Summary of the invention
Technical problem to be solved by this invention is to provide a kind of power system state estimation method based on load voltage static characteristic model at the defective that prior art exists.
The present invention adopts following technical scheme for achieving the above object:
The present invention is characterized in that comprising step down for considering the power system state estimation method of static load characteristic:
(1) reads electric network data among the EMS, comprising: the branch road of transmission line number, headend node and endpoint node numbering, transformer voltage ratio and impedance, series resistance reactance, shunt conductance susceptance;
(2) read the static load characteristic parameter, comprising: load active power, reactive power and relevant voltage performance index during the datum mark steady operation, the static load characteristic model representation is as follows:
Adopt power function model:
Adopt the quadratic polynomial model:
(3) initialization comprises: to quantity of state initial value, the optimization of node order be set, form node admittance matrix, threshold value be set, storage allocation;
(4) input real-time measurement amount z comprises voltage magnitude, generator active power, generator reactive power, part of nodes (promptly having picked out the node of static load characteristic model) load active power and reactive power, circuit head end active power, circuit head end reactive power, line end active power and line end reactive power;
(5) for the load bus of known its static characteristic parameter, make up zero injecting power measurement equation and replenish original load bus power measurement equation, consider that the zero injection rate measurement of static load characteristic is expressed as follows:
Adopt power function model:
Adopt the quadratic polynomial model:
(6) recover iteration count iterations k=1;
(7) calculate the calculated value h (x of each measurement amount by existing quantity of state x (k)
(l)) and Jacobian matrix H (x
(l)), the load bus of wherein known load static models zero injection rate is measured calculated value and is:
Adopt power function model:
Adopt the quadratic polynomial model:
This type of measures, and element is in the corresponding Jacobian matrix:
Adopt power function model:
Adopt the quadratic polynomial model:
(8) ask for state correction amount x
(k), choose
And the correction quantity of state obtains x
(k+1)
(9) judge
Whether less than convergence, if, finish to calculate, carry out the k+1 time estimation otherwise return step (6).
Traditional state estimation utilization is measured and corresponding variance is set up target function, solves to make the quantity of state of target function minimum.Because the measurement amount comprises white Gaussian noise, the inevitable white Gaussian noise that also have of state estimation value in iterative process and last result, and as can be seen by the analysis of state estimation algorithm, state estimation error variance battle array diagonal element is the diagonal element after information matrix is inverted, its diagonal element whatever you like measurement of information matrix increases and increases, the diagonal element of its inverse matrix then decreases, and therefore, the quality of measurement system configuration and what are keys of state estimation effect.
The present invention is on the basis of load modeling identification, the voltage character of load static models have been considered during to the choosing of load power measurement amount, considered the injecting power amount of load point more comprehensively and accurately, utilize accurate voltage character of load static models to replenish the measurement amount that replaces containing random error, at this moment, the load bus injecting power is the performance number of load static models reflection and the zero injecting power of power equation calculated value addition, because it is not containing white Gaussian noise for exact solution, then give bigger weights (10~100 times to the weight of real-time measurement amount) to it, and iterative computation is carried out in substitution, when the iterative Jacobian matrix, need replenish into load model factor for the node of having considered load quiescent voltage characteristic during to self node voltage amplitude differentiate, the Jacobian matrix remainder is constant.The present invention has improved the quality of measurement configuration effectively, and has made the result of state estimation more accurate by having taken into account load voltage static characteristic model.
Embodiment
Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:
The real time execution of electric power system and control need the true operating condition of understanding system, because aspects such as measurement and transmission, there is error unavoidably in the living data that obtain, and state estimation can improve the precision of data to a certain extent.From the Xu Huaipi of Massachusetts Institute Technology in 1969 people such as (F.C.Schweppe) the rudimentary algorithm of Power system state estimation having been proposed---since basic weighted least-squares (the weighted least squares WLS) state estimation algorithm, weighted least-squares method becomes the maximum algorithm of application in the Power system state estimation.WLS tries to achieve the weighted residual quadratic sum with the inverse of the variance of measurement amount error as the weight of corresponding residual error (measurement amount and measure the poor of estimated value), and as target function, expectation obtains making the state vector x of target function minimum with this.Therefore, the q﹠r of measurement system configuration is very important to the state estimation result, and the present invention has considered the load static models on the basis of WLS for the measurement system configuration requirement, in the hope of obtaining more accurate estimated result.
Under the condition of given network connection, branch road parameter and measurement system, non-linear measurement equation can be expressed as:
z=h(x)+v
In the formula, z is a telemetry for the measuring value vector, and the overwhelming majority is the real time data that obtains by remote measurement, and it is the artificial data that are provided with that sub-fraction is also arranged, and is called as pseudo-metric data; H (x) is the true value of measurement amount of hypothesis, the phasor function of being set up by basic circuit laws such as kirchhoffs; X is that n maintains the system state variable; V is an error in measurement, supposes that average is zero, variance is σ
2The normal distribution random vector, it is the m n dimensional vector n.
In Power system state estimation, the type of measurement amount configuration is more than conventional trend, has comprised that not only the injecting power of each node measures P
i, Q
i, can also comprise the power measurement P of branch road
Ij, Q
Ij, P
Ji, Q
JiAnd the voltage of node measures V
iInject meritorious power measurement P with node
i, branch road top active power measures P
IjAnd node voltage measures V
iBe example, measurement equation is shown below:
Node injects active power and reactive power (following all is with polar coordinate representation):
In the above-mentioned measurement equation, Y
IjFor the element between corresponding node i and the j in the node admittance battle array, Y is arranged
Ij=G
Ij+ B
Ij, G wherein
IjFor electricity is led, B
IjBe susceptance; P
iAnd Q
iMeritorious and the idle injecting power for node i, its direction dictates: flow into node i for just, flow out node i for negative.
The node i voltage magnitude:
U
i=U
i
Non-transformer lines i-j goes up top active power and reactive power:
Non-transformer branch road i-j goes up terminal active power and reactive power:
In the above-mentioned measurement equation, y
IjAdmittance value for circuit has
R, X, g, b are respectively line resistance, reactance, electricity is led and susceptance.
For the transformer branch road, measurement equation is shown below:
Transformer branch road i-j goes up top active power and reactive power:
Transformer branch road i-j goes up terminal active power and reactive power:
In the above-mentioned transformer branch road measurement equation, K is the non-standard no-load voltage ratio of transformer.J is the standard side, and no-load voltage ratio is 1; I is non-standard side, and no-load voltage ratio is K; b
TSusceptance for transformer standard side (j side) has
X wherein
TReactance for transformer standard side.
Make up zero and inject active power and reactive power equation:
Adopt power function model:
Adopt the quadratic polynomial model:
In the aforesaid equation, P
I0And Q
I0Load active power and reactive power when being respectively the datum mark steady operation, p
UAnd q
UBe the voltage characteristic index of load meritorious and reactive power, a
p, b
p, c
p(a
q, b
q, c
q) active power (reactive power) that is respectively constant impedance, constant current, firm power load accounts for the percentage of total active power (reactive power), and a is arranged
p+ b
p+ c
p=1 (a
q+ b
q+ c
q=1).This moment, no longer there was random error in load bus injecting power deviation, then Δ P
iWith Δ Q
iIt is zero injecting power.
After the given measurement vector z, the state estimation vector
Be to make target function:
J(x)=[z-h(x)]
TR
-1[z-h(x)]
Reach the value of the x of minimum.Wherein, R
-1Be with
Inverse be the diagonal matrix of diagonal element, in state estimation, play the meaning heavy to the residual error weighting.
Because h (x) is the nonlinear function of x, so can't directly calculate
In order to ask for
At first h (x) is carried out the linearisation hypothesis, ignores after the above nonlinear terms of secondary, obtain:
h(x)=h(x
0)+H(x
0)Δx
In the formula, Δ x=x-x
0,
The H here (x) is the Jacobian matrix that m * n rank measure vector.
At this moment, target function obtains:
J(x)=[Δz-H(x
0)Δx]
TR
-1[Δz-H(x
0)Δx]
Δ z=z-h (x in the formula
0)
Desire to make the target function minimum,, thereby have its differentiate or expansion prescription:
Obtain thus:
When adopting the polar coordinate system expression formula, each measurement amount h
i(x) to quantity of state x
jA partial derivative be calculated as
As follows:
The node voltage amplitude:
Node injects meritorious and reactive power:
Top power on the non-transformer branch road i-j:
Terminal power on the non-transformer branch road i-j:
Top power on the transformer branch road i-j:
Terminal power on the transformer branch road i-j:
Among the present invention, for the node of setting up load voltage static characteristic model, replenished node injecting power value, its injecting power is as follows to the local derviation computational methods of quantity of state:
Work as i=j, when adopting power function model:
Adopt the quadratic polynomial model:
Herein, made relevant treatment for the weight based on the node injecting power of load voltage static characteristic model among the present invention, owing to considered static load characteristic, the injecting power of corresponding node is an exact solution, therefore be considered as not existing random error, then set weight gets higher value so that its proportion in target function is outstanding, and the 10-100 that gets all the other measurement amount weights when specifically calculating doubly.
Then, carry out the iteration correction, wherein, when calculating residual error, considered that the residual error of the node of static load characteristic is according to aforementioned formula:
Adopt power function model:
Adopt the quadratic polynomial model:
Iteration is up to target function J (x
(l)) less than till the threshold values that sets in advance.
The initial information of state estimation is transmitted the measurement signal of returning from telemetering equipment, measurement signal is the measurement amount that comprises random error, basic weighted least-squares (WLS) method for estimating state is that the inverse of the variance measured of utilization is set up the target function of weighted residual as weight, estimates quantity of state.This method model is simple, good convergence, and the estimated quality height is one of method that is most widely used at present.But this method has certain dependence for the precision of measurement amount, i.e. measurement is accurate more, and estimated result is also accurate more.
The present invention is owing to considered the voltage static characteristic model of load bus, in the measurement amount, replenished load bus zero injecting power, make the precision of measurement amount increase, and when iterative computation, given bigger weight, can make its proportion in target function obvious, therefore also correspondingly improve state estimation result's precision.
As shown in Figure 2, figure (a) is a circuit ∏ shape equivalent circuit diagram, serial connection admittance g+j ' b between node i and the node j, and the output of node i, j is connected in series a ground connection susceptance j ' y respectively
cBack ground connection.
Figure (b) is a transformer ∏ shape equivalent circuit diagram, is connected in series between node i and the node j
One of node i serial connection
Back ground connection, one of the output serial connection of j
Back ground connection.J ' expression imaginary part.