CN111740410A - A frequency spatiotemporal dynamic prediction method of power system - Google Patents

Abstract

The invention discloses a method for dynamically predicting the frequency space-time of an electric power system, which comprises the steps of firstly constructing a distance matrix Z and a path matrix L of the electric power system and assigning initial values, then updating the distance matrix Z and the path matrix L through main row and main column elements of the shortest distance matrix Z, and further finding the shortest electrical distance between any two nodes in the electric power system and the path where the shortest electrical distance is located; on the basis, the coupling factors of the test points at the moment of the lowest frequency value under the same fault point are calculated, so that the sequence of the frequency dynamic reaching of the lowest value of each monitoring point after the power system is disturbed is predicted, the time-space dynamic distribution of the power system frequency is predicted, and the safe and stable operation of the power system is better guaranteed.

Description

A frequency spatiotemporal dynamic prediction method of power system

technical field

The invention belongs to the field of electric power technology, and more particularly, relates to a frequency space-time dynamic prediction method of an electric power system.

Background technique

With the rapid development of the national economy, the power load continues to increase, and the scale of the power grid is gradually expanding. The spatial and temporal distribution characteristics of the frequency of the power system under disturbance are of great significance to the security and stability monitoring of the power system, the operation control of the system and the disturbance analysis. When the power system fails, accurate frequency dynamics can not only help determine the penetration rate of wind power, reasonable configuration of frequency-modulating units, reserve capacity, and automatic generation control (AGC) parameter configuration, but also accurate frequency dynamics can help set low-frequency Loading scheme to avoid frequency crash accidents.

In the dynamic process of the power grid, the frequency response of each monitoring point in the system has a spatiotemporal distribution characteristic. The uneven distribution of 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 leads to the difference in the frequency of each node, and the spatiotemporal distribution characteristics of the frequency appear. By mastering the frequency distribution of complex power grids, it is possible to accurately predict the order in which the lowest frequency of each measuring point in the system arrives, and then a more accurate cutting control strategy can be formulated to improve the security and stability of the power system.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a power system frequency spatiotemporal dynamic prediction method, which predicts the order in which the frequency of each monitoring point dynamically reaches the minimum value after the power system is disturbed by the coupling factor at the time of the frequency minimum value, thereby predicting The spatial and temporal dynamic distribution of the frequency of the power system is obtained, so as to better ensure the safe and stable operation of the power system.

In order to achieve the above object of the invention, a method for dynamic spatiotemporal frequency prediction of a power system according to the present invention is characterized in that it includes the following steps:

(1), construct the distance matrix Z and the path matrix L of the power system;

The distance matrix for constructing the power system is Z=[z _ij ] _n×n , where z _ij represents the electrical distance between any node i and node j, and n is the number of nodes in the power system;

Construct a path matrix L=[l _ij ] _n×n , where l _ij represents the intermediate node on the shortest path from non-adjacent node i to node j;

(2), assign initial values to the distance matrix Z and the path matrix L;

其中，

最短路径矩阵L赋初值为：

其中

The initial value of the distance matrix Z is:

in,

The initial value of the shortest path matrix L is:

in

(3), mark the main row and main column elements of the shortest distance matrix Z;

Arbitrarily mark one row and one column from the shortest distance matrix Z, denoted as the k-th row and the k-th column, k∈[1,n], where the k-th row and the k-th column element are recorded as the main row element and main column element;

(4), update the distance matrix Z and the path matrix L;

Update the distance matrix Z: In the distance matrix Z, traverse all the values of k from small to large, and in each value of k, start from the first element that is not in the main row and main column, and compare the elements in turn with The sum of any two elements in the main row and main column, if z _ik +z _kj ≥z _ij , keep the value of element z _ij unchanged; if z _ik +z _kj <z _ij , replace the element with z _ik +z _kj z _ij ;

The updated distance matrix L ^(k) is:

(5) Calculate the shortest electrical distance and path between any two nodes in the power system;

所对应的最短电气距离所在路径记为L_i-j-min；Repeat step (4), when k traverses to n, get the updated distance matrix Z ⁽ⁿ⁾ and path matrix L ⁽ⁿ⁾ ; then make the shortest electrical distance from node i to node j

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

(6) Calculate the inertia time constant of each line in the power system;

(6.1), select all generator nodes in the network topology of the power system, and denote a total of n ₁ ; mark any one of the generator nodes as the generator start node, and the remaining generators as the generator terminal nodes;

(6.2), in combination with step (5), calculate the path from the generator start node to each generator terminal node, and the inertia time constant on the line l _ij on its path;

为第q个发电机始端节点

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,…,n₁，p＝1,2,…,n₁-1；

为第q个发电机始端节点分布在线路l_i-j上的惯性时间常数；z_ij表示线路l_i-j的节点i到节点j的电气距离；

表示第q个发电机始端节点

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；in,

is the starting node of the qth generator

to the pth generator terminal node

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

is the inertia time constant of the qth generator start node distributed on the line l _ij ; z _ij represents the electrical distance from the node i of the line l _ij to the node j;

Represents 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;

(6.3), calculate the inertia time constant T _li-j on each line l _ij in the power system:

(7), calculate the coupling factor at the moment of the lowest frequency value;

(7.1), calculate impedance reference value Z _base and inertia reference value T _base :

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

(7.2) Mark any one of the generator nodes as faulty nodes in the network topology of the power system, and the rest are test nodes;

(7.3), 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λ个测试节点

间的最短电气距离，λ＝1,2,…,n₁-1；

为故障节点v_fault到第λ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λ个测试节点

间的惯性标幺值；in,

For the faulty node v _fault to the λth test node

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

For the faulty node v _fault to the λth test node

per unit value of the shortest electrical distance between;

For the faulty node v _fault to the λth test node

The per-unit value of inertia between ;

(7.4), calculate the coupling factor of each test node at the moment of the lowest frequency value

(8) Predict the frequency and space-time dynamics of the power system

值越小，则该测试点频率最先到达最低值，因此将所有的

按照从小到大的顺序组成序列T_d，记为

从而预测出电力系统的频率时空动态分布。Under the same fault point, the coupling factor of the test point at the time of the lowest frequency

The smaller the value is, the frequency of the test point reaches the lowest value first, so all the

According to the sequence T _d from small to large, denoted as

Thereby, the frequency space-time dynamic distribution of the power system is predicted.

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

The present invention is a frequency spatiotemporal dynamic prediction method of a power system. First, a distance matrix Z and a path matrix L of the power system are constructed and initial values are assigned, and then the distance matrix Z and the path matrix L are updated through the main row and main column elements of the shortest distance matrix Z. , and then find the shortest electrical distance and path between any two nodes in the power system; on this basis, by calculating the coupling factor of each test point under the same fault point at the time of the lowest frequency value, it is possible to predict the power system after disturbance. The order in which the frequency of the monitoring point dynamically reaches the lowest value, and then the time-space dynamic distribution of the frequency of the power system is predicted, so as to better ensure the safe and stable operation of the power system.

At the same time, the method for frequency spatiotemporal dynamic prediction of the power system of the present invention also has the following beneficial effects:

(1) A new distribution method is proposed for the distribution of the inertia of the system: the inertia of each generator in the system is evenly distributed to the line where the shortest electrical distance from the rest of the generators in the system is located. Such processing is beneficial to Simulate the characteristics of the actual power grid and improve the accuracy of frequency spatiotemporal dynamic prediction;

(2) The propagation of disturbance in the system is carried by the transmission line, and the line between the two nodes in the actual power grid is not a straight line in the geographic space. Therefore, the present invention uses the electrical distance between the two nodes in the system to measure the power generation. Geographical distribution of machines in the power system, which can more accurately predict the dynamic frequency of the power system;

(3) The present invention can quickly predict the frequency space-time dynamics after the disturbance of the power system by constructing the coupling factor at the time of the lowest frequency value.

Description of drawings

Fig. 1 is a flow chart of a power system frequency spatiotemporal dynamic prediction method of the present invention;

Fig. 2 is IEEE 10 machine 39 node simulation system diagram;

Figure 3 is the initial value of the distance matrix Z;

Fig. 4 is the distance matrix Z ⁽ⁿ⁾ after updating is completed;

Fig. 5 is the path matrix L ⁽ⁿ⁾ after the update is completed;

Fig. 6 is the time-space distribution diagram of the system frequency after the generator G9 is cut off;

Figure 7 is a time-space distribution diagram of the system frequency after the generator G7 is switched off.

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

In this embodiment, as shown in Figure 1, taking the IEEE 10-machine 39-node power system simulation data as an example, the fault description: when t=5s, the generator G9 is cut off by 41% due to the fault, the simulation time is 50s, and the simulation step size is 50s. If it is 0.0001s, then the difference of 0.001s between the two monitoring points in the power system at the time of the lowest frequency can be regarded as the phenomenon of spatiotemporal distribution.

This embodiment does not take into account the influence of the transformer on the propagation of the dynamic frequency space-time distribution, 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 29. In this example, the monitoring nodes are selected as 39 (generator G1), 19 (generator G4), 23 (generator G7), 25 (generator G8) and 2 (generator G10).

Hereinafter, we will describe in detail a method of the present invention for a power system frequency spatiotemporal dynamic prediction method, as shown in Fig. 1, which specifically includes the following steps:

S1. Construct the distance matrix Z and path matrix L of the power system;

The distance matrix for constructing the power system is Z=[z _ij ] _n×n , where z _ij represents the electrical distance between any node i and node j, and n is the number of nodes in the power system, which is 39;

Construct a path matrix L=[l _ij ] _n×n , where l _ij represents the intermediate node on the shortest path from non-adjacent node i to node j;

S2, assign initial values to the distance matrix Z and the path matrix L;

其中，

结合图2，距离矩阵Z的具体赋初值如图3所示，由于矩阵太大，图3中为代码中矩阵的截图，其中，inf代表∞，0.00025+0.0125i代表0.0005+j0.0125；The initial value of the distance matrix Z is:

in,

Combined with Figure 2, the specific initial value of the distance matrix Z is shown in Figure 3. Since the matrix is too large, Figure 3 is a screenshot of the matrix in the code, where inf represents ∞, 0.00025+0.0125i represents 0.0005+j0.0125;

其中

The initial value of the path matrix L is:

in

S3. Mark the main row and main column elements of the shortest distance matrix Z;

Arbitrarily mark one row and one column from the shortest distance matrix Z, denoted as the k-th row and the k-th column, k∈[1,n], where the k-th row and the k-th column element are recorded as the main row element and main column element;

S4, update the distance matrix Z and the path matrix L;

Update the distance matrix Z: In the distance matrix Z, traverse all the values of k from small to large, and in each value of k, start from the first element that is not in the main row and main column, and compare the elements in turn with The sum of any two elements in the main row and main column, if z _ik +z _kj ≥z _ij , keep the value of element z _ij unchanged; if z _ik +z _kj <z _ij , replace the element with z _ik +z _kj z _ij ;

The updated distance matrix L ^(k) is:

In this embodiment, the main row and main column elements of the labeling distance matrix Z start from the first row and the first column.

S5. Calculate the shortest electrical distance and the path between any two nodes in the power system;

以及节点i到节点j的最短电气距离所在路径记为L_i-j-min；Step S4 is repeated, when k traverses to n, the updated distance matrix Z ⁽ⁿ⁾ is obtained as shown in Figure 4 and the path matrix L ⁽ⁿ⁾ is shown in Figure 5; in Figure 4, 0.5 in the matrix represents 0.00025 +j0.00625, 1 represents 0.0005+j0.0125, 2 represents 0.001+j0.025, and so on; then let the shortest electrical distance from node i to node j

And the path where the shortest electrical distance from node i to node j is located is denoted as L _ij-min ;

In this embodiment, with reference to FIG. 2 and FIG. 4 , the path of the shortest electrical distance between the generator G9 node 29 and the measuring point nodes 39, 19, 23, 25 and 2 in the power system is calculated as:

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→27→17→16→24→23};

L _29-25-min = {29→26→25};

L _29-2-min = {29→26→25→2};)

S6. Calculate the distribution of inertia in the power system;

S6.1. Use the inertia time constant of the generator to measure the inertia, and calculate its inertia distribution for each generator; select all generator nodes in the network topology of the power system, and record them as n ₁ in total; mark any of them One generator node is the generator start node, and the remaining generators are the generator terminal nodes;

S6.2. Calculate the path from the starting node to each terminal node and the inertial time constant on the line l _ij on the path;

For example, the line set l _ij between the start node 29 of the ninth generator and the terminal node 39 of the first generator is calculated.

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 ninth generator start-end node 29 distributed on all lines in the path set l _ij ;

S6.3. After the inertia distribution of all generators in the system is calculated by the above steps, calculate the inertia time constant T _li-j on each line l _ij in the power system:

Take line l _29-26 as an example,

In this embodiment, as shown in FIG. 1 , n ₁ =10, and the inertia distribution on each line in the power system is calculated as shown in Table 1.

Table 1 shows the results of the inertia distribution of the power system lines.

line inertia line inertia line inertia L_29-26 18.99 L_1-39 14.64 L_5-6 15.2 L_26-25 18.99 L_2-3 20.1 L_26-27 14.85 L_25-2 21.48 L_3-4 8.26 L_27-17 14.85 L_2-1 14.64 L_1-5 11.31 L_17-16 26.7 L_16-15 13.78 L_14-13 9.57 L_16-19 33.15 L_15-14 13.78 L_13-10 9.57 L_16-21 14.94 L_21-22 14.94 L_16-24 14.94 L_24-23 14.94

Table 1

S7. Calculate the coupling factor at the moment of the lowest frequency value;

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

Wherein, N is the number of lines in the power system; in this embodiment, n ₁ =10, N = 21, so as to calculate: Z _base =0.0005+j0.0125, T _base =42;

S7.2. With reference to Figure 2, the generator node 29 is the faulty node, and 39, 19, 23, 25 and 2 are the test nodes;

S7.3. The shortest electrical distance and inertia between the fault point 29 of the per-unit fault node and the test nodes 39, 19, 23, 25 and 2:

为故障节点v_fault到第λ个测试节点

间的最短电气距离，λ＝1,2,…,5；

为故障节点v_fault到第λ个测试节点

间的最短电气距离的标幺值；

表示故障节点v_fault到第λ个测试节点

间最短电气距离所在路径

为故障节点v_fault到第λ个测试节点

间的惯性标幺值；in,

For the faulty node v _fault to the λth test node

The shortest electrical distance between λ=1,2,…,5;

For the faulty node v _fault to the λth test node

per unit value of the shortest electrical distance between;

Represents the faulty node v _fault to the λth test node

The path where the shortest electrical distance between

For the faulty node v _fault to the λth test node

The per-unit value of inertia between ;

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 failure node 29 and the test nodes 39, 19, 23, 25 and 2 are shown in Table 2.

Table 2 is the shortest electrical distance and inertia per unit value between the fault point and the measuring point.

29-39 28-19 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 2

S7.4. Calculate the coupling factor of each test node at the moment of the lowest frequency

In this embodiment, the coupling factor of the lowest frequency value between the fault point 29 and the measuring points 39, 19, 23, 25 and 2 is calculated and obtained as shown in Table 3.

Table 3 is the coupling factor of the lowest frequency value between the fault point and the measuring point.

29-39 29-19 29-23 29-25 29-2 t_d 7.112 7.5843 8.5064 2.9019 4.4157

table 3

S8. Predict the frequency and space-time dynamics of the power system

As shown in Table 3, under fault point 29, the coupling factors of test nodes 39, 19, 23, 25 and 2 at the time of the lowest frequency value are in the order of 25→2→39→19→23, and the value of the coupling factor is 25→2→39→19→23 The smaller the value is, the frequency of the test point reaches the lowest value first. Therefore, the order of the frequency dynamic of each test point reaching the lowest value is: G8→G10→G1→G4→G7, so as to predict the frequency space-time dynamics of the power system.

In this embodiment, combined with Fig. 2, it is obtained that the frequency of monitoring points has obvious spatiotemporal distribution phenomenon through refined simulation with PASAP software. The order of the time of the lowest frequency of monitoring points is: G8→G10→G1→G4→G7 , which is consistent with the sequence predicted by the present invention, and the simulation results are shown in Figure 6.

In addition, this example also provides another fault situation. When t=5s, the generator G7 node 23 loses 40% of power generation due to the fault. The monitoring points are selected as node 39 (generator G1), node 19 (generator G4), and node 22. (generator G6) and node 29 (generator G9). According to the method provided by the present invention, it can be calculated that the shortest electrical distance path between the generator G7 and each measuring point 39, 19, 22 and 29 is:

L _23-39-min = {23→24→16→17→18→3→2→1→39}

L _23-19-min = {23→24→16→19}

L _23-22-min = {23→22}

L _23-29-min = {23→24→16→17→27→26→29}

Table 4 shows the shortest electrical distance between fault point 23 and each measuring point 39, 19, 22 and 29 and the coupling factor results of inertia and frequency minimum value.

Table 4 is the shortest electrical distance between the fault point and the measuring point and its inertia and coupling factor per unit value.

23-39 23-19 23-22 23-29 Z^*/pu 8 3 1 6 T^*/pu 3.0867 1.5007 0.2214 2.5064 t_d 11.0867 4.5007 1.2214 8.5064

Table 4

The refined simulation is carried out by PASAP software, and the time-domain simulation result is shown in Fig. 7, and its time-space distribution characteristics are consistent with the space-time characteristics determined by the algorithm of the present invention.

Although 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. A power system frequency space-time dynamic prediction method is characterized by comprising the following steps:

(1) constructing a distance matrix Z and a path matrix L of the power system;

the distance matrix for constructing the power system is Z ═ Z_ij]_n×n，z_ijRepresenting the electrical distance between any node i and a node j, wherein n is the number of nodes in the power system;

constructing a path matrix L ═ L_ij]_n×n，l_ijRepresenting intermediate nodes on the shortest path from the non-adjacent node i to the node j;

(2) assigning initial values to the distance matrix Z and the path matrix L;

the distance matrix Z has an initial value:

wherein,

the shortest path matrix L is assigned with an initial value:

wherein

(3) Marking main row and main column elements of the shortest distance matrix Z;

marking a row and a column from the shortest distance matrix Z at will, marking as the kth row and the kth column, wherein k belongs to [1, n ], and elements of the kth row and the kth column are marked as main row elements and main column elements;

(4) updating the distance matrix Z and the path matrix L;

updating the distance matrix Z: in the distance matrix Z, traversing all values of k from small to large, and in each value of k, starting from the first element which is not in the main row and the main column, sequentially comparing the element with the sum of any two elements in the main row and the main column, if Z is_ik+z_kj≥z_ijThen element z is maintained_ijThe value of (d) is unchanged; if z is_ik+z_kj＜z_ijThen use z_ik+z_kjAlternative element z_ij；

Updating the distance matrix L^(k)Comprises the following steps:

(5) calculating the shortest electrical distance between any two nodes in the power system and the path where the shortest electrical distance is located;

repeating the step (3), and when k traverses to n, obtaining an updated distance matrix Z⁽ⁿ⁾Sum path matrix L⁽ⁿ⁾(ii) a Then let node i to node j have the shortest electrical distance

The corresponding shortest electrical distance path is marked as L_i-j-min；

(6) Calculating an inertia time constant of each line in the power system;

(6.1) selecting all generator nodes in the network topology of the power system, and recording the nodes as n in total₁A plurality of; marking any one generator node as a generator starting end node, and marking the rest generators as generator terminal nodes;

(6.2) calculating the path from the starting end node of the generator to the terminal end node of each generator in combination with the step (5) and the line l on the path_i-jAn inertial time constant of (c);

wherein,

is the starting end node of the q-th generator

To the p-th generator terminal node

Q is 1,2, …, n is the line set on the path of the shortest electrical distance between them₁，p＝1,2,…,n₁-1；

For the q-th starting generator distributed on line l_i-jAn inertial time constant of (c); z is a radical of_ijRepresents a line l_i-jThe electrical distance from node i to node j;

representing the qth generator start node

To the p-th generator terminal node

The shortest electrical distance between the two;

represents an inertia time constant of the qth start-end generator;

(6.3) calculating each line l in the power system_i-jTime constant of inertia of

(7) Calculating the coupling factor at the moment of the lowest frequency value;

(7.1) calculating an impedance reference value Z_baseWith a reference value of inertia T_base：

Wherein N is the number of lines in the power system;

(7.2) marking any one generator node as a fault node and the rest as test nodes in the network topology of the power system;

(7.3) the shortest electrical distance from each per unit fault node to each test node and inertia:

wherein,

for failed node v_faultTo the lambda test node

The shortest electrical distance between them, λ 1,2, …, n₁-1；

For failed node v_faultTo the lambda test node

Per unit value of the shortest electrical distance therebetween;

for failed node v_faultTo the lambda test node

The per unit value of inertia between;

(7.4) calculating the coupling factor of each test node at the moment of the lowest frequency value

(8) Predicting power system frequency space-time dynamics

Coupling factor of test point at the moment of lowest frequency value under the same fault point

The smaller the value, the lowest the test point frequency is reached first, so all will be

The sequence T is formed from small to large_dIs marked as

Therefore, the frequency space-time dynamic distribution of the power system is predicted.

Images