMS device is distant copies remote measurement real time data;

Step B: build the ability to transmit electricity concept based on time effects, the concept of definition time transmission cross-section, time course, described ability to transmit electricity is section ability to transmit electricity and process ability to transmit electricity, pass between described time course and time transmission cross-section is that the set of time transmission cross-section forms time course, realize the infinitesimal analysis that section ability to transmit electricity and process ability to transmit electricity calculate to change, described time transmission cross-section adopts following formula to define:

A _i(t)＝{N _i(t),P _i(t),Ctr _i(t),G _i(t)} (1)

In formula: use A _it () represents time transmission cross-section, N _it () represents time dependent network parameter, P _it () represents time varying system status information amount, Ctr _it () represents time dependent control information amount, G _it () represents time dependent relation/logic;

Step C: the characteristic set up based on pattern-recognition extracts fast algorithm, first adopts Karhunen-Loeve transformation method that the magnanimity real time data characterizing section ability to transmit electricity is carried out dimensionality reduction compression; Adopt power method and inverse power method maximizing and minimum value in the set characterizing section ability to transmit electricity again, make other section ability to transmit electricity numerical value between these two numerical value, improve computing velocity, its concrete methods of realizing is as follows:

P＝(p ₁,p ₂,......p _n) ^T

Wherein: X is power to be asked, P is realtime power proper vector, n × n square formation, it is n dimensional vector; Matrix by the column vector of n Line independent composition, if so only use m feature, then error delta X (m) is

Wherein, X is power to be asked, it is the estimator of X

By the criterion of mean square deviation as the validity of tolerance m proper vector subset, have

Will be set to b _iwith function; In order to by the realtime power characterization time section ability to transmit electricity being mapped to the lower feature space of dimension, and not influence time section ability to transmit electricity size or reduce gap as far as possible, then ask for making the b of the best of minimalization _iwith value,

$\frac{\&PartialD;}{{\&PartialD;b}_i}E{[(p_i-b_i)}^2]=-2[E\left(p_i\right)-b_i]=0---\left(5\right)$

Try to achieve

In other words for the component p of those P do not retained _i, replace just obtaining best b with mean value _ivalue, best b _iafter trying to achieve, try to achieve as follows

∑ _X＝E[(X-E(X))(X-E(X)) ^T] (8)

Formula (8) is the covariance matrix of X, introduces Lagrange multiplier λ in this formula _i, obtain formula (9)

minimum necessary condition is:

Calculating is tried to achieve:

Make become the covariance matrix ∑ of X _xlatent vector, and λ _ibecome i-th eigenvalue of covariance matrix, so the best after trying to achieve, tried to achieve by following formula (12)

Step D: introduce Lagrange multiplier and set up the optimized algorithm based on section ability to transmit electricity and process ability to transmit electricity with Spatio-Temporal Label, for improve computing velocity and calculating accuracy rate, the concrete grammar setting up optimized algorithm is as follows:

Objective function:

$\max f\left(t\right)=\underset{t_b}{\overset{t_e}{\&Integral;}}P\left(t\right)\mathrm{dt}=\mathrm{\&Sigma;}\underset{t_i}{\overset{t_{i+1}}{\&Integral;}}{P}_{\mathrm{avgi}}\left(t\right)\mathrm{dt}=\mathrm{\&Sigma;}{P}_{\mathrm{avg}}\left(\mathrm{\&xi;}\right)(t_{i+1}-t_i)---\left(13\right)$

Equality constraint:

H _i(t)＝0 (14)

Inequality constrain condition:

N _min≤N _i(t)≤N _max(15)

Ctr _min≤Ctr _i(t)≤Ctr _max

G _min≤G _i(t)≤G _max

Wherein: f (t) represents electric flux procedure function, P (t) represents not the effective value of power samples in the same time, P _avgrepresent average power in one-period, N _it () represents time dependent network parameter, Ctr _it () represents time dependent control information amount, G _it () represents time dependent relation/logic; Slack variable n is introduced in three inequality constrains of formula (15) _1i(t), n _2i(t), c _1i(t), c _2i(t), g _1i(t), g _2it (), all slack variables are all greater than 0, then inequality constrain is separately converted to equality constraint

N _i(t)+n _1i(t)＝N _max(16)

N _i(t)-n _2i(t)＝N _min

Ctr _i(t)+c _1i(t)＝Ctr _max

Ctr _i(t)-c _2i(t)＝Ctr _min

G _i(t)+g _1i(t)＝G _max

G _i(t)-g _2i(t)＝G _min

Introduce barrier parameter u, v, w, and barrier parameter is all greater than zero, transform objective function as barrier function, this barrier function is similar to former objective function f (t feasible zone planted agent simultaneously _i), and become very large when border, therefore obtain objective function:

$\begin{array}{c}\max f_i\left(t\right)-u(\mathrm{\&Sigma;}{\mathrm{linn}}_{1i}\left(t\right)+\mathrm{\&Sigma;}{\mathrm{linn}}_{2i}\left(t\right))-v(\mathrm{\&Sigma;}{\mathrm{linc}}_{1i}\left(t\right)+\mathrm{\&Sigma;}{\mathrm{linc}}_{2i}\left(t\right))-\\ w(\mathrm{\&Sigma;}{\mathrm{ling}}_{1i}\left(t\right)+\mathrm{\&Sigma;}{\mathrm{ling}}_{2i}\left(t\right))\end{array}---\left(17\right)$

Make U _i(t)=u ∑ linn _1i(t)+u ∑ linn _2i(t) (18)

V _i(t)＝v∑linc _1i(t)+v∑linc _2i(t)

W _i(t)＝w∑ling _1i(t)+w∑ling _2i(t)

Then objective function is reduced to max f _i(t)-U _i(t)-V _i(t)-W _i(t) (19)

Equality constraint:

H _i(t)＝0 (20)

N _i(t)+n _1i(t)＝N _max

N _i(t)-n _2i(t)＝N _min

Ctr _i(t)+c _1i(t)＝Ctr _max

Ctr _i(t)-c _2i(t)＝Ctr _min

G _i(t)+g _1i(t)＝G _max

G _i(t)-g _2i(t)＝G _min

Solving of this function can be converted into optimization extreme-value problem, introduces Lagrange multiplier λ ₁, λ ₂, λ ₃, λ ₄, λ ₅, λ ₆, order

X _i(t)＝λ ₁(N(t _i)+n ₁(t _i)-N _max)+λ ₂(N(t _i)-n ₂(t _i)-N _min) (21)

Y _i(t)＝λ ₃(Ctr(t _i)+c ₁(t _i)-Ctr _max)+λ ₄(Ctr(t _i)-c ₂(t _i)+Ctr _min)

Z _i(t)＝λ ₅(G(t _i)+g ₁(t _i)-G _max)+λ ₆(G(t _i)+g ₂(t _i)+G _min)

Obtain Lagrangian function max f _i(t)-U _i(t)-V _i(t)-W _i(t)-X _i(t)-Y _i(t)-Z _i(t) (22)

F _i(t)＝max f _i(t)-U _i(t)-V _i(t)-W _i(t)-X _i(t)-Y _i(t)-Z _i(t) (23)

This problem maximum value existent condition is the partial derivative of Lagrangian function to all variablees and Lagrange multiplier is zero, asks local derviation, make derivative be zero, solve above-mentioned formula.