Method for quickly recovering power supply of large-scale power distribution network based on cluster simplified modeling

Abstract

The invention belongs to the technical field of power supply recovery of a power distribution network, and particularly relates to a rapid power supply recovery method for a large-scale power distribution network based on cluster simplified modeling. Firstly, all cluster simplified models are established in a distributed mode; the simplified modeling thought of the cluster only containing two boundary nodes is that a cluster internal network is equivalent to a virtual load node; the simplified cluster modeling thought that the three boundary nodes are located on the same power supply path is that a cluster internal network between the boundary nodes at the two ends is equivalent to a virtual load node, the virtual load node is used for replacing a middle boundary node, and then the virtual load node and the boundary nodes at the two ends are subjected to simplified cluster modeling; according to the simplified modeling thought of the cluster with the multiple boundary nodes located in the different power supply paths, a cluster internal network can be equivalent to a virtual load node and incremental load power attached to the boundary node at the tail end of the main power supply path and the boundary nodes located outside the main power supply path; then, obtaining a simplified network of the power distribution network according to each cluster simplified model; establishing a simplified network power supply recovery model and solving; and finally, constructing a fine power supply recovery model of each cluster and carrying out parallel solving. According to the method, the model dimension and the calculation complexity are remarkably reduced, the power supply recovery efficiency is improved, and meanwhile, the privacy of load users in the cluster is prevented from being leaked.

Description

Technical Field

[0001] The present invention belongs to the technical field of power supply restoration of distribution networks after faults, and in particular relates to a method for quickly restoring power supply of large-scale distribution networks based on cluster simplified modeling. Background Art

[0002] Power supply restoration of distribution network refers to the rapid restoration of power supply to non-faulty areas in the distribution network after a fault occurs. It plays a significant role in improving the reliability of power supply of distribution network, and also helps to improve the system resilience of distribution network and strengthen the emergency response capability of distribution network in the event of faults and disasters. With the large-scale decentralized access of distributed generation (DGs) to distribution network, the structure of distribution network is becoming increasingly complex, and the scale of controllable equipment is becoming increasingly large, which places higher requirements on power supply restoration of distribution network.

[0003] At present, the mainstream distribution network power supply restoration methods mainly use mathematical optimization algorithms, heuristic algorithms, artificial intelligence algorithms and hybrid algorithms, etc., and adopt centralized optimization methods to solve the distribution network power supply restoration problem. For distribution network power supply restoration models with lower complexity and lower dimensions, these mainstream methods can quickly and accurately obtain the global optimal solution. However, when faced with complex distribution network power supply restoration problems with a large scale of DGs, mainstream power supply restoration methods are difficult to efficiently solve high-dimensional power supply restoration models. In addition, the centralized power supply restoration optimization method also has the problem of infringing user privacy. In this context, the present invention proposes a large-scale distribution network rapid power supply restoration method based on cluster simplified modeling, and uses the measurement data of cluster boundary nodes to establish a cluster simplified model, thereby avoiding the problem of infringing user privacy and solving high-dimensional models, improving the flexibility and robustness of distribution network power supply restoration, and at the same time improving the solution rate. Summary of the invention

[0004] In view of the deficiencies in the prior art, the technical problem to be solved by the present invention is to propose a method for quickly restoring power supply in a large-scale distribution network based on cluster simplified modeling.

[0005] The present invention solves the technical problem by adopting the following technical solution:

[0006] A method for rapidly restoring power supply in a large-scale distribution network based on cluster simplified modeling, characterized in that it comprises the following steps:

[0007] Step S1: Distributed establishment of simplified models of each cluster;

[0008] Case 1: Simplified model of a cluster with only two boundary nodes; For a cluster with only two boundary nodes i and j, the simplified modeling idea is to equate the internal network of the cluster to a virtual load node m′, then:

[0009]

[0010] Where: U i and U j denote the voltages at boundary nodes i and j, respectively, and R ij1 and X ij1 They represent the total resistance and total reactance of the branch from the virtual load node m′ to the boundary node i, R ij2 and X ij2 They represent the total resistance and total reactance of the branch from the virtual load node m′ to the boundary node j, respectively. ij,out , P ij,out and Q ij,out They represent the transmission current, active power and reactive power flowing from the boundary node i on the power supply path ij, respectively. ij,in , P ij,in and Q ij,in They represent the transmission current, active power and reactive power flowing from the power supply path ij into the boundary node j, R ij and X ij denote the total resistance and reactance of the branch between boundary nodes i and j, respectively, P m′,load and Q m′,load denote the active and reactive net powers of the virtual load node m′ respectively;

[0011] If there is no feeder switch inside the cluster, the power flow equation of branch im′ is as shown in equation (7). Similarly, the power flow equation of branch m′j can be obtained;

[0012]

[0013] Where: I im′,out , P im′,out , Q im′,out They represent the transmission current, active power and reactive power flowing out of branch im′ from boundary node i, respectively. m′j,out , Q m′j,out They represent the active and reactive power flowing out of the virtual load node m′j, U m' represents the voltage of virtual load node m′;

[0014] If there is a feeder switch S inside the cluster ij , then the virtual load node m′ is split into m1′ and m2′, the branch impedance between the two virtual load nodes m1′ and m2′ is 0, and the active and reactive net powers satisfy equation (8);

[0015]

[0016] Where: and They represent the active and reactive net power of the virtual load node m1′, and They represent the active and reactive net powers of the virtual load node m2′ respectively;

[0017] The power flow equation of branch im1′ is as shown in equation (9). Similarly, the power flow equation of branch m2′j can be obtained;

[0018]

[0019] Where: α ij Indicates feeder switch S ij Status, U m1′ represents the voltage of virtual load node m1′;

[0020] The voltages of virtual load nodes m1′ and m2′ satisfy the following constraints:

[0021]

[0022] In the formula, represents the voltage of virtual load node m2′, M is a constant;

[0023] Case 2: Simplified model of a cluster with three boundary nodes located on the same power supply path; For a cluster with three boundary nodes located on the same power supply path, assuming that boundary node m is located on the power supply path of boundary nodes i and j, the simplified modeling idea is to equate the internal network of the cluster between boundary nodes i and j to a virtual load node m′, and use the virtual load node m′ to replace boundary node m and then perform simplified modeling with boundary nodes i and j. The modeling process is the same as that of case 1.

[0024] If there is a feeder switch inside the cluster, the virtual load node m′ is split into m1′, m2′ and m3′ according to the number of inter-cluster branches, and the branch impedances of the three virtual load nodes are all 0; assuming that the virtual load nodes m1′ and m2′ are connected by feeder switches S ij1 Connection, m2′ and m3′ are connected by feeder switch S ij2 There is an inter-cluster feeder switch S between the virtual load node m2′ and the adjacent cluster. lm , then the active and reactive net powers of virtual load nodes m1′, m2′ and m3′ satisfy equation (13);

[0025]

[0026] In the formula, are the active and reactive net powers of the virtual load node m3′ respectively;

[0027] The power flow equations of branch im1′ and branch m3′j are similar to those of branch im1′ and branch m2′j in case 1. The power flow equation of branch m1′m2′ is shown in equation (14). Similarly, the power flow equation of branch m2′m3′ is obtained.

[0028]

[0029] Where: They represent the active and reactive power flowing out of the virtual load node m1′ and m2′, respectively. are the active and reactive powers flowing out of the virtual load node m2′ and m3′, respectively. lm,out , P lm,out and Q lm,out represents the transmission current, active power and reactive power flowing out of the inter-cluster branch lm from the adjacent cluster boundary node l, R lm and X lm represents the resistance and reactance of the inter-group branch lm;

[0030] The transmission current I of the inter-group branch lm lm,out , Active power P lm,out and reactive power Q lm,out The constraint condition satisfies equation (15), and the voltage equation of the two-end nodes satisfies equation (16);

[0031]

[0032] In the formula, α lm Indicates feeder switch S lm status, and They represent the upper limits of inter-group branch transmission current, active power and reactive power, respectively. l represents the voltage of the adjacent cluster boundary node l;

[0033] Scenario 3: A simplified cluster model with multiple boundary nodes located on different power supply paths;

[0034] Assuming that the boundary nodes e and f are not in the main power supply path ij formed by the boundary nodes i and j, the simplified modeling idea is to equate the internal network of the cluster between the boundary nodes i and j to the virtual load node m′ and the incremental load power attached to the boundary nodes e, f and j;

[0035] 1) Select the bifurcation node m between the main power supply path ij and the remaining paths as the virtual load node m′, calculate the branch impedance from the virtual load node m′ to each boundary node, and the impedance of the branch im′ and the branch m′e is obtained by formula (17). Similarly, the impedance of other branches can be obtained;

[0036]

[0037] In the formula, R im′ , X im′ are the resistance and reactance of branch im′, R im , Xim are the resistance and reactance of branch im, R m′e , X m′e are the resistance and reactance of branch m′e, R ie , X ie are the resistance and reactance of branch ie respectively;

[0038] 2) Voltage U at virtual load node m′ m′ And the active power P flowing from branch im′ into virtual load node m′ im′,in and reactive power Q im′,in Calculated by the following formula:

[0039]

[0040] 3) According to the voltage U of the virtual load node m′ m′ and the measurement data of the downstream boundary nodes, calculate the transmission current, active power and reactive power flowing from the virtual load node m′ to each downstream branch; among which, the transmission current I flowing from the virtual load node m′ to the branch m′e m′e,out , Active power P m′e,out and reactive power Q m′e,out The calculation formula is as follows:

[0041]

[0042] Where U e is the voltage at the boundary node e, R m′e , X m′e are the resistance and reactance of branch m′e, P ie,in , Q ie,in are the active power P flowing from branch ie into boundary node e ie,in and reactive power Q ie,in ;

[0043] 4) Solve the active and reactive net power of the virtual load node m' according to the following formula:

[0044]

[0045] Where P m′f,out , Q m′f,out are the active and reactive power flowing out of the branch m′f from the virtual load node m′, P m′j,out , Q m′j,out are the active and reactive powers flowing out of branch m′j from virtual load node m′, respectively;

[0046] 5) According to the power data of the first and last boundary nodes of the downstream branch of the virtual load node m′, the incremental load active and reactive power of the boundary nodes e, j and f in the cluster simplified network is calculated; where the incremental load active power P of the boundary node e is e,iL and reactive power Q e,iL It is obtained by the following formula:

[0047]

[0048] Step S2: obtaining a simplified network of the entire distribution network according to the simplified models of each cluster, establishing and solving a simplified network power supply restoration model according to the simplified network, and obtaining the inter-cluster feeder switch state;

[0049] The objective function of the simplified network power restoration model is:

[0050]

[0051] Where: N S represents the set of all nodes in the entire simplified network; x m′,L represents the power supply recovery status of the virtual load node m′; P m′,L represents the active power of virtual load node m′; Δt represents the time step of the optimization model; L S Represents the set of all branches in the entire simplified network; N S,PV represents the set of all photovoltaic grid-connected nodes in the entire simplified network; P m′,dec represents the photovoltaic active power reduction of the virtual load node m′; α im′ represents the feeder switch state of branch im′, α im′,0 is the initial value of the switch state of the branch im′ feeder; C P , C PV and C S They represent the user electricity price, photovoltaic active power reduction cost coefficient and switch action cost coefficient respectively;

[0052] Step S3: According to the inter-cluster feeder switch status, a fine power supply restoration model for each cluster is constructed and solved in parallel to determine the intra-cluster feeder switch status and the photovoltaic active power reduction amount;

[0053] The objective function of the fine power restoration model of cluster a is as follows:

[0054]

[0055] Where: represents the set of all nodes in cluster a, x s,L Indicates the power recovery status of any node s in the cluster except the source node, P s,L represents the active power of node s, P ks,out , Qks,out are the active and reactive power flowing out of branch ks from any node k including the source node, R ks is the resistance of branch ks, V N Represents the square of the system rated voltage, P s,dec is the photovoltaic active power reduction amount of node s, represents the set of all photovoltaic grid-connected nodes in cluster a, represents the set of all branches in cluster a, α ks is the feeder switch state of branch ks, α ks,0 It is the initial value of the switch state of the feeder line of branch ks.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. Aiming at the power supply restoration problem of large-scale distribution networks, the present invention is based on the idea of ​​cluster simplified modeling, uses network reconstruction technology, divides the distribution network into different types of clusters according to the network topology, and uses the measurement data of the boundary nodes to establish a cluster simplified model. At the same time, the situation of feeder switches in the network is considered in the simplified modeling process. The simplified modeling of each cluster is completed independently, and the fine power supply restoration model of each cluster can improve the efficiency of power supply restoration of the overall distribution network by parallel solution, while significantly reducing the dimension and computational complexity of the model, and can respond to internal faults of the distribution network cluster more quickly. At the same time, it solves the problems of dimensionality curse and high time and computational overhead costs faced by the mainstream method by centrally establishing and solving high-dimensional power supply restoration models.

[0058] 2. The mainstream power supply restoration optimization method needs to collect information such as active and reactive power consumed by each load user in the distribution network and upload it to the centralized processor of the entire distribution network. Not only is it difficult to collect information, but there is also a risk of privacy leakage for load users. However, the present invention only uses the measurement data of a limited number of cluster boundary nodes to establish a simplified cluster model, and establishes a fine power supply restoration model for each cluster. Each cluster independently makes power restoration decisions within the cluster based on its own cluster fine power supply restoration model. There is no need to upload information such as active and reactive power of load users within the cluster to the centralized processor of the distribution network, thereby ensuring the privacy of load users within the cluster. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a simplified diagram of a cluster containing only two border nodes;

[0060] Figure 2 A simplified schematic diagram of a cluster with three boundary nodes located on the same power supply path;

[0061] Figure 3 A simplified schematic diagram of a cluster with multiple edge nodes located on different power supply paths;

[0062] Figure 4 A distribution network topology diagram of an embodiment;

[0063] Figure 5 A simplified network topology for the entire distribution network;

[0064] Figure 6 To simplify the network power restoration topology;

[0065] Figure 7 Restore topology for power distribution network. DETAILED DESCRIPTION

[0066] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present application is not limited thereto.

[0067] The present invention provides a large-scale distribution network rapid power restoration method based on cluster simplified modeling (hereinafter referred to as method, see Figures 1 to 7 ), including the following steps:

[0068] Step S1: Determine the location where the fault occurs, and establish simplified models of each cluster in a distributed manner; the cluster can be divided into three situations: containing only two boundary nodes, three boundary nodes located in the same power supply path, and boundary nodes located in different power supply paths. Therefore, the simplified cluster model is divided into three types, namely, containing only two boundary nodes, three boundary nodes located in the same power supply path, and multiple boundary nodes located in different power supply paths.

[0069] Case 1: A simplified cluster model with only two boundary nodes;

[0070] like Figure 1 As shown in the figure, for a cluster with only two boundary nodes, the basic idea of ​​simplified modeling is to treat the internal network of the cluster as a virtual load node; measurement devices need to be deployed at boundary nodes i and j to measure the voltage of the boundary node, the transmission current flowing into and out of the branch, and the active and reactive power; the internal network of the cluster with two boundary nodes is equivalent to a virtual load node m'. In order to ensure the accuracy of the simplified network, the total impedance of the branch from the virtual load node m' to the two boundary nodes should be equal to the total impedance of the branch between the boundary nodes i and j. The specific simplified modeling process is as follows:

[0071] According to the branch power flow equation, the voltages at boundary nodes i and j satisfy the following equation:

[0072]

[0073] Where: U i and U j Represent the voltages of boundary nodes i and j respectively; L ij Represents the set of all branches on the power supply path ij; I kl,out, P kl,out and Q kl,out They represent the transmission current, active power and reactive power flowing out of branch kl from node k respectively; R kl and X kl They represent the resistance and reactance of branch kl respectively;

[0074] The transmission current, active power and reactive power flowing out of branch kl from node k satisfy the following equations:

[0075]

[0076] Where: I kl,in , P kl,in and Q kl,in They represent the transmission current, active power and reactive power flowing from branch kl into node l respectively;

[0077] The boundary node voltage balance equation is expressed as:

[0078]

[0079] From (1) and (3), the voltage between the virtual load node m′ and the boundary nodes i and j satisfies the following equation:

[0080]

[0081] Where: U m' represents the voltage of virtual load node m′; I ij,out , P ij,out and Q ij,out I represents the transmission current, active power and reactive power flowing from the boundary node i on the power supply path ij respectively; ij,in , P ij,in and Q ij,in They represent the transmission current, active power and reactive power flowing from the power supply path ij into the boundary node j respectively; R ij1 and X ij1 Respectively represent the total resistance and total reactance of the branch from the virtual load node m′ to the boundary node i; R ij2 and X ij2 They represent the total resistance and total reactance of the branch from the virtual load node m′ to the boundary node j respectively;

[0082] Therefore, the total resistance and reactance R of the branch from the virtual load node m′ to the boundary nodes i and j are ij1 , X ij1 and R ij2 , X ij2 The active and reactive net power P of the virtual load node m′ can be obtained by formula (5): m′,load and Q m′,load From formula (6), we can get:

[0083]

[0084] Where: R ij and X ij denote the total resistance and total reactance of the branch between boundary nodes i and j respectively;

[0085] like Figure 1 As shown in (b), if there is no feeder switch in the cluster, based on R ij1 and X ij1 Construct the power flow equation of branch im′, as shown in equation (7); similarly, based on R ij2 and X ij2 Construct the power flow equation of branch m′j;

[0086]

[0087] Where: I im′,out , P im′,out , Q im′,out They represent the transmission current, active power and reactive power flowing out of branch im′ from boundary node i, respectively. m′j,out , Q m′j,out They represent the active and reactive power flowing out of the virtual load node m′ and branch m′j respectively.

[0088] like Figure 1 As shown in (c), if there is a feeder switch S inside the cluster ij , then m′ can be split into two virtual load nodes m1′ and m2′, and the two virtual load nodes are connected by the feeder switch inside the cluster; the branch impedance between the two virtual load nodes m1′ and m2′ is 0, and the active and reactive net powers satisfy equation (8);

[0089]

[0090] Where: and They represent the active and reactive net power of the virtual load node m1′, and They represent the active and reactive net power of the virtual load node m2′ respectively.

[0091] Based on the feeder switch S ij The state of R ij1 and X ij1 The power flow equation of branch im1′ is constructed as shown in equation (9); similarly, the power flow equation of branch m2′j is constructed;

[0092]

[0093] Where: α ij Indicates feeder switch Sij The state of α ij =0 means disconnection, α ij =1 means closed; U m1′ represents the voltage of virtual load node m1′;

[0094] In order to eliminate the variable product term in equation (9), an auxiliary variable is introduced and Characterize α ij P m′j,out , and α ij Q m′j,load , the relationship between the auxiliary variables and the variable product terms is linearized using McCormick relaxation technique; For example, and The relationship between them is expressed as:

[0095]

[0096] Where: M is a large constant;

[0097] The power flow equation of branch im1′ after linear relaxation is:

[0098]

[0099] The voltages of the two virtual load nodes m1′ and m2′ are affected by the feeder switch state α ij Constraints:

[0100]

[0101] In the formula, represents the voltage of the virtual load node m2′; when the feeder switch S ij When closed, α ij =1,

[0102] Scenario 2: A simplified cluster model with three boundary nodes located on the same power supply path;

[0103] like Figure 2As shown in (a), for a cluster with three boundary nodes located on the same power supply path, boundary node m is located on the power supply path of boundary nodes i and j. The simplified modeling idea is: first, the internal network of the cluster between boundary nodes i and j is equivalent to a virtual load node m′, and the position and net power of the virtual load node m′ are determined according to the measurement data of boundary nodes i and j according to the simplified cluster modeling method containing only two boundary nodes; then the virtual load node m′ replaces the boundary node m, and the cluster is simplified modeled with boundary nodes i and j. The modeling process is the same as that in case one; therefore, the cluster with three boundary nodes located on the same power supply path can also be equivalent to two boundary nodes and one virtual load node.

[0104] like Figure 2 As shown in (b), if there is a feeder switch inside the cluster, the virtual load node m′ is split into three virtual load nodes m1′, m2′ and m3′ according to the number of inter-cluster branches. The branch impedances of the three virtual load nodes are all 0; the virtual load nodes m1′ and m2′ are connected by the feeder switch S ij1 m′2 and m′3 are connected by feeder switch S ij2 There is an inter-cluster feeder switch S between the virtual load node m′2 and the adjacent cluster. lm , then the active and reactive net power of the three virtual load nodes m1′, m2′ and m3′ satisfy the following constraints:

[0105]

[0106] In the formula, are the active and reactive net powers of the virtual load node m3′ respectively;

[0107] The power flow equations of branch im1′ and branch m3′j are similar to those of branch im1′ and branch m2′j in case 1, and will not be described in detail. The power flow equation of branch m1′m2′ is shown in equation (14), and the power flow equation of branch m2′m3′ is the same.

[0108]

[0109] Where: They represent the active and reactive power flowing out of the virtual load node m1′ and m2′, respectively. are the active and reactive powers flowing out of the virtual load node m′2 and m′3 respectively; I lm,out , P lm,out and Q lm,out represents the transmission current, active power and reactive power of the inter-cluster branch lm flowing out of the adjacent cluster boundary node l; R lm and X lm represents the resistance and reactance of the inter-group branch lm;

[0110] The transmission current and power of the branch containing feeder switch are constrained by the switch status of the branch, such as branch m1′m2′ and Branch m2′m3′ and and I of branch lm lm,out , P lm,out and Q lm,out ; Taking the inter-group branch lm as an example, the transmission current, active and reactive power I lm,out , P lm,out and Q lm,out The constraints are as follows:

[0111]

[0112] Where: α lm Indicates feeder switch S lm status, and They represent the upper limits of branch lm transmission current, active power and reactive power respectively;

[0113] The voltages of the nodes at both ends of branch m1′m′2 and branch m2′m3′ are affected by the feeder switch states α ij1 and α ij2 Constraints, the voltage equations of the two-end nodes are similar to equation (12); for the inter-group branch lm, the voltage equations of the two-end nodes are as follows:

[0114]

[0115] Where U l represents the voltage of the adjacent cluster boundary node l.

[0116] Scenario 3: A simplified cluster model with multiple boundary nodes located on different power supply paths;

[0117] like Figure 3 As shown in the figure, for a multi-boundary node cluster where the power supply paths do not completely overlap, the boundary nodes e and f are not on the main power supply path ij (the main power supply path refers to the path with the most nodes) formed by the boundary nodes i and j. The simplified modeling idea of ​​this type of cluster is to equate the internal network of the cluster between the boundary nodes i and j to a virtual load node m′ and the incremental load power attached to the boundary nodes e, f, and j. According to the measurement data of the boundary nodes i, j, e, and f and the simplified cluster model, the simplified modeling process is as follows:

[0118] 1) Select the bifurcation node m of the main power supply path ij and path ie (or path if) as the virtual load node m′. Based on the principle that the branch impedance between the boundary nodes before and after cluster simplification remains unchanged, calculate the branch impedance from the virtual load node m′ to each boundary node. The impedance of branch im′ and branch m′e can be obtained by formula (17). The impedance of other branches can be obtained in the same way.

[0119]

[0120] In the formula, R im′ , X im′ are the resistance and reactance of branch im′, R im , X im are the resistance and reactance of branch im, R m′e , X m′e are the resistance and reactance of branch m′e, R ie , X ie are the resistance and reactance of branch ie respectively;

[0121] 2) Based on the voltage of the boundary node i, the transmission current, active and reactive power flowing into and out of the branch, solve the voltage U of the virtual load node m′ m′ And the active power P flowing from branch im′ into virtual load node m′ im′,in and reactive power Q im′,in , the calculation formula is as follows:

[0122]

[0123] 3) Based on the voltage U of the virtual load node m′ obtained m′ The transmission current, active power and reactive power flowing from the virtual load node m′ to each downstream branch are calculated based on the measurement data of the downstream boundary nodes. Taking branch m′e as an example, the transmission current I flowing from the virtual load node m′ to branch m′e is m′e,out , Active power P m′e,out and reactive power Q m′e,out The calculation formula is as follows:

[0124]

[0125] Where U e is the voltage at the boundary node e, R m′e , X m′e are the resistance and reactance of branch m′e, P ie,in , Q ie,in are the active power P flowing from branch ie into boundary node e ie,in and reactive power Q ie,in; In formula (19), in order to ensure the uniqueness of the solution, the present invention sets the ratio of the branch active and reactive power flowing out of the virtual load node m′ to be the same as the ratio of the branch active and reactive power flowing into the downstream boundary node;

[0126] 4) According to the transmission current, active and reactive power flowing into and out of the branch of the virtual load node m′, the active and reactive net power of the virtual load node m′ is solved, and the calculation formula is as follows:

[0127]

[0128] Where P m′f,out , Q m′f,out are the active and reactive power flowing out of the branch m′f from the virtual load node m′, P m′j,out , Q m′j,out are the active and reactive powers flowing out of branch m′j from virtual load node m′, respectively;

[0129] 5) According to the power data of the first and last boundary nodes of the downstream branch of the virtual load node m′, the incremental load active and reactive power of the boundary nodes e, j and f in the cluster simplified network is calculated; taking the boundary node e as an example, its incremental load active power P e,iL and reactive power Q e,iL It is obtained by the following formula:

[0130]

[0131] At this point, the internal network of the cluster with multiple boundary nodes located in different power supply paths can be equivalent to a virtual load node m′ and the incremental load power attached to the boundary node at the end of the main power supply path and each boundary node located outside the main power supply path; when the cluster contains feeder switches, the power flow modeling idea of ​​the simplified cluster network is similar to that of the simplified cluster network in Case 2, which will not be repeated here.

[0132] Step S2: Based on the simplified models of each cluster, a simplified network of the entire distribution network is obtained; the distribution network centralized controller collects information of each cluster, establishes and solves a simplified network power supply restoration model, and obtains the switch status of the inter-cluster feeder;

[0133] The objective function of the simplified network power restoration model is:

[0134]

[0135] Where: N S represents the set of all nodes in the entire simplified network; x m′,L Indicates the power supply recovery status of the virtual load node m′, and its value is 1 or 0, 1 represents power supply recovery, and 0 represents power failure; P m′,Lrepresents the active power of virtual load node m′; Δt represents the time step of the optimization model; L S Represents the set of all branches in the entire simplified network; N S,PV represents the set of all photovoltaic grid-connected nodes in the entire simplified network; P m′,dec represents the photovoltaic active power reduction of the virtual load node m′; α im′ represents the feeder switch state of branch im′, α im′,0 is the initial value of the switch state of the branch im′ feeder; C P , C PV and C S They represent the user electricity price, photovoltaic active power reduction cost coefficient and switch action cost coefficient respectively;

[0136] The simplified network power supply restoration model mainly considers safety operation constraints, branch power flow constraints, topology constraints and photovoltaic operation constraints;

[0137] 1) Safe operation constraints:

[0138] U min ≤U m′ ≤U max ;m′=m′,m1′,m2′,m3′ (23)

[0139]

[0140] Where: are the upper limits of active and reactive power of branch im′, U max and U min Respectively represent the upper and lower limits of the voltage.

[0141] 2) Branch flow constraints:

[0142] For different types of clusters, the simplified network branch power flow constraints are Equations (8)-(12) and (13)-(16) respectively. Considering the load power supply recovery state and photovoltaic output, the net active power P of the virtual load node m′ is m′,load and net reactive power Q m′,load The expression is as follows:

[0143]

[0144] Where: P m′,PV represents the PV active MPPT value of the virtual load node m′; Q m′,L represents the reactive power of virtual load node m′; Q m′,PV Represents the photovoltaic reactive power of the virtual load node m′.

[0145] 3) Topological constraints:

[0146] βim′ +β m′i =α im′ ;m′=m′,m1′,m2′,m3′ (26)

[0147]

[0148] -α im′ M≤H im′ ≤α im′ M; m′=m′,m1′,m2′,m3′ (29)

[0149] Where: β im′ and β m′i represents the upstream and downstream relationship between nodes, β im′ =1 indicates that virtual load node m′ is the parent node of boundary node i, β im′ = 0 means that virtual load node m′ is not the parent node of boundary node i, β m′i =1 indicates that the boundary node i is the parent node of the virtual load node m′, β m′i = 0 means that the boundary node i is not the parent node of the virtual load node m′, β 0m′ = 0 means that the virtual load node m′ is not the parent node of the source node; ξ(i) represents the set of all boundary nodes that have upstream and downstream relationships with the boundary node i; H im′ represents the virtual power of branch im′; D m′ represents the virtual load of node m′, which is usually set to 1; H m′h represents the virtual power of branch m′h, δ(m′) represents the set of all downstream nodes of virtual load node m′; Equations (28)-(29) represent virtual power flow constraints, which are used to ensure the accuracy of topology constraints when power flow reverse occurs in the network.

[0150] 4) Photovoltaic operation constraints:

[0151]

[0152] Where: θ represents the maximum value of the power factor angle of the photovoltaic inverter.

[0153] To facilitate the solution, the present invention uses second-order cone relaxation and linear substitution to transform the simplified network power restoration model into a mixed integer second-order cone programming model, as shown in the following formula:

[0154]

[0155] Where: V i represents the square of the voltage at node i; i im′,out Represents the square of the transmission current flowing out of branch im′.

[0156] At this point, the present invention constructs a simplified power supply restoration model with a model dimension much lower than that of the original network, and transforms it into an easy-to-solve mixed integer second-order cone programming problem. The state of the inter-group feeder switches can be calculated by the model.

[0157] Step S3: According to the inter-cluster feeder switch status, a fine power supply restoration model for each cluster is constructed and solved to determine the intra-cluster feeder switch status and the photovoltaic active power reduction amount;

[0158] The cluster fine power supply restoration model includes objective functions and constraints; the objective function f of the cluster a fine power supply restoration model is a as follows:

[0159]

[0160] Where: represents the set of all nodes in cluster a, x s,L Indicates the power recovery status of node s (referring to any node in the cluster except the source node), P s,L represents the active power of node s, P ks,out , Q ks,out are the active and reactive power flowing out of branch ks from node k (referring to any node including the source node), R ks is the resistance of branch ks, V N Represents the square of the system rated voltage, P s,dec is the photovoltaic active power reduction amount of node s, represents the set of all photovoltaic grid-connected nodes in cluster a, represents the set of all branches in cluster a, α ks is the feeder switch state of branch ks, α ks,0 It is the initial value of the switch state of the feeder line of branch ks.

[0161] The constraints of the cluster fine power supply restoration model include safe operation constraints, topology constraints, photovoltaic operation constraints and branch power flow constraints. The safe operation constraints, topology constraints and photovoltaic operation constraints are the same as those of the simplified network power supply restoration model and will not be repeated here. The branch power flow constraints are as shown in formula (33):

[0162]

[0163] Where V s represents the square of the voltage at node s, V k represents the square of the voltage at node k, R ks , X ks Respectively represent the resistance and reactance of branch ks, P s,PV represents the photovoltaic active MPPT value of node s, P sh,out , Q sh,outdenote the active and reactive power of branch sh flowing out of node s, δ(s) denotes the set of all downstream nodes of node s, Q s,L represents the reactive power of node s, Q s,PV Represents the photovoltaic compensation amount of node s.

[0164] Example

[0165] This embodiment takes the IEEE-33 node distribution network model as an example to verify the method of the present invention.

[0166] Figure 4 The distribution network topology used in this embodiment includes 4 tie lines, and the tie line switches are denoted as TS1, TS2, TS3 and TS4. The photovoltaic installation information is shown in Table 1. The headend node voltage of the system is set to 1.03pu, the upper and lower limits of the node voltage safety operation are 1.05pu and 0.95pu respectively, the time step Δt of the power supply recovery model is set to 1h, and the electricity price C P Set at 0.4 yuan / kWh, photovoltaic cost reduction C PV The cost of switching is set to 0.7 yuan / kWh and the cost of switching is set to 7 yuan / time. Figure 4 In the three clusters shown, a short circuit fault occurs on the line between nodes 26 and 27 and the faulty line has been isolated.

[0167] Table 1 PV installation node location and capacity

[0168]

[0169] according to Figure 4 As shown in the cluster division, the cluster boundary nodes include nodes 1, 5, 6, 7, 8, 12, 18, 21, 22, 25, 29 and 33. When constructing the cluster simplification model, the boundary node 12 of cluster 3 is located on the power supply path of boundary nodes 8 to 18, so the cluster simplification method in which the three boundary nodes are located on the same power supply path is adopted, and the power supply path from node 6 to node 33 in cluster 2 is simplified in the same way. The power supply paths from the head node 1 to the boundary nodes 5, 21 and 25 of cluster 1 do not completely overlap, so the network simplification method in which the boundary nodes are located on different paths is adopted. According to the cluster simplification method proposed in the present invention, the adjusted IEEE 33-node system is simplified to a simplified network consisting of 15 nodes, as shown in FIG. Figure 5 As shown in the figure, the black nodes represent the cluster boundary nodes in the original network, and the white nodes represent the equivalent virtual load nodes. After the line fault between nodes 26 and 27 is isolated, some virtual load nodes of cluster 2 and the load of boundary node 33 lose power. The red circles in the figure represent the nodes that lose power.

[0170] A simplified network power supply restoration model is constructed for the 15-node simplified network and solved to obtain the switch status of each inter-cluster tie line. A refined power supply restoration model for each cluster is constructed based on the switch status of each inter-cluster tie line to determine the switch status of the feeder within the cluster and the amount of photovoltaic active power reduction. The optimal power supply topology of the simplified network is as follows: Figure 6 As shown, the tie line switch TS4 changes from open to closed, the power-off load is transferred to node 25 and all power is restored. Under the desired power restoration scheme, if Figure 7 As shown, the power-off nodes 27 to 33 are powered by cluster 1 via tie-line switch TS4.

[0171] To verify the effectiveness of the method of the present invention, the present invention is compared with the existing centralized power supply restoration method, wherein the centralized power supply restoration method uses the Cplex solver to centrally solve the distribution network power supply restoration model to obtain the distribution network restoration plan. The comparison results of the two methods are shown in Table 2.

[0172] Table 2 Comparison of power restoration results of different methods

[0173]

[0174] As can be seen from Table 2, the number of switch actions, load recovery rate, and photovoltaic active power reduction of the present invention are exactly the same as those of the centralized power supply restoration method, but the network loss deviation is 0.1kW, the total operating cost differs by 0.04 yuan, and the overall power restoration effect is very close. Compared with the centralized power supply restoration method, the fine power supply restoration model of each cluster constructed by the present invention has a lower dimension, which avoids the high-dimensional problem of the overall solution of the centralized optimization model of the large-scale distribution network, improves the solution efficiency, and the fine power supply restoration model of each cluster can be solved on its own processor, which is more flexible and robust.

[0175] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A method for rapid power restoration of a large-scale distribution network based on cluster simplified modeling, characterized in that: The following steps are involved: Step S1: Distributed establishment of simplified models of each cluster; Case 1: Simplified model of a cluster with only two boundary nodes; For a cluster with only two boundary nodes i and j, the simplified modeling idea is to equate the internal network of the cluster to a virtual load node m′, then: Where: U i and U j denote the voltages at boundary nodes i and j, respectively, and R ij1 and X ij1 They represent the total resistance and total reactance of the branch from the virtual load node m′ to the boundary node i, R ij2 and X ij2 They represent the total resistance and total reactance of the branch from the virtual load node m′ to the boundary node j, respectively. ij,out , P ij,out and Q ij,out They represent the transmission current, active power and reactive power flowing from the boundary node i on the power supply path ij, respectively. ij,in , P ij,in and Q ij,in They represent the transmission current, active power and reactive power flowing from the power supply path ij into the boundary node j, R ij and X ij denote the total resistance and reactance of the branch between boundary nodes i and j, respectively, P m′,load and Q m′,load denote the active and reactive net powers of the virtual load node m′ respectively; If there is no feeder switch inside the cluster, the power flow equation of branch im′ is as shown in equation (7). Similarly, the power flow equation of branch m′j can be obtained; Where: I im′,out , P im′,out , Q im′,out They represent the transmission current, active power and reactive power flowing out of branch im′ from boundary node i, respectively. m′j,out , Q m′j,out They represent the active and reactive power flowing out of the virtual load node m′j, U m' represents the voltage of virtual load node m′; If there is a feeder switch S inside the cluster ij , then the virtual load node m′ is split into m1′ and m2′, the branch impedance between the two virtual load nodes m1′ and m2′ is 0, and the active and reactive net powers satisfy equation (8); Where: and They represent the active and reactive net power of the virtual load node m1′, and They represent the active and reactive net powers of the virtual load node m2′ respectively; The power flow equation of branch im1′ is as shown in equation (9). Similarly, the power flow equation of branch m2′j can be obtained; Where: α ij Indicates feeder switch S ij status, represents the voltage of virtual load node m1′; The voltages of virtual load nodes m1′ and m2′ satisfy the following constraints: In the formula, represents the voltage of virtual load node m2′, M is a constant; Case 2: Simplified model of a cluster with three boundary nodes located on the same power supply path; For a cluster with three boundary nodes located on the same power supply path, assuming that boundary node m is located on the power supply path of boundary nodes i and j, the simplified modeling idea is to equate the internal network of the cluster between boundary nodes i and j to a virtual load node m′, and use the virtual load node m′ to replace boundary node m and then perform simplified modeling with boundary nodes i and j. The modeling process is the same as that of case 1. If there is a feeder switch inside the cluster, the virtual load node m′ is split into m1′, m2′ and m3′ according to the number of inter-cluster branches, and the branch impedances of the three virtual load nodes are all 0; assuming that the virtual load nodes m1′ and m2′ are connected by feeder switches S ij1 Connection, m2′ and m3′ are connected by feeder switch S ij2 There is an inter-cluster feeder switch S between the virtual load node m2′ and the adjacent cluster. lm , then the active and reactive net powers of virtual load nodes m1′, m2′ and m3′ satisfy equation (13); In the formula, are the active and reactive net powers of the virtual load node m3′ respectively; The power flow equations of branch im1′ and branch m3′j are similar to those of branch im1′ and branch m2′j in case 1. The power flow equation of branch m1′m2′ is shown in equation (14). Similarly, the power flow equation of branch m2′m3′ is obtained. Where: They represent the active and reactive power flowing out of the virtual load node m1′ and m2′, respectively. are the active and reactive powers flowing out of the virtual load node m2′ and m3′, respectively. lm,out , P lm,out and Q lm,out represents the transmission current, active power and reactive power flowing out of the inter-cluster branch lm from the adjacent cluster boundary node l, R lm and X lm represents the resistance and reactance of the inter-group branch lm; The transmission current I of the inter-group branch lm lm,out , Active power P lm,out and reactive power Q lm,out The constraint condition satisfies equation (15), and the voltage equation of the two-end nodes satisfies equation (16); In the formula, α lm Indicates feeder switch S lm status, and They represent the upper limits of inter-group branch transmission current, active power and reactive power, respectively. l represents the voltage of the adjacent cluster boundary node l; Scenario 3: A simplified cluster model with multiple boundary nodes located on different power supply paths; Assuming that the boundary nodes e and f are not in the main power supply path ij formed by the boundary nodes i and j, the simplified modeling idea is to equate the internal network of the cluster between the boundary nodes i and j to the virtual load node m′ and the incremental load power attached to the boundary nodes e, f and j; 1) Select the bifurcation node m between the main power supply path ij and the remaining paths as the virtual load node m′, calculate the branch impedance from the virtual load node m′ to each boundary node, and the impedance of the branch im′ and the branch m′e is obtained by formula (17). Similarly, the impedance of other branches can be obtained; In the formula, R im′ , X im′ are the resistance and reactance of branch im′, R im , X im are the resistance and reactance of branch im, R m′e , X m′e are the resistance and reactance of branch m′e, R ie , X ie are the resistance and reactance of branch ie respectively; 2) Voltage U at virtual load node m′ m′ And the active power P flowing from branch im′ into virtual load node m′ im′,in and reactive power Q im′,in Calculated by the following formula: 3) According to the voltage U of the virtual load node m′ m′ and the measurement data of the downstream boundary nodes, calculate the transmission current, active power and reactive power flowing from the virtual load node m′ to each downstream branch; among which, the transmission current I flowing from the virtual load node m′ to the branch m′e m′e,out , Active power P m′e,out and reactive power Q m′e,out The calculation formula is as follows: Where U e is the voltage at the boundary node e, R m′e , X m′e are the resistance and reactance of branch m′e, P ie,in , Q ie,in are the active power P flowing from branch ie into boundary node e ie,in and reactive power Q ie,in ; 4) Solve the active and reactive net power of the virtual load node m′ according to the following formula: Where P m′f,out , Q m′f,out are the active and reactive power flowing out of the branch m′f from the virtual load node m′, P m′j,out , Q m′j,out are the active and reactive powers flowing out of branch m′j from virtual load node m′, respectively; 5) According to the power data of the first and last boundary nodes of the downstream branch of the virtual load node m′, the incremental load active and reactive power of the boundary nodes e, j and f in the cluster simplified network is calculated; where the incremental load active power P of the boundary node e is e,iL and reactive power Q e,iL It is obtained by the following formula: Step S2: A simplified network of the entire distribution network is obtained according to the simplified models of each cluster, a simplified network power supply restoration model is established and solved according to the simplified network, and the inter-cluster feeder switch state is obtained; The objective function of the simplified network power restoration model is: Where: N S represents the set of all nodes in the entire simplified network; x m′,L represents the power supply recovery status of the virtual load node m′; P m′,L represents the active power of virtual load node m′; Δt represents the time step of the optimization model; L S Represents the set of all branches in the entire simplified network; N S,PV represents the set of all photovoltaic grid-connected nodes in the entire simplified network; P m′,dec represents the photovoltaic active power reduction of the virtual load node m′; α im′ represents the feeder switch state of branch im′, α im′,0 is the initial value of the switch state of the branch im′ feeder; C P , C PV and C S They represent the user electricity price, photovoltaic active power reduction cost coefficient and switch action cost coefficient respectively; Step S3: According to the inter-cluster feeder switch status, a fine power supply restoration model for each cluster is constructed and solved in parallel to determine the intra-cluster feeder switch status and the photovoltaic active power reduction amount; The objective function of the fine power restoration model of cluster a is as follows: Where: represents the set of all nodes in cluster a, x s,L Indicates the power recovery status of any node s in the cluster except the source node, P s,L represents the active power of node s, P ks,out , Q ks,out are the active and reactive power flowing out of branch ks from any node k including the source node, R ks is the resistance of branch ks, V N Represents the square of the system rated voltage, P s,dec is the photovoltaic active power reduction amount of node s, represents the set of all photovoltaic grid-connected nodes in cluster a, represents the set of all branches in cluster a, α ks is the feeder switch state of branch ks, α ks,0 It is the initial value of the switch state of the feeder line of branch ks.

2. The method for rapid power restoration of a large-scale distribution network based on cluster simplified modeling according to claim 1 is characterized in that: The constraints of the simplified network power supply restoration model include safety operation constraints, branch power flow constraints, topology constraints and photovoltaic operation constraints; 1) Safe operation constraints: U min ≤U m′ ≤U max ;m′=m′,m1′,m2′,m3′ (23) Where: are the upper limits of active and reactive power of branch im′, U max and U min Respectively represent the upper and lower limits of voltage; 2) The branch power flow constraints of different clusters satisfy their own power flow equations; considering the load power supply recovery state and photovoltaic output, the net active power P of the virtual load node m′ m′,load and net reactive power Q m′,load Satisfy the following formula: Where: P m′,PV represents the PV active MPPT value of the virtual load node m′; Q m′,L represents the reactive power of virtual load node m′; Q m′,PV represents the photovoltaic reactive power of the virtual load node m′; 3) Topological constraints: β im′ +β m′i =α im′ ;m′=m′,m1′,m2′,m3′ (26) -a im′ M≤H im′ ≤α im′ M; m′=m′,m1′,m2′,m3′ (29) Where: β im′ and β m′i represents the upstream and downstream relationship between nodes, β im′ =1 indicates that virtual load node m′ is the parent node of boundary node i, β im′ = 0 means that virtual load node m′ is not the parent node of boundary node i, β m′i =1 indicates that the boundary node i is the parent node of the virtual load node m′, β m′i = 0 means that the boundary node i is not the parent node of the virtual load node m′, β 0m′ = 0 means that the virtual load node m′ is not the parent node of the source node; ξ(i) represents the set of all boundary nodes that have upstream and downstream relationships with the boundary node i; H im′ represents the virtual power of branch im′; D m′ represents the virtual load of node m′; H m′h represents the virtual power of branch m′h, δ(m′) represents the set of all downstream nodes of virtual load node m′; 4) Photovoltaic operation constraints: Where: θ represents the maximum value of the power factor angle of the photovoltaic inverter.

3. The method for rapidly restoring power supply in a large-scale distribution network based on cluster simplified modeling according to claim 1 or 2, characterized in that: The constraints of the cluster fine power supply restoration model include safety operation constraints, topology constraints, photovoltaic operation constraints and branch power flow constraints. The safety operation constraints, topology constraints and photovoltaic operation constraints are the same as those of the simplified network power supply restoration model. The branch power flow constraints are as shown in formula (33); Where V s represents the square of the voltage at node s, V k represents the square of the voltage at node k, R ks , X ks Respectively represent the resistance and reactance of branch ks, P s,PV represents the photovoltaic active MPPT value of node s, P sh,out , Q sh,out denote the active and reactive power of branch sh flowing out of node s, δ(s) denotes the set of all downstream nodes of node s, Q s,L represents the reactive power of node s, Q s,PV Represents the photovoltaic compensation amount of node s.

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