CN113346482B - Method for predicting wide area power system frequency space-time distribution based on SFR model - Google Patents

Abstract

The invention discloses a method for predicting the frequency space-time dynamic distribution of a wide-area power system based on a high-order SFR model. By extending a traditional simplified SFR model, a high-order SFR model is established to predict the inertial center frequency of the wide-area power system; Construct the distance matrix and path matrix between the nodes of the wide-area power system and assign them initial values. By iteratively updating the distance matrix and the path matrix, the shortest electrical distance between any two nodes in the wide-area power system and its path are calculated. The inertial time constant on the line; then mark the faulty node, calculate the shortest electrical distance and inertia between the per-unit faulty node and each test node; finally calculate the frequency space-time distribution factor, and construct the high-order frequency space-time of the wide-area power system Distribute models and predict in real-time the frequency-spatiotemporal dynamic distribution of wide-area power systems.

Description

A Method for Predicting the Spatial and Temporal Distribution of Frequency in Wide Area Power System Based on SFR Model

technical field

The invention belongs to the technical field of power security and stability, and more particularly, relates to a method for predicting the frequency space-time dynamic distribution of a wide-area power system based on a high-order SFR model.

Background technique

my country's power system is currently in a complex state of high voltage level, wide interconnection area, large system scale, high structural complexity, and AC/DC hybrid connection. Frequency, as a key indicator of power quality and operation status monitoring and control of power system, is the key evaluation and control object of power system stability. Wide-area measurement of power grid frequency data has shown that the frequency of each measuring point has obvious dynamic spatiotemporal distribution phenomenon. The establishment of a wide-area system frequency spatiotemporal distribution model is of great significance for improving the stability and control level of wide-area interconnected power grids. When a wide-area power system fails, accurate frequency spatiotemporal dynamics can not only help determine wind power penetration rate, reasonable configuration of frequency-modulating units, reserve capacity, and automatic generation control (AGC) parameter configuration, but also accurate frequency spatiotemporal distribution characteristics can help In order to set the low frequency load shedding plan, avoid the frequency collapse accident.

The frequency response of each monitoring point in the wide-area power system has spatiotemporal distribution characteristics. A high-order frequency response model is established to improve the prediction accuracy of the inertial center frequency of the system, and provide a strong theoretical support for the subsequent research on the spatial and temporal distribution characteristics of frequencies. The uneven distribution of the units and the difference in their inertia are important factors that affect the spatiotemporal distribution of frequencies. Since inertia is an inherent property of the power system, it is manifested as the impedance effect of the system on energy fluctuations caused by external disturbances. Therefore, when the power system is disturbed, the difference in inertia of each node in the system and the difference in the governor parameters lead to the difference in the frequency of each node, and the spatiotemporal distribution characteristics of the frequency appear. Mastering the mapping relationship between the inertia center frequency and the frequency dynamics of each monitoring point in the wide-area system can accurately predict the spatiotemporal dynamics of the wide-area system frequency, and can formulate more accurate frequency cutting control strategies to improve the safety and stability of the power system.

In the prior art, the patent application number is "CN202010573418.7", and the title is "A method of frequency spatiotemporal dynamic prediction of power system". Accurately predict the frequency dynamic process of each measuring point of the system.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a method for predicting the frequency space-time dynamic distribution of a wide-area power system based on a high-order SFR model. The mapping relationship between the frequency dynamics of each measuring point in the power system, so as to build a wide-area power system frequency space-time model, through which the frequency dynamic process of each monitoring point after the wide-area power system disturbance can be accurately predicted, and the frequency of the wide-area power system can be accurately revealed. The spatial and temporal distribution characteristics of the frequency can provide strong theoretical support for formulating precise frequency control strategies, thereby ensuring the safe and stable operation of the power system.

In order to achieve the above purpose of the invention, a method for predicting the frequency space-time dynamic distribution of a wide-area power system based on a high-order SFR model of the present invention is characterized in that, it includes the following steps:

(1), a kind of frequency space-time dynamic distribution method based on high-order SFR model prediction wide-area power system, is characterized in that, comprises the following steps:

(1), establish a high-order SFR model;

及广域电力系统负荷效应阻尼D_L来模拟广域电力系统的阻尼；(1.1) Extend the mechanical gain K _m in the traditional simplified SFR model to be the first-order inertial link k/A+Ts, where k, A, and T are all mechanical gain coefficients, and s represents the S domain; increase the damping of the excitation system

and the wide area power system load effect damping _DL to simulate the wide area power system damping;

(1.2), set high-order SFR model parameters;

Among them, R is the equivalent adjustment coefficient of the wide area power system; T _R is the equivalent reheat time constant of the wide area power system; H is the equivalent inertia time constant of the wide area power system, F _H is the equivalent high voltage of the wide area power system Cylinder work ratio; m is the number of generators in the wide area power system; H _q is the rated capacity of the qth generator in the wide area power system; R _q is the adjustment coefficient of the qth generator in the wide area power system ; F _Hq is the high-voltage cylinder work ratio of the qth generator in the wide area power system; T _Rq is the reheat time constant of the qth generator in the wide area power system; M _base,q is the qth generator Rated capacity; S _base is the benchmark capacity of the wide-area power system;

(2), construct the distance matrix B and the path matrix L between the nodes of the wide-area power system and assign initial values to the distance matrix B and the path matrix L;

(3), by iteratively updating the distance matrix B and the path matrix L, calculate the shortest electrical distance Z _ij-min and its path L _ij-min between any two nodes i, j of the wide-area power system;

(4) Calculate the inertia time constant on each line l _ij in the wide area power system

间的最短电气距离

及其惯性

(5) Mark any faulty node v _fault in the wide-area power system, and per-unitize the faulty node to each test node

the shortest electrical distance between

and its inertia

(6) Introduce frequency space-time distribution factor to some key parameters of high-order SFR model;

(6.1) For each test node, the frequency-space-time distribution factor for calculating the median inertial time constant of the high-order SFR model is:

为第i个测试节点

的惯性时空分布因子；in,

is the i-th test node

The inertial space-time distribution factor of ;

(6.2) For each test node, the frequency space-time distribution factor for calculating the median reheat time constant of the high-order SFR model is:

为第i个测试节点

的再热时间常数时空分布因子；in,

is the i-th test node

The spatiotemporal distribution factor of the reheat time constant;

(6.3) For each test node, the frequency-space-time distribution factor for calculating the work ratio of the medium-value high-pressure cylinder in the high-order SFR model is:

为第i个测试节点

的高压缸做功比例时空分布因子；in,

is the i-th test node

The time-space distribution factor of the high-pressure cylinder work ratio;

(7), take the high-order SFR model after introducing the frequency space-time distribution factor as the frequency space-time distribution model of the wide-area power system;

(8) Using the frequency spatiotemporal distribution model of the wide-area power system to predict the spatiotemporal dynamic distribution of frequency;

的频率变化量；(8.1), when the wide-area power system is disturbed, calculate each test node

the frequency change;

表示发电机的阻尼；D_L表示负荷效应系数；P_d为广域电力系统的功率缺额；Δω_i表示第i个测试节点

的频率变化量；W_i为变量，且满足：

ζ_i为变量，且满足：

where D _g represents the damping of the generator and excitation system,

represents the damping of the generator; _DL represents the load effect coefficient; P _d represents the power deficit of the wide-area power system; Δω _i represents the ith test node

The frequency variation of ; _Wi is a variable and satisfies:

ζ _i is a variable and satisfies:

的频率动态分布；(8.2), calculate each test node after the wide area power system is disturbed

The frequency dynamic distribution of ;

f _i =50+Δω _i

的频率动态。Among them, f _i is the ith test node

frequency dynamics.

The purpose of the invention of the present invention is achieved in this way:

The present invention predicts the frequency space-time dynamic distribution method of the wide-area power system based on the high-order SFR model. By extending the traditional simplified SFR model, a high-order SFR model is established to predict the inertia center frequency of the wide-area power system; and then the wide-area power system is constructed. The distance matrix and path matrix between system nodes are assigned initial values, and the shortest electrical distance between any two nodes in the wide-area power system and its path are calculated by updating the distance matrix and path matrix iteratively, as well as the distance on each line. Inertia time constant; then mark the faulty node, calculate the shortest electrical distance between the per-unit faulty node and each test node and its inertia; finally calculate the frequency space-time distribution factor, build a high-order frequency space-time distribution model of the wide-area power system and real-time Predicting the frequency space-time dynamic distribution of a wide-area power system.

Meanwhile, the present invention also has the following beneficial effects based on the high-order SFR model to predict the frequency space-time dynamic distribution method of the wide-area power system:

(1) Establish a high-order frequency response model to predict the inertial center frequency after the system is disturbed, which improves the accuracy of the model prediction and provides a strong theoretical support for the subsequent research on the frequency space-time distribution.

(2) A new distribution method is proposed for the distribution of system inertia: the inertia of each generator in the system is evenly distributed on the path with the shortest electrical distance from the rest of the generators in the system. The characteristics of the actual power grid after disturbance provide a strong theoretical support for the prediction of the system frequency distribution in time and space.

(3) The mapping relationship between the inertial center frequency and the frequency dynamics of each measuring point of the wide-area system is clarified, and the frequency space-time distribution factor is established to establish a wide-area system frequency space-time distribution model, which can quickly and accurately predict the frequency of each measuring point in the wide-area system. Dynamic process, accurately revealing the spatial and temporal distribution characteristics of wide-area system frequencies.

Description of drawings

Fig. 1 is the flow chart of the present invention's method for predicting the frequency space-time dynamic distribution of a wide-area power system based on a high-order SFR model;

Fig. 2 is the structure diagram of the high-order SFR model;

Figure 3 is a topology diagram of a wide-area complex test system;

Fig. 4 is the updated distance matrix visualization diagram;

Fig. 5 is the updated path matrix visualization diagram;

Fig. 6 is the actual system frequency space-time dynamic diagram under the fault of machine cutting;

Fig. 7 is a frequency space-time dynamic diagram under the prediction of a machine-cutting fault by a wide-area system frequency space-time distribution model;

Fig. 8 is the actual system frequency space-time distribution diagram under the disconnection fault;

FIG. 9 is a frequency space-time dynamic diagram under the prediction of disconnection fault by a wide-area system frequency space-time distribution model.

Detailed ways

The specific embodiments of the present invention are described below with reference to the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be noted that, in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

Example

FIG. 1 is a flow chart of the method of the present invention for predicting the frequency space-time dynamic distribution of a wide-area power system based on a high-order SFR model.

In this embodiment, with reference to Fig. 3, the fault description of the wide-area power system is as follows: when t=5s, the generator G9 shuts down 41% due to the fault, the simulation time is 50s, and the simulation step is 0.0001s, then the wide-area power system The difference of 0.001 second between the two monitoring points in the frequency maximum offset moment can be regarded as a spatiotemporal distribution phenomenon.

In this embodiment, the influence of the transformer on the frequency space-time distribution is not taken into account, that is, when calculating the shortest electrical distance between the two generators and their path, the influence of the transformer is not considered, and the monitoring node is selected after the generator passes through the transformer. bus node. In this example, the monitoring nodes are selected as busbar 39 (generator G1), busbar 19 (generator G4), busbar 23 (generator G7), busbar 25 (generator G8) and busbar 2 (generator G10).

In the following, we will describe in detail the method for predicting the frequency spatiotemporal dynamic distribution of a wide-area power system based on a high-order SFR model in conjunction with FIG. 1, as shown in FIG. 1, which specifically includes the following steps:

S1. Establish a high-order SFR model;

及广域电力系统负荷效应阻尼D_L来模拟广域电力系统的阻尼；拓展完成后，高阶SFR模型结构图如图2所示。S1.1. Extending the mechanical gain K _m in the traditional simplified SFR model is the first-order inertial link k/A+Ts, where k, A, and T are all mechanical gain coefficients, and s represents the S domain; increase the damping of the excitation system

and the load effect damping _DL of the wide-area power system to simulate the damping of the wide-area power system; after the expansion is completed, the structure diagram of the high-order SFR model is shown in Figure 2.

S1.2. Set the parameters of the high-order SFR model;

Among them, R is the equivalent adjustment coefficient of the wide area power system; T _R is the equivalent reheat time constant of the wide area power system; H is the equivalent inertia time constant of the wide area power system, F _H is the equivalent high voltage of the wide area power system Cylinder work ratio; m is the number of generators in the wide area power system; H _q is the rated capacity of the qth generator in the wide area power system; R _q is the adjustment coefficient of the qth generator in the wide area power system ; F _Hq is the high-voltage cylinder work ratio of the qth generator in the wide area power system; T _Rq is the reheat time constant of the qth generator in the wide area power system; M _base,q is the qth generator Rated capacity; S _base is the benchmark capacity of the wide-area power system;

In this embodiment, the parameters of the high-order SFR model of the wide-area power system are tuned, and the tuning results are shown in Table 1;

Table 1 is the parameter values of the high-order SFR model

parameter Higher-order SFR parameters parameter Higher-order SFR parameters F_H 0.4 D_g 0.17 T_R 16 D_L 0.5 T 0.11 k 0.008 A 0.48 H 1 R 0.0555

Table 1

S2. Construct the distance matrix B and the path matrix L between the nodes of the wide-area power system;

Taking each bus in the wide-area power system as a node, the distance matrix between the nodes of the wide-area power system is constructed as B=[b _ij ] _n×n , where b _ij represents the admittance value between node i and node j, n is the number of nodes in the wide-area power system, and the value is 39; the construction path matrix is L=[l _ij ] _n×n , where l _ij represents the intermediate node on the shortest path from node i to node j in the wide-area power system ;

S3, assign initial values to the distance matrix B and the path matrix L;

其中，

Assign the initial value to the distance matrix B:

in,

其中，

Assign the initial value to the path matrix L:

in,

S4, iteratively update the distance matrix B and the path matrix L;

Let k∈[1,n], initialize k=1;

Update the distance matrix B as:

The updated path matrix L is:

When k=n, obtain the updated distance matrix B ⁽ⁿ⁾ and the path matrix L ⁽ⁿ⁾ ; In the present embodiment, the visualization diagram of the updated distance matrix B ⁽ⁿ⁾ is as shown in Figure 4; The visualization diagram of the path matrix L ⁽ⁿ⁾ of , is shown in Figure 5;

S5. Calculate the shortest electrical distance between any two nodes of the wide-area power system and its path;

所对应的最短电气距离所在路径记为L_i-j-min；According to the distance matrix B ⁽ⁿ⁾ and the path matrix L ⁽ⁿ⁾ , calculate the shortest electrical distance Z _ij-min from node i to node j:

The path where the corresponding shortest electrical distance is located is denoted as L _ij-min ;

In this embodiment, the path where the shortest electrical distance between the generator G9 node 29 and the measuring point nodes 39, 19, 23, 25 and 2 in the wide area power system is calculated, as shown in Figure 5, is:

L _29-39-min = {29→26→25→2→1→39}

L _29-19-min = {29→26→27→17→16→19}

L _29-23-min = {29→26→17→17→16→24→23}

L _29-25-min = {29→26→25}

L _29-2-min = {29→26→25→2}

S6. Calculate the inertia time constant of each line in the wide-area power system;

S6.1. In this embodiment, we use the inertia time constant of the generator to measure the inertia, so all the bus nodes connected to the generator are marked in the wide area power system, a total of m; then in the m bus nodes , any bus node is marked as the start node, and the rest of the bus nodes are terminal nodes;

S6.2, calculate the shortest path from each origin node to each terminal node according to the method described in step S5, and the inertial time constant of the line l _ij on the shortest path;

为第q个始端节点

到第p个发电机终端节点

间的最短电气距离所在路径上的线路集合，q＝1,2,…,m，p＝1,2,…,m-1；

为第q个始端发电机分布在线路l_i-j上的惯性时间常数；

表示线路l_i-j的导纳值；

表示第q个发电机始节点

到第p个发电机终端节点

间最短电气距离；

表示第q个始端发电机的惯性时间常数；

表示距离矩阵B⁽ⁿ⁾中始端节点

到终端节点

间的导纳值；in,

is the qth start node

to the pth generator terminal node

The set of lines on the path where the shortest electrical distance between them is located, q=1,2,...,m, p=1,2,...,m-1;

is the inertia time constant of the qth starting generator distributed on the line l _ij ;

represents the admittance value of the line l _ij ;

Indicates the start node of the qth generator

to the pth generator terminal node

The shortest electrical distance between;

Represents the inertia time constant of the qth starting generator;

Represents the start node in the distance matrix B ⁽ⁿ⁾

to the end node

The admittance value between;

For example: calculate the line set l _ij between the generator starting node 29 and the generator terminal node 39 ;

L _29-39-min = {29→26→25→2→1→39}

l _ij =L _29-39-min ={l _29-26 ,l _26-25 ,l _25-2 ,l _2-1 ,l _1-39 }

Calculate the inertia time constant of the generator start-end node 29 distributed on all lines in the path l _ij ;

S6.3. Calculate the inertial time constant on each line l _ij in the wide area power system

In this embodiment, taking lines 1 _29-26 as an example,

In this embodiment, m=10 is taken, and the inertia distribution on each line in the wide-area power system is calculated as shown in Table 2.

Table 2 shows the inertia distribution results of each line in the wide area power system.

line inertia Pu line inertia Pu l_29-26 18.99 0.4498 l_29-26 11.31 0.2693 l_26-25 18.99 0.4498 l_5-6 15.20 0.3619 l_25-2 21.48 0.5114 l_26-27 14.85 0.3536 l_2-1 14.64 0.3486 l_27-17 14.85 0.3536 l_1-39 14.64 0.3486 l_17-16 26.70 0.6357 l_2-3 20.10 0.4786 l_16-15 13.78 0.3281 l_3-4 8.2600 0.1967 l_15-14 13.78 0.3281 l_14-13 9.570 0.2279 l_21-22 14.94 0.3558 l_13-10 9.570 0.2279 l_16-24 14.94 0.3558 l_16-19 33.15 0.7893 l_24-23 14.94 0.3558

Table 2

S7. The shortest electrical distance and inertia between the per-unit fault node and each test node;

S7.1. Calculate the impedance reference value Z _base and the inertia reference value T _base :

Among them, N is the number of lines in the wide area power system;

In this embodiment, m=10, N=21, and it is calculated that: Z _base =0.0005+j0.0125, T _base =42;

S7.2. Mark any node in the wide-area power system as a faulty node, and the rest are test nodes;

In this embodiment, the test nodes can also select the remaining part of the nodes as test nodes, for example: generator node 29 is a fault node, and 39, 19, 23, 25 and 2 are test nodes;

S7.3. The shortest electrical distance and inertia between the per-unit fault node and each test node;

为故障节点v_fault到第i个测试节点

间的最短电气距离，i＝1,2,…,n-1；

为故障节点v_fault到第i个测试节点

间的最短电气距离的标幺值；

为故障节点v_fault到第i个测试节点

间的惯性标幺值；的标幺值；

为故障节点v_fault到第i个测试节点

间的惯性标幺值；in,

For the faulty node v _fault to the i-th test node

The shortest electrical distance between, i=1,2,...,n-1;

For the faulty node v _fault to the i-th test node

per unit value of the shortest electrical distance between;

For the faulty node v _fault to the i-th test node

The per-unit value of inertia between ; the per-unit value of ;

For the faulty node v _fault to the i-th test node

The per-unit value of inertia between ;

In this embodiment, taking the faulty node 29 and the test node 39 as examples:

In this embodiment, the shortest electrical distance and inertia results between the per-unit fault node 39 and the test nodes 39 , 19 , 23 , 25 and 2 are shown in Table 3.

Table 3 is the per-unit value of the shortest electrical distance and inertia between the faulty node and the test point.

29-39 29-19 29-23 29-25 29-2 Z^*/pu 5 5 6 2 3 T^*/pu 2.1129 2.5843 2.5064 0.9019 1.4157

table 3

S8. Introduce frequency spatiotemporal distribution factors to some key parameters of the high-order SFR model;

S8.1. For each test node, calculate the frequency space-time distribution factor of the median inertial time constant of the high-order SFR model as:

为第i个测试节点

的惯性时空分布因子；in,

is the i-th test node

The inertial space-time distribution factor of ;

S8.2. For each test node, the frequency-space-time distribution factor for calculating the median reheat time constant of the high-order SFR model is:

为第i个测试节点

的再热时间常数时空分布因子；in,

is the i-th test node

The spatiotemporal distribution factor of the reheat time constant;

S8.3. For each test node, calculate the frequency space-time distribution factor of the high-order SFR model medium-value high-pressure cylinder work ratio:

为第i个测试节点

的高压缸做功比例时空分布因子；in,

is the i-th test node

The time-space distribution factor of the high-pressure cylinder work ratio;

S9. Use the high-order SFR model after introducing the frequency space-time distribution factor as the frequency space-time distribution model of the wide-area power system;

In this embodiment, the parameters of the high-order frequency space-time distribution model of the wide-area power system calculated under the power-off fault are shown in Table 4.

Table 4 shows the parameters of the spatiotemporal distribution model of the wide-area system under the shutdown fault.

parameter G1 G4 G7 G8 G10 F_H 0.4 0.4 0.4 0.4 0.4 T_R 10.7728 9.3904 9.1024 25.7392 16.5824 H 0.7025 0.8592 1 0.1206 0.2824

Table 4

In this way, we introduce the frequency space-time distribution factor into some coupling parameters of the high-order SFR model, so as to construct the high-order frequency space-time distribution model of the wide-area power system;

S10, using a frequency spatiotemporal distribution model of a wide-area power system to predict the spatiotemporal dynamic distribution of frequency;

的频率变化量Δω_i；S10.1. When the wide-area power system is disturbed, calculate each test node

The frequency variation Δω _i of ;

表示发电机的阻尼；D_L表示负荷效应系数；P_d为广域电力系统的功率缺额，在本实施例中，如图2所示，P_sp为增量功率的设定点，在众多研究过程中，只对P_d感兴趣，所以在本实施例中P_sp＝0；Δω_i表示第i个测试节点

的频率变化量；W_i为变量，且满足：

ζ_i为变量，且满足：

where D _g represents the damping of the generator and excitation system,

represents the damping of the generator; D _L represents the load effect coefficient; P _d is the power deficit of the wide-area power system. In this embodiment, as shown in Figure 2, P _sp is the set point of the incremental power. In many studies During the process, we are only interested in P _d , so in this embodiment, P _sp =0; Δω _i represents the i-th test node

The frequency variation of ; _Wi is a variable and satisfies:

ζ _i is a variable and satisfies:

的频率动态分布；S10.2. Calculate each test node after the wide area power system is disturbed

The frequency dynamic distribution of ;

f _i =50+Δω _i

的频率动态。Among them, f _i is the ith test node

frequency dynamics.

In this embodiment, the frequency space-time distribution model of the wide-area power system can accurately predict the frequency dynamics of each measuring point of the system, and accurately reveal the space-time distribution characteristics of the frequency of the wide-area system.

In this embodiment, the frequency dynamic process of nodes 39, 19, 23, 25 and 2 can be predicted through the parameters of the high-order frequency space-time distribution model of the wide-area power system shown in Table 4, revealing the space-time frequency of the wide-area system frequency. distribution characteristics.

In this embodiment, the refined simulation by PSASP software shows that the frequency of each measuring point has obvious spatiotemporal distribution phenomenon, G8→G10→G1→G4→G7, and the simulation result is shown in FIG. 6 . It can be seen that the frequency of each measuring point predicted by the present invention is completely consistent with the actual system, and the error is extremely small. The prediction result is shown in Figure 7, and the error analysis table is shown in Table 5.

Table 5 is the error analysis table of frequency dynamics under machine cutting fault;

G1 G4 G7 G8 G10 Actual system frequency maximum offset time/s 7.6474 9.020 9.0653 7.4946 7.5738 Time-space distribution model frequency maximum offset moment/s 8.6615 9.2457 9.8046 5.6304 6.6487 Absolute error/s 1.0141 0.2257 0.7397 1.8642 0.9251 Actual system frequency steady state value/Hz 49.9273 49.9273 49.9273 49.9273 49.9273 Space-time distribution model frequency steady-state value/s 49.9432 49.9433 49.9433 49.9418 49.9428 Absolute error/Hz 0.0159 0.016 0.016 0.0145 0.0155 Relative error/% 0.0318 0.032 0.032 0.029 0.031

table 5

In addition, this example also provides another fault situation. When t=5s, the line _115-16 has a three-phase disconnection fault at node 15. The simulation time is 50s, the simulation step is 0.0001s, and the monitoring point is selected as the bus. 19 (generator G4), bus 25 (generator G8), bus 29 (generator G9) and bus 2 (generator G10).

According to the model established by the present invention, the shortest electrical distance between the node 15 and each measuring point 19, 25, 29 and 2 can be calculated as:

L _15-19-min = {15→16→19}

L _15-25-min = {15→14→4→3→2→25}

L _15-29-min = {15→16→17→27→26→29}

L _15-2-min = {15→14→4→3→2}

Table 6 shows the shortest electrical distance and inertia between the per-unit fault point 15 and each measuring point 19, 25, 29 and 2.

Table 6 is the shortest electrical distance and inertia between the fault point and the measuring point.

15-19 15-25 15-29 15-2 Z^*/pu 2 5 5 4 T^*/pu 1.1173 1.7171 2.1230 1.2057

Table 6

In this embodiment, the parameters of the space-time distribution model of the wide-area system obtained by calculation are shown in Table 7.

Table 7 shows the model parameters of the spatiotemporal distribution of the wide-area system under the disconnection fault.

parameter G4 G8 G9 G10 F_H 0.4 0.4 0.4 0.4 T_R 22.32 12.5184 10.736 17.2704 H 0.9336 1.0824 1.1653 0.9856

Table 7

The time-space distribution phenomenon of the frequency of each measuring point is obtained by the refined simulation of PSASP software, G4→G10→G8→G9, and the simulation result is shown in Figure 8. The frequency of each measuring point predicted by a wide-area system frequency space-time distribution model of the present invention is completely consistent with the actual system, and the error is extremely small.

Table 8 is the error analysis table of frequency dynamics under disconnection fault;

G4 G8 G9 G10 Actual system frequency maximum offset time/s 5.3243 5.5463 5.8242 5.4562 Time-space distribution model frequency maximum offset moment/s 5.3352 5.4446 5.6355 5.3338 Absolute error/s 0.0109 0.1017 0.1887 0.1224 Actual system frequency steady state value/Hz 49.8756 49.8756 49.8756 49.8756 Space-time distribution model frequency steady-state value/s 49.8743 49.8760 49.8762 49.8754 Absolute error/Hz 0.0013 0.0004 0.0006 0.0002 Relative error/% 0.0026 0.0008 0.0012 0.0004

Table 8

Although the illustrative specific embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, As long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the inventive concept are included in the protection list.

Claims (1)

1. The method for predicting the frequency space-time dynamic distribution of the wide area power system based on the high-order SFR model is characterized by comprising the following steps of:

(1) Establishing a high-order SFR model;

(1.1) expanding mechanical gain K in the traditional simplified SFR model _m A first-order inertia link k/A + Ts is adopted, wherein k, A and T are all mechanical gain coefficients, and S represents an S domain; increasing excitation system damping

And wide area power system load effect damping D _L To simulate damping of a wide area power system;

(1.2) setting parameters of the high-order SFR model;

wherein R is the equivalent difference adjusting coefficient of the wide area power system; t is _R An equivalent reheat time constant of the wide area power system; h is the equivalent inertia time constant of the wide area power system, F _H Working proportion of the equivalent high-pressure cylinder of the wide-area power system is obtained; m is the number of generators in the wide area power system; h _q Rated capacity of the q generator in the wide area power system; r is _q A difference adjustment coefficient of a q-th generator in the wide area power system is obtained; f _Hq Working proportion of a high-pressure cylinder of a qth generator in a wide-area power system; t is a unit of _Rq A reheat time constant of a qth generator in the wide area power system; m is a group of _base,q Rated capacity of the q-th generator; s _base A reference capacity for a wide area power system;

(2) Constructing a distance matrix B and a path matrix L between nodes of the wide area power system and assigning initial values to the distance matrix B and the path matrix L;

(3) And calculating the shortest electrical distance Z between any two nodes i and j of the wide area power system by iteratively updating the distance matrix B and the path matrix L _i-j-min And its path L _i-j-min ；

(4) Calculating each line l in the wide area power system _i-j Time constant of inertia of

(5) Marking any fault node v in wide area power system _fault Per unit fault node to each test node

The shortest electrical distance between

And inertia thereof

(6) Introducing frequency space-time distribution factors to part of key parameters of the high-order SFR model;

(6.1) for each test node, calculating the frequency space-time distribution factor of the equivalent inertia time constant in the high-order SFR model as follows:

wherein,

for the ith test node

The inertia space-time distribution factor of (c);

(6.2) for each test node, calculating the frequency space-time distribution factor of the equivalent reheating time constant in the high-order SFR model as follows:

wherein,

for the ith test node

The reheat time constant spatial-temporal distribution factor;

(6.3) for each test node, calculating a frequency space-time distribution factor of the work proportion of the medium-value high-pressure cylinder in the high-order SFR model as follows:

wherein,

for the ith test node

The working proportion space-time distribution factor of the high-pressure cylinder;

(7) Taking the high-order SFR model after the frequency space-time distribution factor is introduced as a frequency space-time distribution model of the wide area power system;

(8) Predicting the time-space dynamic distribution of the frequency by utilizing a frequency time-space distribution model of the wide area power system;

(8.1) calculating each test node after the wide area power system is disturbed

The amount of frequency variation of (a);

wherein D is _g Indicating the damping of the generator and the excitation system,

representing the damping of the generator; d _L Representing the load effect coefficient; p _d Is a power deficit of the wide area power system; Δ ω _i Representing the ith test node

Amount of frequency change of；W _i Is variable and satisfies:

ζ _i is variable and satisfies:

(8.2) calculating each test node after disturbance of the wide area power system

Dynamic distribution of frequencies of (a);

f _i ＝50+Δω _i

wherein f is _i For the ith test node

The frequency dynamics of (2).

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