A method for assessing power grid vulnerability taking into account urban water supply services

Abstract

This invention belongs to the field of power system security, and particularly relates to a method for assessing grid vulnerability that takes into account urban water supply services. The method comprises the following steps: 1: constructing a model of the urban power grid and the urban water network; 2: considering the dual grid-water network coupling relationship, analyzing the coupling characteristics of the urban power grid and the urban water network; 3: constructing a cross-layer coupled network model of the urban power grid and the water network; and 4: assessing grid vulnerability that takes into account the loss of urban water supply services based on this cross-layer coupled network model. The model established in this invention supports the analysis of multi-layer fault transmission effects in the power grid and water network, laying the foundation for studying coordinated defense of power-water coupled networks and exploring urban power grid restoration strategies that consider water supply services after disaster scenarios.

Description

Technical Field

[0001] The present invention belongs to the field of power system security, and in particular relates to a power grid vulnerability assessment method taking urban water supply services into account. Background Art

[0002] As infrastructure connectivity continues to improve, the dependence of infrastructure such as water supply, transportation, and natural gas on the power system continues to deepen. If the power system suffers a disaster or deliberate attack, the increasing coupling between power-communications, power-water supply, and power-transportation systems can cause the failure to spread and even trigger a domino effect. Power infrastructure is crucial to the normal operation of cities.

[0003] Modeling coupled urban power grids and water networks is fundamental to assessing the vulnerability of urban power grids under extreme scenarios, including those related to water supply. In recent years, due to the increasing incidence of extreme scenarios such as natural disasters, extensive research has been conducted domestically and internationally on the interconnectedness of urban infrastructure. When studying the interdependencies of urban infrastructure, scholars have categorized the interdependencies between heterogeneous networks into four categories: functional, informational, geographic, and logical. When studying coupled power grids and water networks, most domestic and international researchers focus on modeling their functional coupling. In actual urban power grid-water network coupling, the functional coupling exhibits a hierarchical coupling characteristic based on regional voltage levels. In the backbone network, water booster stations, due to their scale and importance, are powered by urban high-voltage distribution substations. The water network provides cooling water for the power system's power generation units. On the user side, urban medium-voltage distribution transformers provide power to water pumps in high-rise buildings. Some experts have constructed a virtual grid-water network coupling model based on complex network theory, arguing that the failure of any power node in the grid-water network will cause the failure of its coupled water network node with a certain probability. However, in a real grid-water network coupling, only specific water network components, such as pumping stations, are coupled to the grid, leading to fault transmission effects. Other researchers have developed a coupled model of power and water supply backbone networks, considering the functional coupling relationship between substations and water network pumping stations. They have proposed a unified dependency matrix to describe the one-to-one and many-to-one dependencies between substations and pumping stations in a real grid-water network coupling. However, because this model only considers large-scale grid-water backbone networks, it does not consider the coupling relationship between transformers and water pumps on the user side. Some literature considers the functional coupling between distribution network transformers and water distribution network pumps, establishing a one-to-one correspondence between the two, which is inconsistent with the "many-to-one" and "one-to-many" interdependencies in real networks. Some literature considers the booster pump on the end-user side of water use and establishes two coupling modes between the distribution network transformer and the water pump, thereby characterizing the power grid-water network coupling relationship between the distribution network transformer and the user. However, the coupling relationship between the high-voltage distribution substation and the booster pump station is not specifically discussed.

[0004] Current modeling of coupled power-water networks focuses on either the power-water network backbone or the user side. The former cannot analyze the impact of power grid failures on the user side of the water supply, while the latter cannot be used to assess the impact of urban high-voltage distribution network failures on urban water supply. Furthermore, due to the complex coupling relationships and large scale of the distribution network layer, current superposition coupling models are impractical. Therefore, in order to rapidly assess the impact of urban power grids on user-side water supply, further research is needed to establish a cross-layer coupled network model for urban power-water networks. Summary of the Invention

[0005] To address the current problems, the present invention constructs an urban power grid model and an urban water network model respectively, considers the dual power grid-water network coupling relationship of high-voltage distribution substations and water network booster pump stations, medium-voltage distribution transformers and user-side high-rise water pumps, establishes an urban power grid-water network cross-layer coupling network model, and quickly evaluates the impact of the urban high-voltage distribution network on the user-side water supply, thereby evaluating the vulnerability of the urban power grid taking into account the loss of water supply service under intentional attack scenarios.

[0006] The present invention discloses a method for assessing the vulnerability of a power grid taking into account the loss of urban water supply services. The method uses an urban power grid-water network cross-layer coupling network model to assess the impact of a failure in an urban high-voltage distribution network on water users, thereby calculating the vulnerability of the power grid taking into account the loss of urban water supply services. The method specifically includes the following steps:

[0007] Step 1: Construct urban power grid model and urban water network model;

[0008] Step 2: Considering the dual power grid-water network coupling relationship, analyze the coupling characteristics of the urban power grid and urban water network;

[0009] Step 3: Construct a cross-layer coupled network model of the urban power grid and water network;

[0010] Step 4: Based on the urban power grid and water network cross-layer coupled network model, assess the grid vulnerability taking into account the loss of urban water supply services.

[0011] Preferably, the urban power grid model in step 1 specifically includes a power system topology model and a power system energy flow model; the urban water network model specifically includes a water network topology model and a water network energy flow model.

[0012] Preferably, the power system topology model specifically includes a city backbone power grid model and a city medium-voltage distribution network model; wherein the city backbone power grid is composed of a transmission network and a high-voltage distribution network, and the model is as follows:

[0013]

[0014] In the above formula, V p,g For power plant assembly, V p,tis the set of substations of various voltage levels in the power system, E p,l is the set of power lines, n pg 、n pt and n pl Represent the number of power plants, substations and power lines respectively.

[0015] The urban medium-voltage distribution network adopts a closed-loop design and open-loop operation, and its typical structure is radial.

[0016] Preferably, the power system energy flow model is as follows:

[0017]

[0018]

[0019] F l n ≤F l ≤F l m ,l∈E p,l (4)

[0020]

[0021] Wherein, formula (2) represents the line power flow equation, A is the grid branch association matrix; formula (3) represents the node power flow balance equation, P g,n represents the generator output of node n, Pd n represents the load of node n; formulas (4)-(5) are the line flow constraints and generator output constraints, where and Indicates the upper and lower limits of line capacity, and Indicates the upper and lower limits of the output of generator i.

[0022] Preferably, the water network topology model includes a water supply backbone network model and a user-side water supply model; wherein the water supply backbone network model is as follows:

[0023]

[0024] In the above formula, V ws 、V w,p and V w,d are the water source, pumping station and water demand node set of the water network, E w,l is the collection of water distribution pipe sections, n ws 、n wp and n wd Represent the number of water sources, pumping stations and water demand nodes respectively;

[0025] During the user-side water supply process, tap water reaches the end user side through the city's water distribution pipeline. The water supply methods are divided into: 1) Primary water supply: the water company directly supplies water and realizes water supply while meeting the pressure of the tap water network; 2) Secondary water supply: secondary pressurization is carried out on the basis of primary water supply to meet the needs of high-level users.

[0026] High-rise building water supply often involves vertically zoned water distribution along the building's vertical axis, ensuring uniform and moderate water pressure in water equipment and supply pipes. Currently, two secondary water supply methods are used in high-rise buildings: 1) secondary pressurization of municipal tap water to rooftop tanks for supply; and 2) non-negative pressure water supply, which divides the high-rise building into zones and installs booster pumps within each zone, directly pressurizing water based on municipal water pressure. Because method 2 (water supply method 2) lacks a water tank and avoids water contamination, it is currently more commonly used. Therefore, this paper models method 2 (water supply method 2) for high-rise buildings. The user-side water supply model is shown below:

[0027] The user-side water supply model is as follows:

[0028]

[0029] Preferably, the water network energy flow model has the following formula:

[0030] A w Q+Q D =0 (8)

[0031]

[0032] Β w ΔH=0 (10)

[0033] Among them, formula (8) is the node flow equation group, A w is the correlation matrix of the water network, Q is the m×1 vascular segment flow vector, Q D is the n×1-dimensional node flow vector. According to the law of conservation of mass, the sum of the flow values ​​of water flowing into a node should be equal to the sum of the flow values ​​of water flowing out of the node. Equation (9) is the pipe section pressure drop equation group, H is the node head vector, ΔH is the pipe section pressure drop vector. According to the law of conservation of energy, the pressure drop of any pipe section ij connecting node i and node j is equal to the difference in head between node i and node j. Equation (10) is the ring energy equation group, B w is the loop matrix of the water network. In a meshed water network, pipe sections are interconnected to form closed loops, and the algebraic sum of the head losses in each loop must be zero.

[0034] The present invention adopts the node equation solution method, firstly stipulates the constant water head of the water source, gives priority to satisfying the ring energy equation, and then satisfies the node flow continuity equation by adjusting the water head.

[0035] Preferably, the analysis of the coupling characteristics of the urban power grid and the urban water network in step 2 specifically includes: a power grid-water network backbone coupling model and a power grid-water network user side coupling model; wherein the power grid-water network backbone coupling model specifically includes: a power grid-water network backbone topology coupling model and a power grid-water network backbone energy coupling model;

[0036] The topological coupling model of the power grid and water network backbone network can be expressed by the correlation matrix E pt→ps express:

[0037]

[0038] According to formula (11), when When , the high-voltage distribution substation i and the booster pump station j form a "one-to-one" coupling relationship; when When , the high-voltage distribution substation and the booster pump station j form a "many-to-one" coupling relationship.

[0039] The energy coupling model of the power grid and water network backbone is as follows:

[0040]

[0041] In the above formula, η m is the power factor of pumping station m;

[0042] In the power grid-water network user side coupling model, a medium-voltage distribution transformer may provide power support for n high-rise building water pumps. The available dependency edge set It is represented as shown in formula (13):

[0043]

[0044] Formula (13) shows that the medium voltage distribution transformer j and the high-rise water pump set V bp Form a "one-to-many" coupling relationship.

[0045] The dependence relationship between the distribution transformer and the water pump power supply of the high-rise building is a "one-to-n" coupling relationship, which can be expressed by the correlation matrix E dn→bp Indicates that E dn→bp The element value is defined as shown in formula (14):

[0046]

[0047] From formula (14), we can see that That is, the medium-voltage distribution transformer j and the high-rise building water pumps within its power supply range form a "one-to-many" coupling relationship.

[0048] Preferably, the urban power grid-water network cross-layer coupling network model in step 3 specifically includes:

[0049] Due to its radial topological properties, the operation of the urban medium-voltage distribution network depends on the high-voltage distribution substation, which is represented by the dependent edge set, as shown in formula (15):

[0050]

[0051] Formula (15) shows that the high-voltage distribution substation node i provides power support for the set of medium-voltage distribution transformers within its power supply range.

[0052] When constructing the city-level power grid and water network coupling network, the dependency relationship of all high-rise building water pumps within the power supply range of the high-voltage distribution substation on the medium-voltage distribution transformer is equivalent to its dependency relationship with the high-voltage distribution substation i, forming a coupling relationship across multiple voltage levels, and using the mutual dependence edge set express:

[0053]

[0054] Formula (16) shows that the high-voltage distribution substation i and the high-rise building pump set V within its power supply range bp Form a one-to-many coupling relationship.

[0055] Preferably, the evaluation process of step 4 specifically includes: construction of an evaluation index system, analysis of power grid emergency dispatch under intentional attack scenarios, and consequences of urban power grid-water network fault transmission.

[0056] The present invention establishes a city electricity-water cross-layer coupling network model, considers the Nk intentional attack scenario, analyzes the city electricity-water fault conduction effect from the perspective of system operation characteristics, and calculates the grid vulnerability EI of the intentional attack scenario k. k , the evaluation index system is shown in formula (17):

[0057]

[0058] In the above formula, ω1 and ω2 represent the weights of the power grid and water network supply reduction percentages in the vulnerability assessment, which are related to the degree of importance the assessor attaches to the two lifeline facilities of the power grid and water network; ΔPd n and ΔWD m It represents the load loss of grid node n and the water loss of water demand node m after the intentional attack.

[0059] Considering the intentional attack scenario of Nk, the attacked node is taken as the decision variable, and the constraints are shown in formula (18):

[0060]

[0061] Where: a n represents the attack decision variable of node n, a MRepresents the sum k of the number of attacked nodes in this failure scenario.

[0062] After the urban power grid suffers a deliberate attack, the system dispatcher adopts the optimal load shedding defense measure under the current system damage situation. The objective function is to minimize the weighted load shedding loss of the system emergency dispatch, as shown in formula (19):

[0063]

[0064] Where PI n represents the importance of node n, ΔPd n Indicates the load shedding amount of node n.

[0065] The constraints are shown in equations (20)-(23):

[0066]

[0067]

[0068] 0≤ΔP g,i ≤P g,i ,i∈V p,g (twenty two)

[0069] 0≤ΔPd n ≤Pd n ,n∈V p (twenty three)

[0070] Equation (20) represents the line power flow equation. The power flow state of line l depends on the line state z l ; Equation (21) is the node power flow balance equation; Equations (22)–(23) are the generator and node load shedding constraints respectively.

[0071] In formula (20), the line state z l The system node status z after the deliberate attack n The calculation steps are as follows:

[0072] (1) Obtain the status z of each node in the network n

[0073] After a deliberate attack occurs, the state of the node is not only affected by the attack decision variable a n The influence of the adjacent node state z c As shown in formula (24):

[0074]

[0075] Where z n Represents the state of node n; V c represents the set of adjacent nodes connected to node n in the network, zc Represents the state of node c connected to node n.

[0076] (2) Obtain the status of each line in the network l

[0077] The state of each line in the network is related to the state of each node, as shown in formula (25):

[0078]

[0079] Where, Characterizes the initial state of line l, z l Characterizes the state of line l. Formula (25) shows that when Under the condition that node n and its adjacent node c are intact at the same time, line l nc The status is 1 if yes, 0 otherwise.

[0080] Preferably, in the grid vulnerability assessment method considering urban water supply services, the urban grid-water network fault conduction consequence analysis is divided into three levels: substation-pumping station fault conduction consequence analysis, pumping station-node water head fault conduction consequence analysis, and substation, node water head-water supply conduction consequence analysis. The corresponding formulas are:

[0081] X p =T E→p (X t ) (26)

[0082] H=T p→H (X p ) (27)

[0083] Q D =T H→Q (X t ,H) (28)

[0084] The advantages of the present invention are:

[0085] Considering the dual coupling of the power grid-water network backbone coupling model and the power grid-water network user-side coupling model, and considering various coupling modes such as one-to-one power-water supply, partial many-to-one, and partial one-to-many, a cross-layer coupled network model for the urban power grid-water network is proposed. This model supports the analysis of multi-layer fault transmission effects in the power grid-water network, laying the foundation for assessing the impact of damage to the urban power grid on user-side water supply. When considering water supply services, the vulnerability of the urban power grid is affected by both the amount of power grid load loss and the amount of water loss in the water network. The amount of power grid load loss is mainly related to the topological location, importance, and load of the node. The amount of water loss in the water network is specifically related to the coupling relationship between the node and the water network trunk booster pump station, the water pumping service range and scale of the booster pump station, the number of high-rise buildings requiring secondary booster pumping within the node's power supply range, and the water consumption. This lays the foundation for studying the coordinated defense of power-water coupled networks and exploring urban power grid restoration strategies that consider water supply services after disaster scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is a flow chart of a method for assessing the vulnerability of power grids taking into account urban water supply services;

[0087] Figure 2 This is a schematic diagram of the water supply method for high-rise buildings on the user side;

[0088] Figure 3 It is a flow chart for water supply network adjustment calculation. DETAILED DESCRIPTION

[0089] The present invention will be described in detail below with reference to the accompanying drawings.

[0090] The present invention discloses a method for evaluating the vulnerability of a power grid taking into account the loss of urban water supply services. The method adopts a cross-layer coupling network model of an urban power grid and a water network to evaluate the impact of a failure of an urban high-voltage distribution network on the water supply user side, thereby calculating the vulnerability of the power grid taking into account the loss of urban water supply services. Figure 1 As shown, the specific steps include:

[0091] Step 1: Construct urban power grid model and urban water network model;

[0092] Step 2: Considering the dual power grid-water network coupling relationship, analyze the coupling characteristics of the urban power grid and urban water network;

[0093] Step 3: Construct a cross-layer coupled network model of the urban power grid and water network;

[0094] Step 4: Based on the urban power grid and water network cross-layer coupled network model, assess the grid vulnerability taking into account the loss of urban water supply services.

[0095] The urban power grid model specifically includes the power system topology model and the power system energy flow model; the urban water network model specifically includes the water network topology model and the water network energy flow model.

[0096] The power system topology model specifically includes a city backbone power grid model and a city medium-voltage distribution network model. The city backbone power grid consists of a transmission network and a high-voltage distribution network. Power plants, high-voltage transmission substations, and high-voltage distribution substations are considered nodes in the power grid, and the power lines connecting them are considered edges in the power grid for network topology modeling. The model is shown below:

[0097]

[0098] In the above formula, V p,g For power plant assembly, V p,t is the set of substations of various voltage levels in the power system, E p,l is the set of power lines, n pg 、n pt and n pl Represent the number of power plants, substations and power lines respectively.

[0099] The distribution system refers to the section of the power system from the low-voltage busbars of a high-voltage substation to the user end, typically in a radial configuration. Medium-voltage distribution transformers can draw power from one or two 10kV feeders, which can also connect to one or two high-voltage distribution substations, creating connections for single-source power, series power, and T-type series power. Distribution network data is characterized by widespread distribution, high volume, and low magnitude.

[0100] The power system energy flow model is as follows:

[0101]

[0102]

[0103] F l n ≤F l ≤F l m ,l∈E p,l

[0104]

[0105] Among them, the above formulas represent the line power flow equation, A is the power grid branch association matrix; the node power flow balance equation, P g,n represents the generator output of node n, Pd n represents the load of node n; line flow constraints and generator output constraints, where and Indicates the upper and lower limits of line capacity, and Indicates the upper and lower limits of the output of generator i.

[0106] The water network topology model includes a water supply backbone network model and a user-side water supply model. The water supply backbone network consists of a large number of water transmission and distribution pipes with diameters ranging from 50 mm to 2500 mm. Considering the bidirectionality of the water supply pipes, the water network can be abstracted as an undirected complex network. The water supply backbone network model is shown below:

[0107]

[0108] In the above formula, V w,s 、V w,p and V w,d are the water source, pumping station and water demand node set of the water network, E w,l is the collection of water distribution pipe sections, n ws 、n wp and n wd Represent the number of water sources, pumping stations and water demand nodes respectively;

[0109] During user-side water supply, the minimum service head at the user connection point is 10m for the first floor, 12m for the second floor, and 4m for each additional floor above the second. Cities with suitable conditions can appropriately increase the water pressure to meet the 28m service head requirement at the user connection point, equivalent to the minimum head required to deliver water to a six-story residence. Thus, tap water reaches the end user through the city's water distribution pipelines. Water supply methods are categorized as follows: 1) Primary water supply: Direct water supply by the water company, achieved while meeting the pressure of the tap water network; 2) Secondary water supply: Secondary pressurization is applied to the primary water supply to meet the needs of high-rise users.

[0110] The water supply of high-rise buildings is often divided into vertical zones along the high-rise buildings, so that the water pressure of the water equipment and water supply pipes is relatively uniform and moderate. At present, high-rise buildings use two secondary water supply methods: 1) the municipal tap water is pressurized to the water tank on the roof of the building for the second time and then supplied; 2) the high-rise building is divided into zones with no negative pressure, and pressurized water pumps are added in different zones to directly pressurize the water based on the municipal water pressure. Since the water supply method 2) does not have a water tank, it avoids water pollution and is currently used more frequently. Therefore, this paper models the water supply method 2) of high-rise buildings, as shown in the following details. Figure 2 shown.

[0111] The user-side water supply model is as follows:

[0112]

[0113] In this embodiment, the water network energy flow model considers the urban water network components mainly including water sources, water transmission and distribution pipe sections, pumping stations, and water demand nodes. The hydraulic characteristics of the pipe sections and pumping stations are comprehensively considered to perform the pipe network adjustment calculation;

[0114] The hydraulic characteristics of a pipe section refer to the relationship between the flow rate and the hydraulic head of the pipe section. They are closely related to the hydraulic properties and structural properties of the pipe section. The general form is as follows:

[0115] ΔH ij =s ij Q ij |Q ij | n-1 ,ij∈E w,l

[0116] In the above formula, ΔH ij is the pressure drop of the pipe section, that is, the energy loss caused by water flowing through the pipe section; s ij is the pipeline friction coefficient, which is related to the properties of the pipe section itself; Q ij is the flow rate of the pipe section; n is the resistance index of the pipe section.

[0117] The Hazen-Williams formula is used as the head loss formula for the pipe section, where n = 1.852, s ij The value of is shown as follows:

[0118]

[0119] The formula for calculating the head loss of a pipe section is as follows:

[0120]

[0121] In the above formula, C w is the Hezen-Williams coefficient, which is related to the pipe material; D is the pipe diameter; l is the pipe length;

[0122] The hydraulic characteristics of a pump station increase the pressure on the water flow, allowing it to overcome the frictional resistance of the pipe walls and the elevation differences at the water point, ultimately reaching the user node with sufficient pressure. Rated speed centrifugal pumps are generally used in water networks. When operating at a fixed speed, the mathematical relationship between flow rate and head is similar to a parabola, as shown below:

[0123]

[0124] Where ΔH ij is the pump head (m); Q ij is the pump flow rate (m 3 / s); H e is the static head of the water pump; s pis the pump's internal resistance coefficient; n is a consistent parameter in the head loss formula. In a water supply network, a pumping station has multiple pumps, many of which operate in parallel. When multiple pumps operate in parallel, they exhibit overall hydraulic characteristics. When two or more pumps of the same model are connected in parallel, their hydraulic characteristics are as follows:

[0125]

[0126] Where N is the number of parallel pumps.

[0127] Pipeline network adjustment calculation, water supply system steady-state calculation is often called steady-state hydraulic calculation, pipe network adjustment calculation. Its basic task is to determine the unknown hydraulic parameters by solving the steady flow equations based on the given hydraulic parameters. It is shown below:

[0128] A w Q+Q D =0

[0129]

[0130] Β w ΔH=0

[0131] The above equations are node flow equations, A w is the correlation matrix of the water network, Q is the m×1 vascular segment flow vector, Q D is the n×1-dimensional node flow vector. According to the law of conservation of mass, the sum of the flow rates of water flowing into a node should be equal to the sum of the flow rates of water flowing out of the node; the pipe section pressure drop equations, H is the node head vector, ΔH is the pipe section pressure drop vector. According to the law of conservation of energy, the pressure drop of any pipe section ij connecting node i and node j is equal to the difference in head between nodes i and j; is the ring energy equations, B w is the loop matrix of the water network. In a meshed water network, pipe sections are interconnected to form closed loops, and the algebraic sum of the head losses in each loop must be zero.

[0132] The constraints are as follows:

[0133]

[0134]

[0135] Among them, the above formulas are the limits of water storage levels in water storage tanks and pressure limits of water demand nodes in the water network; and are the upper and lower bounds of the water storage height of the water storage tank s, which usually depend on the physical limitations of the water storage tank, and are the upper and lower bounds of the pressure at the water demand node k, respectively.

[0136] The present invention adopts the node equation solution method. First, a constant head is specified at the water source, which prioritizes the ring energy equation. Then, the head is adjusted to satisfy the node flow continuity equation. Since the pipe section pressure drop equation is a nonlinear equation, it is linearized.

[0137] make Substituting in:

[0138] Q ij =c ij (H i -H j )

[0139] By A w Q=-Q D , the above formula can be converted into matrix expression:

[0140] A w CΔH=-Q D

[0141] Then we can get:

[0142]

[0143] Since C is the expression of the pipe flow rate Q, it is necessary to iterate the above formula. The flow chart is as follows: Figure 3 Finally, the pressure H(m) of each water demand node can be calculated.

[0144] Analyze the coupling characteristics of urban power grids and urban water networks, including the power grid-water network backbone coupling model and the power grid-water network user-side coupling model. The power grid-water network backbone coupling model specifically includes the power grid-water network backbone topology coupling model and the power grid-water network backbone energy coupling model.

[0145] The rated voltage of the motors in urban pumping stations is mostly 10kV. In this paper, based on the importance of the pumping stations, it is assumed that each pumping station relies on one or two high-voltage distribution substations that are geographically closest to the grid. Considering the long duration of extreme scenarios, the short-term power supply of energy storage to the pumping station is ignored. The present invention establishes a fully functional coupling relationship between the coupling node substation and the pumping station. The dependence of the high-voltage distribution substation on the power supply of the pumping station is an "n-to-one" coupling relationship, which can be expressed using the correlation matrix E pt→ps Indicates that E pt→ps The element value definition is as follows:

[0146]

[0147] when When , the high-voltage distribution substation i and the booster pump station j form a "one-to-one" coupling relationship; when When , the high-voltage distribution substation and the booster pump station j form a "many-to-one" coupling relationship.

[0148] The power system provides electrical energy support to the pumping stations of the water network. The water pumps operated by the motors can be regarded as loads in the power grid. The installed capacity of the urban water supply pumping station is closely related to the scale of the pumping station. The design flow rate is between 50 and 200 m 3 The installed capacity of the large (2) type water supply pump station with a flow rate of 10 to 30 MW is 10 to 30 MW. The power consumption of the water pump is a quadratic function of the pipe flow rate Q, as shown below:

[0149]

[0150] In the above formula, η m is the power factor of pumping station m;

[0151] In the power grid-water network user side coupling model, a medium-voltage distribution transformer may provide power support for n high-rise building water pumps. The available dependency edge set Represented as follows:

[0152]

[0153] The above formula shows that the medium voltage distribution transformer j and the high-rise water pump assembly V bp Form a "one-to-many" coupling relationship.

[0154] This embodiment establishes a fully functional coupling relationship between the coupling node distribution network transformer and water pump. The dependence of the distribution transformer on the power supply of the high-rise building water pump is a "one-to-n" coupling relationship, which can be expressed by the correlation matrix E dn→bp Indicates that E dn→bp The element value definition is as follows:

[0155]

[0156] From the above formula, we can see that That is, the medium-voltage distribution transformer j and the high-rise building water pumps within its power supply range form a "one-to-many" coupling relationship.

[0157] The urban power grid-water network cross-layer coupling network model is constructed as follows:

[0158] Due to its radial topology, the operation of the urban medium-voltage distribution network depends on the high-voltage distribution substation, which is represented by a set of dependent edges as shown below:

[0159]

[0160] The above formula shows that the high-voltage distribution substation node i provides power support for the medium-voltage distribution transformers within its power supply range.

[0161] When constructing the city-level power grid and water network coupling network, the dependency relationship of all high-rise building water pumps within the power supply range of the high-voltage distribution substation on the medium-voltage distribution transformer is equivalent to its dependency relationship with the high-voltage distribution substation i, forming a coupling relationship across multiple voltage levels, and using the mutual dependence edge set express:

[0162]

[0163] The above formula shows that the high-voltage distribution substation i and the high-rise building pump set V within its power supply range bp Form a one-to-many coupling relationship.

[0164] The evaluation process specifically includes: the construction of an evaluation indicator system, emergency dispatch of the power grid under intentional attack scenarios, and analysis of the consequences of urban power grid-water network fault transmission.

[0165] Considering the operational characteristics of urban power and water networks, this paper uses the amount of system loss to measure the consequences. However, because load loss (MW) and water loss (L / s) are not comparable, the percentage of load reduction used to assess the consequences of a deliberate attack is used.

[0166] This embodiment establishes a city electricity-water cross-layer coupling network model, introduces the Nk intentional attack scenario, analyzes the city electricity-water fault conduction effect from the perspective of system operation characteristics, and calculates the grid vulnerability EI of the intentional attack scenario k. k , the evaluation index system is as follows:

[0167]

[0168] Where ω1 and ω2 represent the weights of the power grid and water network supply reduction percentages in the vulnerability assessment, which are related to the degree of attention paid by the assessor to the two lifeline facilities of the power grid and water network; ΔPd n and ΔWD m It represents the load loss of grid node n and the water loss of water demand node m after the intentional attack.

[0169] Introducing the Nk intentional attack scenario, the attacked node is used as the decision variable, and the constraints are as follows:

[0170]

[0171] Where: a n represents the attack decision variable of node n, a M Represents the sum k of the number of attacked nodes in this failure scenario.

[0172] After a city power grid is intentionally attacked, the system dispatcher adopts the optimal load shedding defense measure under the current system damage. The objective function is to minimize the weighted load shedding loss of the system emergency dispatch, as shown below:

[0173]

[0174] Where PI n represents the importance of node n, ΔPd n Indicates the load shedding amount of node n.

[0175] The constraints are as follows:

[0176]

[0177]

[0178] 0≤ΔP g,i ≤P g,i ,i∈V p,g

[0179] 0≤ΔPd n ≤Pd n ,n∈V p

[0180] The above equations represent the line power flow equation, node power flow balance equation, and generator and node load shedding constraints, respectively. ΔPd can be calculated from these equations.

[0181] Among them, the line state z l The system node status z after the deliberate attack n The calculation steps are as follows:

[0182] (1) Obtain the status z of each node in the network n

[0183] After a deliberate attack occurs, the state of the node is not only affected by the attack decision variable a n The influence of the adjacent node state z c Related, as follows:

[0184]

[0185] Where z n Represents the state of node n; V c represents the set of adjacent nodes connected to node n in the network, z c Represents the state of node c connected to node n.

[0186] (2) Obtain the status of each line in the network l

[0187] The status of each line in the network is related to the status of each node, as shown below:

[0188]

[0189] Where, Characterizes the initial state of line l, z l Characterizes the state of line l. The above formula shows that when Under the condition that node n and its adjacent node c are intact at the same time, line l nc The status is 1 if yes, 0 otherwise.

[0190] The grid vulnerability assessment method considering urban water supply services specifically includes an urban grid-water network fault transmission consequence analysis. The analysis process is divided into three levels: substation-pumping station fault transmission consequence analysis, pumping station-node water head fault transmission consequence analysis, and substation-node water head-water supply transmission consequence analysis. The corresponding formulas are:

[0191] X p =T E→p (X t )

[0192] H=T p→H (X p )

[0193] Q D =T H→Q (X t ,H)

[0194] The specific process is as follows:

[0195] Analysis of the consequences of fault transmission between substation and pumping station

[0196] The failure of the substation on the main grid side will be transmitted to the booster pump station of the water supply main network through its coupling relationship with the water network. The matrix form can be expressed as follows:

[0197] X p =min(I,X t ·E pt→ps )

[0198] Where, E pt→ps is the correlation matrix of the power supply relationship between the high-voltage substation and the pump station, X t is the state matrix of the high-voltage substations in the power grid. If the pumping station is powered by only one substation, when that substation fails, the pumping station stops working; if the pumping station is powered by two substations, it will operate normally unless both substations fail.

[0199] Analysis of the consequences of pump station-node head fault transmission

[0200] Electric-water fault conduction model T p→H Characterize the impact of the failure of a booster pump station in a water network on the overall head within its water supply area. The node head loss is proposed by the hydraulic calculation model of the water network.

[0201] Analysis of the consequences of transmission between substation and node head and water supply

[0202] Fault conduction model T H→Q Based on the dual coupling relationship between the power grid and the water network, the modeling shows that the impact of a power grid attack on the water network side of the water supply is mainly in the following two aspects: 1) After the high-voltage distribution substation cuts its load or fails, the water pumps in the secondary water supply areas of high-rise buildings within its power supply range fail, and high-rise users lose water; 2) After the booster pump station fails due to loss of power supply, insufficient water head reaches the water demand node, resulting in water outages for users.

[0203] In this example, ordinary buildings and high-rise buildings are modeled separately to explore their fault conduction models T H→Q .

[0204] (1) Ordinary residential buildings (floors ≤ n floors)

[0205] Hydraulic calculations for water networks typically use node flow demand-driven calculations. This approach is limited to maintaining constant flow at each node. However, under accident conditions, as pump stations fail, node water pressure drops below the minimum service head, resulting in water shortages. This paper uses a pressure-driven model to calculate the hydraulic characteristics of water networks under accident conditions. This model assumes that node water demand depends on node water supply pressure, effectively avoiding negative pressure under failure conditions and providing more realistic calculation results.

[0206] The Wagner model is used to describe the actual water supply capacity of a node to users when the water pressure at the node is insufficient after a pipe network accident, as shown below:

[0207]

[0208] Where, is the actual water supply of node m; is the water demand of node m under normal conditions; is the minimum water head required for node m; is the water head required at node m under normal circumstances.

[0209] (2) High-rise buildings (floors > n floors)

[0210] From the user-side secondary water supply method, we can see that the disadvantage of the two secondary water supply methods is that when the power supply fails, the water pump will fail due to power outage. For the convenience of research, this paper assumes that high-rise buildings use method (2) for water supply, that is, when the water pump fails due to power outage, the high-rise users will immediately experience water outage. Its mathematical expression is as follows:

[0211]

[0212] Where, and The above formula indicates that when the water pump is working properly, users on the nth floor can use water normally; otherwise, all users on the nth floor will have their water supply cut off.

[0213] The total water loss ΔWD of the water network is calculated by the above formula as follows:

[0214]

[0215] According to the values ​​shown by ΔPd and ΔWD, the vulnerability of the power grid taking into account the urban water supply service can be quantitatively assessed.

Claims

1. A method for assessing the vulnerability of a power grid taking into account urban water supply services, characterized in that: The assessment method uses a city power grid-water network cross-layer coupled network model to assess the impact of a city high-voltage distribution network failure on the water supply user side, thereby calculating the grid vulnerability taking into account the loss of urban water supply service. The method specifically includes the following steps: Step 1: Construct urban power grid model and urban water network model; Step 2: Considering the dual power grid-water network coupling relationship, analyze the coupling characteristics of the urban power grid and urban water network; The analysis of the coupling characteristics of the urban power grid and the urban water network in step 2 specifically includes: a power grid-water network backbone coupling model and a power grid-water network user side coupling model; wherein the power grid-water network backbone coupling model specifically includes: a power grid-water network backbone topology coupling model and a power grid-water network backbone energy coupling model; The correlation matrix E is used for the topological coupling model of the power grid and water network backbone network. pt →ps means: In the above formula, depending on the importance of the pumping station, each pumping station relies on one or two high-voltage distribution substations that are geographically closest to the grid. This means that the high-voltage distribution substation and the pumping station form an "n-to-1" coupling relationship. The energy coupling model of the power grid and water network backbone is as follows: In the above formula, η m is the power factor of pumping station m; The correlation matrix E used in the power grid-water network user side coupling model dn →bp means: In the above formula, the medium-voltage distribution transformer node j and the high-rise building water pumps within its power supply range form a "one-to-many" coupling relationship; Step 3: Construct a cross-layer coupled network model of the urban power grid and water network; The urban power grid-water network cross-layer coupling network model in step 3 specifically includes: The high-voltage distribution substation node i provides power support to the medium-voltage distribution transformers within its power supply range, as shown below: High-voltage distribution substation node i and the set of high-rise building water pumps V within its power supply range bp A one-to-many coupling relationship is formed as follows: Step 4: Based on the urban power grid and water network cross-layer coupled network model, assess the grid vulnerability taking into account the loss of urban water supply services.

2. The method for assessing the vulnerability of a power grid taking into account urban water supply services according to claim 1, characterized in that: The urban power grid model in step 1 specifically includes a power system topology model and a power system energy flow model; the urban water network model specifically includes a water network topology model and a water network energy flow model.

3. The method for assessing the vulnerability of a power grid taking into account urban water supply services according to claim 2, wherein: The power system topology model specifically includes a city backbone power grid model and a city medium-voltage distribution network model; wherein the city backbone power grid is composed of a transmission network and a high-voltage distribution network, and the model is as follows: In the above formula, V p,g For power plant assembly, V p,t is the set of substations of various voltage levels in the power system, E p,l is the set of power lines, n pg 、n pt and n pl They represent the number of power plants, substations and power lines respectively; the urban medium-voltage distribution network adopts a closed-loop design and open-loop operation, and its typical structure is radial.

4. The method for assessing the vulnerability of a power grid taking into account urban water supply services according to claim 2, wherein: The power system energy flow model is as follows: Wherein, formula (2) represents the line power flow equation, A is the grid branch association matrix; formula (3) represents the node power flow balance equation, P g,n represents the generator output of node n, Pd n represents the load of node n; formulas (4)-(5) are the line flow constraints and generator output constraints, where and Indicates the upper and lower limits of line capacity, and Indicates the upper and lower limits of the generator n output.

5. The method for assessing the vulnerability of a power grid taking into account urban water supply services according to claim 2, wherein: The water network topology model includes a water supply backbone network model and a user-side water supply model; wherein the water supply backbone network model is as follows: In the above formula, V w,s 、V w,p and V w,d are the water source, pumping station and water demand node set of the water network, E w,l is the collection of water distribution pipe sections, n ws 、n wp and n wd Represent the number of water sources, pumping stations and water demand nodes respectively; The user-side water supply model is as follows:

6. The method for assessing the vulnerability of a power grid taking into account urban water supply services according to claim 2, wherein: The formula of the water network energy flow model is as follows: A w Q+Q D =0 (8) B w ΔH=0 (10) Among them, formula (8) is the node flow equation group, A w is the correlation matrix of the water network, Q is the m×1 vascular segment flow vector, Q D is the n×1-dimensional node flow vector; Equation (9) is the pipe pressure drop equation group, H is the node head vector, ΔH is the pipe pressure drop vector; Equation (10) is the ring energy equation group, B w is the loop matrix of the water network.

7. The method for assessing the vulnerability of a power grid taking into account urban water supply services according to claim 1, wherein: The evaluation process of step 4 specifically includes: the construction of an evaluation index system, the emergency dispatch of the power grid under intentional attack scenarios, and the analysis of the consequences of urban power grid-water network fault transmission.

8. The method for assessing the vulnerability of a power grid taking into account urban water supply services according to claim 7, characterized in that: The urban power grid-water network fault transmission consequence analysis is divided into three layers: substation-pump station fault transmission consequence analysis, pump station-node water head fault transmission consequence analysis, and substation-node water head-water supply transmission consequence analysis. The corresponding formulas are: X p =T E→p (X t ) H=T p→H (X p ) Q D =T H→Q (X t ,H)。

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