CN112149273B - Fast-convergence alternating-current power grid distributed state estimation method - Google Patents
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Abstract
A method for estimating the distributed state of an alternating current power grid with rapid convergence comprises the following steps: 1) Giving a mathematical model of an alternating current power grid system and a measurement model under the condition that the SCADA measuring instrument and the PMU measuring instrument are mixed for use; 2) Dividing a power grid system into a plurality of areas according to actual conditions, and providing a measurement model of each power grid area; 3) Converting the nonlinear least square problem into an iterative linear least square problem by using a Gauss Newton method, and solving the iterative linear least square problem; 4) A nonlinear distributed state estimation method which is only communicated with neighbors and can be quickly converged is designed through a distributed linear least square method based on a block matrix inversion idea. The invention can rapidly calculate the state estimation value so as to discover the state abnormality in time, and greatly reduce the communication times while ensuring the estimation performance of the system; in addition, local original measurement information and a local state estimation value do not need to be exchanged, so that the privacy of a power grid user is greatly protected.
Description
Technical Field
The invention relates to the field of distributed alternating current power grid state estimation, in particular to a nonlinear least square-based rapid convergence method which is applied to an alternating current power grid to solve the problem of state estimation of a large-scale distributed system.
Background
The power grid system is a large complex network formed by interconnecting hundreds of power buses. Conventional centralized grid systems are typically configured with a central dispatch center that manages the measurement and control signals throughout the grid system via data acquisition and monitoring (SCADA, supervisory Control and Data Acquisition) systems and synchrophasor measurement devices (PMU, phasor Measurement Unit). In order to monitor whether the power grid stably operates, a state estimator is usually installed in a central dispatching center, the state estimator estimates the current state of the power grid system through measurement data of the power grid, and the dispatching center can judge whether the operation of the power grid system is abnormal through the state, and can also take the state as the input quantity of a controller in the power grid system to control the dispatching of electric power. However, as the power demand increases, the scale of the power grid is larger and larger, and the access of new energy power generation enables the power plant to be dispersed in space, so that the defects of large calculation cost, high communication delay, poor fault tolerance and the like of the centralized power grid are more remarkable. Therefore, distributed grid systems with smaller computational and communication costs and greater robustness are attracting more and more attention.
Distributed grid systems typically partition the original system into multiple areas by geographic location or using clustering algorithms, where the areas where line connections exist are neighbor areas. In the distributed system, each region designs a distributed state estimator converged on a centralized state estimation result through the combination of local measurement information and key data provided by a neighbor region, and controls the power dispatching of the region according to the state estimation result. However, in the ac power grid, the measurement and the state of the system have a nonlinear relationship, so that it is difficult to perform distributed decomposition, which makes it difficult to design a distributed state estimator. On the other hand, the jacobian matrix constructed by topology information is usually pathological due to the huge scale of the power grid system, so that the convergence rate of the traditional distributed state estimation method based on matrix inversion design is very slow, and the control difficulty of each link in the power grid system is increased. On the premise of considering the network scale and the calculation efficiency, the design of a fast-convergence distributed state estimation method for a large-scale alternating current power grid system is still challenging.
Disclosure of Invention
In order to solve the problem of slow convergence rate of state estimation in a large-scale distributed alternating current power grid system, the invention provides a rapid convergence alternating current power grid distributed state estimation method, which converts a nonlinear least square problem into an iterative linear least square problem by using a Gaussian Newton method, and designs a rapid convergence nonlinear distributed state estimation method which is only communicated with neighbors by using a distributed linear least square method constructed based on a block matrix inversion idea.
The technical scheme adopted for solving the technical problems is as follows:
A method for estimating the distributed state of an alternating current power grid with rapid convergence comprises the following steps:
1) Establishing an alternating current power grid measurement model;
Defining the voltage of a bus i in a power grid as V i, the voltage phase angle as theta i, the resistance of a line between the bus i and a bus j as r ij, the reactance as x ij, the electric conductivity as g ij, the susceptance as b ij, and the shunt electric conductivity between the bus i and the ground as The shunt susceptance is/>Shunt admittance is/>Shunt admittance over transmission lines between buses is/>Let the state x i＝[Vi θi]T of the power grid, knowing the shunt conductance and shunt susceptance of each bus in the power grid, the resistance and reactance of the transmission line between buses, the measurement model of the AC power grid at the k moment is
Wherein u ii(k),uij (k) is zero-mean Gaussian measurement noise; z ii (k) is a direct measurement of the bus voltage and the voltage phase angle, when the measuring instrument is a SCADA instrument, only the bus voltage can be measured, namely C i = [ 10 ], and when the measuring instrument is a PMU instrument, the voltage and the voltage phase angle can be measured, namelyZ ij (k) is a measure of the transmission line active power P ij (k) and reactive power Q ij (k), with h ij(xi(k),xj(k))T＝(Pij(k),Qij(k))T, where,
Wherein the method comprises the steps of
By augmenting the measurement equations for all buses and transmission lines, a global measurement model z (k) =h (x (k))+u (k) is obtained, assuming a total of m measurements in the grid, there are
2) Dividing a power grid distributed area;
dividing the power grid into a plurality of areas according to the geographic position of the power grid; each power grid area only has local parameter information and measurement data, and parameter information and measurement data on a connecting line with an adjacent area; if the power grid is divided into n areas, global measurement is performed Wherein the measurement model of the region i is
Wherein z ii (k) is the measurement value of bus i 1,...,il in the region, and z ij (k) is the measurement value on the transmission line of bus j 1...jc connecting the region and region j, respectively expressed as
Measuring noise of the measuring instrument in the area i; in general, formula (5) and formula (6) are collectively written as z i(k)＝hi(x(k))+ui (k); in addition, a region connected to the bus-existing transmission line in the region i is defined as a neighbor of the region i, and is denoted as/>
3) Designing a distributed state estimator;
state estimation using the minimum mean square error of residual e (k) =z (k) -h (x (k)) as criterion, i.e. solving the following minimization problem
arg minφ(x(k))
Wherein the value of the state x (k) at the position where the derivative of phi (x (k)) is zero is taken as the estimated value to be calculated, and the following is made
J (x (k)) is abbreviated as J (k); since h i (k) is a nonlinear equation, the above formula has no analytical solution, so the iteration solution is performed by using the Gauss Newton method, and the formula of the p-th iteration is as follows
x(p+1)＝x(p)+Δx(p)， (10)
Wherein Φ -1 is an estimation error covariance matrix, and equation (9) has the same form as the linear least squares estimation; however, in the distributed power grid system, each region only has measurement information of the region, so that each region needs to perform distributed solution on the formula (9) by using a distributed least square estimator to obtain a local state update value delta x i (p), and then update the local state by x i(p+1)＝xi(p)+Δxi (p);
4) Designing a distributed nonlinear least square estimator;
Dividing the distributed estimator into an inner loop part and an outer loop part according to the formula (9) and the formula (10), wherein the inner loop part constructs a distributed linear least square method based on the block matrix inversion idea, and the outer loop part carries out distributed iteration based on the Gaussian Newton method as described in the step 3).
Further, the process of the step 4) is as follows:
step 401, an outer loop initialization phase; setting an initial state estimation value of each node i
Step 402, for the outer loop iteration run k=1, 2,..k, each node i calculates a residual e i(k)＝zi(k)-hi (K), and performs an inner loop (4.3) - (4.6);
Step 403, an inner loop initialization phase; setting the initial estimation error covariance matrix of each node i as follows The linear estimation value is/>For all neighbors/>Initializing settingsMij(0)＝Mi(0)；
Step 404, iterating the round p=1, 2 for the inner loop, p., each node i forCalculation of
And transmitting the calculation results β ij (p) and ψ ij (p) to the node j;
Step 405, each node i receives information sent by a neighboring node and updates the information
Step 406, calculating a linear least squares estimation after inner loop convergence
And is provided withEnding the internal circulation;
step 407, after the inner loop is completed, each node i updates the state
The technical conception of the invention is as follows: firstly, a mathematical model of an alternating current power grid system is given, and a measurement model under the condition that the SCADA measuring instrument and the PMU measuring instrument are mixed is given. Then, the power grid system is divided into a plurality of areas according to actual conditions, and a measurement model of each regional power grid is given. Finally, a rapidly-converged alternating current power grid distributed state estimation method is designed, a nonlinear least square problem is converted into an iterative linear least square problem by using a Gaussian Newton method, and a rapidly-converged nonlinear distributed state estimation method which is only communicated with neighbors is designed by using a distributed linear least square method constructed based on a block matrix inversion idea.
The beneficial effects of the invention are mainly shown in the following steps: the method can immediately make early warning under the condition that the state is abnormal by using a rapid convergence distributed state estimation method, and the method greatly reduces the communication times while ensuring the system performance; in addition, the method does not need to exchange local original measurement information and local state estimation values, and the privacy of the power grid user is greatly protected.
Drawings
FIG. 1 is a schematic diagram of an IEEE 118-bus power grid distributed division system;
FIG. 2 is a block diagram of a distributed state estimator;
fig. 3 is an inner loop iteration simulation diagram and an outer loop iteration estimation error simulation diagram.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 to 3, a method for estimating a rapidly converging distributed state of an ac power grid includes the steps of:
1) Establishing an alternating current power grid measurement model;
Defining the voltage of each bus i in the power grid as V i, the voltage phase angle as theta i, the resistance on the line between the bus i and the bus j as r ij, the reactance as x ij, the conductance as g ij, the susceptance as b ij, and the shunt conductance between the bus i and the ground as The shunt susceptance is/>Shunt admittance is/>Shunt admittance over transmission lines between buses is/>Let the state x i＝[Vi θi]T of the power grid, knowing the shunt conductance and shunt susceptance of each bus in the power grid, the resistance and reactance of the transmission line between buses, the measurement model of the AC power grid at the k moment is
Wherein u ii(k),uij (k) is zero-mean Gaussian measurement noise; z ii (k) is a direct measurement of the bus voltage and the voltage phase angle, when the measuring instrument is a SCADA instrument, only the bus voltage can be measured, namely C i = [ 10 ], and when the measuring instrument is a PMU instrument, the voltage and the voltage phase angle can be measured, namelyZ ij (k) is a measure of the transmission line active power P ij (k) and reactive power Q ij (k), with h ij(xi(k),xj(k))T＝(Pij(k),Qij(k))T, where,
Wherein the method comprises the steps of
By augmenting the measurement equations for all buses and transmission lines, a global measurement model z (k) =h (x (k))+u (k) is obtained, assuming a total of m measurements in the grid, there are
2) Dividing a power grid distributed area;
Dividing the power grid into a plurality of areas according to the geographic position of the power grid, wherein each power grid area only has local parameter information and measurement data, and parameter information and measurement data on a connecting line with an adjacent area; if the power grid is divided into n areas, global measurement is performed Wherein the measurement model of the region i is
Wherein z ii (k) is the measurement value of bus i 1,...,il in the region, and z ij (k) is the measurement value on the transmission line of bus j 1...jc connecting the region and region j, respectively expressed as
Measuring noise of the measuring instrument in the area i; in general, formula (5) and formula (6) are collectively written as z i(k)＝hi(x(k))+ui (k); in addition, a region connected to the bus-existing transmission line in the region i is defined as a neighbor of the region i, and is denoted as/>
3) Designing a distributed state estimator;
state estimation using the minimum mean square error of residual e (k) =z (k) -h (x (k)) as criterion, i.e. solving the following minimization problem
arg minφ(x(k))
Wherein the value of the state x (k) at the position where the derivative of phi (x (k)) is zero is taken as the estimated value to be calculated, and the following is made
For convenience of description, J (x (k)) is abbreviated as J (k); since h i (k) is a nonlinear equation, the above formula has no analytical solution, so the iteration solution is performed by using the Gauss Newton method, and the formula of the p-th iteration is as follows
x(p+1)＝x(p)+Δx(p)， (24)
Wherein Φ -1 is an estimation error covariance matrix, and equation (9) has the same form as the linear least squares estimation; however, in the distributed power grid system, each region only has measurement information of the region, so that each region needs to perform distributed solution on the formula (9) by using a distributed least square estimator to obtain a local state update value delta x i (p), and then update the local state by x i(p+1)＝xi(p)+Δxi (p);
4) Designing a distributed least square estimator;
Dividing the distributed estimator into an inner loop part and an outer loop part according to the formula (9) and the formula (10), wherein the inner loop part constructs a distributed linear least square method based on a block matrix inversion idea, and the outer loop part carries out distributed iteration based on the Gaussian Newton method as described in the step 3);
The process of the step 4) is as follows:
step 401, an outer loop initialization phase; setting an initial state estimation value of each node i
Step 402, for the outer loop iteration run k=1, 2,..k, each node i calculates a residual e i(k)＝zi(k)-hi (K), and performs an inner loop (4.3) - (4.6);
Step 403, an inner loop initialization phase; setting the initial estimation error covariance matrix of each node i as follows The linear estimation value is/>For all neighbors/>Initializing settingsMij(0)＝Mi(0)；
Step 404, iterating the round p=1, 2 for the inner loop, p., each node i forCalculation of
And transmitting the calculation results β ij (p) and ψ ij (p) to the node j;
Step 405, each node i receives information sent by a neighboring node and updates the information
Step 406, calculating a linear least squares estimation after inner loop convergence
And is provided withEnding the internal circulation;
step 407, after the inner loop is completed, each node i updates the state
Referring to fig. 3, the IEEE 118-bus power grid system is first divided into 8 regions according to fig. 1, and the power grid parameters are selected as follows: the CDF file provided by/(labs.ue.uw.edu/pstca/pf 118/pg_tca118bus.htm is exemplified; in addition, the voltage measurement error of the PMU measurement instrument is 0.002, the voltage phase angle measurement error is 0.01, the voltage measurement error and the power measurement error of the SCADA measurement instrument are 0.3, the circles in fig. 1 represent power buses, the 3 rd, 5 th, 9 th, 12 th, 15 th, 17 th, 21 th, 25 th, 28 th, 34 th, 37 th, 40 th, 45 th, 53 th, 56 th, 62 th, 64 th, 68 th, 76 th, 79 th, 85 th, 86 th, 89 th, 92 th, 96 th, 105 th, 110 th and 114 th buses are buses with PMU measurement, the other buses are buses with SCADA measurement instrument, and the connection lines between the circles are transmission lines between the buses; as shown in fig. 3, the simulation experiment starts from a certain initial deviation, and only 4 inner iterations are needed for each outer iteration, so that the simulation experiment can be basically stable, can be converged to the global estimation through 3 outer iterations, and has extremely high convergence rate.
Claims (2)
1. A method for rapidly converging distributed state estimation of an ac power grid, the method comprising the steps of;
1) Establishing an alternating current power grid measurement model;
Defining the voltage of a bus i in a power grid as V i, the voltage phase angle as theta i, the resistance of a line between the bus i and a bus j as r ij, the reactance as x ij, the electric conductivity as g ij, the susceptance as b ij, and the shunt electric conductivity between the bus i and the ground as The shunt susceptance is/>Shunt admittance is/>Shunt admittance over transmission lines between buses is/>Let the state x i＝[Vi θi]T of the power grid, knowing the shunt conductance and shunt susceptance of each bus in the power grid, the resistance and reactance of the transmission line between buses, the measurement model of the AC power grid at the k moment is
Wherein u ii(k),uij (k) is zero-mean Gaussian measurement noise; z ii (k) is a direct measurement of the voltage and the voltage phase angle on the bus, when the measuring instrument is a SCADA instrument, only the bus voltage can be measured, namely C i = [ 10 ], and when the measuring instrument is a PMU instrument, the voltage and the voltage phase angle can be measured, namelyZ ij (k) is a measure of the transmission line active power P ij (k) and reactive power Q ij (k), with h ij(xi(k),xj(k))T＝(Pij(k),Qij(k))T, where,
Wherein the method comprises the steps of
By augmenting the measurement equations for all buses and transmission lines, a global measurement model z (k) =h (x (k))+u (k) is obtained, assuming a total of m measurements in the grid, there are
2) Dividing a power grid distributed area;
dividing the power grid into a plurality of areas according to the geographic position of the power grid; each power grid area only has local parameter information and measurement data, and parameter information and measurement data on a connecting line with an adjacent area; if the power grid is divided into n areas, global measurement is performed Wherein the measurement model of the region i is
Wherein z ii (k) is the measurement value of bus i 1,...,il in the region, and z ij (k) is the measurement value on the transmission line of bus j 1...jc connecting the region and region j, respectively expressed as
Measuring noise of the measuring instrument in the area i; in general, formula (5) and formula (6) are collectively written as z i(k)＝hi(x(k))+ui (k); in addition, the region connected to the bus-existing transmission line in the region i is defined as the neighbor of the region i, and is denoted as/>
3) Designing a distributed state estimator;
state estimation using the minimum mean square error of residual e (k) =z (k) -h (x (k)) as criterion, i.e. solving the following minimization problem
arg minφ(x(k))
Wherein the value of the state x (k) at the position where the derivative of phi (x (k)) is zero is taken as the estimated value to be calculated, and the following is made
J (x (k)) is abbreviated as J (k); since h i (k) is a nonlinear equation, the above formula has no analytical solution, so the iteration solution is performed by using the Gauss Newton method, and the formula of the p-th iteration is as follows
x(p+1)＝x(p)+Δx(p), (10)
Wherein Φ -1 is an estimation error covariance matrix, and equation (9) has the same form as the linear least squares estimation; however, in the distributed power grid system, each region only has measurement information of the region, so that each region needs to perform distributed solution on the formula (9) by using a distributed least squares estimator to obtain a local state update value Δx i (p), and then update the local state by x i(p+1)＝xi(p)+Δxi (p);
4) Designing a distributed least square estimator;
Dividing the distributed estimator into an inner loop part and an outer loop part according to the formula (9) and the formula (10), wherein the inner loop part constructs a distributed linear least square method based on the block matrix inversion idea, and the outer loop part carries out distributed iteration based on the Gaussian Newton method as described in the step 3).
2. The method for rapidly converging ac grid distributed state estimation according to claim 1, wherein the process of step 4) is as follows:
4.1 An outer loop initialization phase; setting an initial state estimation value of each node i
4.2 For the outer loop iteration run k=1, 2..k, each node i calculates the residual e i(k)＝zi(k)-hi (K), and performs the inner loops (4.3) - (4.6);
4.3 An inner loop initialization phase; setting the initial estimation error covariance matrix of each node i as follows The linear estimation value is/>For all neighbors/>Initialization settings/>Mij(0)＝Mi(0)；
4.4 P=1, 2 for the inner loop iteration run, p., P, each node i forCalculation of
And transmitting the calculation results β ij (p) and ψ ij (p) to the node j;
4.5 Each node i receives and updates information sent by neighbor nodes
4.6 Calculating a linear least squares estimate after convergence of the inner loop
And is provided withEnding the internal circulation;
4.7 After the end of the inner loop, each node i updates the state
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