A method and system for evaluating multi-level resilience of power systems based on analytical methods

Abstract

The present invention discloses a multi-level resilience assessment method and system for an electric power system based on an analytical method, including: obtaining a first topological structure of a distribution system and a second topological structure of a transmission system, simplifying the first topological structure and the second topological structure respectively according to node cells; establishing a mixed integer programming model, searching the simplified first topological structure and the second topological structure, and obtaining the energy supply path of the node cells; according to the energy supply path, using an analytical method to calculate the node cell power outage time probability and the node cell maintenance time probability; according to the node cell power outage time probability and the node cell maintenance time probability, obtaining the resilience assessment index of the electric power system; according to the response characteristics and resilience assessment index between the distribution system and the transmission system, evaluating the resilience of the electric power system. The present invention provides a quantitative basis for system planning, operation scheduling and recovery decision-making, reduces load losses, and improves the safety level of the electric power system.

Description

Technical Field

[0001] The present invention relates to the technical field of power system reliability, and in particular to a method and system for evaluating the multi-level resilience of a power system based on an analytical method. Background Art

[0002] With the increasing frequency of natural disasters in recent years, the power grid has suffered more and more low-probability high-impact disaster events. The power grid will experience large-scale power outages, many permanent faults, and it is difficult to restore faulty equipment in time. In order to reflect the ability of the power system to resist extreme natural disasters, reduce fault losses and restore power supply as soon as possible, the concept of power system resilience has been proposed. Resilience is defined as the ability of the power system to respond to disturbance events. At present, the research on the resilience of resilient power systems is mainly oriented towards distribution systems. This is because the distribution system is the last link of the power system, and its control and protection are more complex than the transmission system, and it is more prone to failure. In analyzing the impact of extreme events, less attention has been paid to the transmission network. The existing resilience assessment indicators and assessment methods are also mainly for the distribution network, without considering the impact and role of the transmission network in the system resilience assessment. Summary of the invention

[0003] In order to solve the above technical problems, the present invention provides a multi-level resilience assessment method and system for power systems based on analytical methods, which can guide the line planning of power systems and the reinforcement of components when natural disasters do not occur, predict emergency control during disasters in advance, and carry out emergency repairs and power restoration after disasters, and provide a quantitative basis for system planning, operation scheduling, and recovery decisions.

[0004] In a first aspect, the present invention provides a method for evaluating the multi-level resilience of a power system based on an analytical method, the method comprising:

[0005] Acquire a first topology structure of a power distribution system and a second topology structure of a power transmission system, and simplify the first topology structure and the second topology structure respectively according to node cells, wherein the node cells include distribution node cells and transmission node cells;

[0006] Establishing a mixed integer programming model, searching the simplified first topological structure and the simplified second topological structure through the mixed integer programming model to obtain an energy supply path of the node cell;

[0007] According to the energy supply path, an analytical method is used to calculate the node cell power outage time probability and the node cell maintenance time probability;

[0008] According to the node cell power outage time probability and the node cell maintenance time probability, a resilience evaluation index of the power system is obtained, wherein the resilience evaluation index includes a first resilience evaluation index of the distribution system and a second resilience evaluation index of the transmission system;

[0009] Evaluating the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience evaluation index;

[0010] The step of acquiring a first topology structure of the power distribution system and a second topology structure of the power transmission system, and simplifying the first topology structure and the second topology structure according to node cells respectively comprises:

[0011] According to a first topology network of a power distribution system and a second topology network of a power transmission system, the components in the power distribution system and the components in the power transmission system are divided according to component types, wherein the component types include distribution component types and transmission component types;

[0012] A set of all connected nodes without switch lines is used as a node cell, and the first topology network and the second topology network are simplified according to the node cells.

[0013] Furthermore, the step of acquiring a first topology structure of the power distribution system and a second topology structure of the power transmission system, and simplifying the first topology structure and the second topology structure respectively according to node cells comprises:

[0014] According to a first topology network of a power distribution system and a second topology network of a power transmission system, the components in the power distribution system and the components in the power transmission system are divided according to component types, wherein the component types include distribution component types and transmission component types;

[0015] A set of all connected nodes without switch lines is used as a node cell, and the first topology network and the second topology network are simplified according to the node cells.

[0016] Furthermore, the step of establishing a mixed integer programming model, searching the simplified first topological structure and the simplified second topological structure according to the mixed integer programming model, and obtaining the energy supply path of the node cell includes:

[0017] Establishing an objective function according to the energy supply path of the node cell, and adding constraints to the objective function, wherein the constraints include power distribution constraints and power transmission constraints;

[0018] Establishing a mixed integer programming model according to the objective function and the constraint conditions;

[0019] The mixed integer programming model is iteratively calculated to obtain the energy supply path of the node cell.

[0020] Furthermore, the objective function is expressed by the following formula:

[0021]

[0022] In the formula, x i is the reference variable of whether the load of node i is in the system, P i L is the load of node i, I(m) is the set of nodes in node cell m;

[0023] The constraint condition is expressed by the following formula:

[0024]

[0025] In the formula, is a reference variable for whether the energy supply path passes through the route from node cell s to node cell t, is a reference variable for whether the energy supply path passes through the route from node cell t to node cell s, is a reference variable for whether the energy supply path passes through the route from node cell k to node cell m, is a reference variable for whether the energy supply path passes through the route from node cell m to node cell k, KS is the power node cell set, K is the node cell set, B is the line set, and m is the target node cell;

[0026]

[0027]

[0028] In the formula, x s is the reference variable for whether the energy supply path passes through the node cell s, is the reference variable for whether the line (i, j) has restored power supply, I(s) is the set of nodes in the node cell s, and Bs is the set of all lines in the node cell s;

[0029]

[0030] In the formula, I is the set of system nodes, M(i) and N(i) represent the parent node and child node sets of node i respectively, and P i,j is the active power flowing through line (i, j), represents the upper limit of active power flowing through line (i, j), P i g represents the active power injected by the i-node substation, P i gmaxIndicates the upper limit of active power of the i-node substation;

[0031]

[0032] Where P i,j , Q i,j is the active power and reactive power flowing through line (i, j), and are the upper limits of active power and reactive power flowing through line (i, j), P i g and are the active power and reactive power injected by the i-node substation, P i gmax and are the upper limits of active power and reactive power of the i-node substation, U i is the actual voltage at node i, and are the upper and lower limits of the voltage amplitude at node i, is the reference voltage of line (i, j), R i,j With X i,j are the resistance and reactance of line (i, j).

[0033] Furthermore, the step of iteratively calculating the mixed integer programming model to obtain the energy supply path of the node cell includes:

[0034] Calculating the mixed integer programming model to obtain an objective function value, and obtaining an energy supply path of a node cell according to the objective function value;

[0035] Adding non-repetitive constraints to the mixed integer programming model, and performing iterative calculations on the mixed integer programming model with the non-repetitive constraints according to an iteration condition to obtain all energy supply paths of the node cells;

[0036] The objective function value is expressed by the following formula:

[0037]

[0038] In the formula, e is the number of iterations, P i L is the load of node i;

[0039] The following formula is used to represent the energy supply path of the node cell:

[0040]

[0041] In the formula, is the fth energy supply path of node cell m, is the solution obtained by solving the mixed integer programming model for the gth time;

[0042] The non-repetitive constraint is expressed by the following formula:

[0043]

[0044] In the formula, It is the τth energy supply path of node cell m.

[0045] Furthermore, the step of calculating the node cell power outage time probability and the node cell maintenance time probability by using an analytical method according to the energy supply path includes:

[0046] According to the energy supply path, obtaining a probability event of power outage time of a node cell during an accident and a probability event of maintenance time of a node cell after an accident;

[0047] According to the node cell power outage time probability event in the accident, the node cell power outage time probability is obtained, and according to the node cell maintenance time probability event after the accident, the node cell maintenance time probability is obtained.

[0048] Furthermore, the step of obtaining a resilience assessment index of the power system according to the node cell power outage time probability and the node cell maintenance time probability comprises:

[0049] According to the power outage time probability of the node cell, the expected power outage duration of the node cell is obtained;

[0050] According to the node cell maintenance time probability, the node cell maintenance time expectation is obtained;

[0051] Obtaining the system load loss expectation according to the load of the node cell, the expected duration of the power outage of the node cell and the expected maintenance time of the node cell;

[0052] The expected duration of power outage of the node cell, the expected maintenance time of the node cell and the expected load loss of the system are used as the resilience evaluation indicators of the power system.

[0053] Furthermore, the expected duration of power outage of the node cell is calculated using the following formula:

[0054]

[0055] Where, t D is the power outage time of node cell k in the accident, The power outage time of node cell k in the accident is t D The probability of D The duration of the natural disaster;

[0056] The expected maintenance time of the node cell is calculated using the following formula:

[0057]

[0058] Where, t R is the maintenance time of node cell k after the accident, The maintenance time of node cell k after the accident is t R The probability of R The maximum time required to repair the system until it is fully recovered;

[0059] The system load loss expectation is calculated using the following formula:

[0060]

[0061] In the formula, is the expected load loss of node cell k, K is the set of node cells, P i is the load of node i, and I(k) is the set of nodes in node cell k.

[0062] Furthermore, the step of evaluating the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience evaluation index comprises:

[0063] Obtaining a function curve of the power distribution system according to a first resilience evaluation index of the power distribution system;

[0064] Obtaining a function curve of the power transmission system according to a second resilience evaluation index of the power transmission system;

[0065] A function curve of the power system is obtained according to the response characteristics between the power distribution system and the power transmission system, the first resilience evaluation index, and the second resilience evaluation index.

[0066] In a second aspect, the present invention provides a multi-level resilience assessment system for a power system based on an analytical method, comprising:

[0067] A topology simplification module, used to obtain a first topology of a power distribution system and a second topology of a power transmission system, and simplify the first topology and the second topology respectively according to node cells, wherein the node cells include distribution node cells and transmission node cells;

[0068] The step of acquiring a first topology structure of the power distribution system and a second topology structure of the power transmission system, and simplifying the first topology structure and the second topology structure according to node cells respectively comprises:

[0069] According to a first topology network of a power distribution system and a second topology network of a power transmission system, the components in the power distribution system and the components in the power transmission system are divided according to component types, wherein the component types include distribution component types and transmission component types;

[0070] A set of all connected nodes without switch lines is used as a node cell, and the first topology network and the second topology network are simplified according to the node cells;

[0071] An energy supply path search module is used to establish a mixed integer programming model, and to search the simplified first topological structure and the simplified second topological structure through the mixed integer programming model to obtain an energy supply path of the node cell;

[0072] A probability calculation module, used to calculate the node cell power outage time probability and the node cell maintenance time probability by using an analytical method according to the energy supply path;

[0073] An evaluation index calculation module, used to obtain a resilience evaluation index of the power system according to the node cell power outage time probability and the node cell maintenance time probability, wherein the resilience evaluation index includes a first resilience evaluation index of the distribution system and a second resilience evaluation index of the transmission system;

[0074] The resilience assessment module is used to assess the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience assessment index.

[0075] The above invention provides a method and system for evaluating the multi-level resilience of power systems based on analytical methods. Through the method, various scenarios of the power system are analyzed to obtain high-precision analysis results, which can provide guidance for line planning of the power system before natural disasters occur, reinforcement of components, emergency control during early disaster prediction, and emergency repair and power restoration after disasters, thereby improving the safety level of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flowchart of a method for evaluating multi-level resilience of a power system based on an analytical method provided by an embodiment of the present invention;

[0077] Figure 2 It is a system framework diagram corresponding to the multi-level evaluation method for power system resilience based on analytical method provided in an embodiment of the present invention;

[0078] Figure 3 It is a diagram of the level and stage division of power system resilience assessment;

[0079] Figure 4 yes Figure 1Schematic diagram of the process of step S10;

[0080] Figure 5 yes Figure 1 Schematic diagram of the process of step S20;

[0081] Figure 6 yes Figure 5 Schematic diagram of the process of step S203;

[0082] Figure 7 yes Figure 1 Schematic diagram of the process of step S30;

[0083] Figure 8 yes Figure 1 Schematic diagram of the process of step S40;

[0084] Fig. 9 yes Figure 1 Schematic diagram of the process of step S50;

[0085] Fig.10 It is the improved IEEE-13 node example distribution system topology diagram;

[0086] Fig.11 It is the improved IEEE-13 node example initial diagram and cell simplified diagram;

[0087] Fig.12 It is the improved IEEE-13 node example system function curve;

[0088] Fig.13 It is a structural schematic diagram of a multi-level resilience assessment system for a power system based on an analytical method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0089] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] See also Figure 1 The first embodiment of the present invention proposes a multi-level resilience assessment method for a power system based on an analytical method, comprising steps S10 to S50:

[0091] Step S10, obtaining a first topology structure of a power distribution system and a second topology structure of a power transmission system, and simplifying the first topology structure and the second topology structure respectively according to node cells, wherein the node cells include distribution node cells and transmission node cells.

[0092] See also Figure 2 In view of the existing resilience research which mainly focuses on the distribution system and pays less attention to the transmission system, the present invention combines the transmission system with the distribution system, and divides the natural disaster period into three periods: before the disaster, during the disaster, and after the disaster according to the different responses of the power system at each stage, that is, a multi-level resilience assessment is conducted at the spatial and temporal levels. Figure 3 The characteristics of the power system's resilience at various stages of natural disasters are described as follows:

[0093] 1) Pre-accident preparation planning stage t0-t1: At this time, the disaster has not yet occurred, and the system's resilience is mainly improved through flexible distribution network planning, line reinforcement, and increasing redundant resources.

[0094] 2) Fault evolution stage in the accident t1-(t1+T D ): In this stage, the disaster will cause failures in different areas at different times and affect other areas. At this time, the distribution network will continue to undergo dynamic topological changes to reduce the power outage losses in the accident. In this stage, the system load continues to decrease until the natural disaster ends.

[0095] 3) Post-accident recovery phase (t1+T D )-(t1+T D +T R ): Considering the actual conditions, the maintenance work is carried out after the accident. The dispatch of maintenance personnel after the accident will also cause the network to undergo a topology change at this time, and the lost load of the system will gradually recover until the system recovers. At this point, the system response caused by the natural disaster has ended, but after the response, the loss of the response can also be evaluated, and suggestions for enhancing the resilience of the distribution network can be obtained.

[0096] Under the above conditions, please combine Figure 4 , first simplify the topological structure of the distribution system and the transmission system:

[0097] Step S101 , according to a first topology network of a power distribution system and a second topology network of a power transmission system, components in the power distribution system and components in the power transmission system are divided according to component types, wherein the component types include distribution component types and transmission component types.

[0098] Step S102: taking a set of all connected nodes without switch lines as node cells, and simplifying the first topology network and the second topology network according to the node cells.

[0099] Taking the power distribution system as an example, by analyzing the topological structure of the power distribution system lines, the network components of the power distribution system are simplified and divided into the following four types:

[0100] 1) Power supply nodes, including distribution substation nodes, distributed power supply nodes, etc., whose function is to provide power for the load nodes of the distribution network.

[0101] 2) Load nodes, i.e. user loads in distribution lines. The state of distribution network is observed through the state of load nodes.

[0102] 3) Do not disconnect the lines, including cable lines, overhead lines, etc. The power generated by the power source flows to the load nodes through these lines.

[0103] 4) Switching lines, including circuit breakers, tie switches, etc. Switching lines can not only transmit power from power supply nodes, but also change their own state when the network topology needs to change, thereby realizing load transfer.

[0104] Based on the above-mentioned component types, the principle of component failure and load power outage is formulated, that is, the availability of network components depends on whether the line components fail, and the node components composed of power nodes and load nodes are assumed to be fault-free. However, the load node may experience a power outage due to the failure of the line components.

[0105] Then the node cell is defined, that is, the node cell is a set of all connected nodes without switch lines. Since there is no switch isolation between the nodes inside the cell, when a node fails, all nodes will be cut off by the system, that is, their action states are consistent, and their power outage time in the accident and the maintenance time after the accident are the same. Based on the concept of node cells, the topological structure can be simplified to facilitate subsequent calculations.

[0106] The simplification of the transmission system topology is similar to the simplification of the distribution system topology described above, but the difference between the two is that the network elements of the transmission system are divided into the following types:

[0107] 1) Power supply nodes, including power station nodes, distributed power supply nodes, etc., whose function is to provide power for downstream nodes of the transmission system.

[0108] 2) Downstream nodes, including load nodes directly connected to transmission lines and substation nodes of distribution networks.

[0109] 3) Lines cannot be disconnected, including cable lines, overhead lines, etc., through which the power generated by the power source flows to the downstream nodes.

[0110] 4) Switching lines will change their own state when the network topology needs to change, thereby achieving load transfer.

[0111] The principle of component failure and downstream distribution network outage is specified according to the above component types, that is, the availability of network components depends on whether the line components fail, and it is assumed that no failure will occur for the node components consisting of the power supply node and the downstream node. This reflects the superior-subordinate relationship between the transmission line and the distribution line, in which the status of the distribution network downstream of the distribution network will not affect the upstream transmission line.

[0112] Step S20: establishing a mixed integer programming model, searching the simplified first topological structure and the simplified second topological structure through the mixed integer programming model to obtain an energy supply path of the node cell.

[0113] After simplifying the topological structure, we need to search for the energy supply path of the node cells based on the simplified topological structure, where the energy supply path can be defined as:

[0114] 1) The path starts from a substation or distributed power node cell, passes through other node cells in the middle, and finally ends at its own cell. The energy supply path is the collection of all lines in this path; this reflects the topological properties of the energy supply path;

[0115] 2) After removing any one line from the energy supply path, the definition of 1) cannot be met; this reflects the minimality of the energy supply path, that is, the energy supply path operates radially;

[0116] 3) The energy supply path must meet the safety constraints of the line, which reflects the physical meaning of the energy supply path: even if the node can be connected to the power supply in the topology, it cannot safely restore power due to insufficient power supply. This situation should be avoided.

[0117] In order to obtain the energy supply path set of the node cell, it is necessary to find all the energy supply paths of each cell. The present invention uses mixed integer programming to search for the energy supply path. The specific steps are as follows: Figure 5 As shown:

[0118] Step S201: establishing an objective function according to the energy supply path of the node cell, and adding constraints to the objective function, wherein the constraints include power distribution constraints and power transmission constraints.

[0119] Step S202: establishing a mixed integer programming model according to the objective function and the constraint conditions.

[0120] Step S203, performing iterative calculation on the mixed integer programming model to obtain the energy supply path of the node cell.

[0121] First, we define the planned variable as a 0-1 variable x i , which is used to indicate whether the load of node i is still in the system. If so, the value is 1, otherwise it is 0. If a cell has an energy supply path, all nodes inside it are operating normally. Therefore, the planning objective function is defined as:

[0122]

[0123] Its meaning is whether the line in the target cell m can be restored. If it can be restored, the final result should be:

[0124]

[0125] Otherwise, it means that the cell has no energy supply path, where P i L is the load of node i, and I(m) is the node set in node cell m.

[0126] Next, we construct the constraints of the objective function based on the definition of the energy supply path, including:

[0127] 1) The energy supply path starts from the power source and ends at the target cell, that is:

[0128]

[0129] In the formula, is a reference variable for whether the energy supply path passes through the route from node cell s to node cell t, is a reference variable for whether the energy supply path passes through the route from node cell t to node cell s, is a reference variable for whether the energy supply path passes through the route from node cell k to node cell m, is a reference variable for whether the energy supply path passes through the route from node cell m to node cell k, KS is the set of power node cells, K is the set of node cells, B is the line set, and m is the target node cell. The reference variables in the formula are all 0-1 variables, that is, 1 if it passes, and 0 otherwise.

[0130] 2) In order to meet the minimum requirement, the energy supply path should be radial, with no loops in the middle, that is, each node can only be passed once. That is:

[0131]

[0132] 3) If the energy supply path passes through cell k, then cell k can be restored, and the nodes and lines in cell k will be restored. That is:

[0133]

[0134] In the formula, x s is the reference variable for whether the energy supply path passes through the node cell s, is the reference variable for whether the line (i, j) has restored power supply, I(s) is the node set in the node cell s, Bs is the set of all lines in the node cell s, and similarly, the reference variables here are all 0-1 variables, which are 1 if yes and 0 otherwise.

[0135] It can be clearly seen that the above three constraints are all based on the definition of the energy supply path. Therefore, the above constraints are applicable to both the distribution system and the transmission system. However, due to the characteristics of the distribution system and the transmission system themselves, different constraints need to be defined for each system. For the distribution system, in order to meet safety requirements, considering that the distribution system is located downstream of the power system, the voltage is mainly controlled by the upstream substation, and the voltage fluctuation caused by the disaster is not serious, so a simplified power constraint is added, mainly considering power balance, power capacity and line power flow constraints, namely:

[0136]

[0137] In the formula, I is the set of system nodes, M(i) and N(i) represent the parent node and child node sets of node i respectively, and P i,j is the active power flowing through line (i, j), represents the upper limit of active power flowing through line (i, j), P i g represents the active power injected by the i-node substation, P i gmax Indicates the upper limit of active power of the i-node substation.

[0138] For the transmission system, since the voltage at each node of the transmission system is affected by the power flow, disasters may cause excessive voltage deviation and affect safe operation. Therefore, the transmission system needs to consider the safety constraints of voltage and power at the same time. That is, the constraints of the transmission system are:

[0139]

[0140] Where P i,j , Q i,j is the active power and reactive power flowing through line (i, j), and are the upper limits of active power and reactive power flowing through line (i, j), P i g and are the active power and reactive power injected by the i-node substation, P i gmax and are the upper limits of active power and reactive power of the i-node substation, U i is the actual voltage at node i, and are the upper and lower limits of the voltage amplitude at node i, is the reference voltage of line (i, j), R i,j With X i,j are the resistance and reactance of line (i, j).

[0141] According to the above objective function and constraints, a mixed integer programming model can be constructed. By solving the model, an energy supply path of the target node cell can be obtained. In order to obtain all the energy supply paths of the node cells, it is necessary to iterate the model. The steps are as follows: Figure 6 As shown:

[0142] Step S2031, calculating the mixed integer programming model to obtain an objective function value, and obtaining an energy supply path of the node cell according to the objective function value.

[0143] Step S2032, adding non-repetitive constraints to the mixed integer programming model, and performing iterative calculations on the mixed integer programming model with the non-repetitive constraints according to an iteration condition, to obtain all energy supply paths of the node cells.

[0144] First, set the number of iterations k to 1, solve the above mixed integer programming model, and obtain the objective function value:

[0145]

[0146] In the formula, e is the number of iterations, P i L is the load of node i;

[0147] That is, if the objective function value is the above formula, the currently found energy supply path is valid and is recorded as the fth energy supply path of cell m

[0148]

[0149] in, The solution obtained by solving the mixed integer programming model for the gth time is used, and the next iteration is performed. Otherwise, it is considered that there are no other energy supply paths for m in the system, and the iteration is stopped.

[0150] Let f = f + 1. In the next iteration, the energy supply path obtained in this iteration needs to be removed from the iteration. The specific method is to add a non-repetitive constraint as shown below:

[0151]

[0152] That is, the non-repetitive constraint requires that the previously obtained energy supply path cannot appear again. For the new model after adding the non-repetitive constraint, the new objective function value is re-solved, and then the validity of the energy supply path is continued to be judged according to the above steps. This iteration is carried out until all energy supply paths for all node cells are found.

[0153] Step S30: According to the energy supply path, an analytical method is used to calculate the node cell power outage time probability and the node cell maintenance time probability.

[0154] After obtaining all the energy supply paths of the node cells through the above steps, the present invention adopts an analytical calculation method to solve the probability event of the cell power outage time during the accident and the probability event of the cell maintenance time after the accident, so as to obtain the probability of the event. The specific steps are as follows: Figure 7 As shown:

[0155] Step S301, according to the energy supply path, obtaining the probability event of power outage time of node cells during the accident and the probability event of maintenance time of node cells after the accident.

[0156] Step S302, obtaining the node cell power outage time probability according to the node cell power outage time probability event in the accident, and obtaining the node cell repair time probability according to the node cell repair time probability event after the accident.

[0157] First, we obtain the probability event of the power outage time of the cell in the accident, which can be summarized into the following two cases: 1) Fault in the cell; 2) No fault in the cell, but all energy supply paths fail. It can be easily seen that these two events are disjoint. Therefore, the power outage time of cell k in the accident is t D The probability event can be expressed by the following two disjoint events:

[0158] Event.1: The internal circuit of cell k at t F =T D -t D All energy supply paths are normal at t F -1, at least one of them is intact and F All failures at the moment, T D is the duration of the entire natural disaster. It can be expressed as a probability event:

[0159]

[0160] in, For the line set Set, at least one line has a fault at time t, and for , p(k) is the total number of energy supply pathways of cell k.

[0161] Event.2: Cell k at t F -1=T D -t D -1 time, the power supply is normal, but at t F =T D -t D At time instant, a fault occurs in the line in cell k. This can be expressed as a probabilistic event:

[0162]

[0163] At this time, the probability of power outage time in the accident can be expressed as:

[0164]

[0165] Among them, t D is the power outage time of node cell k in the accident, The power outage time of node cell k in the accident is t D probability.

[0166] Secondly, obtain the probability event of cellular maintenance time after the accident, which can be summarized into the following two situations:

[0167] Event.3: The internal repair time of cell k is greater than or equal to t R The lines are not damaged, and all energy supply paths have a maintenance time greater than or equal to t R The line is faulty, but there is an energy supply path and the internal line has no maintenance time greater than t R Line fault (only the energy supply path takes time t R ). It can be expressed as a probability event:

[0168]

[0169] Among them, T D The duration of the entire natural disaster. k (t R ) is the internal maintenance time of cell k greater than or equal to t R The line collection of The internal maintenance time of the i-th energy supply path of cell k is greater than or equal to t R , p(k) is the total number of energy supply pathways of cell k.

[0170] Event.4: There is maintenance time t inside cell kR The line failure and no maintenance time is greater than t R There is a line fault, and there is an energy supply path with an internal line that has no maintenance time greater than t R Failure (repair of the internal route of the cell takes time t R ). It can be expressed as a probability event:

[0171]

[0172] At this point, the probability of repair time after the accident can be expressed as:

[0173]

[0174] Among them, t R is the repair time of cell k after the accident, The repair time of cell k after the accident is t R probability.

[0175] Step S40, obtaining a resilience assessment index of the power system according to the node cell outage time probability and the node cell maintenance time probability, wherein the resilience assessment index includes a first resilience assessment index of the distribution system and a second resilience assessment index of the transmission system.

[0176] Since the node cells are divided into distribution node cells and transmission node cells, the resilience assessment index of the power system obtained according to the above probability events can be obviously divided into the assessment index of the distribution system and the assessment index of the transmission system. The values ​​of the two may be different, but the calculation method is the same. The steps are as follows: Figure 8 As shown:

[0177] Step S401, obtaining the expected duration of power outage of the node cell according to the power outage time probability of the node cell.

[0178] Step S402: obtaining the node cell maintenance time expectation according to the node cell maintenance time probability.

[0179] Step S403, obtaining the system load loss expectation according to the load of the node cell, the expected power outage duration of the node cell and the expected maintenance time of the node cell.

[0180] Step S404: taking the expected duration of power outage of the node cell, the expected maintenance time of the node cell and the expected load loss of the system as indicators for evaluating the resilience of the power system.

[0181] The evaluation indicators for the distribution system and transmission system that reflect the responses before, during and after a disaster can be set as:

[0182] 1) The expected duration of power outage for each cell in the accident E(t D ), which is used to characterize the performance of the system in an accident.

[0183] 2) The expected maintenance time of each cell after the accident E(t R ), which is used to characterize the performance of the system after an accident.

[0184] 3) The load P carried by each cell is known k , multiplied by the expected power outage time of each cell (i.e., the sum of the expected power outage time during the accident and the expected maintenance time after the accident), the expected value of system load loss E can be obtained. Loss , used to characterize the resilience level of the entire distribution network and for reference in pre-accident planning.

[0185] According to the above probability formula, we can get the expressions of three evaluation indicators, among which the expected duration of power outage of cell k in the accident is E(t D ) can be expressed as:

[0186]

[0187] Among them, t D is the power outage time of node cell k in the accident, The power outage time of node cell k in the accident is t D The probability of D The duration of the natural disaster.

[0188] The expected repair time of cell k after the accident is E(t R ) can be expressed as:

[0189]

[0190] Among them, t R is the maintenance time of node cell k after the accident, The maintenance time of node cell k after the accident is t R The probability of R The maximum time required to repair the system.

[0191] System load loss expectation value E Loss It can be expressed as:

[0192]

[0193] in, is the expected load loss of node cell k, K is the set of node cells, P i is the load of node i, and I(k) is the set of nodes in node cell k.

[0194] After obtaining the above three types of indicators, the approximate function curve of the system can be characterized according to the evaluation indicators, and then the response of the system in each stage of natural disasters can be directly reflected. The function curve uses time as the horizontal axis and system function as the vertical axis, and the system function is taken as the load carried by the system. The above time expectation indicators are superimposed from small to large to simulate the process of system load loss in disasters and the gradual recovery of load after disasters, and finally obtain the approximate system function curve. This curve fully reflects the fault evolution in the accident and the maintenance and recovery after the accident, and the final indicator system load loss expectation is expressed in the figure as the area surrounded by the straight line of the descending part of the curve and the original normal operation, which intuitively reflects the system's resilience index.

[0195] Step S50: evaluating the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience evaluation index.

[0196] After obtaining the indicators of the distribution system and the transmission system that can directly reflect the resilience of the system, it is necessary to evaluate the entire power system based on the response characteristics between the distribution system and the transmission system. The specific steps are as follows: Fig. 9 As shown:

[0197] Step S501: obtaining a function curve of the power distribution system according to a first resilience evaluation index of the power distribution system.

[0198] Step S502: obtaining a function curve of the power transmission system according to a second resilience evaluation index of the power transmission system.

[0199] Step S503: obtaining a function curve of the power system according to the response characteristics between the power distribution system and the power transmission system, the first resilience evaluation index, and the second resilience evaluation index.

[0200] The evaluation of the power system in the present invention is actually to conduct different evaluations according to different objects of concern. When the object of concern is the distribution system, the influence of the upstream transmission lines is not considered. It is only necessary to save the evaluation indicators of the distribution system, and finally obtain the system function curve of the distribution system reflecting the response of each stage before, during and after the disaster, that is, the resilience of the distribution system is evaluated.

[0201] When the object of concern is the transmission system, the impact of the downstream distribution lines is not considered. It is only necessary to save the evaluation indicators of the transmission system and finally obtain the system function curve of the transmission network that reflects the response of the transmission network in each stage before, during and after the disaster. At this time, the result of the transmission system resilience assessment is obtained.

[0202] When the object of concern is the entire power system, it is necessary to combine the transmission system with the distribution system. First, consider the probability of the power outage time probability event at the downstream nodes of the transmission system. When the probability event of a power outage occurs, all downstream nodes will be out of power, and the impact of the distribution system does not need to be considered at this time. When the probability event of a power outage time of 0 is considered, it is necessary to consider the performance of the downstream distribution system under the disaster, search for all feeder lines under the node, and calculate the power outage time probability event and maintenance time probability event of each load node of the distribution line in the natural disaster. Considering the above situation, solve the expected value of the loss of load of the entire system, and finally obtain the evaluation indicators and system function curves of the entire system before, during and after the disaster, that is, the resilience of the entire power system is evaluated.

[0203] The following example illustrates the resilience assessment of the distribution system. The improved IEEE-13 node distribution system has a total of 1 substation node, 12 load nodes and 8 switch lines. Tie switch lines 4-9, 6-7 and 11-12 are added as normally open switches. For specific parameters, please refer to Fig.10 .

[0204] The original topology structure is simplified into 6 node cells according to the switch circuit, and the simplified topology structure is obtained, which is as follows: Fig.11 As shown, according to the above evaluation steps, the evaluation index results shown in Table 1 can be obtained:

[0205]

[0206] Table 1 Evaluation index results of IEEE13 node example

[0207] The expected load loss of the distribution network system in Table 1 is 1.0905×104kWh, which can be used as a reference for network planning. From the results of the intermediate indicators, it can be seen that when the node is located upstream of the power supply, such as cell 2, the power outage time is shorter than that of the downstream cells, such as cells 5 and 6. This is because the failure time of the node located downstream is related to the upstream node. When the upstream node fails, the downstream will also be affected. Based on this, the evaluation indicators can be used to place important loads upstream in the network planning stage, and the length between the power supply and all nodes can be minimized.

[0208] According to the above evaluation indicators, the function curve of the IEEE-13 node example system can be depicted, such as Fig.12As shown in the figure, the system function curve of the distribution system represents the most likely response of the distribution network and is the expected value of all possible scenarios. At 3.879 hours after the natural disaster began, cell 5 failed, resulting in a decrease in system load and a power outage in the system. Since then, the system load has continued to decrease until it reaches 0 due to the evolution of the fault. This is because under the expectation of all fault scenarios, each cell may lose power, causing the system to completely lose load. The probability of all faults occurring in the actual fault scenario is very low. When the natural disaster ends at 12 hours, the maintenance phase begins. At 13.59 hours, cell 2 resumes power supply, the system load increases, and the system function gradually recovers. After cell 3 resumes power supply, all cells resume power supply, and the distribution network resumes normal operation. It can be seen that the approximate system function diagram drawn by the above three types of evaluation indicators fully reflects the fault evolution in the accident and the maintenance and recovery process after the accident, and the expected loss of load of the distribution network is represented in the figure as the area surrounded by the straight line of the descending part of the curve and the original normal operation, which intuitively reflects the level of resilience of the distribution network and can be used as a reference for planning before the accident.

[0209] The present invention provides a multi-level resilience assessment method for power systems based on analytical methods. Compared with traditional methods that only focus on distribution systems and ignore the problem of transmission systems, the present invention combines the distribution system with the transmission system, analyzes various scenarios based on analytical methods, and comprehensively considers the responses at all levels, thereby providing a quantitative basis for system planning, operation scheduling and recovery decisions.

[0210] See also Fig.13 Based on the same inventive concept, a second embodiment of the present invention proposes a multi-level resilience assessment system for a power system based on an analytical method, comprising:

[0211] The topology simplification module 10 is used to obtain a first topology of a distribution system and a second topology of a transmission system, and simplify the first topology and the second topology respectively according to node cells, wherein the node cells include distribution node cells and transmission node cells.

[0212] The energy supply path search module 20 is used to establish a mixed integer programming model, and to search the simplified first topological structure and the simplified second topological structure through the mixed integer programming model to obtain the energy supply path of the node cell.

[0213] The probability calculation module 30 is used to calculate the node cell power outage time probability and the node cell maintenance time probability by using an analytical method according to the energy supply path.

[0214] The evaluation index calculation module 40 is used to obtain the resilience evaluation index of the power system according to the node cell power outage time probability and the node cell maintenance time probability, and the resilience evaluation index includes a first resilience evaluation index of the distribution system and a second resilience evaluation index of the transmission system.

[0215] The resilience assessment module 50 is used to assess the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience assessment index.

[0216] The technical features and technical effects of the multi-level resilience assessment system for power systems based on analytical methods proposed in the embodiments of the present invention are the same as the methods proposed in the embodiments of the present invention, and will not be described in detail here. Each module in the above-mentioned multi-level resilience assessment system for power systems based on analytical methods can be implemented in whole or in part through software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0217] In summary, an embodiment of the present invention proposes a method and system for evaluating the multi-level resilience of an electric power system based on an analytical method. The method obtains a first topological structure of a distribution system and a second topological structure of a transmission system, simplifies the first topological structure and the second topological structure according to node cells, and the node cells include distribution node cells and transmission node cells; establishes a mixed integer programming model, searches the simplified first topological structure and the simplified second topological structure through the mixed integer programming model, and obtains an energy supply path of the node cells; according to the energy supply path, calculates the node cell power outage time probability and the node cell maintenance time probability by an analytical method; obtains a resilience evaluation index of the electric power system according to the node cell power outage time probability and the node cell maintenance time probability, and the resilience evaluation index includes a first resilience evaluation index of the distribution system and a second resilience evaluation index of the transmission system; and evaluates the resilience of the electric power system according to the response characteristics between the distribution system and the transmission system and the resilience evaluation index. The present invention comprehensively considers the responses of the transmission system and the distribution system under natural disasters, combines the two-level systems, and analyzes the resilience level of the entire power system under natural disasters through the analytical method of failure probability. It can be effectively applied to the assessment process of the resilience of the power system, provides a quantitative basis for system planning, operation scheduling and recovery decision-making, and minimizes load losses, thereby improving the safety level of the power system.

[0218] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be directly referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above-mentioned embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0219] The above-mentioned embodiments only express several preferred implementation modes of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in the technical field, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be regarded as the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be based on the protection scope of the claims.

Claims

1. A multi-level resilience assessment method for power systems based on analytical methods, characterized in that: include: Acquire a first topology structure of a power distribution system and a second topology structure of a power transmission system, and simplify the first topology structure and the second topology structure respectively according to node cells, wherein the node cells include distribution node cells and transmission node cells; Establishing a mixed integer programming model, searching the simplified first topological structure and the simplified second topological structure through the mixed integer programming model to obtain an energy supply path of the node cell; According to the energy supply path, an analytical method is used to calculate the node cell power outage time probability and the node cell maintenance time probability; According to the node cell outage time probability and the node cell maintenance time probability, a resilience evaluation index of the power system is obtained, wherein the resilience evaluation index includes a first resilience evaluation index of the distribution system and a second resilience evaluation index of the transmission system; Evaluating the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience evaluation index; The step of acquiring a first topology structure of the power distribution system and a second topology structure of the power transmission system, and simplifying the first topology structure and the second topology structure according to node cells respectively comprises: According to a first topology network of a power distribution system and a second topology network of a power transmission system, the components in the power distribution system and the components in the power transmission system are divided according to component types, wherein the component types include a power distribution component type and a power transmission component type; A set of all connected nodes without switch lines is used as a node cell, and the first topology network and the second topology network are simplified according to the node cells.

2. The method for evaluating the multi-level resilience of a power system based on analytical methods according to claim 1 is characterized in that: The step of establishing a mixed integer programming model and searching the simplified first topological structure and the simplified second topological structure through the mixed integer programming model to obtain the energy supply path of the node cell comprises: Establishing an objective function according to the energy supply path of the node cell, and adding constraints to the objective function, wherein the constraints include power distribution constraints and power transmission constraints; Establishing a mixed integer programming model according to the objective function and the constraint conditions; The mixed integer programming model is iteratively calculated to obtain the energy supply path of the node cell.

3. The method for evaluating the multi-level resilience of a power system based on analytical methods according to claim 2 is characterized in that: The objective function is expressed by the following formula: In the formula, x i is the reference variable of whether the load of node i is in the system, P i L is the load of node i, I(m) is the set of nodes in node cell m; The constraint condition is expressed by the following formula: In the formula, is a reference variable for whether the energy supply path passes through the route from node cell s to node cell t, is a reference variable for whether the energy supply path passes through the route from node cell t to node cell s, is a reference variable for whether the energy supply path passes through the route from node cell k to node cell m, is a reference variable for whether the energy supply path passes through the route from node cell m to node cell k, KS is the power node cell set, K is the node cell set, B is the line set, and m is the target node cell; In the formula, x s is the reference variable for whether the energy supply path passes through the node cell s, is the reference variable for whether the line (i, j) has restored power supply, I(s) is the set of nodes in the node cell s, and Bs is the set of all lines in the node cell s; In the formula, I is the set of system nodes, M(i) and N(i) represent the parent node and child node sets of node i respectively, and P i,j is the active power flowing through line (i, j), represents the upper limit of active power flowing through line (i, j), P i g represents the active power injected by the i-node substation, P i gmax Indicates the upper limit of active power of the i-node substation; Where P i,j , Q i,j is the active power and reactive power flowing through line (i, j), and are the upper limits of active power and reactive power flowing through line (i, j), P i g and are the active power and reactive power injected by the i-node substation, P i gmax and are the upper limits of active power and reactive power of the i-node substation, U i is the actual voltage at node i, and are the upper and lower limits of the voltage amplitude at node i, is the reference voltage of line (i, j), R i,j With X i,j are the resistance and reactance of line (i, j).

4. The analytical method for evaluating the multi-level resilience of a power system according to claim 3, characterized in that: The step of iteratively calculating the mixed integer programming model to obtain the energy supply path of the node cell includes: Calculating the mixed integer programming model to obtain an objective function value, and obtaining an energy supply path of a node cell according to the objective function value; Adding non-repetitive constraints to the mixed integer programming model, and performing iterative calculations on the mixed integer programming model with the non-repetitive constraints according to an iteration condition to obtain all energy supply paths of the node cells; The objective function value is expressed by the following formula: In the formula, e is the number of iterations, P i L is the load of node i; The following formula is used to represent the energy supply path of the node cell: In the formula, is the fth energy supply path of node cell m, is the solution obtained by solving the mixed integer programming model for the gth time; The non-repetitive constraint is expressed by the following formula: In the formula, It is the τth energy supply path of node cell m.

5. The method for evaluating the multi-level resilience of a power system based on analytical methods according to claim 1, characterized in that: The step of calculating the node cell power outage time probability and the node cell maintenance time probability by using an analytical method according to the energy supply path comprises: According to the energy supply path, obtaining a probability event of power outage time of a node cell during an accident and a probability event of maintenance time of a node cell after an accident; According to the node cell power outage time probability event in the accident, the node cell power outage time probability is obtained, and according to the node cell maintenance time probability event after the accident, the node cell maintenance time probability is obtained.

6. The analytical method for evaluating the multi-level resilience of a power system according to claim 5, characterized in that: The step of obtaining the resilience evaluation index of the power system according to the node cell power outage time probability and the node cell maintenance time probability comprises: According to the power outage time probability of the node cell, the expected power outage duration of the node cell is obtained; According to the node cell maintenance time probability, the node cell maintenance time expectation is obtained; Obtaining the system load loss expectation according to the load of the node cell, the expected duration of the power outage of the node cell and the expected maintenance time of the node cell; The expected duration of power outage of the node cell, the expected maintenance time of the node cell and the expected load loss of the system are used as the resilience evaluation indicators of the power system.

7. The analytical method for evaluating the multi-level resilience of a power system according to claim 6, characterized in that: The expected duration of power outage of the node cell is calculated using the following formula: In the formula, t D is the power outage time of node cell k in the accident, The power outage time of node cell k in the accident is t D The probability of D The duration of the natural disaster; The expected maintenance time of the node cell is calculated using the following formula: In the formula, t R is the maintenance time of node cell k after the accident, The maintenance time of node cell k after the accident is t R The probability of R The maximum time required to repair the system until it is fully recovered; The system load loss expectation is calculated using the following formula: In the formula, is the expected load loss of node cell k, K is the set of node cells, P i is the load of node i, and I(k) is the set of nodes in node cell k.

8. The analytical method for evaluating the multi-level resilience of a power system according to claim 1, characterized in that: The step of evaluating the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience evaluation index comprises: Obtaining a function curve of the power distribution system according to a first resilience evaluation index of the power distribution system; Obtaining a function curve of the power transmission system according to a second resilience evaluation index of the power transmission system; A function curve of the power system is obtained according to the response characteristics between the power distribution system and the power transmission system, the first resilience evaluation index, and the second resilience evaluation index.

9. A multi-level resilience assessment system for power systems based on analytical methods, characterized in that: include: A topology simplification module, used to obtain a first topology of a power distribution system and a second topology of a power transmission system, and simplify the first topology and the second topology respectively according to node cells, wherein the node cells include distribution node cells and transmission node cells; The step of acquiring a first topology structure of the power distribution system and a second topology structure of the power transmission system, and simplifying the first topology structure and the second topology structure according to node cells respectively comprises: According to a first topology network of a power distribution system and a second topology network of a power transmission system, the components in the power distribution system and the components in the power transmission system are divided according to component types, wherein the component types include a power distribution component type and a power transmission component type; A set of all connected nodes without switch lines is used as a node cell, and the first topology network and the second topology network are simplified according to the node cells; An energy supply path search module is used to establish a mixed integer programming model, and to search the simplified first topological structure and the simplified second topological structure through the mixed integer programming model to obtain an energy supply path of the node cell; A probability calculation module, used to calculate the node cell power outage time probability and the node cell maintenance time probability by using an analytical method according to the energy supply path; An evaluation index calculation module is used to obtain a resilience evaluation index of the power system according to the node cell power outage time probability and the node cell maintenance time probability, wherein the resilience evaluation index includes a first resilience evaluation index of the distribution system and a second resilience evaluation index of the transmission system; The resilience assessment module is used to assess the resilience of the power system according to the response characteristics between the power distribution system and the power transmission system and the resilience assessment index.

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