CN113379248A - Power grid risk assessment and early warning method based on complex network theory - Google Patents
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Abstract
The invention discloses a power grid risk assessment and early warning method based on a complex network theory, which comprises the steps of 1 establishing an abstract complex network taking a power grid as an object, 2 calculating a node degree index, an index of betweenness, an efficiency loss coefficient index and a network cohesion degree change rate index of each node respectively, 3 compositing each index into a power grid risk index, and 4 outputting a risk assessment result of each node. The invention can realize the risk assessment and early warning of the power grid network.
Description
Technical Field
The invention relates to a power grid risk assessment and early warning method based on a complex network theory, which is used in the field of power grid assessment.
Background
The power grid risk analysis is a precondition for guaranteeing safe and stable operation of a power grid. The risk assessment method comprises two types of deterministic assessment and probabilistic assessment.
Deterministic evaluation is a traditional power grid operation risk evaluation method, and a commonly used N-1 risk evaluation method belongs to the deterministic evaluation category. The deterministic algorithm establishes an expected accident set based on the severity of the accident, and does not consider other different operating states and the possibility of other events, so that the application to the power system with higher and higher uncertainty has certain limitation.
The probabilistic evaluation method gives a statistical rule of probability distribution of the system or the element based on the original data, and comprehensively evaluates the system risk by considering the possibility of occurrence of an expected accident and the severity of the consequences of the expected accident. The traditional probabilistic evaluation method comprises the reliability of a power system and the like, is mostly an off-grid analysis algorithm, and does not consider the influence of the current real-time running state and running environment on the system risk and the influence of future control decision on the risk. Traditional evaluation algorithms, such as load flow calculation, Monte Carlo simulation and the like, have the characteristics of multiple iteration times and long calculation time, and have certain limitations when applied to power grid operation risk evaluation. The probabilistic evaluation method has more comprehensive risk evaluation, but has great defects. Firstly, the modeling accuracy of the method is limited by the information transmission quality in the actual power grid environment, and the risk early warning effect is further influenced. In addition, as the load of the power grid is increased, the coverage area is enlarged, and the coupling degree with the communication system and the comprehensive energy system is improved, the power grid network is more and more complex, the refined modeling occupies great computing resources, the research on the coupling modeling is preliminary, and the risk assessment and the early warning effect are also influenced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a power grid risk assessment and early warning method based on a complex network theory, and can realize power grid network risk assessment and early warning.
One technical scheme for achieving the above purpose is as follows: a power grid risk assessment and early warning method based on a complex network theory comprises the following steps,
in the power grid object, buses, generators and loads in a power grid are nodes, and connecting lines and transformers between the buses are edges;
index one, node degree, is the number of edges associated with the node;
the index two, the betweenness,
wherein C (x) is the betweenness of node x; v is a node set, and h and j are two different nodes; sigmahjIs the shortest path number, σ, between nodes h and jhj(x) The number of the shortest paths between the nodes h and j passing through the node x;
index three, the efficiency loss coefficient, network efficiency e, which is an index quantifying the efficiency of information exchange between network nodes, is obtained by the following formula,
wherein d ishjThe length of the shortest path between the nodes h and j is shown, and m is the total number of the nodes; the efficiency loss coefficient is used as a node evaluation index, and is the percentage of network efficiency loss after a certain node is removed, which is calculated by the following formula,
where E (x) is the efficiency loss coefficient for node x, e0E is the network efficiency obtained after the node x is removed;
index four, the network aggregation change rate, the network aggregation is defined as the reciprocal of the product of the number of nodes and the average path length, which is defined by the following formula,
wherein n is the degree of aggregation of the network and l is the average path length of the edge;
the rate of change of the degree of network cohesion is defined by the following formula,
wherein N (x) is the network cohesion degree change rate of the node x, n0Is the initial network cohesion degree, and n is the network cohesion degree obtained after the node x is removed;
step 3.1, constructing a network node evaluation matrix
X＝(xij)n*p
Where n is the number of nodes, p is the number of single indices, xijThe j evaluation index of the ith node;
step 3.2, the node evaluation matrix is normalized by the following formula,
obtaining a normalized matrix
Z＝(zij)n*p
Step 3.3, the normalized matrix Z is subjected to correlation matrix R ═ R (R)ij)p*pOf the formula
Step 3.4, solving four eigenvalues of the correlation matrix R, obtaining the number m of the principal components according to the following formula,
at the moment, the information utilization rate is more than 85%, and unit eigenvectors corresponding to the previous m eigenvalues are solved
Step 3.5, calculate the principal Components as follows
Step 3.6, summing the principal components according to weight, as shown in the following formula
For risk classification threshold determination, the evaluation value average is used as a reference decision criterion, as follows
Wherein F is the evaluation value of the node k;
for the average evaluation value of all nodes, a node risk classification evaluation criterion was constructed with the evaluation value as a reference, as shown in the following table.
And 4, outputting the qualitative risk evaluation result of each node.
With the increasing complexity of power grids, the existing power grid risk assessment and early warning method modeling method is gradually difficult to deal with different power grid conditions, and the fine modeling has high requirements on data precision and computing resources and does not conform to the actual operation situation of the power grid. The method starts from the network structure of the power grid, analyzes through a complex network theory, has lower data quality requirement and less occupation of computing resources, and realizes the risk assessment and early warning of the power grid network.
Drawings
FIG. 1 is a system wiring diagram of a new England 10 machine 39 node system of an embodiment of the present invention;
fig. 2 is a diagram showing a complex network modeling of a new england 10 machine 39 node system according to an embodiment of the present invention.
Detailed Description
In order to better understand the technical solution of the present invention, the following detailed description is made by specific examples:
the invention discloses a power grid risk assessment and early warning method based on a complex network theory.
G＝(V,E) (1)
Wherein G is a complex network abstract diagram, and V and E are respectively a set of nodes and edges. When the complex network theory is applied to modeling the power system, the buses, the generators and the loads in the power grid are simplified into nodes in the network, and the connecting lines and the transformers between the buses are simplified into edges. On the basis, the situation of an actual power grid is considered, and the following modeling is supplemented:
considering the power flow reversal caused by the power grid network frame reconstruction and the operation state change, the power lines are all bidirectional lines, as shown in formula (2); and self-loop does not exist in the modeling of the patent, as shown in a formula (3).
flij＝flji＝1，i,j∈V，ij,ji∈E (2)
In the formula, V is a set of nodes, and E is a set of edges;
i. j is an element in the node set, namely a node contained in the original power network;
ij. ji is respectively a forward and reverse connecting line between nodes i and j in the power network, and is an element in an edge set, namely the element exists in the original power network and the bidirectional direction is regarded as communication;
flij、fljiconfiguring a mark for the line ij and a mark for the line ji respectively, and not considering the difference between the attribute and the weight of the power line, wherein each element represents the configuration state of the line by a 0-1 parameter, and if the line is known to exist in the original network, the configuration is represented by a parameter 1;
ii is an edge from the node i to the node i, namely, a self-loop of the node i, and does not exist in the edge set, namely, the self-loop does not exist in the original power network and the modeling;
fliiand (3) configuring a mark for the self-loop line of the node i, wherein the configuration state of the line is represented by a parameter of 0-1, and if the line is known to be absent from the original network, the parameter of 0 represents that the line is not configured.
Based on the above assumptions, the power system is modeled as a weightless, bi-directional complex network model.
And 2, evaluating the risk nodes of the power grid and constructing indexes. The purpose of risk assessment of the power system is to assess the degree of potential impact of a disturbance event on the system, and the failure of a node that normally undertakes more power flow delivery will have a greater impact on the system, so the problem is similar to identifying a critical node of the grid. The method identifies the key information nodes of the power grid through the weighting of the complex network indexes.
Index one: degree of node
According to complex network theory, the importance of a node can be quantified by the number of edges associated with the node, i.e., the degree of the node, also referred to as the degree of association.
Index two: center of betweenness
The betweenness centrality is widely applied to complex network analysis. The betweenness centrality of a node is defined as the sum of the number of shortest paths through the node and the total number of shortest paths for all node pairs.
The definition formula is shown as formula (4).
Wherein C (x) is the betweenness of node x; v is a node set, and h and j are two different nodes; sigmahjIs the shortest path number, σ, between nodes h and jhj(x) The shortest path number between nodes h and j through node x.
Index three: coefficient of efficiency loss
To define the efficiency loss factor for a node, we first need to define the efficiency of the network. Network efficiency is an index that quantifies the efficiency of information exchange between network nodes. And calculating the shortest path between all the node pairs, wherein the definition formula is shown as the formula (5).
Where e is network efficiency, dhjIs the shortest path length between nodes h and j, and m is the total number of nodes. The efficiency can effectively measure the length of the whole shortest path of the network, and meanwhile, for the node pairs which are not communicated with each other, the length of the shortest path can be considered as infinity, and index calculation cannot be influenced. In this study, the efficiency loss coefficient is used as a node evaluation index, that is, the percentage of network efficiency loss after a certain node is removed, and the definition formula is shown as formula (6).
Where E (x) is the efficiency loss coefficient for node x, e0For initial network efficiency, e is the network efficiency obtained after node x is removed.
The index is four: aggregate lift coefficient
The smaller the number of nodes in the network, the shorter the shortest path length, and the higher the network aggregation degree. Thus, network aggregation is defined as the inverse of the product of the number of nodes and the average path length. The definition formula is shown as a formula (7).
Wherein n is the degree of aggregation of the network. In the research, a node contraction method is adopted, the nodes are merged with the adjacent nodes, the importance degree of the nodes is quantified and measured according to the network cohesion degree improved by the operation, and the definition formula is shown as a formula (8).
Wherein N (x) is the network cohesion degree change rate of the node x, n0And n is the network cohesion degree obtained after the node x is removed.
And 3, compounding all indexes into a power grid risk index. Based on the above analysis, an index weight determination method and a risk classification threshold determination method are respectively given. For index weight, in order to avoid the influence of subjective factors on weight distribution, the invention adopts a principal component analysis method and determines reasonable weight through statistical analysis of each index. The principal component analysis method steps are as follows:
step 3.1: constructing a network node evaluation matrix X ═ (X)ij)n*pWhere n is the number of nodes, p is the number of single indices, xijThe j-th evaluation index of the ith node.
Step 3.2: the node evaluation matrix is normalized, as shown in formula (9), to obtain a normalized matrix Z ═ Z (Z)ij)n*p。
Step 3.3: obtaining a correlation matrix R (R) for the normalized matrix Zij)p*pAs shown in formula (10).
Step 3.4: and solving four eigenvalues of the correlation matrix R. The number m of principal components is obtained by the following equation (11).
At the moment, the information utilization rate is more than 85%, and unit eigenvectors corresponding to the previous m eigenvalues are solved
Step 3.5: the principal component is calculated as shown in equation (12).
Step 3.6: the principal components are summed by weight as shown in equation (13).
For risk classification threshold determination, the patent uses the evaluation value average as a reference decision criterion, as shown in equation (14).
Wherein F is the evaluation value of the node k;
is the average evaluation value of all nodes. Based on the evaluation value, a node risk classification evaluation criterion is constructed as shown in the following table.
And 4, outputting the qualitative risk evaluation result of each node.
To sum up, the power grid risk assessment and early warning method provided by the patent comprises the following modules: the device comprises an input module, a topology extraction module, a calculation module and an output module. The functions, inputs and outputs of the modules are as follows:
an input module: and realizing the conversion of the input data format. The input is unformatted data and the output is formatted data acceptable to the program.
A topology extraction module: and modeling is realized according to the power grid topology data. The input is formatted power grid topology data, and the output is a complete power grid topology complex network model.
A calculation module: and based on a power grid topological complex network model, performing single index evaluation on the risk of each node, performing weight summation according to a principal component analysis method, and finally giving qualitative evaluation based on a node risk grading evaluation standard. The input is a power grid topological complex network model, and the output is a quantitative and qualitative evaluation result of the risk of each node of the power grid.
An output module: and outputting and visually displaying the node risk assessment result. The input is the quantitative and qualitative assessment result of the risk of each node of the power grid, and the output is the visualized risk assessment result.
Example (b):
the effectiveness of the method provided by the patent is verified by a 39-node power system of a new england 10 machine. The wiring diagram of the power system is shown in fig. 1. Complex network modeling is carried out on the system, buses are equivalent to nodes, transmission lines among the buses are equivalent to edges, and the obtained model is shown in figure 2
The key of the node is evaluated by 4 indexes of node degree, betweenness centrality, efficiency loss coefficient and agglomeration degree change rate respectively, the weight of each single index in the comprehensive index is determined by adopting a principal component analysis method, the average value of importance evaluation is selected as a threshold, and the threshold is used as
69.81, the results are shown in the following table.
According to the evaluation result, the risk nodes are the nodes 16, 14, 4, 17, 3, 2, 15, 5, 26, 19, 25, 13, 27, 6 and 18, and the risk degrees are sequentially decreased. The key nodes have relatively higher risk degree in power grid risk assessment, need to pay attention to the key nodes, and give corresponding risk early warning according to the operation conditions of the nodes.
It should be understood by those skilled in the art that the above embodiments are only for illustrating the present invention and are not to be used as a limitation of the present invention, and that changes and modifications to the above described embodiments are within the scope of the claims of the present invention as long as they are within the spirit and scope of the present invention.
Claims (1)
1. A power grid risk assessment and early warning method based on a complex network theory is characterized by comprising the following steps:
step 1, establishing an abstract complex network G (V, E) taking a power grid as an object,
in the power grid object, buses, generators and loads in a power grid are nodes, and connecting lines and transformers between the buses are edges;
step 2, for any node, the following indexes are obtained,
index one, node degree, is the number of edges associated with the node;
the index two, the betweenness,
wherein C (x) is the betweenness of node x; v is a node set, and h and j are two different nodes; sigmahjIs the shortest path number, σ, between nodes h and jhj(x) The number of the shortest paths between the nodes h and j passing through the node x;
index three, the efficiency loss coefficient, network efficiency e, which is an index quantifying the efficiency of information exchange between network nodes, is obtained by the following formula,
wherein d ishjThe length of the shortest path between the nodes h and j is shown, and m is the total number of the nodes; the efficiency loss coefficient is used as a node evaluation index, and is the percentage of network efficiency loss after a certain node is removed, which is calculated by the following formula,
where E (x) is the efficiency loss coefficient for node x, e0E is the network efficiency obtained after the node x is removed;
index four, the network aggregation change rate, the network aggregation is defined as the reciprocal of the product of the number of nodes and the average path length, which is defined by the following formula,
wherein n is the degree of aggregation of the network and l is the average path length of the edge;
the rate of change of the degree of network cohesion is defined by the following formula,
wherein N (x) is the network cohesion degree change rate of the node x, n0Is the initial network cohesion degree, and n is the network cohesion degree obtained after the node x is removed;
step 3, determining the weight of each index by adopting a principal component analysis method, wherein the method comprises the following steps:
step 3.1, constructing a network node evaluation matrix
X＝(xij)n*p
Where n is the number of nodes, p is the number of single indices, xijThe j evaluation index of the ith node;
step 3.2, the node evaluation matrix is normalized by the following formula,
obtaining a normalized matrix
Z＝(zij)n*p
Step 3.3, the normalized matrix Z is subjected to correlation matrix R ═ R (R)ij)p*pOf the formula
Step 3.4, solving four eigenvalues of the correlation matrix R, obtaining the number m of the principal components according to the following formula,
at the moment, the information utilization rate is more than 85%, and unit eigenvectors corresponding to the previous m eigenvalues are solved
Step 3.5, calculate the principal Components as follows
Step 3.6, summing the principal components according to weight, as shown in the following formula
For risk classification threshold determination, the evaluation value average is used as a reference decision criterion, as follows
Wherein F is the evaluation value of the node k; f is the average evaluation value of all nodes, and a node risk classification evaluation criterion is constructed with the evaluation value as a reference, as shown in the following table.
And 4, outputting the qualitative risk evaluation result of each node.
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