CN106208048A - A kind of congestion management method based on graph theory form - Google Patents

Abstract

The purpose of the invention is to ensure the reliability of power transmission while ensuring economical operation, so that the power grid can achieve optimal operation as much as possible. In order to achieve the above object, the technical solution of the present invention is to provide a congestion management method based on graph theory. The invention transforms the topology of the grid structure into a graph, maps the electrical quantity to the graph and turns it into a weight, and uses the method of graph theory to find a path with the smallest cost and the largest flow for reference by the dispatching department to avoid power flow blockage.

Description

A Congestion Management Method Based on Graph Theory

technical field

The invention relates to a calculation method of an optimal power flow, which seeks an optimal path in the form of graph theory to avoid power flow blocking.

Background technique

With the further deepening and development of my country's power industry system reform and the concept of active distribution network, the gradual marketization of the power industry has become an irreversible trend. The opening of the transmission system is proposed to provide a standardized and fair competition environment for the power generation market. (Power supply bureaus, etc.) use their transmission capacity to transmit power to each other, and must achieve fair distribution and management of transmission capacity, and at the same time ensure the balance of supply and demand and safety and reliability of the system through the transaction and scheduling of various auxiliary services. The opening of the transmission grid has a great impact on the structure, operation, and planning of the power system. There are three issues to be addressed in an open transmission system: transmission losses, transmission pricing, and transmission congestion management. Among them, transmission congestion management is a key issue in the operation of open transmission systems. It is related to the operational efficiency and healthy development of the power market, and has an important impact on the planning and development of power generation and transmission.

Today, as the penetration rate of new energy is getting higher and the power market is gradually opening up, individual operators are more and more involved, and power exchanges are also increasing. The blockage of power transmission lines has gradually become the competition and resource optimization of the entire power market. the bottleneck. Transmission congestion will cause overloading of lines in some areas, resulting in paralysis of power supply and unnecessary losses. The traditional method of using administrative orders to dispatch power generation to eliminate congestion is no longer feasible, and the pressure on dispatching departments is also increasing. A new method must be adopted to ensure the reliability of power transmission while ensuring economic operation, so that the power grid can achieve optimal operation as much as possible, and feedback information to the power grid in real time.

Contents of the invention

The purpose of the invention is to ensure the reliability of power transmission while ensuring economical operation, so that the power grid can achieve optimal operation as much as possible.

In order to achieve the above object, the technical solution of the present invention is to provide a blocking management method based on graph theory, which is characterized in that it includes the following steps:

Step 1. Initialize the transmission capacity of each line in the smart grid structure, and use the Lagrange multiplier method to calculate the bidding price of each node in the smart grid structure;

Step 2. Abstract the smart grid structure into a directed topological network G(V, E), V={v ₁ ,...,v _n } is a vertex sequence, and each vertex in the vertex sequence corresponds to each of the smart grid structure Node, E={e _ij |i=1,...,n, j=1,...,n}, e _ij is a directed topological network G(V, E) connecting vertex v _i and vertex v _j The edge corresponds to the line between the corresponding nodes in the smart grid structure, and acts as a virtual source s and a virtual sink t. In the directed topological network G(V, E), the corresponding All vertices are connected to the virtual source point s, and all vertices corresponding to nodes with load units in the directed topological network G(V, E) are connected to the virtual sink point t;

Step 3. The remaining flow weight of each edge in the directed topological network G(V, E) is the transmission capacity of each line in the smart grid structure, where the edge connecting vertex v _x and vertex v _y is e _xy , Its residual flow weight is c(x, y), and the edge length weight of each edge in the directed topological network G(V, E) is the bidding price of the head-end node of each line in the smart grid structure, where, The edge length weight of the edge e _xy is w(x, y), which is the bidding price of the node corresponding to the vertex v _x ;

Step 4. In the directed topological network G(V, E), take the initial feasible power flow sequence f={f _xy |e _xy ∈ E}, f _xy is the power flow of edge e _xy , where f _sy =c(s , y), and e _sy is the edge connecting the virtual source point s and the vertex v _y , let the rest f _xy =0;

Step 5. Find the minimum path P(s, t) from the virtual source point s to the virtual sink point t on the directed topological network G(V, E), and record the set of all edges forming the minimum path as E(P) ;

Step 6. Assign the maximum possible flow to the minimum path P(s, t):

Update the remaining flow weights of all edges in the set E(P), where the remaining flow weight c(x, y) of the edge connecting the vertex v _x and the vertex v _y in the set E(P) is updated to c(x , y)-f ₀ , where f ₀ =Min{c(x, y)| _exy ∈ E(p)}, for the saturated edge in the minimum path P(s, t), its edge length weight Correspondingly becomes ∞, and for the saturated edge e _xy , when x or y is not equal to s or t, the saturated edge e _xy becomes the reverse edge e _yx , and the residual flow weight of the reverse edge e _yx c(y,x)=f ₀ , let the side length weight w(y,x)=-w(x,y) of the reverse side e _yx form a new directed topological network G′;

Step 7, return to step 6 to recalculate the new directed topological network G′, until the total flow from the virtual source point s to the virtual sink point t is equal to the preset threshold λ or until no more traffic from the virtual source point s can be found The minimum cost path to the virtual sink t, the path at this time is the minimum cost maximum flow.

Preferably, the construction steps of the directed topological network in said step 2 are:

Firstly, the smart grid structure is abstracted into a topological network, which includes directed and undirected edges, and the power flow on the _undirected edge is decomposed into two directed edges. The power flow on the undirected edge e _ij of _j is decomposed into the power flow on the edge e _ij and the power flow on the edge e _ji , making the topological network a directed topological network.

The invention transforms the topology of the grid structure into a graph, maps the electrical quantity to the graph and turns it into a weight, and uses the method of graph theory to find a path with the smallest cost and the largest flow for reference by the dispatching department to avoid power flow blockage.

detailed description

Below in conjunction with specific embodiment, further illustrate the present invention. It should be understood that these examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the teachings of the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of the present application.

A kind of blocking management method based on graph theory form provided by the present invention is based on the following theory:

The smart grid structure is abstracted as a directed topological network G(V, E), where V={v ₁ ,...,v _n } represents a series of vertices (busbars in the power system), E={e _ij |i =1,...,n, j=1,...,n} represents the side (connection line between the busbars in the power system). Transmission costs can be defined in terms of edge lengths. The transmission capacity can be defined in terms of remaining (allowable) flows r _ij . The maximum transmission flow u _ij of each edge in the directed topological network G(V, E), that is, the maximum transmission capacity of each line in the smart grid structure. Therefore, the problem of solving the transmission path with the minimum cost and the maximum transmission capacity in the smart grid structure is transformed into the problem of solving a path with the shortest length and the largest flow in the directed topological network G(V, E), which can be described as: the flow is at the edge e _ij transmission, where the side length is (that is, the cost) c _ij , and there is remaining flow r _ij , the maximum transmission capacity of the line is u _ij . In the abstract graph, two new vertices are added: a virtual source s and a virtual sink t. Among them, the busbar with power generation unit is connected with the virtual source point s in the topology structure as the source point of the flow; the busbar with load unit is connected with the virtual sink point t in the topology structure as the convergence point of the flow.

At the initial moment, the direction of each edge e _ij in G(V, E) is defined by the system by the direction of the current power flow and is constant. But in general, the power flow will change with the power injected into the system, and at this time, the direction of some edges e _ij will change, that is, the so-called undirected edges e _ij ′. During network transformation, these undirected edges e _ij ′ can be converted into directed edges. Each undirected edge e _ij ′ is firstly replaced by two edges e _ij and e _ji , the transmission cost is c _ij , and the remaining capacity is r _ij . In this way, the flow of undirected edge can be decomposed into the flow of edge e _ij and edge e _ji , that is, f _ij and f _ji . When the flow flows from v _i to v _j , the former is valid, and vice versa.

In the abstracted topology graph, find an optimal path that satisfies the two conditions of maximum transmission capacity and minimum transmission cost at the same time. The mathematical model can be described as:

$\mathrm{<span\; class="notranslate">\; min</span>}\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}$

$\begin{array}{cc}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>& \underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}& \mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}\\ <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}& \mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right.\end{array}$

0≤r _ij ≤u _ij , (i, j)∈G

In the formula, f _max is the maximum traffic transmitted by the network.

Concrete steps of the present invention based on above-mentioned principle are:

Step 1. Initialize the transmission capacity of each line in the smart grid structure, and use the Lagrange multiplier method to calculate the bidding price of each node in the smart grid structure;

Step 2. Abstract the smart grid structure into a directed topological network G(V, E), V={v ₁ ,...,v _n } is a vertex sequence, and each vertex in the vertex sequence corresponds to each of the smart grid structure Node, E={e _ij |i=1,...,n, j=1,...,n}, e _ij is a directed topological network G(V, E) connecting vertex v _i and vertex v _j The edge corresponds to the line between the corresponding nodes in the smart grid structure, and acts as a virtual source s and a virtual sink t. In the directed topological network G(V, E), the corresponding All vertices are connected to the virtual source point s, and all vertices corresponding to nodes with load units in the directed topological network G(V, E) are connected to the virtual sink point t;

Step 3. The remaining flow weight of each edge in the directed topological network G(V, E) is the transmission capacity of each line in the smart grid structure, where the edge connecting vertex v _x and vertex v _y is e _xy , Its residual flow weight is c(x, less), and the weight of each edge length in the directed topological network G(V, E) is the bidding price of the head-end node of each line in the smart grid structure, where, The edge length weight of the edge e _xy is w(x, less), which is the bidding price of the node corresponding to the vertex v _x ;

Step 4. In the directed topological network G(V, E), take the initial feasible power flow sequence f={f _xy |e _xy ∈ E}, f _xy is the power flow of edge e _xy , where f _sy =c(s , y), and e _sy is the edge connecting the virtual source point s and the vertex v _y , let the rest f _xy =0;

Step 5. Find the minimum path P(s, t) from the virtual source point s to the virtual sink point t on the directed topological network G(V, E), and record the set of all edges forming the minimum path as E(P) ;

Step 6. Assign the maximum possible flow to the minimum path P(s, t):

Update the remaining flow weights of all edges in the set E(P), where the remaining flow weight c(x, y) of the edge connecting the vertex v _x and the vertex v _y in the set E(P) is updated to c(x , y)-f ₀ , where f ₀ =Min{c(x, y)| _exy ∈ E(p)}, for the saturated edge in the minimum path P(s, t), its edge length weight Correspondingly becomes ∞, and for the saturated edge e _xy , when x or y is not equal to s or t, the saturated edge e _xy becomes the reverse edge e _yx , and the residual flow weight of the reverse edge e _yx c(y, x)=f ₀ , let the side length weight w(y, x)=-w(x, y) of the opposite side e _yx form a new directed topological network G';

Step 7, return to step 6 to recalculate the new directed topological network G', until the total flow from the virtual source point s to the virtual sink point t is equal to the preset threshold λ=f _max or until no more traffic from the virtual The minimum cost path from the source point s to the virtual sink point t, the path at this time is the minimum cost maximum flow.

Claims (2)

1. a blocking management method based on graph theory form, is characterized in that, comprises the following steps: Step 1. Initialize the transmission capacity of each line in the smart grid structure, and use the Lagrange multiplier method to calculate the bidding price of each node in the smart grid structure; Step 2. Abstract the smart grid structure into a directed topological network G(V, E), V={v ₁ ,...,v _n } is a vertex sequence, and each vertex in the vertex sequence corresponds to each of the smart grid structure Node, E={e _ij |i=1,...,n, j=1,...,n}, e _ij is a directed topological network G(V, E) connecting vertex v _i and vertex v _j The edge corresponds to the line between the corresponding nodes in the smart grid structure, and acts as a virtual source s and a virtual sink t. In the directed topological network G(V, E), the corresponding All vertices are connected to the virtual source point s, and all vertices corresponding to nodes with load units in the directed topological network G(V, E) are connected to the virtual sink point t; Step 3. The remaining flow weight of each edge in the directed topological network G(V, E) is the transmission capacity of each line in the smart grid structure, where the edge connecting vertex v _x and vertex v _y is e _xy , Its residual flow weight is c(x, y), and the edge length weight of each edge in the directed topological network G(V, E) is the bidding price of the head-end node of each line in the smart grid structure, where, The edge length weight of the edge e _xy is w(x, y), which is the bidding price of the node corresponding to the vertex v _x ; Step 4. In the directed topological network G(V, E), take the initial feasible power flow sequence f={f _xy |e _xy ∈ E}, f _xy is the power flow of edge e _xy , where f _sy =c(s , y), and e _sy is the edge connecting the virtual source point s and the vertex v _y , let the rest f _xy =0; Step 5. Find the minimum path P(s, t) from the virtual source point s to the virtual sink point t on the directed topological network G(V, E), and record the set of all edges forming the minimum path as E(P) ; Step 6. Assign the maximum possible flow to the minimum path P(s, t): Update the remaining flow weights of all edges in the set E(P), where the remaining flow weight c(x, y) of the edge connecting the vertex v _x and the vertex v _y in the set E(P) is updated to c(x , y)-f ₀ , where f ₀ =Min{c(x, y)| _exy ∈ E(p)}, for the saturated edge in the minimum path P(s, t), its edge length weight Correspondingly becomes ∞, and for the saturated edge e _xy , when x or y is not equal to s or t, the saturated edge e _xy becomes the reverse edge e _yx , and the residual flow weight of the reverse edge e _yx c(y, x)=f ₀ , let the side length weight w(y, x)=-w(x, y) of the opposite side e _yx form a new directed topological network G'; Step 7, return to step 6 to recalculate the new directed topological network G′, until the total flow from the virtual source point s to the virtual sink point t is equal to the preset threshold λ or until no more traffic from the virtual source point s can be found The minimum cost path to the virtual sink t, the path at this time is the minimum cost maximum flow. 2. a kind of blocking management method based on graph theory form as claimed in claim 1, is characterized in that, the construction step of the directed topological network in the described step 2 is: Firstly, the smart grid structure is abstracted into a topological network, which includes directed and undirected edges, and the power flow on the _undirected edge is decomposed into two directed edges. The power flow on the undirected edge e _ij of _j is decomposed into the power flow on the edge e _ij and the power flow on the edge e _ji , making the topological network a directed topological network.