CN104699898A

CN104699898A - Simulation method of electric power system based on compression and division of frequency-related network equivalence

Info

Publication number: CN104699898A
Application number: CN201510097332.0A
Authority: CN
Inventors: 吴文传; 张伯明; 孙宏斌; 胡一中; 郭庆来; 王彬
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2015-03-05
Filing date: 2015-03-05
Publication date: 2015-06-10
Anticipated expiration: 2035-03-05
Also published as: CN104699898B

Abstract

The invention relates to a simulation method of an electric power system based on the compression and the division of frequency-related network equivalence, and belongs to the technical field of the dispatching automation of electric power systems and the simulation of electric grids. The simulation method comprises the following steps: firstly, removing the redundancy of frequency-related network equivalence in a mathematical model through compression processing so as to decrease the whole calculated amount; making frequency-related networks equivalent by sub-block processing, and establishing a plurality of subblocks so as to realize parallel computation. The simulation method can effectively solve the problem that when the frequency-related network equivalence is applied to the electromagnetic transient simulation of the electric power system, the calculated amount of single frequency-related network equivalence module is too large. Through the adoption of the simulation method disclosed by the invention, the simulation velocity of the electric power system can be obviously accelerated, and the practice effect of engineering is satisfied.

Description

Power system simulation method based on compression and block frequency correlation network equivalence

Technical Field

The invention relates to a power system simulation method based on compression and block frequency correlation network equivalence, and belongs to the technical field of power system dispatching automation and power grid simulation.

Background

Power system simulation is one of the important methods for studying transient characteristics of power systems. According to different dynamic processes to be investigated, power system simulation can be divided into electromagnetic transient simulation, electromechanical transient simulation and medium-and long-term dynamic simulation. The electromagnetic transient simulation has the highest precision and is mainly used for researching microsecond-level transient processes of network elements of the power system, such as lightning processes, wave processes, direct-current commutation failure processes and the like. However, the high accuracy is at the cost of large calculation amount, and the electromagnetic transient simulation is not suitable for directly simulating a large-scale power system due to the large calculation amount. Usually, for the whole large system, the network elements of the concerned part (referring to the part which is expected to know the transient process in detail) are reserved, and the network elements of other parts are represented by network equivalence, and then electromagnetic simulation is carried out, so that the purpose of reducing the calculation amount is achieved.

The traditional network equivalence is represented by a norton equivalence model, as shown in fig. 1. The right box is the concerned part of the network; the left-hand box is the network equivalent using the Norton equivalent model, i.e. a Norton equivalent current I_abcAnd a Norton equivalent node admittance matrix Y_abcTo represent the network equivalence of other partial network elements.

The node admittance matrix in the norton equivalent circuit is formed at the fundamental frequency, and therefore can only represent the fundamental frequency characteristics of the network element. In order to accurately represent the Frequency characteristics of the Network element at each Frequency, a Frequency Dependent Network Equivalence (FDNE) is introduced to represent the Network equivalence of other partial Network elements.

FDNE-based network equivalent methods are shown in fig. 2. The right box is the concerned part of the network; the left box is the FDNE-based network equivalent, i.e. a Norton equivalent current I_abcAnd an FDNE as the network equivalent of the other part.

The essence of FDNE is a node admittance matrix as a function of frequency. The mathematical model for an N dimensional FDNE is:

where, s is j2 pi f, f is frequency, j is an imaginary unit, the same applies below;

any element in FDNE is represented as a frequency domain function:

wherein the pole { a_iAnd the residue { c }_iEither both are real numbers or occur in complex conjugate pairs, respectively, the constant term d and the first term h being real numbers and n being the number of poles.

In engineering use, the first order term h is typically taken to be 0, and each element of the FDNE uses a common set of poles a_iAn N × N dimensional FDNE matrix Y(s) can be expressed as:

the above equation is written in the form of a transfer function:

Y(s)＝C(sE-A)^-1B+D，

wherein E is an identity matrix having the same dimension as the matrix A,

A＝diag(A₁ … A_k … A_n)，

A_k＝diag((a_k a_k … a_k)_(1×N))，

B＝diag(B₁ … B_k … B_n)，

B_k＝diag((1 1 … 1)_(1×N))，

C＝[R₁ … R_k … R_n]，

fig. 3 is a block matrix diagram of the FDNE mathematical expression. (excluding D)

The mathematical model of the FDNE can be applied to an electromagnetic transient simulation program of the power system. At each time step of the simulation, the amount of computation O required by an FDNE module is (measured by the number of floating-point number multiplications)

O＝2nN²+N²+2nN。

The computational load of one FDNE module is large compared to other power system component modules, and is briefly described as follows. N in the above formula is the number of poles of FDNE, and in engineering application, in order to ensure simulation accuracy, the value is usually 50-100; in the above formula, N is the dimension of FDNE, and is a three-phase model, so N takes the values of 3,6,9,12 and the like. Therefore, in practical use, the calculation amount of one FDNE module can reach 10⁴The calculation amount of a conventional power system element module is generally 10³The order of magnitude is less.

When the FDNE directly described above is applied to electromagnetic transient simulation of a power system, the calculation amount of a single FDNE module is too large, and the overall simulation efficiency is affected. And there is currently no solution to this problem.

Disclosure of Invention

The invention aims to provide a power system simulation method based on compression and partitioning frequency-dependent network equivalence.

The invention provides a power system simulation method based on frequency-dependent network equivalence, which comprises the following steps:

(1) the mathematical model of the equivalent of the frequency-dependent network for power system simulation, y(s), is:

where N is the dimension of y(s), s j2 pi f, f is the network frequency, j is the imaginary unit, { a }_iIs a pole, { c_iD is a constant term, and n is the number of poles;

(2) compressing the equivalent mathematical model of the frequency correlation network in the step (1), wherein the specific process is as follows:

(2-1) rewriting the above Y(s) into the form of the following formula:

Y(s)＝C(sE-A)^-1B+D，

wherein A ═ diag (A)₁ … A_k … A_n)，A_k＝diag((a_k a_k … a_k)_(1×N))，

B＝diag(B₁ … B_k … B_n)，B_k＝diag((1 1 … 1)_(1×N))，

C＝[R₁ … R_k … R_n]，

E is a unit matrix, and the dimension of E is the same as that of the matrix A;

(2-2) solving the above-mentioned C ═ R₁ … R_k … R_n]The rank of each sub-matrix block in (1) is as follows:

to R_kPerforming singular value decomposition to make R_k＝UΣV^T，

Wherein Σ is diag (σ)₁,σ₂,…,σ_N),σ₁≥σ₂≥…≥σ_N≥0，σ₁，σ₂，...，σ_NIs R_kN singular values of (U ═₁,u₂,...,u_N) And V ═ V (V)₁,v₂,...,v_N)^TAre each R_kThe left and right singular phasors of (a),

setting a judgment threshold lambda, and determining a matrix R by using the judgment threshold lambda_kI.e. the parameter r is incremented from 1 until the following holds:

then the matrix R is determined_kIs r;

(2-3) Pair matrix R_kCompressing, which comprises the following steps: for matrix R_kIs judged, if r satisfies the following condition,then R in the matrix C_kA in matrix A_kAnd B in matrix B_kAre respectively compressed into R'_k、A'_kAnd B'_k：

R'_k＝(u₁,u₂,...,u_r)，

A'_k＝diag((a_k a_k … a_k)_(1×r))，

B'_k＝(v₁,v₂,...,v_r)^T；

If r satisfies the following condition,then R in matrix C_kA in matrix A_kAnd B in matrix B_kKeeping the same;

(2-4) traversing all sub-matrix blocks R in the matrix C_kRepeating the steps (2-2) and (2-3) to realize the compression of the equivalent mathematical model of the frequency correlation network;

(3) partitioning the equivalent mathematical model of the frequency correlation network in the step (1), wherein the specific process is as follows:

dividing the mathematical model Y(s) of the frequency-dependent network equivalent into a plurality of parts according to the following modes:

(4) and (3) applying the mathematical model of the frequency-dependent network equivalent after the compression processing in the step (2) and the blocking processing in the step (3) to the simulation calculation of the power system.

The power system simulation method based on the frequency-dependent network equivalence provided by the invention has the advantages that the method can effectively solve the problem of overlarge calculated amount of a single frequency-dependent network equivalence module when the frequency-dependent network equivalence is applied to power system electromagnetic transient simulation, the calculated amount of a frequency-dependent network equivalence mathematical model is reduced in a compression processing process in the method, the frequency-dependent network equivalence mathematical model is divided into a plurality of blocks for parallel calculation in a blocking processing process, the power system simulation speed is finally obviously accelerated, and the engineering practice effect is satisfactory.

Drawings

FIG. 1 is a schematic diagram of a conventional network equivalence method using a Noton equivalence model.

Fig. 2 is a schematic diagram of an existing network equivalence method based on frequency-dependent network equivalence.

FIG. 3 is a schematic diagram of an equivalent mathematical model of a frequency-dependent network involved in the method of the present invention.

FIG. 4 is a diagram of a mathematical model of the equivalent of the frequency-dependent network after compression in the method of the present invention.

Fig. 5 is a block diagram of the equivalent of the frequency dependent network in the method of the present invention.

Detailed Description

(1) the mathematical model of the equivalent of the frequency-dependent network for power system simulation Y(s) is

Where N is the dimension of y(s), s j2 pi f, f is the network frequency, j is the imaginary unit, { a }_iIs a pole, { c_iD is a constant term, and n is the number of poles; all elements of Y(s) have the same poles, and the residue and constant terms are different.

(2-1) rewriting the above Y(s) into the form of the following formula:

Y(s)＝C(sE-A)^-1B+D，

B＝diag(B₁ … B_k … B_n)，B_k＝diag((1 1 … 1)_(1×N))，

C＝[R₁ … R_k … R_n]，

E is a unit matrix, and the dimension of E is the same as that of the matrix A; as shown in fig. 3.

to R_kPerforming singular value decomposition to make R_k＝UΣV^T，

a decision threshold lambda is set, which is usually chosen to be 0.9999 and can be adjusted according to the required accuracy. Determining a matrix R using a decision threshold lambda_kI.e. the parameter r is incremented from 1 until the following holds:

then the matrix R is determined_kIs r;

R'_k＝(u₁,u₂,...,u_r)，

A'_k＝diag((a_k a_k … a_k)_(1×r))，

B'_k＝(v₁,v₂,...,v_r)^T；

The compressed frequency-dependent network equivalent mathematical model is shown in FIG. 4, for R_kCan reduce the amount of computation to O_{Reduction of}＝2N²+2N-4rN with almost no loss of precision;

since the inherent physical meaning of the frequency-dependent network equivalence is admittance, and the mathematical addition of admittance is equivalent to physical parallel connection, according to the above formula, the frequency-dependent network equivalence can be established into a plurality of parallel-connected parts, as shown in fig. 5, which is an embodiment of the present invention, the frequency-dependent network equivalence is divided into two parts, the calculation amount of each part is about half of that of the original frequency-dependent network equivalence module, and in actual application, the number of sub-modules can be determined according to needs.

Claims

1. A power system simulation method based on frequency-dependent network equivalence is characterized by comprising the following steps:

where N is the dimension of y(s), s j2 pi f, f is the network frequency, j is the imaginary unit, { a }_iIs a poleDot, { c_iD is a constant term, and n is the number of poles;

(2-1) rewriting the above Y(s) into the form of the following formula:

Y(s)＝C(sE-A)^-1B+D，

wherein,

e is a unit matrix, and the dimension of E is the same as that of the matrix A;

to R_kPerforming singular value decomposition to make R_k＝UΣV^T，

then the matrix R is determined_kIs r;

R'_k＝(u₁,u₂,...,u_r)，

A'_k＝diag((a_k a_k…a_k)_(1×r))，

B'_k＝(v₁,v₂,...,v_r)^T；