CN112149273A - A Fast Convergence Method for Distributed State Estimation of AC Power Networks - Google Patents

Abstract

A fast-converging distributed state estimation method for an AC power grid, comprising the following steps: 1) giving a mathematical model of the AC power grid system, and giving a measurement model under the mixed use of SCADA measuring instruments and PMU measuring instruments; 2) according to In practice, the power grid system is divided into multiple regions, and the measurement model of each power grid region is given; 3) The Gauss-Newton method is used to transform the nonlinear least squares problem into an iterative linear least squares problem; A distributed linear least squares method constructed by the idea of block matrix inversion, and a nonlinear distributed state estimation method that only communicates with neighbors and converges quickly is designed. The invention can quickly calculate the state estimation value so as to find the abnormal state in time, and greatly reduces the number of communications while ensuring the system estimation performance; in addition, it does not need to exchange local original measurement information and local state estimation value, which greatly protects the Privacy of grid users.

Description

A Fast Convergence Method for Distributed State Estimation of AC Power Networks

technical field

The invention relates to the field of distributed AC power grid state estimation, in particular to a fast convergence method based on nonlinear least squares, which is applied to the AC power grid to solve the state estimation problem of a large distributed system.

Background technique

The power grid system is a large and complex network composed of hundreds of interconnected power buses. The traditional centralized power grid system is usually equipped with a central dispatch center, which manages the measurement and control signals of the entire power grid system through a data acquisition and monitoring (SCADA, Supervisory Control and Data Acquisition) system and a synchrophasor measurement unit (PMU, Phasor Measurement Unit). . In order to monitor whether the power grid is running stably, the state estimator is usually installed in the central dispatch center. The state estimator estimates the current state of the power grid system through the measurement data of the power grid, and the dispatch center can judge whether the operation of the power grid system is abnormal through the state. , the state can also be used as the input of the controller in the power grid system to control the dispatch of power. However, with the increase of electricity demand, the scale of the power grid is getting larger and larger, and the access of new energy power generation makes the power plants more and more dispersed in space, which makes the centralized power grid computationally expensive, high communication delay, and fault-tolerant performance. Disadvantages are becoming more and more prominent. Therefore, distributed power grid systems with lower computational and communication costs and higher robustness have attracted more and more attention.

The distributed power grid system usually divides the original system into multiple areas according to geographic location or using clustering algorithm, and the areas where there are line connections are neighbor areas. In a distributed system, each region designs a distributed state estimator that converges to the centralized state estimation results through local measurement information combined with key data provided by neighboring regions, and controls the power scheduling in the region according to the state estimation results. However, in the AC power grid, there is a nonlinear relationship between the measurement and the state of the system, so it is difficult to perform distributed decomposition, which brings difficulties to the design of distributed state estimator. On the other hand, due to the huge scale of the power grid system, the Jacobian matrix constructed by topological information is usually ill-conditioned, which leads to a very slow convergence rate of the traditional distributed state estimation method based on matrix inversion design, which makes all links in the power grid system fail to converge. Control becomes more difficult. Considering the network scale and computational efficiency, it is still challenging to design a fast-converging distributed state estimation method for large AC grid systems.

SUMMARY OF THE INVENTION

In order to solve the problem of slow state estimation convergence rate in large distributed AC power grid system, the present invention provides a fast convergence AC power grid distributed state estimation method, which uses Gauss-Newton method to convert nonlinear least squares problem into iterative linear minimum This paper designs a nonlinear distributed state estimation method that only communicates with neighbors and converges quickly through a distributed linear least squares method based on the idea of block matrix inversion.

The technical scheme adopted by the present invention to solve its technical problems is:

A fast-convergent distributed state estimation method for an AC power grid, comprising the following steps:

1), establish the AC power grid measurement model;

分流电纳为

分流导纳为

总线间传输线路上的分流导纳为

令电网的状态x_i＝[V_i θ_i]^T，已知电网中各总线的分流电导与分流电纳，总线之间传输线路的电阻与电抗，则交流电网在k时刻的量测模型为Define the voltage of bus i in the power grid as V _i , the voltage phase angle as θ _i , the resistance on the line between bus i and bus j as r _ij , the reactance as x _ij , the conductance as g _ij , and the susceptance as b _ij , the bus The shunt conductance between i and the ground is

The shunt susceptance is

The shunt admittance is

The shunt admittance on the transmission line between buses is

Let the state of the power grid x _i =[V _i θ _i ] ^T , knowing the shunt conductance and shunt susceptance of each bus in the power grid, and the resistance and reactance of the transmission line between the buses, the measurement model of the AC power grid at time k is:

z_ij(k)是对传输线路有功功率P_ij(k)和无功功率Q_ij(k)的测量，有 h_ij(x_i(k),x_j(k))^T＝(P_ij(k),Q_ij(k))^T，其中，Among them, u _ii (k), u _ij (k) are zero mean Gaussian measurement noise; zi _ii (k) is the 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 =[1 0], when the measuring instrument is a PMU instrument, it can measure the voltage and the voltage phase angle, namely

z _ij (k) is the measurement of active power P _ij (k) and reactive power Q _ij (k) of the transmission line, there are h _ij (x _i (k), x _j (k)) ^T = (P _ij ( k),Q _ij (k)) ^T , where,

in

By augmenting the measurement equations of all buses and transmission lines, the global measurement model z(k)=h(x(k))+u(k) is obtained. Assuming that there are m measurements in the power grid, there are

2), the distribution area division of power grid;

其中区域 i的量测模型为According to the geographical location of the power grid, the power grid is divided into multiple regions; each power grid region only has local parameter information and measurement data, as well as parameter information and measurement data on the lines connected to adjacent regions; Divided into n regions, the global measurement

where the measurement model of region i is

Among them, zi _ii (k) is the measured value of the bus i ₁ ,..., i _l in the area, and zi _ij (k) is the transmission line of the bus j ₁ . . . j _c connected to the area and the area j measurement values, which are expressed as

为区域i内测量仪表的量测噪声；通常，将式(5)和式(6)合写为z_i(k)＝h_i(x(k))+u_i(k)；另外，定义与区域i内总线存在传输线路连接的区域为区域i的邻居，记为

is the measurement noise of the measuring instrument in the area i; usually, formulas (5) and (6) are written together as _zi (k)=hi (x(k))+ _{u i (} k); in addition, define The area connected with the transmission line in the bus in area i is the neighbor of area i, denoted as

3) Design a distributed state estimator;

Using the minimum mean square error of the residual e(k)=z(k)-h(x(k)) as the criterion for state estimation, that is, to solve the following minimization problem

Among them, the value of the state x(k) where the derivative of φ(x(k)) is zero is the estimated value to be calculated, let

J(x(k)) is abbreviated as J(k); since hi (k) is a nonlinear equation, the above formula has no analytical solution, so the Gauss-Newton method is used to solve iteratively, and the formula for the p- _th iteration is:

x(p+1)=x(p)+Δx(p), (10)

Among them, Φ ^-1 is the estimation error covariance matrix, and Equation (9) has the same form as the linear least squares estimation; but in the distributed power grid system, each area only has the measurement information of its own area, so each area needs to Use the distributed least squares estimator to solve equation (9) in a distributed manner to obtain the local state update value Δx _i (p), and then update it by x _i (p+1)=x _i (p)+Δx _i (p) local state;

4) Design a distributed nonlinear least squares estimator;

According to equations (9) and (10), the distributed estimator is divided into two parts: the inner loop and the outer loop. The inner loop part constructs the distributed linear least squares method based on the block matrix inversion idea, and the outer loop part is based on the The Gauss-Newton method described in step 3) performs distributed iteration.

Further, the process of described step 4) is as follows:

Step 401, the outer loop initialization stage; set the initial state estimation value of each node i

Step 402, for the outer loop iteration rounds k=1,2,...,K, each node i calculates the residual e _i (k)=z _i (k) _-hi (k), and executes the inner loop (4.3)-(4.6);

线性估计值为

对于所有的邻居

初始化设置

M_ij(0)＝M_i(0)；Step 403, the inner loop initialization stage; set the initial estimated error covariance matrix of each node i as

The linear estimate is

for all neighbors

Initialize settings

M _ij (0)=M _i (0);

计算Step 404, for the inner loop iteration round p=1,2,...,P, each node i is for

calculate

and send the calculation results β _ij (p) and Ψ _ij (p) to node j;

Step 405, each node i receives the information sent by the neighbor node and updates it

Step 406: Calculate the linear least squares estimate after the inner loop converges

结束内循环；and set

end the inner loop;

Step 407, after the inner loop ends, each node i updates the state

The technical idea of the present invention is as follows: First, the mathematical model of the AC power grid system is given, and the measurement model under the mixed use of the SCADA measuring instrument and the PMU measuring instrument is given. Then, according to the actual situation, the power grid system is divided into multiple regions, and the measurement model of the power grid in each region is given. Finally, a fast-convergent distributed state estimation method for AC power grids is designed. The Gauss-Newton method is used to transform the nonlinear least squares problem into an iterative linear least squares problem, and a distributed linear method is constructed based on the idea of block matrix inversion. Least squares method, design a nonlinear distributed state estimation method that only communicates with neighbors and converges quickly.

The beneficial effects of the present invention are mainly manifested in: using the distributed state estimation method of rapid convergence, an early warning can be made immediately when the state is abnormal, and the method greatly reduces the number of communications while ensuring the system performance; in addition, This method does not need to exchange local original measurement information and local state estimation value, and protects the privacy of grid users to a great extent.

Description of drawings

Fig. 1 is the schematic diagram of the IEEE 118-bus power grid distributed division system;

Figure 2 is a structural diagram of a distributed state estimator;

Fig. 3 is an iterative simulation diagram of the inner loop and an iterative estimation error simulation diagram of the outer loop.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

Referring to Fig. 1 to Fig. 3 , a method for rapidly converging distributed state estimation of an AC power grid includes the following steps:

1), establish the AC power grid measurement model;

分流电纳为

分流导纳为

总线间传输线路上的分流导纳为

令电网的状态x_i＝[V_i θ_i]^T，已知电网中各总线的分流电导与分流电纳，总线之间传输线路的电阻与电抗，则交流电网在k时刻的量测模型为Define the voltage of each bus i in the power grid as V _i , the voltage phase angle as θ _i , the resistance on the line between bus i and bus j as r _ij , the reactance as x _ij , the conductance as g _ij , and the susceptance as b _ij , The shunt conductance between bus i and the ground is

The shunt susceptance is

The shunt admittance is

The shunt admittance on the transmission line between buses is

Let the state of the power grid x _i =[V _i θ _i ] ^T , knowing the shunt conductance and shunt susceptance of each bus in the power grid, and the resistance and reactance of the transmission line between the buses, the measurement model of the AC power grid at time k is:

z_ij(k)是对传输线路有功功率P_ij(k)和无功功率Q_ij(k)的测量，有 h_ij(x_i(k),x_j(k))^T＝(P_ij(k),Q_ij(k))^T，其中，Among them, u _ii (k), u _ij (k) are zero mean Gaussian measurement noise; zi _ii (k) is the 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 =[1 0], when the measuring instrument is a PMU instrument, it can measure the voltage and the voltage phase angle, namely

z _ij (k) is the measurement of active power P _ij (k) and reactive power Q _ij (k) of the transmission line, there are h _ij (x _i (k), x _j (k)) ^T = (P _ij ( k),Q _ij (k)) ^T , where,

in

By augmenting the measurement equations of all buses and transmission lines, the global measurement model z(k)=h(x(k))+u(k) is obtained. Assuming that there are m measurements in the power grid, there are

2), the distribution area division of power grid;

其中区域 i的量测模型为According to the geographical location of the power grid, the power grid is divided into multiple regions. Each power grid region only has local parameter information and measurement data, as well as the parameter information and measurement data on the lines connecting with adjacent regions. Divided into n regions, the global measurement

where the measurement model of region i is

Among them, zi _ii (k) is the measured value of the bus i ₁ ,..., i _l in the area, and zi _ij (k) is the transmission line of the bus j ₁ . . . j _c connected to the area and the area j measurement values, which are expressed as

为区域i内测量仪表的量测噪声；通常，将式(5)和式(6)合写为z_i(k)＝h_i(x(k))+u_i(k)；另外，定义与区域i内总线存在传输线路连接的区域为区域i的邻居，记为

is the measurement noise of the measuring instrument in the area i; usually, formulas (5) and (6) are written together as _zi (k)=hi (x(k))+ _{u i (} k); in addition, define The area connected with the transmission line in the bus in area i is the neighbor of area i, denoted as

3) Design a distributed state estimator;

Using the minimum mean square error of the residual e(k)=z(k)-h(x(k)) as the criterion for state estimation, that is, to solve the following minimization problem

Among them, the value of the state x(k) where the derivative of φ(x(k)) is zero is the estimated value to be calculated, let

For the convenience of description, J(x(k)) is abbreviated as J(k); since hi ( _k ) is a nonlinear equation, the above formula has no analytical solution, so the Gauss-Newton method is used to solve iteratively. The formula is

x(p+1)=x(p)+Δx(p), (24)

Among them, Φ ^-1 is the estimation error covariance matrix, and Equation (9) has the same form as the linear least squares estimation; but in the distributed power grid system, each area only has the measurement information of its own area, so each area needs to Use the distributed least squares estimator to solve equation (9) in a distributed manner to obtain the local state update value Δx _i (p), and then update it by x _i (p+1)=x _i (p)+Δx _i (p) local state;

4), design a distributed least squares estimator;

According to equations (9) and (10), the distributed estimator is divided into two parts: the inner loop and the outer loop. The inner loop part constructs the distributed linear least squares method based on the block matrix inversion idea, and the outer loop part is based on the The Gauss-Newton method described in step 3) carries out distributed iteration;

The process of described step 4) is as follows:

Step 401, the outer loop initialization stage; set the initial state estimation value of each node i

Step 402, for the outer loop iteration rounds k=1,2,...,K, each node i calculates the residual e _i (k)=z _i (k) _-hi (k), and executes the inner loop (4.3)-(4.6);

线性估计值为

对于所有的邻居

初始化设置

M_ij(0)＝M_i(0)；Step 403, the inner loop initialization stage; set the initial estimated error covariance matrix of each node i as

The linear estimate is

for all neighbors

Initialize settings

M _ij (0)=M _i (0);

计算Step 404, for the inner loop iteration round p=1,2,...,P, each node i is for

calculate

and send the calculation results β _ij (p) and Ψ _ij (p) to node j;

Step 405, each node i receives the information sent by the neighbor node and updates it

Step 406: Calculate the linear least squares estimate after the inner loop converges

结束内循环；and set

end the inner loop;

Step 407, after the inner loop ends, each node i updates the state

Combined with Figure 3, the IEEE 118-bus power grid system is firstly divided into 8 regions according to Figure 1, and the power grid parameters are selected as the CDF file provided by the website http://labs.ece.uw.edu/pstca/pf118/pg_tca118bus.htm as For example; in addition, select the voltage measurement error of the PMU measuring instrument to be 0.002, the voltage phase angle measurement error to be 0.01, and the voltage measurement error and power measurement error of the SCADA measuring instrument to be 0.3. The circle in Figure 1 represents the power bus, and the third and fifth , 9, 12, 15, 17, 21, 25, 28, 34, 37, 40, 45, 53, 56, 62, 64, 68, 76, 79, 85, 86, 89, 92, 96, 105, 110 , 114 buses are buses with PMU measurement, other buses are buses with SCADA measuring instruments, and the connection between the circles is the transmission line between the buses; as shown in Figure 3, the simulation experiment starts from a certain initial deviation , each outer iteration only needs 4 inner iterations to be basically stable, and after 3 outer iterations, it can converge to the global estimation, with an extremely fast convergence speed.

Claims (2)

1. A method for rapidly converging distributed state estimation method of AC power grid, characterized in that, the method comprises the following steps; 1) Establish an AC power grid measurement model; Define the voltage of bus i in the power grid as V _i , the voltage phase angle as θ _i , the resistance on the line between bus i and bus j as r _ij , the reactance as x _ij , the conductance as g _ij , and the susceptance as b _ij , the bus The shunt conductance between i and the ground is

The shunt susceptance is

The shunt admittance is

The shunt admittance on the transmission line between buses is

Let the state of the power grid x _i =[V _i θ _i ] ^T , knowing the shunt conductance and shunt susceptance of each bus in the power grid, and the resistance and reactance of the transmission line between the buses, the measurement model of the AC power grid at time k is:

Among them, u _ii (k), u _ij (k) are zero mean Gaussian measurement noise; zi _ii (k) is the direct measurement of the voltage and voltage phase angle on the bus, when the measuring instrument is a SCADA instrument, it can only measure the bus Voltage, namely C _i =[1 0], when the measuring instrument is a PMU instrument, it can measure the voltage and the voltage phase angle, namely

z _ij (k) is the measurement of active power P _ij (k) and reactive power Q _ij (k) of the transmission line, there are h _ij (x _i (k), x _j (k)) ^T = (P _ij ( k),Q _ij (k)) ^T , where,

in

By augmenting the measurement equations of all buses and transmission lines, the global measurement model z(k)=h(x(k))+u(k) is obtained. Assuming that there are m measurements in the power grid, there are

2) Division of distributed areas of power grids; According to the geographical location of the power grid, the power grid is divided into multiple regions; each power grid region only has local parameter information and measurement data, as well as parameter information and measurement data on the lines connected to adjacent regions; Divided into n regions, the global measurement

where the measurement model of region i is

Among them, zi _ii (k) is the measured value of the bus i ₁ ,..., i _l in the area, and zi _ij (k) is the transmission line of the bus j ₁ . . . j _c connected to the area and the area j measurement values, which are expressed as

is the measurement noise of the measuring instrument in the area i; usually, formulas (5) and (6) are written together as _zi (k)=hi (x(k))+ _{u i (} k); in addition, define The area connected with the transmission line in the bus in area i is the neighbor of area i, denoted as

3) Design a distributed state estimator; Using the minimum mean square error of the residual e(k)=z(k)-h(x(k)) as the criterion for state estimation, that is, to solve the following minimization problem argminφ(x(k))

Among them, the value of the state x(k) where the derivative of φ(x(k)) is zero is the estimated value to be calculated, let

J(x(k)) is abbreviated as J(k); since hi (k) is a nonlinear equation, the above formula has no analytical solution, so the Gauss-Newton method is used to solve iteratively, and the formula for the p- _th iteration is:

x(p+1)=x(p)+Δx(p), (10) Among them, Φ ^-1 is the estimation error covariance matrix, and Equation (9) has the same form as the linear least squares estimation; however, in the distributed grid system, each region only has the measurement information of its own region, so each region has the same form as the linear least squares estimation. It is necessary to use the distributed least squares estimator to solve equation (9) in a distributed manner to obtain the local state update value Δx _i (p), and then pass x _i (p+1)=x _i (p)+Δx _i (p) update local state; 4) Design a distributed least squares estimator; According to equations (9) and (10), the distributed estimator is divided into two parts: the inner loop and the outer loop. The inner loop part constructs the distributed linear least squares method based on the block matrix inversion idea, and the outer loop part is based on the The Gauss-Newton method described in step 3) performs distributed iteration. 2. The distributed state estimation method for AC power grid as claimed in claim 1, wherein the process of the step 4) is as follows: 4.1) Outer loop initialization phase; set the initial state estimation value of each node i

4.2) For the outer loop iteration rounds k=1,2,...,K, each node i calculates the residual e _i (k)=z _i (k)-h _i (k), and executes the inner loop ( 4.3)-(4.6); 4.3) Inner loop initialization stage; set the initial estimated error covariance matrix of each node i as

The linear estimate is

for all neighbors

Initialize settings

M _ij (0)=M _i (0); 4.4) For the inner loop iteration rounds p = 1, 2, ..., P, each node i is for

calculate

and send the calculation results β _ij (p) and Ψ _ij (p) to node j; 4.5) Each node i receives the information sent by the neighbor node and updates it

4.6) Calculate the linear least squares estimate after the inner loop converges

and set

end the inner loop; 4.7) After the inner loop ends, each node i updates the state

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