CN107994567A - A kind of broad sense Fast decoupled state estimation method - Google Patents
A kind of broad sense Fast decoupled state estimation method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The present invention proposes a kind of broad sense Fast decoupled state estimation method, and this method comprises the following steps：Measurement is converted, obtains the active measurement of class and the idle measurement of class, and then obtains the measurement equation of the active type measurement of class and the idle type measurement expression of class and the Jacobian matrix of iterative equation；Broad sense Fast decoupled state estimation model is proposed on this basis, using Newton method, to the broad sense Fast decoupled state estimation model solution, obtains state variable estimate.Sample calculation analysis shows that broad sense Fast decoupled state estimation method is respectively provided with power transmission network and power distribution network good adaptability, while branch current magnitudes can be used to measure for broad sense Fast decoupled state estimation method.Simulation example, which demonstrates institute's extracting method, has good convergence and very high computational efficiency, is suitable for the application on site of large scale network.
Description
Technical Field
The invention belongs to the technical field of power system dispatching automation, and particularly relates to a method for estimating a generalized Fast Decomposed State (FDSE).
Background
With the continuous expansion of the scale of the power grid and the development of the smart power grid and the energy internet, more and more mass data need to be processed in time. The State Estimation (SE) as a data filter will continue to play the role of a safe and stable running keystone, and there will be higher demands on the computational performance. The first proposed SE method is a Weighted Least Squares (WLS) based on maximum likelihood estimation. WLS is widely used because of its simple algorithm and good convergence. In order to further improve the calculation efficiency of the WLS, researchers propose a fast decomposed State estimation method (FDSE) based on a decoupling concept of load flow calculation. For most power transmission networks, FDSE has good convergence and high computational efficiency. Nowadays, WLS and FDSE are still excellent algorithms in the SE field, and are widely applied to power grid dispatching control centers at home and abroad. However, it should be noted that FDSE relying on three preconditions has the following limitations: (1) FDSE may not converge when network parameters (such as high R/X ratio) and operating conditions are not satisfied with the decoupling condition; (2) FDSE cannot use Branch Current Magnitude Measurements (BCMMs), which affects the estimation accuracy and even results in not meeting observability, especially for distribution networks with large amounts of BCMMs.
Disclosure of Invention
The present invention aims to solve at least one of the above technical problems to at least some extent or to at least provide a useful commercial choice. Therefore, the invention provides a Generalized Fast decomposed State estimation method (GFDSE).
The specific technical scheme of the invention is that the generalized fast decomposition state estimation method comprises the following steps:
step A, converting the measurement quantity to obtain an active type quantity measurement and a reactive type quantity measurement, and further obtaining a measurement equation represented by the active type quantity measurement and the reactive type quantity measurement and a Jacobian matrix H of an iterative equation of the measurement equation pp And H QQ ；
And B, based on the measurement equation, giving a generalized fast decomposition state estimation model:and solving by using a Newton method to obtain a state variable estimated value.
The method comprises the following steps of:
step A1: the measurement of the quantity is transformed to form an active-type quantity measurement and a reactive-type quantity measurement, wherein the active-type quantity measurement is z P The method comprises the following steps:reactive-like type measurement z Q IncludedTheir computational expressions are: the transformed measurement equations are unified as:
in the formula: theta.theta. i Is the phase angle of node i, θ ij Is the phase angle difference, V, at both ends of branch ij i Is the voltage amplitude of node i; w is a P,i And w Q,i Measuring z for the ith active and inactive quantities P,i And z Q,i The weight of (c); h is a total of P (θ, V) is the active estimation equation, h Q (θ, V) is a reactive power estimation equation; r is P ，r Q The vector is a similar active residual error vector and a similar reactive residual error vector; p i Node i injects active, Q i Node i injects reactive, P ij For active power flow, Q, of branch ij head end ij For the reactive power flow at the head end of branch ij,the active component of the head-end current of branch ij,is the reactive component of the current at the head end of the branch ij;the node i injects an active transformation quantity,the node i is injected with a reactive transformation quantity,the head end of the branch ij has active power flow conversion quantity,for the head end reactive power flow conversion quantity of the branch ij,the head-end current has a conversion amount of the active component,is the reactive component of the head-end current of branch ij,the voltage amplitude value of the node i is converted; g ij Is a series conductance, b ij Is a series of susceptances, g si For the head end of the branch to conduct to ground, b si The head end of the branch is susceptance to the ground; λ = (g) ij +g si )/(b ij +b si )，γ＝-g ij /b ij ；
Step A2: based on the quantity measurement after the conversion in the step A1, forming a Jacobian matrix H of an active part and a reactive part in an iterative equation pp And H QQ 。
For step B, comprising: based on the step A, a generalized fast decomposition state estimation model is provided,solving by Newton's method, includingThe following steps:
step B1: initializing a variable θ 0 ，V 0 Number of iterations k max The convergence condition is as follows: delta theta k <,. Epsilon.and.DELTA.V k &Epsilon, a convergence mark KP = KQ =1;
and step B2: by fast decomposition of iterative equationsComputingAnd Δ θ k And correcting for theta k+1 ＝θ k +Δθ k Judging whether the step is converged, and if so, assigning KP =0; if not, KP =1, and go to step B4;
and step B3: by fast decomposition of iterative equationsComputingAnd Δ V k And correcting V k +1 ＝V k +ΔV k Judging whether the step is converged, if so, assigning KQ =0, otherwise, assigning KQ =1, and going to step B4;
and step B4: judging whether the total is convergent or not, if KP = KQ =0, finishing the calculation, and obtaining a state variable estimation value; if KP =1, go to step B3; if KQ =1, turning to step B2;
in the formula: h pp And H QQ Jacobian matrix, W, of active and reactive parts, respectively P And W Q The weights of active measurement and reactive measurement are respectively.
The step B2 comprises the following steps:
step B21: computing
The step B3 comprises the following steps:
step B31: computing
The invention relates to a generalized Fast decomposition state estimation method (GFDSE), which has good adaptability to both a transmission network and a distribution network (including a high R/X network), and the GFDSE can measure branch current amplitude. The simulation example verifies that the method has good convergence and high calculation efficiency, and is suitable for online application of a large-scale network.
Additional advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
FIG. 1 is a flowchart of a generalized fast decomposition state estimation method according to the present invention.
FIG. 2 is a schematic diagram of a pi branch circuit model.
FIG. 3 is a diagram of an equivalent model of a pi branch.
FIG. 4 is a comparison graph of the numerical stability of the algorithm of the present invention.
Fig. 5 is a graph comparing average single iteration times.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
A generalized fast decomposition state estimation method comprises the following steps:
step A, the measurement is transformed to obtain similar active and reactive measurement and obtain a modified measurement equation and a Jacobian matrix H in an iteration equation pp And H QQ And the method has better reactive and active decoupling characteristics in a high R/X network.
Step A1: the measurement is converted, and if the three-winding transformer is equivalent to three two-winding transformers, all the transformer branches and the transmission line branches can be represented by a pi-shaped path shown in fig. 2.
In FIG. 2 y s ＝g s +jb s ＝1/(r ij +jx ij ) Is a series susceptance, r ij +x ij Is a series impedance, b c For line charging susceptance (to transformer branch b) c = 0); k is the transformation ratio (k =1 for the transmission line), and the equivalent circuit of fig. 2 is shown in fig. 3.
In FIG. 3, g ij ＝g s /k，b ij ＝b s /k，g si ＝(1-k)g s /k 2 ，b si ＝(1-k)b s /k 2 +b c /2，g sj ＝(k-1)g s /k，b sj ＝(k-1)b s /k+b c /2。
If the zero injection power virtual measurement is not considered, the measurement quantities used for power distribution network state estimation generally include four types: measuring the voltage amplitude of the node i; measuring the current amplitude of the branch ij; power measurement P of branch ij ij And Q ij And injection power measurement P of node i i And Q i . The measurement equations for these four measurements are as follows:
in the formula: p is i Node i injects active, Q i Node i injects reactive, P ij For active power flow, Q, of branch ij head end ij For the reactive power flow at the head end of branch ij,the active component of the head-end current of branch ij,is the reactive component of the current at the head end of the branch ij; a. The ij ＝(g si +g ij ) 2 +(b si +b ij ) 2 ；D ij ＝-g si b ij +b si g ij ；g si ,b si ,g ij And b ij The meaning of (1) is the same as that of FIG. 2; the other variables have the same meaning as above.
For the node injection power measurement, the reactive component of the node after the node correction is P i +Q i (ii) a The active component is P i . The modified measurement equation is:
in the formula G ij ,B ij Respectively a real part and an imaginary part of a non-diagonal element of the node admittance matrix; g ii ,B ii Respectively the real part and the imaginary part of the diagonal elements of the node admittance matrix.
For branch workMeasuring the power, namely correcting the branch power measurement by a method for constructing a new measurement function, wherein the active component is;the reactive component isThe modified branch power measurement equation is:
in the formula: λ = (g) ij +g si )/(b ij +b si )，γ＝-g ij /b ij ；
For branch current magnitude measurement: to theta i ,θ j ,V i And V j The first partial derivative is calculated and V =1, theta is used ij =0 to normalize the Jacobi matrix:
in view of the fittingIn the electric network b ij /g ij |>&This decoupling condition of gt, 1 is not satisfied. The branch current amplitude measurement cannot be easily regarded as a reactive component or an active component in the decoupling process. Therefore, the branch current amplitude value measurement needs to be properly modified.
The branch current amplitude measurement equation can be rewritten into the form of equation (15):
from formula (15):namely, the branch current measurement is modified to realize decoupling, and the modified current measurement equation is as follows:
measuring the node voltage amplitude:
V meas ＝V (17)
the voltage amplitude is known as a reactive component from equation (17), and only the node voltage amplitude is involved in the decoupling iteration.
Step A2: forming an iterative Jacobian matrix H in a correction equation pp And H QQ 。
As can be seen from equations (7) and (8), the jacobian matrix in the iteration of the transformed node injecting active power and reactive power is:
from the equations (9) and (10), the jacobian matrix of the active power and the reactive power of the transformed measurement branch is:
from equations (15) and (16), the jacobian matrix in the transformed measurement current iteration is:
in the formulaThe elementsof the Jacobian matrix, and the meaning of the other variables is the same as above.
From equation (17), the jacobian matrix in the transformed measurement voltage iteration is:
the corrected active component and reactive component and their Jacobian matrix H can be obtained pp And H QQ . Wherein
And B, based on the step A, giving a generalized fast decomposition state estimation model:
solving by using a Newton method:
step B1: initializing a variable θ 0 ，V 0 Number of iterations k max The convergence condition is as follows: delta theta k <,. Epsilon.and.DELTA.V k &Epsilon convergence mark KP = KQ =1;
and step B2: by fast decomposition of iterative equationsCalculating Δ z P And Δ θ, and correcting θ k+1 ＝θ k +Δθ k Judging whether the step is converged, and if so, assigning KP =0; if not, KP =1, and go to step B4;
and step B3: by fast decomposition of iterative equationsCalculating Δ z Q And Δ V, and correcting V k +1 ＝V k +ΔV k Judging whether the step is converged, if so, assigning KQ =0, otherwise, assigning KQ =1, and going to step B4;
and step B4: judging whether the total is convergent or not, if KP = KQ =0, finishing the calculation, and obtaining a state variable estimation value; if KP =1, go to step B3; if KQ =1, go to step B2.
In the formula: h pp And H QQ Jacobian matrices for active and reactive parts, respectively; w P And W Q The weights for active and reactive measurements are provided.
The step B2 comprises the following steps:
step B21: calculating out
The step B3 comprises the following steps:
step B31: calculating out
For a better understanding of the present invention and to show the advantages thereof over the prior art, reference is made to the accompanying drawings, which form a part hereof, and in which is shown by way of illustration specific embodiments.
Examples
The IEEE9 node, IEEE14 node, and IEEE30 node systems are used to illustrate the adaptability of the algorithm herein to networks with large impedance ratios. The measurement value is obtained by superimposing white gaussian noise (mean 0, variance τ) on the basis of the power flow calculation result. For voltage measurement, take τ v =0.002pu, taking τ from the power measurement PQ =0.02pu, measuring the current amplitude I =0.01pu. The simulation was performed in 3 cases where the branch maximum impedance ratio r/x was 0.8,1,1.5, respectively.
1. Accuracy analysis
To characterize the state estimation accuracy, the mean error of the state estimation result is defined as:
in the formula:estimating the result for the state variable; x is the number of pf Is the true value of the state variable; n is the total number of state variables.
Table 1 lists the average error of the state estimation results for four cases of 0.8,1,1.2 and 1.5 branch maximum impedance ratios in the IEEE14 node system.
TABLE 1 State estimation mean error under different impedance ratios
In order to further compare the good estimation accuracy in different networks with large impedance, the invention also compares the average error of the IEEE9 node system, the IEEE14 node system and the IEEE30 node system when the maximum impedance ratio is 1.1, and the result is shown in Table 2.
Table 2 mean error of state estimation under different networks
As can be seen from tables 1 and 2, the algorithm of the present invention has good calculation accuracy when dealing with networks having relatively large impedance.
2. Convergence analysis
The algorithm provided by the invention is an improvement of the traditional FDSE state estimation algorithm. In order to illustrate the convergence of the algorithm, the classical WLS state estimation algorithm, the traditional FDSE state estimation algorithm and the algorithm provided by the invention are subjected to simulation analysis respectively.
Table 3 shows the convergence of the respective algorithms in the case where the maximum impedance ratios are different in the IEEE14 node system. From the results, it is found that WLS can be converged efficiently with a minimum number of WLS convergence times. This is because WLS has square convergence. The iteration times of solving by using the FDSE method are greatly increased along with the improvement of the maximum impedance ratio, and when the maximum impedance ratio is greater than 1, the FDSE can not be effectively converged, because the state estimation algorithm based on the P-Q decoupling adopts the traditional power decoupling formula, when the impedance ratio is high, the power decoupling condition is not met any more, and the measurement function does not correctly reflect the network load flow any more, so that the state estimation convergence condition is deteriorated.
TABLE 3 number of iterations for state estimation for each algorithm
Note: DIV: iterative divergence
As can be seen from the data in Table 3, the algorithm of the present invention can be reliably converged under different impedance ratios, and the number of iterations does not change with the change of the impedance ratio. This is because the active and reactive power are caused to affect the voltage amplitude together when decoupling the injected power measurement; when the branch power is decoupled, a new branch measurement function is constructed to enable elements in a Jacobi matrix of an active component of the branch power to a voltage amplitude to be far smaller than corresponding elements of the Jacobi matrix of a voltage phase angle, and simultaneously enable elements in a Jacobi matrix of a reactive component of the branch power to the voltage phase angle to be far smaller than corresponding elements of the Jacobi matrix of the voltage amplitude. This enables the new metrology function to satisfy the decoupling condition. And effective decoupling can be realized for networks with different impedance ratios. But for the coefficient alpha in the reconstructed metrology function P ,β P ,α Q And beta Q The value of (c) is to be explored further.
The convergence times of the IEEE14 algorithm under the corresponding conditions are analyzed for the error variations (plus or minus 0.5 percent and plus or minus 1 percent) of different degrees of the initial iteration values, and the simulation result is shown in FIG. 4. The result shows that the errors of the initial values in different degrees have no obvious influence on the convergence times of the algorithm, namely the algorithm has good numerical stability.
3. Computational efficiency analysis
Table 4 shows the simulation iteration time of the algorithm of the present invention in different systems with WLS and FDSE. It can be seen that the classical WLS method is longer in iteration time due to the recalculation of the Jacobi matrix per iteration. FDSE reduces the matrix calculation scale in iteration through decoupling solution, accelerates the iterative calculation speed to a certain extent, but because the algorithm is not suitable for a network with larger r/x, the iterative convergence time is still longer, even the iterative convergence is not converged. The results in table 4 show that the algorithm of the present invention greatly increases the calculation speed compared to the WLS, and has a similar calculation speed compared to the FDSE with a better convergence condition, and overall, the algorithm of the present invention not only ensures the advantage of a fast FDSE convergence speed, but also ensures the advantage of the WLS algorithm that is suitable for networks with different impedance ratios.
TABLE 4 comparison of the state estimates for each algorithm over the iteration time
Fig. 5 is a comparison of the average single iteration time of the inventive algorithm and the classical WLS algorithm in the IEEE9 node system, the IEEE14 node system and the IEEE30 node system where max (r/x) = 1.1. It can be seen that the single iteration time of the algorithm of the present invention is significantly lower than that of the WLS state estimation algorithm, and the degree of decrease in the single iteration time is more significant as the number of nodes increases. The algorithm Jacobi matrix is a constant matrix, the Jacibo matrix does not need to be recalculated in each iteration, the iterative calculation scale is reduced through power decoupling, and the iterative calculation speed is further improved.
The simulation analysis shows that the estimation method has advantages in power distribution systems with different impedance ratios, and is specifically shown in the following steps: the method has good estimation accuracy and high calculation speed, and has good convergence on networks with different impedance ratios.
The above embodiments describe the technical solutions of the present invention in detail. It will be clear that the invention is not limited to the described embodiments. Various changes may be made by those skilled in the art based on the embodiments of the invention, and any changes which are equivalent or similar to the embodiments of the invention are intended to be within the scope of the invention.
Claims (5)
1. A generalized fast decomposition state estimation method is characterized by comprising the following steps:
step A, converting the measurement quantity to obtain an active type quantity measurement and a reactive type quantity measurement, and further obtaining a measurement equation represented by the active type quantity measurement and the reactive type quantity measurement and a Jacobian matrix H of an iterative equation of the measurement equation pp And H QQ ；
And B, based on the measurement equation, giving a generalized fast decomposition state estimation model:
and solving by using a Newton method to obtain a state variable estimated value.
2. The method of claim 1, wherein step a comprises:
step A1: the measurement of the quantity is transformed to form an active-type quantity measurement and a reactive-type quantity measurement, wherein the active-type quantity measurement is z P The method comprises the following steps:reactive-like type measurement z Q IncludedTheir computational expressions are:
the transformed measurement equations are unified as:
in the formula: theta i Is the phase angle of node i, θ ij Is the phase angle difference, V, at both ends of branch ij i Is the voltage amplitude of node i; w is a P,i And w Q,i Measuring z for the ith active and inactive quantities P,i And z Q,i The weight of (c); h is P (theta, V) is the active power estimation equation, h Q (theta, V) is a reactive power estimation equation; r is P ，r Q The vector is a similar active residual error vector and a similar reactive residual error vector; p is i Node i injects active, Q i Node i injects reactive, P ij For active power flow at the head end of branch ij, Q ij For the reactive power flow at the head end of the branch ij,the active component of the head-end current of branch ij,is the reactive component of the current at the head end of the branch ij;the node i injects an active transformation quantity,the node i is injected with a reactive transformation quantity,the head end of the branch ij has active power flow conversion quantity,for the head end reactive power flow conversion quantity of the branch ij,the head-end current has a conversion amount of the active component,for the reactive component of the head-end current of branch ij,the voltage amplitude transformation quantity of the node i; g ij Is a series conductance, b ij Is a series susceptance, g si For the head end of the branch to conduct to ground, b si The head end of the branch is susceptance to the ground; λ = (g) ij +g si )/(b ij +b si )，γ＝-g ij /b ij ；
Step A2: based on the quantity measurement after the transformation in the step A1, a Jacobian matrix H of an active part and a reactive part in an iterative equation is formed pp And H QQ 。
3. The method of claim 1, wherein step B, based on step A, provides a generalized fast decomposition state estimation model,
solving by using a Newton method, comprising the following steps of:
step B1: initialization variable theta 0 ，V 0 Number of iterations k max The convergence condition is as follows: delta theta k < ε and Δ V k < ε, convergence marker KP = KQ =1;
and step B2: by fast decomposition of iterative equationsComputingAnd Δ θ k And correcting for theta k+1 ＝θ k +△θ k Judging whether the step is converged, and if so, assigning KP =0; if not, KP =1, and go to step B4;
and step B3: by fast decomposition of iterative equationsComputingAnd Δ V k And correcting V k+1 ＝V k +△V k Judging whether the step is converged, if so, assigning KQ =0, otherwise, assigning KQ =1, and going to step B4;
and step B4: judging whether the total is convergent or not, if KP = KQ =0, finishing the calculation, and obtaining a state variable estimation value; if KP =1, go to step B3; if KQ =1, go to step B2;
in the formula: h pp And H QQ Jacobian matrix, W, for the active and reactive parts respectively P And W Q The weights of active measurement and reactive measurement are respectively.
4. The method as set forth in claim 3, wherein said step B2 includes:
step B21: calculating out
5. The method of claim 3, wherein step B3 comprises:
step B31: computing
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