CN107528312B

CN107528312B - Power system state estimation method

Info

Publication number: CN107528312B
Application number: CN201710574224.7A
Authority: CN
Inventors: 王中杰; 余杨
Original assignee: Tongji University
Current assignee: Tongji University
Priority date: 2017-07-14
Filing date: 2017-07-14
Publication date: 2020-04-28
Anticipated expiration: 2037-07-14
Also published as: CN107528312A

Abstract

The invention relates to a power system state estimation method, which comprises the following steps: 1) establishing a power system state estimation model; 2) establishing an estimation objective function based on the power system state estimation model; 3) and introducing derivative information of the estimation objective function, and solving the estimation objective function by using an evolutionary algorithm to obtain the optimal power system state. Compared with the prior art, the method combines the evolutionary algorithm with the derivative information, and introduces the derivative information of the objective function in a structural framework of heuristic search of the evolutionary algorithm to guide search, so that the high-efficiency and accurate state estimation result of the power system is obtained, and the solution goodness can be ensured.

Description

Power system state estimation method

Technical Field

The invention relates to the technical field of power system operation and control, in particular to a power system state estimation method.

Background

The power system state estimation is to estimate the state of each node in the power grid for guiding the scheduling and control of the power system.

Existing power system state estimation methods can be classified into least-squares-based gauss-newton method, semi-positive definite relaxation method, and intelligent algorithm. Each method has certain defects:

based on the least square Gauss Newton method, the global optimum point is difficult to be obtained due to the sensitivity of the Gauss Newton method to the initial point;

a semi-positive definite relaxation method in which the solution obtained does not have a goodness (the first derivative is not 0);

the power system estimation based on the intelligent algorithm is only suitable for small power grids, and as the scale of the power grids becomes larger, the precision and the solving time of the power system estimation cannot meet the requirements.

Therefore, it is necessary to develop a new power system state estimation method.

Disclosure of Invention

The present invention is directed to a method for estimating a state of an electric power system, which overcomes the above-mentioned drawbacks of the prior art.

The purpose of the invention can be realized by the following technical scheme:

a method of power system state estimation, the method comprising the steps of:

1) establishing a power system state estimation model;

2) establishing an estimation objective function based on the power system state estimation model;

3) and introducing derivative information of the estimation objective function, and solving the estimation objective function by using an evolutionary algorithm to obtain the optimal power system state.

In the step 1), the power system state estimation model is as follows:

z＝h(v)+e

wherein z is measurement data, v is power system state, e is measurement error, and h (-) is measurement equation.

In step 2), the estimation objective function is expressed as:

wherein M belongs to M, M is a measurement set, w_mTo correspond to the metrology data weight, Z_mFor corresponding measured data, h_mThe equation for the corresponding measurement.

The step 3) is specifically as follows:

301) setting the number N of population_pIteration end condition and selection probability P_G、P_M；

302) Making the iteration number k equal to 1;

303) a generation step: sequentially judging whether the random generation probability of each individual i is less than P_GIf yes, execute the Nid_k(i)＝id_k(i)+u₁·Dx_k(i) Wherein id_k(i) Represents an individual i in the k-th iteration, representing the power system state, Dx_k(i) Representing the derivative, u, of the individual i of the kth iteration₁Is a weight factor, if not, execute the Nid_k(i)＝id_k(i)+u₂·pdg_k(i) Wherein pdg_k(i)＝pgbest_k-id_k(i)，pgbest_kRepresents the best of the k-th generation of individuals, u₂Is a weight factor;

304) a mutation step: sequentially judging whether the random generation probability of each individual i is less than P_MIf yes, execute Uid_k(i)＝Nid_k(i)+u₃Pdr (i), where pdr (i) is a random vector, u₃Is the weighting factor, if not, step 305) is executed;

305) comparison of Individual nids_k(i) And Uid_k(i) Taking the individual with smaller value as the individual of the next generation;

306) judging whether iteration termination conditions are met, if so, executing step 307), otherwise, making k equal to k +1, and returning to step 303);

307) and obtaining the optimal individual and the corresponding power system state.

The weighting factor u₁、u₂、u₃Are all obeyed to [0,1]A uniform probability distribution.

The iteration termination condition includes reaching a maximum number of iterations or a solution convergence.

Compared with the prior art, the invention has the following advantages:

1) the method combines the evolutionary algorithm with the derivative information, introduces the derivative information of the objective function in a structural framework of heuristic search of the evolutionary algorithm to guide search, overcomes the defect that the global optimum point is difficult to obtain due to the sensitivity of the least square Gaussian Newton method to the initial point, and obtains the efficient and accurate state estimation result of the power system.

2) Different from the problem that the solution of the state of the power system cannot guarantee the solution goodness by solving the power system state through semi-positive definite relaxation, the method guarantees the solution goodness.

3) The method can also carry out rapid and accurate state estimation under a large power system.

4) In the evolutionary algorithm, the generation step aims to generate the next generation of individuals by analyzing derivative information or heuristic information, and the variation step aims to enlarge the search range and avoid precocity, so that the accuracy of the evolutionary algorithm is improved.

Drawings

FIG. 1 is a schematic flow chart of the present invention.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.

The invention provides a power system state estimation method, which comprises the following steps:

1) establishing a power system state estimation model: z is measurement data, v is the state of the power system, e is a measurement error, and h (-) is a measurement equation;

2) establishing an estimation objective function based on the power system state estimation model:

wherein M belongs to M, M is a measurement set, w_mTo correspond to the metrology data weight, Z_mFor corresponding measured data, h_m(. cndot.) is the corresponding measurement equation;

As shown in fig. 1, the step 3) specifically includes:

301) setting the number N of population_pIteration termination conditions (e.g., maximum number of iterations reached or solution convergence, etc.), and selection probability P_G、P_M；

302) Making the iteration number k equal to 1;

303) a generation step: sequentially judging whether the random generation probability of each individual i is less than P_GIf yes, execute the Nid_k(i)＝id_k(i)+u₁·Dx_k(i) Wherein id_k(i) Represents an individual i in the k-th iteration, representing the power system state, Dx_k(i) Representing the derivative, u, of the individual i of the kth iteration₁Obey [0,1 ] for the weighting factor]If not, then executing the Nid_k(i)＝id_k(i)+u₂·pdg_k(i) Wherein pdg_k(i)＝pgbest_k-id_k(i)，pgbest_kRepresents the best of the k-th generation of individuals, u₂As a weighting factor, u₂Same u₁；

304) A mutation step: sequentially judging whether the random generation probability of each individual i is less than P_MIf yes, execute Uid_k(i)＝Nid_k(i)+u₃Pdr (i), where pdr (i) is a random vector, u₃As a weighting factor, u₃Same u₂And u₁If not, go to step 305);

In the case of testing IEEE 30, 57, and 118 node standard power systems, the above methods are compared with least squares-based gauss-newton method and intelligent algorithms (e.g., Genetic Algorithm (GA), particle swarm algorithm (PSO), and differential evolution algorithm (DE)), and the accuracy is compared, as shown in table 1.

TABLE 1 accuracy comparison

In table 1, 1.5999E +005 is a scientific notation, equal to 159990, which indicates the objective function value corresponding to the solved power system state. The smaller the value of the objective function, the more accurate the estimated power system state is represented.

At present, in a state estimation method of a power system, a semi-positive definite relaxation method and an intelligent algorithm (such as a Genetic Algorithm (GA), a particle swarm algorithm (PSO), and a differential evolution algorithm (DE)) are used for calculating for a long time, and a least square-based gauss-newton method is used for calculating for a shortest time. As can be seen from table 1, in a large system, the estimation effect of the intelligent algorithm cannot meet the accuracy requirement, so that the calculation time is ignored, and table 2 shows the comparison result of the calculation time of each method.

TABLE 2 calculation time comparison (unit: seconds)

Test system	Method for producing a composite material	Semi-positive definite relaxation method	Gauss-newton method
				IEEE 30	0.1958	1.62	0.0974
IEEE 57	0.5956	4.32	0.1460
				IEEE 118	4.4398	21.6	0.5284

As can be seen from tables 1 and 2, the most accurate estimation result of the power system state can be obtained within an acceptable time by the method.

The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims

1. A power system state estimation method, characterized in that the method comprises the following steps:

1) Establish a power system state estimation model;

3) introducing the derivative information of the estimated objective function, and using an evolutionary algorithm to solve the estimated objective function to obtain the optimal power system state;

Described step 3) is specifically:

301) Set the population number N _p , the iteration termination condition and the selection probabilities P _G , P _M ;

302) Set the number of iterations k=1;

303) Generation step: for each individual i in turn, determine whether the random generation probability is less than P _G , and if so, execute Nid _k (i)=id _k (i)+u ₁ ·Dx _k (i), where id _k ( i) represents the individual i in the k-th iteration, representing the state of the power system, Dx _k (i) represents the derivative of the individual i in the k-th iteration, u ₁ is the weight factor, if not, execute Nid _k (i)=id _k (i)+u ₂ ·pdg _k (i), where pdg _k (i)=pgbest _k -id _k (i), pgbest _k represents the best individual among the k-th generation individuals, and u ₂ is the weight factor;

304) Mutation step: for each individual i in turn, determine whether the random generation probability is less than P _M , and if so, execute Uid _k (i)=Nid _k (i)+u ₃ ·pdr(i), where pdr(i) is a random vector, u ₃ is a weight factor, if not, then execute step 305);

305) Compare the values of the objective function of individual Nid _k (i) and Uid _k (i), and take the individual with the smaller value as the individual of the next generation;

306) Determine whether the iteration termination condition is met, if so, execute step 307), if not, set k=k+1, and return to step 303);

307) Obtain the optimal individual and its corresponding power system state.

2. The power system state estimation method according to claim 1, wherein in the step 1), the power system state estimation model is:

z=h(v)+e

Among them, z is the measurement data, v is the state of the power system, e is the measurement error, and h(·) is the measurement equation.

3. The power system state estimation method according to claim 1, wherein, in the step 2), the estimation objective function is expressed as:

Among them, m∈M, M is the measurement set, w _m is the corresponding measurement data weight, Z _m is the corresponding measurement data, and h _m (·) is the corresponding measurement equation.

4 . The power system state estimation method according to claim 1 , wherein the weighting factors u ₁ , u ₂ , and u ₃ all obey the uniform probability distribution of [0, 1]. 5 .

5 . The power system state estimation method according to claim 1 , wherein the iteration termination condition includes reaching the maximum number of iterations or solution convergence. 6 .